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Inventory behaviour and market power
International
Journal
of Industrial
INVENTORY
Organization
BEHAVIOUR An Empirical
7 (1989) 269-280.
AND
North-Holland
MARKET
POWER
Investigation*
Yakov AMIHUD New York University, NY 10006, USA and Tel Aviv University, Tel Aviv 69978, Israel
Haim MENDELSON University of Rochester, Rochester, NY 14627. USA Final version
received
June
1988
This paper examines the empirical relation between the market power of a firm and the level and variability of its inventories. We suggest that firms with greater market power hold more inventories and that their inventories are more volatile. These hypotheses were tested on a large sample of industrial firms, using two different measures of market power and applying a number of estimation techniques. The results strongly support our hypotheses.
1. Introduction
The relation between the market power of firms and their inventory behaviour is associated with the price rigidity-industrial concentration link, originally proposed by Means’ (1935) ‘administered prices’ thesis and later contested by Stigler and Kindahl (1970). A positive association between price inflexibility and industrial concentration was found by Scherer (1980) and Carlton (1986a, 1986b). Domberger (1987) found a negative relation between industry concentration and its price response to inflation, and Rotemberg and Saloner (1987b) found that inventory response to unemployment is negatively related to industry concentration. The price-smoothing role of inventories’ provides a theoretical link between market power and inventory behaviour. As demonstrated by Amihud and Mendelson (1982, 1983a, 1983b; henceforth A-M), a firm with market power will use inventory as a wedge between the quantity available *The authors acknowledge helpful comments and suggestions by the Editor, Paul A. Geroski, and by an anonymous referee. ‘Clearly, there are additional reasons for holding inventory; see, e.g., Arrow (1958), Mills ( 1962). 0167-7187/89/%3.50
0
1989, Elsevier
Science Publishers
B.V. (North-Holland)
270
Y Amihud and H. Mendelson, Inventory behauiour and market power
for sale and the quantity shipped to market. When supply is excessive, the firm will inhibit a potential price decline by selling only part of the available quantity, storing the remainder in inventory and curtailing production. Similarly, when demand is relatively high, the firm will deplete its inventories and possibly stock out (and increase production) to take advantage of the favorable prices. Inventories thus absorb demand and supply shocks and enable firms to smooth potentiat price fluctuations or even maintain rigid prices. A-M prove that such price-smoothing inventory policies are optimal for a firm with market power. Since greater market power implies a stronger effect of the firm’s sale quantity on price, it provides a greater incentive for holding inventory to smooth out random fluctuations. Thus, we propose that inventory behaviour is associated with the firm’s market power.2 This paper examines the joint in&a-industry effects of market power on both the level and uariability of inventory. We formulate our hypotheses that both the mean and variance of inventory are increasing functions of the firm’s market power in section 2, and test them empirically in section 3. Our concluding remarks are in section 4. 2. The hypotheses The relation between market power and inventory can be illustrated by contrasting two simple models of the multiperiod competitive firm and the multiperiod monopoly. Compare a monopolistic firm facing a sequence of random downward-sloping demand functions which are independent and identically distributed (i.i.d.) over time to a competitive lit-m which faces a sequence of i.i.d. market prices (horizontal demand functions) which are not affected by the firm’s actions. Both firms are subject to demand shocks observed after their sales decisions. Production takes one period, yielding a random output quantity in the following period. Both firms have to decide in each period on the alfocation of the available quantity (including current production output and accumulated inventory, if any) between immediate sale and storage for the next period. Assume linear production and inventory holding cost functions and that both firms maximize their expected discounted profits. Let the competitive tirm have at the beginning of the period an available quantity x, which is greater than expected due to a positive output shock. Naturally, under perfect competition the probability distribution of the market price P (and, in particular, its expected value E[P]) is independent of the quantity sold by any single firm. If our firm decides to ship quantity q to *Another rationale for a relation between market power and inventory was proposed by Rotemberg and Saloner (1987a): inventories are used in a duopoiy setting to deter deviations from an implicitly collusive agreement, and higher market power is associated with higher inventory.
Y Amihud and H. Mend&on,
lnuentory behaviour and market power
271
the market and to store x-q, its expected revenue will be q. E[P].3 But then, the competitive firm gains nothing by storing x-q: the expected price in the next period is still E[P] which, after discounting, has a present value below E[P], and in addition the firm incurs the inventory holding cost! Thus, the competitive firm will ship the whole quantity x to market. Consider now the analogous situation for a monopolist firm which, unlike the competitive firm, faces a c~ncaue expected revenue function. Having realized a positive output shock, the firm knows that selling a higher quantity will drive down the expected price and the expected marginal revenue. Thus, for a sufficiently large quantity x, the firm will choose to refrain from selling some of it in order to mitigate the associated price decline.4 This is accomplished by storing part of x in inventory and curtailing production for the following period. By the same analysis, if output is unexpectedly low, its sale will bring in a relatively high marginal revenue, inducing the monopoly to deplete inventories and increase production. The declining marginal revenue faced by this firm (i.e., the concavity of the expected revenue function) thus plays an important role in the ‘price smoothing’ motive for holding inventory, suggesting that (other things equal) a firm with greater market power will hold more inventory and will vary its level over time in response to random shocks. A-M (1983a) presented a dynamic multiperiod model to analyze the priceproduction policy of a firm with market power.5 As in the scenario discussed above, the firm faces uncertainty in both demand and output, it has a concave expected revenue function R(.), and its production takes one period. A-M proved that the firm’s optimal sales policy follows a threshold structure: the firm sets a threshold level m such that it will sell all its available quantity up to WI,and will hold any surplus above m in inventory while curtailing production for the next period by the exact amount of the surplus. Given the opening quantity in period t, xr, the carryover inventory will be
‘Note that under demand uncertainty, the firm has to decide on the sale quantity 4 before P is known. 4Consider the extreme case where the expected marginal revenue at x is negative. Then, storing or even disposing of part of x is more profitable than selling it. In general, the firm will act so that the value of the additional revenue it expects to receive in the future for the quantity stored will compensate for the inventory holding cost (including the cost of capital). 5Mills (1962) analyzed the relation between the tirm’s price-cost margin (a measure of market power) and its level of inventory, trading off the cost of stockouts (resulting in lost potential sales) and the cost of carryover inventories. At a higher price-cost margin, the loss associated with a stockout increases whereas the cost of positive carryover inventories remains constant, hence the higher inventory.
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Y Amihud
and H. Mendelson,
Inventory
behaviour
and market
power
(i.e., the positive part of [x,-m]). Denoting the unit inventory by c and the unit production cost by k, the firm determines level m by R’(m) = k -c.
holding cost its threshold
(2)
That is, transferring a unit of product to inventory saves k, the cost of producing a substitute unit, but the firm loses the added revenue that could be realized and pays the inventory carrying cost, a total loss of R’(m) +c. Equating the marginal benefit to the marginal loss gives (2).‘j If we vary the firm’s effective demand function from the downward-sloping demand curve faced by a monopoly to that faced by a competitive lit-m (flat), its elasticity increases and the Lerner (1934) index of monopoly power is reduced. Then, the net loss when refraining from immediate sale increases, and the incentive to hold inventory is lower. From eq. (2), the optimal threshold level m is higher for the more elastic demand curve, hence the inventory (given by the surplus above m) decreases for any given level of the quantity at hand x,. It can be further shown that the quantity produced and hence the quantity at hand - decreases as the demand curve moves towards the competitive (flat) one. It follows that increasing market power increases the average level of inventory. As pointed out above, the price-smoothing effect of inventory is achieved by transforming exogenous shocks into inventory variations rather that into price variations. Thus, for a given probability distribution of the random shocks, smoother prices should be associated with more variable inventories. Since a firm with higher market power has a greater incentive to smooth the sale quantity and price, its inventory should be more variable. This suggests a positive relation between market power and the volatility of inventory.7 By the above analysis, this means that the distribution of the inventory variable I, (= the surplus above the threshold m) is obtained by truncating the distribution of the opening quantity x, at m, retaining only its right tail (in excess of m). Now, lower market power is associated with an increase in the elasticity of demand and a higher threshold level m, thus leaving a less variable (as well as lower) inventory I,. The foregoing discussion leads to two testable hypotheses regarding the 6For a formal proof, see A-M (1983a). ‘We have pointed out that in response to shocks, the monopolist will vary both its inventory and next-period output, whereas a competitive firm will vary neither (under our assumptions). Consistent with this analysis, Smith (1971), Demsetz (1974) and Lustgarten and Mendelowitz (1979) found a significant positive relationship between employment variability and market power (measured by the concentration ratio) across industries. Scherer (1980, Chapter 13) found that across industries, concentration ratios were positively associated with inventory variability.
Y Amihud and H. Mendelson, Inventory behaviour and market power
cross-sectional power:
273
dependence of the level and variability of inventory on market
H,:
Inventory is on average higher for firms with greater market power (after adjusting for sales). H,: The variability of inventory is greater for firms with greater market power (after adjusting for sales).
3. Empirical tests Our hypotheses are that across firms within industries, both the level and the variability of inventory are increasing with market power. Applying the 4-digit SIC industrial classification, we included in our sample industries in the 2xxx and 3xxx groups; these are good-producing manufacturing industries which hold inventories. Our sample consisted of firms with available data in the COMPUSTAT database during 196%1986,* including 38 industries from the 2xxx series with 663 firms and 64 industries from the 3xxx series with 938 firms. The dependent variables in our study are: (i) IA,= the firm’s average level of inventory, and (ii) I vj= the estimated variance of the firm’s inventory, where the subscripts denote firm i in industry j. The data are from the annual financial statements with all variables converted to real terms. Since our key independent variable is the market power of a firm within its industry, we use jrm-specific indices of market power.g Our first measure of a firm’s market power, MPlij, is the Lerner (1934) Index, defined as (price marginal cost)/price, which equals the reciprocal of the elasticity of demand faced by a monopolistic firm.” Correspondingly, MPl, is the price-cost margin of firm i, calculated as [(net sales - cost of goods sold)/net sales] and averaged over the sample period. The second measure of a firm’s market power, MP2,, is the market share of firm i in its industry, j: MP2ij=Sij/[C~~ 1 Sk,]. This measure forms the basis for conventional concentration indices which reflect the inequality in market shares between firms in the industry. For example, when the foursFirms with less than eight consecutive years of data and industries with less than six firms in them were omitted. ‘Other studies in industrial organization on the effects of the industry level of market power apply Indices of concentration such as the four-firm concentration ratio, the Herfindahl index and the Gini coefftcient. “Kwoka (1979) found that industrial price+ost margins are positively correlated with the four-firm concentration ratio and with the Herfindahl index. Hause (1977) discusses the relationship between the Lerner Index and the Cournot-Nash equilibrium solution for the industry. Scherer (1980, Ch. 9) found a positive and significant relation between the industry’s price-cost margin and its four-firm concentration ratio.
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Y Amihud and H. Mendelson, Inventory behaviour and market power
firm concentration ratio is high, the leading four firms have relatively high values of MP2 (and similarly for other industry concentration indices). We thus use two conventional, not unrelated” measures of market power, so that our results are robust to the idiosyncracies of either as a measure of market power. Our inventory equations include a number of natural explanatory variables to control for their effects on inventory behaviour: (i) S, = the firm’s average sales, reflecting its size; (ii) Gij = the growth trend of sales, obtained from the time-series regression of (log) sales on time; (iii) K’S,= the variance of detrended sales; (iv) IZAj=industry average of its firms’ inventory levels; i.e. the industry-j average of the IA, variable; (v) IZF= industry-j average of its firms’ Ivj variable. Variables (i)-(iii) control for obvious firm-specific characteristics which may affect inventory behaviour. In particular, one expects the level and variability of inventory to be strongly associated with the level and growth rate of sales, and inventory volatility to be positively associated with the volatility of sales. Variables (iv) and (v), the industry-averages of the two dependent variables, capture industry characteristics which affect inventory behaviour and control for them when testing the effects of market power. Thus, we estimate the effects of increasing market power on the mean and variance of the firm’s inventory relative to their industry levels. This enables us to estimate the effects of the !%rn’s market power on its inventory while controlling for industry-specific variations.” Our model consists of the following two equations,
(3) log Z ~~= bo + b, . log MP,
+ bz . log S, + b3 ’ log I’S,
+b,.Gij+b,~lOgZZ~~&E;,
where the market power variable MP,
(4) is
either
MPI,
or MP2ij,
E and
E’ are
“If the industry equilibrium is characterized by a Nash equilibrium, then MPl and MP2 are known to be proportional. ‘*The industry-means of the dependent variables account for variables which a&ct inventory at the industry level but not at the individual firm’s level relative to the industrv. Thus, the estimated coeffkients on the firms variables reflect the effect of these factors conditional on the industry factors.
Y Amihud and H. Mendelson, Inventory behaviour and market power
275
residuals, ak and bk (k =O, 1,. . . , 5) are constant coefficients, and the functional form assumes constant elasticities.r3 The estimated market-power coefficients, a, and bl, reflect the cross-firm covariance between market power and the level and variability of inventory conditional on the other firm characteristics as well as on the industry averages. Our hypotheses are: H,: the level of inventory is increasing in market power, i.e., a, ~0; and H,: inventory variability is increasing in market power, i.e., bl ~0. An important problem which affects the estimation of the two-equation model (3)-(4) is the endogeneity of the market-power variable MPl, the price-cost margin, and perhaps MP2 as well. The problem arises since factors which affect price and inventory behaviour also affect the price-cost margin, so the two may be jointly co-determined. To resolve this problem for our two-equation system, we used the Three Stage Least Squares (3SLS) estimation technique, taking the market power variables as endogenous and using the other variables, together with the industry dummy variables, as instruments. The industry dummies enable to fully capture the industry effects on the market-power variables. By using the 3SLS full-information technique, we take advantage of the covariance between the residuals sij and .s; of eqs. (3)-(4). The 3SLS estimates of (3)--(4) are presented in table 1. We estimated separately each of the two major industry groups 2xxx and 3xxx, since the latter includes more durable goods industries, and the separate estimation allows for differences in the coefficients between the two groups. The results strongly support both our hypotheses, H, and H,: the effects of market power on the level and variability of inventory, reflected in the coefficients of both market power variables, are positive and highly significant for both industry groups. In all estimates, the effect of market power on the mean and variance of inventory is higher for industry group 3xxx than for group 2xxx, reflecting the fact that the 3xxx industries .produce more durable goods. The estimated elasticities of average inventory with respect to sales are sightly (and significantly) less than unity in all the equations, implying that the inventory/sales ratio decreases with sales (perhaps due to economies of scale suggested by Economic Order Quantity models). The results in table 1 indicate that the market power effects are of real quantitative significance. The magnitudes of the coefficients imply that market power has a sizeable effect on inventory, an effect which has been so far overlooked. Doubling a firm’s market power, as reflected by its price-cost margin, will be associated with a 35.47% increase in its average inventory in IsThe logarithmic transformation made the non-negative variables conform more closely with the normal distribution. By the Kolmogorov-Smimov nonparametric test, the distribution of the original variables was significantly non-normal, whereas the distribution of the transformed variables was insignificantly different from normal.
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Y Amihud and H. Mendelson, Inventory behaviour and market power
Table
1
Regressions of the Mean and Variance of Firms’ Inventories by the Three Stage Squares method and using White’s heteroskedastic-consistent estimators.
Industry group
Dependent variable
Market power MP
(a) Market power index= MPl 2xxx
3xxx
(relative
Sales variance vs gross
Sales growth G
0.438 (6.39) (6.79)
0.958 (67.82) (61.52)
0.02 (1.10) (1.09)
- 2.03 ( - 6.00) (-6.01)
IV
0.929 (5.84) (6.01)
1.81 (55.75) (52.47)
0.534 (12.41) (12.41)
- 2.33 ( - 2.97) (-2.33)
IA
0.624 (9.65) (9.79)
0.977 (108.54) (97.34)
IV
1.71 (9.61) (9.65)
1.93 (78.94) (75.88)
IV
Industry IIA
averages IIV
profit margin)
IA
(b) Market power index= MP2 2xxx IA 0.116 (4.38) (3.88)
3xxx
Average sales S
Least
0.02 1 (1.60) (1.45)
-0.971 (-5.14) ( - 4.06)
0.582 (16.42) (14.93)
0.419 (0.81) (0.67)
(market share) 0.847 - 0.006 (30.34) ( - 0.32) (27.66) ( - 0.29)
- 1.39 ( - 4.20) ( - 4.27)
0.197 (2.88) (2.80)
1.63 (22.71) (20.65)
0.465 (11.22) (10.54)
IA
0.138 (7.46) (7.86)
0.817 (40.49) (43.38)
- 0.026 (-2.16) (-2.12)
-0.083 ( - 0.52) ( - 0.47)
IV
0.356 (6.98) (7.37)
1.52 (27.87) (29.21)
0.447 (13.60) (13.31)
2.79 (6.46) (5.28)
‘t values are in parentheses. The lower t values heteroskedastic-consistent estimates with 3SLS.
0.09 (3.94) (3.58) 0.09 (3.43) (3.30) 0.085 (6.00) (6.22) 0.101 (5.56) (5.41)
0.186 (5.67) (4.54) 0.160 (3.77) (3.42)
- 0.980
(- 1.27) (-
1.02)
were calculated
0.192 (8.61) (9.30) 0.230 (7.95) (8.24) using
White’s
(1980)
industry group 2xxx, and with a 54.11% increase in group 3xxx. Given the average firm’s level of inventory - $62.34 million in group 2xxx and $53.79 million in group 3xxx (all in 1967 prices) - this implies an average increase of $22.11 million and $29.11 million in the level of inventory in groups 2xxx and 3xxx, respectively. The corresponding percentage increase in the variability of inventory, measured by its variance, is 90.40% for industry group 2xxx and 227% for group 3xxx. Using market share as a measure of market power, the estimated effects on the mean and variance of inventory are still sizeable, although lower. In all these estimates, the effect of market power is distinct from the effect of size, which is accounted for by the sales variable. A natural econometric problem which comes up in this cross-section study is that of heteroskedasticity, due to possible differences in the residual
E Amihud and H. Mendelson, Inventory behauiour and market power
211
variances across firms. We applied White’s (1980) method to estimate heteroskedastic-consistent standard errors which were then used to calculate the t-statistics (see table 1). The significance of the key coefficients is clearly retained. The estimates in table 1 allow for different coefficients for the 2xxx and 3xxx industry groups. To test whether this separation is called for, we compared the results of a pooled estimation, which restricted the regression coefficients to be the same for the two industry groups, to the results of the unrestricted estimation of table 1. The resulting F-statistics exceeded the critical F value at the 1% significance level, strongly rejecting pooled estimation. Our results also confirmed the advantages of jointly estimating eqs. (3)-(4) by 3SLS: the estimated correlation coefficient between the residuals of eqs. (3) and (4) was 0.76 for the 2xxx industries and 0.64 for the 3xxx industries. To examine the robustness of our results, we also estimated (3) and (4) separately using OLS. The OLS results were quite similar to those in table 1, and the estimated coefficients of the market power variables were of the same order of magnitude. Our estimations allowed the regression coefficients to vary between industry groups 2xxx and 3xxx, but assumed that they are the same for all industries within these groups. A far less restrictive estimation allows for different coefficients in each industry. We estimated separately for each industry j the two-equation model
logI~j==b,j+b,jlogMPlij+b,jlOgSij+b,jlOg
V’S~j+b~jGij+s~j,
(6)
which yields a separate coefficient vector for each industry j. Naturally, the variables ZZAj and IZVj which served to control for the industry characteristics in (3)-(4) need not appear in model (E+(6). Also, here we can use only the first market power variable MPl (the price-cost margin) since MP2 (market share) is proportional to the firm’s sales which are included in the equations. Most importantly, in this model all the estimated coefficients akj, bkj (k=O, 1,2 ,..., 4), as well as the variances of the residuals and the correlations between them, are allowed to vary between industries without restriction. We estimated model (5)-(6) for industries with at least 8 firms, resulting in a sample of 81 industries. We obtained a coefficient vector for each industry and averaged the estimated coefficients across all 81 industries. Summary statistics for these 81 vectors are shown in table 2. The estimated coefficient a, of the market-power variable MPl in the average-inventory eq. (5) was 0.214, with a c-statistic of 2.80. The coefficient of MPl in the inventoryvariance eq. (6) was 0.501, with a t-statistic of 2.61, also strongly significant.
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E Amihud and H. Mendelson, Inventory behaviour and market power
Table 2 Summary statistics for the estimated coefficients of model (S)-(6) and the corresponding statistics. Dependent variable
Independent variable
IA
Ml’1 S vs G
IV
MPl s VS G
Mean
Standard deviation
0.214 0.981 -0.009 - 1.077
0.690 0.126 0.150 3.809
0.501 1.931 0.463 0.256
1.73 0.265 0.453 11.118
t value 2.80 70.31 -0.555 -0.254 2.61 65.68 9.19 0.21
test
Range
t-value for standardized coefficients
0.206 0.986 0.006 - .0.714
5.947 0.873 0.855 31.401
1.32 186.09 - 1.70 -7.36
0.405 1.950 0.484 0.629
12.158 1.249 2.570 86.469
6.70 119.30 21.33 2.77
Median
medians of the regression coefficients of MPl were close to the means: 0.206 and 0.405 in eqs. (5) and (6), respectively. The estimated coefficients may be drawn from distributions with unequal variances, which calls for a modified c-test. We standardized the coefficients, dividing each by its estimated standard error from the regressions of the system (5)-(6). This enabled us to test the significance of the estimated coefficients by testing whether the means of the standardized coefficients (which are asymptotically normal with unit variance) are significantly different from zero. The results, presented in the last column of table 2, show that the estimated coefficients of the market power variable are highly significant, with c-statistics of 7.32 for the mean inventory equation and 6.70 for the inventory-variance equation. Finally, since model (5)-(6) includes only firm-related variables, we tested whether there is an industry concentration effect in addition to the estimated firm effect. We thus jointly estimated the effect of the industry’s four-firm concentration ratio, CR4, on the intercept coefficients and the market power coefficients of (5)-(6). The model includes four equations of the form The
Cij = tli
+ pi
log (CR4j) + vii,
where i is an equation index (i= 1,2,3,4), j is an industry index u=1,2,...,81), and the dependent variables Clj=aej, C,j=a,j, C~j=b,j and Cdj= blj were obtained from model (5)-(6). The joint estimation (by the Seemingly Unrelated Regression method) was called for because of the considerable correlations between the four coefficients, and the regressions were weighted by the standard errors of each of the estimated coefficients (C,) to account for obvious heteroskedasticity. If industry concentration has a positive effect on inventory in addition to the intra-industry effects, the
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Y Amihud and H. Mendelson, Inventory behaviour and market power
intercept coefficients u,,~ and boj should be positively related to CR4, i.e., PI and /I3 should be positive. If the intra-industry relation between inventory and market power is affected by the industry’s concentration, b2 and p4 should be different from zero. The results of the joint estimation were as follows:
PI =0.58 (t= 1.86); p2 =0.15 (t=0.95); B3=0.61 (t=2.36);
~,.,=0.13(t=1.00).
This suggests a positive (inter-industry) relation between industrial concentration and both the mean and variance of inventory. 4. Conclusion This paper suggested that inventories are higher and more volatile in firms with greater market power. These hypotheses were tested on a large samples of industrial firms, using two different measures of market power and applying a number of estimation techniques. We accounted for the endogeneity of the market-power variables, for the correlations between the estimated mean and variance of inventory, for heteroskedasticity and for the possible variability of the coefficients across industries. The results strongly supported our hypotheses. Our findings are consistent with the well-known positive relationship between market power and price rigidity. Firms with greater market power have a greater incentive to use inventories to cushion demand and supply shocks, substituting sales and production between periods. For example, firms whose sales decisions affect prices will prefer, in time of excess supply, to hoard inventory (and cut production) rather than allow prices to fall. Our findings thus contribute to the understanding of the link between industrial organization and the transmission mechanism of shocks into economic activity.14 “‘See A-M (1982a,1982b) and Carlton (1986b) individual firms and macroeconomic phenomena.
for the link between
the inventory
policy
of
References Amihud, Y. and H. Mendelson, 1982a, The output-inflation relationship: An inventoryadjustment approach, Journal of Monetary Economics 9, 163-184. Amihud, Y. and H. Mendelson, 1982b, Relative price dispersion and economic shocks: An inventory adjustment approach, Journal of Money, Credit and Banking 14, 390-398.
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Y Amihud and H. Mendelson, Inventory behaviour and market power
Amihud, Y. and H. Mendelson, 1983a, Multiperiod sales-production decisions under uncertainty, Journal of Economic Dynamics and Control 5, 249-265. Amihud, Y. and H. Mendelson, 1983b, Price smoothing and inventory, Review of Economic Studies L, 87-98. Arrow, K.J., 1958, Historical background, in: K.J. Arrow, S. Karlin and H. Scarf, Studies in the mathematical thoery of inventory and production (Stanford University Press, Stanford, CA). Carlton, D.W., 1986a, The rigidity of prices, American Economic Review 76, 637658. Carlton, D.W., 1986b, The theory and the facts of how markets clear: Is industrial organization valuable for understanding macroeconomics?, Mimeograph, forthcoming, in: R. Schmalensee and R. Willig, eds., Handbook of Industrial Organization (North-Holland, Amsterdam). Demsetz, H., 1974, Where is the new industrial state? Economic Inquiry 12, l-12. Domberger, S., 1987, Relative price variability and inflation: A disaggregated analysis, Journal of Political Economy 95, 547-566. Hause, J.C., 1977, The measurement of concentrated industrial structure and the size distribution of firms, Annals of Economic and Social Measurement 6/l, 73-107. Judge, G.G., W.E. Griffiths, R.C. Hill and T. Lee, 1980, The Theory and practice of econometrics (John Wiley & Sons). Kwoka, J.E., 1979, The effect of market share distribution on industry performance, Review of Economics and Statistics 61, 101-109. Lerner, A.P., 1934, The concept of monopoly and the measurement of monopoly power, Review of Economic Studies 1, 157-175. Lustgarten, S. and A.I. Mendelowitz, 1979, The covariability of industrial concentration and employment fluctuations, Journal of Business 52, 291-304. Maddala. G.S.. 1980. Econometrics (McGraw-Hill. New York). Means, G., 1935, Industrial prices and their relative inflexibility Senate Document 13, 74th Coneress. 1st Session (U.S. Government Printing Oflice. Wash&ton. DC). Mills, EYS., 1963, Price, Output and Inventory Policy (Wiley, New York). Rotemberg, J.J. and G. Saloner, 1987a, The relative rigidity of monopoly pricing, American Economic Review 77,917-925. Rotemberg, Julio J. and Garth Saloner, 1987b, The cyclical behaviour of strategic inventories, Working paper (Stanford University, Stanford, California). Smith, D.S., 1971, Concentration and employment fluctuations, Western Economic Review 9, 267-277. Stigler, G.J. and J.K. Kindahl, 1970, The Behavior of Industrial Prices (National Bureau of Economic Research, New York). White, H., 1980, A heteroskedasticity-consistent covariance matrix estimator and direct test for heteroskedasticity, Econometrica 48, 817-838.
Journal
of Industrial
INVENTORY
Organization
BEHAVIOUR An Empirical
7 (1989) 269-280.
AND
North-Holland
MARKET
POWER
Investigation*
Yakov AMIHUD New York University, NY 10006, USA and Tel Aviv University, Tel Aviv 69978, Israel
Haim MENDELSON University of Rochester, Rochester, NY 14627. USA Final version
received
June
1988
This paper examines the empirical relation between the market power of a firm and the level and variability of its inventories. We suggest that firms with greater market power hold more inventories and that their inventories are more volatile. These hypotheses were tested on a large sample of industrial firms, using two different measures of market power and applying a number of estimation techniques. The results strongly support our hypotheses.
1. Introduction
The relation between the market power of firms and their inventory behaviour is associated with the price rigidity-industrial concentration link, originally proposed by Means’ (1935) ‘administered prices’ thesis and later contested by Stigler and Kindahl (1970). A positive association between price inflexibility and industrial concentration was found by Scherer (1980) and Carlton (1986a, 1986b). Domberger (1987) found a negative relation between industry concentration and its price response to inflation, and Rotemberg and Saloner (1987b) found that inventory response to unemployment is negatively related to industry concentration. The price-smoothing role of inventories’ provides a theoretical link between market power and inventory behaviour. As demonstrated by Amihud and Mendelson (1982, 1983a, 1983b; henceforth A-M), a firm with market power will use inventory as a wedge between the quantity available *The authors acknowledge helpful comments and suggestions by the Editor, Paul A. Geroski, and by an anonymous referee. ‘Clearly, there are additional reasons for holding inventory; see, e.g., Arrow (1958), Mills ( 1962). 0167-7187/89/%3.50
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for sale and the quantity shipped to market. When supply is excessive, the firm will inhibit a potential price decline by selling only part of the available quantity, storing the remainder in inventory and curtailing production. Similarly, when demand is relatively high, the firm will deplete its inventories and possibly stock out (and increase production) to take advantage of the favorable prices. Inventories thus absorb demand and supply shocks and enable firms to smooth potentiat price fluctuations or even maintain rigid prices. A-M prove that such price-smoothing inventory policies are optimal for a firm with market power. Since greater market power implies a stronger effect of the firm’s sale quantity on price, it provides a greater incentive for holding inventory to smooth out random fluctuations. Thus, we propose that inventory behaviour is associated with the firm’s market power.2 This paper examines the joint in&a-industry effects of market power on both the level and uariability of inventory. We formulate our hypotheses that both the mean and variance of inventory are increasing functions of the firm’s market power in section 2, and test them empirically in section 3. Our concluding remarks are in section 4. 2. The hypotheses The relation between market power and inventory can be illustrated by contrasting two simple models of the multiperiod competitive firm and the multiperiod monopoly. Compare a monopolistic firm facing a sequence of random downward-sloping demand functions which are independent and identically distributed (i.i.d.) over time to a competitive lit-m which faces a sequence of i.i.d. market prices (horizontal demand functions) which are not affected by the firm’s actions. Both firms are subject to demand shocks observed after their sales decisions. Production takes one period, yielding a random output quantity in the following period. Both firms have to decide in each period on the alfocation of the available quantity (including current production output and accumulated inventory, if any) between immediate sale and storage for the next period. Assume linear production and inventory holding cost functions and that both firms maximize their expected discounted profits. Let the competitive tirm have at the beginning of the period an available quantity x, which is greater than expected due to a positive output shock. Naturally, under perfect competition the probability distribution of the market price P (and, in particular, its expected value E[P]) is independent of the quantity sold by any single firm. If our firm decides to ship quantity q to *Another rationale for a relation between market power and inventory was proposed by Rotemberg and Saloner (1987a): inventories are used in a duopoiy setting to deter deviations from an implicitly collusive agreement, and higher market power is associated with higher inventory.
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the market and to store x-q, its expected revenue will be q. E[P].3 But then, the competitive firm gains nothing by storing x-q: the expected price in the next period is still E[P] which, after discounting, has a present value below E[P], and in addition the firm incurs the inventory holding cost! Thus, the competitive firm will ship the whole quantity x to market. Consider now the analogous situation for a monopolist firm which, unlike the competitive firm, faces a c~ncaue expected revenue function. Having realized a positive output shock, the firm knows that selling a higher quantity will drive down the expected price and the expected marginal revenue. Thus, for a sufficiently large quantity x, the firm will choose to refrain from selling some of it in order to mitigate the associated price decline.4 This is accomplished by storing part of x in inventory and curtailing production for the following period. By the same analysis, if output is unexpectedly low, its sale will bring in a relatively high marginal revenue, inducing the monopoly to deplete inventories and increase production. The declining marginal revenue faced by this firm (i.e., the concavity of the expected revenue function) thus plays an important role in the ‘price smoothing’ motive for holding inventory, suggesting that (other things equal) a firm with greater market power will hold more inventory and will vary its level over time in response to random shocks. A-M (1983a) presented a dynamic multiperiod model to analyze the priceproduction policy of a firm with market power.5 As in the scenario discussed above, the firm faces uncertainty in both demand and output, it has a concave expected revenue function R(.), and its production takes one period. A-M proved that the firm’s optimal sales policy follows a threshold structure: the firm sets a threshold level m such that it will sell all its available quantity up to WI,and will hold any surplus above m in inventory while curtailing production for the next period by the exact amount of the surplus. Given the opening quantity in period t, xr, the carryover inventory will be
‘Note that under demand uncertainty, the firm has to decide on the sale quantity 4 before P is known. 4Consider the extreme case where the expected marginal revenue at x is negative. Then, storing or even disposing of part of x is more profitable than selling it. In general, the firm will act so that the value of the additional revenue it expects to receive in the future for the quantity stored will compensate for the inventory holding cost (including the cost of capital). 5Mills (1962) analyzed the relation between the tirm’s price-cost margin (a measure of market power) and its level of inventory, trading off the cost of stockouts (resulting in lost potential sales) and the cost of carryover inventories. At a higher price-cost margin, the loss associated with a stockout increases whereas the cost of positive carryover inventories remains constant, hence the higher inventory.
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power
(i.e., the positive part of [x,-m]). Denoting the unit inventory by c and the unit production cost by k, the firm determines level m by R’(m) = k -c.
holding cost its threshold
(2)
That is, transferring a unit of product to inventory saves k, the cost of producing a substitute unit, but the firm loses the added revenue that could be realized and pays the inventory carrying cost, a total loss of R’(m) +c. Equating the marginal benefit to the marginal loss gives (2).‘j If we vary the firm’s effective demand function from the downward-sloping demand curve faced by a monopoly to that faced by a competitive lit-m (flat), its elasticity increases and the Lerner (1934) index of monopoly power is reduced. Then, the net loss when refraining from immediate sale increases, and the incentive to hold inventory is lower. From eq. (2), the optimal threshold level m is higher for the more elastic demand curve, hence the inventory (given by the surplus above m) decreases for any given level of the quantity at hand x,. It can be further shown that the quantity produced and hence the quantity at hand - decreases as the demand curve moves towards the competitive (flat) one. It follows that increasing market power increases the average level of inventory. As pointed out above, the price-smoothing effect of inventory is achieved by transforming exogenous shocks into inventory variations rather that into price variations. Thus, for a given probability distribution of the random shocks, smoother prices should be associated with more variable inventories. Since a firm with higher market power has a greater incentive to smooth the sale quantity and price, its inventory should be more variable. This suggests a positive relation between market power and the volatility of inventory.7 By the above analysis, this means that the distribution of the inventory variable I, (= the surplus above the threshold m) is obtained by truncating the distribution of the opening quantity x, at m, retaining only its right tail (in excess of m). Now, lower market power is associated with an increase in the elasticity of demand and a higher threshold level m, thus leaving a less variable (as well as lower) inventory I,. The foregoing discussion leads to two testable hypotheses regarding the 6For a formal proof, see A-M (1983a). ‘We have pointed out that in response to shocks, the monopolist will vary both its inventory and next-period output, whereas a competitive firm will vary neither (under our assumptions). Consistent with this analysis, Smith (1971), Demsetz (1974) and Lustgarten and Mendelowitz (1979) found a significant positive relationship between employment variability and market power (measured by the concentration ratio) across industries. Scherer (1980, Chapter 13) found that across industries, concentration ratios were positively associated with inventory variability.
Y Amihud and H. Mendelson, Inventory behaviour and market power
cross-sectional power:
273
dependence of the level and variability of inventory on market
H,:
Inventory is on average higher for firms with greater market power (after adjusting for sales). H,: The variability of inventory is greater for firms with greater market power (after adjusting for sales).
3. Empirical tests Our hypotheses are that across firms within industries, both the level and the variability of inventory are increasing with market power. Applying the 4-digit SIC industrial classification, we included in our sample industries in the 2xxx and 3xxx groups; these are good-producing manufacturing industries which hold inventories. Our sample consisted of firms with available data in the COMPUSTAT database during 196%1986,* including 38 industries from the 2xxx series with 663 firms and 64 industries from the 3xxx series with 938 firms. The dependent variables in our study are: (i) IA,= the firm’s average level of inventory, and (ii) I vj= the estimated variance of the firm’s inventory, where the subscripts denote firm i in industry j. The data are from the annual financial statements with all variables converted to real terms. Since our key independent variable is the market power of a firm within its industry, we use jrm-specific indices of market power.g Our first measure of a firm’s market power, MPlij, is the Lerner (1934) Index, defined as (price marginal cost)/price, which equals the reciprocal of the elasticity of demand faced by a monopolistic firm.” Correspondingly, MPl, is the price-cost margin of firm i, calculated as [(net sales - cost of goods sold)/net sales] and averaged over the sample period. The second measure of a firm’s market power, MP2,, is the market share of firm i in its industry, j: MP2ij=Sij/[C~~ 1 Sk,]. This measure forms the basis for conventional concentration indices which reflect the inequality in market shares between firms in the industry. For example, when the foursFirms with less than eight consecutive years of data and industries with less than six firms in them were omitted. ‘Other studies in industrial organization on the effects of the industry level of market power apply Indices of concentration such as the four-firm concentration ratio, the Herfindahl index and the Gini coefftcient. “Kwoka (1979) found that industrial price+ost margins are positively correlated with the four-firm concentration ratio and with the Herfindahl index. Hause (1977) discusses the relationship between the Lerner Index and the Cournot-Nash equilibrium solution for the industry. Scherer (1980, Ch. 9) found a positive and significant relation between the industry’s price-cost margin and its four-firm concentration ratio.
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firm concentration ratio is high, the leading four firms have relatively high values of MP2 (and similarly for other industry concentration indices). We thus use two conventional, not unrelated” measures of market power, so that our results are robust to the idiosyncracies of either as a measure of market power. Our inventory equations include a number of natural explanatory variables to control for their effects on inventory behaviour: (i) S, = the firm’s average sales, reflecting its size; (ii) Gij = the growth trend of sales, obtained from the time-series regression of (log) sales on time; (iii) K’S,= the variance of detrended sales; (iv) IZAj=industry average of its firms’ inventory levels; i.e. the industry-j average of the IA, variable; (v) IZF= industry-j average of its firms’ Ivj variable. Variables (i)-(iii) control for obvious firm-specific characteristics which may affect inventory behaviour. In particular, one expects the level and variability of inventory to be strongly associated with the level and growth rate of sales, and inventory volatility to be positively associated with the volatility of sales. Variables (iv) and (v), the industry-averages of the two dependent variables, capture industry characteristics which affect inventory behaviour and control for them when testing the effects of market power. Thus, we estimate the effects of increasing market power on the mean and variance of the firm’s inventory relative to their industry levels. This enables us to estimate the effects of the !%rn’s market power on its inventory while controlling for industry-specific variations.” Our model consists of the following two equations,
(3) log Z ~~= bo + b, . log MP,
+ bz . log S, + b3 ’ log I’S,
+b,.Gij+b,~lOgZZ~~&E;,
where the market power variable MP,
(4) is
either
MPI,
or MP2ij,
E and
E’ are
“If the industry equilibrium is characterized by a Nash equilibrium, then MPl and MP2 are known to be proportional. ‘*The industry-means of the dependent variables account for variables which a&ct inventory at the industry level but not at the individual firm’s level relative to the industrv. Thus, the estimated coeffkients on the firms variables reflect the effect of these factors conditional on the industry factors.
Y Amihud and H. Mendelson, Inventory behaviour and market power
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residuals, ak and bk (k =O, 1,. . . , 5) are constant coefficients, and the functional form assumes constant elasticities.r3 The estimated market-power coefficients, a, and bl, reflect the cross-firm covariance between market power and the level and variability of inventory conditional on the other firm characteristics as well as on the industry averages. Our hypotheses are: H,: the level of inventory is increasing in market power, i.e., a, ~0; and H,: inventory variability is increasing in market power, i.e., bl ~0. An important problem which affects the estimation of the two-equation model (3)-(4) is the endogeneity of the market-power variable MPl, the price-cost margin, and perhaps MP2 as well. The problem arises since factors which affect price and inventory behaviour also affect the price-cost margin, so the two may be jointly co-determined. To resolve this problem for our two-equation system, we used the Three Stage Least Squares (3SLS) estimation technique, taking the market power variables as endogenous and using the other variables, together with the industry dummy variables, as instruments. The industry dummies enable to fully capture the industry effects on the market-power variables. By using the 3SLS full-information technique, we take advantage of the covariance between the residuals sij and .s; of eqs. (3)-(4). The 3SLS estimates of (3)--(4) are presented in table 1. We estimated separately each of the two major industry groups 2xxx and 3xxx, since the latter includes more durable goods industries, and the separate estimation allows for differences in the coefficients between the two groups. The results strongly support both our hypotheses, H, and H,: the effects of market power on the level and variability of inventory, reflected in the coefficients of both market power variables, are positive and highly significant for both industry groups. In all estimates, the effect of market power on the mean and variance of inventory is higher for industry group 3xxx than for group 2xxx, reflecting the fact that the 3xxx industries .produce more durable goods. The estimated elasticities of average inventory with respect to sales are sightly (and significantly) less than unity in all the equations, implying that the inventory/sales ratio decreases with sales (perhaps due to economies of scale suggested by Economic Order Quantity models). The results in table 1 indicate that the market power effects are of real quantitative significance. The magnitudes of the coefficients imply that market power has a sizeable effect on inventory, an effect which has been so far overlooked. Doubling a firm’s market power, as reflected by its price-cost margin, will be associated with a 35.47% increase in its average inventory in IsThe logarithmic transformation made the non-negative variables conform more closely with the normal distribution. By the Kolmogorov-Smimov nonparametric test, the distribution of the original variables was significantly non-normal, whereas the distribution of the transformed variables was insignificantly different from normal.
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Table
1
Regressions of the Mean and Variance of Firms’ Inventories by the Three Stage Squares method and using White’s heteroskedastic-consistent estimators.
Industry group
Dependent variable
Market power MP
(a) Market power index= MPl 2xxx
3xxx
(relative
Sales variance vs gross
Sales growth G
0.438 (6.39) (6.79)
0.958 (67.82) (61.52)
0.02 (1.10) (1.09)
- 2.03 ( - 6.00) (-6.01)
IV
0.929 (5.84) (6.01)
1.81 (55.75) (52.47)
0.534 (12.41) (12.41)
- 2.33 ( - 2.97) (-2.33)
IA
0.624 (9.65) (9.79)
0.977 (108.54) (97.34)
IV
1.71 (9.61) (9.65)
1.93 (78.94) (75.88)
IV
Industry IIA
averages IIV
profit margin)
IA
(b) Market power index= MP2 2xxx IA 0.116 (4.38) (3.88)
3xxx
Average sales S
Least
0.02 1 (1.60) (1.45)
-0.971 (-5.14) ( - 4.06)
0.582 (16.42) (14.93)
0.419 (0.81) (0.67)
(market share) 0.847 - 0.006 (30.34) ( - 0.32) (27.66) ( - 0.29)
- 1.39 ( - 4.20) ( - 4.27)
0.197 (2.88) (2.80)
1.63 (22.71) (20.65)
0.465 (11.22) (10.54)
IA
0.138 (7.46) (7.86)
0.817 (40.49) (43.38)
- 0.026 (-2.16) (-2.12)
-0.083 ( - 0.52) ( - 0.47)
IV
0.356 (6.98) (7.37)
1.52 (27.87) (29.21)
0.447 (13.60) (13.31)
2.79 (6.46) (5.28)
‘t values are in parentheses. The lower t values heteroskedastic-consistent estimates with 3SLS.
0.09 (3.94) (3.58) 0.09 (3.43) (3.30) 0.085 (6.00) (6.22) 0.101 (5.56) (5.41)
0.186 (5.67) (4.54) 0.160 (3.77) (3.42)
- 0.980
(- 1.27) (-
1.02)
were calculated
0.192 (8.61) (9.30) 0.230 (7.95) (8.24) using
White’s
(1980)
industry group 2xxx, and with a 54.11% increase in group 3xxx. Given the average firm’s level of inventory - $62.34 million in group 2xxx and $53.79 million in group 3xxx (all in 1967 prices) - this implies an average increase of $22.11 million and $29.11 million in the level of inventory in groups 2xxx and 3xxx, respectively. The corresponding percentage increase in the variability of inventory, measured by its variance, is 90.40% for industry group 2xxx and 227% for group 3xxx. Using market share as a measure of market power, the estimated effects on the mean and variance of inventory are still sizeable, although lower. In all these estimates, the effect of market power is distinct from the effect of size, which is accounted for by the sales variable. A natural econometric problem which comes up in this cross-section study is that of heteroskedasticity, due to possible differences in the residual
E Amihud and H. Mendelson, Inventory behauiour and market power
211
variances across firms. We applied White’s (1980) method to estimate heteroskedastic-consistent standard errors which were then used to calculate the t-statistics (see table 1). The significance of the key coefficients is clearly retained. The estimates in table 1 allow for different coefficients for the 2xxx and 3xxx industry groups. To test whether this separation is called for, we compared the results of a pooled estimation, which restricted the regression coefficients to be the same for the two industry groups, to the results of the unrestricted estimation of table 1. The resulting F-statistics exceeded the critical F value at the 1% significance level, strongly rejecting pooled estimation. Our results also confirmed the advantages of jointly estimating eqs. (3)-(4) by 3SLS: the estimated correlation coefficient between the residuals of eqs. (3) and (4) was 0.76 for the 2xxx industries and 0.64 for the 3xxx industries. To examine the robustness of our results, we also estimated (3) and (4) separately using OLS. The OLS results were quite similar to those in table 1, and the estimated coefficients of the market power variables were of the same order of magnitude. Our estimations allowed the regression coefficients to vary between industry groups 2xxx and 3xxx, but assumed that they are the same for all industries within these groups. A far less restrictive estimation allows for different coefficients in each industry. We estimated separately for each industry j the two-equation model
logI~j==b,j+b,jlogMPlij+b,jlOgSij+b,jlOg
V’S~j+b~jGij+s~j,
(6)
which yields a separate coefficient vector for each industry j. Naturally, the variables ZZAj and IZVj which served to control for the industry characteristics in (3)-(4) need not appear in model (E+(6). Also, here we can use only the first market power variable MPl (the price-cost margin) since MP2 (market share) is proportional to the firm’s sales which are included in the equations. Most importantly, in this model all the estimated coefficients akj, bkj (k=O, 1,2 ,..., 4), as well as the variances of the residuals and the correlations between them, are allowed to vary between industries without restriction. We estimated model (5)-(6) for industries with at least 8 firms, resulting in a sample of 81 industries. We obtained a coefficient vector for each industry and averaged the estimated coefficients across all 81 industries. Summary statistics for these 81 vectors are shown in table 2. The estimated coefficient a, of the market-power variable MPl in the average-inventory eq. (5) was 0.214, with a c-statistic of 2.80. The coefficient of MPl in the inventoryvariance eq. (6) was 0.501, with a t-statistic of 2.61, also strongly significant.
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Table 2 Summary statistics for the estimated coefficients of model (S)-(6) and the corresponding statistics. Dependent variable
Independent variable
IA
Ml’1 S vs G
IV
MPl s VS G
Mean
Standard deviation
0.214 0.981 -0.009 - 1.077
0.690 0.126 0.150 3.809
0.501 1.931 0.463 0.256
1.73 0.265 0.453 11.118
t value 2.80 70.31 -0.555 -0.254 2.61 65.68 9.19 0.21
test
Range
t-value for standardized coefficients
0.206 0.986 0.006 - .0.714
5.947 0.873 0.855 31.401
1.32 186.09 - 1.70 -7.36
0.405 1.950 0.484 0.629
12.158 1.249 2.570 86.469
6.70 119.30 21.33 2.77
Median
medians of the regression coefficients of MPl were close to the means: 0.206 and 0.405 in eqs. (5) and (6), respectively. The estimated coefficients may be drawn from distributions with unequal variances, which calls for a modified c-test. We standardized the coefficients, dividing each by its estimated standard error from the regressions of the system (5)-(6). This enabled us to test the significance of the estimated coefficients by testing whether the means of the standardized coefficients (which are asymptotically normal with unit variance) are significantly different from zero. The results, presented in the last column of table 2, show that the estimated coefficients of the market power variable are highly significant, with c-statistics of 7.32 for the mean inventory equation and 6.70 for the inventory-variance equation. Finally, since model (5)-(6) includes only firm-related variables, we tested whether there is an industry concentration effect in addition to the estimated firm effect. We thus jointly estimated the effect of the industry’s four-firm concentration ratio, CR4, on the intercept coefficients and the market power coefficients of (5)-(6). The model includes four equations of the form The
Cij = tli
+ pi
log (CR4j) + vii,
where i is an equation index (i= 1,2,3,4), j is an industry index u=1,2,...,81), and the dependent variables Clj=aej, C,j=a,j, C~j=b,j and Cdj= blj were obtained from model (5)-(6). The joint estimation (by the Seemingly Unrelated Regression method) was called for because of the considerable correlations between the four coefficients, and the regressions were weighted by the standard errors of each of the estimated coefficients (C,) to account for obvious heteroskedasticity. If industry concentration has a positive effect on inventory in addition to the intra-industry effects, the
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Y Amihud and H. Mendelson, Inventory behaviour and market power
intercept coefficients u,,~ and boj should be positively related to CR4, i.e., PI and /I3 should be positive. If the intra-industry relation between inventory and market power is affected by the industry’s concentration, b2 and p4 should be different from zero. The results of the joint estimation were as follows:
PI =0.58 (t= 1.86); p2 =0.15 (t=0.95); B3=0.61 (t=2.36);
~,.,=0.13(t=1.00).
This suggests a positive (inter-industry) relation between industrial concentration and both the mean and variance of inventory. 4. Conclusion This paper suggested that inventories are higher and more volatile in firms with greater market power. These hypotheses were tested on a large samples of industrial firms, using two different measures of market power and applying a number of estimation techniques. We accounted for the endogeneity of the market-power variables, for the correlations between the estimated mean and variance of inventory, for heteroskedasticity and for the possible variability of the coefficients across industries. The results strongly supported our hypotheses. Our findings are consistent with the well-known positive relationship between market power and price rigidity. Firms with greater market power have a greater incentive to use inventories to cushion demand and supply shocks, substituting sales and production between periods. For example, firms whose sales decisions affect prices will prefer, in time of excess supply, to hoard inventory (and cut production) rather than allow prices to fall. Our findings thus contribute to the understanding of the link between industrial organization and the transmission mechanism of shocks into economic activity.14 “‘See A-M (1982a,1982b) and Carlton (1986b) individual firms and macroeconomic phenomena.
for the link between
the inventory
policy
of
References Amihud, Y. and H. Mendelson, 1982a, The output-inflation relationship: An inventoryadjustment approach, Journal of Monetary Economics 9, 163-184. Amihud, Y. and H. Mendelson, 1982b, Relative price dispersion and economic shocks: An inventory adjustment approach, Journal of Money, Credit and Banking 14, 390-398.
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Amihud, Y. and H. Mendelson, 1983a, Multiperiod sales-production decisions under uncertainty, Journal of Economic Dynamics and Control 5, 249-265. Amihud, Y. and H. Mendelson, 1983b, Price smoothing and inventory, Review of Economic Studies L, 87-98. Arrow, K.J., 1958, Historical background, in: K.J. Arrow, S. Karlin and H. Scarf, Studies in the mathematical thoery of inventory and production (Stanford University Press, Stanford, CA). Carlton, D.W., 1986a, The rigidity of prices, American Economic Review 76, 637658. Carlton, D.W., 1986b, The theory and the facts of how markets clear: Is industrial organization valuable for understanding macroeconomics?, Mimeograph, forthcoming, in: R. Schmalensee and R. Willig, eds., Handbook of Industrial Organization (North-Holland, Amsterdam). Demsetz, H., 1974, Where is the new industrial state? Economic Inquiry 12, l-12. Domberger, S., 1987, Relative price variability and inflation: A disaggregated analysis, Journal of Political Economy 95, 547-566. Hause, J.C., 1977, The measurement of concentrated industrial structure and the size distribution of firms, Annals of Economic and Social Measurement 6/l, 73-107. Judge, G.G., W.E. Griffiths, R.C. Hill and T. Lee, 1980, The Theory and practice of econometrics (John Wiley & Sons). Kwoka, J.E., 1979, The effect of market share distribution on industry performance, Review of Economics and Statistics 61, 101-109. Lerner, A.P., 1934, The concept of monopoly and the measurement of monopoly power, Review of Economic Studies 1, 157-175. Lustgarten, S. and A.I. Mendelowitz, 1979, The covariability of industrial concentration and employment fluctuations, Journal of Business 52, 291-304. Maddala. G.S.. 1980. Econometrics (McGraw-Hill. New York). Means, G., 1935, Industrial prices and their relative inflexibility Senate Document 13, 74th Coneress. 1st Session (U.S. Government Printing Oflice. Wash&ton. DC). Mills, EYS., 1963, Price, Output and Inventory Policy (Wiley, New York). Rotemberg, J.J. and G. Saloner, 1987a, The relative rigidity of monopoly pricing, American Economic Review 77,917-925. Rotemberg, Julio J. and Garth Saloner, 1987b, The cyclical behaviour of strategic inventories, Working paper (Stanford University, Stanford, California). Smith, D.S., 1971, Concentration and employment fluctuations, Western Economic Review 9, 267-277. Stigler, G.J. and J.K. Kindahl, 1970, The Behavior of Industrial Prices (National Bureau of Economic Research, New York). White, H., 1980, A heteroskedasticity-consistent covariance matrix estimator and direct test for heteroskedasticity, Econometrica 48, 817-838.