The demand for nominal and real money balances in a large macroeconomic system.

• Author: Cutler, Harvey

1. Introduction

   Cointegration has become a popular empirical technique used to estimate the existence and stability of money demand relationships. A common approach has been to estimate a single equation system with real money balances (M1), real income and an interest rate, although Hafer and Jansen [13], Friedman and Kuttner [10] and Stock and Watson [29] find only minimal support for this specification. Baba, Hendry and Starr [6] estimate a more complicated Ml relation by including specific opportunity cost variables and find stronger support for the M1 relation using post WWII data.

   There have been four reasons put forth to explain the lack of a cointegrating relation between M1, real income and the interest rate. Stock and Watson [29] conclude that a stable money demand relation exists in data from 1900-89 but not for the post-war period alone. Their explanation is that sufficient variation exists in the longer sample to identify money demand, but excessive multicollinearity among variables during the post-war period prevents unique identification.

   Baba, Hendry and Starr [6] (BHS) maintain that misspecification of the M1 relation is the reason for poor results. They augment the money demand function with inflation, a measure of long term bond yield and risk, and learning curve weighted yields on newly introduced M1 and M2 assets. BHS claim their specification is able to account for the missing money period of 1975-76, the velocity decline of 1982-83 and the M1 explosion of 1985-86 while standard M1 models cannot. Friedman and Kuttner [10] offer a third reason why the simple money demand equation fails. They estimate a single equation model for several periods and conclude that a money demand vector exists over the 1960.2-79.4 period for M1. However, when data is included up to 1990.4, they are unable to estimate the money demand relationship. Friedman and Kuttner conclude that the money demand relationship may have broken down in the 1980s.

   A fourth explanation relates to the work of Phillips [27] and Johansen [18], who demonstrate that if important variables are omitted from a cointegration analysis, an incorrect number of vectors and biased estimates of the coefficients will result. In addition, the estimates will generally be inefficient. To demonstrate these points in a macroeconomic context, Cutler, Davies, Rhodd and Schwarm (CDRS) [7] consider money demand in conjunction with consumption, investment and import markets, and are able to identify a simple money demand representation better than using a single money market alone.

   All of the research cited above used real money balances which constrains the price elasticity to unity prior to estimation. In this paper, we use a model similar to CDRS, except that we separate money and prices to allow for a separate estimation of the price elasticity. In several time periods, the elasticity is estimated to be less than unity. Therefore, real money balances may be not always be consistent with the data and implied economic behavior. In addition, the results for our money market improve relative to the CDRS specification. We obtain more reasonable elasticities for consumption and investment, and we have greater success in identifying all markets.

   Our macroeconomic system, with its multiple markets, originates with King, Plosser, Stock and Watson [21].(1) They combine real GNP, consumption, investment, real money balances, nominal interest rates and the inflation rate into cointegrating vectors that represent money, consumption and investment markets. We augment their model by including imports and an import market as a fourth vector. We also use the ex-post real interest rate instead of the inflation rate and separate money and prices in order to test for a unitary price elasticity in the money market.

   To demonstrate gains from systems estimation, we compare single equation and systems estimates using a method developed by Johansen and Juselius [19]. Examining the period 1960.2-90.4, we use a more systematic rolling regression approach to deal with the sensitivity of sample periods. We find more support than other researchers for an Ml vector during the post-war period, which may be due to the efficiency gains of full system estimation as well as splitting Ml and the price level. We also conclude that the price elasticity of money demand is not unity for the late 1980s, which suggests that monetary decisions are based more on nominal than real money balances in this later period.

   Section II presents the four market macroeconomic system we use to reduce the biases and inefficiencies associated with estimating partial systems. Section III presents the empirical procedures, results and the speeds of adjustment. Then, three special issues are analyzed in section IV: the role of the price level in creating equilibrium in the system; the specific gains in efficiency from using a full system; and the implications of a price elasticity in the money demand function that is not unity. Section V contains a brief conclusion.

2. Economic Model

   We are motivated to construct a more complete system than has been typically used to analyze money demand. Our approach is expressed in the following simple macroeconomic relations:

   [C.sub.t] = [a.sub.0] + [a.sub.1][Y.sub.t] + [a.sub.2][r.sub.t] + [e.sub.t] (1)

   [I.sub.t] = [b.sub.0] + [b.sub.1][Y.sub.t] + [b.sub.2][r.sub.t] + [u.sub.t] (2)

   [M.sub.t] = [d.sub.0] + [d.sub.1][Y.sub.t] + [d.sub.2][r.sub.t] + [d.sub.3][P.sub.t] + [v.sub.t] (3)

   I[M.sub.t] = [g.sub.0] + [g.sub.1][Y.sub.t] + [g.sub.2][r.sub.t] + [z.sub.t] (4)

   where Y is real GNP, C is real consumption, I is real investment, r is the expost real interest rate, M is money balances, P is the price level, IM is real imports and t is a time subscript.(2) The variables [e.sub.t], [u.sub.t], [v.sub.t] and [z.sub.t] are error terms.

   This system of equations implies four cointegrating vectors: equation (1) gives a simple consumption function; (2) is the investment function; (3) is money demand; and (4) is an import equation. The first two equations are standard and simple representations of their respective markets, but the import and money demand functions are somewhat different than traditional versions. We captured the effects of the traditional import demand model, which includes income and relative prices, through conditioning variables discussed below. The real interest rate is also included to make the import equation a variation of the consumption function, with the same variables driving import and domestic demand after adjusting for foreign relative price and interest rate effects. The main variation in the money demand equation is that the price level and nominal money balances are used instead of real money balances.

   These four equations represent logically distinct but clearly interrelated markets.(3) Each equation represents a long-run equilibrium relation with the error terms capturing disequilibria in each market; hence each is a separate cointegrating vector. As an example, the model predicts that C, Y and r must satisfy equation (1) over time such that [e.sub.t] is a stationary process. Thus, the seven variables in the system are combined into four equations whose residuals are unique stationary processes.

   The King et al. system may be viewed as a special case of the above system. They use consumption, investment, income, a nominal interest rate, real money balances (M2) and inflation to create a restricted version of equations (1), (2) and (3). Their consumption vector is represented as a "great ratio," which in effect imposes the restriction that [a.sub.1] = 1 in the system above. The investment vector is constructed in a similar fashion, with [b.sub.1] = 1, and their money vector is similar to ours except that the coefficient [d.sub.3] is restricted to unity. Their model differs from ours in two additional respects. King et al. reflect the real interest rate by using the inflation rate and nominal interest rate which, on the surface, is not of great consequence. Also, we introduce a foreign sector by examining the role of imports explicitly and exports implicitly through conditioning, whereas King et al. examine a closed system.

3. Empirical Procedures and Results

   In this section, we first review the procedures used to analyze our system and then focus on an overview of the results. The overview presents results of single and joint tests done on the full system and also on single equation models. At the end of this section, issues concerned with the increased efficiency and reduced bias obtained from full system estimation are addressed and the speed of adjustment coefficients are evaluated.

   Empirical Procedure

   The seven variables included in our system are [X[prime].sub.t] = [[Y.sub.t][C.sub.t][I.sub.t][M.sub.t][P.sub.t][r.sub.t]I[M.sub.t]], which are expected to lead to four cointegrating vectors.(4) (Each variable is defined in the appendix). However, there are other associated variables, such as government expenditures and foreign sector variables, that influence movements in [X.sub.t]. Johansen and Juselius [19] and Baba, Hendry and Starr [6] have pointed out that when cointegrated systems become too large, estimation and interpretation can be difficult. Therefore, it has become common practice to introduce conditioning variables that do not affect the size of the system.

   Conditioning variables are used to eliminate unwanted influences that might affect the estimates of the cointegrating vectors. Since they are not in any hypothesized vectors, it would be inappropriate to include them in the system; conditioning variables are, however, influential and their effects need to be included. We have chosen real government expenditures and real exports because they help determine the level of real GNP and other variables in our system. Foreign variables are used to specify the import sector correctly. We elected to include a foreign interest rate and...