The Scarcity Rate of Interest
Monetary Policy and
the Capital Scarcity Rate of Interest
Richard A. Stanford
Professor of Economics, Emeritus
Furman University
Greenville, SC 29613
Furman University
Greenville, SC 29613
<Take-Aways From This Essay>
<Essays Menu>
Introduction
Many commentators and textbooks that purport to explain interest rates treat them only as returns to financial instruments. Little if any attention is given to the underlying real basis of interest rates. The natural rate of interest, described by Knut Wicksell in 1898, is no longer a "hot topic" in economics or finance literature, but it may be mentioned in passing on the way to describing interest rates as purely financial phenomena. My intent in this work is to describe a variation on the natural rate concept and argue that it is fundamental to understanding both the real and the financial aspects of interest rates. Charts provided by the Federal Reserve Bank of St. Louis (Federal Reserve Economic Data, FRED) have been downloaded to illustrate most relationships.
Economists conventionally identify four “factors of production,” land, labor, capital, and entrepreneurship, and the so-called returns to them, respectively: rent, wage, interest, and profit. Since interest is specified as the return to real capital (physical productive capacity, e.g., plant, equipment, housing), the "true" interest rate in any region is a measure of the scarcity of capital in the region relative to the demand for it. This true interest rate is referred to in this essay as the "capital scarcity rate of interest," or simply as the "scarcity interest rate." Rates of return can be computed for any of the factors of production, so the term "scarcity interest rate" will be taken to refer to the rate of return to the region's stock of capital rather than to any of the region's other resource endowments.
The Natural Rate of Interest
The scarcity rate of interest corresponds loosely to the concept of the "natural rate" of interest introduced by Knut Wicksell in 1898 (Geldzins und Güterpreise; English translation, "Interest and Prices," 1936). Wicksell defined the natural rate as "a certain rate of interest on loans which is neutral in respect to commodity prices and tends neither to raise nor to lower them" (https://en.wikipedia.org/wiki/Neutral_rate_of_interest#:~:text=The%20neutral%20rate%20of%20interest%2C%20previously%20called%20the,keeping%20inflation%20constant.%20It%20cannot%20be%20observed%20directly). In modern parlance, this rate is described as a "neutral rate" of interest,
The neutral rate of interest (also called the long-run equilibrium interest rate, the natural rate and, to insiders, r-star or r*) is the short-term interest rate that would prevail when the economy is at full employment and stable inflation: the rate at which monetary policy is neither contractionary nor expansionary. It is a function of the economy’s underlying characteristics and is not set by the Federal Reserve. (Sam Boocker, Michael Ng, and David Wessel, https://www.brookings.edu/articles/the-hutchins-center-explains-the-neutral-rate-of-interest/).
The neutral rate of interest might be understood as the interest rate that would obtain in equilibrium at full employment in a non-money-using economy, i.e., a pure barter economy. Even in a barter economy, investment in productive capacity, e.g., building a fence around a chicken coop, would be expected to yield real returns in the forms of more eggs and consumable chickens that are protected from predators. And those real returns can be expressed as a greater or lesser percentage rate of return in comparing results before and after construction of the fence. In a money-using economy, money serves as a denominator of value rather than the real value itself. The monetization of the values of real things with a common currency results in prices that enable comparisons of values and computation of financial interest rates.
In a money-using economy, the fundamental reason that interest is paid for the use of money over some period of time is that money can be used to claim (i.e., acquire) real capital goods which increase productive capacity. The only two reasons to demand loanable funds are to use them to purchase real capital equipment and to purchase consumer goods. The reason that interest is paid on consumer loans is that loanable funds have to be bid away from purchasing real capital goods. Consumer loan interest rates often are higher than commercial loan rates simply because consumers have to out-bid commercial borrowers to capture some of the loanable funds.
The capital scarcity interest rate is region specific. Due to the effect of diminishing returns, the scarcity rate of interest is higher in regions where capital is scarce and lower in regions where capital is more abundant. The scarcity interest rate would be expected to fall as capital becomes more abundant with on-going economic development. It would rise if capital were to become scarcer, e.g., when equipment is destroyed by a natural disaster or war, or if gross investment in the region should become less than depreciation so that the nominal capital stock shrinks.
Scarcity rates of interest may be lower in more developed parts of the world that are capital-abundant; we should expect scarcity rates to be higher in lesser developed regions of the world that are capital-scarce relative to local demands for capital. The marginal productivities of new capital investments would be higher in capital-scarce regions, inviting "offshore" investments in those regions by firms located in other regions with more abundant capital and thus lower marginal productivities of capital. Growth rates in capital-scarce regions may slow as their capital stocks increase with ensuing development.
Economic activities that affect and are affected by the capital scarcity interest rate:
The Capital Scarcity Rate of Interest
Interest is a real phenomenon attributable to the ability of real (rather than financial) capital to increase human productivity. Interest would be paid "in kind" in a barter economy. Interest is the return to scarce real capital in the same sense that the wage is the return to scarce labor. Both returns are positive as long as the respective factors of production are scarce and they are productive. In this sense, the capital scarcity interest rate can never become zero or negative unless the quantity of real capital becomes superabundant.
In a money-using economy, the fundamental reason that interest is paid for the use of money over some period of time is that money can be used to claim (i.e., acquire) real capital goods which increase productive capacity. The only two reasons to demand loanable funds are to use them to purchase real capital equipment and to purchase consumer goods. The reason that interest is paid on consumer loans is that loanable funds have to be bid away from purchasing real capital goods. Consumer loan interest rates often are higher than commercial loan rates simply because consumers have to out-bid commercial borrowers to capture some of the loanable funds.
The capital scarcity interest rate is region specific. Due to the effect of diminishing returns, the scarcity rate of interest is higher in regions where capital is scarce and lower in regions where capital is more abundant. The scarcity interest rate would be expected to fall as capital becomes more abundant with on-going economic development. It would rise if capital were to become scarcer, e.g., when equipment is destroyed by a natural disaster or war, or if gross investment in the region should become less than depreciation so that the nominal capital stock shrinks.
Scarcity rates of interest may be lower in more developed parts of the world that are capital-abundant; we should expect scarcity rates to be higher in lesser developed regions of the world that are capital-scarce relative to local demands for capital. The marginal productivities of new capital investments would be higher in capital-scarce regions, inviting "offshore" investments in those regions by firms located in other regions with more abundant capital and thus lower marginal productivities of capital. Growth rates in capital-scarce regions may slow as their capital stocks increase with ensuing development.
Economic activities that affect and are affected by the capital scarcity interest rate:
The Scarcity Rate and the Neutral Rate
The concept of the scarcity rate of interest is not as restricted as that of the natural or neutral interest rate. The scarcity interest rate accommodates monetary transactions and policy, and it enables consideration of disequilibria in both real and financial markets as they are linked to each other. The scarcity rate concept is posited relative to the real capital stock in a region. The neutral interest rate concept takes no explicit account of the capital stock or of regional differences of installed capital.
If all the conditions specified for the neutral rate were met, the scarcity rate in a region would converge upon the neutral rate in that region. It is in this sense that, with due consideration to disequilibrium conditions, the neutral rate in a region might serve as a proxy for the scarcity rate in that region. Neither the neutral interest rate nor the scarcity interest rate is observable or trackable, but inferences may be drawn about the value of a regional scarcity interest rate by observing what is happening in regional markets.
Although the neutral or natural rate of interest is not directly observable, yields on longer-term government bonds that are essentially riskless have served as proxies for the natural rate of interest. James Mackintosh, writing in The Wall Street Journal September 2, 2016, notes that
As shown in Chart 1, yield rates on 20- and 30-year term U.S. Treasury Securities indeed have come down over the period between 1982 and 2020. The mystery of the "permanently lower growth" posited by Mackintosh may be explained by the diminishing returns to the increasing stocks of real capital in developed countries such as the U.S., Canada, the U.K., and certain E.U. countries.
Yield rates on long-term bonds often are taken as proxies for the natural rate of interest. However, as specified for the natural rate of interest, the economy is rarely in equilibrium at full employment with stable inflation and no involvement by a central bank. It would be more appropriate to construe the yields on long-term bonds as proxies for the capital scarcity interest rate for which non-equilibrium states are not precluded.
Long-term U.S. Treasury security yields shadow the capital scarcity interest rate only imperfectly. Long-term bond issuance has been interrupted on two occasions: issuance of the 20-year bond was suspended between 1987 and 1993, and the 30-year bond was not issued between 2002 and 2006. Beginning in 2020 the declining paths of the yields on U.S. Treasury long-term securities were disturbed by the Federal Reserve’s effort to address inflation by increasing the interest rate paid to banks on their deposited reserves. The fact that the 20- and 30-year bond yield rate paths depicted in Chart 1 are not smooth but rather exhibit up/down changes from quarter to quarter implies disequilibrium states and market adjustments to the changing capital scarcity interest rate.
Has the U.S. recently experienced “permanently lower growth” as contended by Mackintosh? The top panel of Chart 2 shows the path of real GDP from 1955 to 2023. The mild upward concavity of the path suggests that the GDP growth rate may have increased slightly over the period. The middle panel of Chart 2 shows real GDP on a per capita basis. With decreasing indigenous birth rates offset by immigration, the near linear up-sloping path of per capita real GDP also belies the contention that growth has become permanently lower. The annual percent changes of real GDP from previous periods shown in the bottom panel of Chart 2 may exhibit a very slight downward trend that implies only a slight diminishing of the real GDP rate of growth.
As noted above, if all the conditions specified for the natural rate were met, the scarcity rate would converge upon the natural rate. Since natural rate equilibrium conditions rarely obtain in the real world, we will assume that Douglas and Sindreu's comment applies to the capital scarcity rate of interest rather than to the natural rate of interest.
If central bankers are postulating their monetary policies on tracking or shadowing the scarcity rate of interest, then one is led to wonder why don't they simply let market interest rates naturally adjust to the scarcity rate. This may happen anyway since central bankers often delay changing their administered-price rates (the reserve balances interest rate or the Federal Funds target rate) until market rate pressures for a change are already palpable, i.e., market participants "price in" their expectations of a near-future rate change. When they do this, central bankers are simply following the market rather than leading the market or managing market interest rates.
A problem is that the scarcity interest rate is not an observable rate that can be tracked, but it might be approximated by the yield rates on long-term bonds. If investment increases following a decrease of the Federal Funds rate due to the central bank lowering the reserve balances interest rate, the implication may be that market rates were below the scarcity rate. The increasing investment may increase the supply of corporate bonds relative to bond demand, causing their prices to fall and their yield rates to rise back toward the scarcity rate. If investment decreases following an increase of the Federal Funds rate due to the central bank increasing the reserve balances rate, the implication may be that market rates were above the scarcity rate. The decreasing investment may decrease the supply of corporate bonds relative to bond demand, causing their prices to rise and their yield rates to fall back toward the scarcity rate.
Donald Luskin, writing in The Wall Street Journal, February 16, 2017, described how a market interest rate rule might work:
Capital often is thought of as a fixed input to which labor is the variable input that is added. But in some production processes the amount of labor is fixed (e.g., members of the family on a family farm) while the amount of capital can be varied by acquiring more or disposing of some equipment. Quadrant VI of Chart 10 illustrates diminishing returns to capital, given a fixed amount of labor, L2. The previous paragraph could be repeated with L and K swapped to reveal the phenomenon of diminishing returns to capital illustrated by the downward concavity of the Q = f ( K | L2 , . . . ) function beyond the K1 amount of capital and the downward slope of the MPK curve beyond the K2 amount of capital. It is this phenomenon that underlies the capital scarcity rate of interest.
The figures in quadrants VII and VIII of Chart 10 show that every point along a Q slice of the production function for a fixed amount of one factor is also on a Q slice for a fixed amount of the other factor. In the quadrant VII diagram, as the amount of labor is increased in a fixed plant K2, the slope of the Q function path decreases but the slopes of the cross-cutting K slices increase. Another way to describe this is that with an increasing amount of L, given the K2 plant, the marginal product of L decreases while the marginal product of K increases. And this also would be true in quadrant VIII as the amount of capital is increased for use by a fixed amount of labor L2. Increasing the amount of capital, given a fixed amount of labor, will increase the marginal product of labor even as the marginal product of capital decreases.
Technological advance that improves the efficiency of both of the factors of production would shift the 3-D surface 0ABC0 upward and outward along both of their axes to forestall the effects of diminishing returns to both factors. The marginal product curves of both factors also would shift upward and outward to forestall the effects of diminishing returns. Technological advance that improves the efficiency of only one of the productive factors will skew the surface upward and outward only along the axis of that factor. Such technological advance would forestall diminishing returns to that factor and increase the productivity of the other factor.
Yield Rates Vary Inversely with Market Prices
A simple example illustrates that yield rates vary inversely with market prices. A zero-coupon bond (one that promises no interest payment) would sell in the bond market only at a price lower than face (or par) value. The formula for computing the nominal yield rate on a zero-coupon bond is (face value - market price) / face value. For example, if a 1-year term bond with face value of $1000 can be purchased for $950, its nominal yield rate would be [ (1000 - 950) / 1000 ] = .05 or 5 percent. If a purchaser is willing to pay a higher price of $960 for this bond, the nominal yield rate would be lower: [ (1000 - 960) / 1000 ] = .04 or 4 percent.
Bonds are supplied to the market by corporations seeking funds to finance investments and by governments needing to finance budgetary deficits. In Figure 2 an increase in the supply of bonds from S1 to S2, other things unchanged for bond demand, results in a decrease in the price of bonds from P1 to P2, with corresponding rise in the yield rate. A decrease in the supply of bonds to S3 would elicit an increase in the price of bonds to P3 and a fall in their yield rate.
When private parties have more money than they want to hold in their bank accounts (or under their mattresses), they can purchase goods and services, or they can purchase financial instruments in the bond market. When they do the latter, the demand for bonds increases as in Figure 1, pushing bond prices higher and yield rates lower. When private parties want to hold more money than they have, they can cut back on their purchases of goods and services relative to their continuing income flows, or they can sell some of their financial instruments in the bond markets. To the extent that they do the latter, the supply of bonds increases as in Figure 2, pushing bond prices lower and yield rates higher.
The supply of bonds may be affected by the intents of businesses to finance capital investments, the needs of governments to finance deficits or dispose of surpluses, and the intent of the central bank to execute monetary policy. Changing interest rate differentials between domestic and foreign locales may also induce bond demand or supply shifts. It is the market forces of demand and supply in the bond market that cause bond prices to change and their yield rates to change in the opposite direction.
Changes in the prices of bonds (and thus their yield rates) become transmitted to the prices (and yields) of other types of financial instruments via the process of arbitrage, i.e., the simultaneous purchase and sale of different types of financial instruments or financial instruments in different local markets. Arbitrageurs are successful if they are able to operate by the criterion of “buy low, sell high.” If they are successful, they will both capture profits and precipitate convergence of prices (and yields) across the markets. Unsuccessful arbitrageurs will suffer losses and tend to destabilize markets, and they may cause interest rates on different types of financial instruments to diverge.
Monetary Policy Transmission Mechanism
A monetary policy transition mechanism consists of the steps in the linkage between an action taken by a monetary authority and the ultimate goal that is expected (or hoped) to be impacted. On analogy, it is a bit like the transmission in an automobile that conducts power from the engine to the drive wheels. This analogy is imperfect because, unless the auto transmission is worn or damaged, the power conducted to the drive wheels is certain (although with some loss of power, the longer and the more steps in the linkage).
A better analogy might be the transmission mechanism entailed in the effort by a classic 8-ball billiards game player to cause one of his balls to drop into a pocket. Upon "breaking" the racked set of balls,
And like the 8-ball billiards game, the monetary policy transmission mechanism is complex and has many linkages, each of which may fail the monetary authority's intent. The steps in the Fed's pre-2008 policy linkage was
Possible monetary policy process obstruction may occur if market participants key their decisions on their perceptions of the scarcity rate of interest that is different from the announced policy rate. In an open-economy world, policy process obstruction may be brought about by unexpected trade and capital flows that affect the relevant money supply, financial instrument prices, and yield rates. Monetary policy interruption may be caused by unexpected spending changes as occurred in 2019-2022 due to the Covid pandemic and supply chain congestion, in 2022-2024 by unexpected military hostilities, by natural disasters, and by ensuing climate change.
Repurchase and Reverse Repurchase Operations
Open market operations may be implemented by the Fed in the process of "unwinding" its huge portfolio acquired in three episodes of "quantitative easing" between 2008 and 2014. The Federal Reserve Bank of New York (FRBNY) website currently identifies the only other open market operations as repurchase and reverse repurchase operations. In a repo auction, security dealers bid on borrowing money from the Fed, offering U.S. Treasury securities as collateral. They implicitly "sell" the securities to the Fed on the day of agreement, and then repurchase them the next day. In a reverse repo auction, dealers offer interest rates at which they would lend money to the Fed. They implicitly "buy" securities from the Fed on the day of agreement, and the Fed repurchases them the next day. Repurchase agreements are made at the initiative of the trading desk at FRBNY which implements monetary policy at the behest of the Federal Open Market Committee (FOMC).
Economic Growth and Development
Due to the effect of diminishing returns, the scarcity rate of interest is higher in regions where capital is scarce and lower in regions where capital is more abundant. Regional differences in scarcity rates invite interregional capital flows. The high capital scarcity interest rate should entice investment spending both by locals and by foreigners contemplating off-shore investments. The capital scarcity interest rate would be expected to fall as capital becomes more abundant with on-going economic development.
Economists distinguish between economic growth and economic development. "Growth," taken to be an improvement in the material well-being of humans, is usually measured as the rate of increase of per capita real income or output of a society. "Real" means that adjustments have been made to eliminate the effects of inflation so that the real component of nominal income increase can be examined. "Per capita" means that some measure of the total output of a society, typically its Gross Domestic Product (GDP), has been divided by the population of the society to get a measure of income on a per-person basis.
"Development" is understood to mean change in the structure of society. The various dimensions of social structure include economic, social, political, moral, religious, and environmental. Development is both a requisite of growth and a consequence of growth--they are inseparable.
A serious problem is that development is typically disruptive of social structures, and thus entails costs. While by definition growth yields only benefits, development seems to involve mostly costs. A rational judgment of whether a process of development cum growth is desirable should be based on the relationship between the benefits of growth against the costs of development, i.e., Bg/Cd. If the value of the ratio of Bg/Cd is greater than 1, the growth-development process is desirable. It is undesirable if the value of the Bg/Cd ratio is less than 1.
Economists make the case that the most effective poverty alleviating vehicle over the past couple of centuries has been economic growth that has been enabled by economic development, and that market economies are more favorable to development than are authoritarian economies.
The suffering of the poor may be less amenable to relief by sharing the existing wealth than by a process of economic development that increases the society's stock of capital (which is part of its physical wealth) due to its high scarcity rate of return to capital. The poor are helped via the "spill-over effects" of employment and income generation, and in terms of a growing volume of lower-priced consumables that are more affordable to the poor.
Interregional Trade and Comparative Advantage
Trading relationships among nations exhibit variations in scarcity interest rates that correspond to their resource endowments. Since the pure theory of trade abstracts completely from references to nation states, it is necessary to shift from the language of "international trade" to that of "interregional trade." Different regions of the world have different endowments of natural, human, and capital resources. Different regions within nation states also may exhibit divergent scarcity interest rates.
Due to the principle of diminishing returns, regions that are richly endowed with capital resources can be expected to exhibit lower capital scarcity rates of interest than trading partner regions that are deficient of capital resources but well endowed with natural and human resources. Economists have enunciated the so-called principle of comparative advantage to explain regional specialization in the production of goods and services.
It is a fact of physical nature that resources are unequally distributed across the earth's geographic space. Some resources approach ubiquity (found everywhere); others are concentrated by regions. Resources that are found in only one or two places on earth may be referred to as geographic uniquities. Examples include rare elements or precious gems or metals, agricultural commodities that grow only under very special conditions, and natural tourist attractions. Populations of regions possessing such uniquities are fortunate in having access to such resources which they are able to exploit; populations elsewhere are correspondingly unfortunate. Populations of regions devoid of such uniquities may acquire them (or things produced using them) by engaging in interregional trade or military aggression to capture them.
There are few perfect ubiquities or uniquities among productive resources. Most resources are found in many places across the globe, although in greater or lesser geographic concentrations. Goods and services requiring those resources as inputs may be produced more cheaply in regions where they are found in abundance than in other regions where they are scarce.
Economists have developed the principle of comparative advantage to explain regional specialization in the production of goods and services. According to this principle, people in each region should specialize in producing those goods and services that can be produced most efficiently in their region compared to other regions. "Most efficiently" means at least opportunity cost (in terms of other goods and services foregone) compared to the other regions. Since the production of goods becomes geographically specialized, people in different regions must trade their specialties for the specialties of people in other regions.
Generalization in consumption is enabled everywhere through trade even though there is regional specialization in production. It can be shown with theoretical exercises as well as empirical information that those who specialize their production according to the principle of comparative advantage and trade with one another enjoy higher welfare than they would under conditions of autarky.
It is sometimes suggested that there are regions of the world that are essentially devoid of productive advantages, whereas other regions seem to possess all of the advantages (veritable "Gardens of Eden"). This problem can be resolved by further refining the definition of comparative advantage. A region's absolute advantages include all of those things that it can produce at lower opportunity costs than can be achieved in other regions. A region's absolute disadvantage is anything that can be produced elsewhere at lower costs in terms of other goods and services which must be foregone.
It may well be that opportunity costs of most things are lower in one region relative to all others, but this does not mean that the region should generalize in production. Its comparative advantages lie in producing those things for which it has greatest absolute advantage(s), while the comparative advantages of other regions lie in producing the things for which they have least absolute disadvantages. They should still specialize in production, but the one in its greatest absolute advantage and all the rest in their least absolute disadvantages. It follows logically from this definition of comparative advantage that it is not possible for a region to have no comparative advantage(s). Furthermore, it can be shown that all of the regions of the world, the sparsely-endowed as well as the abundantly endowed, will enjoy higher welfare with specialization according to the principle of comparative advantage and trade with one another unencumbered by politically imposed constraints.
Modern elaborations of the theory of comparative advantage recognize at least five bases for regional comparative advantages: capital and other resource endowments, cultural preferences, known technologies, scale economies, and company-specific knowledge. The first three are endogenous to locale; the last two technically are independent of geography but may become location specific at the discretion of production decision makers.
It would be highly unlikely in any of these cases that perfect specialization (i.e., only product X is produced in region A and only product Y is produced in region B) would result. Both goods would continue to be produced in both regions, but in each region more of the comparative advantaged good would be produced and less of the comparative disadvantaged good(s). Also, the real world is composed of many regions, some of which are similar to others in respect to resource endowments, preferences, or technologies, and different from the other regions in various respects. The basis for comparative advantage of each may lie in one of these areas or a combination of them. Empirical evidence indicates that a larger volume of the world's trade is conducted among regions that are similar in income levels and preferences than among regions that are widely divergent in any of these areas.
Unless offset by regional decrease of capital in non-comparative-advantaged industries (e.g., by non-replacement of worn equipment, natural disaster, or war), the process of investing in capital to increase regional specialization in comparative-advantaged industries should be expected to decrease the marginal productivity of the region's capital stock and cause its capital scarcity rate of interest to decrease.
Industrial Policy
As trading relationships become more open and free with on-going globalization, specialization of production toward each nation's real comparative advantages ensues. Regions with abundant natural and human resources but meager stocks of capital will experience increasing specialization in producing products that employ intensively their abundant resources. But the government of a region with a meager stock of physical capital may wish to promote industrial investment in production activities for which the region does not have comparative advantages.
As industrial investment increases specialization in the non-comparative advantaged production processes, the formerly comparative advantaged processes become despecialized. Jobs will be threatened and businesses in comparative advantage production will suffer declining sales and profits attributable to the ensuing process of comparative advantage despecialization. Those who feel threatened can be expected to appeal to their congressional or parliamentary representatives to provide protection for the domestic industry in the form of tariffs or non-tariff barriers to trade.
Industrial policy has been described as government picking winners and identifying losers among the resident industries within the nation, and then acting to encourage and support the chosen winners. The most likely reason for an industrial policy to fail is that bureaucratic choices of national-champion industries may not correspond to the nation's natural or acquired comparative advantages. If an administration chooses to support non-comparative-advantaged domestic industries, production costs will be higher than in potential trading-partner nations that do possess the respective comparative advantages. Consumers of the nation will pay higher product prices for domestically-produced goods and enjoy lower levels of welfare than they might have enjoyed if they had consumed comparable imports from regions possessing the respective comparative advantages.
Various U.S. states have practiced forms of industrial policy in their efforts to attract industry or particular firms to locate plants within their borders. The principle underlying state-level industrial policy is the contention that since capital is generally more mobile geographically than is labor, capital should move to sites where it can employ capable and well-trained labor. States vie with one another to demonstrate that their labor forces are capable and well-trained, and that they possess the physical and financial infrastructure to support the sought-after industry. State-level industrial policy may cause market interest rates to diverge from the region’s scarcity rate.
A variant of industrial policy, import-substitution industrialization (ISI), was adopted as development vehicle in several capital-scarce nations during the second half of the twentieth century. The idea was to try to "birth" and protect from global competition non-comparative-advantaged "infant" domestic industries until they could "grow up" and somehow attain comparative advantages on world markets. In the meanwhile, domestic consumers would pay the price of protection in the form of higher prices of domestically-produced goods compared to the lower prices of imports. But the ISI strategy has been discredited in favor of export-oriented development (EOD), i.e., identifying and pursuing development of nations' actual comparative advantages in producing both industrial goods and primary products that can be exported to pay for lower-priced imports.
Industrial policy may cause market-determined interest rates to diverge from the region’s scarcity rate. Industrial policy that only shifts investment from comparative-advantaged production to non-comparative-advantaged production may cause little change in the gross capital stock of the region and thus leaves the capital scarcity interest rate of the region unchanged. Industrial policy that increases the region's capital stock by stimulating investment in non-comparative-advantaged production as capital investment in comparative-advantaged production continues may cause the scarcity interest rate of the region to increase as the marginal productivity of capital in the region declines. This phenomenon may have occurred with South Carolina's industrial policy that stimulated investment in the automobile, tire, aircraft, and other "tech" industries as investment continued to sustain capital engaged in South Carolina's agriculture.
Protectionist Policy
Governments often resort to various forms of protectionist policy when domestic industries are threatened by foreign competition. The most common forms of protection of a domestic industry are tariffs imposed on imports, non-tariff barriers to restrict the inflow of imports, and subsidies that promote domestic industries which compete with imports. If the region has been capital abundant with a low capital scarcity interest rate, these protection measures will tend to increase the capital scarcity interest rate of the region. In a capital scarce region with a high capital scarcity interest rate, the imposition of protectionist measures will tend to lower the capital scarcity interest rate.
A tariff is a tax on an imported good that is paid, not by the exporter, but by the consumers in the nation whose government imposes the tariff. The effect of the imposition of a tariff by the government is to raise the price of the imported product to domestic consumers, which, if the domestic demand for the import is sufficiently elastic with respect to price, will reduce the volume of the import, thereby providing a modicum of protection to the domestic industry. With the tariff in place, domestic producers will be able to sell their product at the higher imported price, although a smaller quantity. The increased price of the import has the effect of worsening the nation's terms of trade; since the foreign-made product now costs more to domestic consumers, each unit of a domestically produced export can buy only a smaller quantity of the import. However, if the domestic demand for the import is sufficiently inelastic, the tariff may not greatly decrease the amount of the product imported.
Once a tariff is imposed, the domestic market price of the product rises. Domestic producers are all too happy to accept the higher price although it may still not be as high as the pre-trade domestic price. Domestic production increases. At the higher market price, domestic consumption falls and the quantity of the product imported decreases. These effects will be relatively small if the world supply is fairly inelastic with respect to price, but the effects will become larger if world supply increases and becomes more elastic.
Non-tariff barriers (NTBs) include quotas on imports, health and safety restrictions on imports, import packaging and labeling requirements, discriminatory performance standards for imports, etc., that are intended to curb imports or raise their delivered prices. Both tariffs and NTBs may cause market-determined interest rates to diverge from the region’s scarcity rate.
Protectionist measures that only shift investment from comparative-advantaged production to non-comparative-advantaged production may cause little change in the gross capital stock of the region and thus leave the capital scarcity interest rate of the region unchanged. Protectionist measures that increase the region's capital stock by stimulating investment in non-comparative-advantaged production as capital investment in comparative-advantaged production continues may cause the scarcity interest rate of the region to increase as the marginal productivity of capital in the region declines.
Lags in the Adjustment Process
Economists refer to the time between when a macroeconomic change occurs and when it is recognized by government officials as the recognition lag, and the time between recognition of such a change and the taking of some action to offset it as the response lag. Needless to say, the lags are both variable in duration and themselves unpredictable. The response lag for monetary policy may be a matter of days or weeks, while that for fiscal policy may be months or quarters. In democratic societies, fiscal policy actions must be proposed, debated, and legislated, processes that often are very time consuming.
There is yet another lag which may eclipse the first two in duration. It is the so-called reaction lag, the period between when an action is taken and the effects of the action fully work through the economy. The reaction lag usually involves a multiplier process of consecutive rounds of respending. Experience in the U.S. economy suggests that the multiplier effect of a fiscal policy action may be completed in as little as a year, but may not be fully worked out in more than two years. The duration of the reaction lag is therefore even less predictable than are the recognition and response lags. The three lags together may span a period of as little as a year, or as much as three or more years. These lags taken together put the government in the position of having to implement a compensating policy even before some event shocks the economy.
This brings us to the most serious problem of implementing any government policy in the interest of stabilizing the economy. It is that the natural adjustment mechanisms of the economy will likely have reversed the direction of change of the economy by the time that the policy designed to deal with the original problem finally has its effect. For example, in a contracting economy, expansionary fiscal and monetary policies are called for. But by the time the contraction can be confirmed, expansionary policy implemented, and the multiplier process completed, the economy of its own volition will likely have begun its recovery. So the expansionary monetary policy impacts an already-expanding economy. A similar, but reversed, scenario can be depicted for an economy entering a period of expansion. Because of variable and unpredictable time lags in the implementation of macropolicy, government's well-intentioned efforts to stabilize the economy often end up destabilizing it--"booming the boom," or "depressing the depression."
Macroeconomic Adjustment to International Disturbances
As the world economy becomes progressively more open and economically integrated, the vehicles for macroeconomic adjustment to internationally-sourced disturbances attain ever greater significance. Basically, there are only three macroeconomic adjustment vehicles: exchange rates, domestic prices (including interest rates), and domestic employment (and incomes). A progression of "if statements" identifies the relevant adjustment possibilities:
1. If exchange rates are allowed sufficient flexibility, they may serve as "shock absorbers" for the domestic economy against internationally-sourced disturbances.
2. If exchange rates are fixed by government authorities, domestic prices assume the burden of adjustment.
3. If domestic prices are insufficiently flexible, the adjustment process must descend upon domestic employment and incomes.
4. If government authorities employ macropolicy to stabilize domestic prices, employment, and incomes, exchange rate flexibility must serve as the adjustment vehicle.
5. If government authorities attempt both to stabilize domestic prices and employment and to fix exchange rates, there is no effective vehicle of macroeconomic adjustment to international disturbances. In the absence of an effective adjustment vehicle, payments imbalances will persist.
An important conclusion emerges from these considerations: the degree of domestic macroeconomic stability of a nation may depend upon the degree of flexibility that its government accords to rates of exchange between its currency and other currencies. As a general rule, we may expect domestic macroeconomic conditions in any economy to be more volatile in response to international disturbances the less flexible are its exchange rates. Fixing or stabilizing exchange rates forces the adjustment to international disturbances upon domestic macroeconomic conditions of prices and employment.
How does U.S. macropolicy mesh with these adjustment vehicles? The top and middle panels of Chart 11 have been brought forward to Chart 12 to be compared to the U.S. dollar-to-euro spot exchange rate in the bottom panel. The exchange rate path shown in this panel demonstrates that U.S. exchange rates are not fixed; their flexibility provides a modicum of shock absorption to both domestic- and internationally-sourced disturbances.
The Federal Reserve does practice macropolicy in its pursuit of price stability, but the interest rate targets that it sets may cause market-determined interest rates to diverge from regional capital scarcity interest rates. It cannot be said that any U.S. authority implements fiscal policy with consistency. The Congress typically legislates spending bills with respect to politically-perceived program needs and only occasionally with regard to employment and income deficiencies. The Treasury Department of the executive branch of the U.S. government is tasked with implementing Congressional legislation to finance federal government expenditures, including regular annual deficits. The sporadic nature of these hodge-podge fiscal actions are not oriented primarily toward achieving macroeconomic stability of employment and incomes. The incoherence of U.S. macropolicy may be a source of the price, employment, and income instability that has been experienced.
Exchange Rates During the Great Recession
The 2008 “Great Recession” was an internal disturbance to the U.S. economy that had international repercussions. The bottom panel of Chart 12 shows that the dollar appreciated as the dollar price of the euro fell from $1.58 in June 2008 to $1.27 in November 2008 (i.e., the euro price of the dollar increased from 0.63 euro to 0.79 euro).
In the effort to alleviate emerging recessions since 2008, the Fed engaged in four rounds of quantitative easing (QE1, November 2008; QE2, November 2010; QE3, September 2012; QE4, March 2020) by increasing the reserves of depository institutions. Following QE1, the dollar depreciated as the price of the euro rose from $1.27 in February 2009 to $1.49 in November 2009 (i.e., the euro price of the dollar decreased from 0.79 euro to 0.68 euro).
Quantitative easing in the U.S. is implemented by the Federal Reserve when it purchases bonds from depository institutions, paying for the bonds by increasing their reserves. The increased reserves enable lending that increases the quantity of money in circulation to stimulate business investment and consumer spending in the economy. The increasing quantity of money in circulation may cause market-determined interest rates to diverge from the capital scarcity interest rate and set in motion adjustment processes. The increasing quantity of money in circulation won’t change the capital scarcity interest rate unless it induces investment that causes a change in the capital stock of the region.
As the Fed buys bonds during a quantitative easing action, bond supplies decrease on U.S. financial markets relative to bond demands, bidding up bond prices and decreasing bond yield rates. The proceeds from selling bonds at higher bond prices motivate businesses and governments to issue new bonds to finance investment and spending plans. Some of the new bond issuers are foreign businesses and governments who receive payment in dollars that must be converted to their own currencies for repatriation. The repatriation of these funds shows up in the middle panel of Chart 12 in a capital account deficit. The U.S. capital account, roughly in balance in 2008, had a deficit of nearly $5.88 billion in 2009. A deficit in the capital account implies that money is flowing out of the country and suggests that the nation is increasing its possession of foreign assets (e.g., bonds).
The increasing supply of dollars on foreign exchange (FX) markets during 2009 depressed the euro price of the dollar from 0.79 euro to 0.68 euro. Deficits in the capital account (middle panel of Chart 12) weakened the dollar (bottom panel of Chart 12) when dollar proceeds of bond sales by foreigners were converted to foreign currencies on FX markets for repatriation. Subsequently, the weakened dollar stimulated exports of U.S. products and services, increasing the demand for dollars on FX markets to purchase U.S. goods and services (top panel of Chart 12) and reversing the dollar appreciation attributed to the quantitative easing. In 2010 the dollar price of the euro fell from $1.49 in November 2009 to $1.22 in June 2010 (i.e., the euro price of a dollar rose from 0.67 euro to 0.82 euro). Even with this dollar depreciation, the U.S. trade balance deficit increased from $379.7 million in 2009 to $432.0 million in 2010 as American imports continued to exceed its exports.
Similar patterns may be discerned in each of the subsequent episodes of quantitative easing. Following the brief 2020 recession, the pattern for QE4 differed from the earlier quantitative easing episodes in that the disturbance was externally sourced by the Covid19 pandemic and the clogging of west-coast supply chains.
<Essays Menu>
Regressions on monthly data, July 1954 through October 2024, for Federal Funds and 10-Year Treasury Bills, with dependent variable lags and leads.
Regressions on monthly difference data, July 1954 through October 2024, for Federal Funds and 10-Year Treasury Bills, with dependent variable lags and leads.
Regressions on monthly data, July 1954 through October 2024, for Federal Funds and 10-Year Treasury Bills, with dependent variable lags and leads, beginning row 326 (July 1981).
Regressions on monthly difference data, July 1954 through October 2024, for Federal Funds and 10-Year Treasury Bills, with dependent variable lags and leads.
<Essays Menu>
The concept of the scarcity rate of interest is not as restricted as that of the natural or neutral interest rate. The scarcity interest rate accommodates monetary transactions and policy, and it enables consideration of disequilibria in both real and financial markets as they are linked to each other. The scarcity rate concept is posited relative to the real capital stock in a region. The neutral interest rate concept takes no explicit account of the capital stock or of regional differences of installed capital.
If all the conditions specified for the neutral rate were met, the scarcity rate in a region would converge upon the neutral rate in that region. It is in this sense that, with due consideration to disequilibrium conditions, the neutral rate in a region might serve as a proxy for the scarcity rate in that region. Neither the neutral interest rate nor the scarcity interest rate is observable or trackable, but inferences may be drawn about the value of a regional scarcity interest rate by observing what is happening in regional markets.
Although the neutral or natural rate of interest is not directly observable, yields on longer-term government bonds that are essentially riskless have served as proxies for the natural rate of interest. James Mackintosh, writing in The Wall Street Journal September 2, 2016, notes that
The new debate in central banking is over whether long-run interest rates are lower than in the past, thanks to permanently lower growth. Investors seem to share the view of many policy makers that they are: Long-dated bond yields have plummeted around the world. . . . . The president of the Federal Reserve Bank of San Francisco, John Williams, set the tone for the gathering of central bankers at Jackson Hole, Wyo., last month when he published a widely read letter suggesting the long-run "natural" rate of interest has come down drastically in the past 25 years.
(http://blogs.wsj.com/economics/2016/09/02/think-you-know-the-natural-rate-of-interest-think-again/)
Chart 1a shows the Holston-Laubach-Williams estimates of R-star, the natural rate of interest for the U.S. from 1985 to 2022. A comparison of Charts 1 and 1a shows that the Holston-Laubach-Williams estimates have fallen along with the 20- and 30-year bond yield rate since 2000.
Yield rates on long-term bonds often are taken as proxies for the natural rate of interest. However, as specified for the natural rate of interest, the economy is rarely in equilibrium at full employment with stable inflation and no involvement by a central bank. It would be more appropriate to construe the yields on long-term bonds as proxies for the capital scarcity interest rate for which non-equilibrium states are not precluded.
Long-term U.S. Treasury security yields shadow the capital scarcity interest rate only imperfectly. Long-term bond issuance has been interrupted on two occasions: issuance of the 20-year bond was suspended between 1987 and 1993, and the 30-year bond was not issued between 2002 and 2006. Beginning in 2020 the declining paths of the yields on U.S. Treasury long-term securities were disturbed by the Federal Reserve’s effort to address inflation by increasing the interest rate paid to banks on their deposited reserves. The fact that the 20- and 30-year bond yield rate paths depicted in Chart 1 are not smooth but rather exhibit up/down changes from quarter to quarter implies disequilibrium states and market adjustments to the changing capital scarcity interest rate.
Has the U.S. recently experienced “permanently lower growth” as contended by Mackintosh? The top panel of Chart 2 shows the path of real GDP from 1955 to 2023. The mild upward concavity of the path suggests that the GDP growth rate may have increased slightly over the period. The middle panel of Chart 2 shows real GDP on a per capita basis. With decreasing indigenous birth rates offset by immigration, the near linear up-sloping path of per capita real GDP also belies the contention that growth has become permanently lower. The annual percent changes of real GDP from previous periods shown in the bottom panel of Chart 2 may exhibit a very slight downward trend that implies only a slight diminishing of the real GDP rate of growth.
The Capital Stock and the Capital Scarcity Interest Rate
As shown in the top panel of Chart 3, real (adjusted for inflation) gross private domestic investment in the U.S. has increased during the second half of the twentieth century and into the twenty-first century, with brief downturns only during recessions. The middle panel in Chart 3 shows net (after allowing for depreciation) private domestic investment from 1960 to 2024. Except for when it was negative in 2009, net investment increased the stock of real capital in the U.S. as shown in the bottom panel of Chart 3.
The effect of diminishing returns to the increasing capital stock suggests that the real GDP growth rate should be declining and that the capital scarcity interest rate should be decreasing. Two phenomena that have offset the effect of diminishing returns to capital are technological advance that increases the productivity of the increasing capital stock, and net positive immigration. Immigration has offset the declining indigenous birth rate in the U.S. to enable continuing growth of the U.S. labor force that complements the increasing stock of capital. And technological advance has promoted investment and served as a recession recovery vehicle. With the ever-increasing U.S. capital stock, we might expect the capital scarcity interest rate to decline, but technological advance and positive net immigration may have prevented the capital scarcity interest rate from declining.
The productivity of any resource, human or physical, can be measured as the ratio of a produced amount ("output") to the quantity of the resource used in producing the output. While labor productivity can be measured as the ratio of output per man-hour (assumed homogeneous) used in the production of the output, real capital is so diverse that it is impossible to measure the region-wide productivity of capital per se. However, a region's overall ("total factor") productivity can be measured. It increases when more output is produced by all of the resources employed in producing the output.
The upper panel of Chart 13 shows an index (2017=100) of U.S. non-farm business labor productivity during the second half of the twentieth century and in the early 21st century. The lower panel of Chart 13 shows U.S. total factor productivity over the same period and on the same scale. While both productivity index paths increase and reach 100 in 2017, the fact that the index values of total factor productivity in most years prior to 2017 were higher than the index values of labor productivity in the same years implies that the productivity of capital was increasing as well.
The productivity of a nation's capital stock may increase with investment in more efficient equipment and advancing technology, or by using more labor to complement existing equipment. Even with a declining indigenous birth rate, immigration has enabled the U.S. population (and its labor force) to grow as fast or faster than the capital stock to increase the nation’s total factor productivity as shown in the lower panel of Chart 13.
Increasing total factor productivity may have enabled the U.S. capital scarcity interest rate to remain higher than implied by the falling long-term security yield rates shown in Chart 1. The U.S. capital scarcity interest rate apparently has remained higher than capital scarcity interest rates in many developed countries by enough to attract foreign direct investment to the U.S. The upper panel of Chart 14 shows the increasing rest-of-world foreign direct investment in the U.S. The lower panel of Chart 14 shows U.S. direct investment abroad, implying that U.S. businesses have found even higher capital scarcity interest rates in countries with lesser capital stocks that warrant off-shore direct investment.
Regional capital scarcity rates in the U.S. appear to have diverged. Diminishing returns to historic real capital accumulation in what now are called “rust-belt” states likely have caused their capital scarcity interest rates to decrease. Capital scarcity interest rates in the so-called “sun-belt” states have been higher by enough to attract capital inflows, not only from other regions within the U.S., but also from Europe and Asia. The U.S. state of South Carolina is an example of an internal region that has received substantial foreign direct investment since the middle of the twentieth century.
The capital scarcity interest rate is described as a real return on a real stock of capital without regard to money. But in a money-using economy almost everything is valued in money prices, and yields are computed on financial instruments that are valued in money terms. How do rates of return on financial instruments relate to the capital scarcity interest rate?
In a financial sense, interest is the price for the use of a dollar's (or other local currency unit's) worth of credit for a year. The issuance or sale of a financial instrument by a business firm or a government agency is an implicit demand for credit. The prices of financial instruments are determined by the interaction between forces of demand for and supply of them in loanable funds markets (i.e., bank lending and bond markets). Yield rates on financial instruments are understood to be their market-determined interest rates (as distinguished from the scarcity interest rate determined by resource endowments in the region). Yield rates, which vary inversely with the market prices of financial instruments, also may vary by risk factors and terms to maturity.
U.S. Treasury bill prices are market-determined prices because they are "closing market bid quotations on the most recently auctioned Treasury bills in the over-the-counter market as obtained by the Federal Reserve Bank of New York at approximately 3:30 PM each business day" (https://home.treasury.gov/policy-issues/financing-the-government/interest-rate-statistics). Parties other than the Treasury may engage in the market in which Treasury bills are traded. Banks and other financial interests, both domestic and foreign, may enter the bond market to purchase and sell Treasury and corporate securities by bidding and offering bond prices (not yield rates). If they can get better price deals than offered by the Treasury, market participants will trade with each other rather than with the Treasury. Market yield rates by terms to maturity are calculated from the average prices of bond trades each day. Market yield rates may differ from administered rates set by the Fed's Open Market Committee at its most recent meeting. They may also differ from the region's scarcity rate of interest.
Commentators, pundits, and even financial professionals often personify markets, speaking as if they are persons who behave and know things about the economy and financial markets. Is there reason to think that market bond prices and the yield rates calculated from them contain any special information apart from the interest rates set by monetary authorities? The bond market is comprised of the many individual and institutional traders who buy and sell bonds. Their knowledge and expectations are exhibited in the demands for and supplies of bonds by term categories. The bond prices from which the yield rates are calculated change to reflect increasing or decreasing demands for the bonds relative to the supplies of such bonds. Increasing bond prices (and falling yield rates) indicate that the demand for bonds in that term category recently have increased relative to supply (or that supply has decreased). Decreasing bond prices (and increasing yield rates) indicate that demand for such bonds recently has decreased relative to supply (or that supply has increased). So, yes, recent changes of the average yields by terms to maturity represent the collective understandings and expectations of bond traders about economic and financial conditions, and they may reflect market adjustments relative to the scarcity rate of interest in the region.
The demand for loanable funds is a derived demand that is a function of the demand for the final goods and services that can be produced with the real capital, investment in which was financed by the loanable funds. Market forces cause yield rates on long-term financial instruments to gravitate toward the scarcity interest rate in the region. Market yield rates that exceed the region's scarcity interest rate can be expected to dampen investment spending, decreasing the supply of bonds coming onto financial markets relative to bond demand, raising their prices and lowering their yield rates toward the scarcity rate in the region. Market yield rates below the region's scarcity interest rate can be expected to stimulate investment spending so that the demand for additional loanable funds increases, increasing the supply of bonds coming onto financial markets relative to bond demand, decreasing bond market prices and raising their yield rates toward the region's scarcity rate of interest. These outcomes will be different if bond market demands or supplies change in the same directions as supplies or demands change or at different rates of change.
As depicted in the lower panel of Chart 4, yield rate inversions often have been followed by recessions within a few months. The 8/13/2019 yield rate inversion shown in the upper panel of Chart 4 was followed by a brief recession in early-2020 attributed to 2019 holiday season supply chain congestion and the Covid19 pandemic. This recession may have dampened investment plans, decreasing the supply of bonds relative to the demand for bonds, raising their prices and lowering their yield rates relative to the scarcity rate of interest. The fact that a longer and deeper recession expected by prognosticators had not happened by early 2024 suggested that a "soft landing" from the supply chain and pandemic disruption had occurred as long-term yield rates again approached the scarcity rate of interest.
Yield rates may invert when supplies of longer-term bonds decrease (or demands increase) to cause longer-term bond prices to rise and their yield rates to fall relative to those for shorter-term bonds. Or, yield rates may invert when supplies of shorter-term bonds increase (or demands decrease) to cause shorter-term bond prices to fall and their yield rates to rise relative to those for longer-term bonds. Yield rate inversion may involve a combination of these conditions.
A scenario for a yield rate inversion might occur when expectation of an economic downturn leads business firms to cut back on investment spending financed by supplying longer-term corporate bonds to the market. As the supplies of longer-term bonds decrease relative to the demands for them, their prices rise and their yield rates fall relative to yield rates on shorter-term bonds. The decreasing longer-term yield rates may even fall below the scarcity rate of interest.
If longer-term interest rates remain lower than shorter-term interest rates along an inverted yield curve, eventually business firms will have incentive to shift their demands for loanable funds to finance new investment spending. They may do so by increasing the supply of longer-term corporate bonds with higher prices and lower yield rates relative to the demands for such bonds while decreasing the supply of shorter-term corporate bonds. This will put downward pressure on the longer-term bond prices and upward pressure on the shorter-term bond prices. The yield rate inversion will be alleviated by the rise of longer-term yield rates and the fall of shorter-term yield rates. If longer-term yield rates had fallen below the scarcity rate of interest, they may increase back toward the scarcity rate in the adjustment process.
The Emergence of Federal Reserve Monetary Policy Tools
Natural adjustment processes in a region tend to cause market interest rates to gravitate toward the region's scarcity rate. But monetary policy may induce market interest rates to diverge significantly from the scarcity rate in their region. Monetary policy that induces market rates to fall below the scarcity rate will stimulate spending in the economy and may cause inflation. Monetary policy that causes market rates to rise above the scarcity rate will have depressive effects on the region to diminish the rate of inflation (or possibly even to cause deflation).
Classical textbook explanations of the Federal Reserve's monetary policy tools have described the discount rate, open market operations, and the required reserve ratio. But the Federal Reserve's monetary policy "tool box" has changed over time.
By mid-twentieth century the Federal Reserve's monetary policy tools included the discount rate, open market operations, and the required reserve ratio. Having found during the Great Depression that changes to the required reserve ratio may have drastic and undesirable effects on the banking system, the Fed abandoned the required reserve ratio as a policy tool except for use in extreme circumstances or to make policy corrections.
During the latter half of the twentieth century, the main policy tools became the discount rate and open market operations (purchases and sales of bonds issued by the Treasury and government agencies). The discount rate is the interest rate that commercial banks pay to borrow reserves from the Federal Reserve when they suffer a deficiency of required reserves. It is a "discount rate" in the sense that a bank negotiates a stipulated loan amount from the Fed and receives a lesser amount (the difference being the discount) but pays back to the Fed the full stipulated amount of the loan. For example, if a bank negotiates a $1 million loan from the Fed and receives proceeds of $950,000, it must pay back the full $1 million for a discount rate of 5 percent.
With the emergence of the so-called "Federal Funds" market that enabled commercial banks to borrow reserves from each other, commercial bank borrowing from the Fed diminished, rendering the discount rate an ineffective policy tool. Federal Funds are banks' excess reserves that may be loaned overnight to other banks. The rate that the borrowing bank pays to the lending bank is negotiated between the two banks. The effective Federal Funds rate is the weighted average rate for all of these negotiations.
A new tool was introduced in 2008 as the Fed initiated the process of "quantitative easing" in the effort to stem the "Great Recession." Quantitative easing entailed purchases of large quantities of bonds from commercial banks. The Fed paid for the bonds by crediting the reserves of commercial banks. Since most banks then had large amounts of excess reserves (in excess of legal requirements), the Federal Funds rate decreased toward zero, rendering it useless as a monetary policy tool. To put a floor under the Federal Funds rate and provide the Fed with some modicum of control, the Fed started paying interest on commercial banks' reserves on deposit at the Fed. As noted by Edmund L. Andrews and Michael M. Grynbaum in a New York Times column on October 7, 2008, "Paying interest on reserves allows the central bank to set a floor on interest rates and retain at least some control over monetary policy." The Federal Funds rate can be expected to settle at this floor because banks would be unwilling to lend their excess reserves to other banks at a lower rate than they can earn on excess reserves deposited at the Fed. In 2017 the Fed announced that it would continue the policy of "ample reserves."
After 2008 the Fed's main policy tool became the interest rate that it pays to commercial banks on their reserve balances on deposit at the Fed. Changing this interest rate induces the effective Federal Funds rate to follow it, with the presumption that market-determined interest rates will follow the Federal Funds rate. The Fed uses repurchase and reverse repurchase operations to bring this about.
The upper panel of Chart 5 shows Federal Funds rates from 1955 to 2024. During 2008 to 2013, the Federal Funds rate was nearly zero as the Fed set the target Federal Funds rate at zero in an effort to promote recovery from the 2007-2008 financial crisis.
The lower panel of Chart 5 shows yield rates on 10-year constant maturity Treasury securities to enable comparison to the Federal Funds rate. The 10-year Treasury Bill, the U.S. security that is most liquid and most widely traded in the world, serves as a benchmark for setting home mortgage rates in the U.S. Casual observation suggests that the 10-year Treasury Bill rate moves nearly in lockstep with the Federal Funds rate, but it is not clear whether changes of either lead changes in the other. Regressions on data for these two variables do not reveal significant dependent variable lag or lead relationships or for month-to-month differences of both variables with dependent variable lags or leads.
The media (print, audio, video) foster the notion that the Fed dictates interest rates and causes them to change as the vehicle for implementing monetary policy. This is of course a fiction, although a convenient one for reporting the actions of the Fed and assessing its monetary policy intent. If the Fed wished to implement a “tight” monetary policy to dampen inflationary pressures, it would make public announcement that it was raising the Federal Funds rate by some percent (usually expressed as a number of basis points, e.g., 50 for a half-percent change). What it was in fact doing was announcing a new rate target. Once a target rate change was announced the Fed would act behind the scenes to reset its reserves balance interest rate and cause market-determined rates to approach the newly announced target. The Open Market Committee would become a bond market trader, entering the market to purchase bonds to induce bond prices to rise (yield rates to fall), or to sell bonds to induce bond prices to fall (yield rates to rise).
Changing financial market conditions precipitate the need or opportunity for lenders to change interest rates. However, market-determined interest rates may become “sticky” if lenders are conditioned by periodic Fed announcements of interest rate target changes. If the Fed is widely predicted or expected to announce a rate change in the near future, lenders may wait for the announcement as the excuse or trigger for changing their lending rates. If this happens, it indeed gives the appearance that the Fed has been able to dictate a change of interest rates. But if the Fed has been waiting on market pressures for a rate change to build, it has followed the market rather than led the market to cause rates to change.
Aftermath of the Great Recession
In the eight years following the so-called "Great Recession" of 2008, the U.S. economy continued to be sluggish with a real growth rate below 2 percent per annum. The U.S. CPI inflation rate lingered below the Fed's announced goal of 2 percent per annum. To induce the inflation rate to approach its announced goal, the Fed attempted to enable increased commercial bank lending by increasing bank reserves with four episodes of "quantitative easing" between 2008 and 2021 as depicted in Chart 6. But in an environment of fear, anxiety, and pessimism, the Fed couldn't force bankers to lend or prospective borrowers to borrow. Most of the increased liquidity ended up in commercial bank excess reserves and business cash hoards rather than in circulation to stimulate spending.
The quantitative easing between 2008 and 2015 provided the U.S. banking system with what in Fed terminology is called "ample reserves." In 2017 the Fed indicated that it intends to continue to implement a policy of systemwide ample reserves. This would appear to render both the discount rate and the Federal Funds rate irrelevant as policy tools even if changes of the reserve balances interest rate can elicit changes of the Federal Funds rate. However, even with ample reserves systemwide, there usually are a few commercial banks whose loan officers have approved a sufficient amount of new loans during a day so as to put the banks in deficient reserve positions at the end of the day. Banks suffering a deficiency of reserves would need to borrow Federal Funds overnight to cover their deficiencies.
Changes of the Federal Funds rate prompted by changes in the Fed's reserve balances interest rate will percolate through the financial markets by arbitrage. Also, some banks (how many?) await announcement of changes in the Committee's target Federal Funds rate or in the Fed's reserve balances interest rate as signals to change their own lending rates. To the extent that some banks must borrow Federal Funds and other banks adjust their loan rates on the Fed's changing rate signals, changes of the reserve balances interest rate may confer "at least some control over monetary policy" as suggested by Andrews and Grynbaum. But this control is likely to be modest and tenuous at best, especially if the Federal Funds rate is induced to diverge too far from the scarcity rate of interest.
The Reserve Balances Interest Rate
Both the pre-2008 and post-2008 monetary policy transmission mechanisms are lengthy, complex, uncertain, and fraught with the potential for failure. Other than open market operations, the reserve balances interest rate is the only monetary policy tool now actively employed by the Fed. Recently, open market operations have been devoted to "unwinding" the Fed's huge portfolio of bonds acquired in the three episodes of quantitative between 2008 and 2015. This increase of the supply of bonds coming onto the market is likely to depress bond prices and increase yield rates unless offset by other Fed policy actions.
The Fed's reserve balances interest rate has become its "go to" monetary policy tool in the twenty-first century. The Fed now executes monetary policy by adjusting the interest rate that it pays on commercial banks' reserves in order to change the Federal Funds rate. The reserve balances interest rate is an administered price rather than a market-determined price. Although the Fed now relies on manipulation of this interest rate as its main policy tool, it may be a delusion to think that a central bank changing an administered rate can cause market-determined interest rates to change very much from the scarcity rate of return on real capital. Allowing for risk and term differences, market interest rates are determined ultimately by the scarcity of real capital relative to the demand for it.
Market forces may cause market interest rates to gravitate toward the scarcity rate of interest, and these forces may frustrate central bank intent. If the central bank intends to promote long-term growth or short-term recovery from a recent downturn, it might try to stimulate investment and other interest-sensitive spending by inducing the Federal Funds rate to decrease below the scarcity interest rate. The lower Federal Funds rate will percolate through the financial markets by arbitrage to stimulate bank borrowing. The increased bank borrowing transforms more of banks' excess reserves to become required reserves. If excess reserves diminish far enough, banks with insufficient reserves to cover their loans may be forced to borrow reserves on the Federal Funds market (or from the Fed itself), thereby bidding the Federal Funds rate back up toward the scarcity rate.
A similar analysis can describe a situation when the economy is overheating with inflation higher than tolerable. If the central bank intends to curb investment and other interest-sensitive spending by inducing the Federal Funds rate to increase above the scarcity rate, it may raise the interest rate paid on reserve balances which serves as a floor for the Federal Funds rate. The higher Federal Funds rate will percolate through the financial markets by arbitrage to dampen bank borrowing. The decreased bank borrowing releases more of banks' required reserves to become excess reserves. The increasing excess reserves will decrease borrowing on the Federal Funds market, thereby bidding the Federal Funds rate back down toward the scarcity rate.
Fed officials became concerned that a low reserve balances interest rate and low Federal Funds interest rates (1/2 percent per annum) enabled little monetary control. They began stair-stepping the rates upward in early 2017 and continued to do so until mid-2019 when the economy showed signs weakening during the emerging Covid pandemic that dampened consumer spending. Coincidentally, supply-chain chokes emerged in the run up to the 2019 Christmas season to further dampen consumer spending.
The top and middle panels of Chart 8 show stepwise increments of the excess reserves interest rate and the interest rate paid on reserve balances from 2016 to 2024. The bottom panel confirms that the effective Federal Funds rate moved in lockstep with the reserve balances rate.
Jason Douglas and Jon Sindreu, writing in The Wall Street Journal, December 11, 2016, say that
As shown in the top panel of Chart 3, real (adjusted for inflation) gross private domestic investment in the U.S. has increased during the second half of the twentieth century and into the twenty-first century, with brief downturns only during recessions. The middle panel in Chart 3 shows net (after allowing for depreciation) private domestic investment from 1960 to 2024. Except for when it was negative in 2009, net investment increased the stock of real capital in the U.S. as shown in the bottom panel of Chart 3.
The effect of diminishing returns to the increasing capital stock suggests that the real GDP growth rate should be declining and that the capital scarcity interest rate should be decreasing. Two phenomena that have offset the effect of diminishing returns to capital are technological advance that increases the productivity of the increasing capital stock, and net positive immigration. Immigration has offset the declining indigenous birth rate in the U.S. to enable continuing growth of the U.S. labor force that complements the increasing stock of capital. And technological advance has promoted investment and served as a recession recovery vehicle. With the ever-increasing U.S. capital stock, we might expect the capital scarcity interest rate to decline, but technological advance and positive net immigration may have prevented the capital scarcity interest rate from declining.
The productivity of any resource, human or physical, can be measured as the ratio of a produced amount ("output") to the quantity of the resource used in producing the output. While labor productivity can be measured as the ratio of output per man-hour (assumed homogeneous) used in the production of the output, real capital is so diverse that it is impossible to measure the region-wide productivity of capital per se. However, a region's overall ("total factor") productivity can be measured. It increases when more output is produced by all of the resources employed in producing the output.
The upper panel of Chart 13 shows an index (2017=100) of U.S. non-farm business labor productivity during the second half of the twentieth century and in the early 21st century. The lower panel of Chart 13 shows U.S. total factor productivity over the same period and on the same scale. While both productivity index paths increase and reach 100 in 2017, the fact that the index values of total factor productivity in most years prior to 2017 were higher than the index values of labor productivity in the same years implies that the productivity of capital was increasing as well.
The productivity of a nation's capital stock may increase with investment in more efficient equipment and advancing technology, or by using more labor to complement existing equipment. Even with a declining indigenous birth rate, immigration has enabled the U.S. population (and its labor force) to grow as fast or faster than the capital stock to increase the nation’s total factor productivity as shown in the lower panel of Chart 13.
Increasing total factor productivity may have enabled the U.S. capital scarcity interest rate to remain higher than implied by the falling long-term security yield rates shown in Chart 1. The U.S. capital scarcity interest rate apparently has remained higher than capital scarcity interest rates in many developed countries by enough to attract foreign direct investment to the U.S. The upper panel of Chart 14 shows the increasing rest-of-world foreign direct investment in the U.S. The lower panel of Chart 14 shows U.S. direct investment abroad, implying that U.S. businesses have found even higher capital scarcity interest rates in countries with lesser capital stocks that warrant off-shore direct investment.
Regional capital scarcity rates in the U.S. appear to have diverged. Diminishing returns to historic real capital accumulation in what now are called “rust-belt” states likely have caused their capital scarcity interest rates to decrease. Capital scarcity interest rates in the so-called “sun-belt” states have been higher by enough to attract capital inflows, not only from other regions within the U.S., but also from Europe and Asia. The U.S. state of South Carolina is an example of an internal region that has received substantial foreign direct investment since the middle of the twentieth century.
The capital scarcity interest rate is described as a real return on a real stock of capital without regard to money. But in a money-using economy almost everything is valued in money prices, and yields are computed on financial instruments that are valued in money terms. How do rates of return on financial instruments relate to the capital scarcity interest rate?
In a financial sense, interest is the price for the use of a dollar's (or other local currency unit's) worth of credit for a year. The issuance or sale of a financial instrument by a business firm or a government agency is an implicit demand for credit. The prices of financial instruments are determined by the interaction between forces of demand for and supply of them in loanable funds markets (i.e., bank lending and bond markets). Yield rates on financial instruments are understood to be their market-determined interest rates (as distinguished from the scarcity interest rate determined by resource endowments in the region). Yield rates, which vary inversely with the market prices of financial instruments, also may vary by risk factors and terms to maturity.
U.S. Treasury bill prices are market-determined prices because they are "closing market bid quotations on the most recently auctioned Treasury bills in the over-the-counter market as obtained by the Federal Reserve Bank of New York at approximately 3:30 PM each business day" (https://home.treasury.gov/policy-issues/financing-the-government/interest-rate-statistics). Parties other than the Treasury may engage in the market in which Treasury bills are traded. Banks and other financial interests, both domestic and foreign, may enter the bond market to purchase and sell Treasury and corporate securities by bidding and offering bond prices (not yield rates). If they can get better price deals than offered by the Treasury, market participants will trade with each other rather than with the Treasury. Market yield rates by terms to maturity are calculated from the average prices of bond trades each day. Market yield rates may differ from administered rates set by the Fed's Open Market Committee at its most recent meeting. They may also differ from the region's scarcity rate of interest.
Commentators, pundits, and even financial professionals often personify markets, speaking as if they are persons who behave and know things about the economy and financial markets. Is there reason to think that market bond prices and the yield rates calculated from them contain any special information apart from the interest rates set by monetary authorities? The bond market is comprised of the many individual and institutional traders who buy and sell bonds. Their knowledge and expectations are exhibited in the demands for and supplies of bonds by term categories. The bond prices from which the yield rates are calculated change to reflect increasing or decreasing demands for the bonds relative to the supplies of such bonds. Increasing bond prices (and falling yield rates) indicate that the demand for bonds in that term category recently have increased relative to supply (or that supply has decreased). Decreasing bond prices (and increasing yield rates) indicate that demand for such bonds recently has decreased relative to supply (or that supply has increased). So, yes, recent changes of the average yields by terms to maturity represent the collective understandings and expectations of bond traders about economic and financial conditions, and they may reflect market adjustments relative to the scarcity rate of interest in the region.
The demand for loanable funds is a derived demand that is a function of the demand for the final goods and services that can be produced with the real capital, investment in which was financed by the loanable funds. Market forces cause yield rates on long-term financial instruments to gravitate toward the scarcity interest rate in the region. Market yield rates that exceed the region's scarcity interest rate can be expected to dampen investment spending, decreasing the supply of bonds coming onto financial markets relative to bond demand, raising their prices and lowering their yield rates toward the scarcity rate in the region. Market yield rates below the region's scarcity interest rate can be expected to stimulate investment spending so that the demand for additional loanable funds increases, increasing the supply of bonds coming onto financial markets relative to bond demand, decreasing bond market prices and raising their yield rates toward the region's scarcity rate of interest. These outcomes will be different if bond market demands or supplies change in the same directions as supplies or demands change or at different rates of change.
Normal and Inverted Yield Curves
Longer-term bonds typically earn higher yield rates than shorter-term bonds to reflect the temporal remoteness of their proceeds at maturity. The higher yield rate rewards the long-term bond holder for the opportunity cost of doing without the funds spent in acquiring the bond for a longer period of time until the bond matures. A "normal" term relationship is illustrated in the upper panel of Chart 4 by the blue path for 1/2/2018. But the yield relationship occasionally may become "inverted" when yields on longer-term bonds are below those on shorter-term bonds as illustrated in Chart 4 by the red path of 8/13/2019. On this date, yield rates on 5-year bonds were lower than those on 3-month and 2-year bonds.
As depicted in the lower panel of Chart 4, yield rate inversions often have been followed by recessions within a few months. The 8/13/2019 yield rate inversion shown in the upper panel of Chart 4 was followed by a brief recession in early-2020 attributed to 2019 holiday season supply chain congestion and the Covid19 pandemic. This recession may have dampened investment plans, decreasing the supply of bonds relative to the demand for bonds, raising their prices and lowering their yield rates relative to the scarcity rate of interest. The fact that a longer and deeper recession expected by prognosticators had not happened by early 2024 suggested that a "soft landing" from the supply chain and pandemic disruption had occurred as long-term yield rates again approached the scarcity rate of interest.
Yield rates may invert when supplies of longer-term bonds decrease (or demands increase) to cause longer-term bond prices to rise and their yield rates to fall relative to those for shorter-term bonds. Or, yield rates may invert when supplies of shorter-term bonds increase (or demands decrease) to cause shorter-term bond prices to fall and their yield rates to rise relative to those for longer-term bonds. Yield rate inversion may involve a combination of these conditions.
A scenario for a yield rate inversion might occur when expectation of an economic downturn leads business firms to cut back on investment spending financed by supplying longer-term corporate bonds to the market. As the supplies of longer-term bonds decrease relative to the demands for them, their prices rise and their yield rates fall relative to yield rates on shorter-term bonds. The decreasing longer-term yield rates may even fall below the scarcity rate of interest.
If longer-term interest rates remain lower than shorter-term interest rates along an inverted yield curve, eventually business firms will have incentive to shift their demands for loanable funds to finance new investment spending. They may do so by increasing the supply of longer-term corporate bonds with higher prices and lower yield rates relative to the demands for such bonds while decreasing the supply of shorter-term corporate bonds. This will put downward pressure on the longer-term bond prices and upward pressure on the shorter-term bond prices. The yield rate inversion will be alleviated by the rise of longer-term yield rates and the fall of shorter-term yield rates. If longer-term yield rates had fallen below the scarcity rate of interest, they may increase back toward the scarcity rate in the adjustment process.
The Emergence of Federal Reserve Monetary Policy Tools
Natural adjustment processes in a region tend to cause market interest rates to gravitate toward the region's scarcity rate. But monetary policy may induce market interest rates to diverge significantly from the scarcity rate in their region. Monetary policy that induces market rates to fall below the scarcity rate will stimulate spending in the economy and may cause inflation. Monetary policy that causes market rates to rise above the scarcity rate will have depressive effects on the region to diminish the rate of inflation (or possibly even to cause deflation).
Classical textbook explanations of the Federal Reserve's monetary policy tools have described the discount rate, open market operations, and the required reserve ratio. But the Federal Reserve's monetary policy "tool box" has changed over time.
By mid-twentieth century the Federal Reserve's monetary policy tools included the discount rate, open market operations, and the required reserve ratio. Having found during the Great Depression that changes to the required reserve ratio may have drastic and undesirable effects on the banking system, the Fed abandoned the required reserve ratio as a policy tool except for use in extreme circumstances or to make policy corrections.
During the latter half of the twentieth century, the main policy tools became the discount rate and open market operations (purchases and sales of bonds issued by the Treasury and government agencies). The discount rate is the interest rate that commercial banks pay to borrow reserves from the Federal Reserve when they suffer a deficiency of required reserves. It is a "discount rate" in the sense that a bank negotiates a stipulated loan amount from the Fed and receives a lesser amount (the difference being the discount) but pays back to the Fed the full stipulated amount of the loan. For example, if a bank negotiates a $1 million loan from the Fed and receives proceeds of $950,000, it must pay back the full $1 million for a discount rate of 5 percent.
With the emergence of the so-called "Federal Funds" market that enabled commercial banks to borrow reserves from each other, commercial bank borrowing from the Fed diminished, rendering the discount rate an ineffective policy tool. Federal Funds are banks' excess reserves that may be loaned overnight to other banks. The rate that the borrowing bank pays to the lending bank is negotiated between the two banks. The effective Federal Funds rate is the weighted average rate for all of these negotiations.
A new tool was introduced in 2008 as the Fed initiated the process of "quantitative easing" in the effort to stem the "Great Recession." Quantitative easing entailed purchases of large quantities of bonds from commercial banks. The Fed paid for the bonds by crediting the reserves of commercial banks. Since most banks then had large amounts of excess reserves (in excess of legal requirements), the Federal Funds rate decreased toward zero, rendering it useless as a monetary policy tool. To put a floor under the Federal Funds rate and provide the Fed with some modicum of control, the Fed started paying interest on commercial banks' reserves on deposit at the Fed. As noted by Edmund L. Andrews and Michael M. Grynbaum in a New York Times column on October 7, 2008, "Paying interest on reserves allows the central bank to set a floor on interest rates and retain at least some control over monetary policy." The Federal Funds rate can be expected to settle at this floor because banks would be unwilling to lend their excess reserves to other banks at a lower rate than they can earn on excess reserves deposited at the Fed. In 2017 the Fed announced that it would continue the policy of "ample reserves."
After 2008 the Fed's main policy tool became the interest rate that it pays to commercial banks on their reserve balances on deposit at the Fed. Changing this interest rate induces the effective Federal Funds rate to follow it, with the presumption that market-determined interest rates will follow the Federal Funds rate. The Fed uses repurchase and reverse repurchase operations to bring this about.
The upper panel of Chart 5 shows Federal Funds rates from 1955 to 2024. During 2008 to 2013, the Federal Funds rate was nearly zero as the Fed set the target Federal Funds rate at zero in an effort to promote recovery from the 2007-2008 financial crisis.
The lower panel of Chart 5 shows yield rates on 10-year constant maturity Treasury securities to enable comparison to the Federal Funds rate. The 10-year Treasury Bill, the U.S. security that is most liquid and most widely traded in the world, serves as a benchmark for setting home mortgage rates in the U.S. Casual observation suggests that the 10-year Treasury Bill rate moves nearly in lockstep with the Federal Funds rate, but it is not clear whether changes of either lead changes in the other. Regressions on data for these two variables do not reveal significant dependent variable lag or lead relationships or for month-to-month differences of both variables with dependent variable lags or leads.
The media (print, audio, video) foster the notion that the Fed dictates interest rates and causes them to change as the vehicle for implementing monetary policy. This is of course a fiction, although a convenient one for reporting the actions of the Fed and assessing its monetary policy intent. If the Fed wished to implement a “tight” monetary policy to dampen inflationary pressures, it would make public announcement that it was raising the Federal Funds rate by some percent (usually expressed as a number of basis points, e.g., 50 for a half-percent change). What it was in fact doing was announcing a new rate target. Once a target rate change was announced the Fed would act behind the scenes to reset its reserves balance interest rate and cause market-determined rates to approach the newly announced target. The Open Market Committee would become a bond market trader, entering the market to purchase bonds to induce bond prices to rise (yield rates to fall), or to sell bonds to induce bond prices to fall (yield rates to rise).
Changing financial market conditions precipitate the need or opportunity for lenders to change interest rates. However, market-determined interest rates may become “sticky” if lenders are conditioned by periodic Fed announcements of interest rate target changes. If the Fed is widely predicted or expected to announce a rate change in the near future, lenders may wait for the announcement as the excuse or trigger for changing their lending rates. If this happens, it indeed gives the appearance that the Fed has been able to dictate a change of interest rates. But if the Fed has been waiting on market pressures for a rate change to build, it has followed the market rather than led the market to cause rates to change.
Aftermath of the Great Recession
In the eight years following the so-called "Great Recession" of 2008, the U.S. economy continued to be sluggish with a real growth rate below 2 percent per annum. The U.S. CPI inflation rate lingered below the Fed's announced goal of 2 percent per annum. To induce the inflation rate to approach its announced goal, the Fed attempted to enable increased commercial bank lending by increasing bank reserves with four episodes of "quantitative easing" between 2008 and 2021 as depicted in Chart 6. But in an environment of fear, anxiety, and pessimism, the Fed couldn't force bankers to lend or prospective borrowers to borrow. Most of the increased liquidity ended up in commercial bank excess reserves and business cash hoards rather than in circulation to stimulate spending.
The quantitative easing between 2008 and 2015 provided the U.S. banking system with what in Fed terminology is called "ample reserves." In 2017 the Fed indicated that it intends to continue to implement a policy of systemwide ample reserves. This would appear to render both the discount rate and the Federal Funds rate irrelevant as policy tools even if changes of the reserve balances interest rate can elicit changes of the Federal Funds rate. However, even with ample reserves systemwide, there usually are a few commercial banks whose loan officers have approved a sufficient amount of new loans during a day so as to put the banks in deficient reserve positions at the end of the day. Banks suffering a deficiency of reserves would need to borrow Federal Funds overnight to cover their deficiencies.
Changes of the Federal Funds rate prompted by changes in the Fed's reserve balances interest rate will percolate through the financial markets by arbitrage. Also, some banks (how many?) await announcement of changes in the Committee's target Federal Funds rate or in the Fed's reserve balances interest rate as signals to change their own lending rates. To the extent that some banks must borrow Federal Funds and other banks adjust their loan rates on the Fed's changing rate signals, changes of the reserve balances interest rate may confer "at least some control over monetary policy" as suggested by Andrews and Grynbaum. But this control is likely to be modest and tenuous at best, especially if the Federal Funds rate is induced to diverge too far from the scarcity rate of interest.
The Reserve Balances Interest Rate
Both the pre-2008 and post-2008 monetary policy transmission mechanisms are lengthy, complex, uncertain, and fraught with the potential for failure. Other than open market operations, the reserve balances interest rate is the only monetary policy tool now actively employed by the Fed. Recently, open market operations have been devoted to "unwinding" the Fed's huge portfolio of bonds acquired in the three episodes of quantitative between 2008 and 2015. This increase of the supply of bonds coming onto the market is likely to depress bond prices and increase yield rates unless offset by other Fed policy actions.
The Fed's reserve balances interest rate has become its "go to" monetary policy tool in the twenty-first century. The Fed now executes monetary policy by adjusting the interest rate that it pays on commercial banks' reserves in order to change the Federal Funds rate. The reserve balances interest rate is an administered price rather than a market-determined price. Although the Fed now relies on manipulation of this interest rate as its main policy tool, it may be a delusion to think that a central bank changing an administered rate can cause market-determined interest rates to change very much from the scarcity rate of return on real capital. Allowing for risk and term differences, market interest rates are determined ultimately by the scarcity of real capital relative to the demand for it.
Market forces may cause market interest rates to gravitate toward the scarcity rate of interest, and these forces may frustrate central bank intent. If the central bank intends to promote long-term growth or short-term recovery from a recent downturn, it might try to stimulate investment and other interest-sensitive spending by inducing the Federal Funds rate to decrease below the scarcity interest rate. The lower Federal Funds rate will percolate through the financial markets by arbitrage to stimulate bank borrowing. The increased bank borrowing transforms more of banks' excess reserves to become required reserves. If excess reserves diminish far enough, banks with insufficient reserves to cover their loans may be forced to borrow reserves on the Federal Funds market (or from the Fed itself), thereby bidding the Federal Funds rate back up toward the scarcity rate.
A similar analysis can describe a situation when the economy is overheating with inflation higher than tolerable. If the central bank intends to curb investment and other interest-sensitive spending by inducing the Federal Funds rate to increase above the scarcity rate, it may raise the interest rate paid on reserve balances which serves as a floor for the Federal Funds rate. The higher Federal Funds rate will percolate through the financial markets by arbitrage to dampen bank borrowing. The decreased bank borrowing releases more of banks' required reserves to become excess reserves. The increasing excess reserves will decrease borrowing on the Federal Funds market, thereby bidding the Federal Funds rate back down toward the scarcity rate.
Recent Policy Experience
The Fed's recent concern has been to gain control of the rate of inflation that exceeded its target 2 percent per annum in 2021. Supply-chain congestion and the Covid pandemic of 2019-2020 likely caused market-determined interest rates to fall below the scarcity rate. The result was declining investment and other interest-sensitive spending that precipitated a brief recession in 2020. The U.S. inflation rate as measured by the Trimmed Mean PCE is depicted in Chart 7. By this measure, inflation rose to 5 percent per annum by mid-2023 before beginning to decrease in late 2023.
The Trimmed Mean PCE inflation rate produced by the Federal Reserve Bank of Dallas is an alternative measure of core inflation in the price index for personal consumption expenditures (PCE). The data series is calculated by the Dallas Fed, using data from the Bureau of Economic Analysis (BEA). Calculating the trimmed mean PCE inflation rate for a given month involves looking at the price changes for each of the individual components of personal consumption expenditures. The individual price changes are sorted in ascending order from “fell the most” to “rose the most,” and a certain fraction of the most extreme observations at both ends of the spectrum are thrown out or trimmed. The inflation rate is then calculated as a weighted average of the remaining components. The trimmed mean inflation rate is a proxy for true core PCE inflation rate. The resulting inflation measure has been shown to outperform the more conventional “excluding food and energy” measure as a gauge of core inflation. (https://fred.stlouisfed.org/series/PCETRIM12M159SFRBDAL)
Fed officials became concerned that a low reserve balances interest rate and low Federal Funds interest rates (1/2 percent per annum) enabled little monetary control. They began stair-stepping the rates upward in early 2017 and continued to do so until mid-2019 when the economy showed signs weakening during the emerging Covid pandemic that dampened consumer spending. Coincidentally, supply-chain chokes emerged in the run up to the 2019 Christmas season to further dampen consumer spending.
The top and middle panels of Chart 8 show stepwise increments of the excess reserves interest rate and the interest rate paid on reserve balances from 2016 to 2024. The bottom panel confirms that the effective Federal Funds rate moved in lockstep with the reserve balances rate.
Market Rates and the Scarcity Rate
As suggested by James Mackintosh in a The Wall Street Journal column on September 2, 2016, a message for monetary policy is that "A declining natural rate of interest in major economies gives central banks less ammunition to stabilize the economy." (http://blogs.wsj.com/economics/2016/09/02/think-you-know-the-natural-rate-of-interest-think-again/) If the effective Federal Funds rate follows a decrease of the central bank's reserve balances interest rate, the Fed has less "room" to maneuver by further lowering the Federal Funds rate. Once the Federal Funds rate reaches zero, the Fed may be able to do so only if it is willing to decrease the interest rate paid on reserve balances far enough to take the Federal Funds rate into the negative range. Even then, there is no compelling reason to think that a decrease of the interest rate paid on reserve balances will induce private sector investors to increase investment spending if they are obsessed with geopolitical uncertainty.
Jason Douglas and Jon Sindreu, writing in The Wall Street Journal, December 11, 2016, say that
Central bankers respond that their policies are merely tracking changes in the so-called natural rate, an interest rate determined by powerful economic impulses.
. . . .
By shadowing their estimate of the natural rate, they hope to keep inflation stable and the economy growing at its full potential. Undershoot the rate and they aim to spur faster growth and inflation. Overshoot it and the economy and price rises should slow.
(http://www.wsj.com/articles/central-bankers-zeal-for-the-natural-rate-draws-skeptics-1481476667)
. . . .
By shadowing their estimate of the natural rate, they hope to keep inflation stable and the economy growing at its full potential. Undershoot the rate and they aim to spur faster growth and inflation. Overshoot it and the economy and price rises should slow.
(http://www.wsj.com/articles/central-bankers-zeal-for-the-natural-rate-draws-skeptics-1481476667)
As noted above, if all the conditions specified for the natural rate were met, the scarcity rate would converge upon the natural rate. Since natural rate equilibrium conditions rarely obtain in the real world, we will assume that Douglas and Sindreu's comment applies to the capital scarcity rate of interest rather than to the natural rate of interest.
If central bankers are postulating their monetary policies on tracking or shadowing the scarcity rate of interest, then one is led to wonder why don't they simply let market interest rates naturally adjust to the scarcity rate. This may happen anyway since central bankers often delay changing their administered-price rates (the reserve balances interest rate or the Federal Funds target rate) until market rate pressures for a change are already palpable, i.e., market participants "price in" their expectations of a near-future rate change. When they do this, central bankers are simply following the market rather than leading the market or managing market interest rates.
A problem is that the scarcity interest rate is not an observable rate that can be tracked, but it might be approximated by the yield rates on long-term bonds. If investment increases following a decrease of the Federal Funds rate due to the central bank lowering the reserve balances interest rate, the implication may be that market rates were below the scarcity rate. The increasing investment may increase the supply of corporate bonds relative to bond demand, causing their prices to fall and their yield rates to rise back toward the scarcity rate. If investment decreases following an increase of the Federal Funds rate due to the central bank increasing the reserve balances rate, the implication may be that market rates were above the scarcity rate. The decreasing investment may decrease the supply of corporate bonds relative to bond demand, causing their prices to rise and their yield rates to fall back toward the scarcity rate.
Donald Luskin, writing in The Wall Street Journal, February 16, 2017, described how a market interest rate rule might work:
. . . the new rule goes something like this: Interest rates should be
set at the level that the market would produce by itself if the Fed
didn't exist. . . . . It would, in the end, effectively reduce the Fed from an all-powerful economic meddler to a mere clearing house for
banking-system reserves. (https://www.wsj.com/articles/yellen-gives-conservatives-something-to-cheer-1487290524)
One might wonder why it would be necessary for a monetary authority to set a rate that the market would reach by
itself anyway. Why even have a monetary authority that only attempts to
emulate what the financial markets would do if it did not exist? The delays
entailed in recognition, action, and reaction time lags can render Fed policy
actions disruptive of natural stabilizing forces resident in the economy.
Indeed, policy actions may actually aggravate economic instability. Economic
stability may well be served by restricting the Fed to being "a mere clearing
house for banking-system reserves" and providing a money supply adequate
to the needs of a growing economy.
Monetary Policy in an Open-Economy World
International capital flows motivated by international interest rate, inflation rate, and income change differentials will affect the domestic economy, irrespective of the intent of the central bank. The middle panel of Chart 11 shows the variability of the U.S. capital account between 1999 and 2023, often in deficit, near balance in 2005, 2008, and 2012, in surplus only in 2001 and 2017. In many of these years, deficits in both the trade and capital accounts have decreased the quantity of money in circulation and the reserves of depository institutions as payments were made to foreigners to import goods and services and to invest abroad.
The bottom panel of Chart 11 shows the reserves of U.S. depository institutions between 1999 and 2024. In the aftermath of the 2008 “Great Recession,” the Fed’s implementation of four episodes of quantitative easing (labeled QE1, QE2, QE3, and QE4 in Chart 11) from 2008 to 2020 were blunted by trade deficits during that period, and by capital account deficits in 2009-2011 and 2013-2016.
In an open-economy world, the central bank may attempt to offset or neutralize the monetary effects of trade and capital flows so that domestic monetary targets may be pursued. However, if the central bank does this, it renders inoperable any natural adjustment mechanisms that would correct trade and capital flow imbalances. The consequence would be continuing depreciation or appreciation of the nation's exchange rate vis-a-vis the currencies of other nations. Exchange rate changes may buy time to allow the nation to correct fundamental imbalances by adjusting its domestic prices and incomes, but if the central bank is neutralizing the effects of trade and capital flows on the domestic economy, these fundamental adjustments may never occur.
It is perhaps heroic to think that the Federal Reserve Board of Governors can effectively exert global control over interest rates or the money supply that is relevant to spending behavior in the U.S. economy. Dollar balances held by Americans and foreigners in other countries can facilitate both trade and financial transactions in the domestic economy. By virtue of the large volume of dollars in use in the world, the dollar has become a de facto world currency. Americans may borrow Eurodollars, Petrodollars, or Asiadollars for spending and investment in the U.S. economy or anywhere else in the world. This means that the dollar-denominated domestic money supply is a fiction or at least an irrelevant target. In order to effectively exercise monetary policy in efforts to stabilize the U.S. economy, the Fed would have to target not just the global dollar money supply, but also aggregates of any and all currencies held by Americans and foreigners anywhere in the world that might be converted to dollars and spent in the U.S. economy.
The loanable funds market now is global in scope because American citizens can buy and sell U.S. Treasury bonds, foreign government-issued securities, and domestic and foreign corporate securities anywhere in the world where markets have emerged to enable such trading. And foreigners (non-citizens of the United States) may negotiate loans from U.S. banks and trade securities in U.S. bond markets which in reality have become global markets.
The international trading of securities tends to eliminate bond price differences globally, and thus to equalize yield rates globally on same-term securities. As soon as international bond price differences are detected, securities traders will engage in international arbitrage to capture profits and eliminate the price and yield rate differences. Buying low and selling high will cause lower prices to rise and higher prices to fall until prices converge. But the international arbitrage that eliminates international price and yield rate differences may cause bond yield rates to become higher or lower than region-specific scarcity interest rates. These differences may induce local decreases or increases of investment spending.
There are only a few nations whose central banks might be able to implement monetary policy on global scale: the U.S., the U.K., the E.U., Japan, and China. When the central banks of any of these nations or regions set out to execute monetary policy, even in respect only to their own currencies or only the amounts in circulation in their own economies, they may have important macroeconomic consequences for other economies of the world, and they may not achieve the intended effects in their own economies.
It is difficult to implement monetary policy as a means of offsetting private-sector changes of spending because the linkages between money-supply changes and spending are only indirect and imprecise. The monetary policy transmission mechanism works either through influencing market interest rates that affect interest-sensitive purchases, or through the diminishing marginal utility of money balances which induces consumer spending changes. At this stage of our understanding, it is not possible with any degree of precision to effect the right monetary policy action to elicit just the appropriate offsetting change of spending.
Even more troubling than these minor difficulties is the fact that it is never possible to perfectly predict changes of aggregate spending, and it may not be possible to predict such changes at all. More often than not, the first evidence of a change of aggregate spending occurs some number of months or quarters after the fact. This puts the Fed in the position of reacting to such changes rather than concurrently offsetting them.
And then there is the proverbial "elephant in the room." We live and operate in an open-economy world. In an open economy, the reserves of commercial banks and the money supply are affected both by trade flows and by international capital flows. For example, if the nation experiences a favorable balance in its trade accounts (e.g., it is in surplus when it exports more than it imports), its domestic businesses will be receiving payments either in its domestic currency or in foreign currencies which must be converted to its domestic currency, and the effect necessarily is to expand the domestic money supply and commercial bank reserves irrespective of central bank intent. Monetary contraction would necessarily follow from trade deficits that decrease the domestic money supply. The top panel of Chart 11 shows the variability of the U.S. trade balance, continually in deficit between 1999 and 2023.
International capital flows motivated by international interest rate, inflation rate, and income change differentials will affect the domestic economy, irrespective of the intent of the central bank. The middle panel of Chart 11 shows the variability of the U.S. capital account between 1999 and 2023, often in deficit, near balance in 2005, 2008, and 2012, in surplus only in 2001 and 2017. In many of these years, deficits in both the trade and capital accounts have decreased the quantity of money in circulation and the reserves of depository institutions as payments were made to foreigners to import goods and services and to invest abroad.
The bottom panel of Chart 11 shows the reserves of U.S. depository institutions between 1999 and 2024. In the aftermath of the 2008 “Great Recession,” the Fed’s implementation of four episodes of quantitative easing (labeled QE1, QE2, QE3, and QE4 in Chart 11) from 2008 to 2020 were blunted by trade deficits during that period, and by capital account deficits in 2009-2011 and 2013-2016.
In an open-economy world, the central bank may attempt to offset or neutralize the monetary effects of trade and capital flows so that domestic monetary targets may be pursued. However, if the central bank does this, it renders inoperable any natural adjustment mechanisms that would correct trade and capital flow imbalances. The consequence would be continuing depreciation or appreciation of the nation's exchange rate vis-a-vis the currencies of other nations. Exchange rate changes may buy time to allow the nation to correct fundamental imbalances by adjusting its domestic prices and incomes, but if the central bank is neutralizing the effects of trade and capital flows on the domestic economy, these fundamental adjustments may never occur.
It is perhaps heroic to think that the Federal Reserve Board of Governors can effectively exert global control over interest rates or the money supply that is relevant to spending behavior in the U.S. economy. Dollar balances held by Americans and foreigners in other countries can facilitate both trade and financial transactions in the domestic economy. By virtue of the large volume of dollars in use in the world, the dollar has become a de facto world currency. Americans may borrow Eurodollars, Petrodollars, or Asiadollars for spending and investment in the U.S. economy or anywhere else in the world. This means that the dollar-denominated domestic money supply is a fiction or at least an irrelevant target. In order to effectively exercise monetary policy in efforts to stabilize the U.S. economy, the Fed would have to target not just the global dollar money supply, but also aggregates of any and all currencies held by Americans and foreigners anywhere in the world that might be converted to dollars and spent in the U.S. economy.
The loanable funds market now is global in scope because American citizens can buy and sell U.S. Treasury bonds, foreign government-issued securities, and domestic and foreign corporate securities anywhere in the world where markets have emerged to enable such trading. And foreigners (non-citizens of the United States) may negotiate loans from U.S. banks and trade securities in U.S. bond markets which in reality have become global markets.
The international trading of securities tends to eliminate bond price differences globally, and thus to equalize yield rates globally on same-term securities. As soon as international bond price differences are detected, securities traders will engage in international arbitrage to capture profits and eliminate the price and yield rate differences. Buying low and selling high will cause lower prices to rise and higher prices to fall until prices converge. But the international arbitrage that eliminates international price and yield rate differences may cause bond yield rates to become higher or lower than region-specific scarcity interest rates. These differences may induce local decreases or increases of investment spending.
There are only a few nations whose central banks might be able to implement monetary policy on global scale: the U.S., the U.K., the E.U., Japan, and China. When the central banks of any of these nations or regions set out to execute monetary policy, even in respect only to their own currencies or only the amounts in circulation in their own economies, they may have important macroeconomic consequences for other economies of the world, and they may not achieve the intended effects in their own economies.
Conclusion
Five compelling implications emerge from this study:
1. The natural rate of interest is an abstract concept that does not exist in reality.
2. The capital scarcity rate of interest is a real phenomenon that conditions and drives both financial and real economic activity on global scale.
3. Regional capital scarcity rates change as regional resource endowments change.
4. Regional differences in scarcity rates invite interregional capital flows.
5. The efficacy of central bank monetary policy is a delusion in a globally open-economy world in which economic and financial interests adjust their activities in pursuit of the capital scarcity rates of interest in their respective regions.
<>
<Essays Menu>
Take-Aways From This Essay:
- Automatic adjustment forces in a market economy cause long-term yield rates to gravitate toward the scarcity rate of interest in each region.
- U.S. Treasury 20- and 30-year bond rates have trended downward over the past half-century due to diminishing returns to capital.
- Long-term bond yield rates may proxy the scarcity rate of interest.
- Divergence of market yield rates from the scarcity rate of interest may initiate increased or decreased interest-sensitive spending.
- The Fed attempts to manipulate market yield rates by influencing the Federal Funds rate.
- Prior to 2008 the Fed influenced the Federal Funds rate with open market operations.
- Since 2008, the Fed has dominated the Federal Funds rate by setting the interest rate paid to banks on their reserves on deposit at the Fed.
- The Fed's reserve balances interest rate policy to influence the Federal Funds rate appears to have been successful in alleviating inflation and sustaining employment to bring about a "soft landing" in early 2024.
- The soft landing may have resulted because as the economy recovered from the Covid pandemic and supply-chain congestion, market yield rates moved back toward the natural rate of interest, irrespective of the Federal Funds rate.
- The characteristics of an open-economy world may render the Fed's monetary policy tools of modest capability.
Diminishing Marginal Utility of Money
The link between money supply increases and consumer spending is what economists refer to as the "diminishing marginal utility" of money balances. The sense of this is that when the money supply increases, the additional dollars held by a rational and normally risk-averse person (i.e., neither a gambler nor a miser) mean ever less to him. When the utility (a.k.a. "satisfaction") of the last dollar added to a person's money holding drops below the utility of a dollar's worth of something that he could buy, it becomes rational to part with the dollar and buy the item. The vernacular of this is that "money burns a hole in the pocket." If the additional spending adds to the demand for items relative to their supplies, prices may be bid up. When this happens across the spectrum of the goods that are consumed, inflation occurs.
The phenomenon of the diminishing marginal utility of money balances may not always work as predicted. Distributions of pandemic relief funds during 2021 seem to have resulted in hoarding as some of the funds were held rather than being spent by consumers. A possible explanation is that pandemic distribution recipients suffered sufficient uncertainty about the future that they held back on spending the funds. When the pandemic appeared to be alleviated, the release of pandemic hoardings caused aggregate demand to increase faster than could be accommodated by supply increases, resulting in rising inflation in late 2021 and early 2022.
The marginal utility of money balances may also work in reverse. If the money supply decreases such that individual money balance holdings decrease, the marginal utility of the remaining money balances held will increase for normal, risk-averse money balance holders (neither misers nor gamblers), inducing them to decrease their spending. When the marginal utility of a dollar held rises to exceed the marginal utility of something that the dollar could buy, a rational consumer will suspend further spending. Hoarding behavior may be explained for people who experience increasing marginal utility as their money balances increase (e.g., misers).
It is important to remember that money held as assets of banking institutions is not in circulation. As the Fed begins to "unwind" its bond portfolio in 2022 by selling bonds, it will siphon money from the bank accounts of bond purchasers, thereby reducing the quantity of money in circulation. The expectation is that the majority of people are normal, rational, and risk-averse (neither misers nor gamblers) so that the marginal utilities of their held money balances will increase, thereby reducing consumer spending and curbing inflation.
Arbitrage
Changes in the prices of bonds (and thus their yield rates) become transmitted to the prices (and yields) of other types of financial instruments via the process of arbitrage, i.e., the simultaneous purchase and sale of different types of financial instruments. Arbitrageurs are successful if they are able to operate by the criterion of “buy low, sell high.” Buying will tend to increase price in the lower-price market; selling will tend to lower price in the higher-price market. If they are successful, they will both capture profits and precipitate convergence of prices (and yields) across the markets. Unsuccessful arbitrageurs will suffer losses and tend to destabilize markets, and they may cause interest rates on different types of financial instruments to diverge.
Diminishing Returns
Diminishing returns is the physical phenomenon underlying the capital scarcity rate of interest. Most real world production processes exhibit the phenomenon of diminishing returns, i.e., beyond some point, output begins to increase at a decreasing rate. A graphic model of a diminishing returns production process is illustrated in Chart 9. The back walls of a 3-dimension (3rd order) production surface are illustrated in quadrant I as outlined by the path 0ABC0 in which product output (Q) is on the vertical axis, and amounts of labor (L) and capital (K) are on the right and left floor axes, respectively. The total product function label Q = f ( L , K | . . . ) may be read, "output is a function of the amounts of labor and capital, given fixed amount of all other inputs."
Marginal Products of Labor and Capital
The figure in quadrant V of Chart 10 depicts for the K2 amount of capital the average product curve, APL = (Q / L), and the marginal product curve, MPL = (ΔQ / ΔL) for the smallest possible ΔQ. Marginal product measures the rate of change of total product, i.e., the slope of the Q function along the K2 slice from E to F, G, H, and J. APL at first is greater than MPL but turns down and passes through the peak of MPL at the L2 amount of labor. Beyond the L2 amount of labor, MPL decreases (slopes downward) until it reaches zero on the labor axis at L5, corresponding to the maximum amount of product that can be produced, given the K2 installed plant. The downward sloping range of the MPL cuve illustrates the phenomenon of diminishing returns to labor, given the K2 amount of capital.Capital often is thought of as a fixed input to which labor is the variable input that is added. But in some production processes the amount of labor is fixed (e.g., members of the family on a family farm) while the amount of capital can be varied by acquiring more or disposing of some equipment. Quadrant VI of Chart 10 illustrates diminishing returns to capital, given a fixed amount of labor, L2. The previous paragraph could be repeated with L and K swapped to reveal the phenomenon of diminishing returns to capital illustrated by the downward concavity of the Q = f ( K | L2 , . . . ) function beyond the K1 amount of capital and the downward slope of the MPK curve beyond the K2 amount of capital. It is this phenomenon that underlies the capital scarcity rate of interest.
The figures in quadrants VII and VIII of Chart 10 show that every point along a Q slice of the production function for a fixed amount of one factor is also on a Q slice for a fixed amount of the other factor. In the quadrant VII diagram, as the amount of labor is increased in a fixed plant K2, the slope of the Q function path decreases but the slopes of the cross-cutting K slices increase. Another way to describe this is that with an increasing amount of L, given the K2 plant, the marginal product of L decreases while the marginal product of K increases. And this also would be true in quadrant VIII as the amount of capital is increased for use by a fixed amount of labor L2. Increasing the amount of capital, given a fixed amount of labor, will increase the marginal product of labor even as the marginal product of capital decreases.
Technological advance that improves the efficiency of both of the factors of production would shift the 3-D surface 0ABC0 upward and outward along both of their axes to forestall the effects of diminishing returns to both factors. The marginal product curves of both factors also would shift upward and outward to forestall the effects of diminishing returns. Technological advance that improves the efficiency of only one of the productive factors will skew the surface upward and outward only along the axis of that factor. Such technological advance would forestall diminishing returns to that factor and increase the productivity of the other factor.
Yield Rates Vary Inversely with Market Prices
A simple example illustrates that yield rates vary inversely with market prices. A zero-coupon bond (one that promises no interest payment) would sell in the bond market only at a price lower than face (or par) value. The formula for computing the nominal yield rate on a zero-coupon bond is (face value - market price) / face value. For example, if a 1-year term bond with face value of $1000 can be purchased for $950, its nominal yield rate would be [ (1000 - 950) / 1000 ] = .05 or 5 percent. If a purchaser is willing to pay a higher price of $960 for this bond, the nominal yield rate would be lower: [ (1000 - 960) / 1000 ] = .04 or 4 percent.
Bond Demand and Supply
The yield rates or rates of return on bonds vary inversely with the prices of those bonds. The bond yield rates are implicitly the interest rates on the bonds.
In the bond market, demand and supply
are presumed to be normally sloped relative to the prices of the bonds
as illustrated in Figures 1 and 2. Since financial instruments exhibit
a wide range of denominations, the "quantity of bonds" on the
horizontal axis should be understood not in terms of a number of such
financial instruments, but rather as an amount of financing demanded or
supplied by such instruments. For purpose of exposition, a standard
bond of fixed denomination, e.g., $1 million, might be assumed so that
the horizontal axis units can be understood as the number of such
bonds. An increase in the demand for bonds from D1 to D2
in Figure 1, other things unchanged relative to the supply of
bonds, results in an increase in the price of bonds from P1
to P2, and a corresponding fall in their yield rate. If the
demand for bonds should decrease from D1 to D3,
the price of bonds would fall to P3 and the yield rate
would rise.
Bonds are supplied to the market by corporations seeking funds to finance investments and by governments needing to finance budgetary deficits. In Figure 2 an increase in the supply of bonds from S1 to S2, other things unchanged for bond demand, results in a decrease in the price of bonds from P1 to P2, with corresponding rise in the yield rate. A decrease in the supply of bonds to S3 would elicit an increase in the price of bonds to P3 and a fall in their yield rate.
When private parties have more money than they want to hold in their bank accounts (or under their mattresses), they can purchase goods and services, or they can purchase financial instruments in the bond market. When they do the latter, the demand for bonds increases as in Figure 1, pushing bond prices higher and yield rates lower. When private parties want to hold more money than they have, they can cut back on their purchases of goods and services relative to their continuing income flows, or they can sell some of their financial instruments in the bond markets. To the extent that they do the latter, the supply of bonds increases as in Figure 2, pushing bond prices lower and yield rates higher.
The supply of bonds may be affected by the intents of businesses to finance capital investments, the needs of governments to finance deficits or dispose of surpluses, and the intent of the central bank to execute monetary policy. Changing interest rate differentials between domestic and foreign locales may also induce bond demand or supply shifts. It is the market forces of demand and supply in the bond market that cause bond prices to change and their yield rates to change in the opposite direction.
Changes in the prices of bonds (and thus their yield rates) become transmitted to the prices (and yields) of other types of financial instruments via the process of arbitrage, i.e., the simultaneous purchase and sale of different types of financial instruments or financial instruments in different local markets. Arbitrageurs are successful if they are able to operate by the criterion of “buy low, sell high.” If they are successful, they will both capture profits and precipitate convergence of prices (and yields) across the markets. Unsuccessful arbitrageurs will suffer losses and tend to destabilize markets, and they may cause interest rates on different types of financial instruments to diverge.
Monetary Policy Transmission Mechanism
A monetary policy transition mechanism consists of the steps in the linkage between an action taken by a monetary authority and the ultimate goal that is expected (or hoped) to be impacted. On analogy, it is a bit like the transmission in an automobile that conducts power from the engine to the drive wheels. This analogy is imperfect because, unless the auto transmission is worn or damaged, the power conducted to the drive wheels is certain (although with some loss of power, the longer and the more steps in the linkage).
A better analogy might be the transmission mechanism entailed in the effort by a classic 8-ball billiards game player to cause one of his balls to drop into a pocket. Upon "breaking" the racked set of balls,
- the player lines up his cue stick on the cue ball and
- pokes it with sufficient force and proper direction
- to roll toward one of his balls (striped or solid) and
- hit it at just the right angle and with enough force
to cause it to roll toward a pocket and drop into it.
And like the 8-ball billiards game, the monetary policy transmission mechanism is complex and has many linkages, each of which may fail the monetary authority's intent. The steps in the Fed's pre-2008 policy linkage was
- first to announce a change in the Federal Funds target rate,
- then engage in open market operations
- to alter the excess reserves positions of commercial banks which would
- induce desired changes in the demand or supply of loanable funds (bank lending and bond market activity)
- so that financial instrument (bond) prices would change to cause
- the market-determined Federal Funds rate to move toward the announced Federal Funds target rate and
- yield rates on financial instruments to move toward the announced Federal Funds target rate
- with expectation (or hope) that just enough force had been applied to cause spending in the economy to change in the direction intended by the Federal Funds target rate announcement
- without precipitating (further) recession or inflation.
- first to announce a change in the interest rate paid to commercial banks on their reserve balances on deposit at the Fed
- so as to impose a floor below the nominal market-determined Federal Funds rate,
- rendering it a de facto administered rate under the indirect control of the Fed which would
- pull market-determined interest rates toward the Federal Funds rate
- to induce desired changes in the demand or supply of loanable funds (bank borrowing and bond market activity)
- so that market-determined financial instrument prices would change to cause
- yield rates on financial instruments to move toward the announced reserve deposits interest rate
- with expectation (or hope) that just enough force had been applied to cause spending in the economy to change in the direction intended by the reserve deposits rate announcement
- without precipitating (further) recession or inflation.
Possible monetary policy process obstruction may occur if market participants key their decisions on their perceptions of the scarcity rate of interest that is different from the announced policy rate. In an open-economy world, policy process obstruction may be brought about by unexpected trade and capital flows that affect the relevant money supply, financial instrument prices, and yield rates. Monetary policy interruption may be caused by unexpected spending changes as occurred in 2019-2022 due to the Covid pandemic and supply chain congestion, in 2022-2024 by unexpected military hostilities, by natural disasters, and by ensuing climate change.
<Return to Monetary Policy in an Open-Economy World>
<Return to The Reserves Balance Interest Rate>
Repurchase and Reverse Repurchase Operations
Open market operations may be implemented by the Fed in the process of "unwinding" its huge portfolio acquired in three episodes of "quantitative easing" between 2008 and 2014. The Federal Reserve Bank of New York (FRBNY) website currently identifies the only other open market operations as repurchase and reverse repurchase operations. In a repo auction, security dealers bid on borrowing money from the Fed, offering U.S. Treasury securities as collateral. They implicitly "sell" the securities to the Fed on the day of agreement, and then repurchase them the next day. In a reverse repo auction, dealers offer interest rates at which they would lend money to the Fed. They implicitly "buy" securities from the Fed on the day of agreement, and the Fed repurchases them the next day. Repurchase agreements are made at the initiative of the trading desk at FRBNY which implements monetary policy at the behest of the Federal Open Market Committee (FOMC).
Economic Growth and Development
Due to the effect of diminishing returns, the scarcity rate of interest is higher in regions where capital is scarce and lower in regions where capital is more abundant. Regional differences in scarcity rates invite interregional capital flows. The high capital scarcity interest rate should entice investment spending both by locals and by foreigners contemplating off-shore investments. The capital scarcity interest rate would be expected to fall as capital becomes more abundant with on-going economic development.
Economists distinguish between economic growth and economic development. "Growth," taken to be an improvement in the material well-being of humans, is usually measured as the rate of increase of per capita real income or output of a society. "Real" means that adjustments have been made to eliminate the effects of inflation so that the real component of nominal income increase can be examined. "Per capita" means that some measure of the total output of a society, typically its Gross Domestic Product (GDP), has been divided by the population of the society to get a measure of income on a per-person basis.
"Development" is understood to mean change in the structure of society. The various dimensions of social structure include economic, social, political, moral, religious, and environmental. Development is both a requisite of growth and a consequence of growth--they are inseparable.
A serious problem is that development is typically disruptive of social structures, and thus entails costs. While by definition growth yields only benefits, development seems to involve mostly costs. A rational judgment of whether a process of development cum growth is desirable should be based on the relationship between the benefits of growth against the costs of development, i.e., Bg/Cd. If the value of the ratio of Bg/Cd is greater than 1, the growth-development process is desirable. It is undesirable if the value of the Bg/Cd ratio is less than 1.
Economists make the case that the most effective poverty alleviating vehicle over the past couple of centuries has been economic growth that has been enabled by economic development, and that market economies are more favorable to development than are authoritarian economies.
The suffering of the poor may be less amenable to relief by sharing the existing wealth than by a process of economic development that increases the society's stock of capital (which is part of its physical wealth) due to its high scarcity rate of return to capital. The poor are helped via the "spill-over effects" of employment and income generation, and in terms of a growing volume of lower-priced consumables that are more affordable to the poor.
Interregional Trade and Comparative Advantage
Trading relationships among nations exhibit variations in scarcity interest rates that correspond to their resource endowments. Since the pure theory of trade abstracts completely from references to nation states, it is necessary to shift from the language of "international trade" to that of "interregional trade." Different regions of the world have different endowments of natural, human, and capital resources. Different regions within nation states also may exhibit divergent scarcity interest rates.
Due to the principle of diminishing returns, regions that are richly endowed with capital resources can be expected to exhibit lower capital scarcity rates of interest than trading partner regions that are deficient of capital resources but well endowed with natural and human resources. Economists have enunciated the so-called principle of comparative advantage to explain regional specialization in the production of goods and services.
It is a fact of physical nature that resources are unequally distributed across the earth's geographic space. Some resources approach ubiquity (found everywhere); others are concentrated by regions. Resources that are found in only one or two places on earth may be referred to as geographic uniquities. Examples include rare elements or precious gems or metals, agricultural commodities that grow only under very special conditions, and natural tourist attractions. Populations of regions possessing such uniquities are fortunate in having access to such resources which they are able to exploit; populations elsewhere are correspondingly unfortunate. Populations of regions devoid of such uniquities may acquire them (or things produced using them) by engaging in interregional trade or military aggression to capture them.
There are few perfect ubiquities or uniquities among productive resources. Most resources are found in many places across the globe, although in greater or lesser geographic concentrations. Goods and services requiring those resources as inputs may be produced more cheaply in regions where they are found in abundance than in other regions where they are scarce.
Economists have developed the principle of comparative advantage to explain regional specialization in the production of goods and services. According to this principle, people in each region should specialize in producing those goods and services that can be produced most efficiently in their region compared to other regions. "Most efficiently" means at least opportunity cost (in terms of other goods and services foregone) compared to the other regions. Since the production of goods becomes geographically specialized, people in different regions must trade their specialties for the specialties of people in other regions.
Generalization in consumption is enabled everywhere through trade even though there is regional specialization in production. It can be shown with theoretical exercises as well as empirical information that those who specialize their production according to the principle of comparative advantage and trade with one another enjoy higher welfare than they would under conditions of autarky.
It is sometimes suggested that there are regions of the world that are essentially devoid of productive advantages, whereas other regions seem to possess all of the advantages (veritable "Gardens of Eden"). This problem can be resolved by further refining the definition of comparative advantage. A region's absolute advantages include all of those things that it can produce at lower opportunity costs than can be achieved in other regions. A region's absolute disadvantage is anything that can be produced elsewhere at lower costs in terms of other goods and services which must be foregone.
It may well be that opportunity costs of most things are lower in one region relative to all others, but this does not mean that the region should generalize in production. Its comparative advantages lie in producing those things for which it has greatest absolute advantage(s), while the comparative advantages of other regions lie in producing the things for which they have least absolute disadvantages. They should still specialize in production, but the one in its greatest absolute advantage and all the rest in their least absolute disadvantages. It follows logically from this definition of comparative advantage that it is not possible for a region to have no comparative advantage(s). Furthermore, it can be shown that all of the regions of the world, the sparsely-endowed as well as the abundantly endowed, will enjoy higher welfare with specialization according to the principle of comparative advantage and trade with one another unencumbered by politically imposed constraints.
Modern elaborations of the theory of comparative advantage recognize at least five bases for regional comparative advantages: capital and other resource endowments, cultural preferences, known technologies, scale economies, and company-specific knowledge. The first three are endogenous to locale; the last two technically are independent of geography but may become location specific at the discretion of production decision makers.
It would be highly unlikely in any of these cases that perfect specialization (i.e., only product X is produced in region A and only product Y is produced in region B) would result. Both goods would continue to be produced in both regions, but in each region more of the comparative advantaged good would be produced and less of the comparative disadvantaged good(s). Also, the real world is composed of many regions, some of which are similar to others in respect to resource endowments, preferences, or technologies, and different from the other regions in various respects. The basis for comparative advantage of each may lie in one of these areas or a combination of them. Empirical evidence indicates that a larger volume of the world's trade is conducted among regions that are similar in income levels and preferences than among regions that are widely divergent in any of these areas.
Unless offset by regional decrease of capital in non-comparative-advantaged industries (e.g., by non-replacement of worn equipment, natural disaster, or war), the process of investing in capital to increase regional specialization in comparative-advantaged industries should be expected to decrease the marginal productivity of the region's capital stock and cause its capital scarcity rate of interest to decrease.
Industrial Policy
As trading relationships become more open and free with on-going globalization, specialization of production toward each nation's real comparative advantages ensues. Regions with abundant natural and human resources but meager stocks of capital will experience increasing specialization in producing products that employ intensively their abundant resources. But the government of a region with a meager stock of physical capital may wish to promote industrial investment in production activities for which the region does not have comparative advantages.
As industrial investment increases specialization in the non-comparative advantaged production processes, the formerly comparative advantaged processes become despecialized. Jobs will be threatened and businesses in comparative advantage production will suffer declining sales and profits attributable to the ensuing process of comparative advantage despecialization. Those who feel threatened can be expected to appeal to their congressional or parliamentary representatives to provide protection for the domestic industry in the form of tariffs or non-tariff barriers to trade.
Industrial policy has been described as government picking winners and identifying losers among the resident industries within the nation, and then acting to encourage and support the chosen winners. The most likely reason for an industrial policy to fail is that bureaucratic choices of national-champion industries may not correspond to the nation's natural or acquired comparative advantages. If an administration chooses to support non-comparative-advantaged domestic industries, production costs will be higher than in potential trading-partner nations that do possess the respective comparative advantages. Consumers of the nation will pay higher product prices for domestically-produced goods and enjoy lower levels of welfare than they might have enjoyed if they had consumed comparable imports from regions possessing the respective comparative advantages.
Various U.S. states have practiced forms of industrial policy in their efforts to attract industry or particular firms to locate plants within their borders. The principle underlying state-level industrial policy is the contention that since capital is generally more mobile geographically than is labor, capital should move to sites where it can employ capable and well-trained labor. States vie with one another to demonstrate that their labor forces are capable and well-trained, and that they possess the physical and financial infrastructure to support the sought-after industry. State-level industrial policy may cause market interest rates to diverge from the region’s scarcity rate.
A variant of industrial policy, import-substitution industrialization (ISI), was adopted as development vehicle in several capital-scarce nations during the second half of the twentieth century. The idea was to try to "birth" and protect from global competition non-comparative-advantaged "infant" domestic industries until they could "grow up" and somehow attain comparative advantages on world markets. In the meanwhile, domestic consumers would pay the price of protection in the form of higher prices of domestically-produced goods compared to the lower prices of imports. But the ISI strategy has been discredited in favor of export-oriented development (EOD), i.e., identifying and pursuing development of nations' actual comparative advantages in producing both industrial goods and primary products that can be exported to pay for lower-priced imports.
Industrial policy may cause market-determined interest rates to diverge from the region’s scarcity rate. Industrial policy that only shifts investment from comparative-advantaged production to non-comparative-advantaged production may cause little change in the gross capital stock of the region and thus leaves the capital scarcity interest rate of the region unchanged. Industrial policy that increases the region's capital stock by stimulating investment in non-comparative-advantaged production as capital investment in comparative-advantaged production continues may cause the scarcity interest rate of the region to increase as the marginal productivity of capital in the region declines. This phenomenon may have occurred with South Carolina's industrial policy that stimulated investment in the automobile, tire, aircraft, and other "tech" industries as investment continued to sustain capital engaged in South Carolina's agriculture.
Protectionist Policy
Governments often resort to various forms of protectionist policy when domestic industries are threatened by foreign competition. The most common forms of protection of a domestic industry are tariffs imposed on imports, non-tariff barriers to restrict the inflow of imports, and subsidies that promote domestic industries which compete with imports. If the region has been capital abundant with a low capital scarcity interest rate, these protection measures will tend to increase the capital scarcity interest rate of the region. In a capital scarce region with a high capital scarcity interest rate, the imposition of protectionist measures will tend to lower the capital scarcity interest rate.
A tariff is a tax on an imported good that is paid, not by the exporter, but by the consumers in the nation whose government imposes the tariff. The effect of the imposition of a tariff by the government is to raise the price of the imported product to domestic consumers, which, if the domestic demand for the import is sufficiently elastic with respect to price, will reduce the volume of the import, thereby providing a modicum of protection to the domestic industry. With the tariff in place, domestic producers will be able to sell their product at the higher imported price, although a smaller quantity. The increased price of the import has the effect of worsening the nation's terms of trade; since the foreign-made product now costs more to domestic consumers, each unit of a domestically produced export can buy only a smaller quantity of the import. However, if the domestic demand for the import is sufficiently inelastic, the tariff may not greatly decrease the amount of the product imported.
Once a tariff is imposed, the domestic market price of the product rises. Domestic producers are all too happy to accept the higher price although it may still not be as high as the pre-trade domestic price. Domestic production increases. At the higher market price, domestic consumption falls and the quantity of the product imported decreases. These effects will be relatively small if the world supply is fairly inelastic with respect to price, but the effects will become larger if world supply increases and becomes more elastic.
Non-tariff barriers (NTBs) include quotas on imports, health and safety restrictions on imports, import packaging and labeling requirements, discriminatory performance standards for imports, etc., that are intended to curb imports or raise their delivered prices. Both tariffs and NTBs may cause market-determined interest rates to diverge from the region’s scarcity rate.
Protectionist measures that only shift investment from comparative-advantaged production to non-comparative-advantaged production may cause little change in the gross capital stock of the region and thus leave the capital scarcity interest rate of the region unchanged. Protectionist measures that increase the region's capital stock by stimulating investment in non-comparative-advantaged production as capital investment in comparative-advantaged production continues may cause the scarcity interest rate of the region to increase as the marginal productivity of capital in the region declines.
Lags in the Adjustment Process
Economists refer to the time between when a macroeconomic change occurs and when it is recognized by government officials as the recognition lag, and the time between recognition of such a change and the taking of some action to offset it as the response lag. Needless to say, the lags are both variable in duration and themselves unpredictable. The response lag for monetary policy may be a matter of days or weeks, while that for fiscal policy may be months or quarters. In democratic societies, fiscal policy actions must be proposed, debated, and legislated, processes that often are very time consuming.
There is yet another lag which may eclipse the first two in duration. It is the so-called reaction lag, the period between when an action is taken and the effects of the action fully work through the economy. The reaction lag usually involves a multiplier process of consecutive rounds of respending. Experience in the U.S. economy suggests that the multiplier effect of a fiscal policy action may be completed in as little as a year, but may not be fully worked out in more than two years. The duration of the reaction lag is therefore even less predictable than are the recognition and response lags. The three lags together may span a period of as little as a year, or as much as three or more years. These lags taken together put the government in the position of having to implement a compensating policy even before some event shocks the economy.
This brings us to the most serious problem of implementing any government policy in the interest of stabilizing the economy. It is that the natural adjustment mechanisms of the economy will likely have reversed the direction of change of the economy by the time that the policy designed to deal with the original problem finally has its effect. For example, in a contracting economy, expansionary fiscal and monetary policies are called for. But by the time the contraction can be confirmed, expansionary policy implemented, and the multiplier process completed, the economy of its own volition will likely have begun its recovery. So the expansionary monetary policy impacts an already-expanding economy. A similar, but reversed, scenario can be depicted for an economy entering a period of expansion. Because of variable and unpredictable time lags in the implementation of macropolicy, government's well-intentioned efforts to stabilize the economy often end up destabilizing it--"booming the boom," or "depressing the depression."
Macroeconomic Adjustment to International Disturbances
As the world economy becomes progressively more open and economically integrated, the vehicles for macroeconomic adjustment to internationally-sourced disturbances attain ever greater significance. Basically, there are only three macroeconomic adjustment vehicles: exchange rates, domestic prices (including interest rates), and domestic employment (and incomes). A progression of "if statements" identifies the relevant adjustment possibilities:
1. If exchange rates are allowed sufficient flexibility, they may serve as "shock absorbers" for the domestic economy against internationally-sourced disturbances.
2. If exchange rates are fixed by government authorities, domestic prices assume the burden of adjustment.
3. If domestic prices are insufficiently flexible, the adjustment process must descend upon domestic employment and incomes.
4. If government authorities employ macropolicy to stabilize domestic prices, employment, and incomes, exchange rate flexibility must serve as the adjustment vehicle.
5. If government authorities attempt both to stabilize domestic prices and employment and to fix exchange rates, there is no effective vehicle of macroeconomic adjustment to international disturbances. In the absence of an effective adjustment vehicle, payments imbalances will persist.
An important conclusion emerges from these considerations: the degree of domestic macroeconomic stability of a nation may depend upon the degree of flexibility that its government accords to rates of exchange between its currency and other currencies. As a general rule, we may expect domestic macroeconomic conditions in any economy to be more volatile in response to international disturbances the less flexible are its exchange rates. Fixing or stabilizing exchange rates forces the adjustment to international disturbances upon domestic macroeconomic conditions of prices and employment.
How does U.S. macropolicy mesh with these adjustment vehicles? The top and middle panels of Chart 11 have been brought forward to Chart 12 to be compared to the U.S. dollar-to-euro spot exchange rate in the bottom panel. The exchange rate path shown in this panel demonstrates that U.S. exchange rates are not fixed; their flexibility provides a modicum of shock absorption to both domestic- and internationally-sourced disturbances.
The Federal Reserve does practice macropolicy in its pursuit of price stability, but the interest rate targets that it sets may cause market-determined interest rates to diverge from regional capital scarcity interest rates. It cannot be said that any U.S. authority implements fiscal policy with consistency. The Congress typically legislates spending bills with respect to politically-perceived program needs and only occasionally with regard to employment and income deficiencies. The Treasury Department of the executive branch of the U.S. government is tasked with implementing Congressional legislation to finance federal government expenditures, including regular annual deficits. The sporadic nature of these hodge-podge fiscal actions are not oriented primarily toward achieving macroeconomic stability of employment and incomes. The incoherence of U.S. macropolicy may be a source of the price, employment, and income instability that has been experienced.
Exchange Rates During the Great Recession
The 2008 “Great Recession” was an internal disturbance to the U.S. economy that had international repercussions. The bottom panel of Chart 12 shows that the dollar appreciated as the dollar price of the euro fell from $1.58 in June 2008 to $1.27 in November 2008 (i.e., the euro price of the dollar increased from 0.63 euro to 0.79 euro).
In the effort to alleviate emerging recessions since 2008, the Fed engaged in four rounds of quantitative easing (QE1, November 2008; QE2, November 2010; QE3, September 2012; QE4, March 2020) by increasing the reserves of depository institutions. Following QE1, the dollar depreciated as the price of the euro rose from $1.27 in February 2009 to $1.49 in November 2009 (i.e., the euro price of the dollar decreased from 0.79 euro to 0.68 euro).
Quantitative easing in the U.S. is implemented by the Federal Reserve when it purchases bonds from depository institutions, paying for the bonds by increasing their reserves. The increased reserves enable lending that increases the quantity of money in circulation to stimulate business investment and consumer spending in the economy. The increasing quantity of money in circulation may cause market-determined interest rates to diverge from the capital scarcity interest rate and set in motion adjustment processes. The increasing quantity of money in circulation won’t change the capital scarcity interest rate unless it induces investment that causes a change in the capital stock of the region.
As the Fed buys bonds during a quantitative easing action, bond supplies decrease on U.S. financial markets relative to bond demands, bidding up bond prices and decreasing bond yield rates. The proceeds from selling bonds at higher bond prices motivate businesses and governments to issue new bonds to finance investment and spending plans. Some of the new bond issuers are foreign businesses and governments who receive payment in dollars that must be converted to their own currencies for repatriation. The repatriation of these funds shows up in the middle panel of Chart 12 in a capital account deficit. The U.S. capital account, roughly in balance in 2008, had a deficit of nearly $5.88 billion in 2009. A deficit in the capital account implies that money is flowing out of the country and suggests that the nation is increasing its possession of foreign assets (e.g., bonds).
The increasing supply of dollars on foreign exchange (FX) markets during 2009 depressed the euro price of the dollar from 0.79 euro to 0.68 euro. Deficits in the capital account (middle panel of Chart 12) weakened the dollar (bottom panel of Chart 12) when dollar proceeds of bond sales by foreigners were converted to foreign currencies on FX markets for repatriation. Subsequently, the weakened dollar stimulated exports of U.S. products and services, increasing the demand for dollars on FX markets to purchase U.S. goods and services (top panel of Chart 12) and reversing the dollar appreciation attributed to the quantitative easing. In 2010 the dollar price of the euro fell from $1.49 in November 2009 to $1.22 in June 2010 (i.e., the euro price of a dollar rose from 0.67 euro to 0.82 euro). Even with this dollar depreciation, the U.S. trade balance deficit increased from $379.7 million in 2009 to $432.0 million in 2010 as American imports continued to exceed its exports.
Similar patterns may be discerned in each of the subsequent episodes of quantitative easing. Following the brief 2020 recession, the pattern for QE4 differed from the earlier quantitative easing episodes in that the disturbance was externally sourced by the Covid19 pandemic and the clogging of west-coast supply chains.
<Essays Menu>
Regressions on monthly data, July 1954 through October 2024, for Federal Funds and 10-Year Treasury Bills, with dependent variable lags and leads.
SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 2 10YrTB PERIODS LAGGED: 0 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 1 FF COEF OF MULTIPLE CORRELATION (R): 0.9051 CORRECTED R: 0.9051 COEF OF MULTIPLE DETERMINATION (R^2) 0.8192 CORRECTED R^2: 0.8192 STANDARD ERROR OF THE ESTIMATE: 1.2317 MEAN SQUARED ERROR: 1.5172 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 7067.2774 843 REMOVED BY REGRESSION: 5789.7906 1 F-VALUE: 3816.0894 RESIDUAL: 1277.4868 842 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FF 0.9051 0.7337 0.0119 61.7745 0.0000 CONSTANT (A) 2.2223 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 2 10YrTB PERIODS LAGGED: 1 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 1 FF COEF OF MULTIPLE CORRELATION (R): 0.9049 CORRECTED R: 0.9049 COEF OF MULTIPLE DETERMINATION (R^2) 0.8188 CORRECTED R^2: 0.8188 STANDARD ERROR OF THE ESTIMATE: 1.2332 MEAN SQUARED ERROR: 1.5207 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 7056.3455 842 REMOVED BY REGRESSION: 5777.4456 1 F-VALUE: 3799.2273 RESIDUAL: 1278.9000 841 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FF 0.9049 0.7329 0.0119 61.6379 0.0000 CONSTANT (A) 2.2300 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 2 10YrTB PERIODS LAGGED: 2 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 1 FF COEF OF MULTIPLE CORRELATION (R): 0.9037 CORRECTED R: 0.9037 COEF OF MULTIPLE DETERMINATION (R^2) 0.8166 CORRECTED R^2: 0.8166 STANDARD ERROR OF THE ESTIMATE: 1.2402 MEAN SQUARED ERROR: 1.5381 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 7045.7816 841 REMOVED BY REGRESSION: 5753.7859 1 F-VALUE: 3740.8640 RESIDUAL: 1291.9957 840 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FF 0.9037 0.7314 0.0120 61.1626 0.0000 CONSTANT (A) 2.2412 SIMPLE LINEAR REGRESSION: Y = A + B(1)*X ________________________________________ DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 2 10YrTB PERIODS LAGGED: 3 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 1 FF COEF OF MULTIPLE CORRELATION (R): 0.9023 CORRECTED R: 0.9023 COEF OF MULTIPLE DETERMINATION (R^2) 0.8142 CORRECTED R^2: 0.8142 STANDARD ERROR OF THE ESTIMATE: 1.2481 MEAN SQUARED ERROR: 1.5578 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 7035.3224 840 REMOVED BY REGRESSION: 5728.3293 1 F-VALUE: 3677.1947 RESIDUAL: 1306.9931 839 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FF 0.9023 0.7298 0.0120 60.6399 0.0000 CONSTANT (A) 2.2531 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 2 10YrTB PERIODS LAGGED: 5 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 1 FF COEF OF MULTIPLE CORRELATION (R): 0.8989 CORRECTED R: 0.8989 COEF OF MULTIPLE DETERMINATION (R^2) 0.8081 CORRECTED R^2: 0.8081 STANDARD ERROR OF THE ESTIMATE: 1.2684 MEAN SQUARED ERROR: 1.6088 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 7015.2898 838 REMOVED BY REGRESSION: 5668.7352 1 F-VALUE: 3523.6086 RESIDUAL: 1346.5546 837 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FF 0.8989 0.7261 0.0122 59.3600 0.0000 CONSTANT (A) 2.2792 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 2 10YrTB PERIODS LAGGED: 10 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 1 FF COEF OF MULTIPLE CORRELATION (R): 0.8922 CORRECTED R: 0.8922 COEF OF MULTIPLE DETERMINATION (R^2) 0.7960 CORRECTED R^2: 0.7960 STANDARD ERROR OF THE ESTIMATE: 1.3073 MEAN SQUARED ERROR: 1.7090 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 6970.4841 833 REMOVED BY REGRESSION: 5548.5860 1 F-VALUE: 3246.6627 RESIDUAL: 1421.8981 832 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FF 0.8922 0.7184 0.0126 56.9795 0.0000 CONSTANT (A) 2.3355 ________________________________________Conclusion: 10YrTB data are highly correlated to simultaneous FF data beginning at row 1 (July 1954), but there is no significant lag of 10YrTB after FF.
SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 1 FF PERIODS LAGGED: 0 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 2 10YrTB COEF OF MULTIPLE CORRELATION (R): 0.9051 CORRECTED R: 0.9051 COEF OF MULTIPLE DETERMINATION (R^2) 0.8192 CORRECTED R^2: 0.8192 STANDARD ERROR OF THE ESTIMATE: 1.5195 MEAN SQUARED ERROR: 2.3089 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 10754.8987 843 REMOVED BY REGRESSION: 8810.8345 1 F-VALUE: 3816.0894 RESIDUAL: 1944.0642 842 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTB 0.9051 1.1166 0.0181 61.7745 0.0000 CONSTANT (A) -1.6482 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 1 FF PERIODS LAGGED: 1 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 2 10YrTB COEF OF MULTIPLE CORRELATION (R): 0.9013 CORRECTED R: 0.9013 COEF OF MULTIPLE DETERMINATION (R^2) 0.8124 CORRECTED R^2: 0.8124 STANDARD ERROR OF THE ESTIMATE: 1.5478 MEAN SQUARED ERROR: 2.3958 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 10740.3694 842 REMOVED BY REGRESSION: 8725.5372 1 F-VALUE: 3642.0784 RESIDUAL: 2014.8322 841 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTB 0.9013 1.1113 0.0184 60.3496 0.0000 CONSTANT (A) -1.6163 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 1 FF PERIODS LAGGED: 2 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 2 10YrTB COEF OF MULTIPLE CORRELATION (R): 0.8930 CORRECTED R: 0.8930 COEF OF MULTIPLE DETERMINATION (R^2) 0.7975 CORRECTED R^2: 0.7975 STANDARD ERROR OF THE ESTIMATE: 1.6081 MEAN SQUARED ERROR: 2.5861 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 10728.8366 841 REMOVED BY REGRESSION: 8556.4992 1 F-VALUE: 3308.6294 RESIDUAL: 2172.3374 840 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTB 0.8930 1.1008 0.0191 57.5207 0.0000 CONSTANT (A) -1.5556 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 1 FF PERIODS LAGGED: 3 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 2 10YrTB COEF OF MULTIPLE CORRELATION (R): 0.8829 CORRECTED R: 0.8829 COEF OF MULTIPLE DETERMINATION (R^2) 0.7795 CORRECTED R^2: 0.7795 STANDARD ERROR OF THE ESTIMATE: 1.6782 MEAN SQUARED ERROR: 2.8164 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 10716.2332 840 REMOVED BY REGRESSION: 8353.3155 1 F-VALUE: 2966.0076 RESIDUAL: 2362.9177 839 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTB 0.8829 1.0879 0.0200 54.4611 0.0000 CONSTANT (A) -1.4812 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 1 FF PERIODS LAGGED: 5 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 2 10YrTB COEF OF MULTIPLE CORRELATION (R): 0.8628 CORRECTED R: 0.8628 COEF OF MULTIPLE DETERMINATION (R^2) 0.7444 CORRECTED R^2: 0.7444 STANDARD ERROR OF THE ESTIMATE: 1.8067 MEAN SQUARED ERROR: 3.2640 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 10687.5542 838 REMOVED BY REGRESSION: 7955.5572 1 F-VALUE: 2437.3384 RESIDUAL: 2731.9970 837 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTB 0.8628 1.0619 0.0215 49.3694 0.0000 CONSTANT (A) -1.3300 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 1 FF PERIODS LAGGED: 10 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 2 10YrTB COEF OF MULTIPLE CORRELATION (R): 0.8183 CORRECTED R: 0.8183 COEF OF MULTIPLE DETERMINATION (R^2) 0.6697 CORRECTED R^2: 0.6697 STANDARD ERROR OF THE ESTIMATE: 2.0547 MEAN SQUARED ERROR: 4.2219 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 10633.3159 833 REMOVED BY REGRESSION: 7120.7142 1 F-VALUE: 1686.6228 RESIDUAL: 3512.6017 832 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTB 0.8183 1.0053 0.0245 41.0685 0.0000 CONSTANT (A) -1.0003 ________________________________________Conclusion: FF data are highly correlated to simultaneous 10YrTB data beginning at row 1 (July 1954), but there is no significant lag of FF after 10YrTB (i.e., lead of 10YrTB ahead of FF).
Regressions on monthly difference data, July 1954 through October 2024, for Federal Funds and 10-Year Treasury Bills, with dependent variable lags and leads.
DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 4 10YrTBDIF PERIODS LAGGED: 0 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 3 FFDIF COEF OF MULTIPLE CORRELATION (R): 0.3288 CORRECTED R: 0.3288 COEF OF MULTIPLE DETERMINATION (R^2) 0.1081 CORRECTED R^2: 0.1081 STANDARD ERROR OF THE ESTIMATE: 0.2515 MEAN SQUARED ERROR: 0.0633 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 59.5722 841 REMOVED BY REGRESSION: 6.4413 1 F-VALUE: 101.8376 RESIDUAL: 53.1309 840 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FFDIF 0.3288 0.1805 0.0179 10.0915 0.0000 CONSTANT (A) 0.0013 ________________________________________ DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 4 10YrTBDIF PERIODS LAGGED: 1 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 3 FFDIF COEF OF MULTIPLE CORRELATION (R): 0.0782 CORRECTED R: 0.0782 COEF OF MULTIPLE DETERMINATION (R^2) 0.0061 CORRECTED R^2: 0.0061 STANDARD ERROR OF THE ESTIMATE: 0.2656 MEAN SQUARED ERROR: 0.0706 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 59.5719 840 REMOVED BY REGRESSION: 0.3646 1 F-VALUE: 5.1664 RESIDUAL: 59.2073 839 SIG: 0.0219 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FFDIF 0.0782 0.0429 0.0189 2.2730 0.0219 CONSTANT (A) 0.0018 ________________________________________ DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 4 10YrTBDIF PERIODS LAGGED: 2 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 3 FFDIF COEF OF MULTIPLE CORRELATION (R): 0.0158 CORRECTED R: 0.0158 COEF OF MULTIPLE DETERMINATION (R^2) 0.0002 CORRECTED R^2: 0.0002 STANDARD ERROR OF THE ESTIMATE: 0.2666 MEAN SQUARED ERROR: 0.0711 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 59.5696 839 REMOVED BY REGRESSION: 0.0148 1 F-VALUE: 0.2080 RESIDUAL: 59.5548 838 SIG: 0.6534 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FFDIF 0.0158 0.0086 0.0190 0.4561 0.6534 CONSTANT (A) 0.0019 ________________________________________ DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 4 10YrTBDIF PERIODS LAGGED: 3 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 3 FFDIF COEF OF MULTIPLE CORRELATION (R): 0.0052 CORRECTED R: 0.0052 COEF OF MULTIPLE DETERMINATION (R^2) 0.0000 CORRECTED R^2: 0.0000 STANDARD ERROR OF THE ESTIMATE: 0.2668 MEAN SQUARED ERROR: 0.0712 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 59.5673 838 REMOVED BY REGRESSION: 0.0016 1 F-VALUE: 0.0224 RESIDUAL: 59.5657 837 SIG: 0.8759 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FFDIF -0.0052 -0.0028 0.0190 -0.1496 0.8759 CONSTANT (A) 0.0019 ________________________________________Conclusion: 10YrTBDIF monthly difference data are moderately correlated to simultaneous FFDIF monthly difference data beginning at row 3 (September 1954), but there is no significant lag of 10YrTBDIF after FFDIF.
DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 3 FFDIF PERIODS LAGGED: 0 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 4 10YrTBDIF COEF OF MULTIPLE CORRELATION (R): 0.3288 CORRECTED R: 0.3288 COEF OF MULTIPLE DETERMINATION (R^2) 0.1081 CORRECTED R^2: 0.1081 STANDARD ERROR OF THE ESTIMATE: 0.4582 MEAN SQUARED ERROR: 0.2099 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 197.7342 841 REMOVED BY REGRESSION: 21.3803 1 F-VALUE: 101.8376 RESIDUAL: 176.3539 840 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTBDIF 0.3288 0.5991 0.0594 10.0915 0.0000 CONSTANT (A) 0.0030 ________________________________________ DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 3 FFDIF PERIODS LAGGED: 1 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 4 10YrTBDIF COEF OF MULTIPLE CORRELATION (R): 0.3717 CORRECTED R: 0.3717 COEF OF MULTIPLE DETERMINATION (R^2) 0.1382 CORRECTED R^2: 0.1382 STANDARD ERROR OF THE ESTIMATE: 0.4506 MEAN SQUARED ERROR: 0.2031 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 197.7104 840 REMOVED BY REGRESSION: 27.3223 1 F-VALUE: 134.5367 RESIDUAL: 170.3880 839 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTBDIF 0.3717 0.6780 0.0585 11.5990 0.0000 CONSTANT (A) 0.0034 ________________________________________ DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 3 FFDIF PERIODS LAGGED: 2 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 4 10YrTBDIF COEF OF MULTIPLE CORRELATION (R): 0.1437 CORRECTED R: 0.1437 COEF OF MULTIPLE DETERMINATION (R^2) 0.0206 CORRECTED R^2: 0.0206 STANDARD ERROR OF THE ESTIMATE: 0.4806 MEAN SQUARED ERROR: 0.2310 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 197.6599 839 REMOVED BY REGRESSION: 4.0802 1 F-VALUE: 17.6633 RESIDUAL: 193.5797 838 SIG: 0.0001 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTBDIF 0.1437 0.2621 0.0624 4.2028 0.0001 CONSTANT (A) 0.0043 ________________________________________ DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 3 FFDIF PERIODS LAGGED: 3 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 4 10YrTBDIF COEF OF MULTIPLE CORRELATION (R): 0.0142 CORRECTED R: 0.0142 COEF OF MULTIPLE DETERMINATION (R^2) 0.0002 CORRECTED R^2: 0.0002 STANDARD ERROR OF THE ESTIMATE: 0.4859 MEAN SQUARED ERROR: 0.2361 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 197.6593 838 REMOVED BY REGRESSION: 0.0400 1 F-VALUE: 0.1693 RESIDUAL: 197.6194 837 SIG: 0.6841 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTBDIF -0.0142 -0.0260 0.0631 -0.4115 0.6841 CONSTANT (A) 0.0048 ________________________________________Conclusion: FFDIF monthly difference data are moderately correlated to simultaneous 10YrTBDIF monthly difference data beginning at row 3 (September 1954), but there is no significant lag of FFDIF after 10YrTBDIF (i.e., lead of 10YrTBDIF ahead of FFDIF).
Regressions on monthly data, July 1954 through October 2024, for Federal Funds and 10-Year Treasury Bills, with dependent variable lags and leads, beginning row 326 (July 1981).
SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 2 10YrTB PERIODS LAGGED: 0 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 1 FF COEF OF MULTIPLE CORRELATION (R): 0.9251 CORRECTED R: 0.9251 COEF OF MULTIPLE DETERMINATION (R^2) 0.8558 CORRECTED R^2: 0.8558 STANDARD ERROR OF THE ESTIMATE: 1.1907 MEAN SQUARED ERROR: 1.4178 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 5081.9878 518 REMOVED BY REGRESSION: 4348.9776 1 F-VALUE: 3067.3808 RESIDUAL: 733.0102 517 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FF 0.9251 0.8468 0.0153 55.3839 0.0000 CONSTANT (A) 2.0025 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 2 10YrTB PERIODS LAGGED: 1 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 1 FF COEF OF MULTIPLE CORRELATION (R): 0.9226 CORRECTED R: 0.9226 COEF OF MULTIPLE DETERMINATION (R^2) 0.8512 CORRECTED R^2: 0.8512 STANDARD ERROR OF THE ESTIMATE: 1.1999 MEAN SQUARED ERROR: 1.4398 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 4991.2761 517 REMOVED BY REGRESSION: 4248.3519 1 F-VALUE: 2950.7042 RESIDUAL: 742.9242 516 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FF 0.9226 0.8370 0.0154 54.3204 0.0000 CONSTANT (A) 2.0251 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 2 10YrTB PERIODS LAGGED: 2 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 1 FF COEF OF MULTIPLE CORRELATION (R): 0.9191 CORRECTED R: 0.9191 COEF OF MULTIPLE DETERMINATION (R^2) 0.8447 CORRECTED R^2: 0.8447 STANDARD ERROR OF THE ESTIMATE: 1.2148 MEAN SQUARED ERROR: 1.4756 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 4892.8094 516 REMOVED BY REGRESSION: 4132.8635 1 F-VALUE: 2800.7580 RESIDUAL: 759.9459 515 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FF 0.9191 0.8256 0.0156 52.9222 0.0000 CONSTANT (A) 2.0536 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 2 10YrTB PERIODS LAGGED: 3 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 1 FF COEF OF MULTIPLE CORRELATION (R): 0.9145 CORRECTED R: 0.9145 COEF OF MULTIPLE DETERMINATION (R^2) 0.8364 CORRECTED R^2: 0.8364 STANDARD ERROR OF THE ESTIMATE: 1.2358 MEAN SQUARED ERROR: 1.5273 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 4797.3158 515 REMOVED BY REGRESSION: 4012.2816 1 F-VALUE: 2627.0355 RESIDUAL: 785.0342 514 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FF 0.9145 0.8136 0.0159 51.2546 0.0000 CONSTANT (A) 2.0853 ________________________________________Conclusion: 10YrTB data are highly correlated to simultaneous FF data beginning at row 326 (July 1981), but there is no significant lag of 10YrTB after FF (i.e., lead of FF ahead of 10YrTB).
SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 1 FF PERIODS LAGGED: 0 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 2 10YrTB COEF OF MULTIPLE CORRELATION (R): 0.9251 CORRECTED R: 0.9251 COEF OF MULTIPLE DETERMINATION (R^2) 0.8558 CORRECTED R^2: 0.8558 STANDARD ERROR OF THE ESTIMATE: 1.3008 MEAN SQUARED ERROR: 1.6922 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 6065.3423 518 REMOVED BY REGRESSION: 5190.4961 1 F-VALUE: 3067.3808 RESIDUAL: 874.8462 517 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTB 0.9251 1.0106 0.0182 55.3839 0.0000 CONSTANT (A) -1.4408 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 1 FF PERIODS LAGGED: 1 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 2 10YrTB COEF OF MULTIPLE CORRELATION (R): 0.9247 CORRECTED R: 0.9247 COEF OF MULTIPLE DETERMINATION (R^2) 0.8551 CORRECTED R^2: 0.8551 STANDARD ERROR OF THE ESTIMATE: 1.2844 MEAN SQUARED ERROR: 1.6497 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 5875.1341 517 REMOVED BY REGRESSION: 5023.8841 1 F-VALUE: 3045.3145 RESIDUAL: 851.2501 516 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTB 0.9247 0.9944 0.0180 55.1844 0.0000 CONSTANT (A) -1.3822 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 1 FF PERIODS LAGGED: 2 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 2 10YrTB COEF OF MULTIPLE CORRELATION (R): 0.9217 CORRECTED R: 0.9217 COEF OF MULTIPLE DETERMINATION (R^2) 0.8495 CORRECTED R^2: 0.8495 STANDARD ERROR OF THE ESTIMATE: 1.2946 MEAN SQUARED ERROR: 1.6760 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 5734.3236 516 REMOVED BY REGRESSION: 4871.2047 1 F-VALUE: 2906.5180 RESIDUAL: 863.1189 515 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTB 0.9217 0.9795 0.0182 53.9121 0.0000 CONSTANT (A) -1.3272 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 1 FF PERIODS LAGGED: 3 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 2 10YrTB COEF OF MULTIPLE CORRELATION (R): 0.9175 CORRECTED R: 0.9175 COEF OF MULTIPLE DETERMINATION (R^2) 0.8418 CORRECTED R^2: 0.8418 STANDARD ERROR OF THE ESTIMATE: 1.3143 MEAN SQUARED ERROR: 1.7274 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 5611.1453 515 REMOVED BY REGRESSION: 4723.2866 1 F-VALUE: 2734.4096 RESIDUAL: 887.8587 514 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTB 0.9175 0.9647 0.0184 52.2916 0.0000 CONSTANT (A) -1.2715 ________________________________________Conclusion: FF data are highly correlated to simultaneous 10YrTB data beginning at row 326 (July 1981), but there is no significant lag of FF after 10YrTB (i.e., lead of 10YrTB ahead of FF).
Regressions on monthly difference data, July 1954 through October 2024, for Federal Funds and 10-Year Treasury Bills, with dependent variable lags and leads.
SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 4 10YrTBDIF PERIODS LAGGED: 0 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 3 FFDIF COEF OF MULTIPLE CORRELATION (R): 0.3019 CORRECTED R: 0.3019 COEF OF MULTIPLE DETERMINATION (R^2) 0.0911 CORRECTED R^2: 0.0911 STANDARD ERROR OF THE ESTIMATE: 0.2628 MEAN SQUARED ERROR: 0.0691 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 39.2869 518 REMOVED BY REGRESSION: 3.5807 1 F-VALUE: 51.8458 RESIDUAL: 35.7062 517 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FFDIF 0.3019 0.2780 0.0386 7.2004 0.0000 CONSTANT (A) -0.0120 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 4 10YrTBDIF PERIODS LAGGED: 1 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 3 FFDIF COEF OF MULTIPLE CORRELATION (R): 0.1014 CORRECTED R: 0.1014 COEF OF MULTIPLE DETERMINATION (R^2) 0.0103 CORRECTED R^2: 0.0103 STANDARD ERROR OF THE ESTIMATE: 0.2729 MEAN SQUARED ERROR: 0.0745 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 38.8242 517 REMOVED BY REGRESSION: 0.3995 1 F-VALUE: 5.3642 RESIDUAL: 38.4247 516 SIG: 0.0197 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FFDIF 0.1014 0.0929 0.0401 2.3161 0.0197 CONSTANT (A) -0.0184 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 4 10YrTBDIF PERIODS LAGGED: 2 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 3 FFDIF COEF OF MULTIPLE CORRELATION (R): 0.1597 CORRECTED R: 0.1597 COEF OF MULTIPLE DETERMINATION (R^2) 0.0255 CORRECTED R^2: 0.0255 STANDARD ERROR OF THE ESTIMATE: 0.2705 MEAN SQUARED ERROR: 0.0732 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 38.6631 516 REMOVED BY REGRESSION: 0.9865 1 F-VALUE: 13.4851 RESIDUAL: 37.6766 515 SIG: 0.0005 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FFDIF 0.1597 0.1461 0.0398 3.6722 0.0005 CONSTANT (A) -0.0178 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 4 10YrTBDIF PERIODS LAGGED: 3 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 3 FFDIF COEF OF MULTIPLE CORRELATION (R): 0.0670 CORRECTED R: 0.0670 COEF OF MULTIPLE DETERMINATION (R^2) 0.0045 CORRECTED R^2: 0.0045 STANDARD ERROR OF THE ESTIMATE: 0.2736 MEAN SQUARED ERROR: 0.0748 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 38.6411 515 REMOVED BY REGRESSION: 0.1734 1 F-VALUE: 2.3176 RESIDUAL: 38.4676 514 SIG: 0.1244 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 FFDIF 0.0670 0.0612 0.0402 1.5224 0.1244 CONSTANT (A) -0.0198 ________________________________________Conclusion: 10YrTBDIF monthly difference data are moderately correlated to simultaneous FFDIF monthly difference data beginning at row 326 (July 1981), but there is no significant lag of 10YrTBDIF after FFDIF.
SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 3 FFDIF PERIODS LAGGED: 0 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 4 10YrTBDIF COEF OF MULTIPLE CORRELATION (R): 0.3019 CORRECTED R: 0.3019 COEF OF MULTIPLE DETERMINATION (R^2) 0.0911 CORRECTED R^2: 0.0911 STANDARD ERROR OF THE ESTIMATE: 0.2854 MEAN SQUARED ERROR: 0.0815 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 46.3480 518 REMOVED BY REGRESSION: 4.2243 1 F-VALUE: 51.8458 RESIDUAL: 42.1238 517 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTBDIF 0.3019 0.3279 0.0455 7.2004 0.0000 CONSTANT (A) -0.0209 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 3 FFDIF PERIODS LAGGED: 1 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 4 10YrTBDIF COEF OF MULTIPLE CORRELATION (R): 0.2908 CORRECTED R: 0.2908 COEF OF MULTIPLE DETERMINATION (R^2) 0.0846 CORRECTED R^2: 0.0846 STANDARD ERROR OF THE ESTIMATE: 0.2823 MEAN SQUARED ERROR: 0.0797 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 44.9229 517 REMOVED BY REGRESSION: 3.8000 1 F-VALUE: 47.6818 RESIDUAL: 41.1229 516 SIG: 0.0000 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTBDIF 0.2908 0.3116 0.0451 6.9052 0.0000 CONSTANT (A) -0.0187 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 3 FFDIF PERIODS LAGGED: 2 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 4 10YrTBDIF COEF OF MULTIPLE CORRELATION (R): 0.1294 CORRECTED R: 0.1294 COEF OF MULTIPLE DETERMINATION (R^2) 0.0167 CORRECTED R^2: 0.0167 STANDARD ERROR OF THE ESTIMATE: 0.2805 MEAN SQUARED ERROR: 0.0787 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 41.2105 516 REMOVED BY REGRESSION: 0.6896 1 F-VALUE: 8.7642 RESIDUAL: 40.5209 515 SIG: 0.0036 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTBDIF 0.1294 0.1328 0.0449 2.9604 0.0036 CONSTANT (A) -0.0187 ________________________________________ SIMPLE LINEAR REGRESSION: Y = A + B(1)*X DEPENDENT VARIABLE (Y) IS MATRIX COLUMN: 3 FFDIF PERIODS LAGGED: 3 INDEPENDENT VARIABLE (X) IS MATRIX COLUMN: 4 10YrTBDIF COEF OF MULTIPLE CORRELATION (R): 0.0929 CORRECTED R: 0.0929 COEF OF MULTIPLE DETERMINATION (R^2) 0.0086 CORRECTED R^2: 0.0086 STANDARD ERROR OF THE ESTIMATE: 0.2799 MEAN SQUARED ERROR: 0.0783 ANALYSIS OF VARIANCE: SUMS OF SQUARES DEGREES OF FREEDOM TOTAL: 40.6185 515 REMOVED BY REGRESSION: 0.3506 1 F-VALUE: 4.4751 RESIDUAL: 40.2679 514 SIG: 0.0327 INDEP VAR SIMPLE R COEF (B) S.E. COEF T-VALUE SIGNIFICANCE 1 10YrTBDIF 0.0929 0.0948 0.0448 2.1154 0.0327 CONSTANT (A) -0.0180 ________________________________________Conclusion: FFDIF monthly difference data are moderately correlated to simultaneous 10YrTBDIF monthly difference data beginning at row 326 (July 1981), but there is no significant lag of FFDIF after 10YrTBDIF (i.e., lead of 10YrTBDIF ahead of FFDIF).
<Essays Menu>
Comments
Post a Comment