The Disequilibrium Real Wage Rate Hypothesis: An Empirical Evaluation

This paper examines the validity of the hypothesis that the level of the real wage rate, inclusive of employers’ expenditures for social insurance and employment or payroll taxes, is a major obstacle to a return to “high” employment in industrial countries.1 The hypothesis is tested by estimating a production function, solving it for the real wage rate that would be consistent with the high-employment level of labor input given the existing capital stock, and comparing this “warranted” wage with the actual real wage. This exercise is carried out for the manufacturing sectors of the seven largest industrial countries (the United States, Canada, Japan, France, the Federal Republic of Germany, Italy, and the United Kingdom). For each country the estimate of the high-employment level of labor input makes due allowance for regional and skill mismatches between labor supply and demand. A by-product of the analysis is the light the study casts on the relative contribution of low capital formation and high energy prices to the decline in the growth of labor productivity during the 1970s and early 1980s.

Abstract

This paper examines the validity of the hypothesis that the level of the real wage rate, inclusive of employers’ expenditures for social insurance and employment or payroll taxes, is a major obstacle to a return to “high” employment in industrial countries.1 The hypothesis is tested by estimating a production function, solving it for the real wage rate that would be consistent with the high-employment level of labor input given the existing capital stock, and comparing this “warranted” wage with the actual real wage. This exercise is carried out for the manufacturing sectors of the seven largest industrial countries (the United States, Canada, Japan, France, the Federal Republic of Germany, Italy, and the United Kingdom). For each country the estimate of the high-employment level of labor input makes due allowance for regional and skill mismatches between labor supply and demand. A by-product of the analysis is the light the study casts on the relative contribution of low capital formation and high energy prices to the decline in the growth of labor productivity during the 1970s and early 1980s.

This paper examines the validity of the hypothesis that the level of the real wage rate, inclusive of employers’ expenditures for social insurance and employment or payroll taxes, is a major obstacle to a return to “high” employment in industrial countries.1 The hypothesis is tested by estimating a production function, solving it for the real wage rate that would be consistent with the high-employment level of labor input given the existing capital stock, and comparing this “warranted” wage with the actual real wage. This exercise is carried out for the manufacturing sectors of the seven largest industrial countries (the United States, Canada, Japan, France, the Federal Republic of Germany, Italy, and the United Kingdom). For each country the estimate of the high-employment level of labor input makes due allowance for regional and skill mismatches between labor supply and demand. A by-product of the analysis is the light the study casts on the relative contribution of low capital formation and high energy prices to the decline in the growth of labor productivity during the 1970s and early 1980s.

The disequilibrium real wage rate hypothesis is based largely on the observation that, at least in manufacturing, the real wage rate defined from the employer’s standpoint—that is, the nominal wage rate deflated by the value-added deflator rather than by the consumer price index—has tended to grow faster than labor productivity during the past decade and a half. This growth has led to a rise in the share of labor costs in value added and to a corresponding decline in the capital share (see Table 1).2 Although suggestive, this development alone can hardly be viewed as proof that the real wage rate is now too high. It could be that the increase in the labor share was warranted by long-run changes in production techniques, in the price of energy, or in the relative availability of labor and capital. The production function approach allows us to examine these possibilities and to subject the disequilibrium real wage rate hypothesis to a more rigorous test.3

Table 1.

Labor Productivity and Real Wage Rates in Manufacturing in Seven Industrial Countries, 1956–821

(Average annual rate of growth in percent; for SL, average level in percent)

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Sources: See the Appendix.

Notation: Y, real value added; K, gross fixed capital stock in constant prices (before any adjustment for changes in the mean age of the capital stock); L, labor in man-hours; w/p, real wage rate calculated by using the deflator of value added; SL, share of labor costs in value added originating in manufacturing.

Average rate of growth during 1962–69.

Average level during 1961–69.

The purview of the paper is limited in three respects. First, only the manufacturing sector is considered. Obviously, conditions in that sector are not necessarily indicative of conditions in other sectors. Furthermore, the narrow focus on one sector leads to a number of conceptual problems (for example, it is difficult to define precisely the high-employment level of labor input for the manufacturing sector). Second, the capital stock is viewed as an exogenous variable, and no attempt is made to explain investment. It is possible that a disequilibrium real wage rate reduces investment, which would in turn reduce the growth of the warranted real wage rate. The result could be a vicious circle, with higher and higher unemployment. In the absence of an explanation of investment, these dynamic considerations are outside the scope of the present paper.4 Third, prices in the goods markets, including prices of manufactures, intermediate inputs used in the manufacturing sector, and consumer goods, are also viewed as exogenous variables. This last assumption implies that the exchange rate is taken as given, a point addressed in the concluding section.

Section I of the paper describes the theoretical framework that is used in the empirical investigation. Section II discusses the empirical results. Some concluding remarks are presented in Section III.

I. The Theoretical Framework

In the first part of this section a simple production model is used to clarify the main issues under consideration. Two more complex models are then derived to provide a realistic framework for the empirical analysis. Model A is limited to two factors of production—labor and capital—whereas model B views energy as a complement to capital. Finally, the major difficulties inherent in the measurement of the actual flows of labor and capital services, as well as in the measurement of the high-employment flow of labor services, are considered.

a simple model

The main production characteristics of a large and diversified manufacturing sector can be represented by the following aggregate, constant elasticity of substitution (CES) production function with constant returns to scale:

Y=γeλt[(1δ)Lβ+δKβ]1/β(1)

where

  • Y = net output (real value added)

  • t = time trend for disembodied productivity change

  • L = flow of labor services

  • K = flow of capital services.

This specification assumes that the marginal rate of substitution between labor and capital is, in effect, independent of the amount of raw materials (N) and energy (E) being used; that is, it assumes that a change in the price of N or E does not call for a change in K/L. Under such conditions, N and E are said to be “weakly separable” from K and L, and one can study the relation between K, L, and the value-added Y without taking account of N and E. (See Leontieff (1947).)

Aside from the assumption of weak separability, function (1) is fairly general. In particular, it allows the elasticity of substitution between labor and capital (η, η = 1/(1 + (β)) to take any value except the exact value of unity, for which the function is not defined. The function approaches the Cobb-Douglas function as P approaches zero. It does assume that technology is of the “putty-putty” type (with the same possibility to choose among different ratios of labor to capital services at the time of purchase of equipment and throughout the working life of the equipment), rather than of the “putty-clay” type (with the choice becoming more limited after purchase of the equipment). This assumption, however, does not seem to do much violence to the facts. Even after purchase of equipment, there is often considerable room for variation in the ratio of labor to capital services so that, whenever there is a sudden decline in the economically useful capital stock, the demand for labor does not necessarily decline as assumed in the “putty-clay” model.

The assumption of constant returns to scale is also acceptable because, in the seven countries under consideration here, the manufacturing sector is already so large that a further increase in its size does not in itself entail important economies of scale. As new products and new production techniques appear, there is often an opportunity for further economies of scale. Such changes, however, occur gradually over time and are unrelated to the levels of capital and labor in the manufacturing sector. Thus, these changes are more appropriately taken into account by the rate of disembodied productivity change, λ, than by the introduction of economies of scale in the aggregate production function.5

To simplify the theoretical analysis as well as the future econometric estimation, it is convenient to work with a linear approximation of equation (1). This approximation is obtained by writing equation (1) in logarithmic form, applying a Taylor’s series expansion to ln Y about a value of β, which is then allowed asymptotically to approach zero, and dropping the terms involving powers of β higher than 1. This simplification involves no loss of economic realism because the new function provides a good approximation of the CES function over the relevant range of variations for L, K, and the various parameters (Kmenta (1967)). The new function is

lnY=lnγ+λt+(1δ)lnL+δlnK12β(1δ)δ[ln(K/L)]2.(2)

If K is given, entrepreneurs will recruit labor up to the point where the marginal product of labor is equal to the real wage rate; that is,

YL=wp(3)

where w is the money wage rate and p the deflator of value added.

Given that

lnYlnL=YL.LY(4)

the equilibrium condition (3) is equivalent to

lnYlnL=wp.LY=SL=1SK(5)

where sL is the “labor share of income,” and SK is the capital share. We refer to SL as the labor share of income because that is the expression used in most of the economic literature. As noted above, however, what really matters from the standpoint of the demand for labor is the cost of labor—so that employment or payroll taxes have to be included in w and SL, even though they do not represent an income for labor.

After carrying out the partial differentiation of function (2), equation (5) can be written as

SL=1δ+βδ(1δ)ln(K/L).(6)

To have equilibrium in the labor market, L must correspond to its high-employment value, L. The corresponding equilibrium labor share is

S¯L=1δ+βδ(1δ)ln(K/L¯).(7)

The high-employment real wage rate (w/p¯) is obtained by calculating the high-employment level of output (Y) from equation (2) and inserting Y and L in equation (5). In logarithmic form, the result is

ln(w/p¯)=ln(Y¯/L¯)+ln(S¯L)=lnγ+λt+δln(K/L¯)12β(1δ)δ[ln(K/L¯)]2+ln(S¯L).(8)

From equations (7) and (8), we conclude that an increase in the high-employment labor share (S¯L) resulting from a rise in the real wage rate in excess of the rise in labor productivity is at times warranted. In this simple model, it is the evolution of K/L and the value of β that determine if it is warranted. More precisely, S¯L is positively related to K/L if β is positive (that is, if η < 1) and negatively related to this ratio if β is negative (that is, if η > 1). The high-employment equilibrium real wage rate (w/p¯) is positively related to Y¯/L¯ and to S¯L. More fundamentally, w/p¯ is increasing at a rate that corresponds to the rate of disembodied productivity change only if K/L is constant. If K/L is rising, this will boost the increase in w/p¯, especially if β is positive and large.

The other conclusion to be derived from this simple model is that, whereas the gap between the actual real wage rate (w/p) and the warranted rate (w/p¯) is a meaningful indicator of the magnitude of the disequilibrium, the gap between the actual and the warranted labor share can be misleading. From equation (6) it is clear that an undue rise in the real wage rate that leads to a decline in the demand for labor, and therefore to a rise in K/L, could ultimately result in a decline rather than a rise in the labor share. This will be the case whenever β is negative (that is, η > 1). In the more likely case, where β is positive, the labor share will rise, but only by a small amount if β is small. Thus, neither the sign nor the magnitude of the deviation between the actual and the warranted labor share can be taken as a reliable indicator of a real wage rate disequilibrium. When focusing on the share, one should compare the warranted share (S¯L) with the “normalized” share (S˜L) corresponding to the actual real wage rate and to the labor productivity at high employment (that is, S˜L=L¯w/Y¯p). The information provided by this latter comparison is, of course, the same as that provided by a comparison of the actual and the warranted real wage rate.

two more complex models

The above model, while providing a useful introduction to the concepts of a warranted labor share and a warranted real wage rate, needs to be extended considerably before becoming usable for empirical work. First, we will retain the assumption of weak separability for both raw materials and energy and extend the model to take into account the variability in some of the parameters of the production function and the econometric problems raised by estimation of the function. After developing this new model, model A, we will relax the assumption of weak separability with respect to energy. The resulting model, which assumes energy-capital (E-K) complementarity, is model B.

Model A

Whereas in the short run all the parameters in equation (2) can be assumed to be constant, the rate of disembodied productivity change λ and the factor weights δ and (1 − δ) are likely to change in the longer run. The parameter λ is a “catch-all” parameter that represents the multitude of factors that explain why output tends to grow faster than measured inputs; thus, it would be surprising if λ did not change as these factors evolve. This is well recognized in the economic literature. What is less well recognized, but possibly even more important in the present context, is that δ may also change over time and affect the high-employment equilibrium labor share as production techniques and the pattern of production become more, or less, labor-intensive. Such a change in δ could help to explain the evolution of the labor share over the past three decades. The labor share remained roughly constant in most major industrial countries throughout the second half of the 1950s and the whole of the 1960s, despite a doubling or tripling of the ratio of capital to labor. Equation (6) indicates that such a development is consistent with firm equilibrium and with a constant δ only if the production function is of the Cobb-Douglas type (β = 0). But if β is zero and δ is constant, then all of the change in the labor share experienced in the 1970s and early 1980s should be viewed as a move away from equilibrium because the equilibrium labor share would be constant. A plausible alternative is that β is different from zero and that the labor share during the first period was constant because the effect of the increase in the ratio of capital to labor was offset by the effect of the change in δ. A different rate of change for the ratio of capital to labor in the second period could then have led to a different evolution of the labor share.

Allowing λ and δ to change without using many degrees of freedom is not an easy task. For λ, in particular, it is difficult to impose any a priori restriction, so that one cannot avoid a systematic search for statistically significant shifts, despite the cost in terms of degree of freedom. For this reason, this parameter will hereafter be written as λt. For δ, the change should be fairly gradual, and over the plausible range of variation one can assume a simple linear function of time (δ=δ0+δ1t).

Even with this restriction on the way δ can change over time, the number of parameters in equation (2) is too large for reliable econometric estimation from a single equation. With periods of observation limited to 20 to 30 years, there is simply too much multicollinearity among the main variables. Frequently, this problem is solved by jointly estimating the production function and the demand for labor. In the present context, however, this method has to be modified for two reasons.

First, the demand for labor corresponding to a CES production function with λt, and δ=δ0+δ1t is as follows:6

lnL=11+β[ln(δ0+δ1t)βlnγ]11+βln(w/p)β1+βλtt+lnY.(9)

It is apparent that there are two trend elements in equation (9) and that the equation would therefore fail to contribute anything to the estimation of either δ1 or λt.

Second, the demand for labor is derived under the assumption that labor is paid its marginal product. Most studies do take into account that this assumption is plausible only in the longer run by considering equation (9) as a long-term demand for labor. The lagged value of lnL is then added to the right-hand side of equation (9) to reflect the gradual adjustment of the actual demand for labor to its longer-run equilibrium value. The problem is that this specification does not differentiate between the adjustment of L to Y over the cycle, which is often rapid, and the adjustment of L to w/p, which may be quite slow.7 Furthermore, because the cyclical movement in Y is usually the dominant factor, the estimated coefficient of adjustment may exaggerate the rapidity with which the equilibrium between the real wage rate and the marginal product of labor is re-established. Thus, imposing equation (9) on the data is nearly equivalent to imposing the constraint that deviations of the real wage rate from the equilibrium value corresponding to the amount of employed labor cannot last more than a few years. Therefore, the change in the labor share of income experienced in most industrial countries over the past 10 to 15 years would have to be viewed as a phenomenon fully warranted by factors such as changes in production techniques and in the relative amounts of labor and capital within firms. Such an assumption would hardly be appropriate in the context of the present study.8

The approach adopted here to solve the problem of multi-collinearity is to use the share equation (6) rather than the normal demand-for-labor equation. The major advantage of equation (6) is that the rate of disembodied productivity change (λt) does not enter into it, but the relative weight of capital (δ0 + δ1t) does. Thus, equation (6) is a powerful tool to obtain an estimate of δ0 and δ1. Because it is also derived under the assumption that labor is paid its marginal product, equation (6) will be assumed to hold only on a cyclically adjusted basis, rather than in each phase of the cycle. Furthermore, it will only be assumed to have held during 1955–69 for the European countries and during 1955–73 for the United States and Canada, periods for which there is no reason to expect that the real wage rate was out of equilibrium.9 For Japan, equation (6) will also be assumed to have held during 1955–73, even though the extremely low labor share during this period suggests that labor was possibly paid less than its marginal product as a result of an implicit social consensus that a high profit rate was the best way to rebuild the capital stock.

After taking account of the considerations discussed above, we obtain the two functions that make up model A:

lnY=lnγ+λtt+(1δ0δ1t)lnL+(δ0+δ1t)lnK12β(1δ0δ1t)(δ0+δ1t)[ln(K/L)]2(10)
SL=(1δ0δ1t)+β(δ0+δ1t)(1δ0δ1t)ln(K/L)(11)

where

  • SL = the trend-through-peaks value of SL adjusted downward so that the average of SL is equal to the average of SL

  • L’ = the trend-through-peaks value of L adjusted downward so that the average of L’ is equal to the average of L.

Again, equation (11) is imposed on the data only through 1969 in European countries and through 1973 in the United States, Canada, and Japan.

Once the parameters of the model have been estimated from equations (10) and (11), the labor share and the real wage consistent with high-employment equilibrium can be derived from the modified versions of equations (7) and (8):

S¯L=(1δ0δ1t)+β(δ0+δ1t)(1δ0δ1t)ln(K/L¯)(12)
ln(w/p¯)=ln(Y¯/L¯)+ln(S¯L)=ln(S¯L)+lnγ+λtt+(δ0+δ1t)ln(K/L¯)12β(1δ0δ1t)(δ0+δ1t)[ln(K/L¯)]2.(13)

The most noticeable difference between model A and the simpler model discussed earlier is that model A recognizes that a trend increase in the real wage rate that exceeds the increase in labor productivity at high employment (Y¯/L¯) is warranted when there is a reduction in the capital weight δ (that is, when δ1 < 0). Such a situation arises when the pattern of production is shifting toward less capital-intensive industries. An evolution in the opposite direction would call for a growth of the real wage rate that is below the growth of Y¯/L¯.

Model B

Weak separability is broadly accepted as a realistic assumption for raw materials (N), but whether it is a realistic assumption for energy (E) is open to debate. Berndt and Wood (1979) and others have argued that in many instances energy and capital must be viewed as complements. In other words, once entrepreneurs have optimized the energy efficiency of their capital stock on the basis of the relative prices of capital and energy, they are largely unable to change K/L without changing E/L. Under such conditions, the relevant production model would involve the following two-level production function:

Y*=Y*(L,K*)K*=K*(K,E)(14)

where

  • Y* = value added corresponding to L, K, and E

  • K* = a composite variable reflecting the joint input of capital and energy.

With E-K complementarity, a marked increase in the relative price of energy, as in 1973–74 and in 1979–80, would lead entrepreneurs to increase their demand for labor and decrease their demand for both energy and capital. Assuming that the functional form for the Y* level remains as assumed in equation (10), the labor share and the real wage rate consistent with high-employment equilibrium would still be determined by equations (12) and (13), respectively, but after substituting K* for K The labor share would now be the share of labor income in Y*, and the real wage rate would be defined in terms of p*, the deflator of Y*. In equations (10) and (11), SL would have to be replaced by SL* (the cyclically adjusted share of labor income in Y*), and Y would have to be replaced by Y*. An increase in the price of energy leading to a decline in K*/L would shift the distribution of incomes corresponding to Y* against labor if β > 0, and in favor of labor if β < 0.

Because the practical relevance of E-K complementarity is still in doubt, we will derive estimates of the warranted real wage rate under each of the polar assumptions: E-K complementarity (model B), and weak separability of energy (model A). In model B the composite variable K* will be derived by using the linear approximation to the CES functional form (as for output in equation (2), but without the time trend); that is,

lnK*=δElnE+(1δE)lnK12βEK(1δE)δE[ln(E/K)]2.(15)

measurement issues

The first part of this subsection considers the measurement of L and K; the second part considers the measurement of L. The measurement of the other variables is relatively straightforward and is described in the Appendix, as are data sources for the calculations. The only point that needs to be noted here is that for France and Italy the national accounting figures on nominal value added in manufacturing include inventory appreciation—an element that should not be regarded as income either to labor or to fixed capital. For France, we adjusted the figures by using data on inventory appreciation for the whole nonagricultural economy. For Italy, we made an even rougher adjustment on the basis of the observed relation between inflation and inventory appreciation in the other six countries. For both countries, but especially for Italy, the distributional labor and capital shares are thus subject to (possibly sizable) errors.

Measurement of L and K

There is no generally accepted way to measure the flows of labor and capital services. In this paper, we can only provide a brief analysis of the measurement problems and an explanation of what we did. As in most other studies, the present analysis uses series on man-hours worked10 and on the gross capital stock11 as proxies for the unavailable series on the flows of labor and capital services. As is well known, this procedure requires that an additional variable be inserted in the production function to pick up cyclical movements in the intensity of use of labor and capital.12 The reason is that fluctuations in output corresponding to unanticipated changes in aggregate demand do not immediately result in corresponding changes either in the number of man-hours worked or in the level of capital stock. Initially, unexpected variations in demand lead to changes in the intensity of use of labor and capital; that is, the amounts of services obtained from a given number of man-hours and from a given capital stock vary. Gradually, however, the number of man-hours and the level of capital stock are changed, and their intensity of use is brought back to normal. As in Artus (1977), we will assume that the cyclical variable, to be denoted as D and introduced with a coefficient of 1, is a lagged function of the actual rate of change of output, net of the expected long-run rate of change (μ). More specifically, it will be assumed that

lnD=ρ[ln(Y/Y1)μ]L(16)

where the notation [ ]L indicates a geometrically distributed lag operator. The expected long-run rate of change of output will be approximated by a ten-year lagged moving average of ln(Y/Y−1).

Even with D in the production function, there are still various measurement problems that must be considered. For L, the main problem is that the available data on man-hours do not reflect the level of education and technical expertise of the work force. In the present context, however, it is likely that the problem is not too severe because those changes occur only gradually. Even when demographic and economic developments lead to a marked increase in the growth of the work force and to a decline in its mean age, there is no strong reason to assume that the average level of education and technical expertise is affected. Although new entries in the labor force tend to be younger and better educated, they also have less on-the-job experience.13 Thus, the measurement error in L can be assumed to be highly collinear with a simple time trend. It could lead to a bias in the econometric estimates of the trend coefficients (λt and δ1) but the estimates of the other coefficients would be unaffected. Even more important, the estimates of S¯L and (w/p¯) would also be unaffected.

For K, the remaining problems are more severe. All of them are results of the fact that, currently, the only practical method to obtain an estimate of the gross capital stock is the rather mechanical one of cumulating past investment flows, net of discards. This method, if applied carelessly, may lead to a growing measurement error that, this time, would not necessarily be collinear with the trend rates already in the model. Three considerations are especially important.

First, the cumulation of real investment flows does not take proper account of the fact that a piece of machinery bought in year t + 1 embodies more technical knowledge and is thus more efficient than one bought in year t. The reason is that the price series used to deflate the investment flows tend to exaggerate the amount of inflation because the price increases that reflect the efficiency increases are not properly separated from the price increases that reflect inflation. When there is a decline in the growth of investment, as after 1973, it is likely that this decline will be followed by a temporary decline in the growth of the average efficiency of the capital stock because of the temporary reduction in the proportion of relatively new equipment in the total stock of equipment. Such a decline in the growth of the average efficiency of the capital stock will not be reflected in the capital stock series obtained by cumulating investment flows. To reduce this kind of measurement error, the capital stock series used in this study were adjusted by an efficiency scalar that is a function of the mean age of the capital stock. (A detailed description of how this adjustment was carried out can be found in the Appendix.)

Second, voluntarily or as a result of government regulation, firms purchase equipment that produces products that are omitted from the measured gross national product (GNP). In particular, firms purchase equipment to reduce environmental pollution. As long as the proportion of such investment in total investment is constant, the problem is not severe because the rate of growth of the “productive” capital stock is unaffected. In the United States, Canada, and Japan, however, new government regulations led to an upward shift of that proportion in the late 1960s and early 1970s. The data published by the U.S. Department of Commerce indicate that the proportion of pollution-abatement investment in total U.S. investment in manufacturing rose from about 1 percent in the mid-1960s to about 8 percent in the mid-1970s, then declined gradually to around 5 percent in the late 1970s and early 1980s.14 A series for expenditure on pollution abatement was derived from these data, and it was subtracted from the U.S. investment series to get a measure of “productive” investment. No precise data are available for Canada and Japan, but, as a rough adjustment for the jump in pollution-abatement expenditures, the investment figures for these two countries were reduced by 5 percent from 1969 onward. If anything, this adjustment is probably on the low side.

Third, the major unanticipated structural changes that took place in the aftermath of the 1973–74 and 1979–80 oil price increases are likely to have caused the premature obsolescence of part of the capital stock. Capital is heterogeneous and specialized. Sudden changes in the structure of demand faced by firms and the relative costs of using specific energy-intensive equipment leave some equipment without any economic value even though it may be relatively new. Even in less extreme cases, there may be an incentive for firms to speed up the replacement of some equipment by more energy-efficient equipment. Of course, a one-time loss of equipment does not lead to a permanent decline in the capital stock because normal obsolescence would, in any case, eventually lead to the discard of this equipment. Unless premature obsolescence is taken into account, however, the capital stock can be seriously overestimated in the first few years that follow the demand or supply shock.

The extent of this phenomenon in the aftermath of the 1973–74 and 1979–80 oil price increases is still an unsettled issue. Economists such as Baily (1981) take the large decline in the market value of corporations relative to the replacement cost of tangible assets, Tobin’s q, as an indication that a large part of the capital stock (perhaps 20 percent) was prematurely discarded just after the first wave of oil price increases, and that presumably as much was discarded after the second wave. Others, such as Bosworth (1982), compare the historical cost valuation of gross stocks derived from surveys conducted by the U.S. Bureau of the Census with the results derived from the perpetual inventory method of valuation with a fixed-discard pattern and conclude that only a small part of the capital stock (perhaps 2 to 3 percent) was prematurely discarded. Both methods have important weaknesses. Tobin’s q is likely to reflect many factors that have little if anything to do with the effective size of the gross capital stock and the flow of services that can be derived from it. The historical cost valuation of gross stocks derived from surveys is notoriously unreliable. The estimates of gross capital stock used in the present study assume that 10 percent of the existing capital stock was prematurely retired during 1974–76, and that the same proportion was prematurely retired during 1980-82. Because this estimate is highly tentative, a sensitivity analysis was carried out with a 5 percent and a 15 percent estimate.

Measurement of L

To obtain an estimate of the high-employment labor input in manufacturing (L) that is consistent with the definition of high employment for the whole economy, we use the method developed in Artus and Turner (1978). This method is based on the estimation of the following simple equation relating the actual labor input in manufacturing (L) to a nonlinear time trend and to the unemployment rate in the whole economy (U):

ln(L)=a0+a1t+a2t2+a3t3a4U.(17)

At cyclical peaks, the value of L is calculated as

ln(L¯)=ln(L)+a^4(UU¯)(18)

where U is the unemployment rate corresponding to a situation of high employment in the whole economy, and â4 is the estimated value of a4.

In between peaks, the value of L is calculated by fitting log-linear trends between the successive peak values of L obtained from equation (18). After the last cyclical peak, the assumed growth rate of L is an extrapolation of the estimated rate between the last two observed cyclical peaks. The extrapolated figures are adjusted, when necessary, for changes in demographic factors and in the length of the normal work week.

The most difficult task is to estimate the high-employment rate U; that is, the rate where labor shortages become widespread because the residual unemployment is due to the normal turnover in the labor market and to regional and skill mismatches between labor supply and demand. In this study, the estimate of U is derived from the “Beveridge curve,” a graphical presentation of the inverse relationship between unemployment and vacancies.15 More specifically, U is defined as the unemployment rate where the curve becomes nearly vertical, with large increases in vacancies associated with only small reductions in the unemployment rate. Allowance is made for shifts in the curve and, therefore, for shifts in U that reflect changes in the amount of frictional and mismatch unemployment. Over the past decade, however, some of the countries considered here experienced few, if any, years in which the number of vacancies was high, so that it is difficult to draw complete Beveridge curves for this period. In such cases, we examine whether the unemployment rates corresponding to relatively low numbers of vacancies have changed from the 1960s to the 1970s and early 1980s, and we assume that the vertical part of the curve has shifted by the same amount as the part corresponding to relatively low numbers of vacancies. For Italy, where there are no data on vacancies, U was derived by using a more ad hoc method (see the Appendix).

Table 2 presents the main results related to the estimation of L. A striking result is the large value of â4 for Japan, which reflects the effect of labor-sharing arrangements and the apparent greater ease with which the service sector absorbs the increase in labor force during periods of slow growth in the manufacturing sector. Another striking result is the marked reduction in the growth rate of L in Japan and in European countries during the past decade and a half. This reduction reflects a marked increase in the value of U during this period (see the Appendix), as well as an acceleration of the historical trend in the allocation of the labor force in favor of the service sector (possibly caused by the rapid growth of government services), a change in comparative advantages in relation to the newly industrialized countries, and special factors such as North Sea oil in the United Kingdom. Despite the reduction in the growth rate of L, we find that at the cyclical peak in 1979–80 there were still sizable gaps between L and L in Japan, France, the Federal Republic of Germany, and Italy. In contrast, the gaps were fairly small in the United States, Canada, and the United Kingdom because in these countries the residual unemployment, even though very high, seemed to correspond to frictional and mismatch unemployment. By 1982 the gaps were large in all seven countries.

Table 2.

Actual (L) and High-Employment (L) Labor Input in Manufacturing, Latest Peak Year and 19821

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Notation: U, unemployment rate in the whole economy; U, unemployment rate corresponding to high employment in the whole economy; L, actual labor input in manufacturing in man-hours worked (for the United States, man-hours paid); L, high-employment labor input corresponding to the definition of the L series. The unemployment rate is in percent of the civilian labor force (except for Japan, France, and the United Kingdom, where it is in percent of the total labor force).

Parentheses enclose standard errors. The estimates are obtained by using least-squares methods and annual observations of the period 1955–82.

The latest peak year for L is 1979 for the United States, Canada, France, the Federal Republic of Germany, and the United Kingdom and 1980 for Japan and Italy.

Average rate of growth during 1962–69.

These estimates of L are, of course, subject to a large margin of error. In particular, they assume that: (1) at each cyclical peak, the relation between aggregate unemployment (in excess of U) and man-hours worked in manufacturing is the same; (2) the change in the distribution of employment among sectors between two cyclical peaks is due to long-run changes in comparative advantage and in the pattern of demand, rather than to real wage problems in manufacturing; (3) the rate of change of U and the rate of change in the distribution of employment among sectors between the last two cyclical peaks, 1973–74 and 1979–80, can be extrapolated to the early 1980s. On balance it is much more likely that these assumptions lead to an underestimation, rather than an overestimation, of L during the late 1970s and early 1980s, at least in Japan and in European countries. One cannot but wonder whether the marked shift in the distribution of employment toward the service sector, especially government services, that took place in Japan and in European countries between the years 1973–74 and 1979–80 was really warranted by long-run growth considerations. In part this shift may itself be the result of an excessive real wage rate in manufacturing. Some of the persons that could not get a job in this sector (because labor contracts prevented entrepreneurs from offering them a wage corresponding to their marginal product) were probably recruited in the government sector to limit the rise in unemployment, or they may have been absorbed by the private service sector in occupations involving very low marginal product and very low real wages. In addition, it may be unduly pessimistic to extrapolate into the early 1980s the rapid rise in U observed between the years 1973–74 and 1979–80. Indeed, the evidence does not suggest a further shift of the Beveridge curve in the early 1980s, except possibly in France and the United Kingdom.

II. Empirical Results

Parameters of models A and B were estimated for the seven largest industrial countries by using nonlinear least-squares methods and annual observations. For the production function, the observation sample is 1961–82 for the Federal Republic of Germany and 1955–82 for the other six countries.16 For the share function, the observation sample is 1961–69 for the Federal Republic of Germany; 1955–73 for the United States, Canada, and Japan; and 1955–69 for France, Italy, and the United Kingdom.17 In the estimation, the share functions for the United States, Canada, France, and Italy had to be adjusted for first-order autocorrelation by using the Cochrane-Orcutt method, and a systematic search was made for significant changes in the value of the rate of disembodied productivity growth (λt). The estimated values of the parameters were then used to calculate the warranted labor shares and real wage rates.

parameter estimates

Model A

The parameter estimates for model A are presented in Table 3. We find that the rate of disembodied productivity growth increased during the 1960s and then fell back during the 1970s and early 1980s. The only exception is the Federal Republic of Germany, where the rate of disembodied productivity growth was constant throughout the period 1961–82. An examination of the regression residuals for 1981 and 1982 suggests that productivity growth may have picked up again in the United Kingdom in recent years, but it is still too early to say. These results corroborate the findings of Denison (1982), Bosworth (1982), and others, that a significant part of the decline in the growth of labor productivity during the last decade is not accounted for by the decline in the rate of capital accumulation. This is true even when, as in the present study, the rate of capital accumulation is adjusted downward to take account of the rise in pollution-abatement investment and premature obsolescence.18

Table 3.

Estimates of Parameters, Model A1

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Parentheses enclose asymptotic standard errors.

For these countries, the share function had to be adjusted for first-order autocorrelation. The estimates of the coefficients of autocorrelation are: United States, 0.78 (0.09); Canada, 0.50 (0.15); France, 0.60 (0.19); and Italy, 0.82 (0.06).

The trend rates of growth of disembodied productivity are in percent per year.

The estimate of 4.87 (0.15) is for the 1955–58 and 1962–66 periods. For 1959–61, the estimate is 9.39 (0.42).

The weights of capital services are indicated in percent. The trend rates of change in these weights are in percentage points per year.

The estimate of 0.45 (0.03) is for the 1955–70 period. For 1971–82, the estimate is −0.08 (0.07).

SE denotes the standard error of estimate of the estimated equation. The standard error is in percent for the production function and in percentage points for the share function. The R2 is not given because it conveys little information in the present case.

Aside from the evolution of λt over time, it is striking how much λt, varies among countries and how stable the cross-country differences are. For the past three decades, λt has tended to be about 3 percentage points higher in Japan and 2 percentage points higher in France and Italy than in the United States, Canada, and the United Kingdom. The Federal Republic of Germany, by avoiding a decline in λt, has moved from the low group during the 1960s and early 1970s to the middle group during the last ten years. These large and persistent differences have obvious implications, not only for the growth of the real wage rate but also for employment and capital formation. During the last ten years, manufacturing production had to grow by more than 4 percent a year in Japan and by more than 2 to 3 percent a year in France, the Federal Republic of Germany, and Italy to lead to an increase in the demand for labor and capital services in manufacturing. In the United States, Canada, and the United Kingdom, the same result could be achieved with an increase in production of only slightly more than 1 percent.

We find that in most countries the weight on the capital stock, δ, is increasing over time; that is, δ1 is positive. Again, this is not a surprising result; the tendency for a gradual increase in the capital intensity of production techniques has been in evidence for quite a long time. For Japan, however, the data suggest that the tendency for an increase in δ was interrupted during 1971–82. A possible reason for this development is that Japan experienced a marked change in its structure of production during this period as a result of a deliberate policy to move away from industries involving high levels of raw material and energy imports. Many of these industries, such as the steel industry, were also capital intensive. In addition, the value of δ was already quite high during the second half of the 1950s and during the 1960s—much higher than in other industrial countries.

The parameter β is positive for all countries; the corresponding elasticity of substitution between labor and capital (η, with η = 1/(1 + β)) is thus lower than 1. For most countries, η is between 0.5 and 0.8, a result that matches the finding of other studies, such as those by Griffin and Gregory (1976) and Pindyck (1979). The important implication of this result is that a rise in the capital-labor ratio tends to increase the equilibrium labor share of incomes (see equation (12)). In periods when the capital-labor ratio rises rapidly, this effect may dominate the effect of the gradual rise in the weight on the capital stock, and the equilibrium labor share may increase. In other periods the weight effect may dominate, and the equilibrium labor share may decrease.

The estimates of the parameter p are between 0.4 to 0.5 for most countries. This means that a sudden decline in the rate of growth of output of 10 percentage points is normally accompanied by a decline in the intensity of use of labor and capital resources within firms corresponding to a decline in total factor productivity of 4 to 5 percent. Then, the intensity of use of labor and capital is gradually brought back to normal as firms reduce their work force and their capital stock (see equation (16)). In the second year, assuming no further shock, the apparent total factor productivity is only 1½ to 2½ percent below what it would have been without the output decline. In Japan the adjustment is significantly slower. Factor productivity is cut by 7 percent the first year, and it takes four years for the reduction in productivity to become less than 2 percent.

Practically all the parameter estimates have low asymptotic standard errors. This result, however, should not be viewed as an indication that the estimates are highly precise and reliable. First, from a statistical standpoint we are working with fairly small samples, so that the asymptotic standard errors have limited relevance. Unfortunately, the small-sample properties of estimates for parameters in these nonlinear models are unknown. Second, the estimates for δ0, δ1, and β are, for all practical purposes, determined by the share function. When both equations are estimated separately, the estimates of δ0, δ1, and β derived from the share function19 are practically identical to the estimates presented in Table 3, whereas the estimates derived from the production function have often implausible values and high standard errors. Therefore, the estimates presented in Table 3 must be viewed as highly dependent on the assumption that, during the estimation period, SL was in fact the equilibrium labor share corresponding to the cyclically adjusted level of employment.

The results above are based on the assumptions that during 1974–76, and then again during 1980–82, 10 percent of the existing capital stock was prematurely retired. When the assumption was changed from 10 to 15 percent (and then from 10 to 5 percent), the estimated values of λt for the 1970s and early 1980s were raised (and then lowered), but only by 0.1 to 0.2. All the other estimates remained roughly unchanged.

Model B

The first step in the estimation of model B is the estimation of βEK and δE, the parameters that are needed to calculate the flow of services corresponding to the K* input (see equation (15)). In this study, the parameter δE is assumed to be equal to the share of energy cost in the total of energy and capital costs in 1972, the last year before the first wave of oil price increases. To obtain an estimate of δEK, we have used the following equation:

SE=1δ+βEKδ(1δ)ln(K/E)(19)

which is the equivalent of equation (6) for the competitive allocation of income between capital and energy. Focusing on the 1972–82 period of doubling real energy prices, we have solved equation (19) for the value of βEK corresponding to the observed changes in SE and in ln(K/E).20 The results, in Table 4, indicate that the value of βEK is in the order of 2 to 3, which corresponds to a relatively small elasticity of substitution (ηEK) of 0.25 to 0.35.21 For purposes of the present study, we have taken a value of βEK of 2.5 for all seven countries. Because this estimate is subject to a large margin of error, experiments with estimates ranging from 1.5 to 3.5 were carried out, with little effect on the estimates of the other parameters of model B or on the estimates of the equilibrium labor shares and real wage rates.

Table 4.

Estimates of βEK, Model A1

(βEK=Δ7282SE/δE(1δE)Δ7282ln(K/E))

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In this table, SE refers to the share of energy cost in the total of energy and capital costs, while δE refers to the weight of energy in the constant elasticity of substitution (CES) function defining the composite E-K input. The value of δE is approximated by the value of SE in 1972. The symbol Δ72−82SE refers to the change in SE from 1972 to 1982.

For Canada, the estimate refers to the change in In (K/E) from 1972 to 1982, net of the change from 1962 to 1972. The adjustment was made to take account of what appeared to be a long-run trend in In (K/E).

The estimated values of the other parameters of model B are presented in Table 5. The results are similar to those obtained for model A, with two exceptions. First, as could be expected, the estimated value of δ0 is now significantly larger. In all cases, it is approximately equal to the share of capital and energy cost in the total value added corresponding to capital, energy, and labor in the mid-1950s. Second, the reduction in the value of λt from the 1960s to the 1970s and early 1980s is now smaller, but in general not by much. Thus, even when the reduction in energy use achieved during the past ten years is explicitly taken into account, as it is in model B, there is still a sizable unexplained reduction in the rate of growth of disembodied productivity.

Table 5.

Estimates of Parameters, Model B1

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Parentheses enclose asymptotic standard errors.

For these countries, the share function had to be adjusted for first-order autocorrelation. The estimates of the coefficients of autocorrelation are: United States, 0.81 (0.08); Canada, 0.81 (0.09), France, 0.60 (0.21); and Italy, 0.83 (0.05).

The trend rates of growth of total disembodied productivity are indicated in percent per year.

The estimate of 4.22 (0.19) is for the 1955–58 and 1962–66 periods. For 1959–61, the estimate is 7.76 (0.52).

The weights of capital services are indicated in percent. The trend rates of change in these weights are in percentage points per year.

The estimate of 0.50 (0.03) is for the 1955–70 period. For 1971–82, the estimate is −0.12 (0.07).

SE denotes the standard error of estimate of the estimated equation. The standard error is in percent for the production function and in percentage points for the share function. The R2 is not given because it conveys little information in the present case.

warranted labor shares and real wage rates

A comparison of the normalized and the warranted labor shares derived from model A corroborates the disequilibrium real wage rate hypothesis (see Chart 1). By the early 1980s, the normalized share is well above the warranted share in all seven countries except Canada. The gap between the normalized and the warranted shares is particularly large in France, the Federal Republic of Germany, and the United Kingdom, where it reaches about 10 percentage points. The gap is smaller, but still about 5 percentage points, in the United States, Japan, and Italy.

Chart 1.
Chart 1.

Actual (SL), Normalized (S¯L), and Warranted (S¯L) Labor Shares1in Seven Industrial Countries, Model A

(In percent)

Citation: IMF Staff Papers 1984, 002; 10.5089/9781451946918.024.A001

1 Labor shares of value added at factor cost, net of inventory appreciation.

The date at which this gap appears differs among countries. In France and Italy, the normalized share starts to move above the warranted share in the late 1960s and early 1970s, and the move accelerates with the first wave of oil price increases in 1973–74. During the second half of the 1970s, the gap stabilizes in France and declines in Italy. In both countries, the second wave of oil price increases in 1979–80 is absorbed without much change in the gap. In the United States, the gap becomes sizable only with the second wave of oil price increases. In Japan, the Federal Republic of Germany, and the United Kingdom, the gap emerges with the first wave of oil price increases, stabilizes or even starts to contract, and then increases again with the second wave. For Japan, the growth of the gap from 1978 to 1982 reflects an average increase in the nominal wage rate of close to 7 percent a year coupled with an average decrease in the value added deflator of 0.5 percent. With an estimated growth rate of labor productivity at high employment (Y¯/L¯) of 5 percent, the Japanese case illustrates how adjustment can be extremely successful in nominal terms (in the sense of eliminating inflation) without being fully successful in real terms.

These results are broadly similar to those derived by looking at the deviations of the actual labor shares from their historical averages during, say, 1955–69 as measures of the disequilibrium in income distribution. (See Chart 1.) The reason is twofold. First, the evolution of the normalized shares is not all that different from the evolution of the actual shares. Differences have a tendency to appear during periods of recession such as 1974–75 and 1982, when the actual shares often move above the normalized shares because the reductions in the amounts of employed labor lag the reductions in production. Except in Japan, however, the lag is relatively small, so that these differences are quickly resorbed. Moreover, the estimated elasticities of substitution between labor and capital are not extremely small, so that even in recent years it does not matter too much if we consider the actual labor share (which corresponds to K/L) rather than the normalized share (which corresponds to K/L).22 Second, the estimates of the warranted shares for the 1970s and early 1980s are rather similar to the estimates of the warranted shares for 1955–69, which on average are themselves similar to the actual shares during 1955–69. Again, the main reason is that the estimated elasticities of substitution are not very different from 1, so that the warranted shares remain relatively stable despite sizable changes in the rates of increase of K/L.

Even though the new results are broadly similar to those derived from simple comparisons of actual shares, the differences between the two sets of results are far from negligible, suggesting that comparisons of actual shares are at times misleading. For example, for the United Kingdom and, especially, for Italy the warranted labor share is estimated to be higher during the 1970s and early 1980s than during 1955–59, so that a simple comparison of actual shares exaggerates the magnitude of the disequilibrium in recent years. For Japan, the comparison of actual shares is even more misleading. The actual labor share jumps up in the first half of the 1970s, mainly in 1974–75, and then stabilizes, suggesting that Japan adjusted much better to the second wave of oil price rises than to the first. What the new results show, however, is that the jump in the labor share that took place in the first half of the 1970s was not a severe problem. First, it started from a position where the actual share was significantly below the warranted share. Second, it was largely related to the presence of temporary labor hoarding, as shown by the much smaller increase in the normalized share. Third, there was a gradual increase in the warranted share during that period because of a rapid increase in K/L (see Tables 1 and 2). By contrast, during the late 1970s and early 1980s, labor hoarding was slowly reduced, and the stability of the actual share hides a further rise in the normalized share. Moreover, the warranted share stopped rising because the growth of K/L decelerated sharply.

The normalized and the warranted labor shares derived from model B are depicted in Chart 2. All the shares are now expressed as percentages of the total of labor, capital, and energy costs, rather than of the total of only labor and capital costs. For the United States, Canada, and Italy, the hypothesis of E-K complementarity leads to results that differ from those derived from the traditional production model. With reference to the 1980s, the normalized share is now found to be roughly equal to the warranted share in the United States and Italy, and actually smaller than the warranted share in Canada. For the other four countries, however, the estimates of the gaps between the normalized and the warranted shares remain roughly unchanged.

Chart 2.
Chart 2.

Actual (SL), Normalized (S˜L), and Warranted (SL) Labor Shares1, Model B

(In percent)

Citation: IMF Staff Papers 1984, 002; 10.5089/9781451946918.024.A001

1 Labor shares of total cost of capital, labor, and energy inputs; that is, labor shares of the sum of value added at factor cost (net of inventory appreciation) and energy cost.

To understand why the results of model B differ from those of model A, one must consider the effects of E-K complementarity on both the warranted labor shares and the normalized labor shares. The warranted shares tend to rise less, or decline more, in model B than in model A during the past ten years because, with the decline in the use of energy (Table 6), K*/L rises less rapidly than K/L. Because the coefficients of K*/L and K/L are larger for the United States, France, and the United Kingdom than for the other four countries, the warranted shares of the former countries are affected more than are those of the latter countries. These differences are small, however, because the coefficients of K*/L and of K/L for the former countries are still relatively small. The normalized shares also tend to rise less, or decline more, in model B than in model A during the past ten years because of the increase in the cost of energy used (included in Y*p* but not in Yp). But in this case there are relatively large differences among countries. The share of the cost of energy in the total cost of production rose significantly more in the United States, Canada, Japan, and Italy, than in the other three countries during the past ten years (see the last column of Table 6). Furthermore, since the effect of a given rise in the share of energy costs on the normalized labor share is proportionate to the relative size of labor and capital costs, the resulting reduction in the normalized labor share was much larger in the United States, Canada, and Italy than in Japan.

Table 6.

Energy Use and Cost in Manufacturing, 1972–821

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Sources: See the Appendix.

Notation: E, energy use in millions of tons of oil equivalent; Y*, real value added, including the value added corresponding to energy; pe, price of energy in local currency; p*, deflator of Y* in local currency.

In trillions of local currency.

Chart 3 depicts the wage gaps corresponding to the two models. As noted above, these gaps are equal to the corresponding gaps between the normalized and the warranted labor shares scaled by the ratios of value added (inclusive of energy costs for model B) over warranted labor costs under conditions of high employment. For France, Japan, the Federal Republic of Germany, and the United Kingdom, the two models yield a wage gap of 12 to 16 percent for the early 1980s. For the United States and Italy, model A gives a gap in the order of 5 percent, whereas model B gives no significant gap. For Canada, model A suggests no gap, but model B suggests that the real wage rate is, if anything, on the low side.

Chart 3.
Chart 3.

Deviation of Actual from Warranted Real Wage Rate1

(In percent)

Citation: IMF Staff Papers 1984, 002; 10.5089/9781451946918.024.A001

1 A positive number indicates that the actual real wage rate (measured by the relevant value-added deflator) exceeds the real wage rate consistent with the chosen high-employment norm.

A sensitivity analysis indicates that the wage gaps are relatively robust to variations in the estimates of the gross capital stocks and of the high-employment labor inputs. For example, we recalculated the wage gaps for 1982 from model B after reducing our estimates of the gross capital stock by 10 percent. This change decreased the warranted real wage rate and increased the wage gap to 16 to 18 percent in Japan, France, the Federal Republic of Germany, and the United Kingdom; to 3 to 5 percent in the United States and Italy; and to about 0 percent in Canada. When we recalculated the wage gaps after raising our estimates of the high-employment labor input by 10 percent, rather than reducing capital by 10 percent, the estimates of the wage gaps were increased by a further 2 to 3 percentage points.

Finally, we recalculated the wage gaps after reducing our estimates of the high-employment labor input for 1982 to the level of the actual labor input. Even under this extreme—and quite unrealistic—assumption that all the unemployment observed in 1982 was due to regional and skill mismatches between labor supply and demand, we still found a wage gap of 5 to 8 percent in France, Japan, and the Federal Republic of Germany and of about 3 percent in the United Kingdom. This finding is worrisome because it implies that, in the four countries concerned, the level of the real wage rate may be an obstacle not only to a return to high employment, but even to the maintenance of the 1982 level of employment.

An analysis of the factors that led to the emergence of these gaps is outside the scope of the present study, but the evolution of the rate of growth of warranted real wage rates provides an insight into this question. Table 7 gives the estimates corresponding to model B, both in terms of the deflator of output, p*, and in terms of consumer prices, pc. The estimates corresponding to model A would be similar, except that for the United States, Canada, and Italy the post-1973 rate of growth would be somewhat lower. The most noticeable result is the extremely sharp deceleration in the rate of growth of the warranted real wage rate in terms of p* in all seven countries after 1972. This deceleration was attributable partly to a decline in the growth of disembodied productivity (λ) and partly to a decline in the growth of the ratio of the composite capital-energy input to the labor input (K*/L). The deceleration attributable to this ratio was especially marked during the period 1979–82, when energy use fell sharply and investment was depressed. In general, the change in the terms of trade between manufactures and consumer goods (p*/pc) was positive during 1973–78 and negative during 1979–82. Thus, the change reduced the deceleration of the growth of the warranted real wage rate in terms of consumer prices at first, and then increased it. During 1979–82, the rate of growth of the warranted real wage rate in terms of consumer prices was negative in the United States, Japan, and the United Kingdom. In the other four countries, it was only 1 to 2 percent.

Table 7.

Sources of Growth in Warranted Real Wage Rates in Manufacturing, Model B1

(Percentage change in warranted rate attributable to each source)

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Notation: λ, rate of disembodied productivity change; K*/L, ratio of the E-K combined input to labor; δ1, rate of increase in the weight of capital; w/p*¯, warranted real wage rate in terms of the deflator of value added corresponding to labor, capital, and energy; p*/pc, ratio between the deflator of value added and consumer prices; w/pc¯, warranted real wage rate in terms of consumer prices; w/pc, actual real wage rate in terms of consumer prices.

Average rate of growth during 1962–69.

In all seven countries, except the United Kingdom, the adjustment to the deceleration in the growth of the warranted real wage rate in terms of consumer prices was considerable, with the rate of growth of the actual real wage rate declining by 2 percentage points or more from 1956–69 to 1979–82.23 Thus, it would be an exaggeration to say that the rate of growth of the real wage rate was rigid. There actually was a great deal of flexibility, but not always enough. The two most obvious cases in which flexibility has fallen short of that needed in recent years are Japan and the United Kingdom, where the actual real wage rate in terms of consumer prices has kept growing at a rate of 2 to 3 percent, instead of declining in line with the warranted rate.

For France and the Federal Republic of Germany, the other two countries where there is currently a large gap, it is really in the early and mid-1970s that the gap emerged, at a time when the rate of growth of the warranted real wage rate was still relatively high. But, in recent years, the growth of the actual real wage rate has nearly kept in line with the low growth of the warranted rate. These findings suggest that in these two countries the problem is not so much a systematic tendency for inertia in the adjustment of real wages to supply shocks—as argued by Branson and Rotemberg (1980), Sachs (1979, 1983), and others—as it is a failure to reverse the unwarranted increases in real wages of the early and mid-1970s. These increases, at least in France, had as much to do with the wage explosion of the early 1970s as with the supply shocks of the mid-1970s.

Finally, our results for Japan and the United Kingdom can be compared with the results obtained by Lipschitz and Schadler (1984; this issue) in their study of these two countries. To facilitate the comparison, we show in Chart 4 the wage gap indices derived from their complete model on a 1963 basis, as well as our own results derived from model A,24 also in an index form with a 1963 basis. Because the absolute levels of wage gaps derived in our study for these two countries are close to zero in 1963, the corresponding index numbers can still be viewed as conveying information on the absolute size of the gaps. In Lipschitz and Schadler’s study, however, the focus of the analysis is on the change in the wage gaps over time, and these authors do not make any attempt to assess the absolute levels of the gaps.

Chart 4.
Chart 4.

Japan and the United Kingdom: Comparison of Estimated Wage Gaps1in Lipschitz and Schadler (1984) and in Present Study

(1963 = 100)

Citation: IMF Staff Papers 1984, 002; 10.5089/9781451946918.024.A001

1 The wage gap is measured simply as an index of the actual over the warranted real wage level.

Keeping the difference of focus of the two studies in mind, they both indicate that between 1963 and the early 1980s there was a marked rise in the real wage rate in Japan and in the United Kingdom that was unwarranted by the change in the production factors taken into account in the studies. For the United Kingdom, however, Lipschitz and Schadler find a much larger unwarranted rise than we do, mainly because they assume that the potential supply of labor to the manufacturing sector in man-hours increased in line with the growth of the total U.K. labor force (about 0.2 percent a year) throughout the period 1963–82. In our study, the methodology used results in a slight reduction in this potential supply during 1963–69 and then a much more rapid reduction during 1970–82. In the timing of the rise in the gaps, there is a marked difference between the two studies only for Japan. There are two principal reasons for this difference. First, Lipschitz and Schadler assume a constant rate of technical progress, whereas the present study finds a rate of technical progress that is significantly lower during 1971–82 than during 1967–70. Second, for Japan Lipschitz and Schadler use the series on capital stock of the Japanese Economic Planning Agency, series that appear to include an adjustment for pollution-abatement investment and for the early discards resulting from the two waves of energy price increases that is smaller than the one in our own series. Thus, their rate of capital accumulation declines much less than ours during the 1970s and, especially, the early 1980s. The net effect of these elements is that the warranted real wage rate increases faster in our study than in theirs during the late 1960s and the early 1970s, leading to a sharper decline in the wage gap, and then increases more slowly, leading to a sharper rise in the wage gap.

III. Concluding Remarks

We began this paper by noting that the marked increase in the share of labor costs in value added that took place during the 1970s and early 1980s in the manufacturing sector of most major industrial countries does not necessarily imply that the real wage rate is now too high and is causing unemployment. The increase could be warranted by long-run changes in production techniques, in the price of energy, and in the relative availability of labor and capital. After taking into account these considerations, we conclude that, as far as the manufacturing sector is concerned, there are indeed strong reasons to believe that in France, the Federal Republic of Germany, and the United Kingdom the real wage rate is too high, in the sense of being incompatible with high employment. In particular, in these three countries we did not find any evidence that a large part of the actual increase in the share of labor costs in value added is warranted by long-run changes in production techniques, in the price of energy, or in the relative availability of labor and capital. For Canada and the United States, however, the results indicate that there is no real wage problem. For Japan and Italy the results are less conclusive. For Japan, the results indicate that the large increase in the share of labor costs in value added is not fully warranted by concomitant changes in the factors considered in the study. At the same time, the initial labor share was so small that this increase may be less of a problem than it is in France, the Federal Republic of Germany, and the United Kingdom. For Italy, the results suggest that there is no real wage problem, but poor data prevent any firm conclusion in this regard. These findings are derived from an analysis in which the capital stock and the exchange rate are assumed to be exogenous. Moreover, they apply only to the manufacturing sector as a whole; there obviously can be a real wage problem in specific industries, even when the average real wage for the manufacturing sector is not unduly high.25

Although derived from a model that is more elaborate than previous ones, the estimates of the warranted real wage rates on which these conclusions are based must still be regarded as tentative, for at least three reasons.

First, it is difficult to measure the actual flows of labor and capital services and, even more so, the high-employment labor supply in manufacturing. The sensitivity analysis carried out in the present study indicates that the order of magnitude of the warranted real wage rate is relatively robust to plausible variations in the values taken by these variables; nevertheless, the resulting uncertainty is far from negligible. To reduce this uncertainty would require an extension of the study to other sectors of the economy so as to estimate simultaneously the warranted allocation of labor among the various sectors and the warranted real wage rates in all sectors. This extension would be especially useful for countries, such as the United Kingdom, that have recently experienced a major break in the historical pattern of relative growth of their manufacturing and nonmanufacturing sectors. Reducing uncertainty would also require better data on the flow of capital services. The main problem in this regard is the lack of reliable information on the extent of premature obsolescence resulting from the two waves of oil price increases.

Second, the estimates suffer from a number of country-specific problems. For Italy, and to a lesser extent for France, the data on nominal value added in manufacturing are somewhat unreliable because of the lack of adequate information on inventory appreciation. Possible errors in our own estimate of inventory appreciation are as likely to have led to an undervaluation as an overvaluation of the wage gap in the early 1980s. For Japan, the main problem arises from the possible inadequacy of the base period. The extremely low share of labor costs in value added during the 1950s and 1960s—20 to 30 percentage points lower than in other industrial countries—may have resulted partly from an implicit social consensus that a high profit rate was the best way to rebuild the capital stock, rather than exclusively from a low marginal product of labor. In this case, our estimate of the wage gap in the early 1980s could be too high.

Third, an aggregate production function for a whole economic sector is an inherently crude empirical tool because the conditions necessary for aggregation over firms and industries are never fully satisfied, particularly if workers are not paid their marginal products. Not much can be done about this, short of confining studies at the level of the firm or industry. There are, however, some aspects of the production function approach used here that are susceptible to further improvements. The two that are particularly worth singling out concern the complementarity between capital and energy and the evolution of the relative weights of labor and capital over time. More work is needed to determine how much of the energy input should be viewed as a complement to capital and how much should be viewed as weakly separable. More work is also needed to test our assumption that the evolution of the relative weights of labor and capital was the same during the 1970s and early 1980s as it was during the 1950s and 1960s.

These limitations mean that the estimates are far from precise. They do not mean that the estimated wage gaps for France, the Federal Republic of Germany, and the United Kingdom merely reflect statistical artifacts. There is more uncertainty in the case of Japan because of the possible problem with the base period, but we doubt whether this problem can completely explain the measured gap.

An important factor reinforcing our belief that the order of magnitude of the gaps is right is the evolution of unemployment in the countries studied. Unemployment can be classical (caused by an unduly high real wage rate), structural (caused by turnover and by regional and skill mismatches), or Keynesian (caused by a deficiency of aggregate demand). Thus, one should not expect a close cross-country correlation between the unemployment rate and the size of the wage gap. As of early 1984, however, the unemployment rate in France, the Federal Republic of Germany, and the United Kingdom is between 5 to 7 percentage points above our estimate of the structural rate for the early 1980s (see the Appendix), and this gap does not seem to be declining.26 In contrast, the unemployment rate is only 2 to 3 percentage points above the structural rate in the United States and Canada, and the spread is decreasing from month to month. In Japan, the economic and social system is such that the rise in unemployment has been quite moderate; nevertheless, employment in manufacturing fell 4 percent from early 1974 to 1982. This is striking, partly because the total labor force increased by 9 percent during this period and partly because, as recently as the 1960s, employment in manufacturing was rising three times faster than the whole labor force.

Last but not least, we regard our findings as particularly worrisome because of the developments in exchange rates in recent years. The extremely sharp appreciation of the U.S. and Canadian dollar in relation to the other major currencies has had important effects on the relative international price competitiveness of the corresponding countries. It also has probably affected the profitability of their exports of manufactures—decreasing export profitability in the United States and Canada, and increasing export profitability in the other countries. It is not a good omen that, despite these developments, there still seems to be a real wage problem for the manufacturing sector as a whole in most of the large industrial countries outside North America.

APPENDIX: Data Sources and Methodology

value added and labor cost in manufacturing

The data on value added in manufacturing, at factor cost in nominal and real terms, were obtained from national account statistics. The national account data in nominal terms are net of inventory appreciation, except for France and Italy. For France, we adjusted these data by using an estimate of inventory appreciation derived from the data on inventory appreciation for the whole non-agricultural economy. For Italy, we had to make an even rougher adjustment on the basis of the observed relation between inflation and inventory appreciation in the other five countries.

A problem with the data on value added in real terms is that they are derived by using the double-deflation method. As Bruno (1984) has shown, double deflation may introduce a downward bias in the measurement of the growth rate of real value added when the average price of raw materials and energy changes monotonically relative to the price of output. There actually is little risk of a double-deflation bias because of changes in raw material prices as far as the whole 1973–82 period is concerned. In relative terms, the average price of raw materials used in manufacturing declined slowly from 1955 to 1972, rose sharply in 1973–74, declined sharply in 1975, and then entered a new period of slow decline that was interrupted by a brief rise in 1978–79. Thus, as long as the weights used for recent years are not based on the abnormal relative price of 1973–74, which is not the case in any of the seven countries considered here, the bias from the change in the relative price of raw materials will be small. The doubling in the real price of energy from 1972 to 1982, coming after a period of gradual decline, is a more serious problem. Whenever possible, we have sought to avoid this potential source of bias by using series of real value added that are based on post-1973 weights from 1972 onward and on pre-1973 weights for 1955–72. But for four countries—the United States, Canada, France, and Italy—this could not be done because national accounts statistics based on post-1973 weights are not yet available. For these countries, therefore, the estimate of λt in model A for the post-1972 period may be biased downward. However, a comparison of the data on real value added based on post-1973 weights with the data based on pre-1973 weights for Japan, the Federal Republic of Germany, and the United Kingdom suggests that the bias is not very large (say, an average of 0.2 to 0.3 percentage points a year for the whole period 1973–82). There is no problem in model B because the cost of energy is not subtracted from gross output.

The data on labor cost were also obtained from national accounts statistics. Labor costs include not only the wage bill, but also all fringe benefits, employers’ social security contributions, and employment and payroll taxes.

man-hours worked in manufacturing

For all countries except France, the data were provided by the U.S. Department of Labor, Bureau of Labor Statistics, Office of Productivity and Technology (hereafter referred to as the BLS). Except for the United States, where the only data available are for man-hours paid, the data are for man-hours worked. For France, the series for the whole manufacturing sector were derived by aggregating the series for the food, intermediate, capital, and consumer-goods industries provided by the Institut National de la Statistique et des Etudes Economiques (INSEE).

overall unemployment and vacancy rates

The data on unemployment and vacancies were obtained from Organization for Economic Cooperation and Development, Main Economic Indicators (Paris: OECD, various issues). The data on unemployment are expressed as percentages of the civilian labor force, except for Japan, France, and the United Kingdom, where they are percentages of the total labor force. The data on vacancies are percentages of the civilian labor force for the Federal Republic of Germany; percentages of the total labor force for Japan, France, and the United Kingdom; and in index form for the United States and Canada.

The unemployment rate corresponding to a situation of high employment in the whole economy was estimated by using the Beveridge-curve method (see Section I of the text, under “Measurement Issues”). The estimates are as follows: for the United States, 3.4 percent for 1955–69, 4.8 percent for 1972–74, and 5.7 percent for 1977–80; for Canada, 3.4 percent for 1955–68, 5.5 percent for 1972–74, and 7.2 percent for 1977–80; for Japan, 1.1 percent for 1955–71,1.3 percent for 1972–78, and 1.6 percent for 1978–80; for France, 1 percent for 1955–68, 2.6 percent for 1972–78, and 3.6 percent for 1979–80; for the Federal Republic of Germany, 0.7 percent for 1961–71 and 2.2 percent for 1975–80; and for the United Kingdom, 1.2 percent for 1955–66, 1.8 percent for 1969–71, 2.6 percent for 1973–76, and 4.6 percent for 1978–80. No estimate was made for years in which the observations fell between two Beveridge curves. (In the present study, an estimate is required only for years corresponding to a cyclical peak for the number of man-hours worked in manufacturing.) For Italy, the Beveridge-curve method could not be used because there are no data on vacancies. From 1955 to 1974, we used a “trend-through-peaks” method, with the unemployment rate at each cyclical peak in employment assumed to be equal to U. For the 1980 peak, we assumed somewhat arbitrarily that U was equal to 6.5 percent, about 1 percentage point above the unemployment rate reached at the 1974 cyclical peak.

gross fixed capital stock in manufacturing

Estimates of gross fixed capital stock in manufacturing, without adjustment for changes in its mean age, were derived from data on gross fixed capital formation in constant prices by using the perpetual inventory method, which consists in cumulating past investment flows and deducting the equipment discarded from the stock. Except for Japan, the calculation starts from a benchmark estimate of the capital stock at the beginning of 1920. For Japan, the calculation starts from a 1950 benchmark estimate. The capital stock at the beginning of year t—Kt—was calculated by the formula:

Kt=K0ert+Σi=1n(1ϕi)Ati(20)

where ert is the proportion of the initial (1920) capital stock that remains at the beginning of year t, At−i is the capital stock installed in year t−i; ϕi is the proportion of the capital stock corresponding to At−i that has been retired by the beginning of year t;t is zero at the beginning of 1920; and At−i is set equal to zero before 1920.

In the calculation, it is assumed that the capital stock installed in year t is a lag function of the investment flows,

At=0.30It+0.50It1+0.20It2(21)

where the coefficients take into account the average time needed for new projects to be completed and to become fully productive.27

The calculations were made separately for machinery and equipment and for structures, with an average service life of 15 years for machinery and equipment and 35 years for structures.28 Actual retirements from capital stock accumulated after 1920 were calculated following a Winfrey S-3 distribution, with discards starting at 45 percent of the average life.29 Special adjustments were made for damages suffered during World War II. Moreover, the energy price increases of 1973–74 and 1979–80 were estimated to have brought about the early discard of, respectively, 10 percent of the capital stock of early 1974 during 1974–76 and 10 percent of the capital stock of early 1980 during 1980–82. (For further explanation of these adjustments for energy price increases, see Section I of the text, under “Measurement Issues.”)

Data on gross fixed capital formation in manufacturing, valued at constant prices and disaggregated into machinery (and equipment) and structures, were obtained from the following sources.

Canada

Series for 1926–81 are from Statistics Canada, Fixed Capital Flows and Stocks, 1926–78 (Ottawa: Statistics Canada, 1980 and subsequent issues).

United States

Series for 1920–82 are from unpublished data supplied by John Musgrave (U.S. Department of Commerce, Social and Economic Statistics Administration, Bureau of Economic Analysis, Washington).

Japan

Series for 1950–81, on total gross fixed capital formation in manufacturing in current prices, are from Japan, Economic Planning Agency, Annual Report on National Income Statistics (Tokyo: The Agency, various issues). These series were deflated by using the deflator of private investment in plant and equipment for the whole economy, available from the same source. The series in constant prices were disaggregated into machinery (and equipment) and structures, on the basis of data supplied by the Japanese Ministry of International Trade and Industry.

France

Series for 1920–69 are from Jacques Mairesse, “L’Evaluation du Capital Fixe Productif,” Les Collections de L’INSEE (Paris), Serie C, (Nos. 18–19, November 1972). Series for 1970–81 are from unpublished data supplied by Jacques Mairesse (Institut National de la Statistique et des Etudes Economiques, Paris).

Federal Republic of Germany

Series for 1920–66 are from Wolfgang Kirner, Zeitreihen für das Anlagevermögen der Wirtschaftbereiche in der Bundesrepublik Deutschland (Berlin: Duncker & Humblot, 1968). Series for 1967–81 are based on data provided by the IFO Institute (Institut für Wirtschaftsforschung, Munich).

Italy

Series for 1921–50 are from Istituto Centrale Di Statistica, Sommario Di Statistiche Storiche Dell’Italia, 1861–1965 (Rome: The Institute, 1968). Series for 1951-81 are from OECD, National Accounts of OECD Countries (Paris: OECD, various issues). These sources provide only aggregate data. The disaggregation of data into machinery (and equipment) and structures is based on the study in Centro Studi Confindustria, Lo’stock’di capitale nell’industria Italiana (Rome: The Center, 1979), and on more recent data provided by Giuseppe Rosa (Centro Studi Confindustria, Rome). The series for Italy refer to manufacturing, mining, and utilities.

United Kingdom

Series for 1920–38 are from C.H. Feinstein, Domestic Capital Formation in the United Kingdom 1920–38 (Cambridge, England: Cambridge University Press, 1965). Series for 1939–45 are from G.A. Dean, “The Stock of Fixed Capital in the United Kingdom in 1961,” Journal of the Royal Statistical Society (London), Series A, Vol. 127 (Part 3, 1964). Series for 1949–82 are from U.K. Central Statistical Office, National Income and Expenditure (London: Her Majesty’s Stationery Office, various issues).

Data on investment for 1982 were obtained from various published and unpublished sources or were based on Fund staff estimates; they must be considered very preliminary.

In the calculation of the series on capital stock, the post-1965 data on investment for the United States were adjusted by netting out the pollution-abatement investment obtained from the June issues of the Survey of Current Business (Washington, U.S. Department of Commerce, various years). For Canada and Japan, the post-1969 data on investment were cut by 5 percent to take into account that, with the intensification of the efforts to reduce pollution, there had also been a marked increase in the proportion of investments that do not contribute to value added in these two countries. (See Section I of the text, under “Measurement Issues,” for further explanation.)

Estimates of the mean age of the capital stock were obtained from the same investment data, with the same adjustments for war, energy price increases, and the drive to reduce pollution. Here also, the calculations were made separately for machinery and equipment and for structures. The mean age (Z) was calculated by the formula:

Zt=(tK0ert+Σi=1ni(1ϕi)Ati)/Kt.(22)

For each of the two types of capital goods, the estimate of the capital stock adjusted for deviations of the mean age from the 1967 level was then defined as:

Kt=Kteϕ(ZtZ1967)(23)

where the rate of embodied technical progress, ϕ, is equal to 0.02 for machinery and equipment and to 0.05 for structures.30

Finally, data on the total capital stock were obtained by summing the adjusted stocks of machinery and equipment and of structures.

energy use in manufacturing

Data on total final consumption of energy in manufacturing, in millions of tons of oil equivalent, were obtained from International Energy Agency, Energy Balances of OECD Countries (Paris: OECD, various issues).31 The data exclude the consumption of energy products for purposes other than energy generation.

Indices of the average prices of energy inputs in the manufacturing sector were provided by the International Energy Agency (OECD, Paris) on request. Estimates of average prices in units of local currency were derived by using these indices and the data on prices of individual energy products in 1978 published in International Energy Agency, Energy Conservation in the International Energy Agency—1978 Review (Paris: OECD, 1979); in Claire P. Doblin, The Growth of Energy Consumption and Prices in the USA, FRG, France, and the UK, 1950–80 (Laxenburg, Austria: International Institute for Applied Systems Analysis, 1982); and in U.S. Department of Energy, Energy Information Administration, International Energy Evaluation System, International Energy Prices, 1955–1980, Service Report, SR/STID/81-21 (Washington: DOE, December 1981).

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*

Mr. Artus, Assistant Director of the Research Department, is a graduate of the Faculty of Law and Economics in Paris and of the University of California at Berkeley.

The author acknowledges his debt to his colleagues in the Research Department and in area departments of the Fund for helpful comments and suggestions.

1

Malinvaud (1977, 1982) presents an updated theoretical analysis of the relation between inappropriate real wages and unemployment. Sachs (1979, 1983), Branson and Rotemberg (1980), Drèze and Modigliani (1981), Bruno and Sachs (1982), Giersch (1982), Kouri, Braga de Macedo, and Viscio (1982), Grubb, Jackman, and Layard (1983), Knight (1983), Steinherr (1983), and Lipschitz and Schadler (1984; this issue) are some of the principal advocates of the view that the level of the real wage rate is a major obstacle to a return to high employment in European countries. Sachs (1983) and others have found evidence of inappropriately high real wages in the United States and in Japan but have not detected marked effects on unemployment in these two countries.

2

There is also some evidence that in several countries the share of labor costs in value added has risen in other sectors during the past decade and a half, but this evidence is difficult to interpret. Sectors such as transport, communication, and utilities are largely under public control in most industrial countries, so that the profit motive does not play an important role in determining their demand for labor. In the private service sector, it is difficult to define the share of labor costs because of the high proportion of persons working on their own account.

3

Among the studies listed in footnote 1, Knight (1983) and Lipschitz and Schadler (1984) use a production function approach to allow for the effect of changes in the relative availability of labor and capital on the warranted share of labor costs in value added. They ignore, however, the possible effect of changes in production techniques and in the price of energy on this share. The other studies mentioned assume that any sustained gap between the growth of the real wage rate (defined from the employer’s standpoint) and the growth of labor productivity implies a disequilibrium situation. The drawbacks of such an assumption and the need for a comprehensive production function approach have rightly been stressed by Basevi and others (1983).

4

A discussion of these dynamic effects can be found in Malinvaud (1977, 1982) and in Bruno and Sachs (1982).

5

The assumption of constant returns to scale was tested as part of the empirical study by adding a scale parameter to equation (1). This parameter was not found to be significantly different from unity.

6

The demand for labor is derived under the assumption that the flow of capital services is given. To derive it, it is more convenient from a mathematical standpoint to use equation (1) rather than its linear approximation, represented by equation (2).

7

A possible solution would be to have a separate, distributed lag on w/p and Y, but here again there would be a problem of multicollinearity. The major change in w/p took place in the early 1970s, and it would be difficult to disentangle its effect on the demand for labor from the effect of the likely concomitant change in the rate of technical progress.

8

Consideration of the conditions in the steel and shipbuilding industries in European countries during the 1970s and early 1980s suggests that a disequilibrium situation, involving low or negative profitability and an excess of labor, can at times last more than a decade.

9

In European countries, the wage explosion of late 1969 is usually considered to mark the beginning of the real wage problem. In the United States and Canada, the beginning of the problem is usually traced to the 1973–74 oil price increase.

10

For the United States, the only data available are for man-hours paid. See the Appendix for data sources.

11

“Gross capital stock” refers to the equipment that has not been discarded. In this context, if some equipment has lost x percent of its initial efficiency, then x percent of the equipment is considered to have been discarded. By contrast, the net capital stock excludes not only discards, but also the depreciation of the equipment that has not been discarded. This depreciation reflects the fact that the equipment, while retaining its original efficiency, has a remaining life expectancy that is shorter than on the date of purchase. In the main, the net capital stock can be viewed as the discounted value of the expected stream of capital services to be derived from the existing capital stock. Thus, the net value of equipment will normally start declining well ahead of any decline in the flow of services that can be derived from that equipment. For this reason, no attempt is made to use the net capital stock in the present study.

12

The other equations involve variables such as SL, S¯L, w/p¯, and L that are not influenced by cyclical developments.

13

It has been argued that various other factors, especially the male-female ratio, should be taken into account in the calculation of the amount of labor input. This has led Perry (1971), Perloff and Wachter (1980) and others to calculate weighted indices of man-hours, with the weights based on the relative pay scales for the various components of the labor force. For the manufacturing sector, however, these indices have usually been found to deviate little from simple indices based on the unweighted man-hours. A good review of issues related to the measurement of labor services can be found in Baily (1981).

14

See the article “Capital Expenditures by Business for Pollution Abatement” in each June issue of the Survey of Current Business, U.S. Department of Commerce, Bureau of Economic Analysis (Washington). See also the November 1982 issue.

15

For a discussion of the theoretical underpinning of the Beveridge curve, see Bowden (1980).

16

Before 1961, the data for the Federal Republic of Germany exclude Berlin and Saarland; therefore, they are not directly comparable with the data for subsequent years.

17

The estimation was carried out with the minimum-distance estimation routine of the Research Analysis Language (RAL) program. To enable estimation of the production and share functions as a system of two simultaneous equations, the variables in the share functions were set at zero during 1970–82 or 1974–82, depending on the group of countries. The estimation was then carried out for the period through 1982. The standard error of estimate of each equation was recalculated after reducing the number of degrees of freedom for the observations in the share functions corresponding to 1970–82 or 1974–82.

18

As explained in the Appendix, in the United States, Canada, France, and Italy the estimated value of λt for 1973–82 in model A may be biased downward to a small extent because the data on real value added for this period are calculated on the basis of the pre-1973 relative price of energy.

19

The estimates are as follows (an asterisk indicates significance at the 5 percent level; parentheses indicate standard errors):

article image

These estimates are based on the ordinary least-squares method and have the usual statistical properties. The standard errors are often much larger than those presented in Table 3, but most of them are still relatively small.

20

This method assumes that SE and ln(K/E) were relatively stable during the pre-1972 period. For Canada, where K/E was declining at a marked rate during the 1960s and early 1970s, the 1972–82 change in ln(K/E) was calculated in terms of deviations from the 1962–72 tendency.

21

This estimate of ηEK can be compared with the E-K gross substitution elasticities of 0.133 for the U.S. manufacturing sector, 0.501 for Canadian manufacturing in Ontario, and 0.650 for Canadian manufacturing in British Columbia that were obtained by Berndt and Wood (1979) on the basis of pre-1972 data. The estimate implies that an increase in the price of energy may lead to a decline in the demand for capital services. For example, a 100 percent increase in the price of energy could lead to an increase in pK* of 15 percent (assuming that energy represents initially 15 percent of the total energy and capital cost), an increase in p* of 5 percent (assuming that energy represents initially 5 percent of the total labor, capital, and energy cost), and a decline in the demand for K* of 7 percent (assuming an elasticity of substitution of 0.7 between K* and L and a fixed amount of L). With an elasticity of substitution of 0.3 between K and E, the ratio of E to K would change by 30 percent. The final result would be a drop in the demand for E of 32 percent and a drop in the demand for K of 2 percent (averaging to the drop in K* of 7 percent, given the 15 percent weight on E and the 85 percent weight on K).

22

From equation (12), we see that if L is 1 percent greater than L, the equilibrium share corresponding to K/L will be smaller than that corresponding to K/L by β(δ0 + δ1t)(1 − δ0 − δ1 t). On the basis of the estimates presented in Table 3, this difference ranges from plus 0.002 in the United States to 0.0005 in Canada.

23

This adjustment is more sizable than it appears because payroll taxes rose sharply during 1979–82 in France, Italy, the United Kingdom, and Japan, so that the growth of the take-home wage was even lower than the growth of the gross wage considered here (see Steinherr (1983)). In contrast, payroll taxes in the United States were reduced during this period, decreasing the need for a cut in the take-home wage.

24

We choose model A to facilitate the comparison with the results of Lipschitz and Schadler, which do not take account of the effects of energy prices on the shares of labor costs in value added.

25

The present study ends in 1982; however, the preliminary data available for 1983 suggest that, except in the United Kingdom, little progress was made toward adjustment during that year. The share of labor costs in value added in manufacturing may have declined by 1 to 2 percentage points in the United States, Canada, France, and the Federal Republic of Germany and may have risen by 1 to 2 percentage points in Japan and Italy. With cyclical developments taken into account, this represents probably a small decline in the wage gap in 1983—by, say, 2 percentage points—in France and Germany, a small rise in Japan, and not much change in the other countries. In contrast, the share of labor costs may have declined by about 4 percentage points in the United Kingdom—a decline that, once the modest economic recovery is taken into account, may represent a decline in the wage gap of 4 or 5 percentage points.

26

A comprehensive empirical analysis showing that increases in labor shares (or in product wages) have had a negative effect on employment growth in Europe can be found in Steinherr (1983).

27

Extensive studies of the lag from start of construction to completion have been made by Mayer (1960). The coefficients of equation (21) are based on Mayer’s results and on an assumed start-up period of two quarters.

28

These estimates are based on the 1942 edition of U.S. Treasury Department, Bulletin F (Washington: Government Printing Office), which remains the standard reference for calculations of capital stocks in the United States. A recent survey by Blades (1983) found that calculations of capital stocks made in other industrial countries are normally based on discard rates similar to the U.S. rates. The two important exceptions are Japan, with more rapid discard rates, and the United Kingdom, with slower discard rates. Given that most capital goods are similar throughout the industrial world, however, there was little reason in the context of the present study to assume that the “economic efficiency” of capital goods changed persistently at markedly different rates in the various countries.

29

The Winfrey S-3 distribution is described in National Technical Information Service, Fixed Nonresidential Business Capital in the United States, 1925–73 (Springfield, Virginia: NTIS, 1974).

30

The estimates of 0.02 and 0.05 were initially suggested by Solow (1957) in his pioneering article. Econometric results consistent with these estimates were obtained in Artus and Turner (1978).

31

The data published by the International Energy Agency refer to the industrial sector, but the definition of the industrial sector used by the Agency is comparable with the definition of the manufacturing sector used in national accounts statistics.