Monetary policy, banking, and growth.

Haslag, Joseph H.

I. INTRODUCTION

Fischer and Modigliani [1978] exhaustively list the costs associated with inflation. In recent years, a growing body of evidence is consistent with the notion that slower output growth may be added to the Fischer-Modigliani list. Specifically, analyses by Kormendi and Meguire [1985], Fisher [1991], DeGregario [1992], Gomme [1993], Wynne [1993], Barro [1996], and others, find a negative correlation between the inflation rate and output growth both across countries and over time.(1) Moreover, the studies consistently find that the growth rate response to a change in the inflation rate is quite large. The different studies produce a range of correlation coefficients: a country in which the inflation rate is 10% will grow between 1/4- and 3/4-percentage points slower than a country in which the inflation rate is 0%.

The purpose of this paper is to determine whether a reasonably calibrated model economy can account for the size of the regression coefficients. The model economy is a modified version of a member of the Ak class in which bank deposits are used to finance capital accumulation. In this model economy, fiat money is valued because the bank is required to hold reserves against its deposits. (Throughout this paper, bank deposits is used in a narrow sense to include only those deposits against which a reserve requirement applies.) Because monetary policy has two tools at its disposal, it is possible to conduct two separate policy experiments. The results from these experiments, particularly the inflation rate experiment, sheds light on the potential importance on the share of investment financed through bank deposits.

Researchers have long been interested in the interaction between financing and growth. Schumpeter [1911] argued that the financial sector, more specifically its stage of development, affected a country's growth rate.(2) Cameron [1967] described financial development in Scotland, England, and France in the late 18th and early 19th centuries. Cameron concluded that Scotland and England entered the Industrial Revolution ahead of France because it had the financial infrastructure capable of financing capital accumulation on the needed scale. King and Levine [1993] find that countries with more developed financial sectors tend to grow faster than countries with less developed financial sectors. It seems natural, therefore, to investigate whether the means of financing can yield any insights into the inflation-growth relationship.

Other researchers have also quantified the effect that movements in the inflation rate has on the growth rate. In particular, Jones and Manuelli [1995] use several variants of economies in which people hold fiat money to satisfy a cash-in-advance constraint. They demonstrate that large growth rate effects cannot be accounted for in these model economies. In these models, inflation does not materially alter capital accumulation rates, affecting instead the allocation between the credit good and cash good purchases. Jones and Manuelli find small growth rate effects in an economy in which the tax code has nominally denominated depreciation rates. In two papers that focus on inflation and growth, Chari, Jones and Manuelli [1995, 1996] consider economies in which capital accumulation can be financed through either bank deposits or directly. As in the economy specified in this paper, reserve requirements are applied against bank deposits. Agents can avoid the inflation tax by using the direct financing means more intensively. Consequently, the growth rate effects are muted in the Chari-Jones-Manuelli model economies and are too small to account for the size of the regression coefficients reported in Kormendi and Mcguire, Fischer, and Barro.

In this paper, I assume that all investment is financed through bank deposits. With this extreme assumption, the model economy can account for the size of the growth rate effects observed in the data.(3) Thus, there is a potentially useful lesson learned from the quantitative results in the all-bank-financing economy and those reported in Chari-Jones-Manuelli. Taken together, the results imply that the fraction of investment financed through bank deposits plays an important role in the size of the growth rate effects. In other words, the results suggest that the large growth rate effects found by Kormendi and Mcguire and the others could be arise because countries with high average inflation rates also finance a large fraction of investment through banks. Thus, the chief contribution is to suggest that large growth rate effects stem from monetary policy and an unsophisticated intermediary.

The organization of this paper is as follows. In section II, I examine the cross-country evidence, asking whether the data suggest that countries with high reserve requirements or high inflation rates grow more slowly than those with low reserve requirements. The evidence suggests that reserve requirements and inflation each are quantitatively important. I specify the general equilibrium model in section III. The model is capable of qualitatively accounting for the stylized facts obtained in section II. In section IV, I calibrate the model and run some simple computational experiments to calculate the impact that movements in the anticipated inflation rate and reserve requirement ratios would have in the model. I briefly discuss the paper's results in section V.

II. SOME SUGGESTIVE EMPIRICAL EVIDENCE

In this section, I examine the relationship between per-capita output growth and both the inflation rate and reserve requirement ratio. Following the earlier empirical papers, time-averaged measures are used. The evidence, therefore bears on questions of the following type: Do countries with high average inflation rates (reserve ratio) tend to grower faster or slower than countries with low average inflation rates (reserve ratio)?

There is a problem with measuring reserve requirements. Ideally, an average marginal reserve ratio would be constructed. However, countries frequently change the definition of deposits against which reserve requirement apply. Moreover, countries do not report the distribution of banks by size. The distribution is critical to constructing the average marginal reserve ratio.(4)

The solution used here is to calculate the average reserve requirement ratio. Using data available from International Financial Statistics (IFS), I calculate the ratio of bank reserves to the sum of checkable, or sight, deposits plus saving accounts. (These deposit categories are predominantly the ones against which reserve requirements apply.) The implicit assumption is that excess reserves ratio is insignificant because it is small and nearly constant, so that the reserve ratio is treated as being a binding constraint.(5) For each country, policies are checked to ensure that reserve requirements are a policy tool.

To be included, a country must have annual observations for per-capita output, consumer prices, bank reserves, and deposits, for the period 1965-1990. As noted above, each country must also have reserve requirements and those must apply for at least thirteen years (half the sample observations) during the period 1965-1990. From the IFS, I find 60 countries that satisfy all these criteria. For this set, I calculate the mean values of per-capita output growth, the inflation rate, and the reserve ratio for each country. (A list of the countries and the mean values for each data series is in a Data Appendix that is available from the author upon request.)

A first pass through the data looks at summary statistics for the cross-country data. As Table I shows, countries are identified as "high" and "low" reserve requirement countries. High means that the average reserve requirement ratio is more than one standard deviation above the full-sample mean. For the 12 countries identified as having "high" reserve requirements, the mean reserve requirement ratio is 30%. The mean growth rate of per-capita output for these 12 countries is 1.5%. Similarly, for the 10 countries identified as having "low" reserve requirements, the mean reserve requirement is 3.4% and mean output growth is 2.9%. Thus, a crude identification scheme suggests that countries with high reserve requirements do grow slower than countries with low reserve requirements.

I also examine differences between high and low inflation countries. One difference is that I define "high" and "low" as being only 1/2 standard deviation away from the full-sample average.(6) There are 12 countries with average inflation rate less than 1/2 standard deviation below the mean inflation rate. For these "low" inflation countries, the mean rate of output growth is 4.6%. Nine countries were identified as "high" inflation countries, and their mean growth rate is 1.2%. This evidence supports the notion that high inflation countries tend to grow more slowly than low inflation countries.

Table II reports the simple correlations for the output growth, inflation rate, and reserve requirements, using the full sample. The data show a negative correlation between reserve requirement and growth and between inflation and growth. Interestingly, there is a positive correlation between the inflation rate and reserve requirement.(7) Thus, the simple correlations support the evidence presented in Table I; high-inflation and high-reserve requirement countries tend to grow slower than low-inflation and low-reserve requirement countries. In addition, high-reserve requirement countries tend to have higher inflation.

Lastly, I report the results of three per-capita output growth regressions in Table III. Per capita output growth is always the dependent variable. In one, the reserve ratio is the single independent variable; in another, the inflation rate is the lone independent variable; and in the third, both reserve requirements and inflation are explanatory variables. The key result from these regressions is that there is a significant negative correlation between the monetary policy variables and per-capita output growth in the bivariate regressions.(8) While this evidence qualitatively repeats the evidence presented in the simple correlations, the regression estimates provide a quantitative measure of the size of the co-movements. To my knowledge, no one has run the regression with the reserve ratio as a right-hand-side variable. Note that the estimated coefficient on the inflation rate is between -0.02 and -0.04, which is intersects with the range of coefficient estimates found in earlier studies.

TABLE I

Summary Statistics Across Countries

 Mean Std. Dev.

Full-sample:

rr 15.3% 10.8%
infl 11.9% 12.1%
py 2.2% 1.9%

High reserve requirement countries:

rr 30.0%
py 1.5%

Low reserve requirement countries:

rr 3.4%
py 2.9%

High inflation countries:

infl 30.0%
py 1.5%

Low inflation countries:

infl 3.4%
py 2.9%

As Table III shows, the coefficient on both the inflation rate and reserve requirement ratio are negative, but neither is statistically significant. The size of the coefficients is roughly the same in the trivariate regressions as in the bivariate regressions.(9) Note that the standard errors for the coefficients have increased for both variables. One possible explanation for the disappearance of statistical significance is that multicollinearity is present. Indeed, the correlations presented in Table II indicate that reserve requirements and inflation are positively correlated with a correlation coefficient of 0.5, and could therefore, account for significant correlations the bivariate regressions that disappear in the trivariate regressions.

Overall, the evidence suggests that countries with high reserve requirements or high inflation rates systematically grow more slowly than countries with low reserve requirements or low inflation rates. As an aside, countries with low reserve ratios also tend to have low inflation rates.

III. THE MODEL

The economic environment consists of three types of decision makers: firms, households, and banks. In each period, firms maximize profits in a perfectly competitive markets for both inputs and outputs. Firms produce a single consumption good, [Y.sub.t], where t = 0, 1, 2, ... indexes periods. Production is accomplished using a common-knowledge technology, represented by

(1) [Y.sub.t] = A[K.sub.t] A [greater than] 0

where K denotes capital. Equation (1) specifies a constant-returns technology in which the quantity K is interpreted as a composite of both physical and human capital.(10) The firm pays the rental price, q, for the composite input and sells the output at the price, p. Note that p is measured in units of fiat money while q is the real rental price of capital. For this representative firm, let A = q. King and Rebelo [1990] and Rebelo [1991] explore the properties of this linear production technology. The authors show that the linear production function captures most of the long-run policy implications of more general convex models of endogenous growth in which the accumulation of multiple capital goods is considered explicitly.

TABLE II

Simple Correlation Coefficients

 Reserve Requirement Inflation Rate

Output growth -0.27 -0.23
Inflation rate 0.53 -

Over time, capital depreciates at the rate [Delta] and is expanded by investment X. I assume that the consumption good is costlessly transformed into the capital good at a one-for-one rate. Thus, the law of motion for capital is expressed as

(2) [K.sub.t+1] = (1 - [Delta])[K.sub.t] + [X.sub.t].

All capital must be intermediated.(11) For simplicity, assume there is a single bank operating in a free-entry environment. Hence, the bank behaves as if operates in a perfectly competitive environment. Deposits are costlessly transformed into the capital good. The bank accepts deposits and chooses its assets. The legal requirement puts a lower bound on the fraction of nominal deposits that the bank holds in the form of fiat money. For cases in which fiat money is rate of return dominated, the reserve requirement is a binding constraint. Formally, the period-t profit maximization condition is:

(3) [Mathematical Expression Omitted]

where p[r.sup.b] is bank profits, m is the amount of reserve balances carried by the banks, [D.sub.t] denotes the quantity of goods deposited last period and carried over to period t, and R is then interpreted as the gross real return offered on deposits. The initial stock of reserves, [M.sub.0], is given. The bank's period-t profit is maximized subject to [K.sub.t] + [M.sub.t]/[p.sub.t] [less than or equal to] [D.sub.t] (the balance-sheet equation) and [M.sub.t-1] [greater than or equal to] [[Gamma].sub.t-1][p.sub.t-1][D.sub.t] (the reserve requirement), where [Gamma] denotes the reserve requirement ratio. The bank's zero-profit condition implies that the real return offered on deposits, [R.sub.t], equals (1 - [[Gamma].sub.t-1]) [A + 1 - [Delta]] + [[Gamma].sub.t-1] [p.sub.t-1]/[p.sub.t]. In addition, I assume that [p.sub.t-1]/[p.sub.t] [less than] A + 1 - [Delta] so that reserves are rate of return dominated. Rate-of-return dominance ensures that banks hold reserves up to the amount required; that is, [M.sub.t-1] = [[Gamma].sub.t-1] [p.sub.t-1] [D.sub.t].

[TABULAR DATA FOR TABLE III OMITTED]

Households in this model economy are atomistic, infinitely lived with momentary preferences described by a CES utility function

(4) [Mathematical Expression Omitted]

where c is the quantity of the consumption good, 0 [less than] [Beta] [less than] 1 is the time rate of preference, and [Sigma] [greater than] 0 where 1/[Sigma] is the elasticity of intertemporal substitution. Population is assumed constant such that there is no aggregation bias in treating movements in per-capita quantities as equal to movements in aggregate quantities.

In each period t, the government makes a lump-sum transfer equal to [G.sub.t] units worth of the consumption good. I assume that seignorage revenue is the only means of financing the transfer. The government budget constraint, therefore, is

(5) [G.sub.t] = ([M.sub.t] - [M.sub.t-1]) / [p.sub.t].

This transfer, combined with income and the gross return on goods deposited at banks, is used by households to purchase the consumption good and deposits that will be carried over into the next period. Formally, the household's date-t budget constraint is

(6) [R.sub.t][D.sub.t] + [G.sub.t] = [c.sub.t] + [D.sub.t+1]

where [D.sub.t] denotes the deposits (measured in units of the consumption good) carried forward to date t from date t-1.

In addition, the representative household faces a terminal constraint. Consistent with this terminal constraint is the notion that the household can sell claims against future deposits, but never at a value greater than can be repaid. The terminal constraint is

(7) [Mathematical Expression Omitted]

which guarantees that the period budget constraints (6) can be combined into an infinite horizon, present value budget constraint. Since the marginal utility of consumption goes to infinity as consumption goes to zero, an interior solution for [c.sub.t] and [D.sub.t+1] is guaranteed. Consumers take the initial positive quantity deposits, [D.sub.0], and the sequences [Mathematical Expression Omitted] (where [Gamma] denotes the reserve requirement ratio), [Mathematical Expression Omitted], [Mathematical Expression Omitted], and [Mathematical Expression Omitted], as given when maximizing (4) subject to (6) and (7).

The government commits to a sequence of [Mathematical Expression Omitted], [Mathematical Expression Omitted], such that the sequence of interest rates is determined for given values of A and [Delta]. The government takes the initial stock of deposits, [D.sub.0], and the sequence of deposits, [Mathematical Expression Omitted], as given, and can infer the sequence of the price level, [Mathematical Expression Omitted], that is consistent with the path for the money stock. The date-t price level is determined by the money market equilibrium condition:

(8) [M.sub.t-1] = [[Gamma].sub.t-1] [D.sub.t][p.sub.t-1].

The implication is that the sequence of transfer payments is determined by the sequence of fiat money, the sequence of reserve requirement ratios, and, implicitly, the sequence of prices. Money carried over from date t-1 purchases 1 / [p.sub.t] units of the date t consumption good. Hence, the gross rate of return on fiat money is [p.sub.t-1]/[p.sub.t]. Throughout this paper, I assume that A + (1 - [Delta]) [greater than] [p.sub.t-1] / [p.sub.t].

The demand for money represented in equation (8) characterizes one part of the bank's asset allocation decision. Because money is rate-of-return dominated, the bank will invest all deposits above the required amount in capital; that is, [K.sub.t] = (1 - [[Gamma].sub.t])[D.sub.t]. The return to the bank's portfolio (and hence, to depositors) is represented as:

(9) [R.sub.t] = (1 - [[Gamma].sub.t-1])[A + (1 - [Delta])] + [[Gamma].sub.t-1] [p.sub.t-1] / [p.sub.t].

where A + (1 - [Delta]) is the gross return on capital after replacement, and [p.sub.t-1]/[p.sub.t] is the gross return on fiat money balances. The return on deposits is simply a weighted average of the returns to the two assets held by banks, with the weight being a function of the reserve requirement ratio. With [p.sub.t-1]/[p.sub.t] [less than] A + (1 - [Delta]) (rate of return dominance), equation (9) implies that the return offered by banks is inversely related to changes in the reserve requirement ratio.

The representative person's first-order condition implies that output, deposits, and consumption grow at the rate [[Rho].sub.t] between dates t - 1 and t. Along the balanced growth path, the rate is expressed as

(10) [[Rho].sub.t] = [([Beta][R.sub.t]).sup.1/[Sigma]] = [([Beta][(1 - [[Gamma].sub.t-1])(A + 1 - [Delta]) + [[Gamma].sub.t-1][p.sub.t-1] / [p.sub.t]]).sup.1/[Sigma]].

Equation (10) implies that the economy's growth rate is inversely related to the reserve requirement ratio. Romer [1985] and Freeman [1987] show how reserve requirements could crowd out capital. Their results, however, apply to the effect that changes in reserve requirements have on the level of output. One immediately sees that in the limit, with [Gamma] = 0, monetary policy is divorced from output growth. As in Jones and Manuelli [1995], if one considers a case in which reserve requirements are absent, then the rate of return on capital is independent of changes in money growth.(12) In this paper, the reserve requirement ratio affects capital accumulation through the gross return offered by the agent's portfolio. The intuition behind this effect is straightforward. According to the Keynes-Ramsey rule, a decline in the return to the agent's portfolio relative to the time rate of preference increases current consumption, depressing capital accumulation and reducing growth.(13)

Equation (10) also implies that the economy's growth rate is inversely related to the gross rate of money growth, denoted [Theta], and, hence, to inflation. Suppose the supply of money follows the rule: [M.sub.t] = [Theta][M.sub.t-1]. As noted above, the rate-of-return dominance condition requires that [Theta] [greater than] 1 and [Gamma] [greater than] 0 so that the reserve requirement is a binding constraint. Using equation (8), and recognizing that [D.sub.t+1] / [D.sub.t] = [Rho], then for a given gross rate of growth, [Theta] = [Rho][Pi]. In equation (9), a constant gross rate of money creation implies that [p.sub.t-1]/[p.sub.t] = 1 / [Pi]. As money growth rises, the inflation rate rises and the rate of output growth falls. The intuition is the same for an increase in the reserve requirement ratio; higher inflation drives down the return offered on deposits, making date-t consumption more attractive. With a positive reserve requirement ratio, higher inflation makes money balances less attractive. Instead of influencing the tradeoff between cash goods and credit goods, as occurs in the models with a cash-in-advance constraint, higher inflation results in a lower return on intermediated capital, translating into slower output growth. Thus, the mechanism highlights the role that monetary policy actions have on intertemporal substitution.

For a constant reserve requirement ratio and constant money growth, output, consumption, and deposits all grow at the same rate across time; that is, [Rho] = [{[Beta][(1-[Gamma]) [A + (1 - [Delta])] + [Gamma] / [Pi]]}.sup.1/[Sigma]]. As King and Rebelo note, the representative person in this model economy has finite utility if and only if [Beta][[Rho].sup.1-[Sigma]] [less than] 1. This condition holds in all the experiments conducted in this paper.

IV. MONETARY POLICY AND GROWTH

In this section, I conduct the monetary policy experiments, focusing on the growth rate effects and welfare effects.

Calibration

Obviously, to proceed one must select a set of parameter values. For this analysis, the model's period is assumed to correspond to one year. Following Jones and Manuelli, I set [Sigma] = 2 and [Delta] = 0.1. My benchmark case calibrates both monetary policy variables to their full-sample means. Hence, [Pi] = 1.119 and [Gamma] = 0.153.(14) As noted above, selecting the inflation rate determines [Rho], and with these two values pins down the model's rate of money growth by [Theta] = [Pi][Rho]. With [Gamma] = 0.153 and A = 0.165, the gross after-reserve-requirement return on deposits is 1.039, so that [Beta] = 0.9819 = (1.02/1.039). With these parameter settings, the gross real return on capital is 1.065.

Computational Experiments

I proceed by examining the effects that changes in the inflation rate and reserve requirement ratio have in the model. Specifically, I am interested in computing the growth-rate effects and welfare effects for the model when one considers changes in the monetary policy variables in isolation. One can then determine how "close" the model's estimates are to those presented in the cross-country regressions.

I begin with the case in which the inflation-rate effects are computed. For this experiment, I use [Gamma] = 0.153 and vary the inflation rate between 0% and 99%. The question is, "What would the growth rate be for an economy in which the expected inflation rate is [[Pi].sub.0], where [[Pi].sub.0] [element of] [1.0, 1.99]?" Figure 1 plots the output growth rate and inflation rate combinations obtained for this set of expected inflation rates. The plot shows that the model economy's growth rate is nearly a linear response to movements in the inflation rate over the range of inflation rates considered.(15) A ten-percentage-point reduction in the inflation rate adds roughly 0.65 percentage points to the rate of output growth. The model economy's effect is, therefore, nearly double the size of the regression coefficient reported in Table III. Recall that the range of empirical estimates is between 1/4- and 3/4-percentage-points.

Hence, the growth rate effect in the model economy is inside this range.

I consider the another experiment, holding the inflation rate at 11.9% ([Pi] = 1.119) and letting the reserve requirement vary between 0% and 99% (that is, [[Gamma].sub.0] [element of] [0,0.99]). Figure 2 plots the output growth rate and reserve requirement combinations for this case. Here, a 10-percentage-point reduction in the reserve requirement ratio adds slightly more than 0.8-percentage-points to output growth. As with the inflation rate, the reserve-requirement effects using the benchmark parameter settings are large compared with the estimated coefficient, which estimates that per-capita real GDP growth would fall a slightly less that -0.5-percentage points for every 10-percentage-point reduction in the reserve ratio.

Note that in equation (10), monetary policy affects the real return on deposits through a product of the reserve requirement and the inflation rate. One way to diminish the size of the inflation-rate effect, for example, would be to lower the reserve-requirement setting in the computational experiments. Likewise for the reserve-requirement effect, lower the inflation rate from its benchmark setting. I set the inflation rate at 3%, running the same computational experiments as presented in Figure 1. For this case, a 10-percentage-point reduction in the reserve requirement results in the growth rate of output rising 0.45-percentage-points, which is in line with the parameter estimates obtained from the actual data. Similarly, if the reserve requirement is set at 5% and using the same range of inflation values, the computational experiment estimates the effect of lowering the inflation rate 10-percentage-points would result in output growth increasing by 0.22-percentage-points.

Because the monetary policy effects are so large, one would expect that the welfare costs of monetary policy would also be large. Next, I compute the welfare costs of both inflation and reserve requirements, using this model economy. The measure of welfare requires comparison of the sequences of consumption under the alternative policies. Let [Mathematical Expression Omitted] denote the sequence of consumption when the policy instrument is set equal to initial value and let [Mathematical Expression Omitted] be the sequence of consumption under the new policy setting. when the reserve requirement is 10%. Then the calculation is

(11) [Mathematical Expression Omitted].

Then [Phi] measures the percentage-change in consumption that would be necessary to make the agent just as well off in the initial policy setting as in the new policy setting. To simulate the consumption path, a special case of the model is established in which the initial capital stock, [K.sub.0], is set equal to 1. Welfare is measured as [Phi].

I consider four cases. In the first two, I calculate the welfare costs of eliminating the reserve requirement ratio. I consider two inflation-rate settings; one in which [Pi] = 11.9% and another in which [Pi] = 3%. Thus, in addition to the benchmark parameter settings, I can calculate the welfare costs for a case in which the growth-rate effects are quite close to those found in the data. Table IV reports the welfare costs for these four cases. Note that date-1 consumption falls as the reserve requirement falls. Agents, substitute away from consumption towards capital as the return on capital rises. The welfare costs of the reserve requirement is 10.6% when inflation rate is at 11.9% and is 2.9% when the inflation rate is 3%. Note that the welfare costs follow the change in the growth rate; that is, for a given change in reserve ratios, welfare costs are smaller when the initial inflation rate is lower.

The bottom part of Table IV considers two cases in which a moderate (10%) inflation is eliminated. In the first case [Gamma] = 0.153 while in the second case, I set [Gamma] = 0.05.(16) The welfare costs of eliminating a moderate inflation is [TABULAR DATA FOR TABLE IV OMITTED] 7.1% at the high reserve requirement setting and 0.7% when reserve requirements for the low-reserve-requirement setting.(17)

V. DISCUSSION

In this paper, I examine a general equilibrium model with endogenous growth. The economy has a monetary equilibrium because banks accept deposits that face a reserve requirement. Furthermore, banks are the only means to finance capital accumulation. The model, therefore, quantitatively assesses monetary policy effects on economic growth via a banking system. The main contribution of the paper is to show that a model economy, reasonably calibrated, can produce large growth rate subject to one key proviso - all investment is intermediated through bank deposits.

The findings suggest that large growth rate effects arise under very particular conditions. More specifically, the results show that movements in the inflation rate can result in large, opposing effects on the growth rate effects when bank deposits account for a large fraction of investment financing. In general, suppose that [Rho] = [([Beta]Q).sup.1/[Sigma]], where Q = [Omega]R + (1 - [Omega])[R.sup.nb], where R is defined as in equation (9) and [R.sup.nb] denotes the return from the alternative financing technology. Here, 0 [less than or equal to] [Omega] [less than or equal to] 1 is the fraction of total capital accumulation financed through bank deposits. In equilibrium, arbitrage is eliminated when R = [R.sup.nb]. As inflation rises, equation (10) implies that R fails. The imbalance between the return on deposits and the return on the alternative store of value means that people will substitute away from bank deposits which, by definition, results in a lower value for [Omega]. It is straightforward to show that a decrease in the fraction of investment financed through bank deposits implies that the growth-rate effect is smaller.(18) Chari, Jones and Manuelli showed that growth-rate effects are small when one calibrates a model economy with a nonbank sector. This paper contributes to the examination of growth-rate effects by showing that growth-rate effects can be large for economies in which all investment is financed through bank deposits.

In view of the results forwarded in this paper and those by Chari, Jones and Manuelli, there is a natural follow-up question. Do the large growth-rate effects occur because countries with high average inflation rates tend to have very small nonbank sectors. Alternatively, do these high-inflation countries finance a large of share investment through bank deposits. If the answer is yes, the theory can help to account for large growth-rate effects are present in cross-country evidence.

I would like to thank Leonardo Auernheimer, Scott Freeman, Rik Hafer, Gary Hansen, Greg Huffman, Larry Jones, Finn Kydland, Doug Pearce, Mark Wynne, Carlos Zarazaga, seminar participants at North Carolina State University, Texas A&M University, and the 1995 meetings of the Society for Economic Dynamics and Control, and an anonymous referee for helpful comments on earlier drafts of this paper. Jeremy Nalewaik provided excellent research assistance. Any remaining errors are solely my responsibility. The views expressed herein do not necessarily represent those of the Governors of the Federal Reserve System nor the Federal Reserve Bank of Dallas.

1. Levine and Renelt [1992] find the evidence on the inflation-output growth relationship is somewhat fragile when one accounts for other potential factors that would influence growth. Levine and Renelt use a standard set of conditioning variables, including investment spending. As the reader will see later in this paper, the model economy posits that inflation and reserve requirements affect the gross real return on deposits, which inhibits capital accumulation. Thus, one would expect to see that capital accumulation and monetary policy variables are inversely related. See footnote 8 for the correlation coefficients between these two monetary policy measures and investment.

2. Some of the links between intermediaries and growth have been formalized. See, for instance, the papers by Greenwood and Jovanavic [1990] and Bencivenga and Smith [1991].

3. Two caveats raise doubts about whether the large growth-rate effects are indeed present. One is that countries with high inflation also tend to be countries with volatile inflation. Are the regression results appropriately identifying the effect that movements in the average inflation rate has on output growth.

Alternatively, perhaps the causality runs output growth to inflation. Kockerlakota [1996] demonstrates that a reasonably calibrated model economy with a simple quantity theory can yield large effects from movements in output growth rates to the inflation rate.

4. To illustrate the problem, note that the Federal Reserve distinguished U.S. commercial banks by geographic location until the 1960s. Commercial banks designated as "Reserve city banks," for example, faced a higher reserve requirement ratio than those banks designated "country banks." Later, the Federal Reserve switched to a scheme in which the bank's deposit size was the factor determining the applicable reserve requirement ratio.

5. This is a reasonable approximation for the U.S. Excess reserves are a small fraction of deposits, and the excess reserve-to-deposit ratio moves very little over time.

6. The standard deviation on the inflation rate is large relative to the mean. Consequently, identifying "low" inflation countries as those with average inflation rates at least one-standard-deviation below the sample mean, I would have no countries in the sample. I therefore choose one-half-standard-deviation to identify low and high inflation countries.

7. Haslag and Hein [1995] find a similar result using U.S. time series.

8. I also examine the correlation between the investment share of output and the two monetary policy measures, using the same sample of countries and time-averages. The estimated correlation coefficient between inflation and the investment share variable is -0.12 and the estimated correlation coefficient between the reserve ratio and investment share is -0.36. Each correlation coefficient is statistically significant at the 5% confidence level.

9. The coefficient on the inflation rate is only about half the size of the coefficients reported in Fischer. What appears to be responsible for the coefficient being only -0.2, instead of Fischer -0.4, is the sample and estimation technique. Fischer had a shorter horizon [1970-1985], a slightly larger sample (73 countries) and used a pooled time-series cross section approach. Shortening the horizon gives greater weight to the relatively high-inflation, low-growth period experienced by many countries in the 1970s. It is not too surprising, therefore, that he finds a somewhat larger inflation-rate coefficient.

10. The linear specification assumes that these two forms of disaggregated capital are perfect substitutes in production. Barro [1990] shows that each type of capital can have decreasing returns alone, but constant returns in both applied together.

11. This illiquidity assumption is adapted from Bryant and Wallace [1980] and Freeman [1987]. In both papers, this technology generates the need for financial intermediation. Essentially, the primitive intermediary serves a pooling function for small savers.

12. More specifically, this model differs from Jones and Manuelli and Chari, Jones and Manuelli by assuming that all fiat money is held as bank reserves. If one were to include a cash-in-advance constraint, capital would be lower as people hold deposits and cash to finance future consumption. However, as Jones and Manuelli showed, higher inflation would affect the allocation between the cash and credit good, but the rate of growth.

13. Jones and Manuelli [1990] briefly discuss the negative effect a decrease in the (after-tax) return has on output growth across two countries.

14. Using the sample mean for the reserve ratios means that the model economy generates too large an M/Y ratio. In the model economy, M/Y is roughly three times larger than the sample mean for the countries (about 0.18 in the model economy and 0.06 is the sample mean). The M/Y ratio will fall if one introduces investment financing other than bank deposits.

15. If the inflation rate rises to say 1500%, the output growth response flattens substantially. Thus, the model economy asymptotically (w.r.t. the inflation rate) approaches a lower bound for the growth rate. In other words, there is a maximum rate at which the model economy will decline.

16. One justification for this reserve requirement setting is that banks would hold some reserve even with positive inflation. In the model economy, the reserve requirement is binding. Perhaps, in a more complicated environment, the difference between required reserves and desired reserves is smaller because the desired reserve ratio is not zero. Of course, this is pure speculation since the more complicated environment is not specified here.

17. Note that the welfare cost of inflation is also large for stationary economies in which a reserve requirement is present. I compute the value of [Phi] for a calibrated model economy in which the production technology is [Ak.sup.0.33]. For the parameter settings used in this paper (except [Beta] = 1/1.065), the welfare cost of a 10% inflation is greater than 13% of consumption. In the steady-state model economy, higher inflation causes the rate of return to fall, which, in turn, causes a decline in the level of steady state capital. With less capital, the steady-state level of consumption is lower.

To assess how much the welfare cost estimates differ depending on how valued fiat money is introduced, see the estimates reported in Cooley and Hansen [1989] and Ireland and Dotsey [1996].

18. The change in [Omega] for a given change in the inflation rate is one possible way to a measure an economy's financial sophistication.

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Haslag, Joseph H.: Sr. Economist and Policy Advisor, Federal Reserve Bank of Dallas, Tex., Phone 1-214-922-5157, Fax 1-214-922-5194, E-mail [email protected]