Implicit returns on conventional demand deposits: An empirical comparison

ROSEMARY ROSSITER Ohio Uniuersity

TONG HUN LEE University

of Wisconsin,

Milwaukee

Implicit Returns on Conventional Demand Deposits: An Empirical Comparison* This paper compares the relative performance of alternative series of implicit returns on conventional demand deposits by estimating for each series a set of equations derived from a generalized CES utility model for a liquid asset portfolio. This approach offers the unique advantage of explaining money holdings with a substantially larger number of degrees of freedom than originally available, while avoiding multicollinearity even in the presence of several interest’ rate variables in the model. An implicit return series obtained by Barre and Santomero (1972) performs the best among all of the available seven series tested based on the criteria of a generalized measure of goodness-of-fit and a robustness of coefficient estimates.

1. Introduction Although the Depository Institutions Deregulation and Monetary Control Act of 1980 has led to the introduction of several types of transaction accounts which bear explicit interest rates, questions have arisen again regarding the implicit return paid on conventional demand deposits. Economists have long suspected that the return on conventional demand deposits is not zero and have measured alternative series of positive returns, usually net of service charges. Today, as new questions arise regarding specification of a stable money demand function, it seems quite worthwhile to evaluate all available measures of implicit returns on conventional demand deposits to choose the best series for possible extension. The purpose of this paper is to evaluate the relative performance of seven alternative series of implicit returns by estimating a generalized CES utility function of monetary assets. In order to secure a maximum number of degrees of freedom, we employ joint estimation procedures while making appropriate corrections for serial correlation and obtain a generalized measure of goodness-of-fit. Empirical results are quite robust, confirming the usefulness of the *The referees

authors wish for constructive

Journal

of Macroeconomics,

Copyright 0 1988 0164-0704/88/$1.50

to express comments

by Louisiana

Fall

their appreciation to the editor which led to the final version

1987, Vol. 9, No. 4, pp. State University Press

613-624

and anonymous of this paper.

613

Rosemary Rossiter and Tong Hun Lee joint estimation procedures and providing usefulness of each alternative measure.

2. Alternative

Measures

of Implicit

unique

evidence

on the

Returns

Startz (1979) categorizes three approaches to the measurement of implicit return. First was the traditional approach employed in many early studies that treats the implicit return as zero or even negative due to service charges, as, for example, in Feige (1964) or Lee (1966, 1967, 1969). Th e second approach, called the modified traditional hypothesis, states that commercial banks had been partially successful over the years in circumventing legal prohibitions against explicit returns and had, in fact, been providing some positive implicit returns. The third hypothesis assumes that competition among commercial banks was so effective as to have all marginal profit from deposits passed on to deposit holders. A positive implicit return series for the years 1950-1968 is first calculated by Barro and Santomero (1972), based on a private survey of service charges remitted by major commercial banks. Later Becker (1975) constructs a series using non-interest expenses of commercial banks for 1952-1971. Startz proposes two implicit return series using functional cost data for 1959-1976, or a pooled time-series and cross-sectional approach for 1954-1975. Finally, Klein (1974) assumes the implicit return on demand deposits was equal to r(1 - R/D), where r was the marginal return on investment derived from demand deposits and R/D was the average reserve deposit ratio. The return on commercial paper serves as a proxy for the unobservable marginal return on investment. Klein’s series, originally available through 1970, is extended by Offenbacher (1979).

3. A Generalized

CES Utility

Model

While implicit returns can be utilized in conventional money demand functions, the approach taken here assumes that consumers hold various assets because they possess different degrees of moneyness. Chetty’s model (1969)-extended along the lines of Moroney and Wilbratte (1976), Boughton (1981), and Rossiter and Lee (1984)-develops this direct utility approach by employing a generalized CES utility function to measure elasticities of substitution.’ ‘Although more flexible utility functions are available in the literature, not useful for our purposes because they involve more parameters and leviate the problem of multicollinearity as treated in this paper.

614

they are do not al-

Zmplicit

Returns

on Conventional

Demand

Deposits

Specifically, the approach taken here assumes that the consumer possesses a generalized utility function that is neither homothetic nor separable from income, such that -l/p

u

=

ycP-P%

&f-P

+

pi

ycPr-Ped

x;Pl

i=l

[

The budget

5

constraint

1

.

is

P xi +i-. Lo = (1 + RJ i-1 (1 + RJ ’ PM

(53

where P is the price level, M is currency plus demand deposits, and & is the implicit return on money holdings, defined as the weighted average of a zero return on currency and the implicit return on demand deposits. In what follows, Xi represents time and savings deposits at commercial banks (TD), X2 denotes savings and loan shares (SL), X3 indicates mutual savings bank deposits (MS), Y is income, and Ri is the interest rate on the ith deposit. All assets are measured as holdings at the end of a period in real terms. First-order conditions for optimum portfolio behavior may be derived and rearranged to obtain an estimating equation for each near-money. However, unlike the specification in Chetty’s (1969) paper, money rather than a near-money is selected as a dependent variable, producing the following estimating equations: lnM=-

1 1 +

In -!!P

PIP1

1 + l+P

In

1 + R,

1 +

Pl

-+-

1 + RI

In X1

l+P

+ (P - PO) - (PI - Pfw In y + E 1; l+P lnM=-

1 1+

lnPP2P2 + &In-+ 1 + P P

+(P-PwP2.-PwIny+E2; l+P

1 + R, 1 + R2

1 +

P2

-lnX2 l+P and

(4)

In M = 1+ P

P3P3

1 +

P 615

Rosemary Rossiter and Tong Hun Lee + (P - PW - (P3 - PQ In y + E 3;

(5)

l+P

where the E’S are added as disturbance terms. The second-order conditions for an optimum requires that the p’s are in the open interval between -1 and 0; thereby implying that the coefficients of the relative price term, ln[(l + R,)/(l + I$)], and the asset term, lnX,, are greater than unity and zero, respectively. To allow for first-order autoregressive errors, we assume that the disturbance terms of the estimating equations at time t have a general specification as

(6)

where the ui’s are normally

distributed

with

and

for i or j = 1, 2, and 3. This specification of errors is quite general: if all pV = 0, it is Zellner’s case (1962) of contemporaneous correlation, but no autocorrelation; if pr = 0 only for i # j, it is Parks’ (1967) specification of first-order autocorrelation; and finally, if pti # 0 for all i and j, it becomes a general specification of the vector autoregressive process of Guilkey and Schmidt (1973). Inspection of the estimating equations (3-5) shows that the coefficients of the relative price terms are the same across the equations. When estimating the equations jointly as a system, the coefficients can be constrained to be the same, eliminating an overidentification problem which has flawed many previous applications of Chetty’s original model. Moreover, joint estimation has the effect of increasing the available degrees of freedom, while the constraint improves the efficiency of the estimates when, in fact, such a constraint holds true in the population. In order to search for evidence regarding the implicit return series that performs the best, we will examine the coefficient of 616

Implicit

Returns on Conventional

Demand

Deposits

determination, R& proposed by Buse (1979) for the seemingly unrelated regressions model when the disturbance terms are autocorrelated or heteroscedastic. Since the RE is a generalized measure applicable to a system of equations, it will indicate goodness-of-fit of alternative return series in our model. We will also check on the coefficients of the relative price terms in order to examine the impact on money holdings of the implicit returns on demand deposits. In addition, by checking both the significance and the relative magnitudes of the 1nXi coefficients, we note the implications for specification bias in measuring the relative substitutability among different assets.

4. Empirical

Results

Since the observations on implicit returns are most commonly available for 1954-1968, the analysis below concentrates on this period.2 With fifteen annual observations for each equation, our joint estimation of three equations increases the degrees of freedom to forty-five, a major improvement over single-equation least-squares estimation of the traditional money demand function. Moreover, since each of our joint-estimating equations contains only one interest rate ratio, the presence of several interest rate variables in our model does not cause multicollinearity as it would in a single-equation model. When the equations (3-5) are estimated by Zellner’s procedure, the Barro-Santomero series performs most promisingly while Klein’s series is unsatisfactory with a coefficient on the relative price term significantly below unity. Because autocorrelation is suspected, Zellner estimates are not presented here. Rather, we present a re-estimation using Parks’ method to allow for first-order autoregressive errors. As seen in Table 1, the Barro-Santomero series again out performs each of the other measures of implicit returns. The goodnessof-fit measure, Ri, is 0.950, much larger than that obtained for any other series. Moreover, the Barro-Santomero series provides robust

‘Data cited in Bulletin. not Startz liminary compared

on each implicit return are obtained from published Section 2, while service-charge data is obtained from In this analysis, we include a Startz (A) series taken (1) of his Table 1. The Startz (1) series only begins result for 1959-1975 suggested that this series fit the to some of the other series.

works of the authors the Federal Reserve from his Table 4 but in 1959, and a preequations poorly as

617

Durbin’s t-statistics g for system = 0.950

& Santomero

14.129** (1.595)

1.848** (0.396) 1.102

0.247** (0.056)

Barro

(iii)

0.740** (0.160) 1.865

7.621** (1.730)

Durbin’s t-statistics G for system = 0.900

Charges

0.211** (0.047)

0.207** (0.046)

(ii) Service

0.658** (0.147)

7.459** (1.802)

InTD

2.058

= 0

Constant

I(1 + Rm)/ (1 + RJ]

Estimates Using Parks’ Constrained

Durbin’s t-statistics R$ for system = 0.897

(i) &

Implicit Return

TABLE 1.

0.303** (0.109)

0.314** (0.098)

0.314** (0.099)

1nY

2.520** (0.215)

2.038** (0.351)

2.069** (0.352)

Constant

Joint Estimation,

0.703

0.071** (0.025)

0.540

-0.021 (0.032)

0.640

-0.036 (0.032)

1nSL

1nY

0.394** (0.047)

0.589** (0.062)

0.589** (0.063)

1955-1968

1.379** (0.252)

1.387** (0.340)

1.391** (0.333)

Constant

0.385

0.3OQ** (0.107)

0.997

0.168 (0.143)

1.322

0.151 (0.148)

1nMS

0.341** (0.113)

0.442** (0.141)

0.432** (0.147)

InY

7.396**

Note:

Standard Symbols

errors * and

Durbin’s t-statistics g for system = 0.873

in parentheses. ** indicate significance

2.377** (0.626)

at the

0.873

0.012 (0.091)

-1.309 (1.001)

(vi)

Klein

1.381

Durbin’s t-statistics g for system = 0.885

1.281** (0.299)

0.064 (0.067)

0.175** (0.058)

A

8.183** (2.253)

1.729** (0.463)

(v) Stark

@.3w 1.420

Becker

Durbin’s t-statistics $ for system = 0.904

(iv)

0.05

and

0.258 (0.205)

0.315** (0.115)

0.378** (0.146)

0.01

levels,

2.243** (0.462)

2.042** (0.379)

2.641** (0.299)

respectively.

0.007

-0.145** (0.035)

1.050

-0.041 (0.031)

0.951

-0.068** (0.028)

0.604** (0.084)

0.582** (0.068)

0.479** (0.060)

3.279** (1.398)

1.229** (0.248)

1.379** (0.199)

2.971

-0.504* (0.264)

0.626

0.326** (0.129)

0.120

0.177 (0.111)

0.803** (0.289)

0.258** (0.129)

0.262** (0.116)

Rosemary Rossiter and Tong Hun Lee estimates of all coefficients and other relevant statistics. First, the constrained coefficient on the relative price term across the equations is significantly greater than unity, indicating that money holdings are explained very well by the implicit return as expected by theory. Second, all of the estimated coefficients on the asset terms are positive and highly significant, showing that the relative substitutabilities of various savings deposits for money are estimated with considerable precision.3 Finally, using a t-test on residuals in a manner suggested by Durbin (I970), we find no serial correlation in any regression.4 Thus, allowing for autoregressive errors in Parks’ method clearly improves the fit of this regression, providing more efficient and reliable estimates. Table 1 also shows that while the other series are not fully satisfactory, the service-charge ratio and the zero rate of return perform reasonably well. Although Rgs are not larger than 0.90, estimated coefficients on the relative price terms and 1nTD terms are highly significant with expected signs and magnitudes. It is also encouraging to find that the Startz (A) series gives similar coefficient estimates. However, Ri for the Startz (A) series is smaller than that for either the service-charge ratio or the zero rate of return, indicating a limited usefulness of this series. Beyond this, the two remaining series are not theoretically tractable for explaining the demand for money. While the Becker series gives an incorrect negative coefficient on 1nSL at a highly significant level, the Klein series performs the worst as it yields incorrect significant coefficients on two asset terms as well as the relative price term. If the disturbance terms are generated by a vector autoregressive process in (6), the estimation method proposed by Guilkey 3As explained in detail in our earlier paper (1984), the smaller the coefficient on h-&,, the greater would be the substitutability between money and the ith asset, using R.G.D. Allen’s elasticity of substitution. Our estimates for the period 19551968 in row (iii) of Table 1 imply that the elasticity of substitution between money and savings and loan shares is largest, the elasticity of substitution between money and commercial bank time deposits is second, and the elasticity of substitution between money and mutual savings bank deposits is smallest. In our 1984 paper, we obtained the same ranking for the period of 1952-1966, but found a shift in substitutability in the subsequent period. The present study indicates that such a shift had not occurred until the mid-1966’s. One plausible explanation is that although certificates of deposit at commercial banks began appearing in the 1966’s they became more available as years progressed. Also, maximum rate ceilings were first imposed on savings and loan shares in 1966, making these shares less attractive. Earlier evidence on this can be found in a study by Lee (1972). ‘Durbin shows that this t-test is asymptotically equivalent to his h-test.

620

Zmplicit Returns

on Conventional

Demand

Deposits

and Schmidt provides an asymptotically more efficient estimator. Despite reservations about loss of small sample efficiency, we reestimated each set of equations by the Guilkey-Schmidt procedure. Results in general conform closely to those in Table 1, but are not presented here due to space limitations. We can specify, however, that once again the Barro-Santomero series performed most satisfactorily, while the Klein series was the worst. Thus, the main results of this paper have not been altered either by a particular specification of the disturbance terms or by a specific estimation technique. Since alternative return series are evaluated on the basis of goodness-of-fit, a question may arise as to whether it is appropriate to impose an a priori constraint that the coefficient of the relative price term is the same across equations. Using an F-test based on alternate estimation methods, we tested the null hypothesis that the relative price coefficient is the same across equations, but the null hypothesis can not be statistically rejected.’ This means that our particular formulation of the utility function containing the restriction is appropriate in evaluating the relative performance of the alternative series of implicit returns. We might also mention that although the 1nXi’s are treated as exogenous, this assumption is not likely to cause significant simultaneous equation bias, as confirmed in our 1984 study. Before concluding, comparisons of our results with those of others are in order. While we know of no other studies that attempt as comprehensive an examination of alternative implicit returns as presented here, several authors compare two or three series at a approach and time. First, Santomero (1979) uses a single-equation Theil’s test of specification error to compare the Barro-Santomero series with the Becker and Klein series. Our result that the BarroSantomero series outperforms the Becker or Klein series is consistent with Santomero’s findings. Second, Carlson and Frew (1980) argue that the Klein series inappropriately uses the commercial paper rate and presents evidence that its use led to serious biases. Again, our results are very similar. Lastly, Allen (1983) estimates a single-equation money demand function using the Barro-Santomero, Becker, or Startz series, but fails to find evidence that any series entered the equation significantly. In our view, our joint estimation ‘For instance, in the case of Barre-Santomero series using Parks’ method, null hypothesis could not be rejected with an F&ratio of 1.185 at the 0.05 Also, the null hypothesis could not be rejected in using any other series.

this level.

621

Rosemary Rossiter and Tong Hun Lee approach using virtually the same data alleviates the problems of multicollinearity and smallness of observations which cause Allen’s estimates to be imprecise.

5. Concluding

Remarks

Empirical results from our model show that the Barro-Santomero series performs far better than any other measure of implicit return. Although other measures are not fully satisfactory, either the service-charge ratio or the zero rate of return out performs the Startz (A), Startz (l), Becker, or Klein series, indicating the limited usefulness of the latter series. In particular, the Klein series is the least satisfactory, followed by the Becker series, both of which provide significantly biased estimates along with very low R2,‘s. While we use a different approach and also utilize all of the available series for comparison, our results in part are consistent with those of either Santomero or Carlson and Frew, thus indicating the validity of our findings in general. In view of the evidence presented here, it would seem quite worthwhile to update the Barro-Santomero series. Although conducting an appropriate survey would be time-consuming, the information obtained would be valuable not only for future empirical studies of the demand for money, but also for determination of the true yield on transaction accounts that bear explicit rates of return. Received: March 1987 Final version: July 1987

References Allen, S. “A Note of the Implicit Interest Rate on Demand Deposits.” Journal of Macroeconomics 5 (1983): 233-39. Barro, R., and A. Santomero. “Household Money Holdings and the Demand Deposit Rate.” Journal of Money, Credit and Banking

4 (1972): 397-413. Becker, W. “Determinants of the United States Currency-Demand Deposits Ratio.” Journal of Finance 30 (1975): 57-74. Boughton, J. “Money and Its Substitutes.” Journal of Monetary

Economics 8 (1981): 375-86. Buse, A. “Goodness-of-Fit in the Seemingly Unrelated Regressions Model.” Journal of Econometrics 10 (1979): 109-13. 622

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on Conventional

Demand

Deposits

Carlson, J., and J. Frew. “Money Demand Responsiveness to the Rate of Return on Money: A Methodological Critique.” Journal of Political Economy 88 (1980): 598-607. Chetty, V.K. “On Measuring the Nearness of Near-Monies.” American Economic Review 59 (1969): 270-81. Durbin, J. “Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables.” Econometrica 38 (1970): 410-21. Feige, E.L. The Demand for Liquid Assets: A Temporal Cross-Sectional Analysis. Englewood Cliffs, N. J. : Prentice-Hall, 1964. Guilkey, D.K., and P. Schmidt. “Estimation of Seemingly Unrelated Regressions with Vector Autoregressive Errors.” Journal of American Statistical Association 68 (1973): 642-47. Klein, B. “Competitive Interest Payments on Bank Deposits and the Long-Run Demand for Money.” American Economic Review 64 (1974): 931-49. Lee, T. H. “Substitutability of Non-Bank Intermediary Liabilities for Money: The Empirical Evidence.” Journal of Finance 21 (1966): 441-87. -. “Alternate Interest Rates and the Demand for Money: The Empirical Evidence.” American Economic Review 57 (1967): 116881. -. “Alternate Interest Rates and the Demand for Money: Reply.” American Economic Review 59 (1969): 412-17. -. “On Measuring the Nearness of Near-Monies: Comment.” American Economic Review 62 (1972): 217-20. Moroney, J., and B. Wilbratte. “Money and Money Substitutes.” Journal of Money, Credit and Banking 1 (1976): 181-98. Offenbacher, E.K. The Substitutability of Monetary Assets. Ph.D. diss., University of Chicago, 1979. Parks, R.W. “Efficient Estimation of a System of Regression Equations when Disturbances Are Both Serially and Contemporaneously Correlated.” Journal of the American Statistical Association 62 (1967): 500-Q. Rossiter, R., and T.H. Lee. “Statistical Tests of Relative Substitutabilities of Near-Monies Over Time.” Journal of Macroeconomics 6 (1984): 249-64. Santomero, A. “The Role of Transactions Costs and Rates of Return on the Demand Deposit Decision.” Journal of Monetary Economics 5 (1979): 343-64. Startz, R. “Implicit Interest on Demand Deposits.” Journal of Monetary Economics 5 (1979): 515-34. 623

Rosemary Rossiter and Tong Hun Lee Zellner, A. “An Efficient Method of Estimating Seemingly lated Regressions and Tests for Aggregation Bias.” Journal American Statistical Association 57 (1962): 348-68.

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Unre-

of the