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

• Author: Morrison, Catherine J.

1. 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.

2. 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...