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:

where

• e = $\underset{n\to \infty }{\lim }{(1+\frac{1}{n})}^n$

• Y_t = actual output at time t

• K_t = capital stock at time t

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

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

• z_t = 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

• k_t,l_t = intensity of use of capital and labor, respectively, at time t

• u_t= 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 k_t and l_t, 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 l_t was introduced to take account of cyclical fluctuations in the intensity with which the actually employed labor force, L_t, is used, ¹² it is known that L_t 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,

where u_t is a random shock, U_t 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, U_ft, ¹⁴ into equation (2). That is, letting D be the set of values of t corresponding to cyclical peaks,

Values of $L_t^p$ for t ∉ D were computed by fitting log-linear trends between successive points $L_t^p,t\in D$. ¹⁵ Once a full series $L_t^p$ is obtained, this and the actual capital stock series, K_t, are substituted in equation (1), with l_t and k_t each equal to unity. The result is a complete capacity output series, $Y_t^c$. Capacity utilization is computed by taking $(Y_t/Y_t^c)\times 100$ 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 (Y_t/K_t), t = 1, …, T, where Y_t and K_t 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:

where a₀, a₁ and û_t 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 Y_t/K_t series, as depicted in Figure 1. The adjusted trend Y/K ratio—call it (Y_t/K_t)^c—is 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

SURVEY OF MEASURES OF CAPACITY UTILIZATION

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

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SURVEY OF MEASURES OF CAPACITY UTILIZATION

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

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SURVEY OF MEASURES OF CAPACITY UTILIZATION

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

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where

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

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

where observed K_t and L_t are assumed to be fully utilized for t ∈ D. The estimate of $\alpha \left(\hat{\alpha }\right)$ is taken as the geometric average of labor’s share for t ∈ D

where W_t is the hourly wage rate, T′ is the number of peak output points (e.g., the number of elements in D), and exp x ≡ e^x. Next, setting $Z_t=\log Y_t-(1-\hat{\alpha })K_t-\hat{\alpha }{L}_t,t\in D$, one chooses Ĉ, $\hat{r}$, and û_t for t ∈ D in

so that $\underset{t\in D}{\mathrm{\Sigma }}{\hat{u}}_t^2$ is minimized. Capacity output, $Y_t^c$ is then defined as

where $L_t^p$ t = 1, …, T is the L_t series adjusted for cyclical variation. Thus, peak values in Y_t, 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 l_t and k_t equal to unity at cyclical peaks and to zero otherwise, and then proceeding with the estimation. This treatment of l_t and k_t, 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

where L_t is labor in hours, measured in “efficiency units,” ³⁴ $Y_t^c$ is capacity output, and n and T are finite numbers. It is assumed that

(i) Computing potential labor, $L_t^p$. 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 $L_t^p$ proceeds by con-structing $L_{ti}^p$ where i = 1, …, 8, and corresponds to eight age-sex groups in the population. ³⁶ The term $L_{ti}^p$ is obtained from the following expression:

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 $L_{ti}^p$s according to equation (7), one first needs the ${\hat{l}}_{ti}$s and the Û_tis.

The basic cyclical variable used to adjust U_ti and l_ti is the unemployment rate for males aged 25–54 years; call it $U_t^m$ 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 X_ti ≡ log[l_ti/(1-l_ti)]³⁹ ${\hat{l}}_{ti}$ is found as follows. Coefficients for the following eight separate regressions are computed:

where Z_t is a collection of variables not of interest here. Given a set of estimates $\begin{array}{c}\{{\hat{a}}_i,{\hat{b}}_i,{\hat{c}}_i,{\hat{d}}_i\}\end{array}$ for i = 1, …, 8, the CEA simulates the preceding equations setting $U_t^m$ = 2.5 for all values of t, yielding a series called, say, $\begin{array}{c}{\hat{x}}_{ti}\end{array}$ for each i. That is,

Then, ${\hat{l}}_{ti}=\exp \left({\hat{X}}_{ti}\right)/[1+\exp \left({\hat{X}}_{ti}\right)]$ 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 ${{\hat{l}}^{\prime }}_{ti}={\hat{l}}_{ti}C{P}_{ti}/\left[{\mathrm{\Sigma }}_i{\hat{l}}_{ti}C{P}_{ti}\right]$ coefficients are estimated for the following eight separate regressions:

The benchmark series, Û_ti, is obtained for each i by setting $U_t^m$ 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 $\begin{array}{c}{\hat{x}}_{ti}\end{array}$.

Now that ${\hat{l}}_{ti}$ and Û_ti have been computed, the $L_{ti}^p$s are obtained by using equation (7). The $L_{ti}^p$s 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, $Y_t^c$. Clark and Luckett employ the following model for the evolution of labor productivity:

where u_t 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

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

Substituting equation (8) in the preceding equation yields

leaving an equation specified entirely in terms of observable variables.

Let ${\hat{b}}_s$, 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 d_t, i=0, …, m can be computed from ${\hat{b}}_s$, s = 0, …, n, so that

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 $L_t^p$, 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, $K_t^{*}$, as

where $Y_t^{*}$ and $P_t^{*}$ represent permanent income and relative output prices, respectively, at time t. (The model is specified for annual data.) The expressions $Y_t^{*}$ and $P_t^{*}$ are defined as

and

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

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

All coefficients in equation (14) are econometrically identified. If Y_t 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 $Y_t^c$, capacity output, by solving

for $Y_t^c$. 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:

where Δ is the first-difference operator, ⁴⁸ U_t is the rate of unemployment,⁴⁹ Y_t is real GNP, e_t 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 Y_t as a distributed lag on past values of ΔU_t

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

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 $a_i^{\prime }$, 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 $U_t^f$, t = –n, –(n–1), …, 0, 1, …, T, ⁵² substituting this for U_t 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

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, Q_t; data on the capital stock provided by the Bureau of Labor Statistics, K_t; ⁵⁹ and year-end estimates of capacity, C_t, and capacity utilization, CU_t, provided by MGH.

An initial, implicit estimate of capacity for each industry is found by taking $C_t^{\prime }$ = Q_t/CU_t. However, $C_t^{\prime }$ is implausibly irregular over time and also exhibits a procyclical bias. ⁶⁰ The series $C_t^{\prime }$ is smoothed by trending and by making use of K_t and C_t. This is done as follows.

Letting X_1t = ($C_t^{\prime }$/Q_t, the following regressions are estimated:

and

where t represents a time trend and u_t and e_t 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 $a_1^{\prime }=\exp \left({\hat{a}}_1\right),b_1^{\prime }=\exp \left({\hat{b}}_1\right)$, etc., one obtains

and

This gives the two smoothed estimates of capacity: ${\hat{X}}_{1t}$ × K_t, and ${\hat{X}}_{2t}$ × C_t. The final capacity estimate, $C_t^{*}$, for an industry is the arithmetic mean of the two

The annual FRB measure of capacity utilization for an industry, C$U_t^{*}$, is computed as follows: ⁶¹

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

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).