A Survey of Measures of Capacity Utilization

LAWRENCE J. CHRISTIANO*

Abstract

LAWRENCE J. CHRISTIANO*

LAWRENCE J. CHRISTIANO*

In economic statistics, capacity utilization is a measure of the intensity with which a national economy (or sector, or firm) makes use of its resources. The term is associated with a number of different concepts and methods of measurement, of which several are reviewed in this paper.

The paper has three parts. Section I discusses selected methods for arriving at numerical estimates of capacity utilization and related statistics, comparing them from the point of view of simplicity of computation, data revision problems, and the theoretical concepts to which they correspond.

Section II presents data on capacity utilization for the manufacturing sectors of nine industrial countries. Historical observations on several measures are given for each country, and the relationships between them are examined in the light of the discussion of Section I. Section II shows that differences in concept and method of calculation do not fully explain the discrepancies1 among published data.

Conclusions appear in Section III, which also mentions another approach—complementary to that used in Section II—to comparing alternative measures of capacity utilization.

I. Empirical Measures of Capacity Utilization

This section discusses several methods that have been developed to measure capacity utilization for an industry or an entire economy. Economy-wide measures of capacity utilization are usually referred to as the “output gap” and represent the degree of underutilization of all resources, not merely capital. More frequently used are measures of the rate of capacity utilization for an economic sector, particularly manufacturing. The latter is often chosen partly for reasons of convenience and partly for historical reasons. The choice of the manufacturing sector is convenient because it is characterized by relative homogeneity in inputs and outputs and because it is an important sector of economic activity. 2 Furthermore, at least in the United States, continuous-process manufacturing industries, such as cement, steel, paper, and petroleum refining, were the first ones for which capacity utilization rates were computed. These measures are easy to compute by using the engineering concept, which in these cases would nearly coincide with most other concepts. 3 When they proved useful for this group of industries, it “seemed likely that broad measures for at least all manufacturing and possibly a still wider group of industries would be helpful in analyzing general business conditions.” 4

The two basic approaches to measuring capacity utilization are (1) to infer it from available data and (2) to ask businesses what their capacity is.

DATA-BASED METHODS

Production function

An example of this approach can be found in Artus (1977),5 where a production function (Cobb-Douglas) is fitted to the published data. 6 This approach bears a similarity to the engineering concept in that it treats an industry as if it were a machine and does not explicitly take costs into account. On the other hand, it is similar to the practical capacity concept in that it attempts to measure statistically the “normal” relations between inputs and outputs, taking account of the fact that inputs are sometimes underutilized. In this sense, it takes costs into account implicitly. Moreover, when relative costs of inputs not explicitly accounted for in the production function are known to have shifted significantly, the effects of this shift in changing the historical relations between outputs and the inputs explicitly accounted for may be captured in part by using such devices as dummy variables. 7

Artus’s econometrically estimated production function captures long-run relationships between inputs and outputs in the sense that it is estimated by using time-series data in which both capital and labor vary. In this sense, the capacity utilization figures generated indicate the degree of utilization of all inputs rather than, say, only capital.

Data used in the production function approach are relatively noncontroversial, with the exception of the capital stock. Difficulties in constructing a satisfactory capital stock series constitutes a weakness in measures of capacity utilization that use this variable.

Capital stock data are constructed 8 by using the “perpetual inventory” method. This starts by establishing a benchmark year when the size of the capital stock is “known.” 9 A time series is constructed by adding gross investment net of discards. The problem is that some investment projects take years to give rise to increased production capability, while others bear fruit more quickly. Also, some investments (say, those relieving bottlenecks) may be enormously productive, while investment that, for example, refurbishes an office building may contribute little to productive potential. 10 Additionally, the capital stock figures are biased to the extent that there are errors in estimates of how much investment goes toward replacing worn out or obsolete capital. Finally, all the usual difficulties associated with expenditure deflators also apply to this series, although with the added difficulties that any given period’s capital stock figure makes use of the investment deflator of the current period and of all past periods.

It is not clear how serious these problems are. Some of them (for example, the variable duration of investment projects) may cancel out in the aggregate. Ultimately, the matter is an empirical question. 11 In any event, it is clear that capital stock series should be interpreted with caution.

Artus’s (1977) production function is as follows:

Yt=Aert(ktKteθMt)β(ltLt)αedzteut(1)

where

  • e = limn(1+1n)n

  • Yt = actual output at time t

  • Kt = capital stock at time t

  • Mt = mean age of the capital stock at time t

  • Lt = labor in terms of hours worked at time t

  • zt = 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

  • kt,lt = intensity of use of capital and labor, respectively, at time t

  • ut= error term (assumed to be distributed normally) at time t

  • A, r, θ, β, α, d = parameters to be estimated

Estimates of the parameters of the model are computed using a pooled cross section of time series for several industrial countries in Artus (1977), with updated estimates in Artus and Turner (1978). The variables kt and lt, which are unobserved, are replaced with functions of current and past rates of change in output in order to capture their cyclical variation. Use of these variables makes it possible to estimate the equation using all available data, not merely those that represent efficient points of production.

Once the parameters of the production function have been estimated, one additional step is required before a capacity output series can be computed. While the variable lt was introduced to take account of cyclical fluctuations in the intensity with which the actually employed labor force, Lt, is used, 12 it is known that Lt itself fluctuates procyclically. An attempt is made to quantify this phenomenon in order to estimate what employment would have been had the economy been at full employment throughout the period studied. The adjustment procedure assumes that percentage changes in manufacturing employment (in hours) are proportional to percentage point changes in the economy-wide unemployment rate.13 That is,

log(Lt)=a0+a1t+a2t2+a3t3+a4Ut+ut(2)

where ut is a random shock, Ut is the unemployment rate for the population 18 years of age and over, and log denotes logarithm to the base e. Once the parameters of equation (2) are estimated, full employment for cyclical peaks is computed by substituting an “arbitrarily” chosen value for full employment, Uft, 14 into equation (2). That is, letting D be the set of values of t corresponding to cyclical peaks,

log(Ltp)=a0+a1t+a2t2+a3t3+a4UfttD

Values of Ltp for tD were computed by fitting log-linear trends between successive points Ltp,tD. 15 Once a full series Ltp is obtained, this and the actual capital stock series, Kt, are substituted in equation (1), with lt and kt each equal to unity. The result is a complete capacity output series, Ytc. Capacity utilization is computed by taking (Yt/Ytc)×100 for all values of t.

The particular advantage of the production function method as applied in Artus (1977) is that it makes possible a decomposition of potential output growth into changes in the capital stock, the labor force, technical progress, and even such factors as the rise in energy prices. 16 A problem with the method is that, unless the parameters of the production equation are re-estimated sufficiently frequently, utilization rates will become increasingly biased. Furthermore, whenever the parameters are re-estimated, the entire historical series is revised.

Trend through peaks

This measure uses a method associated with Klein and with Wharton Econometric Forecasting Associates, Inc. (WEFA). 17 Like the production function method, it attempts to measure the degree of utilization of all inputs. The method applied to a sector such as manufacturing is as follows. First, historical (seasonally adjusted) figures for each of several manufacturing industries (for example, primary metals, electrical machinery, and chemicals) are plotted. It is assumed that the “major” 18 peaks in the series represent output where resources in the economy are utilized at 100 per cent of capacity. Then, a straight line is drawn between the major peaks and is extrapolated (using the same slope as the line connecting the previous two peaks) beyond the last one. According to Klein (in U.S. Congress (1962, p. 55)):

“In declining industries, a maximum attained within the period studied is selected and capacity is kept constant at this level.” The line drawn is taken to be capacity output. Capacity utilization is the ratio of actual output to contemporaneous points on the line drawn. The capacity utilization figures so derived are aggregated to the industry level using peak output value-added weights.

The measure is attractive in that it is simple and is easily computed from published data, but there are criticisms of the procedure.

(a) It is unreasonable to assume that each “major” peak represents the same intensity of resource utilization. If, for example, the economy fails to surpass what is perceived as a major peak, not because it has reached its productive potential but because of a decline in demand, calculated utilization rates in a neighborhood of the peak would be biased upward.

(b) It is unreasonable to assume that potential output grows at a constant arithmetic rate between peaks. This growth is expected to be somewhat uneven, similar in pattern to investment activity, which is procyclical.

(c) The most serious objection raised is that the capacity figures since the most recent peak are subject to substantial revision when a new peak occurs. If projected capacity growth is greater than actual capacity growth, the computed capacity utilization rate becomes increasingly biased downward. The same is true, mutatis mutandis, if projected capacity growth is less than actual capacity growth. Thus, capacity utilization data for recent periods, computed using the WEFA method, are considered unreliable. This is particularly true at times when the economy is suspected of having undergone a structural shift, or when the rate of capital accumulation and/or growth in the labor force have changed.

The production function method avoids the first two objections and part of the third. Substantial shifts in structural parameters are also difficult for this method to accommodate.

The WEFA measure of capacity utilization for an aggregate of industries, such as the manufacturing sector, never exceeds 100 per cent. It also never actually equals 100 per cent, even though the industries whose capacity utilization measures are included equal 100 per cent at every major peak. This is so because all industries do not generally reach a major peak at the same time.

Output/capital ratio

This measure relies on the existence of a stable proportional relation between the stock of capital and potential output. The method assumes that fluctuations in the observed output/capital ratio are due largely to deviations in output from its potential. The method is used by Panić (1978), formerly with the British National Economic Development Office (NEDO), the Deutsches Institut für Wirtschaftsforschung (DIW),19 and Statistics Canada. 20 It overcomes some of the difficulties (especially criticisms (b) and (c)) of the WEFA measure by relating growth and fluctuations in capacity to investment activity. A problem of its own constitutes those associated with the capital stock, mentioned earlier in connection with the production function method.

For illustration, let us look at the method used by Panić (1978). First he constructs an actual output/capital ratio series (Yt/Kt), t = 1, …, T, where Yt and Kt are output and the capital stock, respectively, at time t. Next, he constructs a “capacity” output/capital series by fitting a linear trend 21 to the actual output/capital series, as follows:

(YtKt)=a0+a1t+u^tt=1,,T(3)

where a0, a1 and ût are fitted by least squares. The capacity output/capital ratio is taken to be the points on a line with time derivative a1, raised just enough so that it touches only one of the observed Yt/Kt series, as depicted in Figure 1. The adjusted trend Y/K ratio—call it (Yt/Kt)cis the assumed capacity output/ capital ratio. As stated previously, the method assumes that actual and capacity output/capital ratios differ because of deviations of output from its potential. That is, it is assumed that

(YtKt)c=(YtcKt)=100CUtYtKt(4)
Figure 1
Figure 1

SURVEY OF MEASURES OF CAPACITY UTILIZATION

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

where

CUt=(YtYtc)×100

is defined as the capacity utilization rate. The final step in calculating capacity utilization, obvious from equation (4), is to take the ratio of the observed to capacity output/capital stock ratio and multiply by 100: 22

[(YtKt)(YtKt)c]×100=[(YtKt)100CUtYtKt]×100=CUtt=1,,T

The method is similar to the WEFA approach in that it is simple to carry out and is based on published, available data. 23 It has an advantage over the WEFA method in that it takes into account the effects of changes in the rate of investment on potential output between production peaks.

The method is also similar to the production function approach, particularly the approaches that make use of linearly homogeneous production functions. 24 For the latter, output per unit of capital is a function only of the capital/labor ratio. 25 To the extent that the latter changes in a trendlike way in response to similar changes in relative input costs, the two approaches can be expected to yield similar results. The production function method is more general than the output/capital method because it can take account of nontrendlike shifts in the capital/labor ratio. The advantages of the production function approach, however, must be weighed against the loss of simplicity and ease of computation. 26

Modified trend through peaks

There are several ways of improving on the WEFA assumptions that growth in potential output is constant and arithmetic between peaks and that current growth is equal to that obtaining prior to the most recent peak. One way is to assume that potential output growth, outside observed output peaks, is positively related to the contemporaneous rate of investment between peaks, as is done using the output/capital ratio method. Another method, basically that used in Dhrymes (1976), constructs the nonpeak potential output series by using information on developments in employment in addition to information on the capital stock. Dhrymes applies his method separately to the manufacturing, mining, and “other” (everything in gross national product (GNP) except mining and manufacturing) sectors.

The method is as follows. First, one constructs an employment series that is adjusted for cyclical variations in output. 27 Next, the peak levels in output are identified (as is done for WEFA). Then, a Cobb-Douglas production function is fitted to these points by using the factor shares approach. 28 (Let the set D be the subset of indices t = 1, 2, …, T that correspond to peak output.) The production function is

Yt=AertKt(1α)LtαeuttD

where observed Kt and Lt are assumed to be fully utilized for tD. The estimate of α(α^) is taken as the geometric average of labor’s share for tD

α^=exp1T[ΣtDlog(WtLtYt)]

where Wt is the hourly wage rate, T′ is the number of peak output points (e.g., the number of elements in D), and exp x ≡ ex. Next, setting Zt=logYt(1α^)Ktα^Lt,tD, one chooses Ĉ, r^, and ût for t ∈ D in

Zt=C^+r^t+u^t

so that ΣtDu^t2 is minimized. Capacity output, Ytc is then defined as

Ytc=(expC^)er^tKt(1α^)(Ltp)α^t=1,,T

where Ltp t = 1, …, T is the Lt series adjusted for cyclical variation. Thus, peak values in Yt, assumed to represent capacity output, are joined 29 by a curve that takes into account developments in both labor and the capital stock within the context of the estimated historical relation between these and output.

This modified “trend through peaks” method is somewhat attractive relative to the pure production function method in that it is benchmarked using the assumption that observed peaks represent points of full resource utilization. This is attractive to the extent that this simple assumption seems compelling. The method has a further advantage in its simplicity of computation.

Dhrymes’s modified trend through peaks approach bears a strong resemblance to Artus’s method. Effectively, Dhrymes’s method amounts to setting lt and kt equal to unity at cyclical peaks and to zero otherwise, and then proceeding with the estimation. This treatment of lt and kt, however, entails a loss of degrees of freedom, which makes it difficult to estimate as many parameters as Artus does. Thus, the Artus method has a relative advantage that, because it makes use of a sufficient number of observations, also makes statistical hypothesis testing practical.

The advantage of the modified approach over that of the WEFA method is that it makes more efficient use of available information regarding what happens to potential output between peaks and, most important, what has been happening since the most recent peak. A disadvantage in relation to the WEFA method, which the modified approach shares with the production function approach, is that when enough new data become available and the production function is re-estimated, the entire historical capacity output time series is revised. 30 However, since the modified trend through peaks method is benchmarked to unchanging peak output levels, one expects that revisions using this method will be less significant than those for the pure production function method.

Inverted demand for factor inputs

This approach, generally used for estimating potential output for the aggregate economy, is basically the following. First, one estimates the desired quantity of labor or capital input as a function of income and other variables. Second, given the estimated demand function, the desired input level is replaced with the actual input level in the equation, and the equation is solved for income. Assuming that the relationship between desired input and income holds at efficient points of production, the income series computed in the second step of the procedure can be taken as an estimate of potential output.

Two examples of this approach are discussed here. The first, using a labor demand function, is the method used by the U.S. Council of Economic Advisers (CEA). The second approach, which makes use of a capital (or investment) demand function, was proposed by Hickman (1964). 31

CEA method. 32 The method described here is one used to compute the potential GNP series presented in the Economic Report of the President, Transmitted to the Congress January 1979 (Washington, 1979, pp. 72-76).

The approach begins with the following demand for labor function: 33

log(Lt/Ltp)=Σs=0nbslog(Yts/Ytsc)t=1,...,T(5)

where Lt is labor in hours, measured in “efficiency units,” 34 Ytc is capacity output, and n and T are finite numbers. It is assumed that

Σs=0nbsapproximately equals 1(6)

(i) Computing potential labor, Ltp. The concept of the potential labor force has been discussed in the section, Production function. The method used by the CEA is more sophisticated than the one used by Artus. The CEA method is possible in the context of aggregate employment35 because the necessary data are available, but this is not true for Artus, who studied the manufacturing sector.

The method used to construct a series Ltp proceeds by con-structing Ltip where i = 1, …, 8, and corresponds to eight age-sex groups in the population. 36 The term Ltip is obtained from the following expression:

Ltip=CPtil^ti(1U^ti/100)i=1,...,8t=1,...,T(7)

where CP is the civilian noninstitutional population and l and U are the labor force participation rate 37 and unemployment rate, respectively. The circumflex over l and U indicates that they are adjusted for cyclical fluctuations. 38 The subscripts ti indicate that the associated variable is an observation at time t for age-sex group i. To compute the Ltips according to equation (7), one first needs the l^tis and the Ûtis.

The basic cyclical variable used to adjust Uti and lti is the unemployment rate for males aged 25–54 years; call it Utm is assumed to exhibit little trend, and its high employment level is set at 2.5. (The group represented by males aged 25–54 years is a subset of one of the groups with a label i: males aged 25–64 years.)

Defining Xti ≡ log[lti/(1-lti)]39 l^ti is found as follows. Coefficients for the following eight separate regressions are computed:

Xti=ai+biUmt+ciUmt1+diZti=1,,8

where Zt is a collection of variables not of interest here. Given a set of estimates {a^i,b^i,c^i,d^i} for i = 1, …, 8, the CEA simulates the preceding equations setting Utm = 2.5 for all values of t, yielding a series called, say, x^ti for each i. That is,

x^ti=a^i+(b^i+c^i)2.5+d^iZti=1,,8t=1,,T

Then, l^ti=exp(X^ti)/[1+exp(X^ti)] is computed for all values of i and t.

Next, a moving high employment/unemployment benchmark is computed for each group i. This is done with the assumption that the primary reason for the shift of a group benchmark unemployment rate is changes in the group’s proportional representation in the labor market. 40

Letting l^ti=l^tiCPti/[Σil^tiCPti] coefficients are estimated for the following eight separate regressions:

Uti=ei+fiUmt+gil^tii=1,,8

The benchmark series, Ûti, is obtained for each i by setting Utm to its benchmark value, 2.5, and simulating the equation using the estimated coefficients. This is done in the same way as was done to obtain x^ti.

Now that l^ti and Ûti have been computed, the Ltips are obtained by using equation (7). The Ltips are then aggregated by using weights corresponding to each group’s relative wage. This gives full employment labor hours in efficiency units.

(ii) Computing potential GNP, Ytc. Clark and Luckett employ the following model for the evolution of labor productivity:

log(YtcLtp)=f(t)+ut(8)

where ut is a random term. The expression f(t) describes the growth in productivity over time as follows:

f(t) = a + bt + d(t)

d(t) being a term that embodies alternative assumptions concerning the performance of U.S. labor productivity growth in the last decade. 41

Rewriting equation (5), the expression becomes

log(Lt)=Σs=0nbslog(Yts)+log(Ltp)Σs=0nbslog(Ytsc)

Recalling equation (6) and assuming that Ytc does not fluctuate much, 42 the preceding equation can be rewritten:

log(Lt)=Σs=0nbslog(Yts)log(YtcLtp)

Substituting equation (8) in the preceding equation yields

log(Lt)=Σs=0nbslog(Yts)f(t)ut(9)

leaving an equation specified entirely in terms of observable variables.

Let b^s, s = 0, …, n be the econometrically estimated coefficients in equation (9). Substitute these in equation (5). The latter equation is then “inverted,” yielding the output gap as a function of lagged values of the input gap. That is, for any value of a scalar, m, a set dt, i=0, …, m can be computed from b^s, s = 0, …, n, so that

log(YtYtc)Σi=0mdilog(LtiLtip)(10)

where the symbol ≃ means an equality holds strictly only for large values of m. 43

The output gap and potential output are then derived by substituting the series Ltp, discussed earlier, in equation (10) and making the appropriate transformations.44

Hickman’s demand-for-capital approach. 45 This approach expresses the demand for capital, Kt*, as

logKt*=a1+a2logYt*+a3logPt*+a4t(11)

where Yt* and Pt* represent permanent income and relative output prices, respectively, at time t. (The model is specified for annual data.) The expressions Yt* and Pt* are defined as

a2logYt*=a21logYt+a22logYt1

and

a3logPt*=a31logPt+a32logPt1

Substituting equation (12) in equation (11) does not yield an econometrically estimable equation, since Kt* is not observed. Hickman posits a partial adjustment model for the latter

logKtlogKt1=b(logKt*logKt1)0<b<1(13)

Substituting equations (12) in equation (11) and the result in equation (13) gives (adding an error term, ut)

logKtlogKt1=blogKt1+ba1+ba21logYt+ba22logYt1+ba31logPt+ba32logPt1+ba4t+ut(14)

All coefficients in equation (14) are econometrically identified. If Yt does not change very much from year to year, one can set â2 = â21 + â22, where â21 and â22 are the ordinary least-squares estimates of a21 and a22, respectively. Finally, one computes Ytc, capacity output, by solving

logKt=a^1+a^2logYtc+a^31logPt+a^32logPt1+a^4t(15)

for Ytc. Equation (15) is the demand function, equation (11), with the actual capital stock substituted for the desired capital stock. As was pointed out in the introduction to this section, the relationship between output and capital represented by equation (11), and hence equation (15), is what is assumed to prevail under conditions of efficient production.

To test his “new” measure of capacity utilization, Hickman (1964, p. 549) compares it with those computed by five other sources and concludes: “These findings appear to confirm the validity of the new estimation technique.”

The advantage of the “inverted demand function” approach to measuring capacity utilization is that it is not necessary to estimate the underlying production relations. 46

Whether computing capacity utilization indirectly by making inferences from the observed behavior of businesses (by the inverted demand approach) is superior to one of the more direct methods (e.g., trend through peaks, production function) is primarily an empirical question that remains open.

Okun’s law 47

Okun’s procedure is different from the others described in that it makes use of a statistical relationship between percentage point changes in the unemployment rate and percentage changes in real GNP. According to Perry (1977, p. 1): “Okun’s law, which … [links] marginal output to marginal changes in unemployment rates, is probably the most robust macroeco-nomic relationship yet developed.”

A version of Okun’s law is estimated using the following regression equation:

ΔUt=d(t)+a0ΔlogYt+a0ΔlogYt1+a2ΔlogYt2+a3ΔlogYt3+et(16)

where Δ is the first-difference operator, 48 Ut is the rate of unemployment,49 Yt is real GNP, et is a random shock, and d(t) is a collection of dummy variables. Once the parameters of the Okun’s law equation have been estimated, the equation can be “inverted” to express Δlog Yt as a distributed lag on past values of ΔUt

ΔlogYt=Σi=0naiΔUti(17)

where for any value of n, the ai i= 0, …, n may be computed from the estimated coefficients of equation (16).50 Equation (17), integrated into level form, gives 51

logYt=Σi=0naiUti+C(18)

where C is a constant. Equation (18) describes the path in actual real output as it has been historically related to the path in the actual unemployment rate. Assume that the coefficients ai, i = 0, 1, …, n would have held if the economy had been at full employment during the period studied. Representing the full employment/unemployment path by Utf, t = –n, –(n–1), …, 0, 1, …, T, 52 substituting this for Ut in the right-hand side of equation (18) and subtracting the result from equation (18), the Okun’s law estimate of the output gap is

log(YtYtc)=Σi=0nai(UtiUtif)(19)

The output gap is found by taking the antilog of the term on the left-hand side of equation (19) and multiplying the result by 100. Capacity output is then computed in the usual way. 53

The Okun’s law method relies less on economic theory than do any of the previously discussed data-based methods. 54 It places its faith in a robustness that has been observed in the statistical relationship between the unemployment rate and real output. The method relies on the assumption that the same statistical relations prevailing in the historical data would have applied if the economy had been at full employment during the period studied. The weakness in the method, especially since the 1970s, has centered on the choice of the full employment benchmark and, in particular, on the assumption that it is constant. In the words of Perry (1977, p. 2), a constant unemployment rate, “used as a benchmark for measuring potential output, has moved noticeably away from measuring a constant degree of labor utilization measured in efficiency units.”55 There are several ways of minimizing this problem.

First, the discussion in the section (i) Computing potential labor showed how a moving benchmark aggregate unemployment rate can be computed. This could be used instead of a constant benchmark. Another approach, presented in Luckett (1979), is to use the unemployment rate for males aged 25–54 years, instead of the economy-wide unemployment rate. The former data series are less subject to trend than are the latter, and hence a constant benchmark is more appropriate in this case. 56 The consequence of applying the Okun’s law method in this way, according to Luckett (p. 22), produces measures of capacity output “remarkably similar” to those produced by the CEA method.

The FRB “eclectic” approach 57

The U.S. Federal Reserve Board (FRB) method of computing capacity utilization in manufacturing is a combination of data-based and survey-based methods. The method is to construct capacity utilization measures for each manufacturing industry covered by the surveys of businesses conducted by the McGraw-Hill Book Company (MGH). A weighted sum of the individual figures is calculated, giving a measure for the manufacturing sector as a whole. 58

The FRB measure makes use of the Federal Reserve’s December index of industrial production, Qt; data on the capital stock provided by the Bureau of Labor Statistics, Kt; 59 and year-end estimates of capacity, Ct, and capacity utilization, CUt, provided by MGH.

An initial, implicit estimate of capacity for each industry is found by taking Ct = Qt/CUt. However, Ct is implausibly irregular over time and also exhibits a procyclical bias. 60 The series Ct is smoothed by trending and by making use of Kt and Ct. This is done as follows.

Letting X1t = (Ct/Qt, the following regressions are estimated:

log(X1t)=a1+b1t+et

and

log(X2t)=a2+b2t+ut

where t represents a time trend and ut and et are shocks. (Dummy variables are also included, but are excluded here for simplicity.) As usual, estimated values of parameters are represented by a circumflex. Then, letting a1=exp(a^1),b1=exp(b^1), etc., one obtains

X^1t=a1(b1)t

and

X^2t=a2(b2)t

This gives the two smoothed estimates of capacity: X^1t × Kt, and X^2t × Ct. The final capacity estimate, Ct*, for an industry is the arithmetic mean of the two

Ct*=1/2(X^1t×Kt+X^2t×Ct)

The annual FRB measure of capacity utilization for an industry, CUt*, is computed as follows: 61

CUt*=(QtCt*)×100

Quarterly and monthly rates are obtained by linear interpolation.

The method is considered superior to the WEFA approach because it provides more reliable estimates of capacity output after the most recent output peak. It is also considered superior to the survey-based methods because it does not contain the cyclical bias observed in those. A problem with the FRB method is that the coefficients in equation (20) have to be re-estimated frequently; otherwise, biases are likely to emerge.62

SURVEY-BASED METHODS

Another way of compiling estimates of capacity utilization is to survey businesses. As Phillips (1963, p. 284) notes: “The obvious advantage of the … survey method is that direct questions relating to capacity are responded to by persons likely to know the answers.” This approach also has the advantage that it makes possible the compilation of kinds of information that would be practically impossible using data-based methods. For example, surveys can include questions on firms’ preferred operating rates; what the source, if any, of their production constraints are; and their intentions regarding capital expenditure in the upcoming months.

Indeed, it may seem that the existence of “direct” measures of capacity utilization renders redundant the indirect, data-based methods discussed in the section, data-based methods. It will be shown, however, that the survey approach is not an unmixed blessing and that, like its indirect counterparts, it has not only the advantages 63 cited but also some disadvantages.

Two kinds of survey are discussed next; they are informally referred to as Type #1 and Type #2. Afterward, some difficulties in the interpretation of the surveys are reviewed. Most of these surround the question of how business people define the concept of capacity, which many survey questionnaires leave unspecified. In reviewing these issues it should be kept in mind, however, that they bear primarily on the level of capacity utilization reported by the surveys and not necessarily on its direction of movement. To the extent that the variety of definitions of capacity employed and other sources of bias remain constant for successive surveys, the direction of movement in the published rates may not be affected.

Type #1 surveys

Surveys of this kind collect information used to calculate utilization rates. Examples of institutions that make use of this method are the Institut für Wirtschaftsforschung, Munich (IFO);64 the U.S. Department of Commerce, Bureau of Economic Analysis (BEA); 65 the U.S. Bureau of the Census (Census); 66 the McGraw-Hill Book Company (MGH); 67 the MITI index of operating ratio of Japan (MITI); 68 the Business Tendency Survey of the Netherlands (NBTS); 69 and the business survey in Italy by Istituto Nazionale per lo Studio della Congiuntura (ISCO). 70 All these surveys apply to the manufacturing sector.

An example of what is asked of respondents in this kind of survey is the BEA survey question reported in Hertzberg, Jacobs, and Trevathan (1974, p. 49): “At what percentage of manufacturing capacity did your company operate in (month and year)?” While respondents are not given a precise definition of capacity, according to the BEA survey (p. 50): “Replies received and conversations with respondents indicate that most companies use a measure of maximum practical capacity in answering the questions.” The BEA questionnaire does give some idea of the meaning of capacity by instructing respondents to “follow the company’s usual operating practices with respect to the use of productive facility, overtime, work shifts, holidays, etc.” With regard to product mix, the BEA instructs respondents as follows: “When any of your facilities permit the substitution of one product for another, use a product mix at capacity which is most nearly similar to the composition of your actual (month and year) output.”

Surveys differ in the extent to which capacity is defined. MGH, for example, does not define capacity at all in its survey and does not ask respondents to specify their meaning of the term. As Gang (1974, p. 65) states: “… as we all know, a formal definition tends to limit responses to a question.” Respondents to the Census survey, on the other hand, are given a fairly precise definition of capacity. 71

Aside from the problem that the response rate might suffer if capacity were defined too precisely or made too complicated, respondents may not be able to interpret or answer the question. 72 In any event, any attempt to define capacity with complete precision is not really possible and soon encounters increasingly troublesome ambiguities. According to Panić (1978, p. 16): “It can be argued, for instance, that managers of a firm are the best judges of what its ‘capacity’ is … and that if they themselves are unable to ascertain this nobody else can.”

Type #2 surveys

Another type of survey yields estimates on the percentage of firms that are operating at full capacity. Examples of this for the manufacturing sector are the Swedish Business Tendency Survey (SBTS), 73 the National Institute of Statistics and Economic Studies (INSEE) 74 in Paris, the CBI, 75 and the BEA-1. 76

Several types of question are asked by institutions that make use of this kind of survey. An article by Glynn (1969, p. 186) reports that the CBI asks for a “yes” or “no” answer to the question: “Is your present level of output below capacity (i.e. are you working below a satisfactorily full rate of operation?)”

An article by Wimsatt (1964, p. 10) reports that BEA-1 asks respondents to place themselves in one of three categories: “Taking into account your company’s current and prospective sales for [year] how would you characterize your [month year] plant and equipment facilities:—more plant and equipment facilities;—about adequate;—existing plant and equipment exceeds needs?” (The proportion of firms choosing the first category can be taken as an approximation to “the per cent of firms who are at full capacity.”)

The BEA-1 method clearly relates only to the rate of utilization of capital, while the CBI question appears ambiguous in this regard. With reference to the latter, the results of a special CBI inquiry reported by Panić (1978, p. 16) suggest that “… two-thirds of [respondents] think only in terms of capital utilisation.” The remainder included other resources, such as labor and raw materials, in their consideration.

The SBTS is similar to the CBI in that firms are asked (Ruist and Söderström, 1975, p. 370) to respond “yes” or “no” to the question: “Is the firm now running at full capacity production?” Studying the results of the SBTS survey applied to the engineering industry (excluding shipyards) for the period 1968-73, Ruist and Söderström (1975, p. 371) find: “It is quite clear that, at least for this industry, the firms do not consider utilization of capital alone when they report on capacity utilization.” They conclude that firms are guided not by their utilization of any particular factor of production but by the possibility/impossibility of increasing production on short notice.

The INSEE survey reports the proportion of firms unable to increase their production owing to shortages of capital, labor, or supplies. 77 In this case, the question clearly intends for respondents to interpret capacity constraints broadly. However, it remains an open question to what extent the pattern found by Ruist and Söderström in relation to SBTS holds here also.

Difficulties in interpreting survey results

It has already been indicated that it is not always clear how businesses choose to define capacity when responding to survey questionnaires. Since the definition is often left to the respondent, it may be interpreted in the narrow, capital utilization sense, or in the wider sense, that is, the extent to which all resources (capital, labor, land, and raw materials) are utilized. Moreover, even when the questionnaire defines which of the two meanings is intended, the time horizon that businesses have in mind in evaluating their capacity also introduces uncertainty for interpretation.78

Other factors making for difficulties in interpreting survey results are as follows:

(a) Uncertainties prevail regarding respondents’ definitions of capacity beyond those already mentioned. If the predominantly used concept is that of practical capacity, then it is not clear what the status of marginal plant and equipment is. For example, are they included in periods of high demand and excluded otherwise? A similar possible source of ambiguity exists concerning the number of shifts assumed. 79 To what extent is the meaning of capacity a function of the level of demand, that is, to what extent do respondents employ the idea of preferred capacity? 80

Many firms (e.g., petroleum refineries) customarily use the notion of engineering capacity. Further, according to the Department of Commerce (1978, p. B-1): “Other industries use different methods in their capacity estimation. They might envision capacity as the maximum number of man-hours of their labor force, a past peak performance period, a share of market output or use any of a number of other methods.” These other methods may or may not differ significantly from what they would report under a practical capacity concept. However, to the extent that they do, ambiguity is introduced into the meaning of capacity utilization figures produced from surveys.

(b) Even if respondents are instructed to assume a “normal” product mix and/or a “reasonable work pattern,” these may be difficult or impossible to define for firms that produce thousands of products and for which demand is shifting.

(c) Survey estimates are subject to sampling errors. Since surveys cover only a subsample of the population, the results depend to a certain extent on the particular subsample that happens to be chosen. An estimate of the resulting sampling error is provided by the “standard error of estimate,” which is calculated for some surveys. For example, the Department of Commerce (1978, p. 25) estimate of capacity utilization for industry in the fourth quarter of 1977 was 71 per cent, while the estimated standard error was 1 per cent. That is, the true population capacity utilization measure is estimated to be greater than or equal to 70 per cent and less than or equal to 72 per cent, with two-thirds probability.81 Since the size of the standard error is inversely related to the sample size, one survey is better, ceteris paribus, than another if its sample size is larger.

(d) Survey estimates are also subject to measurement error. Total errors in capacity utilization figures are likely to be greater than the standard error of estimate because further errors are introduced in collecting, transmitting, and reporting data. Also, errors are introduced by such factors as nonresponse and poor design of the sample.

(e) Many surveys, for example, CBI, MGH, and BEA, are company based. A number of firms, however, have operations in more than one economic sector. Hence, classification of these firms into one sector or another can be somewhat arbitrary, as is the weight assigned to the estimated capacity utilization rate for the purpose of aggregation. The advantage of company-based surveys is that the results can be published on a reasonable schedule. Also, these data are preferred when they are to be used with other company-classified data, such as profits or investment. 82 Another kind of survey, such as the Census Survey, is establishment83 based. This avoids some of the classification problems of the company-based survey. The larger sample on which such a survey is based, however, means that it takes considerably longer for the results to become available.

(f) Basic data used to compile survey-based capacity utilization figures are necessarily highly disaggregated. Hence, the aggregation problem is particularly relevant to these measures. One expects, ceteris paribus, that the greater the level of disaggregation, the larger the final aggregate estimate of capacity. Thus, it is not surprising that the Census utilization rate figures, which are establishment based, are consistently lower than the company-based figures of the MGH and BEA surveys for the years 1973 to 1977.84

Relationship between Type #1 and Type #2 surveys

A difficulty in interpreting results from surveys of Type #2 is that they do not provide a measure of the degree to which firms are working below capacity. If, say, 50 per cent of firms are operating at full capacity, it is important to have an idea of the rate of operation of the other firms. It would be useful, in this respect, to know what relationship there is, if any, between the proportion of firms operating at full capacity and the degree of utilization for the industry as a whole. This would also make it possible to check for consistency with other measures of capacity utilization, such as the Type #1 version and data-based methods. This is especially important in view of the uncertainty that surrounds these measures. Attempts to analyze the relationships between the results of Type # 1 and Type #2 surveys can be found in Enzler (1968 a; 1968 b), Ruist and Söderström (1975), and Panić (1978). These are not reviewed here.85

The last two parts of this section are devoted to a discussion of two properties of survey-based measures of capacity utilization. They suggest a persistent underutilization of resources and suspiciously little cyclical fluctuation in utilization rates.

Surveys show more unused capacity

Section II of this paper shows that capacity utilization rates compiled from surveys tend to be lower than those computed by data-based methods. One possible reason for this is that survey-based figures are computed by using more highly disaggregated data than are the data-based figures. Furthermore, data-based methods, in making use of the observed relations between inputs and outputs, may yield results closer to the wide interpretation 86 of capacity utilization than do survey methods. Capacity may often be interpreted in the latter in a sense closer to the engineering concept.

A number of other reasons might explain why measured capacity utilization rates obtained from surveys tend to be lower than those obtained by other methods. Under some conditions, firms choose voluntarily to maintain excess capacity (low utilization). If the phenomenon is fairly consistent through time, it may not reveal itself in the data-based utilization rate figures. This underutilization would appear in the survey-based figures, however, to the extent that the excess capacity is included in reported capacity.

There are several reasons why capital might be kept idle intentionally.87

(a) A firm in an industry with increasing returns to scale might build a larger plant than is justified by its current market share in the expectation of a future expansion.

(b) Fluctuating demand may make it rational for a firm to maintain spare capacity so that it does not lose customers to competitors in periods of peak demand. An example of this is the airline industry.

(c) Fluctuations in input prices make it economical to maintain idle plant capacity for periods of time. A prime example of this is the “fluctuation” in wages over the 24-hour day. Since workers demand higher wages to work at night then during the day, it is often considered wise to keep plants idle at night.

(d) An argument from the literature on imperfect competition suggests that industries that are less than perfectly competitive will intentionally maintain idle plant capacity. This is the profit-maximizing output choice for firms that face a declining demand curve.

Factors making for unintended idleness include an unexpected drop in international competitiveness, a failure of expected demand to materialize, a strike or other unexpected shortage in a key input, etc. It seems likely, however, that data-based measures would capture idleness of this kind.

Surveys show less amplitude in capacity utilization

In commenting on utilization rates computed from surveys, Perry (1973, p. 711) states: “It appears that respondents ‘find’ capacity when output rises sharply, and ‘lose’ it when output slackens.” As is shown in Section II, capacity utilization rates compiled by using surveys exhibit a procyclical bias that is not evident in the other measures.

Several reasons have been offered to explain this: 88

(a) In periods of high demand, firms include marginal plant and equipment in calculating their capacity, while they exclude it in periods of low demand.

(b) Firms increase the number of shifts and amount of overtime that they consider “normal” in calculating their capacity when demand is high; the opposite happens when demand is low.

(c) Firms that have hundreds of outputs find it difficult to define their capacity output, and therefore they use employment as a proxy. The procyclical movement in labor productivity, however, makes the use of this a source of bias.

(d) Respondents are included in a sampling population for several successive surveys. If it is difficult for a respondent to estimate the firm’s rate of capacity utilization, the respondent might report again the rate that was reported in the previous survey.

A study by de Leeuw (1979) suggests that (b) is not, in practice, very important as an explanation of the cyclical bias in survey measures. To arrive at this conclusion, he makes use of detailed information provided by the Census survey, which shows no increase in capacity utilization from the fourth quarter of 1975 to the fourth quarter of 1976, even though this was a period of vigorous expansion in manufacturing output. De Leeuw (1979, p. 47) reports that responses to the Census survey indicate no increase in the number of shifts per day and days per week assumed at capacity during the same period.

De Leeuw does find evidence in the Census survey indicating that (c) may be an important source of bias. He groups Census survey questionnaire responses with those that probably do use employment in calculating capacity (39 per cent of the total), those that cannot be classified (40 per cent), and those that probably do not use employment (22 per cent). He finds that the latter registered a significant increase in capacity utilization between the fourth quarters of 1975 and 1976. The others did not, presumably because increased output and capacity utilization came from higher productivity per worker and not from higher employment. De Leeuw estimates that (c) accounts for 37 per cent of the difference in variability between the BEA measures and an average of the FRB and WEFA measures. The latter do not exhibit cyclical bias.

Using results from the BEA survey, de Leeuw (1979, p. 49) concludes that (d) may also be a significant source of bias, as special tabulations prepared from the BEA survey responses show an “enormous frequency of no-change reports.” After examining other data, he concludes that “the true frequency of no change is much less than reported in the BEA survey.”

De Leeuw finds some evidence to suggest that large companies report “no change” less frequently than the small ones do, perhaps because the former take greater care in filling out the questionnaire. This would help to explain why the BEA survey shows less amplitude than does the MGH survey. 89 The latter replies more heavily on large firms, while the former, taken from a broader sample, includes many small firms.90 De Leeuw estimates that (d) accounts for 21–42 per cent of the difference in variability between the BEA measure and an average of the WEFA and FRB measures. Thus, according to De Leeuw, (c) and (d) together explain about 58–79 per cent of the cyclical bias in the BEA measure. De Leeuw does not discuss the possible significance of (a).

II. Capacity Utilization in Nine Industrial Countries

This section examines data on the utilization of manufacturing capacity for nine industrial countries: the United States, France, Sweden, the United Kingdom, Italy, Japan, the Netherlands, Canada, and the Federal Republic of Germany. 91 Special attention is given to the U.S. measures of manufacturing capacity utilization because the number and variety of measures available make the United States well suited to be a case study of a number of factors raised elsewhere in the paper. Thereafter, the discussion continues for the eight other countries and concludes with a summary of the findings.

U.S. CAPACITY UTILIZATION RATES FOR MANUFACTURING

Annual historical observations on five measures of capacity utilization in the United States are given in Chart 1. These are the BEA, FRB, WEFA, MGH, and Artus production function measures. The shortest series is the BEA, which begins in 1968.

Chart 1.
Chart 1.

United States: Capacity Utilization, 1948–78 1

(Actual output as a percentage of capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, paragraph (ii), in the text.

Several characteristics are shown in the chart. First, in the 1970s, the MGH and BEA measures showed low utilization rates by comparison with the WEFA measure and Artus. (That the FRB measure has a mean similar to that of MGH is not surprising, since the former is benchmarked to the latter.) Something of a reversal occurs in the period 1958 to 1966, however, when the WEFA measure produced the lowest utilization rate. Indeed, when viewed over the past 20 years, the WEFA measure indicates a rising trend in capacity utilization, while the others register a modestly falling rate. This appears not to be due simply to a greater orientation to capital utilization on the part of survey measures. The Artus index, like the WEFA measure, is a measure of the utilization of all resources, but does not exhibit the same rising trend. 92

Second, the data exhibit the same turning points in the 1970s, while there is less agreement in the 1950s and 1960s. For example, the FRB and WEFA measures reach a trough in 1961, while the MGH measure reaches a local peak in the same year. 93

Finally, it can be seen that the BEA measure clearly has a lower variance over the period 1968–78. Measured variances of the Artus and WEFA data appear to be greater over the longer run because of the steep rise registered by both during the 1960s. 94

Implicit capacity 95 and the FRB index of manufacturing output (ACTUALQ) are illustrated in Chart 2. For convenience of presentation, a common trend term has been removed from all data.96 The procyclical bias of the BEA measure emerges quite plainly in the chart. The MGH measure also exhibits procyclical movements, but less so than the BEA measure. Also, these data are implausibly irregular, given the expectation that capacity grows fairly smoothly over time. The other capacity figures do exhibit smoothness, something ensured by the way in which these data are constructed. The FRB measure exhibits the least cyclical movements, while the procyclical movements in the Artus and FRB implicit capacity measures are very slight.

Chart 2.
Chart 2.

United States: Manufacturing Capacity, Detrended, 1948–78 1

(Deviation from trend in ACTUALQ)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnotes 91 and 96, in the text.

There is some disagreement in the data regarding recent developments in capacity. The FRB and BEA measures indicate a rise during the period 1977–78, while the others point to a decline, relative to trend. The rise in the BEA measure may well be due to its known bias and to the sharp contemporaneous rise in manufacturing output. However, the rise in the FRB measure cannot be explained so easily.

Charts 3 through 6 illustrate the results of attempts to adjust the MGH and BEA measures (MGHADJ and BEAADJ, respectively) for cyclical bias. The adjustment procedure removed that part of cyclical variation in implicit capacity that is explained by cyclical movements in output and not by changes in the capital stock. 97 The results of these adjustments confirm what appeared earlier: the BEA measure is more subject to cyclical bias than is the MGH measure. It was estimated that an increase of 1 per cent in output induces BEA survey respondents to report an increase of 0.5 per cent in their capacity. For the MGH measure, reported capacity was estimated to increase by about 3/10 of 1 per cent with an increase of 1 per cent in output. 98

Chart 3.
Chart 3.

United States: Published and Adjusted BEA Capacity, 1968–781

(Indices of capacity output and actual output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnotes 91 and 97, in the text.

Chart 3 shows that the adjusted BEA implicit capacity series are substantially different from the actual series and are considerably smoother. In Chart 4 it is seen that the adjustment significantly increases the amplitude of the BEA utilization rate. 99

Chart 4.
Chart 4.

United States: Published and Adjusted BEA Utilization Rates, 1968–78 1

(Actual output as a percentage of capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnotes 91 and 97, in the text.

Chart 5 shows that the effect of the adjustment of the MGH capacity measure is much less considerable.100 Similarly, the adjusted MGH utilization rate is not as significantly different from the adjusted version as the BEA measure is.

Chart 5.
Chart 5.

United States: Published and Adjusted Mcgraw-Hill Capacity, 1954–78 1

(Indices of capacity output and actual output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnotes 91 and 97, in the text.

One rather interesting thing occurs as a result of the adjustment. The movement in the adjusted MGH utilization rate is opposite to that of the unadjusted rate in 1957–58 (Chart 6). The dip in output in that period was associated with a greater fall (in percentage terms) in MGH-reported capacity, causing the reported utilization rate to rise. When the fall in reported capacity was adjusted for bias, the utilization rate fell. This is to be expected in a recession year and is what is reported by the other capacity utilization rate measures. (See Chart 1.)

Chart 6.
Chart 6.

United States: Published and Adjusted Mcgraw-Hill Capacity, 1954–78 1

(Actual output as a percentage of capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnotes 91 and 97, in the text.

To summarize, it appears that, disregarding the systematic differences in level, 101 the direction of movement of the several utilization measures was about the same in the 1970s. For earlier periods, however, it is difficult not to agree (looking at Chart 1) with Perry (1973, p. 704) when he stated: “The answer to the crucial question of how much unused capacity exists in American industry depends to an altogether unacceptable degree on which of the widely used measures one looks at.”

CAPACITY UTILIZATION RATES FOR MANUFACTURING IN EIGHT OTHER INDUSTRIAL COUNTRIES

Charts 7 through 20 illustrate capacity utilization and, where relevant, implicit output data and actual output data for eight industrial countries.

Chart 7.
Chart 7.

France: Capacity Utilization, 1961–78 1

(Actual output as a percentage of capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, paragraph (ii), in the text.

For France102 and Sweden, only survey results of the Type #2 are reported, in addition to the Artus production function estimates. (See Charts 7 and 8.)103 Substantial volatility is evident in the INSEE and SBTS data. The same high variance is exhibited in the CBI results depicted in Chart 9, suggesting that this may be a property of Type #2 surveys generally. Charts 7 and 8 show that the directions of movement (short-term trends) are about the same for the Artus and Type #2 survey measures. Therefore, these measures appear to be generally consistent for these countries.104

Chart 8.
Chart 8.

Sweden: Capacity Utilization, 1961–781

(Actual output as a percentage of capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, paragraph (ii), in the text.
Chart 9
Chart 9

United Kingdom: Capacity Utilization, 1958–78 1

(Actual output as a percentage of capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, paragraph (ii), in the text.

From the point of view of international comparisons, it is interesting to note the substantial difference in the average levels of the SBTS and INSEE measures. This difference does not appear to be due simply to different utilization rates, since the Artus data for the two countries are quite similar. 105 As was pointed out previously, the INSEE survey explicitly requests respondents to interpret capacity broadly. On the other hand, SBTS respondents are left free to respond on the basis of the narrow definition of capacity. A more careful investigation than is made here may show that it is this difference in interpretation that accounts for the difference in mean between the two series. 106

For the United Kingdom, Panić’s (1978) output/capital and Artus’s production function methods appear to yield similar results, not only in terms of direction of movement but also in terms of level. The two nearly converged by 1971, after being 2–5 percentage points apart in the early 1960s.

As was observed earlier, the CBI survey results are considerably more volatile than the Artus and Panić measures. 107 A problem from the point of view of international comparability that was encountered for France and Sweden also seems to arise with the CBI measure. While Artus’s data for the United Kingdom are on average generally the same as those for Sweden and France, the CBI survey results clearly fall between the SBTS and INSEE results in terms of level. As was indicated, this suggests that differences between these Type #2 measures are primarily related to differences in the surveys themselves rather than to differences in actual operating rates.

Comparing the CBI measure with those of Panić and Artus, there seems to be general agreement on the direction of movement of utilization. 108 Two exceptions are the periods 1964–65 and 1976–77. (See Chart 9.) Over these periods, Panić and Artus report declines, while the CBI measure indicates an increase in capacity utilization. The increase in the CBI indicator was greater in the second period than in the first, while at the same time the decline in Artus’s measure was greater in the first period than in the second.

Chart 10 reveals the convergence in the measured utilization rates of Artus and Panić as reflected in a convergence in implicit capacity output. A difference between the two series is a dip of capacity below trend as estimated by Artus for the period 1972–75. 109 Capacity returns to its trend level in 1974–75 by undergoing its most rapid rate of growth in the period 1961–77, according to Artus’s measure. 110 This seems surprising given that, at the same time, manufacturing output entered its steepest decline of the period 1961–77. Of course, it is possible that businesses might have been adding very rapidly to their stock of plant and equipment—thus expanding capacity output—even though manufacturing output was falling. However, this would be hard to reconcile with the contemporaneous behavior of Panić’s estimates of capacity output, which do not exhibit the same high growth rate in 1974-75. 111 Developments in the capital stock are the primary factor behind changes in capacity output for Panić’s measure.

Chart 10.
Chart 10.

United Kingdom: Capacity Output, 1958–781

(Indices of actual output and capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, in the text.

Another difference between Panić and Artus is that the latter’s estimate of the rate of growth in capacity is greater than the former’s in the period 1975–77. This is reflected in the difference in the two utilization rate measures in 1977. If Artus does indeed overestimate the rate of growth in capacity in 1976–77, this would explain the opposite movement in the CBI measure and Artus’s utilization rates during the period, a discrepancy that was pointed out earlier. (See Chart 9.)

Thus, while there seems to be general agreement among the several measures of capacity utilization for the U.K. manufacturing sector, there are also some puzzling differences.

Chart 11 presents three measures of capacity utilization for Italy. The Bank of Italy (BDI) measure is a trend through peaks type. The ISCO, BDI, and Artus measures exhibit roughly the same turning points and short-term trends. There are several exceptions, however. During the period 1961–63, the BDI and Artus measures move in opposite directions. The latter first rises, then falls, while at the same time the BDI measure registers a dip followed by a rise in utilization. Also, in the period 1967–69, Artus registers a significant fall and recovery in the utilization rate, which is hardly reflected in the BDI series. Conflicting signals like these would be confusing for a policymaker trying to decide between stimulus and restraint.

Chart 11.
Chart 11.

Italy: Capacity Utilization, 1953–771

(Actual output as a percentage of capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, paragraph (ii), in the text.

An example of a case where use of several utilization measures might be advantageous is offered by the period 1971–72. Over this period, the Artus measure indicates conditions of increasing slack, while the BDI measure suggests rising utilization. To the extent that there is safety in numbers, the Artus measure in this period seems to be the most reliable, since ISCO is also signaling a fall in utilization over the same period.

While in some cases it may be possible to resolve the conflicting signals of capacity utilization rates by examining underlying concepts and methods of construction, such an examination does not seem helpful over the period 1971–72. The Artus and BDI estimates employ the broad meaning of capacity, while the ISCO measure may, if anything, be focused more on the utilization of capital. On the other hand, the disagreement over developments in 1971–72 does not arrange the several measures into these same groups. 112

Additionally, it can be seen in Chart 11 that the Artus measure registers a sharp fall in utilization in 1976–77, significantly greater, perhaps, than the BDI or ISCO measures indicate. A similar occurrence appeared in connection with the United Kingdom in Chart 9.

Finally, the lower variability and mean value of the ISCO measure should be noted. Possible explanations for these properties of survey measures have been discussed earlier. 113 That the BDI measure is generally lower than that of Artus is probably due to the fact that the former is computed at a lower level of aggregation than the latter. 114

Little remains to be said about the contents of Chart 12 that was not already noted indirectly in the discussion of Chart 11. One may note that the ISCO implicit capacity measure exhibits a greater procyclical movement than do the BDI or Artus measures.

Chart 12.
Chart 12.

Italy: Capacity Output, 1960–781

(Indices of actual output and capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, in the text.

Turning to Japan (Chart 13), it can be seen that there are two periods, 1969–70 and 1971–72, when the MITI and Artus measures differ substantially. Also, the lower mean 115 and the variability of the MITI survey measure are evident in Chart 13, while its procyclical character is evident in Chart 14.116

Chart 13.
Chart 13.

Japan: Capacity Utilization, 1961–781

(Actual output as a percentage of capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, paragraph (ii), in the text.
Chart 14.
Chart 14.

Japan: Capacity Output, 1963–771

(Indices of actual output and capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, in the text.

Differences between the NBTS and Artus measures for the Netherlands are quite substantial for 1976–77. (See Chart 15.) The same suspicious decline in the Artus utilization rate that appeared in connection with the United Kingdom and Italy (Charts 9 and 11) over the period is evident here, too. The NBTS measure exhibits rising utilization in 1976–77.

Chart 15.
Chart 15.

Netherlands: Capacity Utilization, 1961-781

(Actual output as a percentage of capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, paragraph (ii), in the text.

The sharp trough and peak evident in the Artus data for 1972 and 1974, respectively, find an almost imperceptible echo in the contemporaneous NBTS data. The lower variability, presumably, is due largely to the procyclical bias observed in other survey data. The bias is confirmed here by inspecting Chart 16. A surprisingly strong growth in capacity output implicit in the Artus data in the years 1974–77 is also evident there.

Chart 16.
Chart 16.

Netherlands: Capacity Output, 1961–781

(Indices of actual output and capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, in the text.

For Canada, it appears that there is considerable agreement among the measures of capacity utilization presented in Chart 17: the Artus measure, that of the Canadian Department of Industry, Trade and Commerce (DITC), and that of Statistics Canada (STATCAN). Two periods of “disagreement” between the series are 1967–68 and 1973–74. 117 In the first case, the Artus measure indicates increasing slack, while the others are registering increased utilization. The opposite occurs in the period 1973–74 when the Artus measure indicates increasing utilization and the other two register growing slack. As was noted in a similar context with respect to Italy, these differences do not seem to be explicable in terms of differences in the concepts underlying the Artus, STATCAN, and DITC measures (DITC and Artus are closer to the wide sense of capacity utilization, while STATCAN is closer to the capital utilization meaning of the term).

Chart 17.
Chart 17.

Canada: Capacity Utilization, 1961–781

(Actual output as a percentage of capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, paragraph (ii), in the text.

The greatest degree of agreement for all the countries studied is observed among the measures of capacity utilization for the Federal Republic of Germany, shown in Chart 19, where directions of movement are basically the same in all periods. 118 The German data are also unusual in that the IFO survey-based measure exhibits about the same amplitude as the DIW output/capital ratio measure. 119 The mean of the IFO measure is lower than the others, particularly in the 1970s. On the other hand, this was only marginally true of the DIW measure during the 1960s. The capacity data in Chart 20 do suggest some cyclical bias in the IFO measure, but this is not as pronounced as shown elsewhere. For example, in 1967, a recession year, a local peak occurs in the IFO implicit capacity output series. Also, the 1974–76 recession in output is reflected very little, if at all, in the IFO measure of capacity. Finally, the relatively rapid rate of growth in the Artus measure of capacity in the late 1970s, evident for other countries, also shows up for the Federal Republic of Germany; however, it is possible to attempt to explain this discrepancy on the basis of differences in the concepts underlying the measures. Both the ISCO and DIW measures can be expected to be closer to the strict interpretation of capacity utilization than the Artus measure is.

Chart 18.
Chart 18.

Canada: Capacity Output, 1961–781

(Indices of actual output and capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, in the text.
Chart 19.
Chart 19.

Federal Republic of Germany: Capacity Utilization, 1962-771

(Actual output as a percentage of capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, paragraph (ii), in the text.
Chart 20.
Chart 20.

Federal Republic of Germany: Capacity Utilization, 1962–771

(Indices of actual output and capacity output)

Citation: IMF Staff Papers 1981, 001; 10.5089/9781451956573.024.A005

1 For sources and explanatory information, see footnote 91, in the text.

SUMMARY

To summarize, figures for capacity utilization for nine countries have been examined from the point of view of short-term movements, trend, volatility, and level. First, a general agreement between indicators regarding short-term movements was noted. In this regard, countries fall into roughly three categories. The first, where agreement is complete, 120 includes the Federal Republic of Germany and Sweden. An intermediate group includes the United Kingdom, France, Canada, and Japan—as well as the Netherlands, perhaps. The country for which there is the greatest disagreement regarding short-term trends is Italy. The United States would be included in the first group if one examines only the 1970s and in the third group if the 1960s were also taken into account.

The Artus measure indicates a decline in utilization in all countries in the last part of the period studied, except for the Federal Republic of Germany and the United States. Cases where this decline in the Artus measure is significantly greater than is indicated by the other measures are the United Kingdom and—particularly—Italy and the Netherlands. In each of these cases, discrepancies cannot be explained in terms of the concepts underlying the measures involved. This suggests a possible bias in the Artus measures.121

Data for most of the nine countries exhibit a downward trend in utilization in the 1970s. Exceptions arise in the STATCAN, WEFA, and, to a lesser extent, the BDI and DIW measures. Each of these measures (particularly WEFA) differs in its assessment of trend from other measures in their corresponding countries. This casts some doubt on the reliability of these estimates as indicators of long-term trends, at least for Canada, the Federal Republic of Germany, the United States, and Italy. 122

From the point of view of volatility, the data fall into three categories. First, Type #2 survey data exhibit by far the greatest amplitude, compared with the other measures studied. Further, the data-based measures consistently display greater amplitude than do the Type #1 survey measures. Reasons for the relatively low amplitude in Type #1 data were given earlier. Based on that evidence and on the procyclical movements of Type #1 measures (not present in the data-based measures) exhibited in the charts, it appears that the differences in volatility between data-based measures and Type #1 surveys are the result of bias in the latter.123

Differences in level were also noted among the data. These differences, however, are of little concern, since in most cases they can be explained by the way the data are constructed or by examining what it is that they are intended to measure. For example, the fact that the Artus measure consistently indicates the highest level of capacity utilization is due primarily to the fact that it is also computed at a higher level of aggregation than is any other measure in this study. Further, the Artus measure is constructed in a way that takes into account all resources, rather than only a subset, such as capital. Other measures, such as the survey-based ones studied, are thought to reflect capital utilization to a greater degree and thus to overstate available capacity. 124

III. Conclusion

The evidence presented in this paper shows that capacity utilization is not comparable—in terms of agreement on concepts and methods of compilation—to, say, GNP, production, prices, etc. It was shown that, disregarding differences in level, which are due to differences in data construction, there are—especially for some of the nine countries studied—periods in which measures give conflicting signals regarding current short-term trends in the economy. These differences could not be explained simply in terms of differences in underlying concepts or in data construction. Until it can be determined with relative confidence why measures differ when they do, a degree of unreliability is introduced into all the figures. Consequently, while it goes beyond the scope of this paper to make an in-depth examination of these differences, such a study seems worthwhile. Investigating why the degree of disagreement between measures of capacity utilization varies from country to country would seem to present a fruitful avenue of inquiry.

One approach to resolving the discrepancies between alternate measures of capacity utilization would be to investigate, in greater detail than was done here, the way in which they are constructed. Another approach would be to compare their explanatory power in equations explaining investment, prices, profits, trade, productivity, etc. 125 Examples of such equations may be found in Forest (1978), Schultze (1963), and Perry (1973). Perry compares the performance of WEFA and MGH in equations that use capacity utilization to predict capacity growth, investment, and prices. Jorgensen (1971) and Taubman and Wilkinson (1970) discuss the role of capacity utilization in explaining investment. In Artus (1970) and Deppler and Ripley (1978), capacity utilization is used to explain trade flows.

A comparison of the performance of alternate measures of capacity utilization in equations like the ones presented in the sources just cited could produce several results. First, some or several measures could consistently turn out not to be useful. What is more likely is that comparative advantages will be shown to be a function of the context in which measures are used. Such a study might also find useful applications for differences in rates of change and levels in utilization rates.126

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*

Mr. Christiano, a graduate of Columbia University, the London School of Economics and Political Science, and the University of Minnesota, was an economist in the General Statistics Division of the Bureau of Statistics when this paper was prepared.

1

Reference is made to discrepancies unlikely to be explained by sampling error.

2

This point is made in Artus (1977, p. 2).

3

Concepts of capacity utilization fall roughly into two categories—those that concern the degree of utilization of capital only (capacity utilization in the “narrow” sense) and those that concern the degree of utilization of all resources, including capital (the “wide” sense). The “engineering” concept of capacity is in the former category and is defined as the maximum output that can be produced using a given plant and equipment. Under the “minimum average cost” concept, discussed in Chamberlin (1947), capacity output is identified as a level of output at which average costs are at a minimum. When the average cost curve is a short-run one, the minimum average cost concept corresponds to a capital utilization concept. When the average cost curve is a long-run one, the minimum average cost concept more closely approximates capacity utilization in the wide sense. (These alternative interpretations of the minimum average cost concept were pointed out in Cassels (1937).) The “practical capacity” concept is defined as the maximum output that is possible given a fixed plant and equipment and “realistic operating conditions.” The latter are related to such things as machine maintenance requirements and reasonable expectations of productivity from the work force. (See Department of Commerce (1978), especially p. A-l.) The concept of “preferred capacity” is defined as the level of output that firms wish to produce given current market demand conditions. A more detailed review of these and other concepts of capacity is provided in an earlier version of this paper, entitled “Capacity Utilization: Concepts, Measurements, and Uses,” which is available upon request from the General Statistics Division, Bureau of Statistics, International Monetary Fund, Washington, D.C. 20431.

4

See de Leeuw (1979, p. 45).

5

A nontechnical discussion of Artus’s estimation techniques may be found in Artus (1979). There, he discussed the implications of his findings for the current economic situation.

6

Among the industrial countries, none (insofar as the author is aware) publishes capacity utilization figures based on aggregate production functions. However, the Bank of England experiments internally with these figures, as does Japan’s Economic Planning Agency. The latter are discussed in a publication of the Organization for Economic Cooperation and Development—OECD (1977). The Deutsche Bundesbank (1973) has also studied the use of production functions for the purpose of estimating potential output.

7

The post-1974 rise in fuel prices represents such a shift in relative input costs. For an effort to measure potential output for the U.S. private business sector, using what is basically a production function approach but which incorporates energy and its price explicitly, see Rasche and Tatom (1977). Perry (1977, p. 3) argues that “giving [the impact of energy prices] a prominent role in modifying potential output measures is mistaken.”

8

For a detailed description of the method, see Artus (1977, pp. 23-25).

9

To the extent that the benchmark is sufficiently in the past, errors in estimating the size of the capital stock in that year are of diminishing importance for recent observations.

10

In the past decade, an increasing proportion of investment funds has been spent on pollution control equipment and worker safety measures. According to a U.S. study by the McGraw-Hill Book Company, referred to by Ragan (1976, p. 16, footnote 15), “… air and water pollution control as a percentage of manufacturers’ capital spending rose steadily from 2.8 percent in 1967 to 9.1 percent in 1975. Expenditures for worker protection have also become substantial. In 1972 … they accounted for 3.0 percent of capital spending, and current projections indicate that in 1976 the percentage will reach 3.3 percent.” Presumably, these changes in the composition of investment have produced a shift in the relation of the stock of capital to potential output, for example, by reducing the trend rate of technical progress. Updated estimates of the equations in Artus (1977), presented in Artus and Turner (1978) for ten countries (Belgium, Canada, France, the Federal Republic of Germany, Italy, Japan, the Netherlands, Sweden, the United Kingdom, and the United States), find three where the trend rate of (“disembodied”) technical progress dropped significantly in the 1970s: Japan, Canada, and the United States. The declines may also have occurred for reasons other than the change in the composition of investment.

11

Summarizing his experience using capital stock measures empirically, Perry (1977, p. 3) states: “If capital is ignored, it is for a simple pragmatic reason: one cannot find an important or statistically significant role for capital in a freely estimated aggregate production function or any equivalent relation that one might use in estimating potential output.” This suggests the possibility that the issues raised in the text are of limited practical importance.

12

According to Artus (1977, p. 4): “…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.” For an alternative way of taking account of the observed procyclical movements in output per worker, which relies more explicitly on economic theory, see Lucas (1970) and Sargent (1978; 1979, Ch. XVI). Sargent and Wallace (1974) show that this approach, which involves carefully treating the way in which input and output data are averaged over time prior to statistical estimation, does not work in the case of the Cobb-Douglas production function.

13

For a fuller explanation of the reasoning behind this, see Artus (1977, p. 3).

14

This variable is given a time subscript to indicate that it is not constant throughout the estimation period. For example, for the United States, Uft = 4 for t = 1955–70 and Uft = 4.5 for t > 1970. (See Artus (1977, p. 18).)

15

The symbol ∈ denotes “is an element of.” Similarly, ∉ denotes “is not an element of.”

16

For estimates of these, see Artus (1977, p. 12, Table 2) and Artus and Turner (1978, p. 9, Table 3). A Bank of England publication (1978, p. 347), disappointed with the results in Artus and Turner (1978) as they apply to the United Kingdom, states: “It is, however, uncertain how much credence should be placed on the precise results of such calculations attempting to estimate the effect of investment on the growth of potential output. Estimates of physical investment are known to be subject to wide margins of error; the concept of potential output is elusive and not capable of unambiguous measurement; and, though this is a traditional area of research in economics, it has not proved possible to distinguish with any degree of confidence the separate effects of labour and capital on potential output.”

17

See Klein and Summers (1966). Others using this measure are the Bank of Italy—BDI (available on a quarterly basis in the IMF Data Fund) and the Canadian Department of Industry, Trade and Commerce (quarterly historical series presented in its “Rate of Capacity Utilization”).

18

Deciding whether a peak is major or not is a matter of judgment and constitutes a shortcoming of the method. This point is made in, among other places, Ragan (1976, p. 15).

19

Data are published in DIW, Wochendienst.

20

Published on a quarterly basis in Statistics Canada Daily.

21

There is—not only for the United Kingdom but also for industrialized countries in general—a declining trend in the output/capital ratio. This may be due to decreasing productivity of capital resulting from an increase in capital intensity, or it may be due to other factors.

22

The expression to the right of the first equality is obtained by substituting from equation (4).

23

Difficulties associated with computing the capital stock from published investment data were briefly discussed in the section, Production function.

24

The Artus method (discussed earlier) does not impose constant returns to scale (i.e., linear homogeneity), which in that case means (α + β) = 1. As it happens, Artus’s estimates of (α + β) are close to unity for most of the countries in his study.

25

This is easy to show. Let Y = f (K, L) be a linear homogeneous production function. Then, λY = f (λK, λL) for λ > 0. Setting λ=1K,Y/K=f(1,L/K)=g(LK).

26

It stands repetition, in favor of the production function method, that the output/capital ratio approach utilizes only the least reliable of the series employed in a production function—the capital stock.

27

The adjustment could be carried out using the method applied by Artus and described earlier, in the section, Production function. The adjustment is not, in fact, done in Dhrymes (1976).

28

This approach reduces the opportunities for inaccuracies in the capital stock series to affect the overall calculations. The method is discussed in what follows in the text.

29

In fact, it is not strictly true that the method simply draws “lines through peaks,” since the peaks themselves end up being adjusted somewhat. That is, YtcYt for tD to the extent that ût ≠ 0 and LtpLt for tD However, the expectation is that YtcYt is small for t ∈ D.

30

Recall that, under the modified trend through peaks method and the production function method, the historical capacity output series are computed by using parameters estimated from available data (e.g., for Artus’s method, the parameters are A, r, θ, β, α, and d in equation (1)). As new data become available with the passage of time and as equations are re-estimated, parameter estimates will change, producing the change in the entire historical capacity output series mentioned in the text. The WEFA method does not involve parameter estimates, so that the availability of new data does not result in changes in computed capacity output for the period prior to the previous peak. (Capacity output data subsequent to the previous peak are revised when a new peak in the data occurs.)

31

The reader who is not concerned with the details underlying the two approaches discussed here may go on to the section, Okun’s law, without breaking the continuity of the text.

32

This is described in Clark (1979) and in a follow-up paper by Luckett (1979). While Clark’s paper ranges more widely, Luckett’s limits itself to the method actually used by the CEA.

33

No attempt is made to rationalize this equation in a rigorous way. Clark (1979, p. 151) describes it simply as specifying a relationship between input and output gaps. Equations (5) and (8) should be compared with equations (4) and (5) in Luckett (1979, p. 11 and p. 14). In Clark, one finds not only equation (5)equation (8′), p. 156—but also a more complicated version where the left-hand side of equation (5) is replaced by a combination of labor and capital. In defense of an equation like (5), Clark (1979, p. 156) states: “If the capital input measure is sufficiently poor, ignoring capital will produce better estimates.” This point has been emphasized elsewhere in this paper as well. In using equation (5), the CEA has, in fact, “ignored” capital. On the other hand, Clark (p. 156) finds that the results using either approach are “virtually identical.” (The reader is referred to footnote 11, where another reason for ignoring capital is offered.)

There is no theoretical reason why equation (5) should not be specified in the reverse, regressing the output gap on past input gaps. In fact, as will be obvious later, the latter specification would simplify the procedure by eliminating a step. Sims (1972) provides a way of rejecting one of the two alternative specifications of equation (5) on statistical grounds. He applies his “Granger-causality” test in a context similar to the present one in Sims (1974), where he reports evidence that can be interpreted as favorable to specification (5).

34

This means that data on employment were first disaggregated by age and sex and then aggregated using relative wages as weights. This procedure is sometimes called “Perry weighting,” since a method like this was used by Perry (1971). Such a method was defended some time ago by Walters (1963, p. 22) where he referred to it as aggregating by using “equivalent man-hours.” See Clark (1979) and Luckett (1979) for details.

35

Actually, the data are available only for the nonfarm sector. The CEA method assumes that the deviation of aggregate employment from its potential is equal to deviations in nonfarm employment from its potential. This is valid to the extent that farm employment does not contain an important cyclical component. The reader interested in complete details on the sectors analyzed by the CEA is urged to consult Luckett (1979) and Clark (1979), since space limitations preclude a full discussion here.

36

These are men and women, respectively, ages 16-19,20-24,25-64, and 65 and over.

37

This is defined as the ratio of the civilian labor force to the civilian non-institution population. The civilian labor force is defined as the number of civilian employed plus those unemployed.

38

What this means with respect to Ûti is that the benchmark full employment/unemployment rate for group / is permitted to change over time. The way in which this is estimated to occur is explained later in the text.

39

This is a “logit” transformation on lti that ensures that 0 ≤ l^ti ≤ 1.

40

According to Clark (1979, pp. 148-49): “A relatively high proportion of the labor force in a particular group may make it difficult for members of that group to find satisfactory employment.”

41

One specification of d(t), a “pessimistic” one, implies a once-and-for-all drop in productivity since 1974. A more optimistic one implies that the lower post-1974 labor productivity has been a cyclical phenomenon. See Clark (1979, p. 153) for details.

42

Thatis, YtcYt1cYtnc.

43

Rewrite equation (5) in lag operator form: log(Lt/Ltp) = b(L)log(Yt/Ytc), where b(L)=Σs=0nbsLs and L is such that LsWt ≡ Wt-s for any s. Let D(L) ≡ [b(L)]-1 where D(L)=Σi=0diLi. Assuming that log(Yt/Ytc) is a bounded (infinite) process, it can be shown that a sufficient condition for D(L)log(Lt/Ltp) to be bounded is that the roots of b(L) lie outside the unit circle. Supposing that this is true (say, because the condition was imposed during estimation), then the expression of equation (5) in “inverse” form is log(Yt/Ytc)=Σi=0dilog(Lti/Ltip). Suppose that di is negligible for i > m for some m. Then the expression reduces to log(Yt/Ytc)Σi=0mdilog(Lti/Ltip), which is equation (10) in the text. For a review of lag operator polynomials, see Sargent (1979, Ch. IX) or Dhrymes(1971, Ch. 2).

This “inversion” is the step referred to in footnote 33, which would have been avoided if equation (5) had been specified as the output gap regressed on current and past input gaps.

44

That is, substituting Ltp from section (i) into equation (10) yields a series log (Yt/Ytc) = Zt, say, for t = 1, …, T. The output gap is then exp (Zt) × 100, and potential output is Yt/exp(Zt).

45

See Hickman (1964) for details.

46

Good arguments have been made that the demand for inputs on the part of a firm (or industry) should be derived by solving the “representative” firm’s dynamic optimization problem. This latter approach does involve the parameters of the production function. See, for example, Hansen and Sargent (1980) and Sargent (1978; 1979). The method described in the text poses its own specification problems. Comparing the equations estimated using the production function and inverted factor demand methods, it is to be noted that the former specifies input as exogenous while the latter specifies output as exogenous in the input/output process. Presumably, one of these two specifications is, statistically at least, inappropriate. The methodology of Sims (1972) can be applied to this issue. To what extent this question is of practical significance in the present context is not clear.

48

Here, Δ is such that Δxtxt – xt-1.

49

Usage differs on this point. Luckett (1979) defines Ut as the unemployment rate for males 25–54 years of age. In Clark (1979, p. 160), Ut represents the “overall unemployment rate.”

50

In footnote 43, the lag operator, L, and the subject of “inverting” difference equations, such as equation (16), are discussed. The discussion there applies to the present case as follows: Rewrite the econometrically estimated version of equation (16) as ΔUt=d^(t)+a^(L)ΔlogYt+e^t, where a^(L)=Σi=03a^iLi. Assuming â(L) to be invertible, write a′(L) ≣ [â(L)]-1, where a(L)=Σi=0aiLi. Multiplying by a′(L) produces a(L)ΔUt=a(L)d^(t)+ΔlogYt+a(L)e^t. In practice, a(L)d^(t) is so small that it can be set to zero. The term a′(Lt can also be taken to be zero after setting êt to its expected value. Finally, it is assumed that for some value of i, say n, ai, i > n is negligibly different from zero. Disregarding the latter, one ends up with equation (17) in the text.

51

The reader may verify that equation (18) is indeed the integral of equation (17) by simply calculating log Yt log Yt-1(= ΔlogYt) from equation (18). The result is equation (17).

52

The series Utf is usually set to a constant value, this being estimated from other information. A procedure whereby a nonconstant Utf series could be computed was discussed in the section, CEA method.

53

That is, Yt divided by the output gap, multiplied by 100.

54

The WEFA and CEA methods, however, are close runners-up, as is the Federal Reserve Board method, which is discussed next.

55

Labor measured in “efficiency units” is discussed in footnote 34.

56

This fact plays an important role in the CEA procedures discussed earlier.

57

This approach is discussed in detail in Federal Reserve System (1978).

58

An industry’s weight constitutes that industry’s capacity output as a fraction of the aggregate, valued in base-period value-added weights. For details, see Federal Reserve System (1978, p. 29).

59

U. S. Department of Labor. The construction of Kt is discussed in Federal Reserve System (1978, p. 12, footnote 15).

60

Reasons for the cyclical bias observed in survey-based capacity utilization rates are discussed in the section, Surveys show less amplitude in capacity utilization.

61

Note that while Ct* is an index of capacity relative to base-year output, so is Qt. Hence, base-year output cancels in the ratio, as it should. This is seen as follows. Let Yt and Yt* be actual and capacity output, respectively, in period t. Let Yb be Yt for t = b, where b is the base period (i.e., Yb is base-period output). Then Ct* = (Yt*/Yb) × 100 and Qt = (Yt/Yb) × 100, so that CUt=(Qt/Ct*×100)=(((Yt/Ybt)×100)/((Yt*/Yb)×100))×100=(Yt/Yt*)×100.

62

This point is made by Raddock (1978, p. 12) of the Federal Reserve Board. According to him, one reason for a relatively large revision in the utilization series a few years ago was that equation (20) “had not been re-estimated for too long a time.”

63

Another advantage that is sometimes cited in favor of the survey-based approach is that it provides data on a timely basis (often quarterly) and is not subject to revision as are other published data. For the Confederation of British Industry (CBI) survey, according to Panić (1978, p. 16), respondents are given two weeks to reply to the questionnaire and the results are published two weeks later. As an extreme counterexample, the latest published figure available from the Department of Commerce (Bureau of the Census) survey is the capacity utilization rate for the fourth quarter of 1977. The difference in pub-lication lag depends on whether a survey is company based or establishment based. This point is taken up in paragraph (e) in the section, Difficulties in interpreting survey results.

64

Available quarterly and published by IFO Institut für Wirtschaftsforschung, in IFO Schnelldienst.

65

Available quarterly and described in Hertzberg, Jacobs, and Trevathan (1974).

66

Available annually, but with a considerable lag. The year for which the most recent data are available is 1977. For a detailed discussion, see U. S. Department of Commerce (1978).

67

Discussed in Gang (1974).

68

Published by the Bank of Japan, Statistics Department, in Economic Statistics Monthly; also available in Economic Statistics Annual.

69

Available three times a year from Centraal Bureau voor de Statistiek, in Conjunctuurtest.

70

Available quarterly and published by ISCO, in Quaderni Analitici.

71

For the definition, see Department of Commerce (1978), p. A-l.

72

For example, capacity defined in the least-average-cost sense might require more information than a business actually records.

73

Available quarterly in Konjunkturinstitutet, Konjunktur Barometern.

74

Available quarterly in Institut National de la Statistique et des Etudes Economiques, Tendances de la Conjuncture.

75

Discussed in Glynn (1969).

76

Available quarterly and published by the BEA, in Survey of Current Business. See, for example, Woodward (1979, p. 18, Table 4).

77

See the description associated with item (3.1.6), “Goulots de Productions,” which is published in Institut National de la Statistique et des Etudes Economiques, Tendances de la Conjuncture (June 15, 1979), p. 28.

78

These two points are discussed in Artus (1977, pp. 6–7).

79

For example, if a firm operates more than two shifts a day, marginal costs and average costs may jump, because workers on the third shift must be paid a premium and fixed costs are incurred in starting up previously idled machinery.

80

Preferred capacity is the quantity of output at which the manager of the firm prefers to operate. According to Department of Commerce (1978, p. B-l): “The concepts of preferred and practical capacities are difficult for some respondents to differentiate. Many respondents report the two as identical.” Some surveys also ask what a firm’s preferred capacity is. BEA does so quarterly, and MGH does so occasionally. (See Hertzberg, Jacobs, and Trevathan (1974), pp. 54–55.) McGraw-Hill publishes the “effective operating rate,” which is the ratio of capacity utilization under the practical capacity concept to capital utilization under the preferred capacity concept. (See Gang (1974), p. 65.)

81

More precisely, it is estimated that if intervals of distance 2 percentage points containing in their center capacity utilization rates computed for all (or “arbitrarily many”) logically possible subsamples of the given Census Survey size, two thirds of these would contain the true population capacity utilization rate. For the details of how sampling errors for the Census Survey are computed, see Department of Commerce (1978, p. C-l).

83

According to the International Labour Office (1974, p. 1), the U.S. Department of Labor’s Bureau of Labor Statistics defines an establishment as “… an economic unit which produces goods or services, such as a factory, mine or store. It is generally at a single physical location and it is engaged predominantly in one type of economic activity. Where a single physical location encompasses two or more distinct and separate activities, these are treated as separate establishments, provided that payroll records are available and certain other criteria are met.”

84

See, for example, Department of Commerce (1978, p. xii, Chart E).

85

Another, simpler, approach is presented in Panić (1978), who estimates linear regression relationships between Type #1 and Type #2 measures. His approach can be viewed as a linear approximation to the one discussed by Enzler.

86

The wide interpretation of capacity utilization means the interpretation under which the efficiency of use of all resources is implied. The narrow interpretation refers to the capital utilization usage of the term “capacity utilization.”

87

See Winston (1974). He distinguishes between idleness that is intended ex ante and that which is unintended ex ante. Presumably, survey-based figures reflect both, while data-based figures reflect only the latter.

88

Another reason not included in the list is one suggested by Ruist and Söderström’s (1975) findings in the context of Type #2 surveys. If firms consider capacity output as the level of output that they can achieve on short notice, then reported capacity can be expected to be positively correlated with actual output, thereby reducing the amplitude in reported utilization rates.

89

This is shown in Section II.

90

Another explanation of the higher amplitude of the MGH than BEA measures is also possible. It is simply that the “true” operating rate of large firms varies more over the cycle than that of small firms. This hypothesis is suggested by Ragan (1976, p. 18).

91

The data presented for each country do not necessarily constitute an exhaustive list of available information. For example, two data series that might have been included in this study are Type #1 survey data for Sweden (Albrecht (1979, Table 1)) and for France (Organization for Economic Cooperation and Development (1977)).

Sources of data are as follows:

(i) Manufacturing production data. All data were obtained from the IMF Data Fund under the following line numbers: the United States, the Netherlands, the United Kingdom, France, and Canada—line 66EYCZC; Japan and the Federal Republic of Germany—line 66EYCYB; Sweden—line 66EYBZC; and Italy—line 66EY.CZ. Output data for each country are referred to in the text by the term “Actual Q.”

(ii) Capacity utilization rates. Artus: These were computed by dividing an index of manufacturing output by capacity output for each country and multiplying the result by 100. Data used for these calculations correspond to data found in Artus and Turner (1978). (That is, revisions made in output data subsequent to the time that Artus and Turner performed their calculations were disregarded for the purpose of deriving the Artus capacity utilization rate. To the extent that such revisions have been made, the Artus capacity output data found in Artus and Turner (1978) differ from the Artus capacity output data presented in this paper.) United States: BEA—Data Resources, Inc.; FRB—IMF Data Fund; MGH—Economics Department, McGraw-Hill Book Company, New York City; WEFA; Japan, the Federal Republic of Germany, the United Kingdom, Italy, and Sweden: from each country’s central bank. Exceptions are BDI—see footnote 17—and the Panić measure (obtained from Panić (1978)). Netherlands: Centraal Bureau voor de Statistiek. Canada: STATCAN—Statistics Canada Daily (May 18, 1979); DITC (1979). France: INSEE—Tendances de la Conjuncture, item (3.1.6), various issues.

(iii) Capacity output data. In all cases, these were derived using the “implicit capacity” method, as described for the United States in footnote 95.

(iv) Base years for production indices are as follows: United States—ACTUALQ = 100 in 1967; Canada and the United Kingdom—ACTUALQ = 100 in 1975; Italy, the Netherlands, and the Federal Republic of Germany—ACTUALQ = 100 in 1970; and Japan—ACTUALQ = 100 in 1971. Capacity indices are to be interpreted as capacity output in percentage of actual output in the base year for the corresponding country’s output index. That is, if output were at capacity in the base year, then the capacity index would be 100 in that year. (For an algebraic demonstration of this, see footnote 95.)

92

Since all data exhibit high cyclical variability relative to trend, apparent tendencies in the trend must be interpreted with caution.

93

The correlation matrix for the period 1968–78 is

article image

For the period 1955–78, it is

article image

94

For the period 1968-78: Var (BEA) = 5.97, Var (FRB) = 19.49, Var (WEFA) = 16.38, Var (MGH) = 18.12

For the period 1955–78; Var (FRB) = 20.28, Var (WEFA) = 34.86, Var (MGH) = 20.47

95

“Implicit capacity” is the FRB index of manufacturing output divided by capacity utilization. The result is an index of capacity relative to base-year actual output. This can be seen as follows. Write the FRB index of industrial production as ACTUALQt = 100 × (Yt/Yb), where Yt is actual output in year t and Yb is actual output in the base year. (Yt and Yb are not observed separately.) As before, capacity utilization is defined as CUt = (Yt/ Ytc) × 100, where Ytc is capacity output at time t. The implicit capacity is (ACTUALQt/CUt) × 100 = (Ytc/Yb) × 100, as was asserted.

96

Each variable, call it xt, was replaced by xt = xt - exp (3.93) × exp (0.04t) and t is a time trend, t = 1, 2, 3, …. The coefficients of the trend term were obtained by fitting an exponential growth curve to the production data. The consequence of using this method of transforming the data is that only ACTUALQt has a mean of zero.

97

The method of adjustment was based on regressions identical to those presented in Perry (1973, p. 711). That is, letting Ct Qt, and Kt represent implicit capacity, output, and the capital stock, respectively, the following regression equation was specified: (Ct = (Ytc) × 100, Qt = (Yt/Yb) × 100, where Ytc, Yb, Yt were defined in footnote 95).

log Ct = a + b log Qt + c log Kt

The calculated ordinary least-squares regression estimates were as follows:

article image

(Numbers in brackets are t-statistics.) The adjusted series—BEAADJ and MGHADJ—were then calculated as follows:
BEAADJt=exp(0.51)×Q¯t0.48Kt0.56
MGHADJt=exp(0.86)×Q¯t0.30×Kt0.77

where Q¯t is the trend component in Qt, and was discussed in footnote 96.

98

This is higher than Perry (1973, p. 711) reports. He estimates that an increase of 1 per cent in output induces MGH survey respondents to report an increase of 0.23 per cent in their capacity. Re-estimation of the equation in footnote 97, using Perry’s sample period (1954-72), leaves the results reported in this paper unchanged. Thus, the differences in results are probably due to data revisions and to use of a different capital stock series, rather than to an increase in the cyclical bias of MGH. (Perry states (1973, p. 711) that his capital stock data were “provided by the Federal Reserve System.” Capital stock data used for the computations reported here were provided by WEFA.)

99

Var (BEA) = 5.97 and Var (BEAADJ) = 23.17.

100

The difference in scale of Charts 3 and 5 should be taken into account in comparing the two; this note of caution also applies to comparisons of Charts 4 and 6.

101

These are not of great concern, since they can be explained in terms of differences in data construction and underlying concepts.

102

For the period 1966–77, Var (Artus) = 18.6 and Var (INSEE) = 73.4.

103

Implicit capacity is not graphed for these two countries, since capacity output can be computed only for the Artus measure, and the purpose of the charts is comparison.

104

Another approach to the question of the consistency of these measures was discussed in the section, Relationship between Type #1 and Type #2 surveys. For Sweden (1968–77), correlation (Artus, SBTS) = 0.93. For France (1966–77), correlation (Artus, INSEE) = 0.81.

105

The reader must be cautious in making interchart comparisons because of differences in scale. However, this is not true for Charts 7 and 8, where there is a shift in the origin but not in the scale.

106

In relating this to the results by Ruist and Söderström (1975), one can note the following points: Their results apply to the population of respondents generally and do not exclude the possibility that a sufficiently large minority employs the strict definition of capacity to explain (a part of) the difference between INSEE and SBTS data.

107

For the period 1961–77, Var (CBI) = 101.1, Var (Artus) = 18.4, Var (Panić) = 12.8.

108

Correlation matrix 1961–77:

article image

109

This is due at least partially to the loss of 2.6 per cent in capacity output, estimated by Artus and Turner (1978, p. 5) to have occurred annually beginning in 1974 owing to the rise in oil prices. The loss corresponds to d = −0.026 in equation (1). (The value of d is a constant for all countries.) The “oil price dummy variable” does not explain the deceleration in capacity growth in 1973.

110

This does not agree with the rate of growth in capacity output reported in Artus and Turner (1978, p. 19, Table 10). For the reason for this, see footnote 91, paragraph (ii).

111

Since capacity output using Artus’s approach is a function of capital and employment, developments in the latter might explain the discrepancy in Artus’s and Panić’s estimates of capacity output. Panić’s method does not take account of employment and is closer to the narrow interpretation of capacity utilization.

Another difference between the Artus and Panić methods lies in the way estimates of the capital stock are constructed. For Panić, current investment (net of discards) is assumed to contribute immediately toward an increase in the stock of capital. (See Panić (1978).) For Artus (1977, p. 24), investment contributes to capital growth with a lag. These differences would explain a sudden burst in capacity indicated by the Panić measure being followed by a smooth, delayed rise in the Artus measure of capacity. However, they cannot explain the behavior of the two measures over the period 1974–75. The Artus measure indicates the burst in capacity growth in 1974–75, while the Panić measure exhibits no change in growth rate relative to its trend during the period 1971–77.

112

The differences are not so great that sampling error cannot be ruled out as an explanation.

113

See the sections, Surveys show more unused capacity and Surveys show less amplitude in capacity utilization.

114

The other trend through peaks measure of utilization, that of WEFA, also has a lower mean than the corresponding Artus measure. (See Chart 1.)

115

The MITI utilization rate is, in fact, published as an index, with 1975 = 100. The entire data series was multiplied by 0.73 prior to being graphed. According to Nihon Keizai Shimbun (April 7, 1979), this was the manufacturing rate of capacity utilization in 1975.

116

For the period 1968–77, Var (Artus) = 118.6, Var (MITI) = 72.3, and correlation (Artus, MITI) = 0.98. These figures apply to the utilization rates in Chart 13.

117

In the first period, this may be due to sampling error; this is less likely for the second period.

118

Correlation matrix for 1962–77 is as follows:

article image

119

For the period 1962–77, Var (DIW) = 14.7, Var (IFO) = 14.2, and Var (Artus) = 20.1.

120

While agreement was found in annual trends, there may well be differences in quarterly movements.

121

Of course, sampling error or measurement error in the data used cannot be ruled out as an explanation of the discrepancies.

122

It can be said that—in contrast to other measures of U.S. capacity utilization—WEFA’s rising trend correctly forecasts the inflation of the 1970s, implying that it is not WEFA but the other U.S. measures that are doubtful. The reader can verify that the discrepancies are not easily explained in terms of differences in data construction.

123

An exception, noted earlier, is the IFO measure, which exhibits little procyclical bias. (See Chart 20.) In spite of their bias in measuring changes in the “true” rate of capacity utilization, survey measures may nevertheless be useful as indicators of the perceptions of businesses.

124

For a discussion of this and other reasons why survey-based measures exhibit lower utilization rates than do the data-based measures, see the section, Surveys show less amplitude in capacity utilization.

125

This method of choosing between several statistical measures when there are no compelling theoretical criteria by which to do so is not uncommon. An example is the approach taken by Brillembourg (1977). There, he chooses from alternative measures of a country’s relative price index the one with the greatest explanatory power in the context of the purchasing power parity theory of exchange rates.

126

Sometimes differences in capacity utilization levels are disregarded completely by dividing the data by average capacity utilization over the period studied.

IMF Staff papers: Volume 28 No. 1
Author: International Monetary Fund. Research Dept.