Asymmetric Price Adjustment In a Menu-Cost Model *

Transcription

1 Asymmetric Price Adjustment In a Menu-Cost Model * Jakob B Madsen Department of Economics University of Western Australia Bill Z Yang Department of Economics University of Iowa Abstract. In this paper we demonstrate that the menu-cost model implies asymmetric price adjustment to nominal demand shocks and that the asymmetry is linked to the elasticity of demand and menu costs. These are tested using manufacturing and retailing panel data for the OECD countries. The empirical results give strong support to the menu-cost model. JEL Classification: E3, L16 * Comments from Fhahad Khalil are gratefully acknowledged.

2 1 1 Introduction The menu-cost models of Mankiw (1985) and Akerlof and Yellen (1985) have gained wide acceptance among economists as the leading explanation as to why firms, in the short run adjust quantities instead of prices in response to not too large nominal demand shocks. The menu-cost model suggests that firms only change their prices in the wake of a nominal demand shock if the gain from adjusting prices exceeds the (menu) costs of changing prices. At first inspection it follows that prices are more rigid in manufacturing than in retailing, because retailers have lower menu costs and face a more elastic demand curve than manufacturers. However, in the next section we demonstrate that the implications of menu-cost model are quite different. We show that the menu-cost model implies that firms adjust their prices asymmetrically, and that the asymmetry is linked to menu costs and especially to the elasticity of demand facing the firms; thus the asymmetrical adjustment to nominal demand shocks in the two sectors are different. Using data for retailing and manufacturing for 22 OECD countries over the period 1960 to 1993 we test the implications of the menu-cost model in section 3. Our results are consistent with the predictions of the menu-cost model. We find that prices are flexible upwards, but not downwards and that the downward price stickiness is much more pronounced in manufacturing than in retailing. These results have important macroeconomic implications, which are discussed in section 4. 2 A menu cost model of asymmetric price adjustment To show that the menu cost model implies asymmetrical price adjustment, consider a down stream seller (retailing) and an up stream producer (manufacturer). Let Q = D(p) be the demand function facing the retailer, where Q is quantity demanded and p is price. Suppose that the manufacturer incurs constant unit production costs c and charges the wholesale price p w. Then, the manufacturer seeks to solve 1 max π m = (p w - c)d(p(p w )) p w s.t. p(p w ) = argmax π r = (p - p w )D(p), p which yields first order conditions for the manufacturer (FOC.M) and for the retailer (FOC.R) of 1 This is a version of the double marginalisation model (see Tirole (1988, Ch.4)). In the first stage the manufacturer sets p w ; and in the second stage, the retailer sets p.

3 2 w w p c Dpp ( ( )) w = w w w = 1 p p D'( p( p )) p'( p ) ε m (FOC.M) w p p Dp ( ) = = 1, p pd'( p) ε r (FOC.R) where ε is the elasticity of demand facing the firm. These conditions jointly determine the equilibrium of p * and p w * and in the equilibrium p * = p(p w * ). It follows from comparing (FOC.M) with (FOC.R) that the retailer operates in a more elastic segment on its demand curve than the manufacturer does in the corresponding derived demand curve, provided that p'(p w ) < p/p w. To show that the condition p'(p w ) < p/p w is likely to hold, we derive from the retailer's first order condition the following expression: p'(p w D'( p) ) = w 2 D'( p) + ( p p ) D"( p) Thus, p'(p w ) < p/p w is equivalent to D (p)/[2d (p) + (p - p w ) D (p)] < p/p w, which simply requires that the demand curve D(p) is not too convex. 2 Hence, we have: Proposition 1. If the final demand function D(p) is not too convex in p, then the retailer operates in a more elastic segment on its demand curve than the manufacturer does in the corresponding derived demand curve. 3 Next we examine the relationship between the price elasticity of demand and the net gain from adjusting prices. Let η t be the parameter which represents the state of the demand at time t = 0, 1, where t = 0 represents the last period and t = 1 indicates the current period. Denote the price set in period 0 p 0 and the desired price in period 1 p 1 based on realised η 1. Then the gain from adjusting the price to p 1 can be measured by π( ) = π(p 1 ) - π(p 0 ) = (p 1 - c)d(p 1 ) - (p 0 - c)d(p 0 ) 2 Note that in the equilibrium p/p w > 1. Hence, a stronger version of p'(p w ) < p/ p w is that p'(p w ) = D (p)/[2d (p) + (p - p w ) D (p)] < 1, or equivalently, D (p) + (p - p w ) D (p) < 0. Since the second order condition requires 2D (p) + (p - p w ) D (p) < 0, the condition p'(p w ) < p/p w essentially does not require much more than the second order condition itself. 3 If the manufacturer sets a two-part tariff instead of the uniform price, then the wholesale price will be even lower than that.

4 3 = (p 1 - p 0 )D(p 1 ) + (p 0 - c)(d(p 1 ) - D(p 0 )) = (p 1 - p 0 )D(p 1 )[1 + p 1 (p 0 - c)(d(p 1 ) - D(p 0 ))/p 1 (p 1 - p 0 )D(p 1 )] (p 1 - p 0 )D(p 1 ) [1 - ε (p 0 -c)/p 1 ], From this expression it follows: Proposition 2. As long as a higher state of demand leads producers to desire a higher price and vice versa, then the net gain from adjusting prices is negatively related to the price elasticity of demand in the wake of a positive nominal demand shock, but positively related to the price elasticity of demand in the wake of an adverse nominal demand shock. The intuition behind proposition 2 is the following. If the elasticity of demand is low, a price increase following a positive demand shock has only a marginal impact on sales; thus the firm gains from an upward price adjustment. By contrast, when a price reduction is needed in response to a negative shock, the quantity demanded will only be marginally affected if demand is insensitive to price changes. It follows that there is a low gain from adjusting prices downward and the firm is more reluctant to lower its price. Propositions 1 and 2 jointly imply: Proposition 3. Manufacturers gain more from adjusting their prices upward after a positive nominal demand shock than retailers, whereas retailers gain more than manufacturers by adjusting their price downward after a negative nominal demand shock. Proposition 3 has clear testable implications. However, the tests need to take into account that menu costs are likely to be substantially higher for manufacturing than retailing for the following reasons. 4 Retailers can change prices in a more flexible way than manufacturers because they mainly operate in the domestic spot market. They do not need to print new catalogues and to negotiate new prices with their customers. By contrast, manufacturers are obligated to print new catalogues and to change the contracts with their customers which involves such things as telephone calls and negotiations. If price increases are not based on higher costs, they may create bad will among customers. Furthermore, price changes on manufacturing products sold in the foreign market are complicated by communication difficulties and exchange 4 Menu costs are sometimes defined as the costs of printing catalogues etc. Gordon (1990), however, includes all costs of changing prices such as negotiations, telephone calls, printing of new catalogues, information to the organisation etc, in his definition of menu costs. We follow Gordon's definition here.

5 4 rate fluctuations. Taking into account that manufacturers have higher menu costs than retailers do, Proposition 3 modifies to: Proposition 4. Suppose that menu costs are higher in manufacturing than retailing. Then when there is a positive shock, it is likely that both manufacturers and retailers adjust their prices upwards. However, in response to an adverse demand shock, manufacturers are unlikely to adjust their prices whereas retailers adjust their prices downward. In the next section we turn to empirical testing of the implications of the menu-cost model derived in Proposition 4 using a price mark-up equation. 3 Empirical evidence A standard inflation equation is given by (Nordhaus (1972), Bruno and Sachs (1985)): p va = φ w φθ+ φ yc (1) where a dot over a variable indicates the percentage change of the variable and φ i is a fixed coefficient. Here, p va is the value-added price-deflator, θ is labour productivity, w is total hourly labour costs, and yc is cyclical demand. Denoting retailers' output price p r (consumer prices) and the manufacturing value-added price deflator p m, equation (1) adapted to price-setting in the two markets is p = α p + α t+ α p + α yc + α yc r p im p n (2) p = β w βθ + β yc + β yc m m m p n (3) where p p is manufacturing producer prices of products sold in the domestic market, p im is import prices of manufacturing products, w m is total hourly labour costs in manufacturing, θ m is manufacturing labour productivity, measured as output per hour worked, t is the indirect tax rate, yc p and yc n are positive and negative demand side shocks. In equation (2) consumer prices are determined by input prices plus value-added taxes and aggregate demand shocks. Prices of both

6 5 domestic and foreign products are included to allow for the fact that retailers inputs comprise both domestic and foreign manufactured products. According to Proposition 4, the menu cost model has the two testable implications: H 0 (i): α 4 = β 3 H 0 (ii): β 2 = β 3 H 1 (i): α 4 > β 3 H 1 (ii): β 2 > β 3, where H 1 (i) states that retailers adjust prices downward in response to an adverse demand shock whereas manufacturers are unlikely to do so, and H 1 (ii) states that manufacturers adjust prices upward in the wake of a positive demand shock but are unlikely to adjust prices down in response to an adverse demand shock. Stochastic specification, estimation method and data. Equations (2) and (3) are stochastically specified with all variables, except yc p and yc n, lagged one period to allow for sluggish adjustment. The percentage change variables are approximated by log first differences. The data are pooled across countries to gain efficiency. A further efficiency gain is obtained by allowing for residual correlation across countries. More specifically the following covariance structure is assumed: E(u 2 it ) = σ2 i, E(u it u jt ) = σ ij, i, j = 1, 2, N, and i j, where u is a zero-mean, finite-variance disturbance term, N is the number of cross-sectional units (countries), σ 2 i is the variance for country i and σ ij is the correlation of the disturbance terms across countries. The variance σ 2 i is assumed to be constant over time but to vary across countries (cross-country heteroscedasticity) and the error terms are assumed to be mutually correlated across countries, σ ij, as random shocks are likely to impact on all countries simultaneously. σ 2 i and σ ij are estimated using the feasible generalised least squares method of Kmenta (1986, Ch. 12).

7 6 Fixed effect country dummies are included in all regressions and the general-to-specific model reduction procedure is used with the 1-percent benchmark significance level. Wages are instrumented using the instruments indicated in the notes to table 1. Cyclical demand shocks are identified using cyclical demand shifts in real monetary stock (M1/CPI), real government expenditure, and trade weighted real income as instruments for cyclical real income. Cyclical income is estimated as the residual from regressing the log of real GDP on a time trend and a squared time trend. 5 The exogenous cyclical demand shift variables are calculated using the same principle. Annual data for 22 OECD countries which includes all OECD countries, except Iceland, Mexico, Turkey, and the transitional economies, over the period 1960 to 1993, are used. Hourly total wage costs are measured as compensation to employees divided by employment times weekly hours worked. Labour productivity is measured as real manufacturing GDP divided by hours worked in manufacturing. Estimation results. The results of estimating the stochastic counterparts of equations (2) and (3) are reported in table 1. Before commenting on the results we test whether we can impose the restriction of similar slope coefficients across countries, taking into account that the likelihood of rejecting the null hypothesis, in the classical tests, is an increasing function of the number of observations. We therefore use the alternative formula suggested by Leamer (1978, p114) to calculate the critical value, which overcomes the problem of the classical tests. The critical value computed from Leamer s formula is denoted F(Leamer) in table 1. The F-tests for cross-country slope constancy are clearly well below their critical levels, suggesting that it is valid to impose the same slope coefficients across countries. Table 1. Parameter estimates of equations (2) and (3). The diagnostic tests indicate that the models are well specified. Note that the within country residuals are used to derive the diagnostic tests in order to wipe out individual effects. The 5 Various filters can be used to find cyclical demand. Smith (1992) considers three different filters: 1) the one used above; 2) The first difference filter; and 3) the Hodrick-Prescott filter. Todd finds that these three filters produce cycles which are closely related and that the cyclicality of prices was insensitive to measure.

8 7 coefficients have their expected sign and magnitude. Furthermore, the coefficient on value-added taxes in the estimate of equation (2) is equal to the sum of the coefficients on input prices, which suggests that the estimate is internally consistent. Turning to the predictions of the menu cost model, the Wald tests strongly reject the null hypotheses in favour of the menu cost implied alternative. First, H 0 (i) is rejected: The coefficient estimates reveal that retailers adjust prices downward in response to an adverse demand shock, whereas manufacturers increase their price. Second, H 0 (ii) is rejected in favour of the asymmetrical alternative. The estimates show that manufacturers adjust prices upward in the wake of a positive demand shock but not downward in response to an adverse demand shock. A special concern is the extent to which consumer prices adjust asymmetrically to a demand shock, taking into account the indirect influences from manufacturing producer prices, because consumer prices are more important for aggregate outcomes than manufacturing prices. For instance, the relevant deflator for real balances is consumer prices, and not producer prices, since money transactions are mainly made for consumption purposes (Mankiw and Summers (1986)). The total effect of the asymmetric price adjustment is found by substituting the coefficient estimates of equation (3) into the estimates of equation (2), yielding the long-run coefficient of 0.70 and 0.05 on yc p and yc n. Hence, the total effect is downward rigidity but upward flexibility. 6 As we shall see in the concluding section, this result has important macroeconomic implications. 4 Conclusions and macroeconomic implications As long ago as 1972 Tobin (1972) argued that price adjustment is asymmetric in the sense that positive aggregate demand shocks are more inflationary than adverse demand shocks are deflationary due to two forces: A non-linear Phillips curve, and that the wage inflation is positively related to the variance among markets in excess demand and supply. Similarly, Ball and Mankiw (1994) have demonstrated that in an inflationary environment, positive demand shocks trigger upward price adjustment, whereas adverse demand shocks may not result in lower prices. In the wake of a negative demand shock, the firm has a desire to lower it s relative price. 6 DeLong and Summers (1988) argue that nominal wages are more flexible upward than downward in response to demand shocks. If this asymmetry is taken into account consumer prices will adjust even more asymmetrically to demand shocks than suggested by this estimate.

9 8 However, in the presence of menu costs and trend inflation, it may be optimal for the firm not to change its price because the aggregate inflation will automatically correct the relative price to its desired level in due course. In this paper we have given another reason as to why price adjustment is asymmetric in the presence of menu costs. If the elasticity of demand facing the firm is high, the firm will be reluctant to increase its price in response to a positive demand shock because there is a large revenue loss. However, the revenue gain from lowering its price in the wake of an adverse demand shock is large. Thus, prices are upward, but not downwardly sticky. If, on the other hand, the firm faces a low price elasticity of demand, prices become downwardly sticky. The implications of this feature combined with the fact that menu costs are likely to be substantially higher for manufacturing than retailing, and that retailers face a more elastic demand schedule than manufacturers, are that 1) prices are more flexible upwards than downwards in manufacturing than in retailing; and that 2) retailers adjust prices down in response to an adverse demand shock whereas manufacturers are unlikely to do so. Using data for manufacturing and retailing, we found strong support for the implications of the menu cost model derived in this paper. Furthermore, we found that aggregate prices measured by consumer prices, respond to demand shocks in a highly asymmetric manner. Taking into account that the indirect effects of demand shocks on producer prices feed into consumer prices, we found that consumer prices are quite flexible upward but sticky downward. This result has profound macroeconomic implications. First, it suggests that the output gain in booms is lower than the output loss in recessions. Decreasing real balances counterbalance a positive demand shock; however, an adverse demand shock hardly alters real balances. Hence, an active demand management policy will be able to fill in troughs without shaving off peaks. Second, it implies that sectoral shocks are inflationary. Firms with a higher desired price increase their price; however, the firms with lower desired price do not lower their price symmetrically. This result is consistent with the finding of Fischer (1981) that inflation is positively correlated with relative price variability.

10 9 DATA APPENDIX Value-added price-deflator: Nominal GDP divided by real GDP, OECD, National Accounts, Vol. 1 (NA). Compensation to employees: (NA). Weekly hours worked in non-agricultural activities and in manufacturing: ILO, Yearbook (YB). Employment: OECD, Labour Force Statistics (LFS) and (YB). Indirect and direct tax rates: total indirect and direct taxes divided by nominal GDP (NA). M1: (IFS). Consumer price index: IMF, International Financial Statistics, (IFS). Producer prices: (IFS) and OECD, Main Economic Indicators. Real government expenditure: (NA) GDP: (NA). M1: (IFS). Indirect labour costs: Total hourly labour costs minus direct hourly labour costs (YB). Manufacturing import prices: OECD, Historical Trade Statistics, UN, Statistical Yearbook, World Bank, World Tables, OECD, Trade Statistics and national sources, which are available from the author. Trade weighted income: Total real GDP (NA) in the OECD countries weighted by manufacturing export (OECD, Trade in Commodities) for each country in REFERENCES Akerlof, George and Janet Yellen, 1985, "A Near-rational Model of the Business Cycle with Wage and Price Inertia," Quarterly Journal of Economics, 100, Ball, Laurence and N Gregory Mankiw, 1994, Asymmetric Price Adjustment and Economic Fluctuations, Economic Journal, 104, Bruno, Michael and Sachs, Jeffrey D., 1985, The Economics of Worldwide Stagflation, Harvard University Press: Cambridge, MA. DeLong, J Bradford and Lawrence H Summers, 1988, How Does Macroeconomic Policy Affect Output?, Brookings Papers on Economic Activity, No 2, Fischer, Stanley, 1981, Relative Shocks, Relative Price Variability, and Inflation, Brookings Papers on Economic Activity, No 2, Gordon, Robert, 1990, "What is New-Keynesian Economics?," Journal of Economic Literature, 28, Kmenta, Jan, 1986, Elements of Econometrics, Macmillan. Leamer, Edward E, 1978, Specification Searches: Ad Hoc Inference with Nonexperimental Data. Wiley: NY. Mankiw, Gregory, 1985, "Small Menu Costs and Large Business Cycles," Quarterly Journal of Economics, 100, Mankiw, N Gregory and Lawrence Summers, 1986, Money Demand and Effects of Fiscal Policies, Journal of Money, Credit and Banking, 18, Nordhaus, William D, 1972, "Recent Developments in Price Dynamics," in Otto Eckstein (ed.), The Econometrics of Price Determination, Board of Governors of the Federal Reserve System. Washington D C, Smith, R Todd, 1992, The Cyclical Behavior of Prices, Journal of Money Credit and Banking, 24, Tirole, Jean, 1988, The Theory of Industrial Organization, MIT Press: NY. Tobin, James, 1972, Inflation and Unemployment, American Economic Review, No 62, 1-18.