# Productive and financial performance in U.S. manufacturing industries: an integrated structural approach.

I. Introduction

In the last few years, macroeconomists and industrial organization researchers have reexamined relationships among scale economies, markups, economic profitability and productivity growth. Paul Romer |14~ has emphasized the importance of increasing returns for productivity growth at the aggregate industry or economy level. Empirical evidence supporting this at the industry level has been presented by Robert Hall |4;5~, who reported both significant increasing returns and markups of price over marginal cost in various U.S. manufacturing sectors. Related evidence on the cyclical nature of markups in these industries, suggesting some procyclicality of markup behavior, has been presented by Domowitz, Hubbard and Petersen |3~.

Analysis of the cyclical characteristics of Robert Solow's |16~ productivity residual provided the basis for these empirical studies. The resulting framework is limited, however, by its dependence on a number of restrictive assumptions, which severely hamper analysis of interactions among these characteristics. The purpose of this paper is to extend this type of analysis to consider profit-maximizing markups, economic profitability, scale economies, capacity utilization and productivity growth within an integrated theoretical structural model, and to assess their interactions empirically for two-digit U.S. manufacturing data.

More specifically, using the "new industrial economics" approach outlined by Timothy Bresnahan |2~ in which marginal cost and therefore markups are unobserved but estimated econometrically, I specify an integrated cost and demand structure for each industry. The structure is quite general in that (i) markups and returns to scale are permitted to vary over time (they are not constant parameters); (ii) short- and long-run impacts are distinguished (by explicit recognition of adjustment costs); (iii) quasi-fixity of both capital and labor is incorporated (to accommodate labor hoarding as well as slow adjustment of capital); (iv) input substitution is not constrained a priori (a generalized Leontief restricted cost function based on gross output is employed); (v) nonstatic expectations are allowed for (through an instrumental variable estimation procedure); and (vi) the effects of cost and demand "shocks" are directly represented (by specifying and estimating industry-specific cost, output demand and input demand functions).

Measures of technological and market factors affecting productive and financial performance such as scale economies, utilization and markups by industry are of interest in their own right. However, this general specification not only allows such measures to be computed, but also permits their linkages and their impacts on productivity growth and economic profitability--both secular and cyclical--to be formalized and measured. This is accomplished through analysis of "error biases" that result when using traditional primal multifactor productivity growth measures that fail to take into account the effects of these factors. This facilitates assessment of conjectures such as that by Hall |5~, that evidence of normal economic profits and markups of price over marginal cost in most U.S. manufacturing industries imply substantial scale economies and excess capacity.

The impact of these factors affecting economic performance is measured by estimating structural equations representing input demand and pricing behavior for seventeen 2-digit U.S. manufacturing industries, and aggregated total manufacturing. The data used are annual data from 1949 to 1986 from the Bureau of Labor Statistics on prices and quantities of gross output, and capital, labor, intermediate material, energy and purchased services inputs. The principal empirical findings are that markups have been countercyclical and have an upward trend for most industries, and that excess capacity and the potential to exploit scale economies have tended to expand over time. These factors have caused standard measures of productive performance to overstate the degree of fluctuation and downturn in productivity growth in most U.S. manufacturing industries. In addition, in terms of financial performance, these characteristics of cost and demand tend to offset each other, resulting in approximately normal profits on average, although declining profitability since 1973 is apparent for a number of industries.

II. Modeling Economic Performance and Its Determinants

Fundamental Results Used for the Analysis

To motivate formally the theoretical linkages among productivity growth, markups, scale economies and capacity utilization, I will rely primarily on three results. These results can be combined and employed directly to motivate the use of estimated cost and demand elasticities to measure these factors, and to generalize, refine and interpret productivity growth and profitability measures.

First, I will use the traditional output-side specification of the productivity growth residual motivated by Solow |16~ (the Solow residual):

|Mathematical Expression Omitted~,

where Y and |p.sub.Y~ are output quantity and price, |v.sub.j~ and |p.sub.j~ are corresponding input measures, "|center dot~" denotes a time derivative, t represents time and |S.sub.j~ is the revenue share |p.sub.j~|v.sub.j~/|p.sub.Y~Y. This expression, representing the growth in output that cannot be attributed to growth in inputs--technical change, is based on manipulation of the production function Y = Y(v, t).

With perfect competition, instantaneous adjustment (full utilization) and constant returns to scale (CRTS), this is equivalent (with a sign change) to the cost-side specification capturing the diminution of costs not explained by changes in input prices and derived from the cost function C(Y,p, t):(1)

|Mathematical Expression Omitted~,

where C is total costs and |M.sub.j~ is the cost-share |p.sub.j~|v.sub.j~/C.

Secondly, I will exploit information on the deviation between costs (C) and revenues (|p.sub.Y~Y) due to violation of the assumptions used to motivate the equivalence of (1a) and (1b). This can arise due to imperfect competition (implying |p.sub.Y~ |is not equal to~ MC, where MC = |Delta~C/|Delta~Y represents marginal cost), or to nonconstant returns to scale or fixity (resulting in AC |is not equal to~ MC, where AC |is equivalent to~ C/Y denotes average cost).(2) As shown elsewhere |10~, recognizing these differences results in the relation

|p.sub.Y~Y = C |center dot~ |MC |center dot~ Y/C~ |center dot~ (|p.sub.Y~/MC) = C |center dot~ ||Epsilon~.sub.CY~/(1 + ||Epsilon~.sub.PY~) = C |center dot~ ADJ. (2)

This wedge between revenues and costs relies on two elasticity expressions. The cost elasticity with respect to output ||Epsilon~.sub.CY~ = |Delta~ ln C(Y, |center dot~)/|Delta~ ln Y = MC |center dot~ Y/C is defined with respect to the cost function. The inverse demand elasticity ||Epsilon~.sub.PY~ = ||Delta~|p.sub.Y~(Y, |center dot~)/|Delta~Y~ |center dot~ Y/|p.sub.Y~ stems from the inverse demand function |p.sub.Y~ = |p.sub.Y~ (Y, |Rho~), where |Rho~ is a vector of shift variables for the output demand function. Equation (2) therefore captures the dependence of revenue on both cost- and demand-side elasticities through the adjustment factor ADJ.(3)

Thirdly, a result based on the ||Epsilon~.sub.CY~ elasticity can be used to interpret equation (2) further: |Delta~ ln C/|Delta~ ln Y = (|Delta~C/|Delta~Y)Y/C = MC/AC differs from one if either nonconstant returns (long run fixities) or short run fixities exist. Specifically, as shown in Morrison |10~, ||Epsilon~.sub.CY~ can be defined as:

|Mathematical Expression Omitted~,

where |Mathematical Expression Omitted~ is (the inverse of) returns to scale, L denotes long run, and C|U.sub.c~ is a cost-side measure of capacity utilization.

Motivation of these measures as representations of returns to scale and fixity requires a cost function explicitly incorporating fixed inputs; C(p, Y, t) = G(p, Y, t, x) + ||Sigma~.sub.k~ |p.sub.k~|x.sub.k~, where G(|center dot~) is a variable cost function and x a vector of K quasi-fixed inputs |x.sub.k~ with market prices |p.sub.k~. The associated shadow cost function C* = G(p, Y, t, x) + ||Sigma~.sub.k~|Z.sub.k~|x.sub.k~ can then be defined, where |Z.sub.k~ is the shadow value of |x.sub.k~, - |Delta~G/|Delta~|x.sub.k~. This forms the basis for defining |Mathematical Expression Omitted~ as (MC |center dot~ Y)/C* (where MC = |Delta~C/|Delta~Y = |Delta~G/|Delta~Y), and C|U.sub.c~ as C*/C = (1 - |Sigma~||Epsilon~.sub.Ck~) (where ||Epsilon~.sub.Ck~ = |Delta~ ln C/|Delta~ ln |x.sub.k~).

Putting the second and third results together leads to |Mathematical Expression Omitted~. An important implication of this expression is that when ADJ |is not equal to~ 1 due to ||Epsilon~.sub.PY~ |is not equal to~ 0 from product differentiation or ||Epsilon~.sub.CY~ |is not equal to~ 1 from either scale economies or fixity, the equivalence of (1a) and (1b) is destroyed. Incorporating this information thus requires correcting the ||Epsilon~.sub.Ct~ and ||Epsilon~.sub.Yt~ measures, which in turn has implications for decomposing ||Epsilon~.sub.Yt~ to identify the impacts of the underlying technical and market factors on overall productivity growth or productive performance. In addition, the deviation between |p.sub.Y~Y and C has important implications about financial performance, since if |p.sub.Y~ Y/C = 1 (ADJ = 1) normal profits will be observed. This provides a useful context in which to assess the Hall |5~ contention that capacity utilization and returns to scale may attenuate the profitability arising from market power. In essence this implies that ||Epsilon~.sub.CY~ counteracts |p.sub.Y~/MC, which could potentially occur with excess capacity (so ||Epsilon~.sub.CY~ |is less than~ 1), and markups (so |p.sub.Y~/MC |is greater than~ 1).

If normal profits are observed, this not only suggests that the levels of the markup, capacity utilization and scale economies are such that this condition holds, but also that if ||Epsilon~.sub.CY~ declines (due either to decreases in capacity utilization or increases in potential returns to scale), this will support a larger markup without increasing overall profitability. In terms of the cyclical behavior of markups, this suggests for example that (with CRTS) increases in capacity utilization will be associated with decreases in markups; markups will be countercyclical.(4)

These issues thus have important implications for the correct measurement and interpretation of productive and financial performance. To pursue these implications further, however, the necessary adaptations of traditional productivity growth measures for these characteristics must be formalized, and an empirically implementable model must be developed to allow estimation of the appropriate elasticities. These steps are pursued in the next two sections.

The Implications of These Relationships for Productivity Growth

Recognizing the impacts of markups, scale and fixity has somewhat varied implications for productivity growth measurement. Correcting for imperfect competition requires recognizing that the denominators of the revenue and cost shares differ due to |p.sub.Y~ |is not equal to~ MC, which necessitates an error bias correction to change the input share-weights in the primal measure. Correcting for scale economies requires accommodating a deviation between MC and AC; this implies an error bias correction to change the denominator of the weights on both output and input changes in the cost measure. Allowing for fixities requires one more step; the numerator of both the primal and cost share-weights for the fixed inputs as well as the denominator of the cost shares must be adapted.

More specifically, the deviation between (1a) and (1b) arising from imperfect competition occurs only because |p.sub.Y~Y |is not equal to~ MC |center dot~ Y = C (given ||Epsilon~.sub.CY~ = 1). Thus, reconciling (1a) and (1b) requires recognizing that (1 + ||Epsilon~.sub.PY~) = MC/|p.sub.Y~ = C/|p.sub.Y~Y, so |S.sub.j~ = |M.sub.j~(1 + ||Epsilon~.sub.PY~). Therefore, correcting the ||Epsilon~.sub.Yt~ computation for markups requires computing |Mathematical Expression Omitted~, where ||Epsilon~.sub.PY~ |center dot~ ||Sigma~.sub.j~ |M.sub.j~(|v.sub.j~/|v.sub.j~) may be considered the "error bias" in the usual primal measurement of productivity growth, and M stands for the "Markup correction". The bias therefore depends on the cost shares, the markup, and the growth rates of the inputs.(5)

If scale economies or changes in capacity utilization also exist, the assumption that ||Epsilon~.sub.CY~ = 1 must also be relaxed. To correct for error biases arising from ||Epsilon~.sub.CY~ |is not equal to~ 1, it must be recognized that (1b) is based on the assumption that the cost function can be written as C(p, Y, t) = Yc(p, t) (where c = C/Y), so d ln c/dt = d ln C/dt - d ln Y/dt. However, if ||Epsilon~.sub.CY~ |is not equal to~ 1, this average cost derivative becomes d ln C/dt - ||Epsilon~.sub.CY~ (d ln Y/dt). Thus, to correct for ||Epsilon~.sub.CY~ |is not equal to~ 1 owing to scale economies, the residual ||Epsilon~.sub.Ct~ must be adjusted to

|Mathematical Expression Omitted~

where R represents "adjusted for returns to scale", and the last term is the error bias in traditional measures when CRTS is assumed inappropriately. Since ||Epsilon~.sub.CY~ = MC |center dot~ Y/C = MC |center dot~ Y/AC |center dot~ Y = MC/AC, the adjustment by ||Epsilon~.sub.CY~ restates the change in output in terms of its correct marginal value. The impact of the bias depends on the extent of scale economies and the output growth rate.

If instead ||Epsilon~.sub.CY~ |is not equal to~ 1 because C|U.sub.c~ |is not equal to~ 1 ((1 - |Sigma~||Epsilon~.sub.Ck~) |is not equal to~ 1), the correction requires changing the assumption that |Delta~C/|Delta~|p.sub.j~ = |v.sub.j~ (the cost-minimizing demand for input j) by Shephard's lemma, to recognize that the implied equality of the value of the marginal product and input price is invalid for fixed inputs. The quasi-fixed inputs should therefore be valued in terms of their shadow prices, |Z.sub.k~ (reflecting the true marginal product of |x.sub.k~), instead of the market price |p.sub.k~, and input shares should be measured in terms of C*. This implies an adjustment in the numerator of the share weight on quasi-fixed input changes as well as in the denominator for the weights of all inputs and output.

The resulting corrected expression for ||Epsilon~.sub.Ct~ therefore becomes

|Mathematical Expression Omitted~

where F represents "adjusted for fixity". As above, the last term in this expression can be thought of as an error bias, which in this case depends on the relative growth rates of output and the quasi-fixed inputs.

Incorporating both fixity and returns to scale therefore requires combining (4) and (5). This measure, denoted |Mathematical Expression Omitted~ (where T represents the "total adjustment") accommodates the full error bias in the standard ||Epsilon~.sub.Ct~ measure. Similarly, constructing an adapted primal measure to obtain |Mathematical Expression Omitted~ requires valuing the fixed inputs in the |Mathematical Expression Omitted~ measure at their shadow values.

Once these corrections for the invalid assumptions of CRTS and instantaneous adjustment are made, the independent impacts of scale and utilization changes on productivity growth measures can be identified in terms of a decomposition of the primal measure to reflect the different cost impacts. This decomposition is analogous to the treatment of returns to scale motivated by Ohta |12~; the relationship between the ||Epsilon~.sub.Yt~ and ||Epsilon~.sub.Ct~ measures when ||Epsilon~.sub.CY~ |is not equal to~ 1 is |Mathematical Expression Omitted~. This "decomposition" isolates technical change independently from the characteristics captured in the deviation of ||Epsilon~.sub.CY~ from one, since it separately identifies the different characteristics that cause ADJ |is not equal to~ 1. It therefore facilitates interpretation by distinguishing the various impacts causing fluctuations in the overall productivity growth measure ||Epsilon~.sub.Yt~.

III. Empirical Evidence on Markups, Fixities and Economic Performance

The Estimating Model

In order to implement and evaluate the productivity growth framework developed in the last section, a model is required to separately identify and measure the components of the ADJ measure--the elasticities ||Epsilon~.sub.PY~, |Mathematical Expression Omitted~, and ||Epsilon~.sub.Ck~. The approaches used by Hall |4~, and Domowitz, Hubbard and Peterson |3~ cannot be used to carry out this task, since they rely on an incomplete specification of the underlying cost and demand relations. Instead, a more comprehensive specification employing a production theory approach based on estimation of cost and demand functions such as that developed in Morrison |6~ must be used for this purpose.

The building blocks of this structural model, which provides the basis for the estimated elasticities used below, are a Generalized Leontief restricted cost function and a similarly constructed output demand function. The specification used here assumes capital (K) and labor (L) are quasi-fixed, energy (E), intermediate materials (M), and purchased services (S) are the variable inputs, and adjustment costs are accommodated by including investment in K and L (|Delta~K and |Delta~L) as arguments of the cost function. The shift variables for the output demand function include consumption expenditures, price indexes for imported and consumption goods, the interest rate, and unemployment.

These two functions were used to construct a system of estimating equations including (i) the cost function plus variable input demand equations for E, M and S derived from Shephard's Lemma (|v.sub.j~ = |Delta~C/|Delta~|p.sub.j~); (ii) a short run price setting equation MR = MC using the expressions for marginal revenue (MR = |p.sub.Y~ + (|Delta~|p.sub.Y~/|Delta~Y) |center dot~ Y) and marginal cost (MC = |Delta~G/|Delta~Y); (iii) two Euler equations to reflect adjustment paths of K and L; and, to complete the system, (iv) the output demand equation.(6) The estimating equations and the resulting parameter estimates fully capture the pattern of supply and demand responses underlying the cost and demand elastities necessary for evaluation and interpretation of the impacts of markups, scale and utilization changes on productive and financial performance.

Data and Estimation

Estimation of this model was carried out using U.S. manufacturing data for 1952-1986 for a number of manufacturing industries. The sectors considered include food and kindred products (FO), textiles (TX), apparel and other textile products (AP), paper and allied products (PA), printing and publishing (PP), chemicals and allied products (CM), petroleum and coal products (PC), rubber and miscellaneous plastics (RB), lumber and wood (LW), furniture and fixtures (FN), clay and glass (CL), primary metals (PM), fabricated metal products (FM), machinery (MC), electric and electronic equipment (EL), instruments and related products (IN), and transportation equipment (TQ). In addition, a total manufacturing category (MA), constructed by aggregating the individual sectors using Divisia indexes, was estimated for comparison.

These data are based on series for prices and quantities of output and inputs developed and used by the Bureau of Labor Statistics (BLS) Office of Productivity.(7) The capital data were, however, reconstructed to generate an ex ante capital price measure more closely related to the procedures used by Berndt and Wood |1~. Such a recalculation is required because the "residual" method of capital measurement in the BLS data generates an ex post measure of capital quasi-rents including any returns not captured by other inputs. The demand variables were primarily taken from the Economic Report of the President. The interest rate used is the Moody Baa bond yield.

The model was estimated for each industry separately, using three stage least squares to incorporate the endogeneity of output quantity and price, and to allow for the possibility of non-static expectations on input prices as suggested by Pindyck and Rotemberg |13~. The instruments employed include lagged values of the exogenous variables facing the firm, as well as the world oil price, defense spending, and the political party variables relied on in the Hall studies. The results were quite robust to different specifications of instruments.

The estimated model for each of the manufacturing industries can be used to generate a large number of indexes, elasticities, and other parameter transformations. Since space constraints prohibit detailed analysis of the different sectors, I concentrate here only on a general evaluation of evidence on markups, scale economies and input fixity, and their effects on productivity growth and economic profitability.(8)

Productivity Growth

Traditional multifactor productivity growth indexes ||Epsilon~.sub.Yt~ based on the K,L,E,M,S division of inputs are presented in terms of average annual growth rates (AAGR) in Table I (SICs for the industries are in parentheses).

The AAGRs reflect the existence of a post-1973 productivity growth slowdown, even though the dramatic stagnation apparent immediately after 1973 in indexes representing yearly changes is somewhat masked by including more recent years in the AAGR computations. The industries which show a negative growth rate in the post-1973 period are PP, PM and PC, the latter two of which are capital- and energy-intensive industries which would tend to be heavily affected by energy price shocks. This pattern is evident overall; the industries hardest hit in the mid-1970s include PM, FM, MC, CM, PA, and RB, all of which are capital intensive. These industries also, however, experienced relatively intense international competition during this time period. The only industry that exhibited increasing productivity growth was MC, which includes the computer industry.(9)

The traditional productivity growth indexes appear considerably procyclical, with, for example, declines appearing in most industries around 1970, 1974-75 and 1982-83. One indication of the extent of these fluctuations comes from the standard deviations of these measures, which are rather large--particularly for durable goods industries.

The fluctuations observed, however, are less systematic than it might initially appear, particularly given the emphasis on cyclicality in the recent studies by Hall. The correlations of these indexes with indexes reflecting cyclical trends are not very significant. In particular, when this productivity growth measure is correlated with a standard published capacity utilization measure (the Federal Reserve Board index for manufacturing, FRB) or the C|U.sub.c~ measure resulting from estimation of my model, the correlations tend to be primarily positive but generally statistically insignificant.(10)

The cyclical fluctuations in productivity that do exist, although not pervasive in terms of statistical significance, influence the interpretation of changes in economic performance. Thus, it is useful to see to what extent these variations might be smoothed, and in this sense "explained", by taking into account cyclically related markup, capacity utilization, and returns to scale factors.

TABULAR DATA OMITTED

These factors, and the associated adaptations of traditional productivity growth measures, will now be considered in turn.

Markups

It has been argued that markups might be expected to be cyclical, although controversy remains about whether they are pro- or counter-cyclical.(11) Hall's treatment of the markup does not allow for cyclicality to exist, since it is treated as a constant parameter. However, the hypothesis of counteracting capacity utilization and markups suggests that increasing markups would be accommodated by additional excess capacity, leading to countercyclicality of markups, as noted above. Domowitz, Hubbard and Peterson more directly address this issue by correlating the markup measure with a published measure of capacity utilization, and find some evidence of procyclicality. In the current study, the cyclicality and determinants of the markup are directly incorporated and thus can be more effectively evaluated.

The estimated markup indexes implied by my model are presented in Table II in terms of annual averages. As found by Hall, significant markups do appear to exist, although the estimates of the markups are intuitively more reasonable than those based on the simpler framework of the Hall studies.(12) The year-to-year variations are also important; although the standard deviations are not large, clear tendencies do emerge.

A secular increase in markups over time is evident (although indexes specified in terms of yearly changes suggest significant year-to-year variations). The only industries that exhibit a clear downward trend in markups are AP, LW, PC and PM; this is consistent with intuition given the intensifying international competition in the apparel, lumber and primary metals markets, and the rise in costs of crude materials in the petroleum refining industry which have caused downward pressure on profit margins. Some other industries facing increasing international competition such as CL and FM (and to a lesser extent TX and TQ) appear from the averages to have quite stable TABULAR DATA OMITTED markup behavior. Interestingly, markups in high-technology industries such as CM, EL, MC and IN all increased from 1960-73 to 1973-86.

In general, markups appear to decline during recessions and in that sense seem procyclical. For example for all industries the 1973 and 1979 OPEC shocks are reflected in a downturn in the markup ratio. However, from correlations of the markup with the economic measure of capacity utilization, C|U.sub.c~, the evidence is overwhelmingly in favor of countercyclicality of markups. The correlations of the reported markups with C|U.sub.c~ (and the full cost elasticity ||Epsilon~.sub.CY~) are negative throughout except for the primary metals industry (PM), and are all statistically significant at the one percent level. For total manufacturing (MA), for example, the correlation is -0.419 with a standard error of .088. Correlations with published FRB capacity utilization measures are somewhat more ambiguous; although the correlations are generally negative, they tend to be small and largely insignificant.

Countercyclicality of markups has a well defined impact on productivity growth patterns through the error bias |Mathematical Expression Omitted~. Since |Mathematical Expression Omitted~, and an increase (in absolute value) in ||Epsilon~.sub.PY~ implies a larger markup, an upward trend in the markup will compensate to some extent for a downward trend in the productivity growth rate (as long as inputs in general are increasing). Given the observed tendencies for increasing markups and declining productivity growth, this provides a partial "explanation" for measured downturns in productive performance. More specifically, since this occurs for both secular and cyclical fluctuations (markups are both increasing and countercyclical), this implies that appropriate cost-based productivity growth measures reveal stronger productive performance and less cyclicality in most industries than standard primal measures.

Carrying out this correction for demand factors can, however, be misleading if cost factors such as scale economies exist that should also be accommodated in productivity growth measures, particularly given the offsetting cyclical patterns of these market and technical forces. Additional insights about fluctuations in traditionally measured productivity growth can therefore be obtained by taking into account also the impact of scale economies and fixity.

The Cost Elasticity, ||Epsilon~.sub.CY~, and Its Components

Fixity was incorporated in the Hall studies in the context of long run returns to scale and the effect measured as a constant parameter. In the model developed above, however, short and long run fixity--capacity utilization and scale economies--are independently distinguished as components of the cost elasticity ||Epsilon~.sub.CY~. This allows not only measurement of the levels of these technological factors, but also assessment of their trends, cyclical behavior, and impact on productive and financial performance.

Capacity utilization is by definition procyclical; if output increases, utilization of a given capacity increases. Similarly, if scale economies exist, upward swings in the cycle (output expansion) cause average cost declines, so this component of ||Epsilon~.sub.CY~ will also tend to be procyclical. This procyclicality suggests that increased profitability from countercyclical markups will tend to be offset by excess capacity and the existence of scale economies captured in ||Epsilon~.sub.CY~.

The measured cost elasticity ||Epsilon~.sub.CY~ is presented in terms of annual averages in the second panel of Table II. These measures suggest short and long run scale economies exist and are quite substantial in a number of industries. Scale economies also appear to be increasing, especially in industries which tend to be more capital intensive and have experienced productivity growth stagnation, such as PA, CM, and PM.

One interesting exception to this is the MC industry. Although productivity growth in this industry has been strong and actually increasing, scale economies have also risen substantially. Note also that this industry experienced one of the largest jumps in markups during this period, as did CM, where scale economies also increased. This is in sharp contrast to PM, where a (more modest) expansion of scale economies occurred along with a decline in markups. This suggests declining profitability as well as productivity performance in the primary metals industry, due perhaps to a decline in relative efficiency and increased international competition. To a lesser extent this is true also for AP.

The procyclicality of the ||Epsilon~.sub.CY~ measure is more obvious from indexes based on yearly changes, where, for example, declines are evident for most industries in the downturns of 1969-70, 1974-75 and 1982-83. To a large extent cyclical movements in ||Epsilon~.sub.CY~ are driven by utilization fluctuations, since potential scale economies appear to be increasing over time rather smoothly. In turn, the capacity utilization patterns appearing in the C|U.sub.c~ indexes result primarily from changes in capital utilization, although labor hoarding, and thus procyclicality from changes in work effort, are also evident from fluctuations in the shadow value of labor.

The independent effects of short and long run fixities can be distinguished from the two components TABULAR DATA OMITTED of ||Epsilon~.sub.CY~--C|U.sub.c~ and |Mathematical Expression Omitted~. These measures are presented as annual averages in Table III, and graphically for total manufacturing in Figure 1. The C|U.sub.c~ numbers in Table III show that capacity utilization has been declining in every industry but PC and LW. They also suggest excess capacity virtually everywhere, although overutilization of capacity appears in the CM industry throughout the time period, and in the early years for the textile industry.

The excess capacity has been driven primarily, especially in the post-1973 period, by a low shadow value of capital relative to its market price; in most industries a decline in the |Z.sub.K~/|p.sub.K~ ratio and an increase in |Z.sub.L~/|p.sub.L~ has occurred post-1973. Note also that the levels of C|U.sub.c~ are less than .9 in the PP, RB, LW, FN, CL and PM industries in this time period, indicating that the cost consequences of short-run excess capacity are often greater than 10%.

The bottom panel of Table III indicates, however, that scale economies seem to be driving the evidence of a low and declining ||Epsilon~.sub.CY~ even more than C|U.sub.c~. In particular, long run returns to scale (|Mathematical Expression Omitted~) are very substantial and increasing, especially in the nondurable industries such as TX, AP, PA and CM. Excess capacity therefore exists even in the long run. Precisely why long-run scale economies are increasing over time in all industries except CL and FM is a fascinating topic for further research, since this result could reflect many different internal and external scale factors.

Figure 1 shows graphically this balancing of |Mathematical Expression Omitted~ and C|U.sub.c~ patterns in the observed cost elasticity ||Epsilon~.sub.CY~. Scale economies appear for manufacturing as a whole to be quite large and increasing; |Mathematical Expression Omitted~ is dropping. A more limited downward drift is evident from the capacity utilization measure, as well as much more cyclicality. ||Epsilon~.sub.CY~ thus seems to reflect the cyclical fluctuations of the utilization measure, and the level and secular trend of the |Mathematical Expression Omitted~ measure.

The full effect of error bias corrections to accommodate the deviation of ||Epsilon~.sub.CY~ from one is not immediately obvious a priori, since the bias depends not only on this elasticity, but also on the relative growth rates of output and quasi-fixed inputs. However, in general procyclical variations in ||Epsilon~.sub.CY~ will result in corrections incorporating ||Epsilon~.sub.CY~ |is not equal to~ 1 to smooth the productivity growth measure and thus "explain" a portion of observed secular and cyclical downturns, since procyclicality implies greater output than input changes. These impacts are further explored in the next subsection.

Productive Performance--Productivity Growth Corrected

The significant levels and trends of the measured markup, utilization and scale measures discussed above suggest that adaptations to standard productivity growth indexes to accommodate these effects will facilitate interpretation of trends and fluctuations in these measures. Adapted productivity growth measures incorporating these corrections are presented in Table IV. The measure reported in the first panel of Table IV is a primal-side measure recognizing the markup and error bias corrections but including returns to scale and utilization as well as technical change (|Mathematical Expression Omitted~), whereas that in the second panel is a cost-side measure isolating the impact of technical change (|Mathematical Expression Omitted~).

A comparison of the indexes in Tables I and IV indicate that correcting for error biases resulting from markups and input fixity is quantitatively important. In general productivity growth TABULAR DATA OMITTED appears lower than reflected in the traditional measure for the 1960-73 period, but often is higher after 1973. Thus, the difference between the pre- and post-1973 periods is substantially reduced and the "productivity growth slowdown" somewhat attenuated.

For example, for total manufacturing, unadjusted growth rates for 1960-73 and 1973-86 are 1.610 and 0.489, while corresponding fixity-adjusted values are 0.973 and 0.528. The entries in the first panel of Table IV also suggest that efficiency growth in some industries (including short and long run economies) has been very limited even from the early years of the sample--especially in the PP, CM, PC, PM and IN industries.

A further reduction in the apparent growth of technical change, especially in the earlier part of the sample, is apparent in the second panel of Table IV when the impacts of scale economies are removed; short and long run scale effects have tended to bias technical change measures upward, especially in earlier years when output growth was relatively strong. However, in some industries, notably CL, PM and FN, standard productivity growth measures have instead tended to understate technical change. In addition, evidence of negative productivity growth is less pervasive when scale impacts are recognized; some of the measured productivity decline can be attributed to higher unit costs due to diminished output demand.

In total, corrections to standard productivity growth measures somewhat reduce secular and cyclical fluctuations in productivity growth measures. This "smoothing" of the productivity growth index is apparent from the year-to-year fluctuations summarized in the graph of ||Epsilon~.sub.Yt~ and |Mathematical Expression Omitted~ for total manufacturing in Figure 2--especially for the strong upswings in the early 1960s and closely following the downturns around 1970 and 1975.(13) The muting effect of the corrections is somewhat limited, however, partly because some industries counteract the overall tendency (the standard deviation for |Mathematical Expression Omitted~ is larger than for ||Epsilon~.sub.Yt~ in some industries).(14)

Overall, corrections of productivity growth measures for error biases due to erroneous assumptions about returns to scale and fixity provide some insights into the "explanations" of productivity growth fluctuations. However, it turns out that once these cost factors are recognized, the correction of ||Epsilon~.sub.Yt~ for markups does not significantly affect the evidence of productivity growth, because the offsetting impacts of markups, utilization and scale imply approximately normal profits and thus equivalence of cost and revenue shares. This is developed in the next subsection.

Financial Performance--Profitability

The counteracting effects of markups and utilization/scale on profitability are evident from the average annual levels of |Mathematical Expression Omitted~ in Table V and Figure 3. ADJ TABULAR DATA OMITTED tends to be close to one, suggesting that revenues approximately equal economic costs, and that economic profits are therefore roughly zero on average. Essentially, managers' pricing responses balance the technical and market economic fluctuations encountered, but do not allow for excess profitability on average.

The annual average ADJ measures presented in Table V suggest that over time this balancing act has resulted in an increasing shortfall of revenues over costs of production (including appropriate returns to capital) in U.S. manufacturing industries. Although for total manufacturing normal profits were approximated for the 1960 to 1986 period, a decline in profitability in the post-1973 period is evident for all industries except PC. This trend exhibits little variation, although some procyclicality appears to exist.

This downward trend in the ratio of returns to costs is evident from Figure 3 for manufacturing overall. This Figure illustrates the relatively greater impact on ADJ of the ||Epsilon~.sub.CY~ elasticity than the markup ratio, since ADJ more closely follows the pattern exhibited by the ||Epsilon~.sub.CY~ index. In particular, ||Epsilon~.sub.CY~ pulls down the ADJ measure over time; markups are not keeping pace with changes in technical factors and competition. Thus, even with greater potential for markups, expanding scale economies and restrictions on flexibility due to capital fixity have had a depressing effect on profitability for most U.S. manufacturing industries.

In particular, although before 1973 only six industries had negative economic profits on average, post-1973 the number of such industries more than doubled to thirteen. Only four industries experienced positive economic profit in this later period (FO, PP, CM and PC), with FO and PC the most profitable.

It is interesting to conjecture that these nondurable manufacturing industries were perhaps subject to less intense competition than most of the other industries during this period of massive international expansion of markets. Other industries, even the MC industry which performed better than other durable industries but still fell short of normal profits by 1% on average, tended to be more internationally competitive as well as more energy and capital intensive.

These numbers are dramatic confirmation of much recent discussion about declining competitiveness of U.S. durable goods and textiles industries. It should be noted, however, that the post-1973 decline in profitability was reversing toward the end of this sample; yearly indexes show increasing profitability after 1982, with positive economic profits by the end of the sample for the MC industry. It will be useful to explore this trend further with the availability of more recent data.

This evidence about financial performance, as noted in the previous subsection, provides some insights about the linkage between measures of productive and financial performance. The Hall markup correction to measure input shares in terms of costs instead of revenues will have little impact on average, since ADJ closely approximates one. However, some pattern in the difference between cost and revenue shares is implied by the reduction in profitability over time; a measure based on cost shares will tend to show a somewhat smaller decline in productivity growth over time.

IV. Concluding Remarks

This paper addresses some determinants of productive and financial performance using a structural model allowing formalization and measurement of the relationships among productivity growth, profits, markup behavior, capacity utilization and scale economies. This framework has permitted consideration of whether these market and technical factors generally ignored in productivity growth analysis have been "responsible" for cyclical fluctuations and secular downturns in economic performance observed in U.S. manufacturing industries.

The first "cause" evaluated is the markup of price over marginal cost. Markup indexes embodying a cyclical component constructed for these industries reveal tendencies for markups to increase over time and in cyclical downturns (implying countercyclicality). As a result, traditional primal productivity growth measures, developed in terms of revenue shares and thus implicitly based on the assumption of perfect competition, exacerbate declines over time and in recessionary periods. Adaptation of the measure to reflect cost shares therefore provides some "explanatory power" for productivity performance variation, by smoothing observed fluctuations.

However, fixities in both the short and long run also have an impact on observed economic performance. In the model used here, short run fixities are captured as changes in capacity utilization, and long run "fixities" are reflected as scale economies. Although capacity utilization is by definition procyclical, I find it also appears to have a downward secular trend. At the same time, the extent of scale economies seems to be increasing over time. This is consistent with economic intuition, for in order to obtain normal economic profits, increasing markups must be offset by a combination of increasing excess capacity and scale economies. The empirical results confirm this counteracting effect in U.S. manufacturing industries; economic profits on average have been zero, but have exhibited a downward trend over time as scale economies have more than outweighed rising markups.

Together, these forces tend to offset the explanatory power of adjustments of primal productivity growth measures for markups. However, incorporating the cost characteristics--utilization and scale--still contributes in an important way to "explaining" fluctuations in productivity growth in terms of error biases. Corrections of erroneous assumptions made in traditional computations have a limited but significant smoothing impact on observed trends in productivity growth and technical change.

1. see Ohta |12~ or Morrison |11~ for further elaboration of this equality.

2. Clearly other internal and external factors such as R&D expenditures or infrastructure capital not appropriately reflected in these measures also will affect this relationship. Only these three determinants of the deviation will, however, be taken into account here.

3. The equality of the inverse demand elasticity ||Epsilon~.sub.PY~ and the markup |p.sub.Y~/MC results because (assuming profit maximization so MR = MC, where MR is marginal revenue), |p.sub.Y~/MC = |p.sub.Y~/(|p.sub.Y~ + Y |center dot~ |Delta~|p.sub.Y~(Y, |center dot~)/|Delta~Y) = 1/(1 + ||Epsilon~.sub.PY~) as discussed in Morrison |10~.

4. A somewhat different argument for countercyclical markups, motivated by industrial organization theory, has been presented by Rotemberg and Saloner |15~.

5. See Morrison |10~ for further elaboration of this relationship and the following adaptations.

6. For further details of the model and its application in the current context, see Morrison |6;8~.

7. The data, including detailed data for the capital components, were graciously provided by Michael Harper.

8. The interested reader can pursue the analysis further using the yearly indexes presented in Morrison |8~. The results in the text are presented for all industries in terms of average annual growth rates calculated from the relevant indexes. Computations of most measures referred to in the next subsections can be made directly from the indexes in Morrison |8~. Other results, such as the shadow value ratios underlying the C|U.sub.c~ measures, require further computation.

9. Semiconductors are included in EL, which also experienced very strong productivity growth over this period, particularly in the late 1970s. The relatively strong performance of the MC industry is driven largely by an enormous productivity growth rate in 1984-86.

10. For more details about the correlation patterns in these measures, see Morrison |8~.

11. See Morrison |7;9~ for further elaboration of the cyclicality of markups and its determinants.

12. This is particularly true for the CM, FO, PC and PP industries, for which the Hall estimates are clear outliers (with markup ratios of 20.112, 5.291, - 139.478 and 14.263, respectively).

13. Only these two indexes are graphed since |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~ are so similar that they tend to overlap.

14. This smoothing is also evident from correlations of the corrected productivity residuals with utilization indexes, which are not as statistically significant as those for the standard measures.

References

1. Berndt, Ernst R., and David O. Wood. "Energy Price Changes and the Induced Revaluation of Durable Capital in U.S. Manufacturing During the OPEC Decade." Manuscript, M.I.T. Center for Energy Policy Research, January 1984.

2. Bresnahan, Timothy, "Empirical Studies of Industries with Market Power," in Handbook of Industrial Organization, edited by R. Schmalensee and R. Willig. Amsterdam: North-Holland Press, 1988.

3. Domowitz, Ian R., Glenn Hubbard, and Bruce C. Petersen, "Market Structure and Cyclical Fluctuations in U.S. Manufacturing." Review of Economics and Statistics, February 1988.

4. Hall, Robert E., "The Relation Between Price and Marginal Cost in U.S. Industry." Journal of Political Economy, October 1988, 921-47.

5. -----. "Invariance Properties of Solow's Productivity Residual." National Bureau of Economic Working Paper #3034, July 1989.

6. Morrison, Catherine J., "Quasi-Fixed Inputs in U.S. and Japanese Manufacturing: A Generalized Leontief Cost Function Approach." Review of Economics and Statistics, May 1988, 275-87.

7. -----. "Markup Behavior in Durable and Nondurable Manufacturing: An Applied Production Theory Approach." National Bureau of Economic Research Working Paper #2941, April 1989.

8. -----. "Market Power, Economic Profitability and Productivity Growth Measurement: An Integrated Structural Approach." N.B.E.R. Working Paper No. 3355, May 1990, earlier version of current article.

9. -----. "Markups in U.S. and Japanese Manufacturing: A Short Run Econometric Analysis." Journal of Business and Economic Statistics, Vol. 10, No. 1. 1992, 51-63.

10. -----. "Unraveling the Productivity Growth Slowdown in the U.S., Canada and Japan: The Effects of Sub-equilibrium, Scale Economies and Markups." The Review of Economics and Statistics, Vol. 74, No. 3, 1992, 381-93.

11. -----. A Microeconomic Approach to the Measurement of Economic Performance: Productivity Growth, Capacity Utilization, and Related Performance Indicators. Berlin: Springer-Verlag Press, 1993.

12. Ohta, Makoto, "A Note on the Duality Between Production and Cost Functions: Rate of Returns to Scale and Rate of Technical Progress." Economic Studies Quarterly, 25, 1975, 63-65.

13. Pindyck, Robert S. and Julio J. Rotemberg, "Dynamic Factor Demands, Energy Use and the Effects of Energy Price Shocks." American Economic Review, December 1983, 1066-79.

14. Romer, Paul M., "Increasing Returns and Long-Run Growth." Journal of Political Economy, October 1986, 1002-37.

15. Rotemberg, Julio J. and Garth Saloner, "A Supergame-Theoretic Model of Business cycles and Price Wars During Booms." Quarterly Journal of Economics, 101, 1986.

16. Solow, Robert M., "Technical Change and the Aggregate Production Function." Review of Economics and Statistics, August 1958, 312-20.

In the last few years, macroeconomists and industrial organization researchers have reexamined relationships among scale economies, markups, economic profitability and productivity growth. Paul Romer |14~ has emphasized the importance of increasing returns for productivity growth at the aggregate industry or economy level. Empirical evidence supporting this at the industry level has been presented by Robert Hall |4;5~, who reported both significant increasing returns and markups of price over marginal cost in various U.S. manufacturing sectors. Related evidence on the cyclical nature of markups in these industries, suggesting some procyclicality of markup behavior, has been presented by Domowitz, Hubbard and Petersen |3~.

Analysis of the cyclical characteristics of Robert Solow's |16~ productivity residual provided the basis for these empirical studies. The resulting framework is limited, however, by its dependence on a number of restrictive assumptions, which severely hamper analysis of interactions among these characteristics. The purpose of this paper is to extend this type of analysis to consider profit-maximizing markups, economic profitability, scale economies, capacity utilization and productivity growth within an integrated theoretical structural model, and to assess their interactions empirically for two-digit U.S. manufacturing data.

More specifically, using the "new industrial economics" approach outlined by Timothy Bresnahan |2~ in which marginal cost and therefore markups are unobserved but estimated econometrically, I specify an integrated cost and demand structure for each industry. The structure is quite general in that (i) markups and returns to scale are permitted to vary over time (they are not constant parameters); (ii) short- and long-run impacts are distinguished (by explicit recognition of adjustment costs); (iii) quasi-fixity of both capital and labor is incorporated (to accommodate labor hoarding as well as slow adjustment of capital); (iv) input substitution is not constrained a priori (a generalized Leontief restricted cost function based on gross output is employed); (v) nonstatic expectations are allowed for (through an instrumental variable estimation procedure); and (vi) the effects of cost and demand "shocks" are directly represented (by specifying and estimating industry-specific cost, output demand and input demand functions).

Measures of technological and market factors affecting productive and financial performance such as scale economies, utilization and markups by industry are of interest in their own right. However, this general specification not only allows such measures to be computed, but also permits their linkages and their impacts on productivity growth and economic profitability--both secular and cyclical--to be formalized and measured. This is accomplished through analysis of "error biases" that result when using traditional primal multifactor productivity growth measures that fail to take into account the effects of these factors. This facilitates assessment of conjectures such as that by Hall |5~, that evidence of normal economic profits and markups of price over marginal cost in most U.S. manufacturing industries imply substantial scale economies and excess capacity.

The impact of these factors affecting economic performance is measured by estimating structural equations representing input demand and pricing behavior for seventeen 2-digit U.S. manufacturing industries, and aggregated total manufacturing. The data used are annual data from 1949 to 1986 from the Bureau of Labor Statistics on prices and quantities of gross output, and capital, labor, intermediate material, energy and purchased services inputs. The principal empirical findings are that markups have been countercyclical and have an upward trend for most industries, and that excess capacity and the potential to exploit scale economies have tended to expand over time. These factors have caused standard measures of productive performance to overstate the degree of fluctuation and downturn in productivity growth in most U.S. manufacturing industries. In addition, in terms of financial performance, these characteristics of cost and demand tend to offset each other, resulting in approximately normal profits on average, although declining profitability since 1973 is apparent for a number of industries.

II. Modeling Economic Performance and Its Determinants

Fundamental Results Used for the Analysis

To motivate formally the theoretical linkages among productivity growth, markups, scale economies and capacity utilization, I will rely primarily on three results. These results can be combined and employed directly to motivate the use of estimated cost and demand elasticities to measure these factors, and to generalize, refine and interpret productivity growth and profitability measures.

First, I will use the traditional output-side specification of the productivity growth residual motivated by Solow |16~ (the Solow residual):

|Mathematical Expression Omitted~,

where Y and |p.sub.Y~ are output quantity and price, |v.sub.j~ and |p.sub.j~ are corresponding input measures, "|center dot~" denotes a time derivative, t represents time and |S.sub.j~ is the revenue share |p.sub.j~|v.sub.j~/|p.sub.Y~Y. This expression, representing the growth in output that cannot be attributed to growth in inputs--technical change, is based on manipulation of the production function Y = Y(v, t).

With perfect competition, instantaneous adjustment (full utilization) and constant returns to scale (CRTS), this is equivalent (with a sign change) to the cost-side specification capturing the diminution of costs not explained by changes in input prices and derived from the cost function C(Y,p, t):(1)

|Mathematical Expression Omitted~,

where C is total costs and |M.sub.j~ is the cost-share |p.sub.j~|v.sub.j~/C.

Secondly, I will exploit information on the deviation between costs (C) and revenues (|p.sub.Y~Y) due to violation of the assumptions used to motivate the equivalence of (1a) and (1b). This can arise due to imperfect competition (implying |p.sub.Y~ |is not equal to~ MC, where MC = |Delta~C/|Delta~Y represents marginal cost), or to nonconstant returns to scale or fixity (resulting in AC |is not equal to~ MC, where AC |is equivalent to~ C/Y denotes average cost).(2) As shown elsewhere |10~, recognizing these differences results in the relation

|p.sub.Y~Y = C |center dot~ |MC |center dot~ Y/C~ |center dot~ (|p.sub.Y~/MC) = C |center dot~ ||Epsilon~.sub.CY~/(1 + ||Epsilon~.sub.PY~) = C |center dot~ ADJ. (2)

This wedge between revenues and costs relies on two elasticity expressions. The cost elasticity with respect to output ||Epsilon~.sub.CY~ = |Delta~ ln C(Y, |center dot~)/|Delta~ ln Y = MC |center dot~ Y/C is defined with respect to the cost function. The inverse demand elasticity ||Epsilon~.sub.PY~ = ||Delta~|p.sub.Y~(Y, |center dot~)/|Delta~Y~ |center dot~ Y/|p.sub.Y~ stems from the inverse demand function |p.sub.Y~ = |p.sub.Y~ (Y, |Rho~), where |Rho~ is a vector of shift variables for the output demand function. Equation (2) therefore captures the dependence of revenue on both cost- and demand-side elasticities through the adjustment factor ADJ.(3)

Thirdly, a result based on the ||Epsilon~.sub.CY~ elasticity can be used to interpret equation (2) further: |Delta~ ln C/|Delta~ ln Y = (|Delta~C/|Delta~Y)Y/C = MC/AC differs from one if either nonconstant returns (long run fixities) or short run fixities exist. Specifically, as shown in Morrison |10~, ||Epsilon~.sub.CY~ can be defined as:

|Mathematical Expression Omitted~,

where |Mathematical Expression Omitted~ is (the inverse of) returns to scale, L denotes long run, and C|U.sub.c~ is a cost-side measure of capacity utilization.

Motivation of these measures as representations of returns to scale and fixity requires a cost function explicitly incorporating fixed inputs; C(p, Y, t) = G(p, Y, t, x) + ||Sigma~.sub.k~ |p.sub.k~|x.sub.k~, where G(|center dot~) is a variable cost function and x a vector of K quasi-fixed inputs |x.sub.k~ with market prices |p.sub.k~. The associated shadow cost function C* = G(p, Y, t, x) + ||Sigma~.sub.k~|Z.sub.k~|x.sub.k~ can then be defined, where |Z.sub.k~ is the shadow value of |x.sub.k~, - |Delta~G/|Delta~|x.sub.k~. This forms the basis for defining |Mathematical Expression Omitted~ as (MC |center dot~ Y)/C* (where MC = |Delta~C/|Delta~Y = |Delta~G/|Delta~Y), and C|U.sub.c~ as C*/C = (1 - |Sigma~||Epsilon~.sub.Ck~) (where ||Epsilon~.sub.Ck~ = |Delta~ ln C/|Delta~ ln |x.sub.k~).

Putting the second and third results together leads to |Mathematical Expression Omitted~. An important implication of this expression is that when ADJ |is not equal to~ 1 due to ||Epsilon~.sub.PY~ |is not equal to~ 0 from product differentiation or ||Epsilon~.sub.CY~ |is not equal to~ 1 from either scale economies or fixity, the equivalence of (1a) and (1b) is destroyed. Incorporating this information thus requires correcting the ||Epsilon~.sub.Ct~ and ||Epsilon~.sub.Yt~ measures, which in turn has implications for decomposing ||Epsilon~.sub.Yt~ to identify the impacts of the underlying technical and market factors on overall productivity growth or productive performance. In addition, the deviation between |p.sub.Y~Y and C has important implications about financial performance, since if |p.sub.Y~ Y/C = 1 (ADJ = 1) normal profits will be observed. This provides a useful context in which to assess the Hall |5~ contention that capacity utilization and returns to scale may attenuate the profitability arising from market power. In essence this implies that ||Epsilon~.sub.CY~ counteracts |p.sub.Y~/MC, which could potentially occur with excess capacity (so ||Epsilon~.sub.CY~ |is less than~ 1), and markups (so |p.sub.Y~/MC |is greater than~ 1).

If normal profits are observed, this not only suggests that the levels of the markup, capacity utilization and scale economies are such that this condition holds, but also that if ||Epsilon~.sub.CY~ declines (due either to decreases in capacity utilization or increases in potential returns to scale), this will support a larger markup without increasing overall profitability. In terms of the cyclical behavior of markups, this suggests for example that (with CRTS) increases in capacity utilization will be associated with decreases in markups; markups will be countercyclical.(4)

These issues thus have important implications for the correct measurement and interpretation of productive and financial performance. To pursue these implications further, however, the necessary adaptations of traditional productivity growth measures for these characteristics must be formalized, and an empirically implementable model must be developed to allow estimation of the appropriate elasticities. These steps are pursued in the next two sections.

The Implications of These Relationships for Productivity Growth

Recognizing the impacts of markups, scale and fixity has somewhat varied implications for productivity growth measurement. Correcting for imperfect competition requires recognizing that the denominators of the revenue and cost shares differ due to |p.sub.Y~ |is not equal to~ MC, which necessitates an error bias correction to change the input share-weights in the primal measure. Correcting for scale economies requires accommodating a deviation between MC and AC; this implies an error bias correction to change the denominator of the weights on both output and input changes in the cost measure. Allowing for fixities requires one more step; the numerator of both the primal and cost share-weights for the fixed inputs as well as the denominator of the cost shares must be adapted.

More specifically, the deviation between (1a) and (1b) arising from imperfect competition occurs only because |p.sub.Y~Y |is not equal to~ MC |center dot~ Y = C (given ||Epsilon~.sub.CY~ = 1). Thus, reconciling (1a) and (1b) requires recognizing that (1 + ||Epsilon~.sub.PY~) = MC/|p.sub.Y~ = C/|p.sub.Y~Y, so |S.sub.j~ = |M.sub.j~(1 + ||Epsilon~.sub.PY~). Therefore, correcting the ||Epsilon~.sub.Yt~ computation for markups requires computing |Mathematical Expression Omitted~, where ||Epsilon~.sub.PY~ |center dot~ ||Sigma~.sub.j~ |M.sub.j~(|v.sub.j~/|v.sub.j~) may be considered the "error bias" in the usual primal measurement of productivity growth, and M stands for the "Markup correction". The bias therefore depends on the cost shares, the markup, and the growth rates of the inputs.(5)

If scale economies or changes in capacity utilization also exist, the assumption that ||Epsilon~.sub.CY~ = 1 must also be relaxed. To correct for error biases arising from ||Epsilon~.sub.CY~ |is not equal to~ 1, it must be recognized that (1b) is based on the assumption that the cost function can be written as C(p, Y, t) = Yc(p, t) (where c = C/Y), so d ln c/dt = d ln C/dt - d ln Y/dt. However, if ||Epsilon~.sub.CY~ |is not equal to~ 1, this average cost derivative becomes d ln C/dt - ||Epsilon~.sub.CY~ (d ln Y/dt). Thus, to correct for ||Epsilon~.sub.CY~ |is not equal to~ 1 owing to scale economies, the residual ||Epsilon~.sub.Ct~ must be adjusted to

|Mathematical Expression Omitted~

where R represents "adjusted for returns to scale", and the last term is the error bias in traditional measures when CRTS is assumed inappropriately. Since ||Epsilon~.sub.CY~ = MC |center dot~ Y/C = MC |center dot~ Y/AC |center dot~ Y = MC/AC, the adjustment by ||Epsilon~.sub.CY~ restates the change in output in terms of its correct marginal value. The impact of the bias depends on the extent of scale economies and the output growth rate.

If instead ||Epsilon~.sub.CY~ |is not equal to~ 1 because C|U.sub.c~ |is not equal to~ 1 ((1 - |Sigma~||Epsilon~.sub.Ck~) |is not equal to~ 1), the correction requires changing the assumption that |Delta~C/|Delta~|p.sub.j~ = |v.sub.j~ (the cost-minimizing demand for input j) by Shephard's lemma, to recognize that the implied equality of the value of the marginal product and input price is invalid for fixed inputs. The quasi-fixed inputs should therefore be valued in terms of their shadow prices, |Z.sub.k~ (reflecting the true marginal product of |x.sub.k~), instead of the market price |p.sub.k~, and input shares should be measured in terms of C*. This implies an adjustment in the numerator of the share weight on quasi-fixed input changes as well as in the denominator for the weights of all inputs and output.

The resulting corrected expression for ||Epsilon~.sub.Ct~ therefore becomes

|Mathematical Expression Omitted~

where F represents "adjusted for fixity". As above, the last term in this expression can be thought of as an error bias, which in this case depends on the relative growth rates of output and the quasi-fixed inputs.

Incorporating both fixity and returns to scale therefore requires combining (4) and (5). This measure, denoted |Mathematical Expression Omitted~ (where T represents the "total adjustment") accommodates the full error bias in the standard ||Epsilon~.sub.Ct~ measure. Similarly, constructing an adapted primal measure to obtain |Mathematical Expression Omitted~ requires valuing the fixed inputs in the |Mathematical Expression Omitted~ measure at their shadow values.

Once these corrections for the invalid assumptions of CRTS and instantaneous adjustment are made, the independent impacts of scale and utilization changes on productivity growth measures can be identified in terms of a decomposition of the primal measure to reflect the different cost impacts. This decomposition is analogous to the treatment of returns to scale motivated by Ohta |12~; the relationship between the ||Epsilon~.sub.Yt~ and ||Epsilon~.sub.Ct~ measures when ||Epsilon~.sub.CY~ |is not equal to~ 1 is |Mathematical Expression Omitted~. This "decomposition" isolates technical change independently from the characteristics captured in the deviation of ||Epsilon~.sub.CY~ from one, since it separately identifies the different characteristics that cause ADJ |is not equal to~ 1. It therefore facilitates interpretation by distinguishing the various impacts causing fluctuations in the overall productivity growth measure ||Epsilon~.sub.Yt~.

III. Empirical Evidence on Markups, Fixities and Economic Performance

The Estimating Model

In order to implement and evaluate the productivity growth framework developed in the last section, a model is required to separately identify and measure the components of the ADJ measure--the elasticities ||Epsilon~.sub.PY~, |Mathematical Expression Omitted~, and ||Epsilon~.sub.Ck~. The approaches used by Hall |4~, and Domowitz, Hubbard and Peterson |3~ cannot be used to carry out this task, since they rely on an incomplete specification of the underlying cost and demand relations. Instead, a more comprehensive specification employing a production theory approach based on estimation of cost and demand functions such as that developed in Morrison |6~ must be used for this purpose.

The building blocks of this structural model, which provides the basis for the estimated elasticities used below, are a Generalized Leontief restricted cost function and a similarly constructed output demand function. The specification used here assumes capital (K) and labor (L) are quasi-fixed, energy (E), intermediate materials (M), and purchased services (S) are the variable inputs, and adjustment costs are accommodated by including investment in K and L (|Delta~K and |Delta~L) as arguments of the cost function. The shift variables for the output demand function include consumption expenditures, price indexes for imported and consumption goods, the interest rate, and unemployment.

These two functions were used to construct a system of estimating equations including (i) the cost function plus variable input demand equations for E, M and S derived from Shephard's Lemma (|v.sub.j~ = |Delta~C/|Delta~|p.sub.j~); (ii) a short run price setting equation MR = MC using the expressions for marginal revenue (MR = |p.sub.Y~ + (|Delta~|p.sub.Y~/|Delta~Y) |center dot~ Y) and marginal cost (MC = |Delta~G/|Delta~Y); (iii) two Euler equations to reflect adjustment paths of K and L; and, to complete the system, (iv) the output demand equation.(6) The estimating equations and the resulting parameter estimates fully capture the pattern of supply and demand responses underlying the cost and demand elastities necessary for evaluation and interpretation of the impacts of markups, scale and utilization changes on productive and financial performance.

Data and Estimation

Estimation of this model was carried out using U.S. manufacturing data for 1952-1986 for a number of manufacturing industries. The sectors considered include food and kindred products (FO), textiles (TX), apparel and other textile products (AP), paper and allied products (PA), printing and publishing (PP), chemicals and allied products (CM), petroleum and coal products (PC), rubber and miscellaneous plastics (RB), lumber and wood (LW), furniture and fixtures (FN), clay and glass (CL), primary metals (PM), fabricated metal products (FM), machinery (MC), electric and electronic equipment (EL), instruments and related products (IN), and transportation equipment (TQ). In addition, a total manufacturing category (MA), constructed by aggregating the individual sectors using Divisia indexes, was estimated for comparison.

These data are based on series for prices and quantities of output and inputs developed and used by the Bureau of Labor Statistics (BLS) Office of Productivity.(7) The capital data were, however, reconstructed to generate an ex ante capital price measure more closely related to the procedures used by Berndt and Wood |1~. Such a recalculation is required because the "residual" method of capital measurement in the BLS data generates an ex post measure of capital quasi-rents including any returns not captured by other inputs. The demand variables were primarily taken from the Economic Report of the President. The interest rate used is the Moody Baa bond yield.

The model was estimated for each industry separately, using three stage least squares to incorporate the endogeneity of output quantity and price, and to allow for the possibility of non-static expectations on input prices as suggested by Pindyck and Rotemberg |13~. The instruments employed include lagged values of the exogenous variables facing the firm, as well as the world oil price, defense spending, and the political party variables relied on in the Hall studies. The results were quite robust to different specifications of instruments.

The estimated model for each of the manufacturing industries can be used to generate a large number of indexes, elasticities, and other parameter transformations. Since space constraints prohibit detailed analysis of the different sectors, I concentrate here only on a general evaluation of evidence on markups, scale economies and input fixity, and their effects on productivity growth and economic profitability.(8)

Productivity Growth

Traditional multifactor productivity growth indexes ||Epsilon~.sub.Yt~ based on the K,L,E,M,S division of inputs are presented in terms of average annual growth rates (AAGR) in Table I (SICs for the industries are in parentheses).

The AAGRs reflect the existence of a post-1973 productivity growth slowdown, even though the dramatic stagnation apparent immediately after 1973 in indexes representing yearly changes is somewhat masked by including more recent years in the AAGR computations. The industries which show a negative growth rate in the post-1973 period are PP, PM and PC, the latter two of which are capital- and energy-intensive industries which would tend to be heavily affected by energy price shocks. This pattern is evident overall; the industries hardest hit in the mid-1970s include PM, FM, MC, CM, PA, and RB, all of which are capital intensive. These industries also, however, experienced relatively intense international competition during this time period. The only industry that exhibited increasing productivity growth was MC, which includes the computer industry.(9)

The traditional productivity growth indexes appear considerably procyclical, with, for example, declines appearing in most industries around 1970, 1974-75 and 1982-83. One indication of the extent of these fluctuations comes from the standard deviations of these measures, which are rather large--particularly for durable goods industries.

The fluctuations observed, however, are less systematic than it might initially appear, particularly given the emphasis on cyclicality in the recent studies by Hall. The correlations of these indexes with indexes reflecting cyclical trends are not very significant. In particular, when this productivity growth measure is correlated with a standard published capacity utilization measure (the Federal Reserve Board index for manufacturing, FRB) or the C|U.sub.c~ measure resulting from estimation of my model, the correlations tend to be primarily positive but generally statistically insignificant.(10)

The cyclical fluctuations in productivity that do exist, although not pervasive in terms of statistical significance, influence the interpretation of changes in economic performance. Thus, it is useful to see to what extent these variations might be smoothed, and in this sense "explained", by taking into account cyclically related markup, capacity utilization, and returns to scale factors.

TABULAR DATA OMITTED

These factors, and the associated adaptations of traditional productivity growth measures, will now be considered in turn.

Markups

It has been argued that markups might be expected to be cyclical, although controversy remains about whether they are pro- or counter-cyclical.(11) Hall's treatment of the markup does not allow for cyclicality to exist, since it is treated as a constant parameter. However, the hypothesis of counteracting capacity utilization and markups suggests that increasing markups would be accommodated by additional excess capacity, leading to countercyclicality of markups, as noted above. Domowitz, Hubbard and Peterson more directly address this issue by correlating the markup measure with a published measure of capacity utilization, and find some evidence of procyclicality. In the current study, the cyclicality and determinants of the markup are directly incorporated and thus can be more effectively evaluated.

The estimated markup indexes implied by my model are presented in Table II in terms of annual averages. As found by Hall, significant markups do appear to exist, although the estimates of the markups are intuitively more reasonable than those based on the simpler framework of the Hall studies.(12) The year-to-year variations are also important; although the standard deviations are not large, clear tendencies do emerge.

A secular increase in markups over time is evident (although indexes specified in terms of yearly changes suggest significant year-to-year variations). The only industries that exhibit a clear downward trend in markups are AP, LW, PC and PM; this is consistent with intuition given the intensifying international competition in the apparel, lumber and primary metals markets, and the rise in costs of crude materials in the petroleum refining industry which have caused downward pressure on profit margins. Some other industries facing increasing international competition such as CL and FM (and to a lesser extent TX and TQ) appear from the averages to have quite stable TABULAR DATA OMITTED markup behavior. Interestingly, markups in high-technology industries such as CM, EL, MC and IN all increased from 1960-73 to 1973-86.

In general, markups appear to decline during recessions and in that sense seem procyclical. For example for all industries the 1973 and 1979 OPEC shocks are reflected in a downturn in the markup ratio. However, from correlations of the markup with the economic measure of capacity utilization, C|U.sub.c~, the evidence is overwhelmingly in favor of countercyclicality of markups. The correlations of the reported markups with C|U.sub.c~ (and the full cost elasticity ||Epsilon~.sub.CY~) are negative throughout except for the primary metals industry (PM), and are all statistically significant at the one percent level. For total manufacturing (MA), for example, the correlation is -0.419 with a standard error of .088. Correlations with published FRB capacity utilization measures are somewhat more ambiguous; although the correlations are generally negative, they tend to be small and largely insignificant.

Countercyclicality of markups has a well defined impact on productivity growth patterns through the error bias |Mathematical Expression Omitted~. Since |Mathematical Expression Omitted~, and an increase (in absolute value) in ||Epsilon~.sub.PY~ implies a larger markup, an upward trend in the markup will compensate to some extent for a downward trend in the productivity growth rate (as long as inputs in general are increasing). Given the observed tendencies for increasing markups and declining productivity growth, this provides a partial "explanation" for measured downturns in productive performance. More specifically, since this occurs for both secular and cyclical fluctuations (markups are both increasing and countercyclical), this implies that appropriate cost-based productivity growth measures reveal stronger productive performance and less cyclicality in most industries than standard primal measures.

Carrying out this correction for demand factors can, however, be misleading if cost factors such as scale economies exist that should also be accommodated in productivity growth measures, particularly given the offsetting cyclical patterns of these market and technical forces. Additional insights about fluctuations in traditionally measured productivity growth can therefore be obtained by taking into account also the impact of scale economies and fixity.

The Cost Elasticity, ||Epsilon~.sub.CY~, and Its Components

Fixity was incorporated in the Hall studies in the context of long run returns to scale and the effect measured as a constant parameter. In the model developed above, however, short and long run fixity--capacity utilization and scale economies--are independently distinguished as components of the cost elasticity ||Epsilon~.sub.CY~. This allows not only measurement of the levels of these technological factors, but also assessment of their trends, cyclical behavior, and impact on productive and financial performance.

Capacity utilization is by definition procyclical; if output increases, utilization of a given capacity increases. Similarly, if scale economies exist, upward swings in the cycle (output expansion) cause average cost declines, so this component of ||Epsilon~.sub.CY~ will also tend to be procyclical. This procyclicality suggests that increased profitability from countercyclical markups will tend to be offset by excess capacity and the existence of scale economies captured in ||Epsilon~.sub.CY~.

The measured cost elasticity ||Epsilon~.sub.CY~ is presented in terms of annual averages in the second panel of Table II. These measures suggest short and long run scale economies exist and are quite substantial in a number of industries. Scale economies also appear to be increasing, especially in industries which tend to be more capital intensive and have experienced productivity growth stagnation, such as PA, CM, and PM.

One interesting exception to this is the MC industry. Although productivity growth in this industry has been strong and actually increasing, scale economies have also risen substantially. Note also that this industry experienced one of the largest jumps in markups during this period, as did CM, where scale economies also increased. This is in sharp contrast to PM, where a (more modest) expansion of scale economies occurred along with a decline in markups. This suggests declining profitability as well as productivity performance in the primary metals industry, due perhaps to a decline in relative efficiency and increased international competition. To a lesser extent this is true also for AP.

The procyclicality of the ||Epsilon~.sub.CY~ measure is more obvious from indexes based on yearly changes, where, for example, declines are evident for most industries in the downturns of 1969-70, 1974-75 and 1982-83. To a large extent cyclical movements in ||Epsilon~.sub.CY~ are driven by utilization fluctuations, since potential scale economies appear to be increasing over time rather smoothly. In turn, the capacity utilization patterns appearing in the C|U.sub.c~ indexes result primarily from changes in capital utilization, although labor hoarding, and thus procyclicality from changes in work effort, are also evident from fluctuations in the shadow value of labor.

The independent effects of short and long run fixities can be distinguished from the two components TABULAR DATA OMITTED of ||Epsilon~.sub.CY~--C|U.sub.c~ and |Mathematical Expression Omitted~. These measures are presented as annual averages in Table III, and graphically for total manufacturing in Figure 1. The C|U.sub.c~ numbers in Table III show that capacity utilization has been declining in every industry but PC and LW. They also suggest excess capacity virtually everywhere, although overutilization of capacity appears in the CM industry throughout the time period, and in the early years for the textile industry.

The excess capacity has been driven primarily, especially in the post-1973 period, by a low shadow value of capital relative to its market price; in most industries a decline in the |Z.sub.K~/|p.sub.K~ ratio and an increase in |Z.sub.L~/|p.sub.L~ has occurred post-1973. Note also that the levels of C|U.sub.c~ are less than .9 in the PP, RB, LW, FN, CL and PM industries in this time period, indicating that the cost consequences of short-run excess capacity are often greater than 10%.

The bottom panel of Table III indicates, however, that scale economies seem to be driving the evidence of a low and declining ||Epsilon~.sub.CY~ even more than C|U.sub.c~. In particular, long run returns to scale (|Mathematical Expression Omitted~) are very substantial and increasing, especially in the nondurable industries such as TX, AP, PA and CM. Excess capacity therefore exists even in the long run. Precisely why long-run scale economies are increasing over time in all industries except CL and FM is a fascinating topic for further research, since this result could reflect many different internal and external scale factors.

Figure 1 shows graphically this balancing of |Mathematical Expression Omitted~ and C|U.sub.c~ patterns in the observed cost elasticity ||Epsilon~.sub.CY~. Scale economies appear for manufacturing as a whole to be quite large and increasing; |Mathematical Expression Omitted~ is dropping. A more limited downward drift is evident from the capacity utilization measure, as well as much more cyclicality. ||Epsilon~.sub.CY~ thus seems to reflect the cyclical fluctuations of the utilization measure, and the level and secular trend of the |Mathematical Expression Omitted~ measure.

The full effect of error bias corrections to accommodate the deviation of ||Epsilon~.sub.CY~ from one is not immediately obvious a priori, since the bias depends not only on this elasticity, but also on the relative growth rates of output and quasi-fixed inputs. However, in general procyclical variations in ||Epsilon~.sub.CY~ will result in corrections incorporating ||Epsilon~.sub.CY~ |is not equal to~ 1 to smooth the productivity growth measure and thus "explain" a portion of observed secular and cyclical downturns, since procyclicality implies greater output than input changes. These impacts are further explored in the next subsection.

Productive Performance--Productivity Growth Corrected

The significant levels and trends of the measured markup, utilization and scale measures discussed above suggest that adaptations to standard productivity growth indexes to accommodate these effects will facilitate interpretation of trends and fluctuations in these measures. Adapted productivity growth measures incorporating these corrections are presented in Table IV. The measure reported in the first panel of Table IV is a primal-side measure recognizing the markup and error bias corrections but including returns to scale and utilization as well as technical change (|Mathematical Expression Omitted~), whereas that in the second panel is a cost-side measure isolating the impact of technical change (|Mathematical Expression Omitted~).

A comparison of the indexes in Tables I and IV indicate that correcting for error biases resulting from markups and input fixity is quantitatively important. In general productivity growth TABULAR DATA OMITTED appears lower than reflected in the traditional measure for the 1960-73 period, but often is higher after 1973. Thus, the difference between the pre- and post-1973 periods is substantially reduced and the "productivity growth slowdown" somewhat attenuated.

For example, for total manufacturing, unadjusted growth rates for 1960-73 and 1973-86 are 1.610 and 0.489, while corresponding fixity-adjusted values are 0.973 and 0.528. The entries in the first panel of Table IV also suggest that efficiency growth in some industries (including short and long run economies) has been very limited even from the early years of the sample--especially in the PP, CM, PC, PM and IN industries.

A further reduction in the apparent growth of technical change, especially in the earlier part of the sample, is apparent in the second panel of Table IV when the impacts of scale economies are removed; short and long run scale effects have tended to bias technical change measures upward, especially in earlier years when output growth was relatively strong. However, in some industries, notably CL, PM and FN, standard productivity growth measures have instead tended to understate technical change. In addition, evidence of negative productivity growth is less pervasive when scale impacts are recognized; some of the measured productivity decline can be attributed to higher unit costs due to diminished output demand.

In total, corrections to standard productivity growth measures somewhat reduce secular and cyclical fluctuations in productivity growth measures. This "smoothing" of the productivity growth index is apparent from the year-to-year fluctuations summarized in the graph of ||Epsilon~.sub.Yt~ and |Mathematical Expression Omitted~ for total manufacturing in Figure 2--especially for the strong upswings in the early 1960s and closely following the downturns around 1970 and 1975.(13) The muting effect of the corrections is somewhat limited, however, partly because some industries counteract the overall tendency (the standard deviation for |Mathematical Expression Omitted~ is larger than for ||Epsilon~.sub.Yt~ in some industries).(14)

Overall, corrections of productivity growth measures for error biases due to erroneous assumptions about returns to scale and fixity provide some insights into the "explanations" of productivity growth fluctuations. However, it turns out that once these cost factors are recognized, the correction of ||Epsilon~.sub.Yt~ for markups does not significantly affect the evidence of productivity growth, because the offsetting impacts of markups, utilization and scale imply approximately normal profits and thus equivalence of cost and revenue shares. This is developed in the next subsection.

Financial Performance--Profitability

The counteracting effects of markups and utilization/scale on profitability are evident from the average annual levels of |Mathematical Expression Omitted~ in Table V and Figure 3. ADJ TABULAR DATA OMITTED tends to be close to one, suggesting that revenues approximately equal economic costs, and that economic profits are therefore roughly zero on average. Essentially, managers' pricing responses balance the technical and market economic fluctuations encountered, but do not allow for excess profitability on average.

The annual average ADJ measures presented in Table V suggest that over time this balancing act has resulted in an increasing shortfall of revenues over costs of production (including appropriate returns to capital) in U.S. manufacturing industries. Although for total manufacturing normal profits were approximated for the 1960 to 1986 period, a decline in profitability in the post-1973 period is evident for all industries except PC. This trend exhibits little variation, although some procyclicality appears to exist.

This downward trend in the ratio of returns to costs is evident from Figure 3 for manufacturing overall. This Figure illustrates the relatively greater impact on ADJ of the ||Epsilon~.sub.CY~ elasticity than the markup ratio, since ADJ more closely follows the pattern exhibited by the ||Epsilon~.sub.CY~ index. In particular, ||Epsilon~.sub.CY~ pulls down the ADJ measure over time; markups are not keeping pace with changes in technical factors and competition. Thus, even with greater potential for markups, expanding scale economies and restrictions on flexibility due to capital fixity have had a depressing effect on profitability for most U.S. manufacturing industries.

In particular, although before 1973 only six industries had negative economic profits on average, post-1973 the number of such industries more than doubled to thirteen. Only four industries experienced positive economic profit in this later period (FO, PP, CM and PC), with FO and PC the most profitable.

It is interesting to conjecture that these nondurable manufacturing industries were perhaps subject to less intense competition than most of the other industries during this period of massive international expansion of markets. Other industries, even the MC industry which performed better than other durable industries but still fell short of normal profits by 1% on average, tended to be more internationally competitive as well as more energy and capital intensive.

These numbers are dramatic confirmation of much recent discussion about declining competitiveness of U.S. durable goods and textiles industries. It should be noted, however, that the post-1973 decline in profitability was reversing toward the end of this sample; yearly indexes show increasing profitability after 1982, with positive economic profits by the end of the sample for the MC industry. It will be useful to explore this trend further with the availability of more recent data.

This evidence about financial performance, as noted in the previous subsection, provides some insights about the linkage between measures of productive and financial performance. The Hall markup correction to measure input shares in terms of costs instead of revenues will have little impact on average, since ADJ closely approximates one. However, some pattern in the difference between cost and revenue shares is implied by the reduction in profitability over time; a measure based on cost shares will tend to show a somewhat smaller decline in productivity growth over time.

IV. Concluding Remarks

This paper addresses some determinants of productive and financial performance using a structural model allowing formalization and measurement of the relationships among productivity growth, profits, markup behavior, capacity utilization and scale economies. This framework has permitted consideration of whether these market and technical factors generally ignored in productivity growth analysis have been "responsible" for cyclical fluctuations and secular downturns in economic performance observed in U.S. manufacturing industries.

The first "cause" evaluated is the markup of price over marginal cost. Markup indexes embodying a cyclical component constructed for these industries reveal tendencies for markups to increase over time and in cyclical downturns (implying countercyclicality). As a result, traditional primal productivity growth measures, developed in terms of revenue shares and thus implicitly based on the assumption of perfect competition, exacerbate declines over time and in recessionary periods. Adaptation of the measure to reflect cost shares therefore provides some "explanatory power" for productivity performance variation, by smoothing observed fluctuations.

However, fixities in both the short and long run also have an impact on observed economic performance. In the model used here, short run fixities are captured as changes in capacity utilization, and long run "fixities" are reflected as scale economies. Although capacity utilization is by definition procyclical, I find it also appears to have a downward secular trend. At the same time, the extent of scale economies seems to be increasing over time. This is consistent with economic intuition, for in order to obtain normal economic profits, increasing markups must be offset by a combination of increasing excess capacity and scale economies. The empirical results confirm this counteracting effect in U.S. manufacturing industries; economic profits on average have been zero, but have exhibited a downward trend over time as scale economies have more than outweighed rising markups.

Together, these forces tend to offset the explanatory power of adjustments of primal productivity growth measures for markups. However, incorporating the cost characteristics--utilization and scale--still contributes in an important way to "explaining" fluctuations in productivity growth in terms of error biases. Corrections of erroneous assumptions made in traditional computations have a limited but significant smoothing impact on observed trends in productivity growth and technical change.

1. see Ohta |12~ or Morrison |11~ for further elaboration of this equality.

2. Clearly other internal and external factors such as R&D expenditures or infrastructure capital not appropriately reflected in these measures also will affect this relationship. Only these three determinants of the deviation will, however, be taken into account here.

3. The equality of the inverse demand elasticity ||Epsilon~.sub.PY~ and the markup |p.sub.Y~/MC results because (assuming profit maximization so MR = MC, where MR is marginal revenue), |p.sub.Y~/MC = |p.sub.Y~/(|p.sub.Y~ + Y |center dot~ |Delta~|p.sub.Y~(Y, |center dot~)/|Delta~Y) = 1/(1 + ||Epsilon~.sub.PY~) as discussed in Morrison |10~.

4. A somewhat different argument for countercyclical markups, motivated by industrial organization theory, has been presented by Rotemberg and Saloner |15~.

5. See Morrison |10~ for further elaboration of this relationship and the following adaptations.

6. For further details of the model and its application in the current context, see Morrison |6;8~.

7. The data, including detailed data for the capital components, were graciously provided by Michael Harper.

8. The interested reader can pursue the analysis further using the yearly indexes presented in Morrison |8~. The results in the text are presented for all industries in terms of average annual growth rates calculated from the relevant indexes. Computations of most measures referred to in the next subsections can be made directly from the indexes in Morrison |8~. Other results, such as the shadow value ratios underlying the C|U.sub.c~ measures, require further computation.

9. Semiconductors are included in EL, which also experienced very strong productivity growth over this period, particularly in the late 1970s. The relatively strong performance of the MC industry is driven largely by an enormous productivity growth rate in 1984-86.

10. For more details about the correlation patterns in these measures, see Morrison |8~.

11. See Morrison |7;9~ for further elaboration of the cyclicality of markups and its determinants.

12. This is particularly true for the CM, FO, PC and PP industries, for which the Hall estimates are clear outliers (with markup ratios of 20.112, 5.291, - 139.478 and 14.263, respectively).

13. Only these two indexes are graphed since |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~ are so similar that they tend to overlap.

14. This smoothing is also evident from correlations of the corrected productivity residuals with utilization indexes, which are not as statistically significant as those for the standard measures.

References

1. Berndt, Ernst R., and David O. Wood. "Energy Price Changes and the Induced Revaluation of Durable Capital in U.S. Manufacturing During the OPEC Decade." Manuscript, M.I.T. Center for Energy Policy Research, January 1984.

2. Bresnahan, Timothy, "Empirical Studies of Industries with Market Power," in Handbook of Industrial Organization, edited by R. Schmalensee and R. Willig. Amsterdam: North-Holland Press, 1988.

3. Domowitz, Ian R., Glenn Hubbard, and Bruce C. Petersen, "Market Structure and Cyclical Fluctuations in U.S. Manufacturing." Review of Economics and Statistics, February 1988.

4. Hall, Robert E., "The Relation Between Price and Marginal Cost in U.S. Industry." Journal of Political Economy, October 1988, 921-47.

5. -----. "Invariance Properties of Solow's Productivity Residual." National Bureau of Economic Working Paper #3034, July 1989.

6. Morrison, Catherine J., "Quasi-Fixed Inputs in U.S. and Japanese Manufacturing: A Generalized Leontief Cost Function Approach." Review of Economics and Statistics, May 1988, 275-87.

7. -----. "Markup Behavior in Durable and Nondurable Manufacturing: An Applied Production Theory Approach." National Bureau of Economic Research Working Paper #2941, April 1989.

8. -----. "Market Power, Economic Profitability and Productivity Growth Measurement: An Integrated Structural Approach." N.B.E.R. Working Paper No. 3355, May 1990, earlier version of current article.

9. -----. "Markups in U.S. and Japanese Manufacturing: A Short Run Econometric Analysis." Journal of Business and Economic Statistics, Vol. 10, No. 1. 1992, 51-63.

10. -----. "Unraveling the Productivity Growth Slowdown in the U.S., Canada and Japan: The Effects of Sub-equilibrium, Scale Economies and Markups." The Review of Economics and Statistics, Vol. 74, No. 3, 1992, 381-93.

11. -----. A Microeconomic Approach to the Measurement of Economic Performance: Productivity Growth, Capacity Utilization, and Related Performance Indicators. Berlin: Springer-Verlag Press, 1993.

12. Ohta, Makoto, "A Note on the Duality Between Production and Cost Functions: Rate of Returns to Scale and Rate of Technical Progress." Economic Studies Quarterly, 25, 1975, 63-65.

13. Pindyck, Robert S. and Julio J. Rotemberg, "Dynamic Factor Demands, Energy Use and the Effects of Energy Price Shocks." American Economic Review, December 1983, 1066-79.

14. Romer, Paul M., "Increasing Returns and Long-Run Growth." Journal of Political Economy, October 1986, 1002-37.

15. Rotemberg, Julio J. and Garth Saloner, "A Supergame-Theoretic Model of Business cycles and Price Wars During Booms." Quarterly Journal of Economics, 101, 1986.

16. Solow, Robert M., "Technical Change and the Aggregate Production Function." Review of Economics and Statistics, August 1958, 312-20.

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Author: | Morrison, Catherine J. |
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Publication: | Southern Economic Journal |

Date: | Oct 1, 1993 |

Words: | 7544 |

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