capacity utilization measures_berndt & morrison

American Economic Association

Capacity Utilization Measures: Underlying Economic Theory and an Alternative ApproachAuthor(s): Ernst R. Berndt and Catherine J. MorrisonSource: The American Economic Review, Vol. 71, No. 2, Papers and Proceedings of the Ninety-Third Annual Meeting of the American Economic Association (May, 1981), pp. 48-52Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/1815691 .

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ECONOMICS OF SLACK CAPACITY

Capacity Utilization Measures: Underlying Economic Theory and an Alternative Approach

By ERNST R. BERNDT AND CATHERINE J. MORRISON*

Measures of industrial capacity utilization (hereafter, CU) have been used extensively in helping to explain changes in the rate of investment, labor productivity and inflation. The CU measures have also been used to obtain indices of capital in use, as distinct from capital stock in place. A number of alternative measures of CU are periodically calculated and published; the 1980 Eco- nomic Report of the President, for example, contains three series, that by the Federal Reserve Board, the U.S. Department of Commerce (Bureau of Economic Analysis) and the Wharton School of Finance. Other publicly available series are those prepared by McGraw-Hill Publishing Company, the U.S. Department of Commerce (Bureau of the Census), and Rinfret-Boston Associates, Inc.

Although a host of CU measures is publicly available, it is not at all clear how one should interpret changes over time in each measure or variations among them. A prin- cipal reason underlying these interpretation problems is that the crucial link between underlying economic theory and the con- structed measure of CU is weak.

One way in which this issue has mani- fested itself in the policy domain over the last five years has been with respect to the uncertain effects of dramatic increases in energy prices on capacity output and on CU. Each of the CU measures noted above is computed in such a way that explicitly ignores any role for energy prices. Yet several times during the last decade, though growth to apparently high rates of CU had

taken place, investment and average labor productivity were much lower than ex- pected, and the rate of price increase much greater. In brief, during the last decade the explanatory power of alternative CU measures has dropped sharply. Some have con- jectured that post-OPEC energy price increases may have brought about major changes in the U. S. economy so that old quantitative relationships between measured CU and investment, labor productivity, and price inflation may have been altered substantially.

In order to assess effects of changes in PE on CU, a re-examination of the notion and measurement of CU is needed, based on the framework of the economic theory of the firm. That is the focus of this paper.

I. Theoretical Foundations

The concepts of capacity output and capacity utilization are inherently short-run notions, conditional on the firm's stock of quasi-fixed inputs. Consider a firm with a production function

(1) Y=f(v, x)

where Y is the flow of output, v is an n x 1 vector of variable inputs, and x is a jX 1 vector of service flows from quasi-fixed inputs (inputs fixed in the short run, but available at increasing marginal costs in the long run). As discussed by W. Erwin Diewert, Lawrence Lau and Daniel McFadden, the optimization problem facing the firm is typi- cally characterized as that of maximizing variable profits (revenue minus variable costs), conditional on output price P, prices of the variable inputs Pv,, and x. An altema- tive framework employed in this paper is

*Professor of applied economics, Massachusetts In- stitute of Technology and Canada Council Fellow, University of British Columbia, respectively. Research support through NSF grant 7910488-DAR is gratefully acknowledged.

48



VOL. 71 NO. 2 ECONOMICS OF SLACK CAPACITY 49

based on recent developments in the theory of duality, and puts forth the optimization problem facing the firm as that of minimizing variable costs, conditional on Y, P, and x. In this dual approach, given ap- propriate regularity condition on the production function (1), there exists a dual variable cost function

(2) Cv=g(Y, Pv, X)

where Cv, is average variable cost. Let Px be the vector of rental prices for the quasi-fixed factors, and define average total cost C as

(3) C=Cv +Cf

where C is average fixed cost. The {efinition of capacity output Y* used

here is that level of output for which C is minimized, i.e.,

(4) Y* = h(Pv, x, PX)

This concept of capacity output-that level of output at the minimum point of the short-run average total cost curve-dates back at least to J. M. Cassells, was sug- gested later by Lawrence Klein, and yet has hardly ever been examined empirically. When there are long-run constant returns to scale, Y* also represents a tangency between the long-run and the short-run average total cost curves. In the more general case when there are nonconstant returns to scale, one can define Y* as that level of output at which the short- and long-run average total cost curves are tangent. Hereafter, however, we shall assume long-run constant returns to scale.

It should be noted in passing that this definition of Y* will generally differ from a capacity output level Y** defined as that level of output maximizing variable profits; generally for a competitive firm, Y** will be greater than (less than) Y* when the exoge- nous output price is greater than (less than) the minimum level of short-run average total costs.

Now define the rate of capacity utilization u as actual output Y over capacity output Y*, i.e, u = Y/ Y*. Until recently, empirical efforts to measure Y* and u have

been hampered by the lack of appropriately flexible functional forms and, more im- portantly, by basic developments in the underlying economic theory. Such limitations were noted by Klein. Theoretical contribu- tions by Diewert, Lau, and McFadden, however, have enriched the range of empirical research possibilities substantially, and in particular now enable one to obtain econometric estimates of Y* and u. Some recent estimates. will be discussed later in this paper.

Given a clear notion of economic capacity output and capacity utilization, we now address the issue of how variations in input prices might affect Y* and u. Assume for the moment that there is only one quasi-fixed factor, physical capital (K). An important issue concerns how a change in the price of a variable input such as energy (E) might affect Y*. In particular, does an increase in PE shift the minimum point of the short-run average total cost curve to the right (increasing Y*), to the left (decreasing Y*), or does it merely shift the average cost curve up- ward without affecting Y*? To the best of our knowledge, no published theoretical research has been done concerning such an issue.

In an unpublished paper, Robert Rasche and John Tatom (1 977b) show that if the variable input (in this case, E) and the fixed input K are Hicks-Allen substitutes (comple- ments), then an increase in PE decreases (increases) Y*; if, however, E and K are independent inputs such that long-run substitution elasticities between E and K are zero, then variations in PE do not affect Y*. Intuitively, this phenomenon can be ex- plained as follows. If E and K were substitu- table inputs, with an increase in PE the firm's long-run optimal K/ Y ratio would increase from, say, KO / Y* to K1 / Y*. This implies that, in the short run, the given level of capital KO corresponds with a smaller Y*. Alternatively, if E and K were complemen- tary inputs, an increase in PE would imply a lower long-run optimal K/ Y* ratio; in the short run, the firm's given level of capital KO would then be associated with a large Y*. Obviously, matters become more compli- cated when there are multiple quasi-fixed factors and/or multiple outputs.



50 AEA PAPERS AND PROCEEDINGS MA Y 1981

In their empirical research, Rasche and Tatom (1977a) assumed a Cobb-Douglas function which implies the assumption of K-E substitutability. Conditional on this Cobb- Douglas assumption, Rasche and Tatom concluded that increases in PE since 1973 have reduced the nation's Y* considerably-by about 10 percent-and that there- fore any expansionary monetary or fiscal policy would be ill-advised. Even though published measures of u might indicate some slack capacity, according to Rasche and Tatom the true economic level of u is considerably higher than the published measures would indicate. Results would have been different, of course, had they not assumed K-E substitutability. Space consider- ations preclude our discussing the empirical evidence here on E-K substitutability vs. E-K complementarity; for a recent review, see Berndt and David Wood. What is clear, however, is that the typical published measures of capacity utilization are not very informative in terms of assessing the economic effects of increases in PE.

Another example illustrating the impor- tance of Y* and u is the effect of increases in PE on the recent productivity slowdown in the United States and other industrialized countries. It has long been known that both multifactor productivity and average labor productivity tend to be procyclical. What has surprised economic observers in recent years is that productivity trends have not f6llowed the traditional procyclical patterns, and have shown very little growth in spite of apparently high and at times increasing levels of CU. Since the published measures of CU might be unreliable, comparison of recent productivity trends with those of earlier periods could be misleading if post- 1973 PE variations had affected Y* and u. Clearly, what is needed is additional theoretical and empirical research on the notion and measurement of Y* and u.

II. Recent Estimates of an Economic Measure of CU

Earlier it was noted that developments in the theory of duality now permit estimation of Y* and u with general functional forms.

Three recent empirical studies in this vein are those of Berndt (1980), Morrison, and of Berndt, Morrison, and G. Campbell Watkins. Based on earlier work by Berndt, Melvyn Fuss, and Leonard Waverman, the dynamic optimization problem facing the firm is specified as that of minimizing the present value of costs, given Y, Pv, Px, increasing marginal internal costs of adjustment for x, and positive initial levels of the quasi-fixed inputs.

In Table 1 we reproduce two alternative measures of economic capacity utilization for U.S. manufacturing, 1958-77; both are taken from Berndt (1980, Table 6), where additional details are provided. The first measure is based on a dynamic cost function model with a single quasi-fixed factor K. The other measure incorporates an ob- servation by Walter Oi that certain types of skilled labor should also be considered as quasi-fixed factors; hence the second measure is based on a dynamic model with two quasi-fixed factors, K and W, where W is hours at work of nonproduction (white col- lar) workers in U. S. manufacturing. For purposes of comparison, we also reproduce in Table 1 the Wharton and Federal Re- serve Board (FRB) measures, as well as estimated ratios of short-run marginal cost to long-run average total cost, evaluated at the actual level of output. These measures assume that input supply curves are per- fectly elastic, and represent the cost infla- tionary consequences of producing at output levels different from Y*.

Several comments are in order. First, the economic measures are always greater than unity, whereas the Wharton and FRB fig- ures are always less than unity. To some extent this can be interpreted as merely a scaling convention, since Wharton and FRB measures approaching 90 percent are typi- cally viewed as signifying very near "full capacity." On the other hand, that the economic measures are greater than unity is informative, for it indicates that production is to the right of the minimum point of the short-run average total cost curve, thereby inducing cost-reducing net investment.

Second, simple correlations among the various measures indicate considerable dif-



VOL. 71 NO. 2 ECONOMICS OF SLACK CAPACITY 51

TABLE I-ALTERNATIVE MEASURES OF CAPACITY UTILIZATION, AND RATIO OF ESTIMATED SHORT-RUN MARGINAL COST TO LONG-RUN AVERAGE TOTAL COST

U.S. MANUFACTURING, 1958-77

Capacity Utilization Model with: SMRC/LRAC Model with: FRB Wharton

Year K Fixed W, K Fixed Measure Measure K Fixed W, K Fixed

1958 1.106 1.091 0.752 0.742 1.015 1.026 1959 1.110 1.118 0.819 0.789 1.013 1.030 1960 1.171 1.131 0.802 0.769 1.024 1.035 1961 1.177 1.130 0.774 0.737 1.026 1.036 1962 1.197 1.145 0.816 0.765 1.027 1.038 1963 1.224 1.167 0.835 0.777 1.031 1.044 1964 1.226 1.164 0.856 0.795 1.031 1.042 1965 1.232 1.190 0.896 0.842 1.030 1.045 1966 1.214 1.170 0.911 0.882 1.027 1.040 1967 1.184 1.129 0.869 0.869 1.026 1.033 1968 1.178 1.119 0.871 0.892 1.024 1.030 1969 1.169 1.108 0.862 0.902 1.025 1.029 1970 1.111 1.026 0.793 0.841 1.018 1.012 1971 1.110 1.052 0.784 0.827 1.017 1.015 1972 1.204 1.139 0.835 0.879 1.033 1.037 1973 1.240 1.185 0.876 0.932 1.040 1.049 1974 1.092 1.079 0.838 0.905 1.012 1.018 1975 1.160 1.096 0.729 0.798 1.030 1.026 1976 1.259 1.170 0.795 0.860 1.051 1.048 1977 1.267 1.183 0.819 0.887 1.055 1.052 Mean 1.182 1.130 0.827 0.834 1.028 1.034

ferences. For the single (two) quasi-fixed factor model, simple correlations between the economic measure and the FRB index are .419 (.523), while those between the economic measure and the Wharton index are only .244 (.140). The simple correlation between the Wharton and FRB index is .605. Both economic measures of CU indicate relative peak years in 1965, 1973, and 1977, while peak years for the FRB index are 1966, 1973, and 1977. The Wharton relative peaks are in 1966, 1969, 1973, and 1977. Economic capacity utilization measures are lowest in 1958-59, 1970-71 and 1974-75, essentially coinciding with low points of the Wharton and FRB measures, although the latter both indicate slight downturns in 1961.

The economic capacity utilization measures differ from the Wharton and FRB values in one very important respect, however. According to the FRB measure, the relative peak years of 1973 (.876) and 1977 (.819) were considerably smaller than the 1966 all-time peak (.911), whereas, for the

economic measures the 1973 and 1977 peaks are virtually identical. The Wharton index differs slightly; its all-time peak is 1973 (.932), and the 1966 (.822) and 1977 (.887) peaks are about equal but smaller than that in 1973. One implication of these results is that if one believes these measures of economic CU, then the much heralded 1973-77 productivity slowdown relative to 1965-73 cannot be attributed to the end year 1977 being of lower capacity utilization.

Finally, although not reported in Table 1, we have calculated the effects of increased PEon Y* in U.S. manufacturing. For 1977 the estimated elasticity of Y* with respect to PE is positive (due to E-K complementarity), but quite small. Berndt (1980) reports a 1977 estimate of this elasticity as 0.021 for the only K-fixed model, and 0.047 for the model with both W and K fixed. Hence these fig- ures suggest that although energy price increases have affected Y* in U.S. manufacturing, the quantitative magnitude is mod- est. These small positive estimates contrast



52 AEA PAPERS AND PROCEEDINGS MA Y 1981

sharply with those of Rasche and Tatom (1977a), who used a Cobb-Douglas model and estimated that the elasticity of Y* with respect to PE was about -.10.

II1. Concluding Remarks

We have argued that greater attention should be focussed on developing better notions and measures of CU; we have also reproduced several recent economic measures of CU, and have shown that they often differ considerably from the more familiar FRB and Wharton measures. The Wharton index, it will be recalled, is essentially a ratio of actual Y to potential output, where the latter is based on previous peak values of the output- capital ratio and cumulative net investment. Factor prices and quantities of noncapital inputs are not in- corporated. Another measure of CU is really an engineering notion of capital utilization rather than an economic measure of capacity utilization; this is based on the ratio of actual electricity consumption to the maxi- mum possible electricity consumption, where the latter is obtained using the rated horse- power capacity of electric machinery. For an example of such a procedure, see Murray Foss.

Although we are somewhat reluctant to advocate publication of yet another series of CU, we hope that applied researchers in the future will devote greater attention and care to the economic theory underlying the concept of capacity output, and will publish series which can then be interpreted more clearly.

REFERENCES

E. R. Berndt, "Energy Price Increases and the Productivity Slowdown in United States Manufacturing," in The Decline in Pro- ductivity Growth, Fed. Reserve Bank Bos- ton Conference Proceedings, No. 22, Bos- ton 1980.

, M. A. Fuss, and L. Waverman, "A Dynamic Model of Costs of Adjustment and Interrelated Factor Demands, with an Empirical Application to Energy De-

mand in U.S. Manufacturing," disc. paper no.79-30, Dept. Econ., Univ. British Col- umbia, Nov. 1979.

, C. J. Morrison, and G. C. Watkins, "Dynamic Models of Energy Demand: An Assessment and Comparison," in Ernst R. Berndt and B. C. Field, eds., Measuring and Modelling Natural Re- source Substitution, Cambridge: M.I.T. Press, forthcoming.

and D. 0. Wood, "Engineering and Econometric Interpretations of Energy- Capital Complementarity," Amer. Econ. Rev., June 1979, 69, 342-54.

J. M. Cassels, "Excess Capacity and Monop- olistic Competition," Quart. J. Econ., May 1937, 51, 426-43.

W. E. Diewert, "Applications of Duality The- ory," in Michael D. Intriligator and David A. Kendrick, eds., Frontiers of Quantita- tive Economics, Vol. II, Amsterdam: North-Holland 1974, 106-71.

M. F. Foss, "The Utilization of Capital Equipment: Postwar Compared with Pre- war," Surv. Curr. Bus., June 1963, 43, 8-16.

L. R. Klein, "Some Theoretical Issues in the Measurement of Capacity," Econometrica, Apr. 1960, 28, 272-86.

L. J. Lau, "A Characterization of the Nor- malized Restricted Profit Function," J. Econ. Theory, Feb. 1976, 12, 161-63.

D. F. McFadden, "Cost, Revenue and Profit Functions," in Melvyn A. Fuss and Daniel F. McFadden, eds., Production Econom- ics: A Dual Approach to Theory and Appli- cations, Vol. 1, Amsterdam: North- Holland Publishing Co., 1978, 3- 109.

C. J. Momrison, "Investment Decision of Firms with Non-Static Expectations," unpublished paper, Dept. Econ., Univ. British Columbia, June 1980.

W. Y. Oi, "Labor as a Quasi-Fixed Factor," J. Polit. Econ., Dec. 1962, 70, 538-55.

R. H. Rasche and J. A. Tatom, (1 977a) "The effects of the New Energy Regime on Economic Capacity, Production and Prices," Fed. Res. Bank St. Louis Rev. May 1977, 59, 2- 12.

and , (1977b) "Firm Capacity and Factor Price Changes," xerolith, Fed. Res. Bank St. Louis, not dated.



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