Sluggish price adjustments and the link between money and price.

• Author: Devadoss, Stephen

1. Introduction

   The simple quantity theory of money asserts that, because the velocity of money and full-employment output are constants, if the money supply doubles, the price level must also double [15]. This view of the quantity theory of money is also supported by the policy ineffectiveness proposition put forward by Lucas [16], Sargent and Wallace [20], and Barro [1]. The policy ineffectiveness proposition asserts that real variables like output and unemployment respond only to unanticipated movements in the money supply, but do not respond to anticipated money supply associated with the systematic feedback rules. One of the premises essential to the validity of this proposition is the perfect flexibility of prices. The corollary of the policy ineffectiveness proposition, as expounded by Gordon [12] in invalidating this proposition, is that because output does not respond to anticipated money supply changes and remains at the natural level, the price level responds contemporaneously and proportionately to the anticipated changes in the money supply. This conclusion is also consistent with Barro's hypothesis that "perceived movements in the money stock ... imply equiproportionate, contemporaneous movements in the price level" [3, 565-66]. This one-to-one relationship between the anticipated money supply and the price level has also been shown theoretically by Barro [1] and Hercowitz [13]. It is this conclusion that needs to be tested by accounting for the speed of adjustments of prices.

   The purpose of this study is to explore theoretically and empirically the link between money supply and price levels by incorporating a gradual price adjustment mechanism. More specifically, this study examines (a) the one-to-one relationship between the log of current money stock and the log of the price level purported by Barro [3]; (b) effects of unanticipated money growth on the aggregate price, and (c) importance of anticipated money growth in determining the price level, given the current money stock and the current and lagged values of the unanticipated money growth.

   The key element of the study is the realization that the economy is comprised of markets with differing degrees of price adjustments. Numerous cases of price stickiness can be identified in modern economies as enumerated in survey work by Blinder [4]. Also, for instance, Devadoss and Choi [6] observe that the U. S. agricultural program's price-fixing policies such as price support and storage schemes impart rigidity to commodity prices. Fischer [9] and Phelps and Taylor [19] identify long-term contracts as the cause for nominal rigidities. Gordon [12] notes that adjustment costs and decentralization of decision making can prevent prices from instantaneous and full adjustment to policy shocks. Dexter, Levi, and Nault [7] cite regulated prices for such items as public transportation, property taxes, and telephone and postal charges as reasons for price inertia. Because price sluggishness has such important implications for the new-Keynesian economics or nonclassical rational expectation models, it is important to study the speed of the response of the price level to the money stock, as well as anticipated and unanticipated growth in the money supply.(1)

   In section II, a theoretical model is developed by incorporating gradual price adjustments within a basic equilibrium model of the variety put forward by Lucas [16], Barro [1], and Hercowitz [13] to show that the money stock has less than an equiproportionate effect on the price level. This result is particularly appealing because the localized-market framework of the rational expectation model, which showed a one-to-one relationship between the anticipated money and the price level, is used to invalidate this equiproportional link.

   Section III contains the empirical analysis. More specifically, a money supply forecasting equation is estimated to decompose the actual money growth into perceived and unperceived components. Then the price equation is estimated with current money stock, contemporaneous and lagged values of anticipated and unanticipated monetary policy components, and other pertinent macroeconomic variables as regressors. The empirical results are unfavorable to the hypothesis of a one-to-one relationship between log of money stock and log of prices; rather they lend distinct support to conclusions of a gradual price adjustment model. Also, it is found that the anticipated monetary policy exerts significant influence in determining the aggregate price. The final section concludes with a brief summary and policy implications.

2. Theoretical Model

   The object of this section is to develop a theoretical model by incorporating gradual price adjustments within a basic equilibrium model of the partial information-localized market framework of a rational expectation model to show that the perceived money has less than an equiproportionate effect on the aggregate price.

   According to the partial-information rational expectations model of Hercowitz [13], which is a modified version of the model developed by Barro [1], the economy is comprised of numerous markets indexed by z. Agents in each market have full information about the relevant aggregate variables with a one-period lag, and current information of local market price, [P.sub.t](z). Market participants do not know the current prices in other markets. The key elements of this model are individuals possessing incomplete current information and making supply and demand decisions by responding to relative prices as they are locally perceived. Because of lack of information, participants are not able to differentiate between the aggregate and market-specific shocks. As a result, individuals misinterpret unanticipated aggregate shocks that cause changes in relative prices as market-specific shocks and, in turn, respond by changing their demand and supply behavior to these shocks, which leads to real effects of unperceived aggregate shocks. However, anticipated money growth is perceived by agents in all markets as an economy-wide effect and results in a proportional change in prices. Consequently, anticipated money growth does not affect the relative prices and real economic variables.

   The point of departure of this study is to incorporate sluggish price adjustments in this imperfect information model and demonstrate that the anticipated money has less than an equiproportionate effect on the aggregate price. Sluggish price adjustments in the model capture the various degree of price stickiness across markets.

   Following Hercowitz [13], the log-linear forms of supply and demand functions for commodity z are represented as:

   [Mathematical Expression Omitted]

   [Mathematical Expression Omitted]

   The operator E denotes the expectation conditional on all the available information in market z. [P.sub.t] is the log of economy-wide aggregate price. The supply of commodity z, [Mathematical Expression Omitted], depends on the perceived relative price in that market. The demand for commodity z, [Mathematical Expression Omitted], depends on the perceived relative price and the aggregate shock, M - E[P.sub.t]. The stochastic disturbances [Mathematical Expression Omitted] and [Mathematical Expression Omitted] capture relative supply and demand shifts, respectively. It is assumed that the excess demand shifter, [Mathematical Expression Omitted], is independent and normally distributed with mean zero and variance [Mathematical Expression Omitted].

   Prices in a market may move sluggishly because factors such as adjustment costs, sales contracts, price regulation, government price support policies, and decentralized planning can prevent prices from adjusting instantaneously. As in McCallum [17] and Frydman [10], price sluggishness emulates the partial adjustment formula:

   [Mathematical Expression Omitted]

   where [Mathematical Expression Omitted] is the market clearing price at which supply equals demand. The range of [Gamma](z) from zero to one implies that the degree of price flexibility varies across markets. Markets with [Gamma](z) values closer to zero have more rigid prices. On the other hand, markets with [Gamma](z) values closer to one have fairly flexible prices. Values of [Gamma](z) equal to one, of course, imply perfectly flexible prices. It should be pointed out that sluggish price adjustments are not incompatible with the rational expectation approach. As elucidated by Gordon [12], economic agents realize the price inertia, and thus, take this into account, along with other relevant past information, in forming the expectations rationally.

   To complete the model, the growth rate of money supply, comprising systematic and random components, is specified as:

   [M.sub.t] - [M.sub.t-1] [equivalent to] [Delta][M.sub.t] [equivalent to] [m.sub.t] = [g.sub.t] + [u.sub.t] (4)

   where [g.sub.t] and [u.sub.t] are anticipated and unanticipated money growth at time t, respectively. Thus, [g.sub.t] is the expected money supply growth based on all economy-wide information shared by agents in all markets. Consequently, [g.sub.t] is the same in all markets. The random component, [u.sub.t], is taken to be generated by a temporally independent white noise...