Uncertainty and the Stability of Money Demand Functions for the U.S. Agricultural Sector

Uncertainty and the Stability of Money Demand Functions for the U.S. Agricultural Sector

Ghulam Sarwar,’ Naginder S . Dhaliwa12 and John F. Yanagida3 ‘Graduate research assistant, Department of Agricultural Economics,

University of Nebraska, Lincoln, Nebraska. 2Economist, Policy Branch, Agriculture Canada, Ottawa.

’Professor, Department of Agricultural and Resource Economics, University of Hawaii, Manoa, Hawaii.

Hawaii Agricultural Experiment Station Journal Article No. 3310. Received 17 October 1988, accepted 12 June 1989

INTRODUCTION Since the appearance of Goldfeld’s (1976) paper on ‘‘The Case of Missing Money,” it is widely recognized that conventional specifications of aggregate money demand functions consistently and significantly overpredict actual money demand over the post-1973 period (see Laidler 1985, 145-51, and Judd and Scadding 1982 for useful summaries). It has been argued that events of the 1970s, particularly the rapid inflation in the U.S. after 1973 and the concurrent collapse of the fixed exchange rate system, may have altered responses to standard arguments of the demand-for-money function (Boughton 1981). To resolve this puzzle, much of the recent research on money demand has focused on stability of standard and alternative money demand specifications (Laumas and Mehra 1976; Ram 1982; Laumas and Spencer 1980; Boughton 1981).

Friedman (1970) stressed that, among other things, uncertainty about the future affects the usefulness of money as an asset. Tobin (1958) proposed that risk- averse individuals hold money in part because of uncertainty about future interest rates. Research supports these theoretical arguments, indicating that uncertainty surrounding inflation, exchange rates, and interest rates have influenced the demand for money significantly (Smirlock 1982; Akhtar and Putnam 1980; Slovin and Sushka 1983).

Only a few studies on money demand have appeared in the agricultural economics literature (Barnett 1984; Barnett et al 1981; Penson 1972; LeBlanc et al 1985). The theoretical specification of money demand for the agricultural sector is distinct from the specification for the aggregate economy because of the dual role of money in production and consumption processes of the farm firm. Because the agricultural sector is highly capital intensive,’ its money demand is likely to be more sensitive to interest rates and to other monetary factors than the money demand of some other sectors. To date, however, little is known about the differ-

Canadian Journal of Agricultural Economics 37 (1989) 279-289 279

280 CANADIAN JOURNAL OF AGRICULTURAL ECONOMICS

ential magnitude of such sectoral responses. Even less is known about the stability of agricultural money demand functions.

The objectives of the present paper are to estimate money demand functions for the agricultural sector, to test the stability of resulting functions with and without macroeconomic uncertainty variables, and to compare results of agricultural money demand with those of aggregate money demand.

In the next section, theoretical considerations for including uncertainty variables in money demand functions are discussed. The following section presents money demand functions for agriculture and the aggregate economy. Then, empirical results are presented and differential responsiveness of sectoral money demands are discussed. Stability tests are examined in the section that follows. The last section summarizes the major conclusions.

THE EFFECT OF UNCERTAINTY IN MODELS OF THE DEMAND FOR MONEY

Klein (1977) demonstrated in a choice-theoretic framework that, assuming money demand is interest-rate inelastic, an increase in inflation uncertainty enhances the demand for money. This result becomes theoretically ambiguous, however, when money demand is not interest inelastic.

Unlike inflation uncertainty, interest-rate risk has a theoretically unambigu- ous impact on the demand for money. SIovin and Sushka (1983), using Baumol’s (1952) inventory theoretic model, showed that an increase in interest-rate risk increases the demand for money. The same result emerges from Tobin’s (1958) liquidity preference model in which individuals reduce bond holdings and increase money holdings in response to increased uncertainty of bond returns.

Examining the impact of exchange-rate risk of domestic currency on money demand, Akhtar and Putnam (1980) argued that increased exchange-rate risk may render domestic currency a nonoptimal store of value for international transac- tions. Transactors would then tend to hold smaller amounts of domestic money.

MODEL SPECIFICATION

Agricultural Sector The agricultural farm firm is viewed not only as a production unit but also as a consumption unit. Money is treated as an input in agricultural production as well as in household productiodconsumption.

As an input in agricultural production, the economic rationale for including money balances in the production function relates to the increased efficiency in obtaining inputs necessary for production and marketing of farm products. In a world where production is not instantaneous, money is viewed as an input facili- tating the flow of inputs and outputs (see LeBlanc et a1 1985; Sinai and Stokes

MONEY DEMAND FUNCTIONS 28 1

1972). That is, money facilitates the purchase of inputs in situations where the production process is lengthy and the receipt of revenues is delayed.

Analogous to the concept of household production (see Becker 1971 for a theoretical development), money balance is a good (input) used in the production of household commodities. The farm household is assumed to maximize utility subject to household and farm production functions, resources (goods) availabil- ities and an income constraint.

The objective function can be written as:

Maximize U = U ( Z , , Z,, ..., Z,, C , , C,, ..., C,) (1 1 subject to:

(household production) zi = Zi(X1, x,, . - * , x,, M) (2)

(farm production) N = N X s - d , . . - , X s , . - - , X s + e , M ) (3)

(income) I = P N + ~ (4)

where

Zi = commodities produced and consumed by the farm household (i = 1,

Cj = market goods (including financial assets) obtained outside the house-

M = nominal money balances; X , = inputs used in household and farm production with d inputs used in

N = agricultural production; P = price of agricultural production; r = nonfarm income; and I = total agricultural household income.

2, ..., n);

hold (j = 1, 2, ..., in);

both farm and household production (h = 1,2, ..., s, . . . , s + e) ;

Assume the following market prices: r, = price of input h, Pi = price of goodj, and r = (nominal) cost of holding money balances. Eq. 1 through J2q. 4 can be rewritten in Lagrangean form as:

s + e rn

h= 1 j = 1 U = U(Z1, Z,, . . . , Z,, C , , C,, . . . , C,) + A(Z- Z rJ, - Z Picj - r M) ( 5 )

The first-order conditions, simultaneously solved for M, yield the demand-for- money balances by the farm firm. The resulting reduced-form equation can be written as:


Aggregating over market goods and other inputs, the demand for money can be derived as:

M = f(r, POI, PG, I ) (7) where

POI = price index of inputs used in household and farm production, and PG = price index of market goods.

Assuming that individuals are not subject to money illusion,* which would require deflation of money, income and price index of inputs by the appropriate price index of market goods, the demand for money in log-linear form can be rewritten as:

(8) In m, = a, + a, In r, + a2 In PI, + a3 In Y,

where m = real money balances; PI = deflated price index of inputs used in household and farm production;

Y = real income of the agricultural sector, and t = a subscript denoting years.

Adding macroeconomic uncertainty variables to Eq. 8, it can be written as:3

In m, = a, + a, In r, + a2 In PI, + a3 In Y, + a, In V, + a5 In V,, + a6 In V, (9)

where V, = interest-rate uncertainty;

V,, = exchange-rate uncertainty, and V, = inflation uncertainty.

It is expected that a, < 0, a2 < 0, a3 > 0, a, > 0, a5 < 0, and a6S 0.

Aggregate Economy The demand for real money balances can be specified as a positive function of real income and a negative function of the opportunity cost of holding money (see Laidler 1985)., This latter variable is represented by the rate of interest. Since no definitive evidence emerges from previous studies in favor of using permanent versus current income, or the short-term versus the long-term rates of interest, the following money demand function in log-linear terms is employed:

(10) In @ = b, + h, Y, + b, In r,

where = the desired stock of real money balances;

r = the short-term rate of interest; Y = real income; and t = a subscript denoting years.

MONEY DEMAND FUNCTIONS 283

Because the adjustment of actual to desired money balances is completed within a year (Smirlock 1982), the aggregate money demand function with the inclusion of macroeconomic uncertainty variables is:

In m, = b, + b, In Y, + b, In r, + b, In V, + b4 In V,, (1 1)

where m, is actual real money balance. It is expected that b, > 0, b, < 0, b, > 0, b4 < 0, and b, 3 0.

+ b, In V,

ESTIMATED DEMAND FUNCTIONS The analysis uses annual U.S. data from 1966 through 1985. In the aggregate model, m is M2 (or currency plus demand deposits and time deposits), Y is real gross national product, and r is the yield on four- to six-month prime commercial paper. In the agricultural model, m is the sum of currency plus time and demand deposits held by the agricultural sector; Y is the sum of farm marketing cash receipts and government payments, value of home consumption, and other farm income; PI is the deflated price index of farm inputs; and r is the same as in the aggregate model. Real variables in agricultural and aggregate models are deflated using the implicit gross national product deflator (1972 = 100).

Uncertainty variables are constructed by estimating autoregressive integrated moving average (ARIMA) processes of the dollar/yen exchange rate, yield on four- to six-month commercial paper, and consumer price index quarterly series. Respective models for the three time series are a random walk, ARIMA (2, 1, 1) and ARIMA (5,1,1). Quarterly observations of squared ARIMA residuals of each model are averaged into annual data. A two-year moving average series of the resulting data is computed. The result is then dated as the final year of the corre- sponding two-year moving average period and is used as the associated measure of uncertainty.

Results of agricultural and aggregate money demand functions are presented in Table 1. Each function is estimated with and without uncertainty variables. The aggregate demand equation excluding uncertainty variables is estimated by Cochrane-Orcutt procedure to correct for autocorrelation (rho = 0.54; t-value = 2.57). Remaining equations are estimated using ordinary least squares method.

The models 'appear to be well specified judging from the R2s and f-ratios of estimated parameters. The signs of all coefficients, except the negative but insignificant coefficient of interest-rate uncertainty in the agricultural demand equation, are consistent with theoretical expectations. Functions including uncertainty variables show higher R2s than those that do not. Uncertainty variables explain a higher proportion of the variation in money in agricultural than in aggregate models.

The interest rate enters with the expected negative sign, but the coefficient is significant at the 5% level for agricultural equations alone. Estimated interest-rate elasticity of money demand is - 0.05 for the aggregate economy and - 0.20 for

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(-

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(-

5.96

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(-

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1.59

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the agricultural sector. A t-test for testing equality of coefficients between agricultural and aggregate equations indicates that coefficients are significantly different at the 1% level (t-value = 6.91).5 These results suggest that policy tools, such as open market operations, have a greater immediate impact on agriculture’s money demand relative to the demands of other sectors, probably because of the higher capital intensity in agriculture.

Real income is positively and significantly associated with real money balances in each regression. Estimated income elasticities are lower for agriculture (0.8 1) than for the aggregate economy (1.7 1) under functions excluding uncertainty variables. This pattern reverses, however, when uncertainty variables are included, with income elasticities for agriculture and the aggregate economy of, respectively, 1.60 and 1.33.

Results also indicate that farm operators and households hold less money when prices of factors of production increase.

Exchange-rate risks has the expected negative sign in each equation; the coefficient is, however, significant for the agricultural equation only. Estimated elasticities for agriculture and the aggregate economy are, respectively, -0.041 and -0.007. This result corroborates the notion that the agricultural sector is more exchange-rate sensitive relative to other sectors because of its heavy reliance on export markets. Because the exchange rate is a monetary variable (Frenkel1983), these results further suggest that open market operations have a larger initial impact, via the exchange rate, on money demand in agriculture than in other sectors of the economy.

Coefficients of inflation uncertainty and interest-rate uncertainty are both positive and significant at the 1% level in the aggregate money demand equation. Both variables are statistically insignificant in the agricultural demandequation (although the coefficient of interest-rate uncertainty was negative). These results suggest that, compared with agriculture, other sectors of the economy are more sensitive to uncertainty surrounding inflation and interest rates, probably because of asset fixity in agriculture. The results further imply that policy decisions of the Federal Reserve intended for changing money demand should take into consideration policy impacts on both the level and uncertainty of interest rates.

PARAMETER STABILITY TESTS Parameter stability of estimated models is tested by utilizing three different methods:

the Cooley-Prescott variable parameter regression, Brown, Durbin and Evans (BDE) squares test, and the Chow test.

The former method tests the hypothesis that estimated parameters are not subject to permanent changes over the sample period. A rejection of the hypothesis implies either a gradual shift or a single-point abrupt shift in the parameter vector. The


Table 2. Alternative stability tests for U.S. money demand functions

Estimated" equation

Cooley -Prescott BDE squares Chow test 9(Q2 test F

Agricultural demand: (1) 0.57 (5.37) 1973 7.70 ( 2 ) 0.00 (0.00) 1973 5.35 Aggregate demand: (3) 0.72 (5.34) 1978 3.64 (4) 0.00 (0.00) 1978 2.54 'Equation numbers correspond to equations in Table 1; Both (2) and (4) were estimated with uncertainty variables whereas (1) and ( 3 ) excluded them.

9 'Z = - where u is the standard error of the estimate.

44)

latter case can be tested by the last two methods, with the BDE squares test indicating the point of structural instability and the Chow test measuring the signifi- cance of this instability (for details see Boughton 1981; Batts and Dowling 1984).

Results of the three tests are presented in Table 2. The Cooley-Prescott test indicates that parameters in money demand equations omitting uncertainty variables are subject to permanent changes. The BDE squares test suggests that if parameter instability is occasioned by an abrupt shift in parameters, then it is likely to be in 1973 and in 1978, respectively, for agricultural and aggregate money demand equations., The Chow test indicates that indeed parameter shifts are statistically significant at the 5% level for both agricultural (F, 05, 4, = 3.26) and aggregate demand functions (Fo,05, 3, ,4 = 3.34).

The Cooley-Prescott method uncovers no permanent changes in the parameter vector of demand equations including uncertainty variables. The Chow test, after including the three uncertainty variables, indicates the stability of parameters for the agricultural function at the 1% level (F0,,,, ,, = 8.26) and for the aggregate functionat boththe 1%and5%levels(F'o~o,,,,, = 6.73;F0,,,,,,, = 3.58). These results highlight the importance of uncertainty variables on specifying money demand functions for both the agricultural sector and the aggregate economy.

CONCLUSIONS AND IMPLICATIONS This paper develops and tests money demand functions for the agricultural sector. Results are compared with those of aggregate money demand function. Factors influencing money held by the agricultural sector include real income, interest rates and the aggregate price level of inputs used in agricultural production.

Results suggest that open market operations and volatility of dollar exchange rates have greater immediate impacts on the demand for money in agriculture than in other sectors of the economy. Impacts from open market operations can occur


either through interest rates or through exchange rates. Over time, the feedback relationships between the sectors may produce other differential effects on money demand.

Results of stability tests indicate that annual money demand specifications omitting uncertainty variables yield unstable econometric relationships. The results underscore the importance of uncertainty variables in money demand functions for both agriculture and the aggregate economy.

NOTES ‘Rausser (1985) reported that, based on physical capital alone, the U.S. agricultural sector is twice as capitalized as the manufacturing sector on a per worker basis. ‘This assumption implies that all real variables, such as the interest rate, real money, real income and real wealth, remain unchanged when the price level increases; that is, a doubling of prices induces economic agents to double their nominal money balances, leaving the demand for real money balances unaffected. 3Recognizing that uncertainty variables are not derived from the framework developed here, the purpose is rather to provide empirical verification of theoretical arguments about uncertainty. 4Assuming money as a durable good, Klein (1974) has developed a micro foundation of this functional relationship within the framework of the general theory of demand. 5

C1-C, t =

N,S; + N,S; N , + N~ ’( N , + N 2 - Z J 1~x-J where C , , C, = coefficient values for variable r from two regression equations; N , , N , = number of observations used to estimate each regression;

S:, s: = variance of the estimated coefficients C , and C,, respectively. See Hays and Winkler (1970) or other statistics books for further information on this

statistical test. 60riginally the Quandt log-likelihood ratio test was used to find the point of structural instability. This test suggested that the shift occurred in 1970. This year then served as a base for splitting the sample into two subsamples in order to perform the Chow test. Since our sample starts with 1966, there are only five observations in our subsample (1966-70) to estimate a regression with six explanatory variables. This rendered the Chow test inap- propriate. In place of the Quandt log-likelihood ratio test, we used the Brown, Durbin and Evans (DBE) squares test. The Quandt log-likelihood ratio test, like any other likelihood process, is more appropriate for large samples.

and

ACKNOWLEDGMENT The authors thankthree anonymous Journal reviewers for helpful comments and suggestions.


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Uncertainty and the Stability of Money Demand Functions for the U.S. Agricultural Sector