The Demand For Money: A Structural Econometric Investigation.

• Author: Dutkowsky, Donald H.

Donald H. Dutkowsky [*]

H. Sonmez Atesoglu [+]

This study empirically investigates dynamic microfoundations for the conventional Static money demand equation. An intertemporal substitution model with the addilog utility function yields a money demand relationship that closely approximates the double log specification. Results from previous empirical studies largely support the derived equation. Estimations with quarterly U.S. data support cointegration among real per capita Ml and consumption, and an after-tax long-term interest rate for the post-1980 period. Estimated short-run intertemporal interest rate elasticities of consumption vary from -0.26 to -0.93. Estimated long-run elasticities of substitution between consumption and money range from -0.26 to -0.41.

1. Introduction

   The conventional static money demand equation has been one of the most widely studied relationships in macroeconomics. It generally features real money balances being affected by contemporaneous levels of real income as a proxy for transactions, and a nominal interest rate that describes the opportunity cost of holding money. As Hoffman, Rasche, and Tieslau (1995) discuss, the equation carries important implications across a wide spectrum of macroeconomic theories.

   This relationship has received renewed attention with econometric advances in the area of cointegration. A large body of literature has emerged that investigates long-run properties of the conventional money demand equation for various countries. Evidence with regard to a long-run money demand relationship in the United States, particularly with Ml during the postwar period, is mixed. Miller (1991), Hafer and Jansen (1991), Friedman and Kuttner (1992), Stock and Watson (1993), and Norrbin and Reffett (1995a) find little support for cointegration for the conventional static money demand equation with Ml.

   Some studies, though, have produced more positive results, especially with adjustments in the basic specification. Hoffman and Rasche (1991) find evidence supporting cointegration with a dummy variable to reflect a shift in the deterministic trend in money demand during the 1980s. Baba, Hendry, and Starr (1992) provide support for a long-run relationship with an augmented model that includes risk, inflation, and a measure of the interest rate spread, although Hess, Jones, and Porter (1998) raise doubt regarding this model. Choudhry's (1996) findings indicate cointegration for a money demand model with stock prices. Ball (1998) obtains generally supportive estimation results from the semilog specification of Stock and Watson (1993) after extending the sample period through 1996.

   Hoffman, Rasche, and Tieslau (1995) present perhaps the most supportive empirical findings. With a dummy variable included as in Hoffman and Rasche (1991), they obtain evidence of a stable long-run static money demand relationship for Ml in five industrial countries. A key to their results is the imposition of unitary long-run income elasticity, which the data rarely reject.

   This study empirically examines the dynamic microfoundations of the static money demand relationship. It adapts an intertemporal monetary choice model to produce an operational conventional demand-for-money equation. Our specification has properties that match up well with previous empirical studies on the demand for money. In this way, findings from this research can be interpreted on the basis of the micro-based model to infer structural relationships within intertemporal consumer choice.

   Two main directions for dynamic microfoundations to money demand have been offered. Lucas (1988) provides a cash-in-advance framework, which can be inserted into real business cycle models. Ramey (1992) uses this approach to introduce trade credit to this area. She tests for the relative importance of technology shocks and financial shocks as sources of fluctuations in money. Norrbin and Reffett (1995b) extend Ramey's (1992) framework. They derive two testable equilibrium conditions involving money, trade credit, the nominal interest rate, and output. The authors obtain mixed empirical support for cointegrating relationships implied by their model. Norrbin and Reffett (1996) apply these conditions to interest-bearing and noninterest-bearing media of exchange along with a nominal interest rate. Their findings offer evidence of a long-run relationship.

   Our focus is on the basic approach of McCallum and Goodfriend (1989) and McCallum (1989), also utilized by Barnett (1995), Rotemberg, Driscoll, and Poterba (1995), and Dutkowsky and Dunsky (1996). From first-order conditions associated with the dynamic optimization problem, we derive an explicit relationship for the representative individual between contemporaneous real money balances, real consumption, and the nominal interest rates of money and a nonmonetary asset. Given the addilog specification of utility, the equation closely approximates the double log model used in recent money demand literature. The micro-based model is supported by many of the previous empirical results.

   We also estimate the static money demand relationship that adheres more strictly to the microeconomic foundations. The micro-based demand-for-money equation emphasizes per capita measurement, consumption rather than income, and the use of after-tax interest rates. Quarterly U.S. data serve as the sample. Our results provide strong evidence supporting a long-run relationship for Ml within the static money demand equation for the post-1980 period. Findings from the cointegration tests are robust to the consumption measure as well as the restriction of unitary long-run consumption elasticity.

   This study also presents estimates of several structural parameters within the underlying utility function. It contributes to a literature that derives and tests cointegrating relationships from explicit intertemporal optimization models. Examples include Ogaki (1992) with Engel's Law, Clarida's (1994) investigation of consumption and import demand, and Atkeson and Ogaki (1996) with the intertemporal elasticity of substitution. With cointegration, estimator consistency and accurate information on the extent of parameter uncertainty occurs without the need for instruments. This avoids potential problems involved with poorly correlated instruments, within estimation procedures such as generalized method of moments (see, e.g., Bound, Jaeger, and Baker 1995).

   Estimations with the Johansen (1991) method and the dynamic ordinary least-squares (DOLS) technique of Stock and Watson (1993) generate economically plausible estimates of several utility function parameters. These coefficients allow us to obtain estimates of two well-known structural elasticities. The estimated short-run intertemporal interest rate elasticity of consumption varies from --0.26 to --0.93. Estimates of the long-run elasticity of substitution between consumption and money range from --0.26 to --0.41.

   The paper proceeds as follows. Section 2 presents the theoretical model. In section 3, we discuss how the relationship can be applied to empirical results of previous money demand studies. Section 4 reports estimates of the micro-based money demand equation. Section 5 concludes the study.

2. A Dynamic Model of Static Money Demand

   The formulation uses the basic dynamic optimization framework of McCallum and Goodfriend (1989) and McCallum (1989). [1] It also goes along with the monetary aggregation approaches of Barnett (1995) and Rotemberg, Driscoll, and Poterba (1995) as well as the intertemporal substitution model with money of Dutkowsky and Dunsky (1996). We assume a one-good, two-asset economy. The representative consumer derives utility from same period consumption, leisure, and transactions services rendered by real money balances. The consumer seeks to maximize expected total discounted utility given by

   [E.sub.0] [[[sigma].sup.[infinity]].sub.t=0] [[beta].sup.t]u([c.sub.t], [l.sub.t], [m.sub.t]), [u.sub.c], [u.sub.l], [u.sub.m] [greater than] 0, (1)

   where u() is the concave utility function, [c.sub.t], refers to date t real consumption, [m.sub.t], denotes date t real money balances, that is, money divided by the price of the consumption good, [l.sub.t] is date t leisure, [E.sub.0] denotes the rationally determined expectation based upon information available at date 0, and [beta] refers to the rate of time discount with 1 [greater than] [beta] [greater than] 0. All variables are defined in end-of-period terms.

   The constraint centers around the determination of total real wealth. The consumer holds two assets, money and nonmonetary wealth. Following McCallum and Goodfriend (1989), McCallum (1989), and the monetary aggregation literature, we assume that each asset pays interest at the end of date t on the basis of a nominal interest rate determined at the close of the previous period. With this property, date t real total wealth is given by:

   [A.sub.t] + [m.sub.t] = (1 + [R.sub.t-1])/(1 + [[pi].sub.t]) [A.sub.t-1] + (1 + [r.sub.mt-1])/(1 + [[pi].sub.t])[m.sub.t-1] + [w.sub.t](T - [l.sub.t]) + [TP.sub.t] - [c.sub.t], (2)

   for t = 0, 1, 2, .... The variable [A.sub.t] denotes date t real holdings of the nonmonetary asset; [r.sub.mt] and [R.sub.t] refer to the date t nominal after-tax interest rates on money and nonmonetary wealth, respectively; [[pi].sub.t] = [P.sub.t]/[P.sub.t-1] - 1, or the inflation rate from date t -- 1 to t, with [P.sub.t] being the price of the consumption good; [w.sub.t] is the date t after-tax real wage rate; T refers to the number of hours available; and [TP.sub.t], denotes real date t transfer payments. [2] Because nonmonetary wealth provides no transactions services, it offers a higher return than money, that is, [R.sub.t] [greater than] [r.sub.mt].

   The intertemporal optimization problem here differs in several ways from earlier studies. Because Barnett (1995) and Rotemberg, Driscoll, and Poterba (1995) concentrate on monetary...