Money and Interest Rates

This study describes and reconciles two common, seemingly contradictory views about a key monetary policy relationship: that between money and interest rates. Data since 1960 for about 40 countries support the Fisher equation view, that these variables are positively related. But studies taking expectations into account support the liquidity effect view, that they are negatively related. A simple model incorporates both views and demonstrates that which view applies at any time depends on when the change in money occurs and how long the public expects it to last. A surprise money change that is not expected to change future money growth moves interest rates in the opposite direction; one that is expected to change future money growth moves interest rates in the same direction. The study also demonstrates that stating monetary policy as a rule for interest rates rather than money does not change the relationship between these variables. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. Central banks routinely state monetary policies in terms of interest rates. For example, in October 2001, the European Central Bank stated that it had not changed interest rates recently because it considered current rates “consistent with the maintenance of price stability over the medium term” (ECB 2001, p. 5). In May 2001, Brazil’s central bank “increased interest rates” because it was “worried about mounting inflationary pressure,” according to the New York Times (Rich 2001). And in the first half of 2000, the U.S. Federal Open Market Committee increased the federal funds rate target three times in order to head off “inflationary imbalances” (FR Board 2000). Despite this common practice, central banks do not control interest rates directly. They can target interest rates, but they can only attempt to hit those targets by adjusting other instruments they do control, such as the supply of bank reserves. Changes in these instruments directly affect a country’s stock of money, and financial market reactions to money supply changes are what actually change the level of interest rates. Clearly, in order to hit interest rate targets, central banks must have a reliable view about the relationship between money supply changes and interest rate changes. Economic theory offers two seemingly contradictory views of this relationship. One view, which follows from the interaction of money demand and supply, is that money and interest rates are negatively related: increasing interest rates, for example, requires a decrease in the stock of money. According to this view, money demand is a decreasing function of the nominal interest rate because the interest rate is the opportunity cost of holding cash (liquidity). So a decrease in the supply of money must cause interest rates to increase in order to keep the money market in equilibrium. We call this the liquidity effect view. Another view, which follows from the Fisher equation, is that money and interest rates are positively related: increasing interest rates requires an increase in the rate of money growth. The Fisher equation states that the nominal interest rate equals the real interest rate plus the expected rate of inflation (Fisher 1896). If monetary policy does not affect the real interest rate (and errors in inflation expectations are ignored), then the Fisher equation implies that higher nominal interest rates are associated with higher rates of inflation. Since in the long run, high inflation rates are associated with high money growth rates, the Fisher equation suggests that an increase in interest rates requires an increase in the money growth rate. We call this the Fisher equation view. These two views provide seemingly conflicting answers to the question of how a central bank should translate its interest rate targets into actual changes in the money supply. One view implies that interest rates move in the opposite direction as the money supply; the other, that they move in the same direction. This study presents empirical evidence as well as a simple model to explore this apparent conflict. The empirical evidence supports both views of the relationship between changes in money and changes in interest rates. The model shows that the two views are not, in fact, contradictory. Which view applies at any particular point in time depends on when the central bank’s change in money is to occur and how long the public expects it to last. According to the model, the nominal interest rate at any point in time is determined by current and expected future money growth rates. A surprise increase in the current rate of money growth, for example, causes the nominal interest rate to fall if the public expects the surprise increase to be temporary, that is, if their expectations for future money growth rates are not increased as a result. However, if a surprise increase in current money growth is interpreted by the public as permanent, then the nominal interest rate will rise. A surprise increase only in expected future money growth rates will also raise the nominal interest rate. Our study has three parts. In the first part, we consider the empirical evidence for the two views. We start by considering cross-country correlations between average money growth rates and average nominal interest rates for about 40 countries, both developed and developing. Using longrun averages, we find strong, positive correlations between these variables. The correlations remain positive when the time period over which the averages are taken is as short as one year. We also briefly examine the U.S. experience since 1960, and that is consistent with the long-run crosscountry evidence. We see all of this evidence as support for the Fisher equation view. But we also find empirical evidence consistent with the liquidity effect view. We summarize the results of studies that have considered how a surprise change in the money supply—a so-called monetary policy shock—affects interest rates. Although somewhat mixed, the empirical evidence on balance does support the liquidity effect conclusion that the money–interest rate relationship is negative. A surprise decrease in the money supply, for example, will lead to increases in interest rates. In the second part of the study, we turn to economic theory and present a simple model that incorporates both views of the money–interest rate relationship. The model allows money supply changes within a period to be accompanied by nominal interest rate changes in the opposite direction, which is consistent with the liquidity effect view. The model also allows the long-run average nominal interest rate to move positively, percentage point for percentage point, with the long-run average rate of money supply growth, which is consistent with the Fisher equation view. The model shows that how changes in the money supply affect interest rates depends both on what happens to the money stock today and on what is expected to happen to it in the future. If the money stock is unexpectedly changed today, but future money growth rates are expected to remain unchanged, then interest rates move in the opposite direction. But if the money stock is unexpectedly changed today and future money growth rates are expected to move in the same direction, then interest rates move in that direction too. Finally, in the third part of the study, we shift from one type of monetary policy to another. Up to this point, we have assumed that the monetary policy is stated in terms of the money supply. However, again, because most central banks today state their policies in terms of interest rates, we examine the question of whether money and interest rates have the same relationship when central banks formulate monetary policy in terms of an interest rate rule rather than a money supply rule. We show that they do. We do that by incorporating into our model a version of the so-called Taylor rule, which approximates the way that many central banks currently appear to set monetary policy (Taylor 1993). Under this rule, the central bank has an inflation target, and it raises nominal interest rates when inflation is above target and lowers them when it is below target. We find that under such a policy rule, money growth and interest rates move in opposite directions as long as the inflation target remains unchanged. However, in order to lower that target, a central bank must lower both money growth and nominal interest rates. Empirical Evidence We start our study by examining the empirical evidence relevant to the relationship between money and interest rates. We begin with cross-country and U.S. evidence that turns out to support the Fisher equation view. Then we present a brief review of evidence that supports, to some extent, the liquidity effect view. The Fisher Equation View: A Positive Relationship Evidence that supports the Fisher equation view of the relationship between money and interest rates comes primarily from correlations between these two variables within a cross section of countries. To examine these data, we start by computing the correlation between long-run averages of the two variables. We use the long-run averages because the quantity theory relationship between money growth and inflation, which is an essential part of the link between money growth and interest rates, appears empirically to hold in the long run, but not the short run (Lucas 1980). That is, the correlation between money growth and inflation is strong and positive over long horizons, but much weaker over short horizons. Thus, we expect that the correlation between money growth and nominal interest rates will be much stronger in long-run data than in short-run data. And that is what we find. Correlations over long periods are strong and positive. Correlations over short periods are weaker, but still positive. We use data for a cross section of countries rather than for just one country in order to get a reasonable number of data points on which to base the correlations between the long-run averages. The data we use cover the period from 1961 to 1998 and are from the DRI-WEFA version of the International Monetary Fund’s publication International Financial Statistics (IMF, various dates). For money growth rates, we use the series money (line 34 in the IMF tables), which is essentially a measure of the U.S. M1 definition of the money supply. For nominal interest rates, we use two series: money market rates (line 60b), which is the rates on “short-term lending between financial institutions,” and government bond yields (line 61), which is the “yields to maturity of government bonds or other bonds that would indicate longer term rates.” By using both series, we are able to check that the results are not sensitive to the maturity of the nominal interest rate chosen. For our computations, we use only countries that have data covering at least 14 years on money growth and on one or both interest rates. (See Table 1.) For the money market rate series, we found 43 countries (20 developed and 23 developing) that satisfy these criteria. Because of some data problems, however, we are able to use only 32 of these countries (19 developed and 13 developing) as our short-term interest rate sample. For the government bond yield series, we found 31 countries (18 developed and 13 developing) that satisfy the criteria. However, because one country, Venezuela, has had both money growth and nominal interest rates considerably higher than the other countries with this series (both slightly over 28 percent), we report results for the long-run interest rate sample both with and without data for Venezuela. As can be seen in Table 1, there is considerable overlap between the developed countries in the two samples; the 18 countries with government bond yield data also have money market rate data. (The country with only money market rate data is Finland.) However, there is less overlap between the developing countries in the two samples; only Korea, Pakistan, Thailand, and Zimbabwe appear in both. Long-Run Correlations First we examine the relationships between the average rate of money growth and the average of the annual interest rates over the period from 1961 to 1998. The individual country observations with money market rates and government bond yields (with Venezuela omitted) as the interest rate measures are shown in Charts 1 and 2, respectively. The observations for developed and developing countries are distinguished in the charts. The calculated correlations are reported at the top of Table 2. We find that the long-run correlations between those two variables are all positive and strong—all 0.62 or higher. Further, the correlations for all countries and for developing countries are quite similar regardless of which interest rate series is used. The correlation for developed countries is stronger when the shorter-term interest rates (money market rates) are used than when the longer-term rates (government bond yields) are. Overall, however, the results in the charts and Table 2 indicate that in the long run, at least, countries that have low rates of money growth tend to have low nominal interest rates and countries with high rates of money growth tend to have high nominal interest rates. The high correlations between money growth rates and nominal interest rates suggest that the relationship between these two variables is close to linear. The natural question is, what is the slope of this relationship? That is, how much do nominal interest rates increase for each percentage point increase in money growth? To answer that, we regressed nominal interest rates on money growth for each interest rate sample as a whole and separately for the two subsamples of developed and developing countries. The regression lines based on the entire sample for each interest rate series are also shown in Charts 1 and 2. The points cluster rather tightly around these lines, as the strong correlations indicate. The slope coefficients for the entire two samples and for their subsamples are displayed at the bottom of Table 2. These statistics indicate that nominal interest rates increase about 50–70 basis points for each one percentage point increase in the rate of growth of money. All these coefficients are statistically significantly greater than zero, and most are also significantly less than one, at the 0.05 level. Shorter-Run Correlations Next we examine the correlations between money growth rates and nominal interest rates over shorter time periods. Again, we do this because studies of the relationship between money growth and inflation have found much weaker correlations in short-run data than in long-run data. Our first shorter time period for the cross-country correlations of money growth and interest rates is five years. Our observations for these correlations are obtained by computing, for each country in each of the two interest rate samples, money growth rates and average nominal interest rates during nonoverlapping five-year periods beginning in 1964 and ending in 1998. (For some developing countries, we included observations that only cover four-year periods in order to increase the size of the sample.) The resulting correlations between money growth and nominal interest rates are also reported in Table 2. As is true for other studies, here the correlation between money growth and nominal interest rates is somewhat weaker for the shorter time period. All of the correlations are lower than the corresponding correlations for the entire 1961–98 period. This indicates that the cluster of these observations around a line is less tight than for the longer-run observations. This is illustrated in Chart 3, where for the developed countries in the money market rate sample, we plot both the long-run and five-year observations. Still, as Table 2 reports, all the correlations for the shorter-period averages are quite strong—0.49 or higher. Not only do the correlations weaken as the time horizon is shortened, but the slope of the relationship becomes less steep. This is shown at the bottom of Table 2. With the five-year periods, the slope coefficients for both samples range between 0.35 and 0.63. All of these coefficients are statistically significantly different from both zero and one. Lastly, we examine the correlations at a one-year horizon. Table 2 shows that the one-year correlations are still positive, but they are much lower than the five-year correlations for all categories of countries. The very low correlations mean that at a one-year horizon, money growth and nominal interest rates have only a weak, positive relationship. The U.S. Experience The data for the United States alone tell the same story as the cross-country data. In Chart 4 we plot the time series of ten-year average growth rates for the M1 measure of the money supply and for ten-year average yields on six-month U.S. Treasury bills, beginning with the period 1960–69 and ending with the period 1990–99. The points are plotted at five-year intervals, so the ten-year averages are for overlapping tenyear periods. For these U.S. calculations, we use money data from the Board of Governors of the Federal Reserve System and interest rate data from DRI-WEFA. The chart clearly shows that over the long run, U.S. money growth and nominal interest rates have usually moved together since 1960. In each ten-year period from 1960–69 to 1980–89, the rate of U.S. money growth and the average six-month Treasury bill yield both increased from their levels in the preceding period. And in 1990–99, U.S. money growth and nominal interest rates both decreased. Only in the 1985–94 period did these variables move in opposite directions; money growth rose in this period while nominal interest rates fell. The correlation between average M1 growth and six-month Treasury bill yields for the observations plotted in Chart 4 is 0.83. (If only the four nonoverlapping intervals are used, the correlation is 0.94.) We also examine the correlation between money growth and interest rates in the United States at a one-year horizon. These observations are plotted in Chart 5 along with the ten-year averages just discussed. The correlation for the one-year averages is 0.20. Thus, with U.S. data as well as with cross-country data, the correlation between money and interest rates is weaker over the short run than over the long run. Even over the short run, however, the correlation is still positive. The Liquidity Effect View: A Negative Relationship The correlations presented above seem to support the Fisher equation view that money growth and interest rates are positively related. Still, other evidence does seem to support the opposite, liquidity effect view, that these variables are negatively related. This evidence comes from studies that take a different approach to the idea of a liquidity effect. Since the rational expectations revolution of the 1970s, economic theory has come to recognize that expected and unexpected policy changes can have quite different effects. Thus, rather than define the liquidity effect as involving just changes in the money stock, recent studies make a distinction between the effects of expected and unexpected changes in the money stock—and in other monetary policy variables, as well. What matters for the liquidity effect, the studies assume, is unexpected changes, or shocks, to money and other policy variables. Monetary policy shocks are thought to occur for many reasons. For example, the preferences of policymakers can change, or the preliminary data available when policymakers are making their decisions can have measurement errors. (For more on monetary policy shocks, see Christiano, Eichenbaum, and Evans 1999.) According to the updated version of the liquidity effect view of the money–interest rate relationship, positive monetary policy shocks push interest rates down and negative shocks push them up. There is a huge empirical literature on how monetary policy shocks affect a wide range of economic variables. Since this literature is well-reviewed in the recent articles by Bernanke and Mihov (1998) and by Christiano, Eichenbaum, and Evans (1999), we will here only briefly discuss the major findings that relate to the liquidity effect view of how monetary policy shocks affect interest rates. The bulk of the evidence for this view comes from studies using vector autoregression (VAR) models and post– World War II data for the United States. In these studies, monetary policy shocks are that part of the policy variable that cannot be explained given the information set available at the time. The liquidity effect is found in these studies when the monetary policy variable experiencing the shock is assumed to be M2, nonborrowed reserves, or the federal funds rate. However, when M0 or M1 is the monetary policy variable, the liquidity effect is found to be not statistically significantly different from zero. There is also some evidence that the liquidity effect is weaker after 1980 than before. Nonetheless, on balance, the empirical evidence from VAR models seems to support the existence of a liquidity effect qualitatively, at least in the short run, although researchers do not agree on how large it is quantitatively. Other evidence comes from Cooley and Hansen (1995), who use a different methodology. They find a negative correlation between M1 growth and both ten-year U.S. Treasury bond yields and one-month U.S. Treasury bill yields in quarterly data over the period from the first quarter of 1954 through the second quarter of 1991. The data used in this study have been detrended using the HodrickPrescott (H-P) filter. Since the H-P trend can be thought of as the anticipated part of the data, the detrended M1 series can be interpreted as the monetary policy shock. Under this interpretation, the negative correlation between money and interest rates is evidence of a liquidity effect. A Simple Model Now we present a simple model that is consistent with both views of the relationship between money and interest rates. From this model, we learn that how changes in the money stock affect interest rates depends not only on what is happening to money today, but also on what is expected to happen to money in the future. According to the model, if the money stock is changed today, but future money growth rates are not expected to change, then interest rates move in the opposite direction as the money stock, which is the liquidity effect view. But if the money stock is changed today and future money growth rates are expected to move in the same direction, then interest rates move in that direction too, which is the Fisher equation view. Our model is that recently formulated by Alvarez, Lucas, and Weber (2001). It uses the cash-in-advance structure used by Lucas and Stokey (1987) first and by many studies since and a segmented market structure adapted from the work of Occhino (2000) and Alvarez, Atkeson, and Kehoe (forthcoming). The model’s economy is an exchange economy; it has no production. All agents in the economy have identical preferences, and each receives an identical endowment y of goods at the beginning of each period. Goods are assumed to be perishable; that is, they disappear at the end of the period if not consumed before then. Agents are assumed to be unable to (or to dislike to) consume their own endowments. Hence, they must shop for goods from other agents. However, in this economy, goods are assumed to be very hard to transport, so agents cannot carry their own goods around to barter with other agents. This assumption provides a role in this economy for fiat money, intrinsically worthless pieces of paper. Think of each agent as a household actually consisting of two people: a seller and a shopper. In each period, the seller stays home to sell the household’s goods to other agents for money. The shopper uses the receipts from the previous period’s goods sales to buy goods from other agents. Shoppers spend all their money in each period. Also, assume that shoppers can use a random fraction vt (which can be interpreted as approximately the log of the velocity of money) of their current period sales receipts for their current period purchases. (Note that velocity in the model is (1−vt) .) This introduces uncertainty into the model in the form of velocity shocks. Although households have identical preferences and endowments, they do not necessarily have the same trading opportunities. Specifically, a fraction 1 − λ of households, called nontraders, can only exchange in the market for goods. Nontraders face a budget constraint of the form (1) Ptc N t = vt Pt y + (1−vt−1)Pt−1y where c denotes consumption, P denotes the price level, the subscript denotes the time period, and the superscript the agent type (N = nontrader; T = trader). This budget constraint states that the nominal expenditures on consumption in the current period must equal the fraction of receipts from selling the endowment that can be spent in the current period plus the unspent fraction of receipts from selling the endowment in the previous period. In every period, another fraction 0 < λ ≤ 1 of households, called traders, visit a bond market before going to the goods market. In the bond market, money is exchanged for government bonds, meaning that traders are on the other side of all open market operations engaged in by the monetary authority. As a result, traders absorb all changes in the per capita money supply that occur through open market operations in time period t. If the change in the money supply in period t is Mt − Mt−1 = μt Mt−1, then each trader gets μt Mt−1/λ units of fiat money in the period t bond market (where μt is the money supply growth rate). Since this new money is spent in the goods market, the budget constraint of traders is (2) Ptc T t = (1−vt−1)Pt−1y + vtPty + μ t Mt−1/λ. The resource constraint for this economy is that the households’ total consumption must equal their total endowment, or (3) λct + (1−λ)c N t = y. Substituting equations (1) and (2) into (3) yields (4) Pt y = (1−vt−1)Pt−1y + vtPty + μ t Mt−1. Since the total number of units of fiat money carried into period t is (5) Mt−1 = (1−vt−1)Pt−1y equation (4) is a version of the quantity theory. Specifically, (4) can be rewritten as the growth rate version of that theory: the rate of inflation in this economy (6) πt = (Pt /Pt−1) − 1 equals the rate of money supply growth μt plus the rate of velocity growth vt − vt−1, or (7) πt = μ t + vt − vt−1. Solving (1), (2), and (3) reveals that the consumption of traders is (8) ct = y[1 + (μt /λ)]/(1+μt). As long as not all agents are traders, the consumption of traders increases with the rate of growth of the money supply. This is because traders use the money injections to bid up the prices of goods. That activity lowers the real value of the money balances that nontraders brought into the goods market. Thus, traders are able to bid goods away from nontraders in the goods market. When all agents are traders, however, all agents receive the money injections, so that they all enter the goods market with the same quantity of money. Hence, even though prices get bid up, goods are not reallocated. Note that prices will get bid up by the amount that the money supply increases regardless of the fraction of traders in the economy, because the quantity of the endowment is constant. The determination of nominal interest rates in this economy follows from equilibrium in the bond market and the familiar marginal condition for pricing assets: (9) (1+rt) [U′(ct )/Pt] = (1+ρ) Et[U′(c T t+1)/Pt+1]. Assume that bonds issued in period t are promises to one unit of fiat money in period t + 1, that rt is the nominal rate of interest on those bonds in period t, that Et( ) is an expectation conditional on history in period t and earlier, ρ is the agents’ subjective rate of time preference, and U′ is marginal utility. Then the left side of (9) is the marginal utility of the goods that agents have to give up in order to buy a bond in period t. The right side of (9) is the discounted expected marginal utility of the goods that will be received in period t + 1. The marginal utilities are evaluated at the consumption of traders, because only traders can participate in the bond market. If traders have a momentary utility function that displays constant relative risk aversion (10) U(ct) = c 1 t −γ/(1−γ) where γ is the coefficient of risk aversion, then a useful approximation to (9) is (11) rt = ρ̂ + Et(μ t+1) + φ(Etμ t+1−μ t) + Etvt+1 − vt where ρ̂ − ρ > 0 is a risk correction factor, (12) φ = γ(1−v̄)(1−λ)/λ ≥ 0 and v̄ represents a constant velocity. The equation for the determination of the interest rate (11) is consistent with both views of the relationship between money and interest rates. To see this, assume, again, that the economy has some nontraders (λ < 1) and that velocity is constant (vt = v̄). Assume that in the long run, money growth fluctuates randomly around some mean growth rate μ̄,