Richard Wo Kopcke* From 1950 to 1965 the average annual growth of output per hour for nonfarm, nonresidential business was 2.5 percent; from 1965 to 1978 labor productivity grew only 1.5 percent per year, a decline of 1 percentage point. In manufacturing, the decline was somewhat less, .6 of a percentage point. This erosion of productivity growth suggests that the rate of expansion of potential Gross National Product (GNP) may have dropped a full percent- age point in recent years--whereas potential growth was commonly believed to be almost 4 percent until the mid-1960s, many now believe it is nearer 3 percent. ~ This study concludes that much of the slump in productivity and poten- tial GNP growth resulted from a slower rate of capital accumulation. One- half of the decline in labor productivity for nonfarm nonresidential business is due to slower growth of the stock of plant and equipment. For manufactur- ing, slower capital accumulation may account for the entire drop in produc- tivity growth. Much of the decline in the demand for capital can be attributed to rising inflation since the late 1960s. From the mid-1950s to the early 1970s invest- ment tax incentives increased the demand for capital, but since then rising inflation rates generally have raised business income tax burdens, thereby depressing the demand for capital. The postwar incentives for investment caused the capital stock to grow much faster than employment, temporarily boosting the expansion of poten- tial GNP. Since 1965, however, rising inflation has depressed investment incentives and the rate of capital accumulation, temporarily retardihg the expansion of full-capacity GNP. This study’s analysis suggests that a policy designed to insulate the demand for capital from high inflation could achieve a potential growth rate of 3.5 percent or more during the remainder of this century. * Assistant Vice President and Economist, Federal Reserve Bank of Boston. The author is grateful to Jarius DeWalt for his research assistance. ~ See, for example, various issues of the Economic Report of the President; the issues published in 1962, 1965, and 1979, among others, provide useful comparisons. This paper is not suggesting that 1965 is the year when productivity fell. Analysts first noted a slower productivity growth in the late 1960s and early 1970s. Because 1965 roughly divides the postwar period in half, separating the period of high growth from the years of slower growth, and because the pace of capital accumulat.ion began to drop after 1965, this year provides a useful benchmark for mea- suring the recent productivity slump. The growth of output per hour did not drop dramatically in any single year, rather it has progressively declined over many years perhaps commencing as early as 1965. 26 CAPITAL ACCUMULATION KOPCKE 27 The first two sections of this paper, particularly the second, describe this study’s analytical techniques. Section III compares the growth of output with the employment of capital and labor to show how slower capital accumula- tion since the mid-1960s has depressed the growth of labor productivity. Sec- tions IV and V then describe how the higher income tax burdens on capital, due to higher inflation rates since the mid-1960s, have depressed capital accu- mulation, thereby reducing the growth of potential output. The last section summarizes the study’s principal conclusions. I. The Production Function Two common methods for studying the sources of productivity and out- put growth use either "growth accounting" or production functions. Growth accounting assumes that the earnings of each factor of production equals the value of its product when it is fully employed.2 Output growth may then be attributed to labor or capital by weighing the growth in hours worked and the expansion of the capital Stock by. their respective earnings. For many well- known reasons, though, the earnings of labor and capital may seldom match the value of their product, even in years of "full employment," so growth accounting may poorly describe the sources of productivity growth.3 The production function compares output with the employment of labor and capital services directly to isolate the sources of productivity growth. Accordingly, output is a function of labor and capital inputs. Q = F (K, L). This approach shares one weakness with growth accounting: it is difficult to measure the overall quantity of.labor and capital services because differences in quality among people or plants are difficult to assess? According to the production function, current engineering knowledge determines the maximum, or potential, output per "unit" of material input that can be produced with a given stock of labor and capital. The growth of potential output is then determined by the expansion of the labor force and 2 In many cases, it is the marginal product which presumably equals the factor cost. 3 First, the market value of corporate capital (essentially the prospective value of its prod- uct) seldom equals its replacement cost. In many respects, skilled labor and managers, like plant and equipment, represent an investment whose product may also seldom match its cost. Second, a growing business may hire more labor and Capital than it needs to satisfy current orders if it is preparing to increase future capacity. Third, businesses often do not know in advance howmuch of their product they can sell at particular prices; consequently, the value of labor’s product, for example, may sometimes exceed its wage, and, at other times, this product may fall short of labor’s wage. Wages may not even match the average value of labor’s product because risk- averse firms may hire labor only so long as the expected value of its product exceeds the wage by some protective margin. Fourth, whenever businesses or labor do not merely passively supply their products or services at market prices over which they exert no influence, the earnings of capital and labor are not determined solely by their productivity. For these reasons, among others, factor earnings reflect more than factor productivity alone. 4 1 do not use a "weighted" measure of the labor force for example. See footnote 3. 28 THE DECLINE IN PRODUCTIVITY GROWTH the capital stock as well as by the pace of technical progress that enables a given stock of labor and capital to produce more output from a given flow of material inputs. If the flow of output is compared to the use of only one factor of production--labor, for example--then its productivity depends not only on overall technical progress but also on the employment of the other factors of production--the more capital labor uses, the more output labor can produce. The growth of output per hour worked, therefore, depends on technical pro- gress and the growth of the capital stock. The specific production function used in this study is translogarithmic: (1) In (Q/H) = ao + aeln(E/H) + asln(S/H) +/3e~ln(E)~ + flesln(E)ln(S) + flehln(E)ln(H) + flesln(E)ln(S) ~ + Bssln(S) +/3shln(S)ln(H) + ~3~ ln(E)ln(H) + ~3s~ln(S)ln(H) + fl~ln(H)2 + a(T), E: the stock of producers’ durable equipment; H: hours; Q: value-added; S: the stock of nonresidential structures; o~(T): productivity and technical change. The function, as defined above, has constant returns to scale, and the last term is intended to represent Hicks-neutral technical change and secular variations in total factor productivity.5 II. Estimation of the Production Function Using a Bayesian technique, the parameters of the production function are estimated from postwar data. The stochastic representation of (1) is: (2) In(Q/H) = o~o + o~eln(E/H) + o~sln(S/H) + Oee(ln(E)~ + ln(H)2 - 21n(E)ln(H)) + ties(In(H)2 + ln(E)ln(S)- ln(H)ln(E)- ln(H)ln(S))~ + ~3eh(ln(S)2 + ln(H)2 - 21n(S)ln(H)) + oq(T) + o~2(T)2 + o¢3(T)3 + ~, where T represents a time trend.6 ~ Energy is not a factor of production for value-added. See the extensive discussion in Appendix A. 6 T is unity in 1950:1 and 116 in 1978:4. CAPITAL ACCUMULATION KOPCKE 29 (3) y = X3,+ ~ ~t = P et-I +vt vt~N(O,°2), where y is a vector of n observations on In(Q/H), X is a matrix com- prised of observations on the right-hand-side variables of (2), and y contains the parameters of the production function. The errors, ct, may be represented by a first-order Markov process driven by a normal random variable, v .7 The prior distribution for 3’ is normal with mean g~ and precision matrix (inverse of the variance matrix) N~. The conditional posterior distribution for ~ is defined by the following statistics for each of ten discrete values for p(p= .li, 1 = O ..... 9): (4) let R = -o 10 ...0 [x/~-pZ0p- 1 000...01 0 00 ...1 then N2 = (XtRtRX/a 2 + N~) g2 = N2-t(XtRtRy/a2 + N~gt), where ~2 is the mean squared residual from the normal projection of Ry onto RX. For a given value of p, then, the posterior is conditional on both p and ~2 7 Rather than estimate the more common share equations, the production function is esti- mated directly. The share equations impose strong assumptions about the pricing policy of busi- ness, and, having imposed these assumptions, these share equations suffer from "simultaneous equations problems" at least as severe as the production function itself. For example, a rise in business tax rates will depress capital’s share of after-tax value-added, ceteris paribus, while it raises the marginal user cost of capital.