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The Measurement of Inputs The previous chapter discussed ways to improve the measurement of output. The next task is to identify and measure the factors that explain changes in output: these factors include both tangible and intangible inputs. This chapter examines three types of tangible inputs: labor, physical capital including land, and intermediate inputs, and also includes a brief final section on combining these factors to construct measures of multi-factor productivity. Intangible inputs, which include such factors as technology and economies of scale and which are generally harder to measure, are discussed in the next chapter. LABOR The input of labor into a production process is usually measured in hours of all people engaged in production. These labor-hours can be considered to be a homogeneous input and simply added together, or they can be differentiated and weighted according to some index of labor composition or type. UNWEIGHTED LABOR INPUT Unweighted labor input is usually obtained by multiplying together the number of workers engaged in production and average hours per worker. Where no adequate hours data are available, the number of workers alone can be used to measure labor input. For example, international compari 122

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The Measurement of Inputs 123 sons of productivity in coal mining are often made in tons per worker- shift, with no adjustment for possible differences between countries in the length of shifts. The usual method of obtaining unweighted labor input (combining hours per worker and numbers of workers by multiplying them together) implicitly assumes that output is unaffected by the proportions in which hours and numbers of workers are combined. It assumes that two workers each working 70 hours per week make the same contribution to output as four workers each working 35 hours per week. In both cases the input is simply 140 labor-hours. This assumption is not necessarily correct, especially for extreme cases like the example just given. If fatigue or boredom reduces the intensity of work effort as hours per day or per week exceed some customary level, then two patterns of labor input with equal aggregate hours need not make an equal contribution to output. For this reason, Denison in his analysis of the sources of economic growth introduces an explicit offset to the reduction of labor input represented by a shortening of the average workweek. The offset is based on an estimate of increased efficiency per hour as the workweek is decreased. It is also possible that very short workdays contribute less per hour to output than somewhat longer ones, because of the time lost in starting up and ending the workday. Such an effect is suggested by the fact that part-time workers are sometimes paid less per hour than full-time workers doing otherwise similar work. Despite these possibilities, we proceed on the usual assumption that labor input can be adequately measured by multiplying numbers of workers and average hours. Number of Workers The employment component of present official productivity measures is probably the best measured major component. Employment data come largely from the current employment statistics (CES) program of monthly establishment reports, adjusted to benchmarks from unemployment insurance buts data as these become available. Current Population Survey (cPs) household data are used to measure both employment and hours for the parts of the economy for which establishment statistics are not available. Both establishment and household employment measures, as well as the corresponding hours measures, refer to one week of the month.2 The output measures that form the numerator of productivity ratios generally refer to the whole month. This discrepancy in reference periods can be a source of error in productivity measures if, for example, a major strike or

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124 REPORT OF THE PANEL unusually bad weather occurs during part of a month. Low output and employment concentrated in the employment reference week bias the productivity ratio upward; low output and employment concentrated in the rest of the month bias the productivity ratio downward. This source of error could be corrected by measuring employment and hours in each week, but the costs of doing so would be high and would probably not be justified by the modest benefits involved. There are areas in which the CES program could be substantially improved by enlarging the sample of reporting establishments, particularly in industries with many small establishments and high establishment turnover. This issue falls within the charge of the National Commission on Employment and Unemployment Statistics and so the Panel did not examine it. Hours The hours component of present official measures of productivity, as noted in Chapter 4, is based largely on current data on the paid hours of production and nonsupervisory workers as collected in the CES program. For hours, unlike employment, the accuracy of CES data is not checked against a benchmark. Hours of nonproduction workers in manufacturing and mining and of supervisory workers elsewhere are estimated by various assumptions. Two aspects of the present procedure are unsatisfactory. These are the absence of any direct data on hours for an important and growing portion of the work force and the inclusion of paid leave in the measure of labor input. In 1977, there were 66,945,000 employees on private nonagricultural payrolls, of whom 54,930,000 were production or nonsupervisory workers. This leaves 12,015,000 employees, or 17.9 percent of the total, not covered by current hours data. For 1947, the portion not covered (nonproduction or supervisory employees) was only 12.7 percent of the total. For manufacturing and mining, the ratios of nonproduction workers to all employees are higher than those for all private nonagricultural employment. In 1947, there were 2,639,000 nonproduction workers in mining and manufacturing, or 16.0 percent of total employment; by 1977, the number of nonproduction workers had risen to 5,699,000 or 28.0 percent of total employment. Thus we lack a direct measure of hours for more than one employee in every four in these important industries. Although the Panel believes that it is important to collect direct data on the hours of nonproduction workers, it is not necessary to collect them as frequently as for production workers. The hours of nonproduction workers

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The Measurement of Inputs 125 do not fluctuate from month to month in response to changes in demand as much as the hours of production workers do. It would seem to be sufficient to have an annual supplement to the CES, requesting data- on the actual hours of nonproduction workers for one month of the year or on the regularly scheduled or usual hours of such workers. This would not place a substantial reporting burden on employers, most of whom are required by the Fair Labor Standards Act to keep hours records for all nonexempt employees. Recommendation 7. The Panel recommends that the Bureau of Labor Statistics develop an annual supplement to the current employment statistics (CES) program requesting data on the actual hours of nonproduction and supervisory workers. The second unsatisfactory aspect of current hours data is the use of hours paid for rather than hours spent at the workplace. The difference between the two concepts is leave time paid for directly by employers; this consists primarily of vacations, holidays, and paid sick leave. Hours of paid leave are not direct inputs into the production process and conceptually should not be included in computing a productivity measure. Data from the Survey of Employer Expenditures for Employee Compensa- tion, shown in Table 6-1, indicate that hours at the workplace have been gradually declining as a percentage of hours paid for. The change is small in any one year, but cumulated over many years it could produce a substantial bias in productivity measures. Recommendation 8. The Panel concurs with the recommendation of a 1976 BES task force that recommended that a separate annual survey of hours at the workplace be administered to a subsample of the establishments currently responding to the CES. In principle, hours spent at the workplace but not actually at work (for example, coffee breaks) are also not direct inputs into the production process. Data on hours actually at work as a percentage of hours spent at the workplace have been collected by the Survey Research Center of the University of Michigan for 1965-1966 and 1974-1976 from a small sample of time records kept by workers. The data for married men show that in the 1965-1966 period the ratio of hours actually worked to hours at the workplace was 0.944, and in the 1974-1976 period it was 0.921. For married women the corresponding ratios were 0.926 and 0.854 (Stafford and Duncan 1977~. If this decline in the ratio of hours actually worked to hours at the

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126 REPORT OF THE PANEL TABLE 6-1 Hours at the Workplace as a Percentage of Hours Paid for, Private Nonfarm Economy, 1966-1974 1966 1968 1970 1972 1974 All Industries 94 93.8 93.4 93.4 92.8 Office 93 92.1 91.8 91.6 91.2 Non-office 95 94.7 94.3 94.4 93.7 Manufacturing 93 92.7 92.0 92.1 91.4 Office 92 91.1 90.6 90.6 90.2 Non-office 94 93.3 92.5 92.7 91.9 Nonmanufactunng 95 94.5 94.2 94.0 93.5 Office 93 92.6 92.3 91.9 91.5 Non-office 96 95.7 95.5 95.4 95.0 SOURCE: Bureau of Labor Statistics, Survey of Employer Expenditures for Employee Compensation (EEC Survey). For a description of this survey, see "Report of the BLS Task Force on Hours Worked," March 1976, and U.S. Department of Labor, Bureau of Labor Statistics (1975) BLS Handbook. Chapter 24.Washington, D.C.: U.S. Department of Commerce. workplace is representative of workers generally, it represents another source of downward bias in measured productivity growth. It would be difficult and costly, however, to collect data regularly on hours actually worked based on a large sample of workers. The Panel believes that this is a fruitful subject for private research but does not recommend any attempt at this time to incorporate the concept of time actually worked into official productivity measures. WEIGHTED LABOR INPUT Measures of labor input in which hours of different kinds of labor are added together without any differentiation of the kind of labor being furnished, or the occupations in which it is used, are used in most official measures of productivity. Many private researchers, on the other hand, have weighted labor inputs in various ways to reflect differences in kinds of labor. The case for the use of weighted rather than unweighted labor input data in productivity measurement can be made in several ways. First, it can be argued that different kinds of labor are often distinctly different inputs into a production process. For example, in many production processes, capital is a substitute for unskilled labor, and skilled labor is a complement to capital and therefore itself a substitute for unskilled labor (Rosen 1968~. This line of reasoning suggests the use of occupations as the kinds of labor to be weighted.

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The Measurement of Inputs 127 Second, it can be argued that even when two kinds of labor are complements, the more skilled labor represents a larger number of input units per hour of work. This line of reasoning suggests the use of weights based on some skill-related dimension of labor input, such as years of schooling, formal on-thejob training, or years of experience (for an example involving journeymen and apprentices, see Chapter 2~. When one measures multi-factor productivity, the capital input is automatically weighted in the sense in which we are using this term here. This must be so because there is no common physical unit, such as machine hours, in which capital inputs of various kinds can be measured. The components of measures of capital stock are therefore always combined with value weights, and this weighting carries over into measures of the flows of services that capital provides. This observation suggests a third reason for the weighting of labor inputs in measures of multi-factor productivity, namely, that there will then be greater conceptu- al consistency between the measures of labor and capital inputs. A final reason for the use of weighted labor input is that in some cases a measure based on weighted labor input is appropriate to compare to a measure of wage change. When the mix of types of labor used is changing, an unweighted productivity measure can overstate or understate the rise in the wage of each type of labor that is consistent with constant unit labor cost (see Chapter 24. Although most private productivity researchers use weighted measures of labor input, there has been great variation in the particular kinds of weights selected by different investigators; a review of these weighting schemes is provided in Kunze (in this volume). Whatever scheme is chosen for weighting labor input, the weights used are generally based on the wages or earnings of the kinds of workers distinguished in the weighting scheme. Thus if one decided to weight by educational attainment, the weights would be derived from data on differences in wages or earnings between individuals with different numbers of years of school completed. The rationale for this choice is that in a competitive labor market, wage differences reflect differences in marginal productivity, that is, differences in the value of the contribution to production of the different types of labor. In some cases, however, differences in wages between kinds of labor may not represent differences in marginal productivity that would exist in a perfectly competitive labor market, but may reflect instead imperfections in the labor market. The clearest such cases are differences in wages by race and sex, part of which reflect labor market discrimination. If wage differences reflect a mixture of differential productivity and other unrelated factors, it becomes harder to decide whether their use in weighting labor

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128 REPORT OF THE PANEL input is appropriate. Sex has frequently been used as a weighting factor, while the use of race has generally been avoided. If it is decided to use a weighted measure of labor input, the level of detail in the weighting scheme becomes important. The finer the categories used, the heavier the burden placed on the underlying data sources to provide accurate wage or hourly earnings data for use as weights. The largest differences in earnings can often be seen between fairly broad categories; this suggests diminishing returns to increasing levels of detail in the weighting scheme. Given the lack of consensus among productivity researchers on which of several possible schemes for weighting labor input is best suited to productivity statistics, the Panel does not recommend the use of any particular scheme at this time. Recommendation 9. The Panel recommends that the Bureau of Labor Statistics devote more resources to studying the use of weighted labor input measures. The purpose of this effort would be the preparation of one or more weighted measures of labor input for broad aggregates of economic activity, such as the private business sector. Such weighted labor input measures could be used alone and could. also be used in combination with measures of capital input to measure changes in multi-factor productivity. Both of these measures could help in explaining the changes in the single-factor unweighted measure of labor productivity. Such weighted productivity measures should be considered as comple- ments to, rather than replacements for, the unweighted measures now published. It should be noted that BES has a comparative advantage over private investigators in making estimates of weighted labor inputs since most of the data used for weighting are from BES sources. The preparation of such estimates by a government agency will also have the advantage of converting them from an intermittent effort to a continuous program. PHYSICAL CAPITAL The concept of physical capital input is analogous to that of labor, which is sometimes called human capital. Both represent a time rate of use (or availability for use) in production of the various types of labor and capital, which can be aggregated by weighting each type by its base-period compensation per hour or other time unit. Thus, as pointed out in the

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The Measurement of Inputs 129 previous section, labor input may be measured by combining the hours worked by different categories of workers, weighting each kind by its base- period average hourly compensation. For physical capital it is conceptually possible to combine the machine- hours, plant-hours, etc., weighting each kind of capital by its base-period average hourly compensation (its rental price). In practice, however, this is not how capital input is measured. For labor we have the common denominator of the worker, and we can group workers by occupational or industrial attachment or other categories related to differences in pay and, presumably, in productivity. We can multiply the number of workers by average hours worked to obtain the flow of services. This service flow, in turn, can be multiplied by base-period average hourly compensation to obtain labor input at base-period efficiency (that is, labor productivity)- the share of output obtained (and presumably contributed) by labor. For tangible capital, however, there is no simple physical common denomina- tor such as the worker. Instead, there is a wide variety of each of the major types of tangible capital-structures, machinery and equipment, invento- ries, and land or other natural resources. In addition, there are few markets in which the rental prices of the various types of equipment can be observed. For most capital, only the purchase price or cost at time of acquisition is observable. For capital goods sold in competitive markets, however, the purchase price represents both the cost of production, including a normal profit to the producer, and the present value of the estimated future income stream to the purchaser (under equilibrium conditions). Therefore, these purchase prices (as of a common base year) can be used to aggregate the various types of capital to get a measure of the real gross stock of capital. The common denominator for physical capital is thus the constant dollar or other monetary unit. In practice, the real capital stock is measured either by converting book values to base-period prices through deflation by an appropriate price index or by cumulating real investment and subtracting either retirements to obtain real gross stocks or real capital depreciation to obtain real net stocks. Real capital stock can be adjusted for changes in rates of utilization to reflect the actual flow of capital services (the question of whether or not this adjustment is desirable is discussed below). The adjusted real capital stock can then be multiplied by the base-period rate of return to obtain capital input at base-period efficiency (that is, capital productivity)-the share of output contributed by capital. This multiplication means that both labor and capital inputs are weighted by base-period average compensation so they add to total factor input in constant dollars. As noted in Chapter 3, since the weights reflect the base-period efficiency of the factors, changes in

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130 REPORT OF THE PANEL the ratio of output to real factor inputs measure changes in productive efficiency over time. An alternative approach to measuring inputs, which should give the same results as the approach just described, is to deflate factor compensa- tion by an appropriate index of the average price of the factor. Thus if total labor compensation is deflated by average hourly compensation, the quotient reflects the change in hours worked. Analogously, capital compensation may be deflated by an index of the average rental price of capital goods, and the quotient reflects changes in real capital hours used. Since rental price data for the many types of capital goods that are leased are not generally available, Jorgenson and others have constructed implicit rental price indexes (described below). But since the prices of capital goods and the rates of return on capital stocks are components of such constructed indexes, the problems of estimating capital stocks in current and constant prices are also encountered in this alternative approach. Before we describe the Jorgenson approach, therefore, we discuss the conceptual and statistical problems of measuring capital stocks. CONCEPTUAL PROBLEMS IN ESTIMATING REAL CAPITAL STOCKS There are several specific conceptual problems involved in estimating real capital stocks, to which alternative approaches have been suggested. The major problems are reviewed in this section. Throughout, the term "capital" relates to non-human capital. The Basic Units of Real Stocks of Capital Most estimates of real stocks of capital, gross of depreciation in the case of structures and equipment, seek in principle to approximate measures of the numbers of various types of physical capital goods in their own units (numbers of machines of specified types), combined by base-period price weights. This is true of the occasional estimates that have been prepared by Kuznets, Goldsmith, and Kendrick, and of the continuing estimates published by the Bureau of Economic Analysis (BEA). However, since physical unit data are available for relatively few types of reproducible capital goods, weighted aggregate estimates are generally obtained by directly deflating book values at acquisition prices, taking account of the age structure of the assets. They are also obtained by cumulating real investment estimates for depreciable assets, by type, over a period of years, with allowance for the retirements of capital goods reaching the end of their estimated economic lives in successive years. This is the so-called perpetual inventory method. Given ideal value and price data, deflated

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The Measurement of Inputs 31 values will give the same result as weighting quantities by base-period prices. In a sense, the constant dollar is the common denominator for real capital, as it is for diverse outputs and for diverse labor inputs. For capital, the constant dollar (or other monetary unit) represents the base-period prices of the own-units of the various types of capital goods, which reflect the present values of the expected future income streams and, for reproducible capital, base-period costs including the producer's profits. Changes over time in models or qualities of specific capital goods present problems. In most existing estimates, explicit or implicit adjust- ments are made to allow for the quality change associated with higher cost per unit of the new model at the time of changeover. Some economists have suggested going further and making quality adjustments based on the change in the output-producing capacity of the new model of the capital good (see Chapter 5~. However, Denison pointed out long ago that if capital is measured in terms of its output-producing capacity, the output/capital ratio becomes an uninteresting statistic, since it will tend to show no change between years of comparable rates of capacity utilization and no change in all years if the real capital stock is adjusted for changing utilization rates. It has also been suggested that the value of capital be deflated by a consumer price index in order to measure the real consumption foregone or by average hourly earnings to reflect real labor costs. But the usual approach is to measure real stocks of capital in terms of own-units rather than in terms of substitute variables, whether output-producing capacity, consumption foregone, or real resource costs reflecting productivity changes in capital goods industries (see Kendrick 1961b). Gross Versus Net Depreciable Stock Measures Estimates of the value of depreciable assets (structures and equipment) net of depreciation reflect the decline in value (depreciation) of fixed assets as they age. Assets depreciate primarily because of the shortening of their remaining economic lives as reflected in income-producing capacity, rather than a reduction of annual output-producing capacity, assuming adequate maintenance. The length of economic life of a capital good is usually determined less by physical decay than it is by technological changes that result in new models or types of the capital good, or in competing capital goods, which reduce the net income from the old item by lowering the price of its output. This eventually makes the old equipment obsolete. Creeping obsolescence may also make it optimal to spend less on maintenance, which hastens physical decay. Technological advances and

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132 REPORT OF THE PANEL obsolescence can occur suddenly and unexpectedly for particular goods, but they occur more gradually and predictably for broad categories of capital goods, so that it is possible to make reasonable estimates of average economic lives and mortality distributions. The estimates of average life are necessary for estimating both retirements and depreciation, although for the latter one must also approximate the time rate of depreciation (straight-line, declining balance, etc.~. When the net income-producing capacity of capital goods declines as they age, the shortening of their remaining economic lifetimes usually causes their present value (net stock) to decline even faster. For analysis of capital values and rates of return, the net stock estimates in current prices are clearly appropriate. But in real terms, the output-producing capacity of capital goods generally does not decline much as they age. Since productivity has to do with the relationship of output (not net income) to inputs, a considerable body of expert opinion favors basing measures of inputs of capital services on estimates of real gross stocks, or some variant of them, rather than on real net capital stocks. A variant form of real gross stock estimates may be desirable because the annual output-producing capacity of many types of depreciable assets probably declines somewhat with age because of increasing amounts of downtime for maintenance and repair. Some investigators adjust the real gross stocks of individual depreciable assets downward somewhat over their lifetimes to reflect this phenomenon. Denison (1974) and Gorman (1972), for example, weight real gross stocks two thirds and real net stocks one third to arrive at an adjusted real gross stock series for purposes of productivity estimation. Faucett (1974) has developed an efficiency-decline function for the same purpose. If such an adjustment is not made, the change in the age composition of depreciable assets becomes a variable of potential importance in explaining changes in the output/capital ratio. The issue of which real stock measures to use in productivity ratios is not settled. Some Panel members favor a gross-of-depreciation measure, possibly adjusted for efficiency decay, while others prefer a net-of- depreciation measure. In practice, real gross and net stocks show much the same trends in the U.S. business economy (see Table 6-2~. During recessions, the gross/net ratio tends to rise. Adjustments for Rates of Utilization A strict analogy of capital input to labor input (hours worked) suggests that the real gross stocks of capital should be adjusted to reflect rates of utilization so that the adjusted stocks would approximate the movements of "real capital hours" used. Jorgenson made an adjustment for utilization

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135 Treatment of Financial Assets When the balance sheets of all sectors of a national economy are consolidated, financial assets and liabilities of its residents cancel, and net worth (wealth) consists of tangible capital plus net claims on foreigners. If net income from abroad is included in output-and it is part of the GNP- then net foreign assets must be included in the associated inputs. These net assets represent a net claim of domestic residence on the productive assets of foreign economies. One approach to deflating net foreign claims in current dollars is to use the implicit price deflator for all domestic tangible capital stocks, on the basis that the opportunity cost of foreign investments is the domestic investment foregone. Similarly, for any individual domestic sector of industry, financial assets less liabilities represent a net claim (plus or minus) on the productive capital of other sectors or industries. It can be argued that deflated net financial assets should therefore be added to the real tangible capital stocks of each sector or industry. This would be appropriate if the output measure includes the income from these assets and not appropriate if the output measure is confined to income from the industry's own operations. In effect, then, the real capital stock becomes the real net worth of the sector or industry, gross of depreciation. An additional reason for this treatment is that, at the margin, financial assets may be substituted for physical assets, particularly inventory stocks. Treatment of Leased Capital Goods Firms and other organizations have always rented structures and the associated site land from others (usually the real estate industry), and equipment leases have become increasingly prevalent because of tax advantages. It would be possible to treat the rental payments, deflated by a rental price index, as a real intermediate expense. This treatment causes changes in the output/capital ratio because of changes in institutional practices concerning the purchase or lease of capital goods. An alternative procedure is to shift leased capital to the industry of use in order to obtain more meaningful output/capital ratios. If the real capital stock estimates are the basis for capital input estimates, the rental payments can be capitalized and the capital shifted from the lessor to the using industry Otherwise, the real rental payments can be shifted and added to the real cost (input) of the owned capital used in the several industries or sectors.

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136 ESTIMATING REAL CAPITAL INPUT REPORT OF THE PANEL As discussed earlier, factor compensation may be viewed as the product of quantities of factor services and their prices, the prices reflecting the value of the marginal products of the various types of services. To estimate real factor input, the quantities of services are multiplied by base-period factor prices. For labor, either labor-hours of various categories are multiplied by base-period average hourly compensation, or (what is approximately the same thing) index numbers of hours worked, by category, are weighted by the base-period proportions of labor compensation accounted for by each category (occupational or industry groupings). Analogously, index num- bers of real capital stocks (possibly adjusted for changes in rates of utilization) by significant categories may be weighted by base-period proportions of capital compensation in each category. The real capital indexes approximate the flow of capital services (machine-hours, etc.), while the capital compensation reflects the rental prices of the capital services. There are two major questions regarding real capital input: What are the significant categories of capital stocks and services that should be distinguished? How should the capital compensation (rental price) be measured? For the second question, a major issue is whether capital compensation should be measured gross or net of capital consumption allowances (chiefly depreciation). This is closely related to the question of whether GNP or net national product (NNP) is the preferable output measure. Denison argues that since capital consumption is not desired for its own sake, net capital compensation is the proper weight for capital input, irrespective of whether the real capital stock indicator of services provided is net or gross or some combination of the two. This is consistent with his view (see Chapter 5) that NNP is the appropriate measure of output, given the welfare-oriented definition of final product as consump- tion plus additions to stock (net investment). Jorgenson points out, on the other hand, that no deduction from labor compensation is made for depreciation of human capital, so for the sake of consistency, capital compensation should be measured gross. Jorgenson also emphasizes that differences in the ratio of gross to net flows of capital inputs from different assets mean that gross capital inputs are not proportional to capital stocks. For example, if one considers two assets of equal original cost, one with a useful life of 5 years and the other with a useful life of 10 years, the first must be expected to contribute more gross input per year for its costs to be recovered during its shorter life. Technically, the gross compensation of each factor is the actual cash flow from the factor services, and the estimates of depreciation deducted to

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The Measurement of Inputs 137 obtain the net are, at best, somewhat arbitrary or "stylized." Gross capital compensation is also a more stable variable through time than net capital compensation, for which the volatile profit return is relatively more important. It is interesting that the gross rate of return on gross stocks is generally quite close to the net rate of return on net stock because the ratio of current depreciation allowances to accumulated depreciation reserves does not differ greatly from the ratio of net income to net depreciable capital stocks in years of a high level of economic activity. But the use of gross rather than net capital compensation as a measure of the contribution of the capital input obviously assigns a significantly greater weight to capital input relative to labor input. It also makes it important to distinguish between depreciable and other tangible assets prior to weighting. Although Jorgenson and his associates use gross capital compensation (including property as well as income taxes) as a control total for estimating rental prices, they assume that the net after-tax rate of return is the same on all types of assets within given sectors or industries. For firms, one assumes that managers adjust the amount of investment in each type of asset to equalize marginal rates of return. For industries, even if rates of return to different types of assets differed somewhat, there are no data on that basis. The corporate after-tax rate of return on all assets is imputed to the assets of the noncorporate segment of each industry. Given the net rates of return, prices of assets, rates of replacement, and average tax rates in each industry, Jorgenson is able to determine the rental price of each type of asset by industry. The types of tangible assets he distinguishes are structures, equipment, land, and inventories. In a recent work, he uses 44 different industry groupings of assets (Gollop and Jorgenson 1980~. In distinguishing categories of capital, Jorgenson, like Kendrick and others, measures capital on an industry basis because rates of return differ among industries, even in years of a high level of activity. Presumably this reflects differing productivities of capital and entrepreneurship, although part of the differences in rates of return may be due to temporary disequilibria. The alternative of not weighting by industry, assuming that capital commands equal rates of return in all industries under equilibrium conditions, ignores the existence of differing degrees of risk and uncertain- ty among industries, which require different rates of return to investors. The use of industry weights also causes the aggregate capital input measures to reflect improvements in allocative efficiency. Gollop and Jorgenson compute capital input estimates for sectors by weighting proportionate changes in their indexes of real capital stocks by industry (cross-classified by asset class and legal form of organization) by the average share of each component in sectoral property compensation in

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138 REPORT OF THE PANEL successive pairs of years. Their sectoral indexes thus reflect changes in the composition of capital stock with respect to industry, legal form of organization, and type of asset. Sectoral capital "quality" rises if components with higher flows of capital input (rental price) per unit of capital stock are growing more rapidly. Although Gollop and Jorgenson describe such shift effects as quality change, they do not encompass changes in quality as represented by changes in the output-producing capacity of capital goods associated with innovation. Advances in applied knowledge still show up in the productivity residual. When the real capital input estimates are divided back into the gross capital compensation estimates in current prices, an implicit index of rental price emerges. This index reflects changes in the prices of tangible capital assets; changes in rates of returns on assets (which can be separated into the after-tax rate of return and the average income tax rate); changes in rate of replacement (capital consumption); and changes in the average rate of indirect taxation on property. In principle, the rental price indexes could be constructed to use as deflators for capital compensation, by category; however, the use of capital compensation as weights for the real capital service indexes, by categories, is the more direct procedure. STATISTICAL PROBLEMS For some years, the Bureau of Economic Analysis has prepared annual estimates of real gross and net stocks of structures, equipment, and inventories in current and constant prices for the U.S. private domestic business economy and the farm, manufacturing, and residual nonfarm nonmanufacturing sectors. The stock of residential structures has been estimated in the aggregate and with data permitting, a break between the rental and owner-occupied segments. The BEA iS gradually expanding its wealth estimates to cover all sectors and to provide more industrial detail for the business sector. It will be very useful analytically to have industry capital estimates that are consistent with sector tables. However, BEA does not prepare estimates of the flow of capital inputs from the estimated gross or net stocks. To estimate fixed capital stocks, BEA uses the perpetual inventory method pioneered by Raymond Goldsmith for wealth estimates. This method involves deflating outlays on fixed capital by as many types of capital as the data distinguish and then cumulating this constant-dollar gross investment and subtracting real capital consumption allowances to obtain real net stocks. The price deflators can then be used if desired to inflate the real stocks by type to current replacement costs. The quality of the real gross stock estimates thus depends on the

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The Measurement of Inputs 39 accuracy of the capital outlay estimates, the capital goods price deflators, and the estimates of the lengths of life of the various types of equipment and structures. The recommendations of the Gross National Product Data Improvement Project (Office of Federal Statistical Policy and Standards 1977) for improving the investment estimates and expanding and strengthening the price indexes for producers durable equipment and new construction are directly relevant for improvement of the capital estimates. In addition, current information on the economic lives of capital goods and their decline in efficiency with time would be desirable, not only to improve estimates of the capital stock but also to assist in estimating gross flows of capital inputs from stocks of assets of different kinds. Several studies have been made in the past by the Office of Tax Analysis and Office of Industrial Economics of the U.S. Department of the Treasury as background for the tax codes relating to depreciation allowances. The earth Inventory Planning Study (U.S. Congress, Joint Economic Committee 1974) recommended a special sample survey of discarded assets in the prior year by type of asset by age, which would update and supplement information from older studies. An alternative approach to estimating stocks of fixed capital is to revalue the book values of plant and equipment from original cost to constant and current prices. This method has been used by Kuznets, Creamer, and others (see, for example, Kuzuets 1961~. It involves estimating the age composition of assets by major type and then applying appropriate price indexes to each vintage to value it in the prices of the base or current year. The real stocks based on book values have generally shown much the same trends as those estimated by the perpetual inventory method. The balance sheet data should be more accurate, however, since they comprise assets actually on the books, and presumably firms write off capital goods that are prematurely retired but carry those that are used beyond their estimated economic lives. The Wealth Inventory Planning Study recommended that estimates based on the perpetual inventory approach be benchmarked to estimates developed from book-value data from the various economic censuses, IRS balance sheets, and reports of regulatory agencies. The study recommend- ed that, where necessary, the book-value data be obtained by major categories of equipment and structures, including certain functional groupings that cut across industry lines antipollution, power, construc- tion, transportation, and communications equipment. The study also recommended that the economic census program be expanded to cover several industrial areas that are not now included. In addition, the study recommended that for each major industrial grouping, small sample surveys be conducted to determine the composition of depreciable assets

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140 REPORT OF THE PANEL by type by age. This would obviously permit a more accurate revaluation of book values to constant prices, although rough age distributions can be made on the basis of investment series. Better capital goods price indexes would help in the revaluations of book values and also in the deflation of investment series used in the perpetual inventory approach. Although the Wealth Inventory Planning Study was carried out almost 15 years ago and considerable progress has been made since then, many of its detailed recommendations are still pertinent. They can still provide helpful guidance to the agencies concerned with improving data and estimates on capital. As noted in the report of the study, Measuring the Nation's Wealth, the central role of leadership and coordination must be provided by the Office of Federal Statistial Policy and Standards, now located in the U.S. Department of Commerce. As capital estimates are improved and expanded, it will be analytically useful to have regular official estimates of output/capital ratios to supplement the labor productivity ratios. This will make possible the quantification of savings of capital as well as of labor per unit of output, by industry. It will also make possible experimentation with estimates of multi-factor productivity (see below). Recommendation 10. The Panel recommends that the Census Bu- reau, in its quinquennial economic censuses and annual economic surveys, collect data on beginning and end-of-year inventories by method of valuation. The censuses and surveys should also provide fuller coverage and greater detail on capital outlays, book values of invested capital (gross and net of depreciation), and on depreciation allowances and retirements. The data should distinguish major types of equipment by major industry. The Panel also recommends that a sample survey of the age distribution of fixed assets, by type, and of retirements, by age, during the previous year be taken in order to keep current the retirement factors used in estimating capital stocks. Recommendation 11. The Panel recommends that government agen- cies make use of available estimates of real capital stocks to develop ratios of output per unit of capital in order to determine the savings that have been achieved over time in physical capital per unit of output. INTERMEDIATE INPUTS Intermediate inputs are purchases of goods and services by one firm or industry from another. Examples of intermediate goods are raw materials,

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The Measurement of Inputs 141 such as coal or iron ore used in making steel and wood pulp used in making paper, semifinished goods that require further fabrication, and fuel. Examples of intermediate services include purchased electricity, repair services to equipment, and purchased business services, such as those of lawyers and auditors. At the level of the individual industry, intermediate inputs are often a larger fraction of the value of output than are inputs of labor, capital, and land. That is, value added can be a small fraction of total output.3 Final output of the entire economy is produced by capital and labor inputs, combined through some technology and organization of produc- tion. (See Chapter 3 for a discussion of the factors of production for the whole economy and for portions of the economy.) But for firms and for aggregates of firms that are subsectors of the whole economy, there are three tangible factors of production the basic factors, labor and capital, and intermediate inputs.4 The two models that take all three factors into account for productivity analysis and measurement are the gross output model and the value-added model. The ways in which these models differ in their treatment of intermediate inputs, and the resulting differences in the proper interpreta- tion of productivity change, are discussed in Chapter 3. The important point here is that a measure of intermediate inputs is needed for both models. In the value-added model the value of intermediate inputs is subtracted from gross output to obtain the numerator of the productivity ratio. In the gross output model, intermediate inputs enter into the denominator of the productivity ratio as a separate input. The smaller the sector of the economy, the more important estimates of intermediate inputs are likely to be for productivity analysis. Industry productivity estimates can be of interest themselves or for tracing the ejects of price changes or other disequilibrating factors through the economy. For example, when the prices of some materials rise sharply, as occurred recently for wood and more dramatically for coal and oil, industries that use these materials substitute cheaper materials if possible or they cut down on their use by reducing waste (which often involves substituting capital or labor). The probable result of these economizing actions is that the ratio of the value of intermediate inputs to gross output changes or, alternatively, the ratio of net to gross output changes. A productivity ratio with gross output in the numerator and with labor and capital in the denominator is biased downward if the use of real intermediate inputs is falling relative to other inputs, and it is biased upward if their use is rising.5 In a study of the four industries that manufacture primary paper products, Myers and Nakamura (in this volume) made estimates of real

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142 REPORT OF THE PANEL intermediate inputs, including energy, and found that the ratio of net output to gross output fluctuated in the quinquennial censuses between 1958 and 1972. Their result is expected since these industries are intensive users of energy. Federal and state pollution regulations that influence the rate of installation of new capital goods also affect the choice among inputs in these industries. MEASUREMENT PROBLEMS Because intermediate inputs to one firm are the output of another firm, the problems in their measurement are conceptually the same as the problems of measuring output discussed in Chapter 5, but in practice there are special data and measurement problems. BEA iS the only agency that regularly makes estimates of real intermediate inputs for the nonfarm economy; it uses those estimates to compute annual real gross product originating in manufacturing and mining, in gas and electric utilities, and in railroads (that is, for about 34 percent of gross domestic product in 1977~.6 These estimates do not cover all intermediate inputs consumed in production (see below). BEA uses its estimates, because of their limited coverage, only to calculate an implicit deflator for the double deflation process, and not directly to estimate real value added. (For a discussion of double deflation, see Chapter 4.) The BEA estimates of real intermediate inputs are made at the level of the 85-order input-output table and are available upon request. More up- to-date annual input-output tables are prepared by the INFORUM project of the University of Maryland, under the direction of Clopper Almon. For the more detailed 4-digit industries, there are not yet estimates of intermediate inputs to complement the real gross output per hour measure published by BES and the Census Bureau.7 In the agencies' view, the data for making estimates of intermediate inputs are inadequate at present at this level of industry detail. The most complete source of information on intermediate inputs is the quinquennial economic censuses compiled by the Census Bureau. Estab- lishments are asked to report their consumption of materials and energy by detailed categories in physical units and current-dollar values, although for some portion of materials, such as those not classified by kind, the Census Bureau only reports the dollar value. No information is collected for services except for purchased electricity.

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The Measurement of Inputs CONCLUSIONS 143 It is unsatisfactory to know so little about the use of intermediate inputs. Without collecting further data, it is possible to construct estimates of real inputs of intermediate materials for 4-digit manufacturing and mining industries, and aggregates of these industries, as Myers and Nakamura (in this volume) demonstrate using Census Bureau data on current-dollar value of consumption of materials and unit-value relatives or BES producer price indexes. These estimates might be prepared by the Census Bureau in collaboration with the BEA. Recommendation 12. The Panel recommends that the Census Bureau in its periodic reports on real gross output for detailed industries based on successive quinquennial censuses, include estimates of the real amount of intermediate purchases of materials, including energy, for those detailed industry categories for which data are available. Improvement of benchmark estimates of intermediate inputs require that the Census Bureau expand its coverage of both inputs and industries. The Census Bureau has already taken steps for the 1977 economic censuses to expand its coverage of material inputs in manufacturing and mining for selected industries, but the lack of information on service inputs is a major gap in the data. The Census Bureau currently collects information on total purchased materials and supplies in several of the economic censuses construction, wholesale trade, retail trade, and selected services. At this time there is not enough detail in these censuses to permit reliable estimates of real value added, but as a beginning for more complete coverage, data on purchases of services should be collected for these industries as well as for manufacturing and mining. Recommendation 13. The Panel recommends that, in order to improve the quality of the annual measures of industry productivity, the Census Bureau augment the Annual Survey of Manufactures (and other annual surveys) to include subcategories of the materials input categories. Recommendation 14. The Panel endorses the recommendation of the GNP Data Improvement Project calling for the Census Bureau to collect, as an integral part of each economic census, data on the purchases of intermediate services as well as materials by establish- ments.

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144 REPORT OF THE PANEL Currently, the Census Bureau collects only a lump sum value for materials purchased, except for energy, for which it maintains its quinquennial breakdown. More detail on materials in the annual survey would permit more accurate annual estimates of real intermediate purchases for 4-digit and more aggregated industries. These annual estimates, which might be made by BEA, the Census Bureau, or private researchers, would give a clearer indication of what is happening in the economy as the result of changes in material prices or other changes between census years. There is nothing comparable to the Annual Survey of Manufactures (ASM) for the sectors covered by the other economic censuses, which do not collect data on detailed materials even quinquennially. Since manufac- turing is still a large part of the total economy, 24 percent in 1977, and since so many data are already collected for this sector, more annual detail for manufactures is potentially the most useful for productivity measure- ment and research. MULTI-FACTOR PRODUCTIVITY MEASURES By combining two or more measures of inputs (capital, labor, and intermediate purchases) by some appropriate weighting scheme and dividing this combined measure of inputs into a measure of output, one can obtain a measure of multi-factor productivity. Changes over time in this ratio show the savings in the use of inputs per unit of output that are brought about by technical change and other sources of productivity growth. Multi-factor productivity measures are useful in a number of ways. They help in understanding changes in output per unweighted labor-hour. If the growth rate in the multi-factor measure is less than that of the single-factor labor-hour measure, we know that some of the increase in the labor-hour measure is due to increases in the amount of other inputs per unweighted labor-hour. Multi-factor measures are also useful in monitor- ing and studying the sources of output growth other than those resulting from growth of inputs, including technical change, managerial innova- tions, and improved resource allocation. Changes in multi-factor produc- tivity measures are due entirely to these non-input sources. Recommendation 15. The Panel recommends that the Bureau of Labor Statistics experiment with combining labor and other inputs into alternative measures of multi-factor productivity.

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The Measurement of Inputs NOTES 145 1. It is not always clear in which category of inputs a particular factor belongs: for example, there are discussions of education both in this and the following chapter. 2. The employment concepts used in the establishment and household surveys are not identical. In the household survey each person is counted only once in the establishment and industry where he or she worked the most hours during the survey reference week. In the establishment survey, a worker with more than one job in the reference week will be counted once in each establishment in which he or she worked. 3. For estimates of changes in intermediate inputs by 2-digit industries, see Gollop and Jorgenson (1980~. 4. Note that there are no official productivity estimates for the entire U.S. economy. Even the BES measure for the private business sector excludes some portions of the economy, general government and not-for-profit institutions, from which the private business sector receives intermediate inputs. General government is the largest of the two omitted sectors, and perhaps the inputs of government services, especially if adjusted for quality, are important enough to consider. But public service inputs are more likely to be of interest at a subnational level, that is, for cities and regions where the quality of roads, water, and other locally provided public services may affect production. 5. A labor productivity ratio with gross output in the numerator would also be biased when the use of intermediate inputs is changing. 6. The U.S. Department of Agriculture estimates and publishes real interme- diate purchases as part of its multi-factor input measure for farms. The purchases are broken down into detailed categories of goods (fertilizer, seed, etc.) and services. 7. The BEA plans to begin deflation of materials at the 4-digit level in constructing gross product originating by major sector. These estimates may some day be available on request even if they are not published.