Industrial Composition, Interindustry Effects, and the U.S. Productivity Slowdown

This paper investigates the effect of shifts in output composition on the slowdown of productivity growth in the United States between 1947-67 and 1967-76. I employ a Leontief input-output framework and a Divisia index of aggregate productivity growth to separate the effects of changes in sectoral rates of technical progress from the effects of changes in output composition and interindustry flows on the change in overall productivity growth. Of the approximately 2 percentage point decline in overall total factor productivity growth, 17% to 22% was due to compositional effects and the remainder to other factors. T HE importance of shifts in input or output composition in explaining the recent productivity slowdown in the United States has been a source of some controversy. Estimates of such shift effects vary considerably. For example, Gollop (1982) calculated that resource shifts were actually an offset to the slowdown in productivity growth; Kutscher, Mark, and Norsworthy (1977) estimated that employment shifts had no effect on productivity growth; Thurow (1979) ascribed half of the slowdown between 1965-72 and 1972-77 to employment shifts; and Nordhaus (1972) attributed 77% of the decline from 1948-55 to 1965-71 to employment shifts. In a related paper, the possible reasons for these disparate results were discussed at length (see Baumol and Wolff, forthcoming). Briefly, these differences stem primarily from the use of different concepts and measures. Actually, three different concepts are used in the literature. The first is a " resource allocation" or "equilibrating shift" effect, which measures the increase in productivity that can result from a more efficient allocation of resources (cf. Denison (1979a, 1979b, and 1984); Norsworthy, Harper, and Kunze (1979); and Gollop (1982)). While interesting in itself, this resource reallocation effect is a somewhat limited notion, measuring the movement toward the efficient frontier instead of the outward movement of the frontier over time. The second concept is the so-called "level" effect, which assesses the effect of resource shifts on overall productivity growth by holding constant the productivity levels of the various sectors of the economy (cf. Nordhaus (1972); Kutscher, Mark, and Norsworthy (1977); and Thurow (1979)). This measure was found to be quite arbitrary, depending on the (arbitrary) choice of base year used in the computation. The third is the so-called "rate effect," which assesses the effect of shifts in resources by holding constant sectoral rates of productivity growth (cf. Nordhaus (1972); Baily (1982), and Gollop (1982)). All three authors found that the rate effect had a negligible influence on the productivity slowdown. This measure is the most theoretically sound of the three, and my measure will fall in this category, though differ in significant ways from previous formulations, and show a greater effect on overall productivity growth from compositional changes. I shall first develop a general model to measure such shifts or composition effects from a Leontief input-output framework (sections I and II). Results for the U.S. economy over the 1947-76 period will then be reported, with particular emphasis on accounting for the productivity slowdown after 1967 (sections III, IV, and V). Conclusions and a comparison with other results will be discussed in section VI, VII and VIII. I. The Standard Model Following the work of Peterson (1979), let us define: X,= (column) vector of gross output by sector at time t Y, = (column) vector of final demand by sector at time t at= matrix of inter-industry technical coefficients at time t It = (row) vector of labor coefficients at time t, showing employment per unit of output kt = (row) vector of capital stock coefficients at time t, showing the capital stock required per unit of output p,= (row) vector of prices at time t, showing the price per unit of output of each industry. Received for publication June 27, 1983. Revision accepted for publication October 19, 1984. * New York University. I would like to express my appreciation to Wassily Leontief, William Baumol, M. I. Nadiri, Mark Schankerman, Martin Baily, and Andrew Sharpe for helpful comments and to the Division of Information Science and Technology of the National Science Foundation for financial support.