Measures of Potential Output in Manufacturing for Eight Industrial Countries, 1955–78

The potential output of a sector or a whole economy is a concept that is difficult to define and even more difficult to measure. Nevertheless, the need for such a measure, however imprecise, is not in doubt. The concepts of potential output and the ratio of actual to potential output, hereinafter referred to as the output gap, are in constant use in arguments about the economic situation and the appropriateness of public policies. The output gap has also been found to play a major role as a determinant of investment, price changes, foreign trade flows, etc.1 However, it is important to recognize that estimates of potential output are often misunderstood and misused, and for this reason have sometimes contributed to faulty policy decisions.

Abstract

The potential output of a sector or a whole economy is a concept that is difficult to define and even more difficult to measure. Nevertheless, the need for such a measure, however imprecise, is not in doubt. The concepts of potential output and the ratio of actual to potential output, hereinafter referred to as the output gap, are in constant use in arguments about the economic situation and the appropriateness of public policies. The output gap has also been found to play a major role as a determinant of investment, price changes, foreign trade flows, etc.1 However, it is important to recognize that estimates of potential output are often misunderstood and misused, and for this reason have sometimes contributed to faulty policy decisions.

The potential output of a sector or a whole economy is a concept that is difficult to define and even more difficult to measure. Nevertheless, the need for such a measure, however imprecise, is not in doubt. The concepts of potential output and the ratio of actual to potential output, hereinafter referred to as the output gap, are in constant use in arguments about the economic situation and the appropriateness of public policies. The output gap has also been found to play a major role as a determinant of investment, price changes, foreign trade flows, etc.1 However, it is important to recognize that estimates of potential output are often misunderstood and misused, and for this reason have sometimes contributed to faulty policy decisions.

The concept of potential output is essentially a production concept. It refers to a desirable situation where factors of production are employed at their long-run normal intensity levels. However, the production level corresponding to potential output is not necessarily an optimal level in the broader sense of the term. From some perspectives, it may be desirable to maintain the economy at a lower output level, so as to cut the inflation rate or to improve the balance of payments. By itself, the existence of a gap between actual and potential output does not imply that policy measures should be taken to close it. This point needs to be emphasized.

The purpose of the present study is to estimate consistent series of potential output in manufacturing for a number of industrial countries for the period 1955–75, and to project these series for the medium term (1976–78) on the basis of projected resource availability. These estimates are employed to derive series of output gaps that will be used as cyclical indicators in various other empirical studies. An important aspect of the study deals with the question of whether or not recent developments, such as the increase in the price of energy, pollution control regulations, and the severity of the 1975 world recession, have sharply affected the level and rate of growth of potential output in industrial countries.

The manufacturing sector was chosen as the subject of the study because it is one of the main sectors in industrial countries, is subject to large fluctuations in output, and plays a dominant role in world trade. Technical reasons have also played a role in this selection. The manufacturing sector can be characterized by a more homogeneous set of inputs and outputs than the whole economy or the private nonfarm sector, a factor that greatly increases the efficiency of estimation methods.2 The choice of a sector rather than the whole economy makes it more difficult to define the available full-employment labor force. However, this will be shown to be a manageable problem at the level of the manufacturing sector.

The concept of potential output and the relative merits of the various methods that are used to quantify it are considered in Sections I and II, respectively. The production function method is selected as the best approach. It is this method that is used in Section III to derive series of potential output in manufacturing in Canada, the United States, Japan, France, the Federal Republic of Germany, Italy, the United Kingdom, and Sweden for the period 1955–78. The empirical estimation of the relevant production functions makes use of pooled time-series cross-section techniques. At the cost of imposing certain constraints on the parameters, these techniques allow a large number of variables to be taken into account in the estimation of potential output, such as the evolution of the mean age of the capital stock, the increase in the price of energy, and other factors specific to certain countries.

I. The Concept of Potential Output

There is broad agreement on what is meant by potential output.3 The potential output of an economy is the output that would be realized if the labor force (measured in man-hours) were fully employed, and labor and capital were used at normal intensity. The potential output of a particular sector is defined in terms of the labor force that would be available to that sector if the whole economy were working at full employment. The difficulty, of course, is to define precisely the expressions “full-employment labor force,” “labor force available to a sector,” “capital,” and “normal intensity” of use. It is to this task that the present section is directed. It attempts also to make clear the inherent limitations of the empirical techniques used to estimate potential output by pointing out the complexity of this concept and the difficulty of obtaining the data that are necessary to quantify it.

The meaning of full employment has been discussed extensively in the economic literature and in the political arena. For present purposes, it is necessary to note only that: (1) the size of the labor force is positively related to employment opportunities; and (2) a certain proportion of the persons classified as part of the labor force are unemployed for reasons that have nothing to do with a temporary shortfall of aggregate demand; for example, they may not be able to find a job because of the legal imposition of a minimum wage rate, restrictive practices by labor unions, or simply unrealistic remuneration requests, or they may be voluntarily between jobs. To obtain a realistic estimate of the amount of “cyclical” unemployment, an adjustment must be made to the official series on unemployment to correct for the presence of “structural” unemployment. The full-employment labor force in man-hours can be defined to be the labor force that corresponds to the employment opportunities existing when this adjusted unemployment rate approaches zero.

It is more difficult to evaluate the proportion of the full-employment labor force that is to be allocated to the manufacturing sector. Clearly, there would be no meaningful way to make such an allocation if labor were perfectly mobile among sectors and there were no relation between cyclical variations in activity levels in the various sectors. In practice, however, the labor mobility between the manufacturing sector and other sectors is limited, in particular for skilled labor, and, even more important, there is an extremely high degree of confluence between the activity level in the manufacturing sector and the activity level in the rest of the economy. Thanks to these factors, it is possible to estimate a stable empirical relationship between employment in the manufacturing sector and employment in the whole economy, and to deduce from this relationship the level of employment in manufacturing that corresponds to a fully employed economy.

Obviously, calculations of the full-employment labor force for the whole economy and for the manufacturing sector involve judgmental decisions, in particular, concerning the level of structural unemployment. For this reason, the estimates are open to question. However, the degree of imprecision often tends to be exaggerated. For example, there may be disagreements as to whether 5 per cent or 4 per cent constitutes a fair estimate of the structural unemployment rate in the United States in the 1970s; the difference between estimates of potential output based on these two structural unemployment rates is not unduly large. The uncertainty as to the full-employment labor force in other industrial countries is probably even smaller. The major sources of error in the estimation of potential output will be found elsewhere.

Basically, the difficulties that arise in connection with the measurement of the capital stock are the same as those that arise in the measurement of the labor force. What is relevant is not the capacity (capital stock) of the firms per se but the capacity that can be used by firms to meet market demand. If, because of a permanent shift in demand away from certain products, part of the capital equipment of firms becomes useless, it should not be taken into account. On the other hand, if the shift in demand is transitory, owing to cyclical factors or other temporary disturbances, it should not be interpreted as resulting in a loss of capacity, for in this case potential output and actual output would become nearly synonymous. Similarly, on the production side, a temporary shortage of a specific input should not be interpreted as causing a fall in capacity, while a sharp change in the relative input prices that is of a more lasting nature should be taken into account if it suddenly makes part of the capital stock obsolete. For example, one might justifiably argue that the large increase in the price of energy that took place in late 1973 and early 1974 may have rendered a certain part of the capital stock of the industrial countries obsolete.4 Obviously, these considerations tend to make the concepts of capacity and potential output somewhat fuzzy, for it is difficult to determine what is temporary and what is permanent, even when the relevant time horizon has been defined, let alone quantify the effects of the permanent changes.

The intensity of employed labor and of the capital stock may also vary substantially over the various phases of the economic cycle. As to labor, it is not so much that the frequency and length of coffee breaks increase considerably in periods of slack demand, although this may play a role, but mainly that part of the labor force may become occupied with menial tasks or tasks that do not directly lead to an increase in manufacturing output. The recent 1975 world recession provides us with many examples. In Japan, Unieast Co. of Ashikaga City, a dyer-processor, kept part of its staff busy during the recent recession producing bean sprouts and raising pheasants and beetles.5 On the other hand, in periods of economic booms, employees may be willing to work harder than usual, but only on a temporary basis. There is, of course, no direct way either to measure the intensity of use of labor or to define a normal intensity level. The same difficulty occurs with capital. The intensity of capital use, usually referred to as the level of capacity utilization, is the major adjustment variable in most countries—that is, it is mainly through variations in capacity utilization that the production system adjusts to short-term variations in aggregate demand. In the present study, an indirect method will be used to measure the deviations of the intensity of use of labor and capital from their long-run normal levels. However, the method leads only to an approximation, not a precise estimate.

Before considering measurement problems in more detail, a word must be said about “aggregation problems.” Firms are interdependent, not only because they all compete for primary factors of production, such as labor, but also because they are connected through a web of input-output relationships. This aspect of the production system has led many economists to define potential output as a bottleneck point in a general equilibrium system.6 The recent “raw material crisis,” in particular, has generated much discussion as to whether or not the potential output of the industrial economies had been reduced because of a shortage of certain raw materials. While this definition of the production potential of an economy has undeniable merits, in particular in the study of inflation, it tends to focus too much attention on certain short-term bottlenecks and to neglect the ability of the economic system to move resources in order to eliminate localized bottlenecks. For this reason, no attempt is made here to apply this definition.

II. Measurement Methods

Various methods have been developed to measure the potential output of an industry or of a whole economy. The three main methods are considered here, namely, (i) the survey of firms; (ii) the fitting of trend-through-peaks; and (iii) the estimation of production functions. After reviewing the relative advantages of each method, the production function method is selected as the most promising. This latter method is developed further and applied in Section III.

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.

III. An Empirical Study of Eight Industrial Countries, 1955–78

The production function method is elaborated further in this section. Historical series of potential output in manufacturing are calculated for Canada, the United States, Japan, France, the Federal Republic of Germany, Italy, the United Kingdom, and Sweden for the period 1955–75. An account of the various sources of economic growth is presented, with particular attention given to the detrimental effects of the recent increase in the price of energy. On the basis of this analysis, projections of the rates of growth of potential output for the various countries are made for the period 1976–78. Series of output gaps are also derived for the historical period 1955 through the first half of 1976.

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

Q=Aert(k1KeθY)α(l1L)βedZeu(1)

where

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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,

k1=K°/K(2)

and

l1=L°/L(3)

where K° and 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, Q˙*.15, 16 More specifically, it is assumed that

k1αl1β=(Q˙/Q˙*)γ(Q˙/Q˙*)Lρ(4)

where the dot above a variable indicates that the rate of change of the variable in proportionate terms (i.e., Q˙=Q/Q1 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

Q=Aert+θαYKαLβ(Q˙/Q˙*)γ(Q˙/Q˙*)LρedZeu(5)

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

F=Kα/α+βLβ/α+β=K8L18(6)

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

Q=Aerteθ(α+β)[8Y]Fα+β(Q˙/Q˙*)LρedZeu(7)

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

QO=Aerteθ(α+β)[8Y]Fα+βedZ(8)

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,

AF=QO(LF/L)(18)(α+β)=QO(LF/L)β(9)

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

ln(L)=a0+a1t+a2t2+a3t3+a4U+u(10)

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

ln(LF)=ln(L)+a^4(UU8)(11)

where Us is the structural unemployment rate, and 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 (Q˙/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 (Q˙/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 (Q˙/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 (Q˙/Q˙*) the latter variable was replaced by an instrumental variable. The chosen instrumental variable was the estimated value of (Q˙/Q˙*) obtained by regressing this variable on the current and lagged values of the variable (L˙/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 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=Aerteθ(α+β)[8Y]Fα+β(Q˙/Q˙*)γ(Q˙/Q˙*)LeρdZeu
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The 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.

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 R¯2, SE, and D-W shown on each country line are calculated from the estimated error terms for that country only. The “overall” 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.

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

A 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 (Q˙/Q˙*) and (Q˙/Q˙*)L have roughly similar values for the various countries and relatively small standard errors. The estimates for the coefficients of (Q˙/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 (Q˙/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 411 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

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Numbers 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)

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IV. Summary and Conclusions

The main finding of the present study is that the rate of growth of potential output in manufacturing in a number of industrial countries is now significantly lower than it was in the late 1960s. However, the fall in the rate of growth of potential output is not as large as is often claimed. Japan is the only major industrial country that has experienced a major decline in its rate of growth. The principal reasons for the world-wide slowdown are the lower rate of capital accumulation and the reduction of the normal workweek, rather than the direct effect of the increase in the price of energy. In Japan and the United States, the trend rate of technical progress also seems to have decreased, possibly because a larger part of new investment is devoted to pollution control. The implication of these findings is that in early 1976 output gaps were extremely high in all the major industrial countries.

As to the methodological aspects of the study, it seems that a production function approach can give satisfactory results. Care must, however, be given to the proper specification of the short-term variations in the intensity of use of labor and capital within firms that occur over the cycle. Variations in the mean age of the capital stock also need to be taken into account. Finally, allowance must be made for variations in the trend rate of technical progress. A cross-country study is the only feasible way to take all these factors into account.

The production function employed here also has weaknesses that cannot be ignored. The lack of reliable data on the capital stock, the treatment of technical progress as a residual, and the use of dummy variables of the zero-one kind to identify the effect of the increase in the price of energy cast certain doubts on the precision of the estimates of potential output. The high degree of aggregation employed in the study is also somewhat dangerous. Further studies at the industry level would provide a useful check on some of the results obtained here.

The gaps between actual and potential output in manufacturing that have been calculated must also be used with caution. Clearly, they do not indicate by how much the production level can be raised on short notice. In most cases, a major change in the production level may take place only gradually, regardless of the amount of spare resources available. Localized bottlenecks may also prevent an increase in the overall level of economic activity in the short run, regardless of the resources that are left idle in the rest of the manufacturing sector.

APPENDICES

I. Sources of Statistical Data

Manufactured output indices (Q), 1950–76 (First half)

Annual data on the constant-price value of GDP originating in manufacturing for 1950–75 were obtained from the U.S. Department of Labor, Bureau of Labor Statistics, Office of Productivity and Technology. The semiannual series shown in Appendix II were obtained by benchmarking published monthly or quarterly indices of manufacturing production, seasonally adjusted, on the annual data collected by the U.S. Department of Labor. Preliminary data for the first half of 1976 were obtained from national sources.

Man-hours worked in manufacturing (L), 1950–75

Annual data on man-hours worked in manufacturing for 1950–75 were obtained from the U.S. Department of Labor, Bureau of Labor Statistics, Office of Productivity and Technology. The series for the United States refer to man-hours paid. Seasonally adjusted quarterly series obtained from national sources were bench-marked on the annual estimates to obtain the quarterly series that were used to calculate the full-employment labor force (LF). The advantage of the annual data compiled by the U.S. Department of Labor is that, except for Japan, they are derived from comprehensive national account statistics, while most quarterly series are based on less comprehensive labor surveys.

Unemployment rate in the economy (U), 1955–75

Annual and quarterly data refer to official national series on unemployment for the whole population, 18 years of age or over.

Capital stock (K) and mean age of the capital stock (Y) in manufacturing, 1950–75

Data on the gross fixed capital stock in manufacturing (K) were derived from series on gross fixed capital formation in constant prices by employing 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 K0 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(12)

where ert is the proportion of the surviving initial (1920) capital stock that is not retired during 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.

The capital stock installed in year t is a lag function of the investment flows

At=0.30It+0.50It1+0.20It2(13)

where the coefficients take into account the average time needed for new projects to be completed and become fully productive.32

The calculations are made separately for machinery and equipment, and for structures, except for Japan and Italy where no disaggregated data on investment could be obtained. Information on the service lives of capital assets is quite deficient. Average service lives of 15 years for machinery and 35 years for structures were used.33 Actual retirements from capital stock accumulated after 1920 were calculated following a Winfrey S-3 distribution, with discards starting at 45 per cent of the average life.34 Data on the total capital stock were obtained by summing the stocks of machinery and equipment, and of structures.

Data on the mean age of the capital stock are obtained from the same investment series. Here also, the calculations are made separately for machinery and equipment and for structures. The mean age (YE) of the stock of machinery and equipment (KE) is calculated by the formula

YEt=(tKE0ert+Σi=1ni(1φi)Ati)/KEt(14)

The mean age (YS) of the stock of structures (KS) is calculated in the same way.

The mean age (Y) of the total capital stock is calculated, taking into account the relative value of KE and KS and also an a priori estimate of the relative magnitude of the rates of technical progress embodied in the two kinds of capital, that is,

Yt=ξKEtYEt+(lξ)KStYSt(15)

where ξ is equal to 0.7 to reflect Solow’s hypothesis that the rate of technical progress embodied in machinery and equipment is about two and a half times larger than the rate of technical progress embodied in structures.

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

Canada: Series for 1926–50, Private and Public Investment in Canada 1926–1951, Canada, Department of Trade and Commerce, 1951. Series for 1951–75, Private and Public Investment in Canada—Outlook, Canada, Department of Trade and Commerce, various issues.

United States: Series for 1920–74, unpublished data supplied by Mr. John Musgrave, U.S. Department of Commerce, Social and Economic Statistics Administration, Bureau of Economic Analysis.

Japan: Series for 1950–74, Annual Report on National Income Statistics, Economic Planning Agency, Government of Japan, various issues. The series for Japan are not disaggregated into machinery and equipment, and structures.

France: Series for 1920–69, L’Évaluation du Capital Fixe Productif, Jacques Mairesse, in Les Collections de l’INSÉÉ, Série C, No. 18–19 (November 1972). Series for 1970–74, Estimates based on Rapport sur les Comptes de la Nation, Les Collections de l’INSÉÉ, Série C, various issues.

Federal Republic of Germany: Series for 1920–66, Wolfgang Kirner, Zeitreihen für das Anlagevermögen der Wirtschaftsbereiche in der Bundesrepublik Deutschland, Berlin, 1968. Series for 1967–75, based on series provided by IFO Institute.

Italy: Series for 1921–50, Sommario Di Statistiche Storiche Dell’ Italia, 1861–1965, Instituto Centrale Di Statistica, Rome, 1968. Series for 1951–74, National Accounts for OECD Countries, Organization for Economic Cooperation and Development, various issues. The series for Italy are not disaggregated into machinery and equipment, and structures. They refer to manufacturing, mining, and utilities.

United Kingdom: Series for 1920–38, Domestic Capital Formation in the United Kingdom 1920–38, C.H. Feinstein, Cambridge University Press, 1965. Series for 1939–45, “The Stock of Fixed Capital in the United Kingdom in 1961,” G.A. Dean, Journal of the Royal Statistical Society, Series A, Vol. 127, Part 3, 1964. Series for 1949–74, National Income and Expenditure, U.K. Central Statistical Office, various issues.

Sweden: Series for 1920–55, The Gross Domestic Product of Sweden and its Composition 1861–1955, Östen Johansson, Stockholm Economic Studies, New Series, No. VIII, ed. by Almgrist and Wicksell, Stockholm, 1967. Series for 1956–75, The Swedish Economy, National Institute of Economic Research, various issues.

Data on investments for 1975 were obtained from various published and unpublished sources; they must be considered very preliminary.

In the calculation of the series on capital stock and mean age of the capital stock, adjustments to the investment series were made for war damages. For the Federal Republic of Germany, one third of the capital stock was assumed to have been destroyed during World War II. For Italy, 20 per cent of the capital stock was assumed to have been destroyed. And for France and the United Kingdom, 10 per cent of the capital stock was assumed destroyed.

II. Series on Actual and Potential Output in Manufacturing for Eight Industrial Countries

Table 4.

Canada: Actual and Potential Output in Manufacturing, 1955–78

(Seasonally adjusted)

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Preliminary data.

Table 5.

United States: Actual and Potential Output in Manufacturing, 1955–78

(Seasonally adjusted)

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Preliminary data.

Table 6.

Japan: Actual and Potential Output in Manufacturing, 1955–78

(Seasonally adjusted)

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Preliminary data.

Table 7.

France: Actual and Potential Output in Manufacturing, 1955–78

(Seasonally adjusted)

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Influenced by an exceptionally cold winter in the first quarter of 1963.

Influenced by industrial strikes in May 1968.

Preliminary data.

Table 8.

Federal Republic of Germany: Actual and Potential Output in Manufacturing, 1955–78

(Seasonally adjusted)

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Influenced by an exceptionally cold winter in the first quarter of 1963.

Preliminary data.

Table 9.

Italy: Actual and Potential Output in Manufacturing, 1955–78

(Seasonally adjusted)

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Influenced by industrial strikes in the fourth quarter of 1969.

Influenced by industrial strikes in the first quarter of 1973.

Preliminary data.