Sluggish price adjustments and the link between money and price.

I. 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.

II. 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 process with mean zero and variance [Mathematical Expression Omitted]. However, the posterior expectation of unanticipated money supply depends on local market price, [P.sub.t](z), and thus, it varies across markets.

Since [Mathematical Expression Omitted] is defined as the market clearing price at which supply in (1) is equal to demand in (2), the solution for price [Mathematical Expression Omitted], after substituting for [M.sub.t] from equation (4), can be written as:

[Mathematical Expression Omitted]

where [Lambda](z) = 1/[[[Alpha].sup.s](z) + [[Alpha].sup.d](z)]. Inserting [Mathematical Expression Omitted] into equation (3), we get

[P.sub.t](z) = (1 - [Gamma](z))[P.sub.t-1](z) + [Gamma](z)[1 - [Lambda](z)]E[P.sub.t] + [Gamma](z)[Lambda](z)[[M.sub.t-1] + [g.sub.t] + [u.sub.t] + [[Epsilon].sub.t](z)]. (6)

This price equation is not a reduced-form equation since E[P.sub.t] appears in it. Equation (6) is readily interpreted: [P.sub.t](z) is determined by a set of "demand-pull" variables that include the money supply and the excess demand shifter and a "cost-push" term, E[P.sub.t]. The lagged price captures the effect of gradual price adjustment. Since participants know the prices of their commodities but not the prices in other markets, they form expectations about the economy-wide aggregate price based on [P.sub.t](z) and other available information.

Next, price is determined as a function of exogenous variables by using the method of undetermined coefficients. By utilizing the model's log linearity, a reduced-form solution for the aggregate price is conjectured as:

[P.sub.t] = [[Pi].sub.1][P.sub.t-1] + [[Pi].sub.2][M.sub.t-1] + [[Pi].sub.3][g.sub.t] + [[Pi].sub.4][u.sub.t] (7)

where [Pi]'s are unknown parameters. The aggregate price is determined by its own lag and the current money supply, which, as in (4), consists of [M.sub.t-1], [g.sub.t], and [u.sub.t]. The lagged aggregate price enters the [P.sub.t] equation because the partial adjustment assumption entails that individual market price depends on its lag price (see equation (6)). By realizing that [M.sub.t-1] and [g.sub.t] are fully perceived at time t, whereas the posterior expectation of [u.sub.t] is conditional on market-specific information, the expected aggregate price can be written as:

E[P.sub.t] = [[Pi].sub.1][P.sub.t-1] + [[Pi].sub.2][M.sub.t-1] + [[Pi].sub.3][g.sub.t] + [[Pi].sub.4]E[u.sub.t]. (8)

The key to the formation of the aggregate price expectations is the computation of E[u.sub.t] conditional on the market-specific information, [P.sub.t](z). The conditional expectations of [u.sub.t] are calculated, in effect, by linearly projecting [u.sub.t] on [P.sub.t](z). That is,

[Mathematical Expression Omitted]

Substituting (9) into (8), we find that

[Mathematical Expression Omitted]

The expected aggregate price from (10) is plugged into the market-specific price in (6) to obtain

[Mathematical Expression Omitted]

The general price is obtained by averaging [P.sub.t](z) across all markets(2)

[Mathematical Expression Omitted].

Noting that equations (12) and (7) are equal, the four [Pi] coefficients are determined by matching corresponding terms in the two equations. The resulting solution is

[[Pi].sub.1] = (1 - [Gamma])/(1 + [Lambda][Gamma] - [Gamma]), [[Pi].sub.2] = [Lambda]/([Lambda] + 1/[Gamma] - 1), [[Pi].sub.3] = [Lambda]/([Lambda] + 1/[Gamma] - 1),

and

[Mathematical Expression Omitted].

These [Pi] coefficients and [M.sub.t-1] from equation (4) are substituted into (7) or (12) to obtain the aggregate price [P.sub.t]:(3)

[Mathematical Expression Omitted].

Important results in equation (14) can be readily interfered. First, as in Barro [3, 560], given the current money stock, lagged money stock does not impact the aggregate price,(4) Second, the coefficient of [M.sub.t] is less than one. That is, when prices move sluggishly (i.e., 0 [less than] [Gamma](z) [less than] 1 and thus 0 [less than] [Gamma] [less than] 1), they do not adjust instantaneously to the changes in [M.sub.t]. Consequently, movements in [M.sub.t] are not fully captured by [P.sub.t], and thus, the coefficient of [M.sub.t] is less than one in the Pt equation. This finding confirms the hypothesis that price inertia causes [P.sub.t] to respond less than equiproportionately to the current money stock, and thus, invalidate the conclusion of the policy ineffectiveness proposition.

Third, if prices are perfectly flexible, i.e., [Gamma](z) and [Gamma] are set to one, the coefficients in equation (14) will simplify. Particularly, the coefficients of [M.sub.t] will become one; the lagged prices will drop out; and the ensuing result, after incorporating equation (4), is

[Mathematical Expression Omitted].

In this case, market prices and the aggregate price will change equiproportionately in response to the current money stock changes.

Fourth, the response of aggregate price to changes in unsystematic part of the money growth, [u.sub.t], depends on, in addition to [Gamma], the average elasticity of supply and demand across markets (i.e., [Lambda]). Specifically, given the current money stock, the unanticipated money growth can have negative (positive) effects on market prices if [Lambda] [less than] ([greater than]) 1. This can be seen by examining the numerator of the coefficient of [u.sub.t] in equation (14), which is negative for [Lambda] [less than] 1 and the denominator is always positive.

Fifth, the aggregate price is also a function of its lag because the individual market price depends on its lag price (refer to equation (3)).

III. Empirical Analysis

The framework used in the empirical analysis involves estimation of a policy forecasting equation and a reduced-form price equation. Previous studies by Barro [2; 3], Laumas and McMillin [14], Glick and Hutchison [11], among others, used a two-step procedure: in the first step the money forecasting equation is estimated, and in the second step, the predicted and residual series from the forecasting equation are used, respectively, as the perceived and unperceived money supply growth in the estimation of price equation. Mishkin [18] noted that the two-step procedure ignores possible covariances between the parameters across the money growth and price equations. To remedy this problem, he developed a joint nonlinear procedure in which the forecasting and price equations are simultaneously estimated. For this study, both procedures were used. In the interest of brevity, only the results from the two-step procedure are reported. Furthermore, reporting the results of the two-step procedure allows us a direct comparison of the results of this study to those of Barro [3].

The specification used to forecast the monetary policy is represented by the following equation:

M[G.sub.t] = [X.sub.t-1][Psi] + [u.sub.t] (16)

where M[G.sub.t] is the actual money growth in t, [X.sub.t-1] is the vector of macroeconomic variables pertinent to forecasting M[G.sub.t], [Psi] is the corresponding coefficient vector, and [u.sub.t] is the disturbance term assumed to be generated by a temporally independent white noise and thus uncorrelated with independent variables. The policy forecasting equation is used to decompose the dependent variable into the anticipated and unanticipated components. The predicted values represent the anticipated policy measures and the residuals, the unanticipated measures. Thus, the anticipated money supply growth denoted as [Mathematical Expression Omitted] is equal to [X.sub.t-1] [Psi], and the unanticipated money growth, [Mathematical Expression Omitted], is equal to M[G.sub.t] - [X.sub.t-1] [Psi] = [u.sub.t].

First, the price equation is estimated as a function of unanticipated money growth, and other pertinent variables that influence the aggregate price:

[Mathematical Expression Omitted]

where [P.sub.t] is the log of the GNP deflator, M[S.sub.t] is the log of the money stock, [Epsilon](z) is the error term, n is the number of lags, c is the intercept term, and [Delta] and [Theta] are the coefficients. Following Barro [3], the interest rate (r), real government expenditures deflated with real GNP (G), and time trend (T) are included to explain the movements in the aggregate price.(5)

To test the effectiveness of the anticipated monetary policy in determining the aggregate price, equation (17) is modified to include the anticipated money growth [Mathematical Expression Omitted] as:

[Mathematical Expression Omitted]

where [Beta] is the coefficient vector of the anticipated monetary policy.

Monetary Policy Forecasting Equation

This section deals with specification and estimation of the forecasting equation, also known as feedback rules, of money supply growth. The approach used to specify the feedback rules employs the Granger causality tests in conjunction with Theil's (minimum standard error) criterion to choose the correct lag length of the explanatory variables. Since an appropriate feedback rule should be based on all the available information, the money supply growth was regressed on its own past values and other pertinent monetary policy response macro variables which are readily available to the public for predicting future policy actions. These macro variables include: the real gross national product (GNP), three-month treasury bill rate, inflation rate, nominal GNP growth, unemployment rate, fiscal policy measure, exchange rate, and balance of payments on current accounts.

The first step in the estimation of the feedback equation is to specify an appropriate lag length. Because monetary policies are formulated based on the performance of the macroeconomic variables in the immediate preceding quarters, four to eight lags were considered for each of these variables. Furthermore, as in Click and Hutchison [11], we considered a common lag length for all the explanatory variables. The choice of a common lag length prevents the researchers from searching for alternative specifications that would produce results confirming any a priori belief. Based on Theil's [Mathematical Expression Omitted] criterion, a lag length of seven yielded the highest [Mathematical Expression Omitted]. Following Mishkin [18], we used multivariate Granger tests to determine the significance of these variables in the money supply forecast equation. An F-test, under the null hypothesis that seven coefficients of the individual policy response variables are jointly zero, was carried out. On the basis of this criterion, the lagged money supply growth, fiscal policy measure, unemployment rate, and three-month treasury bill rate were included in the forecast equation.

The OLS estimates of the money supply growth equation based on quarterly data from 1949:1 to 1990:4, with t-statistics in parentheses, are

[Mathematical Expression Omitted]

where MG = M1 money supply growth, F = fiscal policy measure, UN = unemployment rate, IR = change in the three-month treasury bill rate, [Mathematical Expression Omitted] = standard error, and DW = Durbin-Watson statistic. The fiscal policy measure is generated by deflating the change in the real middle-expansion trend budget surplus with potential GNP.(6,7) This measure of fiscal policy is independent of the particular position of the business cycle, and thus, is abstracted from the automatic stabilizing feature of the fiscal policy [14].

Quarterly data are used for the empirical analysis. Data for the GNP deflator, government expenditure, revenues, and real GNP are collected from the National Income and Product Accounts of the United States and various issues of the Survey of the Current Business published by the U.S. Department of Commerce. The data for the money supply and the three-month treasury bill rate are obtained from the St. Louis Federal Reserve Bank. The unemployment rate is collected from the International Financial Statistics.

The F-statistics, reported along with the estimated feedback rules equation, test the explanatory power of the seven lagged values of each variable in predicting the money supply growth. The approximate critical value of F-statistics is 2.05 at the 5% level and 2.70 at the 1% level. The computed F-statistics indicate that all four explanatory variables are significant at the 1% level, and thus, these variables play important roles in predicting the money supply growth. The Durbin-Watson statistic of 2.001 indicates the absence of serial correlation. The lagged values of the money supply growth capture the persistence effects not explained by other independent variables. Sargent and Wallace [20] and Barro [2] have posited that government expenditures and money supply growth have strong interactions. These interactions are evident from the fact that the lagged values of the fiscal policy are significant in predicting the money supply growth. The coefficients of the lagged unemployment rate reflect the counter cyclical response of monetary policy to the unemployment rate. The treasury bill rate captures the policy changes pursued by the government in response to interest rate changes.

With longer time series data as in this study, it is possible that the parameters may not be temporally stable because of policy shifts such as the significant change on the emphasis of interest rates in the formation of monetary policy and the Federal Reserve Operation Procedure changes in 1979. In view of these policy changes, temporal stability of the coefficient estimates was tested for various sample periods using the Chow test. The results reveal that the null hypothesis of stable parameters could not be rejected.(8)

Price Equation

The impacts of the money stock, anticipated and unanticipated monetary policies on the aggregate price level are the focus of this subsection. The predicted values and the residuals from the feedback rules represent the anticipated and unanticipated money growths, respectively. Contemporaneous and lagged values of these anticipated and unanticipated policy components enter the aggregate price equation as explanatory variables. First, the price effects of money supply are determined by estimating equation (17) with the current money stock and unanticipated money growth as regressors. The effect of anticipated money growth is analyzed by estimating equation (18). As noted previously, the interest rate, government expenditures, and time trend are included to gauge the variations in price movements.

The time period for the estimation of the price equation is 1954:1 to 1990:4.(9) Correction for autocorrelation was carried out to ensure the error term [[Epsilon].sub.t] is white noise so that spurious regression phenomenon could be avoided. The price equation is estimated with a fourth-order serial correlation, which generally eliminates most autocorrelation in quarterly macroeconomic time series data. The price equation also includes a polynomial distributed lag (PDL) with a fifth-order polynomial and an endpoint constraint. Earlier studies found that the test results are affected by the lag length (the value of n in equations (17) and (18)) of the perceived and unperceived policy measures [18]. For instance, Mishkin [18] opts for a longer lag by noting that exclusion of relevant variables will result in invalid test statistics; in contrast, inclusion of irrelevant variables will at worst only decrease the power of tests and expound rejections even more telling, but will not yield incorrect test statistics. In view of this suggestion, we estimate the model with a lag length of 20.

Table I reports the results of the effects of the log of the money stock, unanticipated money growth, interest rate, government expenditure, and time trend on the aggregate price level. The results indicate that the fit of the equation is good as reflected by the significance of many of the estimated coefficients and high explanatory power shown by the [R.sup.2] of 0.98. The following important observations can be made from the results in Table I.

The policy ineffectiveness proposition predicts a coefficient of one for the log of the money stock in the price equation as elucidated in Barro [3, 559 and 562]. In contrast, the sluggish price adjustment model predicts that the effect of the log of the money stock will be less than one. The estimated coefficient of the log of the money stock of 0.545 (with standard error of 0.048) is significantly less than one. This result does not lend support to Barro's [3] conclusion that there is a one-to-one effect of the log of the money stock on the log of the aggregate price. Thus, these empirical results do not confirm the conclusions of the policy ineffectiveness proposition, rather they provide strong evidence to the theoretical results of the sluggish price adjustment model.

Barro [3, 559-60 and 564] concludes that for given values of current money stock, interest rates, and other explanatory variables, the current and past values of the unanticipated money growth have negative effects on the price level.(10) Barro [3] included only five lags of unanticipated money growth in the estimation of the price equation in obtaining this result. Mishkin [18] [TABULAR DATA FOR TABLE I OMITTED] suggests that it is important to include longer lags of money growth because exclusion of these lags may lead to incorrect results. In line with Mishkin's [18] conclusion, a longer lag length of 20 used in this study seems appropriate as shown by the significant coefficient estimates of longer lags (Table I). The estimated coefficients of unanticipated money growth through lag seven are negative, which support Barro's [3] results that unperceived money growth has a negative effect on aggregate price for given values of current money stock, interest rates, and government expenditure.

However, the coefficients of the unanticipated money growth after seven lags are positive, and in particular many of the coefficients of longer lags are significant. Thus, use of longer lag lengths, which is the difference from Barro's [3] analysis, generates results that the unanticipated money growth has positive impacts on price in the long run. This result supports the view that inflation in response to money supply shocks is likely to fall at first but will rise in the long run, which would be the case particularly if the economy is beset with high unemployment [21].

The positive impacts of unperceived money growth is also consistent with the partial-information rational expectation model presented in the theoretical section. According to this model, the unanticipated money supply growth is misinterpreted as a market-specific shock because market participants with imperfect information cannot distinguish between aggregate and market-specific shocks. As a result, it takes sometime for the agents to react to the shocks, which explains why the unanticipated money growth has negative impacts in the initial period. Once the agents realize the shocks they respond by increasing prices, which illustrates the positive effects in the later periods. The sum of the coefficient estimates of the unanticipated money growths, which is positive, imply that a 1 percent increase in the unperceived money supply growth will eventually cause the log of aggregate price level to increase by the magnitude of 2.44. Thus the empirical results provide evidence that the unanticipated money growth has a positive effect on the price level.

Other explanatory variables - the interest rate and government expenditures - are positive and significant, which corroborate Barro's [3] findings. The interest rate (the three-month treasury bill rate) variable, r, is included to capture the effect of changes in the expected inflation rates. In addition, the interest rate plays a crucial role in explaining recent movements in the price level. For instance, during the recession from 1990 to 1993, the interest rate steadily declined and reached an all time low in recent history, and inflation was also at relatively low levels.

The government expenditure variable, G, is measured as real government expenditures deflated by real GNP. Thus, movements in this variable denote the changes in government expenditure relative to GNP. A persistent expansionary fiscal policy would lead to higher price levels. This result is supported by the positive and significant coefficient estimate for G. The time trend, T, is included to capture the trend movements in the aggregate price. The positive and significant coefficient estimate of the time trend variable indicates the general upward movement of the aggregate price. Also, since the dependent variable is the log of the aggregate price, inclusion of the time trend as an additional regressor induces stationarity in the price level. This approach assumes that the time series of aggregate price is characterized as stationary fluctuations around a deterministic trend.

Barro [3] argues that given the money stock and the unanticipated money growths, the current and lagged values of actual money growth-or equivalently, the current and lagged values of anticipated - money growths are irrelevant to the determination of the price level.(11) Table II presents the estimated results of the price equation (18) with the inclusion of the anticipated money growths as additional explanatory variables.

The fit of the equation is good as reflected by the significance of the estimated coefficients and high explanatory power of the anticipated and unanticipated money growths. The estimated coefficients of the anticipated money growths are significant, except for the [Mathematical Expression Omitted] and [Mathematical Expression Omitted], as shown by the t-statistics. The high significance level of almost all the coefficients imply that the results unambiguously reject the hypothesis that the anticipated money growths are irrelevant to the determination of prices, and lead to a conclusion that the anticipated monetary policies do matter in effecting the aggregate price. Since the log of the money stock is included as a separate variable, the sign of the anticipated money growth is negative, which is consistent with Barro's [3] result. The sum of the coefficients is significant, indicating that the anticipated monetary policy is not neutral in the long run. The results of long-run non-neutrality can be attributed to the fact that prices adjust only gradually, and thus, the impacts of anticipated money persist over a longer period of time.

[TABULAR DATA FOR TABLE II OMITTED]

The estimated coefficient of the log of money stock variable is 0.715 (with standard error of 0.06), which again unambiguously rejects the hypothesis of the equiproportionate effect of the log of money stock on the log of aggregate price. The effects of unanticipated money growths are similar to the results in Table I in that the impacts are negative only in the first few quarters and positive in the remaining quarters. Of the negative coefficients only the impact of the current unanticipated money growth is significant. On the other hand, most of the positive impacts are significant (from lag 9 through 19). Thus, unanticipated money supply plays an important role in capturing the short-run price fluctuations. In addition, the sum of the coefficient estimates is significant (at the 10 percent level) implying that unperceived monetary policy does influence the aggregate price in the long run.

The impacts of the interest rate, government expenditures, and time trend are positive and significant as in Table I. The price equation was also estimated with the log of the money stock, interest rate, government expenditure, time trend, and anticipated money growths only as explanatory variables. The results of this equation, which are not presented here in the interest of brevity, indicate that the estimated coefficient of the log of the money stock is 0.629 with a standard error of 0.057, and thus, do not confirm the hypothesis of a unit coefficient. The effects of the anticipated money growths are similar to the results shown in Table II. The results of this equation are available upon request.

IV. Conclusions

Differing assumptions regarding price level adjustments to macroeconomic policy changes contribute to some of the long standing disputes between monetarists and Keynesians. Monetarists believe that the economy is comprised of markets with perfectly flexible prices. On the contrary, the Keynesian economy is characterized by nominal rigidities. Perfect flexibility or stickiness of prices has important implications for the conduct of monetary policy. Theoretical studies by Fischer [9], Phelps and Taylor [19], Blinder and Mankiw [5], and Gordon [12] have shown that nominal rigidities provide a role for the anticipated aggregate demand policies to influence the real economic variables. Empirical studies by Gordon [12], Mishkin [18], and Laumas and McMillin [14] have also provided evidence that the anticipated aggregate demand policies have real effects.

The current study highlights the less than perfect link between the money supply and prices when prices adjust sluggishly. More specifically, this paper develops a theoretical model using the partial information-localized market framework of rational expectation models to show that if nominal prices adjust sluggishly, the money stock will have a less than equiproportionate effect on the aggregate price. The empirical evidence provides distinct support to the theoretical findings of the sluggish price adjustment model and rejects the conclusions of the policy ineffectiveness proposition. In particular, the coefficient of the log of the money stock is significantly less than one, ranging from 0.55 in the model with only the unanticipated monetary policy to 0.72 in the model with both the unanticipated and anticipated monetary policies. The unanticipated monetary policy has significant positive impacts on the aggregate price level. The anticipated monetary policy also has a strong influence in determining the aggregate price level.

The policy implications are that there is no dispute that monetary authorities can affect the price level. However, the extent to which they can influence the price depends on the sluggishness of prices in various markets. For the monetary authorities to effectively control inflation, they need to have a good understanding of price adjustment mechanisms in various markets. This understanding is also crucial if the monetary authority wants to stabilize real economic variables such as real GNP and unemployment. Price sluggishness in various markets and the lack of understanding of the price adjustments by policy makers can explain why the economy recovers slowly from recession, and why counter-active policies are often ineffective in curing recession. Given the significance of price stickiness for the conduct of monetary policy, it is worthy of further research to identify major sectors with differing degree of price adjustments, examine the causes of imperfect price flexibility, and quantify the response of nominal and real variables in these sectors to monetary policies.(12) This research issue is currently being explored by the author.

1. Studies that use the framework of nonclassical rational expectation models do view that expectations are rational, but consider wages and prices as imperfectly flexible. The primary conclusions of these studies are that the policy ineffectiveness proposition does not hold, and that anticipated policies do influence real economic variables such as output and unemployment. Chief contributors of these models are Fischer [9], Phelps and Taylor [19], Gordon [12], Mishkin [18], and Blinder and Mankiw [5].

2. The averages of [Gamma](z) and [Lambda](z) are denoted by [Gamma] and [Lambda], respectively. The average of [[Epsilon].sub.t](z) is zero.

3. The solutions of [Pi] coefficients can be substituted into (11) to obtain the market price [P.sub.t](z) and analyze the effects of money supply components on [P.sub.t](z) and also on relative price, i.e., the difference between the market price and the aggregate price.

4. I am indebted to an anonymous reviewer for clarifying this point.

5. Even though these variables are additionally included in the empirical model, it can be readily illustrated that the theoretical analysis of the previous section can be modified to show that the aggregate price equation (14) depends on these three variables. More specifically, equation (7) can be modified to conjecture that the aggregate price is also the function of these three variables, and that the rest of the analysis is carded out as before. The end results are that r, G, and T also enter the price equation (14).

6. Data for the real middle-expansion budget surplus was calculated by deflating the difference between the nominal receipts and expenditures by the GNP deflator. The potential GNP was generated from the predicted values from the regression of the log of real GNP on a constant and a time trend with first-order autocorrelation correction.

7. This definition of fiscal policy measure was introduced by Dornbusch and Fischer [8] in their popular macro-economic text and also employed by Laumas and McMillin [14].

8. For instance, the Chow tests for the sample split at 1969:4, 1975:1, and 1979:4 produced F-statistics of 0.9, 1.1, and 1.7, respectively. These computed F-statistics are not significant at the 1% level, indicating that the parameter estimates of feedback rules are stable.

9. Though the raw data starts at 1947:1, because of the long lags of anticipated and unanticipated policy measures in the price equation and the additional seven lags in the policy forecasting equation, the starting period for the estimation is 1954:1.

10. I gratefully acknowledge an anonymous reviewer for clarifying Barro's conclusion.

11. The equivalency of the test of irrelevancy of actual money growths or anticipated money growths can be shown by substituting [Mathematical Expression Omitted] for [Mathematical Expression Omitted] in equation (18) and rewriting the ensuing equation as

[Mathematical Expression Omitted]

where [Phi] = [[Delta].sub.i] - [[Beta].sub.i]. Thus, this equation with the actual money growths is analogous to the equation (18) with the anticipated money growths.

12. For example, Dexter, Levi, and Nault [7] found that in the Canadian Economy the regulated prices respond relatively slower than the unfettered prices to money supply changes.

References

1. Barro, Robert J., "Rational Expectations and the Role of Monetary Policy." Journal of Monetary Economics, January 1976, 1-32.

2. -----, "Unanticipated Money Growth and Unemployment in the United States." American Economic Review, March 1977, 101-15.

3. -----, "Unanticipated Money, Output, and the Price Level in the United States." Journal of Political Economy, August 1978, 549-80.

4. Blinder, Alan S., "Why are Prices Sticky? Early Results from an Interview Study." American Economic Review, May 1991, 89-96.

5. ----- and N. Gregory Mankiw, "Aggregation and Stabilization Policy in a Multicontract Economy." Journal of Monetary Economics, June 1984, 67-86.

6. Devadoss, Stephen and E. Kwan Choi, "Factor Price Stabilization and the Competitive Firm." American Journal of Agricultural Economics, August 1991, 741-56.

7. Dexter, Albert S., Maurice D. Levi, and Barrie R. Nault, "Freely Determined versus Regulated Prices: Implications for the Measured Link Between Money and Inflation." Journal of Money, Credit, and Banking, May 1993, 222-30.

8. Dornbusch, Rudiger and Stanley Fischer. Macroeconomics. Second Edition. New York: McGraw-Hill, 1981, pp. 438-39.

9. Fischer, Stanley, "Long-term Contracts, Rational Expectations, and the Optimal Money Supply Rule." Journal of Political Economy, February 1977, 191-205.

10. Frydman, Roman, "Sluggish Price Adjustments and the Effectiveness of Monetary Policy Under Rational Expectations: A Comment." Journal of Money, Credit, and Banking, February 1981, 94-102.

11. Glick, R. and M. Hutchison, "New Results in Support of the Fiscal Policy Ineffectiveness Proposition." Journal of Money, Credit, and Banking, August 1990, 288-304.

12. -----. "Price Inertia and Policy Ineffectiveness in the United States, 1890-1980." Journal of Political Economy, December 1982, 1087-117.

13. Hercowitz, Zvi, "Money and the Dispersion of Relative Prices." Journal of Political Economy, April 1981, 328-56.

14. Laumas, G. S., and Douglas W. McMillin, "Anticipated Fiscal Policy and Real Output." Review of Economics and Statistics, August 1984, 468-71.

15. Lothian, James R., "Equilibrium Relationships Between Money and Other Economic Variables." American Economic Review, September 1985, 828-35.

16. Lucas, Robert E., Jr., "Expectations and the Neutrality of Money." Journal of Economic Theory, April 1972, 103-24.

17. McCallum, Bennett T., "Price Level Adjustments and the Rational Expectations Approach to Macroeconomic Stabilization Policy." Journal of Money, Credit, and Banking, November 1978, 418-36.

18. Mishkin, Fredric S., "Does Anticipated Monetary Policy Matter? An Econometric Investigation." Journal of Political Economy, January 1982, 22-51.

19. Phelps, Edmund S. and John B. Taylor, "Stabilizing Powers of Monetary Policy Under Rational Expectations." Journal of Political Economy, February 1977, 163-90.

20. Sargent, Thomas J. and Neil Wallace, "Rational Expectations, the Optimal Monetary Instruments and Optimal Money Supply Rule." Journal of Political Economy, April 1975, 241-54.

21. Stein, Jerome L., "Can the Central Bank Achieve Price Stability?" Review, The Federal Reserve Bank of St. Louis, March/April 1994, 175-203.