creation is one potential source of Seigniorage revenue for a government. Seigniorage—gov- ernment revenue received through creating Revenue and money—is a relatively inexpensive means of raising funds. Take the United States as an example. It costs just a few pennies to print a $100 bill. The resource costs to the U.S. Treasury are more than offset by the value of Joseph H. Haslag Senior Economist and Policy Advisor the goods that could be purchased with the Bank of Dallas $100 bill. It is even less expensive for the Federal Reserve to electronically purchase large quantities of Treasury bonds, notes, and bills from traders in New York. It is important to note that the Federal Reserve returns the pay- ments on its security holdings (less its expenses) to the U.S. Treasury. Consequently, when the The resource costs to the Federal Reserve increases its bond holdings, for example, the U.S. Treasury realizes an effective U.S. Treasury [to print a reduction to its debt expenses.1 The present value of the reduction in Treasury expenses is $100 bill] are more than equal to the amount of money injected by the Federal Reserve’s open market purchase. offset by the value of the The problem is that although money may be cheap to produce, the social costs of money goods that could be purchased creation are almost certainly greater than what the Federal Reserve pays to create it. Indeed, a with the $100 bill. large body of empirical evidence suggests that the rate of is closely correlated with . Thus, faster money creation costs society by eroding the purchasing power of money already in circulation, which is the infla- tion . Though tempted by low production costs, governments must balance the benefits with social costs when deciding how much to rely on seigniorage. The article addresses two questions. First, how much do countries rely on money creation as a source of revenue? The answer to this ques- tion gives some idea of the size of the seignior- age revenue “problem.” For most of the countries, money creation accounts for less than 2 percent of real GDP. The evidence indicates that seigniorage revenue is not the primary source of revenue for a government, but neither is it quantitatively insignificant. Second, are monetary policy settings sys- tematically related to a government’s reliance on real seigniorage revenue, and, if so, what is the relationship? Such evidence should be a useful guide for economic theories—that is, a good theory should be able to account for a government’s reliance on seigniorage revenue versus, say, its reliance on income . Sargent (1986) presents some evidence that very rapid money growth does not translate into greater reliance on real seigniorage rev- enue. He studies monetary policy during four

10 episodes that occurred immedi- seigniorage revenue than countries with low ately following World War I. For two countries, monetary policy settings. An additional implica- Austria and Hungary, Sargent reports data on tion follows from the way in which the measure money growth and the fraction of government of monetary policy is constructed; specifically, spending earned through seigniorage revenue. one can infer that the relationship between the Austria raised about 67 percent of government reserve ratio, which holds the money growth expenditures through money creation in the rate constant, and a country’s reliance on sei- first half of 1919. However, the ratio of money gniorage revenue is concave. The concave rela- creation to government expenditures fell to tionship also holds between the money growth about 40 percent of government expenditures rate and seigniorage reliance when the reserve by 1922. Between 1919 and 1922, Austrian ratio is constant. The implied concavity com- crowns in circulation went from roughly 4.7 plements Sargent’s findings for Austria and billion to nearly 4.1 trillion. For Hungary, Hungary. money creation accounted for more than 45 It is useful to begin with a brief overview percent of its government expenditures in of seigniorage revenue that shows how it fits 1921–22, falling to about 33 percent in 1924 –25. into a broader picture of government finance. Between February 1921 and April 1925, Hungary saw its notes in circulation rise from SEIGNIORAGE REVENUE—AN OVERVIEW 15 billion kronen to 4.5 trillion kronen.2 For these two case studies, the evidence suggests Suppose the government prints new that reliance on money creation decreases as pieces of and uses these newly created the rate of money growth increases. bills to buy goods and services, such as missiles are rare and probably not good or computers, or pay workers’ salaries.3 For sim- laboratories for studying the relationship be- plicity, I assume that the economy has a com- tween monetary policy and seigniorage reve- posite commodity (hereafter, the consumption nue. Still, the Austrian and Hungarian data show good). The government can buy units of this that dramatic increases in the rate of money consumption good with the newly printed growth do not necessarily translate into a money, which is government’s increased reliance on seigniorage (1) (M – M )v , revenue. t t–1 t In this article, I use data from different where M denotes the total quantity of high- countries to identify whether a systematic rela- powered money in the economy (t denotes tionship exists between monetary policy and a time), and v denotes the money’s value in terms country’s reliance on seigniorage revenue. of the units of the consumption good that can Rather than focus on year-to-year realizations, be acquired with one unit of money (that is, the the approach taken in this article is to study the inverse of the price level). Thus, Equation 1 rep- correlation between monetary policy and resents the units of the consumption good that seigniorage over a longer horizon; specifically, can be purchased with newly printed money— the sample mean is computed from a 30-year in other words, real seigniorage revenue. period. Both economic theory and problems Seigniorage revenue is just one part of a with statistical inference point to using a suffi- larger picture. To see the complete picture, it is cient statistic to measure monetary policy. (A necessary to give the government’s income sufficient statistic captures changes in the vari- statement, or budget constraint. To keep things able that the researcher is studying.) Here, the simple, assume that the government issues only monetary policy measure is a combination of one-period, fully indexed bonds.4 For this sim- the money growth rate and the reserve ratio. As ple economy, the government’s budget con- such, the evidence bears on whether countries straint can be written as with a high money growth rate–reserve ratio (2) g + r b = t y + b + (M – M )v . combination also tend, on average, to rely more t t t –1 t t t t t –1 t heavily on seigniorage revenue over these In Equation 2, g is the total quantity of goods longer horizons than countries with a low purchased by the government; the product, rb, money growth rate–reserve ratio combination. is the principal and interest payments, measured The cross-country evidence indicates a in units of the good, that the government owes positive association between the monetary for one-period bonds issued at date t –1;ris policy measure and a country’s reliance on the real gross return (principal plus net interest) seigniorage revenue. Thus, countries with high on government securities worth b goods. Thus, monetary policy settings tend to rely more on the left-hand side of Equation 2 represents

FEDERAL RESERVE BANK OF DALLAS 11 ECONOMIC REVIEW THIRD QUARTER 1998 6 the total expenditures by the government. The rate; that is, 1/p, where p = pt /pt –1. Other things right-hand side characterizes the government’s being equal, the rate of inflation is positively total receipts. The product, ty, represents the related to the rate of money growth. Hence, income tax revenue earned by the government faster money growth means that the real return at rate t, and y is the aggregate level of real on money falls. It follows that faster money income. growth results in a smaller tax base for real Note that in Equation 2 the government seigniorage revenue. has access to an income tax. Representing tax Overall, faster money growth can lead to revenue this way is not necessary. However, either more or less real seigniorage revenue, there is a useful analogy between seigniorage depending on whether the change in the tax revenue and income tax revenue. The relation- rate or the change in the tax base is quantita- ship between the income tax rate and tax reve- tively larger. nue has been popularized in the Laffer curve. Suppose that income, y, is negatively related to Reserve Requirements and the Tax Base the tax rate. With an increase in the tax rate, for There is another monetary policy tool that example, people would report less income.5 could potentially influence real seigniorage rev- The basic supply-side question, therefore, is enue. The reserve requirement stipulates that whether higher tax rates are offset by a lower money balances cannot be less than g percent tax base. Since tax revenues are the product of of bank deposits, where g denotes the reserve these two factors, it is impossible to say, a pri- requirement ratio. Consequently, for a given ori, whether income tax revenues rise or fall in level of deposits, a higher reserve requirement response to an increase in tax rates. implies that the quantity of real money balances increases; that is, a larger tax base. However, Seigniorage Revenue and Money Growth holding the level of deposits constant is An increase in the money growth rate has unlikely. An increase in the reserve requirement an effect on seigniorage that is analogous to the ratio may induce people to decrease their total effect that an increase in the tax rate has on savings and hence their bank deposits. As a income tax revenue. To illustrate this point, I result, people may avoid the inflation tax by modify the expression for seigniorage revenue reducing their bank deposits. to identify a tax rate and tax base. The date t To illustrate this point, people have two quantity of money in circulation is equal to the means of saving: government bonds and money. product of a growth rate and date t – 1 stock. For simplicity, I assume that the real return on Thus, the government bonds, r, is constant and that these bonds dominate money in terms of offer- (3) M = q M , t t t –1 ing a higher rate of return—that is, 1/p < r. where q is the gross rate of money supply In this economy, banks serve a very sim- expansion. With q > 0, the percentage change ple function. I assume that government bonds in the is q – 1. Use Equation 3 are issued in denominations that are too large

to substitute for Mt –1 in Equation 1. The result- for any one saver to acquire. The bank cost- ing government budget constraint is given by lessly pools the funds to acquire these govern- ment bonds. Because the bank maximizes (2¢) g + r b = t y + b + v M (1 – 1/q ). t t t –1 t t t t t t profits in a perfectly competitive market, the The analog to income tax revenue is now more rate of return on deposits will also be r. Each accessible. In Equation 2¢, the total revenue person takes the rate of return on deposits as from money creation is now the product of a given. The reserve requirement stipulates that

tax base, vt Mt, and a tax rate, (1 – 1/q), that is the person hold a fraction of these deposits as positively related to the rate of money growth. money balances.7 Because money is rate of To complete the analogy to the tax reve- return dominated by government bonds, the nue setting, linking the seigniorage tax base to person will not hold any in excess of the seigniorage tax rate is necessary. One way this reserve requirement. The equilibrium return to do this is to assume that the real quantity of on a person’s savings is money—which for seigniorage revenue is the g 1 r tax base—is a function of its real rate of return. ()4 q = • + , 1 + gp1 + g More specifically, let real money balances be positively related to the real return on money. It where q is the gross real return on savings. Note is straightforward to show that the real rate of that q is a weighted average of the rate of return return on money is the inverse of the inflation on real money balances and on government

12 bonds. With 1/p < r, Equation 4 implies that Before reporting any statistics, it is impor- q < r. In other words, the reserve requirement tant to note that the reserve requirement ratio ratio drives a wedge between the return on presents a measurement issue. In principal, the bonds and the return to savings. average marginal reserve requirement ratio— Suppose there is an increase in the reserve the ratio that applies to the next dollar requirement ratio. The quantity of real money deposited—would be measured.10 In practice, balances held by people is gd, where d is the however, measuring this is not so simple. There quantity of goods deposited with banks. For a is a dizzying array of reserve requirements; U.S. given level of deposits, people will hold more banks are currently required to hold reserves money and the tax base rises. Equation 4, how- equal to 3 percent of the first $49.3 million of ever, implies that the real return on savings falls checkable deposits and 10 percent of all as the reserve requirement ratio increases. It deposits above the low-reserve tranche. There- seems reasonable to assume that people’s sav- fore, it matters whether the deposits are going ings are positively related to the real return on into small banks or large banks. In other coun- savings. Therefore, it follows that a higher tries, the reserve requirement structures are reserve requirement ratio will result in a decline even more convoluted.11 in a person’s savings. A decline in savings Equations 1 through 4 are built on the implies a decline in the quantity of bank notion that there is one reserve requirement deposits. As such, g is increasing and d is falling ratio that is the marginal reserve requirement. so that the product—the seigniorage tax base— To compute the marginal reserve requirement could either increase or decrease. ratio, one could use the distribution of deposits The thrust of this section is twofold. First, across the different categories corresponding to real seigniorage revenue is formally defined. the reserve requirement structure. For example, Second, economic theory offers an ambiguous 20 percent of the deposits are in small U.S. picture regarding the effects that monetary banks (with less than $49.3 million in checkable policy settings have on the size of this revenue. deposits) and 80 percent are in large banks. The gist of the economic argument is that The average marginal reserve requirement people try to avoid taxes, so with higher tax ratio would be (0.2•0.03) + (0.8•0.1) = 0.086. rates, whether it be inflation or income, they Unfortunately, neither the United States nor any have an incentive to reduce the quantity of the other countries report the distribution across good being taxed. The remainder of this article deposit categories, which is necessary to con- seeks to establish some preliminary observa- struct such a measure. Consequently, I use the tions on the correlation between a country’s reserve-to-deposit ratio, denoted R/D, (here- reliance on seigniorage revenue and its mone- after reserve ratio) as a proxy for the reserve tary policy settings. requirement ratio. Historically, reserve require- ments have been applied against deposits THE DATA included in what is the U.S. counterpart to M2. Accordingly, I use M2 less currency outside the I obtain the data in this article from bank as my measure of bank deposits. As it is International Financial Statistics. I use annual measured, the reserve ratio ignores any extra observations, spanning the period 1965–94. For information contained in the distribution of each of the variables I examine over this 30-year deposits across the alternative categories. period, I use the sample mean to measure each Instead, different deposit categories are treated country’s central tendency. Unfortunately, obser- as if there is only one type. vations are not available for each country for Table 1 reports summary statistics for the each year. Each country in the sample has at seigniorage ratio, S/Y ; as well as a monetary least fifteen annual observations. The result is a policy measure, g; a tax rate measure, TAX; and sample of sixty-seven countries.8 the growth rate of output, y ¢. On average, Following Fischer (1982), I compute the seigniorage revenue accounts for a fairly small ratio of seigniorage revenue to output, hereafter fraction of total output—about 2 percent.12 Tax S/Y, for each country.9 Here, I use high-powered receipts are, on average, about 22 percent of money as the measure of the money stock (M ). aggregate output. As one would probably One alternative to computing ratios is to convert expect, seigniorage revenue is not the primary each country’s seigniorage to a dollar-equivalent source of government revenue. value. The chief advantage to using ratios is that Generally, the government budget con- no assumptions are required regarding the ex- straint links the variables in Table 1 together. As change rate and purchasing power parity. such, the statistics describe the central tenden-

FEDERAL RESERVE BANK OF DALLAS 13 ECONOMIC REVIEW THIRD QUARTER 1998 Table 1 Summary Statistics

Sample Standard S/Y ratios tend to experience less variability in Variables mean deviation Minimum Maximum the year-to-year reliance on seigniorage. S/Y .0211 .0201 .0025 .0998 The correlation coefficient between a R/D .1712 .1303 .0068 .6402 country’s average reliance on seigniorage reve- g .2085 .1667 .0332 .8981 nue and its sample standard deviation is 0.8462. TAX .2254 .1008 .0537 .5586 Thus, the high correlation coefficient suggests y ¢ .0407 .0181 Ð.0018 .0904 that countries with high seigniorage rates have S/Y Real seigniorage/real GDP the greatest volatility in year-over-year realiza- R/D Bank reserves/deposits (M2 less currency) g Percentage change in high-powered money tions. In other words, countries that rely, on TAX Tax revenue/GDP average, more heavily on money creation as a y ¢ Percentage change in real GDP source of revenue also tend to exhibit the largest variability in reliance from year to year. In contrast, countries that rely relatively little on seigniorage revenue tend to receive about the cies and average dispersion of monetary policy, same fraction of GNP from year to year.13 , and some aggregate measure of Figure 1 focuses on the two monetary pol- economic activity. The money growth rate, g, is icy variables. Specifically, it plots combinations

(Mt /Mt –1) – 1. TAX is the ratio of tax revenue to of the average reserve ratio and the average GNP. Lastly, y ¢ = (Yt /Yt –1) – 1 is the growth rate money growth rate for each country in this sam- of output. ple. The plot suggests that a country with a high One rather interesting finding is how the average reserve ratio has a high average money reliance on seigniorage revenue is distributed. growth rate. Formal statistics support the notion Approximately three-fourths of the countries that the reserve ratio and money growth are collect, on average, less than 2 percent of GNP positively related; the correlation coefficient through money creation. Most of the variation, between the reserve ratio and the money therefore, occurs among those countries in the growth rate is 0.72. top quartile of the distribution. In this sample, Thus, three facts emerge from this prelim- Ghana relies most heavily on seigniorage, col- inary review of the data. These facts serve to lecting revenues equal to 10 percent of output, answer the primary question of how much on average, through money creation. Overall, countries rely on seigniorage revenue. First, for the distribution of S/Y ratios is quite skewed most countries, seigniorage revenue accounts toward the low-seigniorage-reliance tail of the for less than 2 percent of output. Second, coun- distribution. tries with the highest average reliance on Table 1 also reports the range of reserve seigniorage revenue also tend to have the ratios and average money growth rates. The dif- greater year-to-year volatility in the S/Y ratio. ference between the minimum and maximum Third, the evidence suggests that monetary values is substantial. Reserve ratios range from a policy settings are not independent of one low of 0.6 percent to 64 percent. Money growth rates range from 3.3 percent to nearly 90 per- cent. This evidence shows that banks hold a Figure 1 substantial fraction of money against deposits in Cross-Country Plots of Reserve Requirements some countries. It also shows that some coun- Versus Money Growth tries create money at a rapid pace. Percentage change in high-powered money Do countries that rely heavily on seignior- 1 age revenue also exhibit large year-to-year .9 volatility in their earnings from money creation? .8 The answer indicates whether countries tend to .7 rely on seigniorage revenue consistently or if .6

there are periods of heavy reliance on seignior- .5

age interspersed with periods in which coun- .4 tries rely less on it. A positive correlation .3 between the seigniorage ratio and volatility .2 would show that countries with large values of S/Y, for example, also tend to experience .1 0 greater year-over-year variability in the S/Y ratio. 0 .1.2.3.4.5.6.7 Conversely, if the correlation coefficient is neg- Bank reserves/ ative, then countries that have relatively high deposits (M2 less currency)

14 Table 2 Regression Results for Seigniorage Ratios and Monetary Policy Variable another; countries with high money growth rates also tend to have high reserve ratios. Dependent variable: S/Y

Benchmark Financial Financial MONETARY POLICY AND SEIGNIORAGE Variable model sophistication I sophistication II To determine whether a relationship exists constant .011* .0094* .0113* (.0032) (.0034) (.0032) between a country’s monetary policy settings z .3982† .4273† .3835† and its reliance on seigniorage revenue, I pre- (.1788) (.1722) (.1808) sent results from a simple regression. Because z 2 Ð.0915 Ð.1554 Ð.0072 of this potentially nonlinear relationship, I use (1.157) (1.1854) (1.1545) a sufficient statistic, z, to measure monetary y 65‡ .— Ð.338E-06 .— policy settings. Specifically, let z = [R/D/(1 + (.416E-06) R/D)][g/(1 + g)]. The economics motivating this OECD .— .— Ð.006§ decision is sketched out in the box entitled “A (.0033) Case for Combining the Money Growth Rate OECD¥z .— .— Ð1.144* with the Reserve Ratio.” Statistical issues also (.3909) arise, in part, because of the evidence presented OECD¥z 2 .— .— 165.817* in Figure 1. Recall from Figure 1 (and the cor- (37.035) relation coefficient) that countries with high adjusted R 2 .448 .504 .437 average reserve ratios tend to have high average Standard error .0148 .0135 .0149 money growth rates. By studying the contribu- of the estimate tion of each of the monetary policy measures, NOTE: Standard errors in parentheses. multicollinearity is a potential problem; that is, * Significant at the 1 percent level. † Significant at the 5 percent level. if two independent variables are highly corre- ‡ Per capita real GDP in 1965. lated, the standard errors of the coefficients are § Significant at the 10 percent level. inflated, creating inference problems. In meas- uring monetary policy settings with a single variable, I am assuming that z is a sufficient statistic for monetary policy. As a sufficient sta- settings and its reliance on seigniorage reve- tistic, z is useful because changes in it capture nue. If the additional quadratic term in the changes in each of the monetary policy vari- regression is significant, this relationship will ables being studied. As such, z is serving as a vary as z varies. For instance, if the coefficient measure of the overall thrust of monetary policy on z 2 is significantly less than zero, the evi- as it relates to seigniorage revenue. dence suggests that the relationship is concave. One additional property of z is note- Conversely, if the coefficient on the squared worthy. It is straightforward to show that the term is significantly greater than zero, the evi- definition of z implies a concave relationship dence indicates that the relationship is convex.15 between it and each of the two monetary policy The results from the benchmark regres- variables. To illustrate this, consider the effect of sion are reported in column 1 of Table 2.16 The a change in the reserve ratio, holding the coefficient on z is significantly greater than zero, money growth rate constant. As the reserve while the coefficient on z 2 is not significantly ratio increases, z increases also, but the change different from zero. Thus, the evidence is con- in z will be smaller as the reserve ratio sistent with the notion that countries with high increases. In other words, for a given increase monetary policy settings (high z values) tend to in the reserve ratio, z will increase at a dimin- rely more heavily on seigniorage revenue than ishing rate. The same holds if, for example, the do countries with lower monetary policy set- money growth rate increases, holding the tings (low z values). As discussed above, the reserve ratio constant. With a positive coeffi- evidence suggests a positive, concave relation- cient on z, the relationship between the ship between a country’s reserve ratio and seigniorage rate and each of the monetary pol- money growth rate and its reliance on seignior- icy variables is concave.14 age revenue. Further, the adjusted R 2—a meas- In the benchmark regression, I include the ure of the variation in seigniorage that is squared value of z and a constant term as addi- accounted for by the regression variables—indi- tional explanatory variables. In doing so, it is cates the monetary policy measure accounts for possible to assess whether there are any addi- more than 40 percent of the variation in the S/Y tional nonlinearities that characterize the rela- ratio, which is a reasonably good fit for a cross- tionship between a country’s monetary policy country sample.

FEDERAL RESERVE BANK OF DALLAS 15 ECONOMIC REVIEW THIRD QUARTER 1998 A Case for Combining the Money Growth Rate with the Reserve Ratio

In this box, I show that the S/Y ratio, in equilib- bank deposits. Lastly, Equation B.5 is the reserve rium, is a nonlinear function of the reserve require- requirement, dictating that real money balances ment and money growth rate. This application is a cannot be less than g percent of bank deposits. modified version of the economy developed in I assume that deposits offer a greater return Champ and Freeman (1994). The chief feature of than fiat money. Consequently, the typical person the model is that a person engages in market activ- will hold the minimum quantity of fiat money bal- ity for two consecutive periods. In other words, N ances. Equations B.4 and B.5, therefore, imply that people enter market activity at each date t, stay for at = (1 + g)dt . Substitute for a in Equations B.2 and two periods, and then exit. It is equivalent to inter- B.3, and solve Equation B.3 for (1 + g)dt , substitut- pret this setup as one in which people are alive for ing the result into Equation B.2. After the algebra, two periods. In this context for a particular date t, the expression is those entering the market for the first time are “the young,” and those entering the second period of (B.6) y ³ c1t + c2t +1/qt +1, market activity are “the old.” Each person receives labor income when young, but nothing when old. which is the person’s lifetime budget. Time is discrete and is indexed by t = 1, 2, 3, and To maximize lifetime utility, the typical person so on. I assume there are N people at date t = 1 who will choose first- and second-period consumption have only one period in the economy; members of so that this generation are the “initial old.” Preferences are 1 bq identical for all people born at date t and after. (.)B7 = . c c For simplicity, I focus exclusively on a station- 121tt+ ary version of the following economy. All people Equation B.7 is an efficiency condition. It says that born at date t = 1 and later have identical prefer- labor income will be allocated between first- and ences. Thus, without loss of generality, one can second-period consumption so that the benefits focus on the problem of the representative person, received from the last good consumed when young which is characterized by the following equations: (measured by 1/c1t ) are equal to the benefits received from the last good consumed when old (B.1) maxc1,c2 ln(c1t) + bln(c2t +1) (measured by bq/c2t +1). In this economy, the opti- mizing conditions imply that the typical person will (B.2) y ³ c1t + at spend all of the labor income. Hence, Equation B.6 holds with equality. (B.3) c2t +1 £ qt +1at In a stationary equilibrium, c1t = c1t +1 and c 2t +1 = c 2t +2 at any date t, so that one can drop (B.4) at = vt mt + dt the time subscripts. For a stationary equilibrium, Equations B.6 and B.7 imply that c1 = y/(1 + b). (B.5) vt mt ³gdt, With 0 < b < 1, the typical person will spend a fixed fraction of labor income on consumption when where c1t is the young person’s consumption at young. date t; c 2t+1 is old-age consumption by the person One might ask why the equilibrium expression born at date t; b is the person’s discount factor; y is for c1 does not contain q. The answer is that a the person’s labor income; a is the total quantity of change in the gross return on assets has two goods saved by the young person; q is the gross opposing effects on consumption when young: sub- return on savings carried from date t to date t + 1; stitution and wealth. With the substitution effect, an and d is the quantity of goods stored as bank increase in q, for example, makes consumption deposits by the young person. A person can also when young more expensive relative to consump- choose fiat money, which is m. Here, v stands for tion when old. (Note that in the lifetime budget con- the value of fiat money—that is, the quantity of the straint [Equation B.6], 1/q can be interpreted as the consumption good that can be purchased with one price of consumption when old.) Thus, an increase unit of money. The consumption good is perishable. in the gross return to assets would induce people Equation B.1 is a function that describes the to consume less when young and more when old. welfare a representative person receives during a With the wealth effect, when c 2 becomes less market-active period. The person seeks to maximize expensive, consuming more of both c1 and c 2 is welfare by consuming as much of the consumption possible. As such, an increase in q, for instance, good as possible. Equation B.2 represents the two will induce people to consume more when young. options—to save or to consume—that the typical Clearly, the substitution and wealth effects have young person faces when young, while Equation opposing impacts on consumption when young. B.3 indicates that the typical old person can con- With log utility, these effects exactly offset each sume up to the value of principal and interest other. Consequently, in a stationary equilibrium the earned on savings. Equation B.4 shows that savings value of c1 is independent of movements in the are in the form of either real money balances or gross return on assets.

16 A Case for Combining the Money Growth Rate with the Reserve Ratio (continued )

With c1 = y/(1 + b), the level of bank deposits level of deposits is not affected even though q will can be represented as decline. Thus, the model economy predicts that the equilibrium seigniorage ratio will rise in response to g æ b ö (.)B8 d = ç ÷ . an increase in the reserve requirement. 11++g b è ø Next, consider a permanent, unanticipated Next, substituting Equation B.8 into Equation B.5 increase in the money growth rate. With faster yields the expression for the equilibrium value of money growth, Equation B.10 indicates that an real money balances; formally, economy’s reliance on real seigniorage revenue b g will increase. With an increase in g, the tax rate on (.)B9 vm= ¥ y . tt 11+ b + g real seigniorage revenue will rise and the gross return on assets will decline. Because of the utility Here one can see the importance of the equilib- function, the equilibrium quantity of real money bal- rium expression for consumption when young. ances is not affected by the decline in the gross Because of the substitution and wealth effects, real return on assets. Thus, faster money growth neither the quantity of deposits nor the quantity translates into an increase in the seigniorage ratio. of real money balances is affected by changes in For this model economy, the s/y ratio the gross return on assets. The implication is that increases with respect to an increase in either the the tax base for real seigniorage revenue is not reserve requirement ratio or money growth rate, affected by changes in real return on assets. but at a declining rate. For different utility specifica- Expressing the equilibrium value of real tions, substitution and wealth effects would not seigniorage revenue is now possible. Substituting necessarily cancel each other out. Hence, the typi- Equation B.9 into the expression for real seignior- cal person could respond to an increase in q by age revenue yields vt mt (1 Ð 1/q). With g = q Ð 1, increasing consumption when young, thereby sav- I divide the expression by y so that the equilib- ing less. Accordingly, a young person could reduce rium reliance on seigniorage revenue per young holdings of real money balances by enough to see person is a decline in the s/y ratio for a given increase in s b g g either the reserve requirement or the money growth (.B10 )= ¥ ¥ . y 111+ b + g + g rate. The purpose of this box is to illustrate the basic economic trade-offs. Hence, arguing the Equation B.10 indicates that the equilibrium s/y appropriate utility specification is outside the scope ratio is a nonlinear function of the reserve ratio and of this article. the money growth rate.1 Indeed, it is straightforward Overall, Equation B.10 suggests a particular to show that the equilibrium value of s/y is a con- sufficient statistic for assessing the relationship cave function of both the reserve requirement ratio between monetary policy and a country’s reliance and the money growth rate (see note 12). on seigniorage revenue. Throughout the statistical To see how a change in monetary policy analysis, I use the product z = [g/(1 + g)][g/(1 + g)] affects the equilibrium seigniorage ratio, consider a as the measure of monetary policy. permanent, unanticipated increase in the reserve requirement ratio. In this model economy, Equation Note B.5 indicates that the holdings of real money bal- 1 Here, the s/y ratio pertains to the ratio of per capita ances will increase. Remember that the equilibrium levels, which accounts for the use of lowercase letters.

Important differences across countries ance depends, in part, on a country’s financial could alter the relationship between monetary sophistication. Citizens in countries with more policy and the reliance on seigniorage revenue. sophisticated financial structure, for instance, For example, with only z as an explanatory can avoid taxation by shifting to nonreservable variable, the regression’s constant term captures deposits. They can also dodge the tax by shift- any differences between countries. Insofar as ing from currency to, say, credit cards as the differences across countries can be measured, means of payment. It would seem prudent, additional insight may be gained into the rela- therefore, to measure a country’s financial tionship between monetary policy and reliance sophistication to assess whether this omitted on seigniorage. Such measurements indicate variable affects the relationship between a whether the results obtained in this analysis are country’s monetary policy settings and its robust. reliance on seigniorage. A particular concern is the ability of The measure of financial sophistication people to avoid the inflation tax. Such avoid- should not depend on the monetary policy set-

FEDERAL RESERVE BANK OF DALLAS 17 ECONOMIC REVIEW THIRD QUARTER 1998 Figure 2 I report regression results in columns 2 Seigniorage–Income Ratio and and 3 of Table 2. Here, I use two proxies to Monetary Policy Settings measure financial sophistication; one is the Seigniorage ratio, S/Y OECD membership, and the other is per capita 1 real income in 1965. Two different sets of .9 results emerge. Specifically, with per capita real

.8 income as the measure of financial sophis-

.7 tication, the evidence suggests a linear relation-

.6 ship between seigniorage reliance and z. As such, the evidence suggests, as it did when .5 no financial sophistication measures were in- .4 cluded, that countries that rely the most heavily .3 on seigniorage revenue have higher monetary .2 policy settings. .1 Consider, however, the results for a case in 0 which OECD membership is used as a proxy for 0 .02 .04 .06 .08 .1 .12 .14 .16 .18 .2 financial sophistication. These regression results Monetary policy settings, z correspond to the evidence presented in Figure Non-OECD Fitted line (non-OECD) 2. The formal statistical analysis supports the OECD Fitted line (OECD) eyeball difference presented in the figure; that is, the z–S/Y relationship is significantly differ- ent for OECD countries than for non-OECD tings to get an accurate estimate of the coeffi- countries. The coefficient on OECD • z is nega- cient between monetary policy and seigniorage tive and significant, and the coefficient on reliance. In other words, movements in the OECD • z 2 is positive and significant. Thus, the measure should not reflect behaviors related to evidence suggests that the relationship between monetary policy settings, and yet the variable seigniorage rates and monetary policy settings is should be reasonably well correlated with a convex. Indeed, the evidence indicates that an country’s level of financial sophistication. In OECD country reaches a minimum reliance on reality, finding such a measure is quite difficult. seigniorage revenue at a value of z = 0.0023. Two variables are offered as proxies for finan- To illustrate this result, suppose one is cial sophistication: the level of real per capita looking at two OECD countries—country A and GDP in 1965 and a dummy variable indicating country B. Each has a different monetary policy whether the country is a member of the setting, with country A always associated with Organization for Economic Cooperation and the lower value of z. According to the regres- Development (OECD).17 Certainly OECD mem- sion statistics, if z < 0.0023 for both countries, bership and monetary policy settings are con- then country B would rely less on seigniorage ceivably linked as part of a country’s policy revenue than would country A. In contrast, for package. The more modest claim is that OECD z > 0.0023, the regression predicts that country membership and per capita real GDP are less B would rely more on seigniorage revenue than likely to respond to movements in the monetary would country A.18 policy settings than are financial-sophistication The convex relationship exhibited by measures such as bank deposits. OECD countries is puzzling. In the model econ- Figure 2 plots the combination of z and omy described in the box, financial sophistica- S/Y as well as separate fitted lines for non-OECD tion would seem to permit a country’s citizens and OECD countries. Each line is fitted to a to avoid the inflation tax. Given an increase in 2 regression of the form (S/Y )I = c0 + azi + bzi . z, the equilibrium outcome for the S/Y ratio These two fitted lines appear quite different. would either decline or increase, but at a Based on this preliminary look at the data, the decreasing rate as people avoid the inflation evidence suggests that the relationship between tax. In other words, it is reasonable to expect a country’s monetary policy statistic and its that increased tax-avoidance capabilities would reliance on seigniorage revenue is different for result in a more concave relationship between developed countries than it is for less developed a country’s monetary policy settings and its countries. Indeed, the fitted line for the non- reliance on seigniorage revenue, not a more OECD countries is upward sloping, whereas the convex one. one for the OECD countries appears to have Overall, the evidence suggests that there is some curvature. a systematic, positive relationship between a

18 country’s monetary policy settings and its re- were to stand up to further scrutiny, economic liance on seigniorage revenue. Thus, countries theory would need to address the puzzle. One with higher monetary policy settings tend to possible line of research would be to consider a rely more heavily on seigniorage. But compared simple open economy in which two countries with less financially sophisticated countries, the differ in terms of financial sophistication and more financially sophisticated countries tend to monetary policy rules. rely on seigniorage revenue at an increasing Another avenue for future research would rate. The findings with respect to financial be to recognize that monetary policy variables sophistication are difficult to explain and de- and seigniorage revenue are jointly determined. serve more attention. While I have tried to describe the correlations without referring to any monetary policy as CONCLUDING REMARKS “causing” movements in seigniorage revenue, the estimated regressions could be interpreted I present evidence in this article on the as treating monetary policy as exogenous to the importance of seigniorage revenue and its rela- determination of such revenue. Edwards and tionship to monetary policy. I use cross-country Tabellini (1991) examine seigniorage revenue as observations to examine whether the average the outcome of various political forces that money growth rate and average reserve ratio influence, among other things, monetary policy are systematically related to a country’s reliance settings. Thus, future research could attempt on seigniorage revenue. Both economic and sta- to disentangle the relative importance of politi- tistical considerations suggest that some combi- cal factors, controlling for monetary policy nation of the money growth rate and the reserve explicitly. ratio should be used in the empirical analysis. Consequently, a country’s monetary policy set- NOTES ting is measured using a combination variable as opposed to investigating two separate rela- 1 See Cox (1992) for an excellent discussion of the tionships—one between seigniorage reliance practical relationship between the Federal Reserve and the reserve ratio and the other between and the U.S. Treasury. For an interesting description of seigniorage reliance and the money growth rate. seigniorage in medieval times, see Rolnick, Velde, and The main finding in this article is that there Weber (1994). is a systematic, positive relationship between a 2 For reference, the United States raises, on average, country’s monetary policy settings and its re- about 2 percent of federal government expenditures liance on seigniorage revenue. Thus, countries through money creation. that rely most heavily on seigniorage revenue 3 After all the accounting is consolidated for the govern- tend to have the highest values of the monetary ment and the , the net change in the gov- policy measure. There is some additional evi- ernment’s income state is that money creation amounts dence that the relationship between the mone- to a revenue source to cover various expenses. tary policy variable and the seigniorage rate is 4 Bryant and Wallace (1984) offer an explanation for the nonlinear for OECD countries. Here, OECD coexistence of government bonds and money. They membership is used as a proxy for financial argue that the two types of government paper effec- sophistication. The evidence suggests that OECD tively price discriminate between “rich” and “poor” countries rely on seigniorage revenue at an households. increasing rate for given changes in the mone- As far as my assumption about one-period bonds tary policy variable. is concerned, I could examine a more complicated The findings in this article constitute a maturity structure for government debt. Such general- very preliminary investigation of the relation- ity would not alter the conclusions that I reach about ship between seigniorage revenue and mone- seigniorage revenue, but it would mean that I would tary policy. There is always a risk of excluding have to keep tabs on the entire distribution of govern- a key variable in a regression, and that risk ment bonds and when each one matures. certainly holds here. One approach would be 5 The reduction in reported income can come either to control for a host of other environmental from effective avoidance or from people working less factors—for example, a more complete analysis or acquiring less capital. Of course, the discussion of the depth and structure of financial markets. describes what happens to the steady-state level of The most surprising and, in some ways, income. the most interesting results are those differenti- 6 There is no explicit interest on money. Consequently, ating between financially developed and less its one-period rate of return is calculated as the ratio financially developed countries. If these results of the date t price (the potential selling price) to the

FEDERAL RESERVE BANK OF DALLAS 19 ECONOMIC REVIEW THIRD QUARTER 1998 date t – 1 price (the purchase price). Formally, this is native measures of financial sophistication in case the

the ratio of vt /vt –1. With vt = 1/pt, then simple substitu- 1965 GDP value suffers from some time-specific fac- tion yields the expression for the gross real return on tors. The regressions are qualitatively the same as money. those reported in Table 2. 7 Here, the reserve requirement pins down the fraction 18 Three OECD countries in this sample — France, the of a person’s portfolio held in the form of money bal- Netherlands, and Norway—have z values less than ances. This approach is qualitatively the same as one 0.0023. Using the method outlined in Fomby, Hill, and in which the reserve requirement pins down the bank’s Johnson (1984, 58), one can compute the standard portfolio. errors for the value of z at which seigniorage reliance 8 The data set is available from the author upon request. is minimized. With 90 percent confidence, the seignior- 9 Fischer is primarily interested in describing why coun- age-reliance minimizing value of z is between 0.0022 tries maintain national . Computing the and 0.0024. seigniorage-to-GNP ratio demonstrates how important seigniorage is. The ratio represents the command over REFERENCES resources that a government obtains by creating money. 10 The income tax analog is the average marginal tax Bryant, John, and Neil Wallace (1984), “A Price Discrimi- rate. See, for example, Seater (1985). nation Analysis of Monetary Policy,” Review of Economic 11 Historically, the U.S. reserve requirement structure was Studies 51 (April): 279 –88. more convoluted. In the past, for example, it mattered whether the commercial bank was located in a Champ, Bruce, and Scott Freeman (1994), Modelling Reserve Bank city or outside. Monetary Economies (New York: John Wiley and Sons 12 Interestingly, Fischer (1982) presents evidence that Inc.). several governments have made substantial use of seigniorage. In Fischer’s sample, which generally Cox, W. Michael (1992), “Two Types of Paper: The Case covers the period between 1960 and 1978, Argentina for Federal Reserve Independence,” Federal Reserve collected, on average, 6.2 percent of GNP through Bank of Dallas Southwest Economy, Issue 6, November/ money creation. December, 3–8. 13 This result does not bear directly on the relative impor- tance of seigniorage revenue. Rather, it bears on the Edwards, Sebastian, and Guido Tabellini (1991), issue of variability within a country across time. In “Explaining Fiscal Policies and Inflation in Developing short, the reader gains a sense of how the countries in Countries,” Journal of International Money and Finance the sample rely on seigniorage over time. 10 (March): S16 –S48. 14 The effect of a change in the reserve ratio, holding money growth constant, is given by the following de- Fischer, Stanley (1982), “Seigniorage and the Case for a rivative: ¶z/¶(R/D) = W/(1 + R/D)2, where W = g/(1 + g). National Money,” Journal of Political Economy 90 (April): With W > 0, the expression says z is increasing the 295 – 313. reserve ratio. In addition, ¶ 2z/¶(R/D)2 =(–2•W)/(1 + R/D)3, which is negative for W > 0. Fomby, Thomas B., R. Carter Hill, and Stanley R. Johnson 15 To see this relationship, suppose the estimated regres- (1984), Advanced Econometric Methods (New York: sion is given by Springer–Verlag Inc).

S/Y = c + az + bz 2. 0 Rolnick, Arthur J., François R. Velde, and Warren E. For a country with a 1-percentage-point higher aver- Weber (1994), “The Debasement Puzzle: An Essay on age z, an estimate of the change in S/Y is a + 2bz. Medieval Monetary Policy,” Federal Reserve Bank of Thus, a 1-percentage-point change in z depends on Minneapolis Working Paper no. 536 (October). the value of z. 16 In all regressions, the Newey–West procedure is Sargent, Thomas J. (1986), and applied to correct any potential bias in standard Inflation (New York: Harper & Row). errors. In this particular application, heteroskedasticity is the chief worry. Seater, John J. (1985), “On the Construction of Marginal 17 Per capita real GDP comes from the Summers–Heston Federal Personal and Social Security Tax Rates in the Penn World Tables. In addition, regressions are run U.S.,” Journal of Monetary Economics 15 (January): using per capita real GDP for 1980 and 1994 as alter- 121–35.

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