1. the survey of firms

The idea behind the survey method is that if what one is interested in is the level of potential output of firms, then why not simply ask firms about this level? The logic of the argument is powerful, and such surveys are now regularly conducted in a number of industrial countries. This paper will not attempt to review the survey techniques; however, a few general comments can be made.

First, practically all such surveys avoid defining exactly what they attempt to measure. In the McGraw-Hill survey of U. S. manufacturing firms, for example, firms are asked to indicate both their “actual operating rate” and their “preferred operating rate.” Other surveys ask firms to indicate whether they are producing at “full capacity.” Respondents are free to interpret these terms as they wish. It is difficult to know how firms interpret these concepts. In particular, it is not clear whether firms refer, in their reply, to the intensity of use of the capital stock alone, or to an output gap that would also take into account the intensity of use of employed labor and the possibility of increasing labor inputs. For this reason, it is difficult to interpret the results obtained when replies of individual firms are added together to obtain a sumary figure for the whole manufacturing sector.

This weakness of the survey method is not likely to be corrected by designing better surveys. Even if a precise definition of the concept of potential output were included in the survey, it is difficult to see how an individual firm could estimate, in the middle of a recession, the amount of labor it would have if there were no shortfall in aggregate demand and the economy were at full employment. If, as is likely during a recession, each respondent tends to assume that he has, at his disposal, an unlimited supply of labor at a fixed price, an aggregation of the replies will yield a greatly exaggerated view of the potential output of the sector, since the supply of labor is obviously limited when all firms are considered together. Ultimately, what is needed are estimates of the potential output of firms that are based on prices of all inputs, such that the aggregate demand for such inputs corresponds to the aggregate supply that can reasonably be considered available to the manufacturing sector. Firms have no way of knowing what such prices are. They may make some assumptions as to what “normal” input prices are; however, it is doubtful that these assumptions remain unchanged over the various phases of the cycle.⁷

A further imprecision in existing surveys involves the time horizon. Independently of how many unused resources are present in the economy, a move to a significantly higher production level can only be gradual because of delivery lags for raw materials and intermediate inputs, start-up time in previously closed production facilities, and (mainly) the reallocation of resources that may be needed to meet a change in the composition of demand. Ruist and Söderström (1975) have shown that it is this impossibility of increasing production at short notice, rather than the full utilization of any particular factor of production, that seems to guide the replies to surveys. This would also explain Perry’s finding that, “It appears that respondents [in the McGraw-Hill utilization survey] ‘find’ capacity when output rises sharply, and ‘lose’ it when output slackens.” (Perry, 1973, p. 711). This strongly suggests that survey results should be interpreted as a source of information on the existence of short-term bottlenecks, rather than on potential output per se. In particular, the results do not provide an objective measure of the depth of a recession. There is, however, no doubt that surveys are, when cautiously interpreted, a useful source of information on the amount of spare capacity as viewed by entrepreneurs.

2. the fitting of trend-through-peaks

Under the trend-through-peaks method, cyclical peaks in production indices are marked off, and linear segments are fitted between successive peaks. The linear segment between the last two cyclical peaks is extrapolated at its established slope until a new cyclical peak is established. The envelope so defined is considered to indicate potential output. In the United States, the method has been developed mainly by Klein and his associates at the Wharton School.⁸ The Wharton indices for the United States are calculated at the industry level, and then averaged using value-added weights to reach indices for the manufacturing sector.

In addition to its simplicity, this method has the advantage of defining potential output as an attainable level of production, at least for the historical period that extends through the last cyclical peak. By construction, the indices implicitly take into account the interdependence among the various industries and the overall constraint on the availability of labor and other noncapital inputs. However, the method rests on the three strong assumptions: (i) potential output is growing at a constant rate between two successive peaks even when peaks are many years apart; (ii) potential output is reached at each cyclical peak; and (iii) the rate of growth of potential output between the last two cyclical peaks can be extrapolated to the present or to some future date. At least the second and third assumptions do not seem plausible. It is likely that, at cyclical peaks, labor and capital are being used at more than a normal and sustainable intensity level. This would not be too much of a problem if the same intensity level were observed at each peak. The trend-through-peaks method would not yield an absolute measure of potential output, but it would give an indicator that was consistent over time. However, there is no reason to expect the same intensity level to prevail at each peak.⁹ The third assumption seems even less appropriate, particularly at the present time. It is quite doubtful that potential output in many countries is currently growing as fast as it was before 1973 (the most recent peak for most industrial countries). This inability to provide a reliable estimate of potential output after the last peak is a rather crucial weakness, since policymakers are justifiably interested mainly in the level of potential output in the present period and its projected evolution.

3. the estimation of production functions

In the production function approach, information on the evolution of available productive resources is taken into account directly to obtain estimates of potential output. First, a relationship is estimated between the observed volume of production and the amount of resources used in the production process. Then this relationship is employed to calculate the level of output corresponding to full employment of the labor force, with labor and capital being used at normal intensity.

The estimation of aggregate production functions raises many difficulties, which are reviewed here only briefly. At a given point in time, numerous kinds of labor, machinery, and natural resources are used to produce a varied mix of goods. To represent the whole production process by a simple equation, it is necessary to aggregate these various inputs and outputs into a few composite variables. This gives rise to many problems.¹⁰ In particular, the aggregation of various kinds of capital equipment, at different points in their life cycles, into monetary measures has given rise to controversies for years. When the production function is employed to describe the production process over a number of years, further problems arise with respect to the representation of technical progress and of changes in the quality of the labor and capital inputs.¹¹ As indicated in Section I, resources within firms may also be used with various degrees of intensity, and degrees of intensity can only be proxied by other variables. Finally, there are difficulties in quantifying resource availability—in particular, the full-employment labor force.

For all these reasons, the aggregate production function approach cannot be considered a panacea. At the same time, it has the significant advantage of directly taking into account the information available on the amount of productive resources available to the whole sector considered. Difficulties with the production function method are empirical in nature; they can, to some extent, be surmounted by using appropriate econometric techniques and by acquiring better data.

1. methodology

The production function used here is a modified Cobb-Douglas function. The Cobb-Douglas form was selected because its main characteristic, the unitary elasticity of substitution between labor and capital, seems to have been well substantiated by most empirical studies.¹² The specification of the function is

where

Q	=	actual level of output
t	=	time trend for technical change
K	=	gross fixed capital stock
Y	=	mean age of the capital stock
L	=	labor (in man-hours worked)
Z	=	dummy variable taking the value zero through 1973 and one thereafter to account for the effects of the increase in the relative price of energy
k1,l1	=	intensity of use of capital and labor, respectively
u	=	a random distributed error term (with the Gauss-Markov properties)

View Table

Q	=	actual level of output
t	=	time trend for technical change
K	=	gross fixed capital stock
Y	=	mean age of the capital stock
L	=	labor (in man-hours worked)
Z	=	dummy variable taking the value zero through 1973 and one thereafter to account for the effects of the increase in the relative price of energy
k1,l1	=	intensity of use of capital and labor, respectively
u	=	a random distributed error term (with the Gauss-Markov properties)

The mean age of the capital stock is introduced in the equation to take into account embodied technical progress.¹³ Time series on the capital stock, obtained by cumulating gross investment flows in constant prices, net of discards, do not take into account the fact that a piece of machinery bought in period t + 1 is likely to be more efficient than one bought in period t because it embodies more technical knowledge. For this reason, it is not only the size but also the mean age of the capital stock that is important.¹⁴ No attempt is made here to identify long-run changes in the quality of labor inputs.

The Z dummy variable that reflects the effects of the recent increase in the relative price of energy can be given several interpretations. As noted previously, part of the capital stock in industrial countries may have become obsolete because of the sudden oil price change. This could be the case for equipment that is energy intensive or that is used to make products that are heavy users of energy. Perhaps more importantly, the economic crisis in 1974–75 that followed the oil price increase was exceptionally severe and resulted in dislocations in the production system. For all these reasons, the potential output level of industrial countries may have been reduced substantially.

Equation (1) is a highly simplified representation of the production system. In particular, it neglects the multiplicity of factors grouped under the expression “technical change” that are conveniently represented by a log-linear time trend. For that reason, allowances will be made in the empirical study for changes in the trend element, and separate trends will be introduced for factors specific to some countries—for example, the increase in pollution-related investment in the United States and Japan in the 1970s. This allowance for changes in trend rates will increase the flexibility of the model; however, these allowances are a poor substitute for the empirical analysis of the factors accounting for technical change that is needed here. The analysis of technical change is still one of the weakest fields in economics, and this weakness is the major handicap that one faces in the calculation of potential output.

The intensity of use variables, k₁ and l₁, are “cyclical” variables. They represent differences in pressure exerted on capital and labor, reflecting variations in demand pressures in the goods market. Proxy variables for the intensity of use of capital and labor are derived as follows. It is assumed that, in the short run, unexpected variations in output are absorbed by changes in the intensity of use of capital and labor. Then, gradually, the amounts of capital and labor are changed, and their intensity of use is brought back to normal. During the adjustment process, the intensity of use of the inputs will be proportional to the discrepancy between the actual amounts of the inputs and the long-run optimal amounts corresponding to the observed output, that is,

and

where K° and L° are the long-run optimal levels of capital and labor corresponding to the observed output level.

In formulas (2) and (3), K° and L° reflect the current output Q while both K and L, being only gradually adjusted to unexpected changes in the output level, depend on both current and past values of Q. This suggests that the average factor intensity can be proxied by a lag function of the rate of change of the output level, net of the long-term rate of change, ${\dot{Q}}^{*}$.^{15, 16} More specifically, it is assumed that

where the dot above a variable indicates that the rate of change of the variable in proportionate terms (i.e., $\dot{Q}=Q/Q_{-1}$ is considered, and where the notation (---)_L indicates a geometrically distributed lag operator beginning in period t - 1. The rate of change in the current period is introduced separately so as to have a more flexible specification of the adjustment lag.

Equation (4) is based on the hypothesis that each firm adjusts its labor force and capital stock to its output level gradually and always at the same speed. This assumption cannot be maintained when specific measures are taken by the authorities to increase labor retention by firms. Such measures were implemented in Japan, France, Italy, and Sweden in 1975; they may have led to a temporary fall in labor productivity that should not be confused with the more lasting effect of the increase in the price of energy. Dummy variables of the zero-one kind will be introduced to take into account these specific factors.

Replacing k₁ and l₁ in equation (1) by the formula (4), and rearranging terms, yields

Assuming that firms are normally cost minimizers, the ratio α/β can be approximated by the ratio s/(1 – s) of the shares of capital income s and labor income 1 – s in manufacturing.¹⁷ This hypothesis allows the calculation of a factor input variable F defined as

Introducing the F notation, and noting that α = (α + β)s and that β = (α + β) (1 - s), allows equation (5) to be rewritten as

The long-run optimal output QO corresponding to the capital and labor within firms is defined by setting $\dot{Q}$ equal to ${\dot{Q}}^{*}$ and u equal to zero in equation (7), that is,¹⁸

The potential output QF is also defined by assuming normal factor intensity and setting u equal to zero. However, in addition, the deviation between the actual labor force L (measured in man-hours) and the full-employment labor force LF is taken into account, that is,

Series on the full-employment labor force were obtained by estimating a simple labor participation equation of the form

where U refers to the unemployment rate in the whole economy. At cyclical peaks, the value of LF was calculated as

where U_s is the structural unemployment rate, and ${\hat{a}}_4$ the estimated value of a₄.

In between peaks, the value of LF was calculated by fitting log-linear trends between the successive peak values of LF obtained from equation (11). This indirect method was used to minimize the errors that might have resulted from misspecification of the labor participation equation.

2. Empirical results

The first step in the estimation of the parameters of the production function defined by equation (7) is the calculation of the ratio β/α from factor share data.¹⁹ The preferred method is to consider the average shares for a number of years, since the equality between β/α and the factor share must be viewed only as a long-run tendency. For Canada, the United States, Japan, Italy, and the United Kingdom, average factor shares were calculated from annual national account statistics for the period 1955–75. The necessary time series could not be obtained for France, the Federal Republic of Germany, and Sweden. For these countries, the factor shares were read from available input-output tables.²⁰ Estimates of labor shares in incomes allocated to labor and capital are as follows: Canada, 0.67; the United States, 0.73; Japan, 0.58; France, 0.67; the Federal Republic of Germany, 0.64; Italy, 0.64; the United Kingdom, 0.70; and Sweden, 0.69.

Even with the factor share assumption, there are too many parameters in equation (7) to permit unconstrained estimation for individual countries. To reduce problems of multicollinearity and least-squares bias, the rate of embodied technical progress θ and the effect of the increase in the relative price of energy d were assumed to have the same value in all eight countries considered. Further, the geometrical lag distribution ${(\dot{Q}/{\dot{Q}}^{*})}_L$ was also assumed to be the same for all countries. This last hypothesis is not as constraining as it appears, since the constrained lag distribution starts only from the period t - 1, and the current rate of change $(\dot{Q}/{\dot{Q}}^{*})$ is introduced separately in the equation.

The estimation of the parameters of equation (7), taking into account cross-country constraints, was made by least squares from the pooled annual data for the eight countries considered for the period 1955–75. The exponent τ of the geometrical lag distribution ${(\dot{Q}/{\dot{Q}}^{*})}_L$ was estimated by a search procedure (i.e., the value minimizing the standard error of the equation was selected). Nonlinear least-squares techniques had to be used to obtain estimates of α + β that were consistent with the estimates of θ(α + β) and that satisfied the constraint that the value of θ was the same for all eight countries. Finally, to avoid least-squares bias resulting from the presence of the dependent variable Q in the right-hand variable $(\dot{Q}/{\dot{Q}}^{*})$ the latter variable was replaced by an instrumental variable. The chosen instrumental variable was the estimated value of $(\dot{Q}/{\dot{Q}}^{*})$ obtained by regressing this variable on the current and lagged values of the variable $(\dot{L}/{\dot{L}}^{*})$.²¹

Results of the regression analysis are presented in Table 1.²² The goodness-of-fit statistics for the overall equation for individual country samples are satisfactory; however, in each case the high ${\overline{R}}^2$ gives an unduly good impression of the degree of explanatory power of the model. Standard errors on the order of 1 to 2½ per cent are still rather high. Some serial autocorrelation seems to be present in the residuals in subsamples for Canada and France.

Table 1.

Production Function Coefficients¹

$Q=A{e}^{rt}{e}^{\theta (\alpha +\beta )\left[8Y\right]}{F}^{\alpha +\beta }(\dot{Q}/{\dot{Q}}^{*})\gamma (\dot{Q}/{\dot{Q}}^{*})L_e^{\rho }d{Z}_{e^u}$

¹The observation sample consists of annual observations for the eight countries for the period 1955–75. The parameters θ and d are constrained to be the same for all countries; all other parameters may take different values for the various countries.

²${\overline{R}}^2$ is the coefficient of multiple correlation adjusted for degrees of freedom; SE, the standard error of estimate; and D-W, the Durbin-Watson statistic. The ${\overline{R}}^2$, SE, and D-W shown on each country line are calculated from the estimated error terms for that country only. The “overall” ${\overline{R}}^2$, SE, and D-W are calculated from the estimated error terms for the whole cross-country sample. Figures in parentheses are standard errors. The asterisk (*) indicates that an estimate is significant at the 5 per cent significance level.

³Additional trends (with coefficient ${\hat{r}}_a$) were introduced as follows: the United States, 1968–75, ${\hat{r}}_a$ = −0.006* (0.002); Japan, 1970–75, ${\hat{r}}_a$ = −0.013* (0.005); France, 1964–69, ${\hat{r}}_a$ = 0.012* (0.004); the United Kingdom, 1955–60, ${\hat{r}}_a$ = −0.016* (0.006); and Sweden, 1955–61, ${\hat{r}}_a$ = −0.016* (0.004).

⁴A dummy variable, taking the value one in 1975 and zero otherwise, was introduced to take into account the effects of certain labor retention measures. The estimated coefficients are −0.046* (0.021) for Japan, −0.076* (0.026) for France, −0.046* (0.029) for Italy, and −0.051* (0.022) for Sweden.

Table 1.

Production Function Coefficients¹

$Q=A{e}^{rt}{e}^{\theta (\alpha +\beta )\left[8Y\right]}{F}^{\alpha +\beta }(\dot{Q}/{\dot{Q}}^{*})\gamma (\dot{Q}/{\dot{Q}}^{*})L_e^{\rho }d{Z}_{e^u}$

						Goodness-of-Fit Statistics 2
Country	ln A	r	γ	ρ	α+β	${\overline{R}}^2$	SE	D-W
Canada	−1.850	0.030*	0.460*	0.326*	1.009*	0.998	0.016	0.953
	(1.654)	(0.004)	(0.108)	(0.102)	(0.188)
United States 3	−2.411	0.023*	0.473*	0.388*	1.007*	0.995	0.017	1.767
	(1.614)	(0.003)	(0.080)	(0.069)	(0.173)
Japan 3, 4	−4.774*	0.035*	0.500*	0.386*	1.348*	0.999	0.024	1.878
	(1.575)	(0.011)	(0.057)	(0.059)	(0.165)
France 3, 4	−4.752	0.020	0.433*	0.342	1.279*	0.998	0.016	1.167
	(4.564)	(0.018)	(0.167)	(0.180)	(0.626)
Germany, Fed. Rep.	0.344	0.033*	0.455	0.367*	0.837*	0.999	0.009	1.909
	(1.305)	(0.003)	(0.098)	(0.093)	(0.080)
Italy 4	−3.625	0.041*	0.401*	0.245*	1.220*	0.999	0.015	1.832
	(1.416)	(0.001)	(0.124)	(0.110)	(0.095)
United Kingdom 3	−3.291	0.022*	0.510*	0.419*	1.281*	0.994	0.014	1.859
	(2.368)	(0.002)	(0.146)	(0.184)	(0.329)
Sweden 3, 4	−2.751	0.040*	0.419*	0.245*	1.103*	0.999	0.013	1.755
	(1.316)	(0.003)	(0.189)	(0.200)	(0.206)
Constrained parameters and overall goodness-of-fit statistics:
θ = −0.087* (0.030)	d = −0.018* (0.008)					0.999	0.016	1.695

¹The observation sample consists of annual observations for the eight countries for the period 1955–75. The parameters θ and d are constrained to be the same for all countries; all other parameters may take different values for the various countries.

²${\overline{R}}^2$ is the coefficient of multiple correlation adjusted for degrees of freedom; SE, the standard error of estimate; and D-W, the Durbin-Watson statistic. The ${\overline{R}}^2$, SE, and D-W shown on each country line are calculated from the estimated error terms for that country only. The “overall” ${\overline{R}}^2$, SE, and D-W are calculated from the estimated error terms for the whole cross-country sample. Figures in parentheses are standard errors. The asterisk (*) indicates that an estimate is significant at the 5 per cent significance level.

³Additional trends (with coefficient ${\hat{r}}_a$) were introduced as follows: the United States, 1968–75, ${\hat{r}}_a$ = −0.006* (0.002); Japan, 1970–75, ${\hat{r}}_a$ = −0.013* (0.005); France, 1964–69, ${\hat{r}}_a$ = 0.012* (0.004); the United Kingdom, 1955–60, ${\hat{r}}_a$ = −0.016* (0.006); and Sweden, 1955–61, ${\hat{r}}_a$ = −0.016* (0.004).

⁴A dummy variable, taking the value one in 1975 and zero otherwise, was introduced to take into account the effects of certain labor retention measures. The estimated coefficients are −0.046* (0.021) for Japan, −0.076* (0.026) for France, −0.046* (0.029) for Italy, and −0.051* (0.022) for Sweden.

View Table

Table 1.

Production Function Coefficients¹

$Q=A{e}^{rt}{e}^{\theta (\alpha +\beta )\left[8Y\right]}{F}^{\alpha +\beta }(\dot{Q}/{\dot{Q}}^{*})\gamma (\dot{Q}/{\dot{Q}}^{*})L_e^{\rho }d{Z}_{e^u}$

						Goodness-of-Fit Statistics 2
Country	ln A	r	γ	ρ	α+β	${\overline{R}}^2$	SE	D-W
Canada	−1.850	0.030*	0.460*	0.326*	1.009*	0.998	0.016	0.953
	(1.654)	(0.004)	(0.108)	(0.102)	(0.188)
United States 3	−2.411	0.023*	0.473*	0.388*	1.007*	0.995	0.017	1.767
	(1.614)	(0.003)	(0.080)	(0.069)	(0.173)
Japan 3, 4	−4.774*	0.035*	0.500*	0.386*	1.348*	0.999	0.024	1.878
	(1.575)	(0.011)	(0.057)	(0.059)	(0.165)
France 3, 4	−4.752	0.020	0.433*	0.342	1.279*	0.998	0.016	1.167
	(4.564)	(0.018)	(0.167)	(0.180)	(0.626)
Germany, Fed. Rep.	0.344	0.033*	0.455	0.367*	0.837*	0.999	0.009	1.909
	(1.305)	(0.003)	(0.098)	(0.093)	(0.080)
Italy 4	−3.625	0.041*	0.401*	0.245*	1.220*	0.999	0.015	1.832
	(1.416)	(0.001)	(0.124)	(0.110)	(0.095)
United Kingdom 3	−3.291	0.022*	0.510*	0.419*	1.281*	0.994	0.014	1.859
	(2.368)	(0.002)	(0.146)	(0.184)	(0.329)
Sweden 3, 4	−2.751	0.040*	0.419*	0.245*	1.103*	0.999	0.013	1.755
	(1.316)	(0.003)	(0.189)	(0.200)	(0.206)
Constrained parameters and overall goodness-of-fit statistics:
θ = −0.087* (0.030)	d = −0.018* (0.008)					0.999	0.016	1.695

¹The observation sample consists of annual observations for the eight countries for the period 1955–75. The parameters θ and d are constrained to be the same for all countries; all other parameters may take different values for the various countries.

²${\overline{R}}^2$ is the coefficient of multiple correlation adjusted for degrees of freedom; SE, the standard error of estimate; and D-W, the Durbin-Watson statistic. The ${\overline{R}}^2$, SE, and D-W shown on each country line are calculated from the estimated error terms for that country only. The “overall” ${\overline{R}}^2$, SE, and D-W are calculated from the estimated error terms for the whole cross-country sample. Figures in parentheses are standard errors. The asterisk (*) indicates that an estimate is significant at the 5 per cent significance level.

³Additional trends (with coefficient ${\hat{r}}_a$) were introduced as follows: the United States, 1968–75, ${\hat{r}}_a$ = −0.006* (0.002); Japan, 1970–75, ${\hat{r}}_a$ = −0.013* (0.005); France, 1964–69, ${\hat{r}}_a$ = 0.012* (0.004); the United Kingdom, 1955–60, ${\hat{r}}_a$ = −0.016* (0.006); and Sweden, 1955–61, ${\hat{r}}_a$ = −0.016* (0.004).

⁴A dummy variable, taking the value one in 1975 and zero otherwise, was introduced to take into account the effects of certain labor retention measures. The estimated coefficients are −0.046* (0.021) for Japan, −0.076* (0.026) for France, −0.046* (0.029) for Italy, and −0.051* (0.022) for Sweden.

Estimates for the coefficients of the variables $(\dot{Q}/{\dot{Q}}^{*})$ and ${(\dot{Q}/{\dot{Q}}^{*})}_L$ have roughly similar values for the various countries and relatively small standard errors. The estimates for the coefficients of $(\dot{Q}/{\dot{Q}}^{*})$ indicate that in all eight countries considered a 10 per cent fall in the level of output in a given year tends to cause about a 5 per cent fall in factor productivity. In the case of ${(\dot{Q}/{\dot{Q}}^{*})}_L$ the exponent of the geometric distribution was estimated to be 0.76, and the coefficients of these variables ranged from 0.25 to 0.47. Clearly, the resource inputs to firms are adjusted fairly slowly to short-term changes in output levels; therefore, substantial variations in the intensity at which labor and capital are used occurred in the short term.²³ Variations in factor demand were also found to have been influenced by changes in labor legislation. Thus, in Japan, France, Italy, and Sweden, the coefficient of the dummy variable introduced for the specific labor retention measures implemented by the authorities in 1975 is large and statistically significant. Some abnormal labor retention practices may also have played a certain role in other countries in 1975 although they could not be identified.

The estimated values of α + β are consistent with results obtained by other authors. The estimates of α + β are close to one for most countries, that is, no economies of scale are detected.²⁴ Japan is the only country for which α + β is significantly greater than one; this result is not surprising given the transformation from an “infant” state to a “mature” state, experienced by many Japanese industries during the period.

The increase in the efficiency of capital resulting from a fall in the mean age of the capital stock by one year is about 8½ per cent. The result is somewhat higher than the estimates advanced by Solow in his pioneering article (1957). Solow estimated the rate of embodied technical progress to be 5 per cent for machinery and equipment, and 2 per cent for buildings.

A systematic search was made for possible changes in the trend rate of technical progress by introducing separate trends for each cycle (measured from peak to peak) into the equation. Few significant variations in the trend rate were detected, and ultimately only a limited number of these separate trends were kept in the equation. The major exception to this stability of the trend rate is the estimated fall in the trend rate for Japan by 1.3 percentage points, from 3.5 per cent to 2.2 per cent from 1970 onward. Several reasons can be advanced for this fall: (i) part of the investment made during this period was for purposes of reducing pollution rather than increasing output; (ii) environmental constraints may have led to a fall in the degree of returns to scale that is picked up here by the change in the trend rate; and (iii) the opportunity for introducing “new” industries with ready-made technology decreased during that period. The trend rate also fell in the United States by 1.1 percentage points after 1968; here also, the reason may be that the capital stock series do not properly discount pollution-related investments.²⁵ Other significant changes in trend rates include an increase of 1.2 percentage points in the trend rate for France during the period 1964–69, and a lower rate during the 1950s than during the rest of the period for the United Kingdom and Sweden.

The estimated impact effect of higher energy prices and related factors on the level of potential output in industrial countries is about −1.8 per cent. Separate estimates were also calculated for the individual countries, but none differ significantly from the above estimate.²⁶ Two comments are in order here. First, while the estimate looks reasonable, it should be treated with caution. The period 1974–75 is too short and too much influenced by the world recession to permit a very precise estimation of this effect. In fact, the estimate could be too high, because the Z variable may have picked up abnormal transitory cuts in productivity caused by the world recession. Second, the estimate calculated here refers only to the impact effect on factor productivity in the manufacturing sector. Possible long-run effects on the rate of economic growth remain to be assessed.

Parameters for the labor participation function, equation (10), were also estimated by least squares from annual data on the period 1955–75. The estimated elasticity of the employed labor force in man-hours (L) with respect to the unemployment rate is −3.9 (0.5) for Canada, −4.4 (0.3) for the United States, −3.5 (0.7) for France, −4.6 (0.6) for the Federal Republic of Germany, and −2.9 (0.6) for the United Kingdom.²⁷ Reliable estimates could not be obtained for Japan, Italy, and Sweden because cyclical variations in economic activity in these countries led to little, if any, variation in the unemployment rate during the period 1955–75. For those three countries, estimates of the full-employment labor force (LF) were obtained by fitting log-linear trends through the cyclical peaks in quarterly series on man-hours worked (L). For the other five countries, equation (11) was used to calculate the value of LF at the cyclical peaks in the quarterly series on man-hours worked; then, series on the full-employment labor force were obtained by fitting log-linear trends between the peak values of LF. In equation (11), the value of the structural unemployment rate was (arbitrarily) chosen to be: for Canada, 4 per cent for 1955–70 and 4½ per cent after 1970; for the United States, 4 per cent for 1955–70 and 4½ per cent after 1970; for France, 1 per cent for 1955–65, 1½ per cent for 1966–70, and 2 per cent after 1970; for the Federal Republic of Germany, 3½ per cent in 1955, declining linearly to 1 per cent in 1960, ¾ of 1 per cent for 1961–67, 1 per cent for 1968–73, and 1½ per cent after 1973; and for the United Kingdom, 1½ per cent for 1955–67, 2 per cent for 1968–70, and 2½ per cent after 1970.

The estimated values for potential output in manufacturing from 1955 to 1975 are shown in Tables 4–11 in Appendix II. The semiannual series on potential output were derived from the annual series by log-linear interpolation. (The calculation of the series for 1976–78, which appear in those tables, will be explained below.) The tables presented in Appendix II also include series on output gaps, measured as the difference between actual and potential output and expressed as a percentage of potential output, and series on potential output per man-hour.²⁸

The most striking aspect of the results is the sharp deceleration in the rates of growth that took place in several countries during the first half of the 1970s. These include Japan, where the rate of growth fell from more than 13 per cent in 1970 to about 7½ per cent in 1975; the Federal Republic of Germany, where it fell from about 5 per cent in 1970 to 3½ per cent in 1975; and the United States, where it fell from more than 4 per cent in the late 1960s to about 3 per cent in 1975. Because of the impact effect of the increase in the price of energy, the growth of potential output between 1973 and 1974 was small for most of the eight countries considered.

One obtains a better understanding of the reasons for these falling growth rates by looking at what happened to the various sources of growth. In Table 2, the growth rates are divided into several components that correspond to the various factors accounting for the growth of output. The results show clearly that, in most countries, the gradual fall in the rate of growth of the full-employment labor force (in man-hours) (LF),²⁹ and the less rapid increase of the capital stock (K), played a role in the slowing down of the growth of potential output, in addition to the once-for-all cut in potential output related to the increase in the price of energy. For Japan and the United States, the fall in the rate of technical progress is also a major factor contributing to the lower rate of growth of potential output.

Table 2.

Sources of Economic Growth, 1955–75

(Percentage change in potential output attributable to each source) ¹

¹Numbers may not add to totals shown because of rounding errors.

Table 2.

Sources of Economic Growth, 1955–75

(Percentage change in potential output attributable to each source) ¹

Sources	1955–60	1960–65	1965–70	1970–73	1974	1975
Canada
t	3.0	3.0	3.0	3.0	3.0	3.0
LF	0.9	0.8	0.9	0.9	0.9	0.9
K	1.5	0.9	1.6	1.4	1.2	1.3
Y	0.1	—	0.2	−0.1	—	—
Z	—	—	—	—	−1.8	—
QF	5.6	4.8	5.9	5.3	3.3	5.4
United States
t	2.3	2.3	2.1	1.7	1.7	1.7
LF	0.5	0.8	0.9	0.6	0.6	0.6
K	1.0	0.4	0.9	0.8	0.7	0.9
Y	−0.2	−0.1	0.3	−0.1	—	—
Z	—	—	—	—	−1.8	—
QF	3.6	3.4	4.2	2.9	1.2	3.1
Japan
t	3.5	3.5	3.5	2.2	2.2	2.2
LF	6.4	2.9	1.3	0.7	0.7	0.7
K	3.9	6.6	6.4	7.8	6.2	5.6
Y	1.0	0.7	1.1	0.1	−0.3	−0.8
Z	—	—	—	—	−1.8	—
QF	15.7	14.4	12.8	11.2	7.0	7.7
France
t	2.0	2.2	3.0	2.0	2.0	2.0
LF	1.0	0.7	0.2	0.3	0.3	0.3
K	2.7	3.1	2.7	3.7	4.1	3.7
Y	0.1	0.2	0.2	0.6	0.4	−0.3
Z	—	—	—	—	−1.8	—
QF	6.0	6.4	6.2	6.8	5.0	5.9

Federal Republic of Germany
t	3.3	3.3	3.3	3.3	3.3	3.3
LF	0.9	−0.1	0.2	−0.5	−0.5	−0.5
K	3.4	3.1	2.2	2.1	1.6	1.3
Y	0.3	−0.1	−0.3	—	−0.3	−0.4
Z	—	—	—	—	−1.8	—
QF	8.0	6.3	5.5	4.9	2.3	3.6
Italy
t	4.1	4.1	4.1	4.1	4.1	4.1
LF	2.3	1.0	0.5	−0.6	−0.5	−0.5
K	2.0	2.6	1.7	2.1	1.9	2.0
Y	—	0.1	−0.2	0.1	0.2	0.2
Z	—	—	—	—	−1.8	—
QF	8.6	7.9	6.2	5.8	4.0	5.9
United Kingdom
t	0.6	2.2	2.2	2.2	2.2	2.2
LF	0.2	−0.4	−0.5	−1.4	−0.9	−0.9
K	1.9	1.8	1.5	1.4	1.0	1.0
Y	0.2	—	0.1	−0.1	−0.2	—
Z	—	—	—	—	−1.8	—
QF	3.0	3.6	3.3	2.2	0.3	2.2
Sweden
t	2.4	3.7	4.0	4.0	4.0	4.0
LF	0.3	0.2	−1.3	−1.3	−1.3	−0.8
K	2.4	2.9	2.3	2.0	1.9	2.0
Y	—	0.1	−0.1	−0.1
Z	—	—	—	—	−1.8	—
QF	5.3	7.0	5.1	4.6	2.8	5.1

¹Numbers may not add to totals shown because of rounding errors.

View Table

Table 2.

Sources of Economic Growth, 1955–75

(Percentage change in potential output attributable to each source) ¹

Sources	1955–60	1960–65	1965–70	1970–73	1974	1975
Canada
t	3.0	3.0	3.0	3.0	3.0	3.0
LF	0.9	0.8	0.9	0.9	0.9	0.9
K	1.5	0.9	1.6	1.4	1.2	1.3
Y	0.1	—	0.2	−0.1	—	—
Z	—	—	—	—	−1.8	—
QF	5.6	4.8	5.9	5.3	3.3	5.4
United States
t	2.3	2.3	2.1	1.7	1.7	1.7
LF	0.5	0.8	0.9	0.6	0.6	0.6
K	1.0	0.4	0.9	0.8	0.7	0.9
Y	−0.2	−0.1	0.3	−0.1	—	—
Z	—	—	—	—	−1.8	—
QF	3.6	3.4	4.2	2.9	1.2	3.1
Japan
t	3.5	3.5	3.5	2.2	2.2	2.2
LF	6.4	2.9	1.3	0.7	0.7	0.7
K	3.9	6.6	6.4	7.8	6.2	5.6
Y	1.0	0.7	1.1	0.1	−0.3	−0.8
Z	—	—	—	—	−1.8	—
QF	15.7	14.4	12.8	11.2	7.0	7.7
France
t	2.0	2.2	3.0	2.0	2.0	2.0
LF	1.0	0.7	0.2	0.3	0.3	0.3
K	2.7	3.1	2.7	3.7	4.1	3.7
Y	0.1	0.2	0.2	0.6	0.4	−0.3
Z	—	—	—	—	−1.8	—
QF	6.0	6.4	6.2	6.8	5.0	5.9

Federal Republic of Germany
t	3.3	3.3	3.3	3.3	3.3	3.3
LF	0.9	−0.1	0.2	−0.5	−0.5	−0.5
K	3.4	3.1	2.2	2.1	1.6	1.3
Y	0.3	−0.1	−0.3	—	−0.3	−0.4
Z	—	—	—	—	−1.8	—
QF	8.0	6.3	5.5	4.9	2.3	3.6
Italy
t	4.1	4.1	4.1	4.1	4.1	4.1
LF	2.3	1.0	0.5	−0.6	−0.5	−0.5
K	2.0	2.6	1.7	2.1	1.9	2.0
Y	—	0.1	−0.2	0.1	0.2	0.2
Z	—	—	—	—	−1.8	—
QF	8.6	7.9	6.2	5.8	4.0	5.9
United Kingdom
t	0.6	2.2	2.2	2.2	2.2	2.2
LF	0.2	−0.4	−0.5	−1.4	−0.9	−0.9
K	1.9	1.8	1.5	1.4	1.0	1.0
Y	0.2	—	0.1	−0.1	−0.2	—
Z	—	—	—	—	−1.8	—
QF	3.0	3.6	3.3	2.2	0.3	2.2
Sweden
t	2.4	3.7	4.0	4.0	4.0	4.0
LF	0.3	0.2	−1.3	−1.3	−1.3	−0.8
K	2.4	2.9	2.3	2.0	1.9	2.0
Y	—	0.1	−0.1	−0.1
Z	—	—	—	—	−1.8	—
QF	5.3	7.0	5.1	4.6	2.8	5.1

¹Numbers may not add to totals shown because of rounding errors.

The series on potential output were projected through 1978 by making certain assumptions about the growth rates of the variables LF, K, and Y over the period 1975–78. These assumptions, which are shown in Table 3, are presented here only as working hypotheses. The estimates for K and Y are based on projections of investment through 1978. Such projections cannot be considered to be reliable; however, the estimates for K and Y for 1976–78 are rather insensitive, within limits, to the projections for investment, particularly because of the lags introduced between investment flows and the corresponding changes in the capital stock series. (On this last point, see Appendix I.) The assumed growth rates for LF represent an extrapolation of the estimated rate between the last two observed cyclical peaks. The extrapolated figures have been adjusted when necessary for changes in demographic factors and in the length of the normal workweek. The effects of the increases in the price of energy on total factor productivity in industrial countries during that period have been shown to be negligible by Gunning and others (1976); no account is taken of their effects here. The projected growth rates of potential output corresponding to these assumptions are shown in Table 3. For most countries, the fall in the growth rate of potential output is projected to continue through 1978; this result reflects in large part the projected decrease in the rate of capital accumulation, a decrease that is, itself, the (partly delayed) result of the low investment rates observed in most countries in 1974–75 and the relatively slow pickup projected for 1976–77.³⁰,³¹

Table 3.

Projected Growth Rates of Potential Output in Manufacturing, 1975–78

(In per cent)

Table 3.

Projected Growth Rates of Potential Output in Manufacturing, 1975–78

(In per cent)

	Average Rate of Growth of Potential Output		Average Rate of Growth of Explanatory Variables, 1975–78
Country	1975	Projected, 1975–78	Full- employment labor force (in man-hours) (LF)	Capital stock (K)	Mean age of capital stock (Y)
Canada	5.4	5.3	1.3	4.7	0.3
United States	3.1	3.0	0.8	2.9	0.6
Japan	7.7	5.6	0.9	6.9	3.5
France	5.9	4.5	0.4	5.8	2.0
Germany, Fed. Rep.	3.6	3.5	−0.9	3.0	1.6
Italy	5.9	5.1	−0.7	3.7	0.6
United Kingdom	2.2	1.8	−1.0	2.1	1.2
Sweden	5.1	4.8	−1.0	4.3	0.6

View Table

Table 3.

Projected Growth Rates of Potential Output in Manufacturing, 1975–78

(In per cent)

	Average Rate of Growth of Potential Output		Average Rate of Growth of Explanatory Variables, 1975–78
Country	1975	Projected, 1975–78	Full- employment labor force (in man-hours) (LF)	Capital stock (K)	Mean age of capital stock (Y)
Canada	5.4	5.3	1.3	4.7	0.3
United States	3.1	3.0	0.8	2.9	0.6
Japan	7.7	5.6	0.9	6.9	3.5
France	5.9	4.5	0.4	5.8	2.0
Germany, Fed. Rep.	3.6	3.5	−0.9	3.0	1.6
Italy	5.9	5.1	−0.7	3.7	0.6
United Kingdom	2.2	1.8	−1.0	2.1	1.2
Sweden	5.1	4.8	−1.0	4.3	0.6