Disequilibrium goods market model for the U.S.A.: a disaggregated approach.

• Author: Rao, B. Bhaskara

1. Introduction

   The aggregate demand and supply model, augmented with rational expectations, is now seen as a synthesis of the new classical and Keynesian economics. Nevertheless a distinction between these rival paradigms is necessary for the justification and formulation of stabilization policies. Buiter [4], Horne and McDonald [8] and Rao and Srivastava [16; 17] showed that these two models can be distinguished by examining whether the goods market is an equilibrium or disequilibrium market.(1) However, within the general equilibrium framework, Keynesian propositions and policies can also be justified with an equilibrium goods market provided that at least one market (e.g., labor market) is a disequilibrium market [7, 54]. Nonetheless there are other reasons for examining the nature of the goods market. Firstly, the specification and estimation of disequilibrium models differ considerably from the standard methods of estimation of equilibrium models. Secondly, if the goods market is a disequilibrium market, it could have important spillover effects on the labor and financial markets. Thirdly the price adjustment coefficient in a disequilibrium goods market indicates how long a given policy measure can significantly affect the real variables.

   In this paper we shall model and test if the aggregate U.S. goods market is an equilibrium or disequilibrium market. We shall utilize the aggregation approach used by Andrews and Nickell [1] to model the aggregate U.K. labor market. This approach, known as smoothing by aggregation, was originally developed by Muellbauer [9] and has become popular in the recent empirical literature for the following reasons. Firstly, the standard aggregate disequilibrium model (switching model) is based on a rather implausible assumption that the whole economy switches discretely between excess demand and excess supply regimes. Therefore smoothing by aggregation in which the micro markets can be assumed to be in different excess demand and excess supply regimes is more appealing. Secondly, this method offers computational advantages over the switching model which is computationally complicated. Thirdly, inferences about the role of the dispersion of excess demand and supply can be drawn from aggregate data without the need for sector specific data.

   The outline of our paper is as follows. Section II discusses the aggregation procedure and the specification of our model. Section III examines the problem of unit roots in the variables. Empirical results for 1946-1991 are given in section IV. Conclusions and limitations are stated in section V.

2. Specification

   Let there be J micro markets (or sectors) assumed to be of equal size for simplicity.(2) Let the demand and supply functions be

   [Mathematical Expression Omitted]

   [Mathematical Expression Omitted]

   (t = 1, 2, . . ., T; j = 1, 2, . . ., J

   where [P.sub.t] is the price at time t, [X.sub.1t] and [X.sub.2t] denote the values of the other explanatory variables, determining the demand and supply respectively. The demand and supply functions denoted by [Mathematical Expression Omitted] and [Mathematical Expression Omitted] should be thought of as the mean demand and supply functions. Therefore [P.sub.t], [X.sub.1t] and [X.sub.2t] are the same for all the J markets. It should be noted that the presence of market specific demand and supply shocks [u.sub.1tj] and [u.sub.2tj] cause a divergence between prices and quantities in these J markets.

   The disturbance term in each equation is assumed to have a variance component type structure with two components, distributed independently, with zero means and finite variances. The first component does not vary over the micro markets while the second component involving the suffix j does. Furthermore we assume that [u.sub.1tj] and [u.sub.2tj] are independently and identically distributed with respect to the subscripts t and j, with the distribution as bivariate normal having 0 means, [Mathematical Expression Omitted] and [Mathematical Expression Omitted] as variances and [Rho] as the correlation coefficient.

   If it is assumed that some micro markets show excess demand while the remaining ones are in excess supply, the Min. condition should be first applied to each micro market separately and then aggregation should be carried out. Thus if [Q.sub.tj] is quantity transacted at time t in the jth market, we have

   [Q.sub.tj] = Min.(D.sub.tj], [S.sub.tj]). (2)

   Aggregation of (2) gives the total quantity transacted in all the micro markets as

   [Q.sub.t] = [summation over 1] [D.sub.tj] + [summation over 2] [S.sub.tj] (3)

   where [[Sigma].sub.1] depicts the aggregation over all micro markets where [Q.sub.tj] = [D.sub.tj], and [[Sigma].sub.2] denotes the aggregation over all markets in which [Q.sub.tj] = [S.sub.tj]. It is obvious from (3) that [Q.sub.t] will always be smaller than both [summation of] [D.sub.tj] where j = 1 to J and [summation of] [S.sub.tj] where j = 1 to J.

   If there are a large number of micro markets so as to form a continuum, the aggregation by summations in (3) can be obtained through integration. Therefore, the average quantity transacted at any given point of time t can be obtained from the following expression

   [Mathematical Expression Omitted]

   where by virtue of bivariate normality of [u.sub.1tj] and [u.sub.2tj], the joint probability density function is given by

   [Mathematical Expression Omitted].

   Evaluating the integrals gives the expression for the average quantity transacted at time t as follows

   [Mathematical Expression Omitted].

   Therefore the total quantity transacted at time t in all the J micro markets is given by

   [Q.sub.t] = J([a.sub.1][P.sub.t] + [a.sub.2][X.sub.1t] + [u.sub.1t])[1 - [Phi]([m.sub.t])] + J([b.sub.1][P.sub.t] + [b.sub.2][X.sub.2t] + [u.sub.2t])[Phi]([m.sub.t]) - J[Sigma][Phi]([m.sub.t]) (4)

   where

   [Mathematical Expression Omitted]

   [Mathematical Expression Omitted]

   [Phi] and [Phi] stand for the probability density and cumulative distribution functions of m respectively. Note that the variance [[Sigma].sup.2] of ([u.sub.1tj] - [u.sub.2tj]) measures the variability of disequilibrium across the markets. It can be also seen that, at any given moment, the level of output will be less the larger is [Sigma].

   The parameters of the model can be estimated if survey data on the state of excess demand are available [14; 19]. One weakness of this approach is that price determination is exogenous and in the absence of survey data it cannot be...