In the literature, comparisons between absolute levels of productivity in different industries occur frequently. This paper explores the meaning and possible significance of such measures. Prices must be used to permit the required comparison of the outputs of different industries. It is shown that base-year weights produce a valid measure of productivity growth but not of absolute productivity level. Current price weights do yield a valid index of absolute productivity but one that tends to be equal for all industries because of the general equilibrium mechanism that reallocates resources from low-productivity to high-productivity industries.

[Energy-production subsidies are, paradoxically, shown to be likely to increase U.S. dependence on imported oil. Standard studies of net energy yields are shown to be seriously biased upward for two reasons. First, many omit indirect energy inputs, which, our input-output calculation shows, probably causes large errors. Second, those studies all omit the energy opportunity costs of nonenergy inputs (e.g., the fuel substituted elsewhere for the labor used to produce energy). We prove that, absent externalities, any fuel-output subsidy which causes an otherwise unprofitable expansion must yield an incremental fuel output smaller than the increment in energy input plus the energy opportunity costs of other inputs.]

Using U.S. input-output data for the period 1947–1996 and Dictionary of Occupational Titles skill scores, I find that U.S. exports have a high content in cognitive and interactive skills relative to imports, and a low content in motor skills. Moreover, the skill gap between exports and imports has widened over time. Imports are more capital- and equipment-intensive than exports, but the difference has fallen over time. By 1987 exports were more computer-intensive than imports. In contrast, though exports were more R&D-intensive than imports in 1958, they were slightly lower in 1996. Labor productivity also rose faster in export than in import industries, and the unit labor cost of exports declined relative to imports.

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 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 or equilibrating shift 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 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 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.

Survey evidence on the importance of bequests is fairly consistent. Dorothy Projector and Gertrude Weiss (1966), using the 1963 Survey of Financial Characteristics of Consumers, reported that only 17 percent of families had received any inheritance. Paul Menchik and Martin David (1983), using probate records of men who died in Wisconsin between 1947 and 1978, estimated that the average intergenerational bequest amounted to less than one-fifth of average household wealth in 1967 and about 10 percent of the average household wealth of families 65 or over in age. Michael Hurd and Gabriella Mundaca (1989) found from the 1984 Survey on the Economic Behavior of the Affluent data that only 12 percent of households in the top 10 percent of the income distribution reported that more than half their wealth came from gifts or inheritances, and only 9 percent in the 1983 Survey of Consumer Finances. However, William Gale and J. K. Scholz (1994), using the 1983 Survey of Consumer Finances, estimated that at least 51 percent of household wealth is accounted for by inheritances and other intentional wealth transfers. II. Data Sources and Methods

Charles R. Hulten's (1992) article suggested that very little of the productivity slowdown of the 1970's could be attributed to capital-embodied technical change. Hulten estimated that about 20 percent of total technical change (what he termed the residual growth of quality-adjusted output) in U.S. manufacturing over the period from 1949 to 1983 could be ascribed to embodied technical change in machinery and equipment. However, he found very little difference in the contribution of embodied technical change to total technical change between the periods 1949-1973 and 1974-1983, the slowdown period. In my paper (Wolff, 1991), I found a very significant vintage effect, estimated by the change in the average age of the capital stock. My data, drawn from Angus Maddison (1982), covered the G-7 countries over the period 1880-1979 and were based on figures for total capital (structures, machinery, and equipment) and for the entire economy. These results suggested that embodied technical change played a significant role in the productivity falloff of the 1970's. In this paper, I use more recent data for six OECD countries (France, Germany, Japan, the Netherlands, the United Kingdom, and the United States) compiled by Angus Maddison (1991, 1993a, b) and focus on the period from 1950 to 1989. I find here that the vintage effect is, indeed, a very strong determinant of the post-1973 productivity slowdown among OECD countries, explaining on average about two-fifths of the slowdown. The effect varies among countries, from a low of 23 percent in Japan to 69 percent in France. For the United States, the vintage effect appears to account for a little over half of its slowdown. Though it should be stressed that my results do not directly contradict those of Hulten, whose measure of technical change was confined to machinery and equipment within U.S. manufacturing, I will still attempt some reconciliation of my findings with those of Hulten at the end. The discrepancy in results suggests the possibility that the slowdown in investment in public infrastructure after 1973 may have played an important role in the post-1973 productivity slowdown. Moreover, since this is only a note, I will not review the rather extensive literature on the productivity slowdown of the 1970's (see, for example, Edward F. Denison's [1979] and my [Wolff, 1985] review articles), except to list a number of factors that have been examined. The main candidates have included the slowdown in the rate of capital formation, changes in the composition of the labor force, the role of energy price shocks, declines in R&D spending (and/ or the productivity of R&D), changes in the composition of output (mainly, the shift to services), and increased government regulation. Of these, the decline in investment appears to have played a major role, explaining about a fourth to a third of the slowdown in U.S. productivity growth after 1973. In Section I, I present the basic data for the analysis. The basic regression results are presented in Section II. In Section III, I consider other possible factors that may have played a role in the productivity slowdown of the 1970's. Section IV provides a decomposition of labor productivity growth into its various sources, including a vintage effect, estimated by changes in the average age of capital. Section V analyzes the relative importance of each component in the falloff of productivity growth observed among OECD countries after * Department of Economics, New York University, New York, NY 10003. The author would like to express appreciation to Moses Abramovitz, Charles Hulten, and two anonymous referees for their comments and to the Sloan Foundation and C.V. Starr Center for Applied Economics at New York University for financial support.