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The model detailed in the previous section is estimated using data for 35 two-digit industries of the US economy during the period 1947 to 1991. The data set used in our 1996 report was constructed by Jorgenson, Gollop and Fraumeni (1987) for the period 1950-1989. The industry coverage, given in Table A in Appendix 1, is derived from a detailed 80 industry classification that Jorgenson, Gollop and Fraumeni carefully aggregated into 35 larger categories.9 The data set contains the value of gross output and the costs of labor, capital services and intermediate inputs, as well as their price indices, for all industries.10

To extend the data to 1991, the authors reorganized the basic data set taking account of revisions in national income accounts, reclassification of industries and various other adjustments. We compared the old and new data sets for the period 1950-1989 and found that indeed the new data were different in particular industries and over a certain period.11 In Table 3 we present the average ratio of the new revised data and the data sets used in our 1996 study for the period 1950-89. It is clear there are considerable variations and changes in all the relevant variables in a number of industries. The figures in Table 3 are averages of data over a long period and do not indicate the trend and fluctuations in the ratios of the two data sets over time for different industries. Closer examination of the data indicates that these ratios fluctuate and the trends differ considerably across industries. Therefore, the estimates of the model presented in the 1996 report and the results represented in this report may not be directly comparable because of the changes and revisions of the data. However, the general findings of the two studies are quite similar.

The data set we use comes from three sources. One part of the data is provided by Professor Jorgenson, the second part is data on highway and other infrastructure capital, and the third part are aggregate series. A brief description of the data set is in order. Labor and capital inputs have been adjusted for quality changes and the data for materials (or intermediate inputs) are constructed by subtracting value added from gross output. The primary sources of data for public capital are from Jack Faucett Associates and the Bureau of Labor Statistics (BLS). Investment series for each industry are constructed from the Annual Survey of Manufactures, the Census of Manufactures, and from various issues of The Survey of Current Business. Data for labor input have been obtained from NIPA and from Census of Population and Current Population Survey. Data on gross output are from Jack Faucett Associates, the BLS and the Bureau of Economic Analysis (BEA).

The labor input data have been adjusted as follows. Jorgenson and Fraumeni divide labor input into hours worked and average labor quality. NIPA provides hours worked by industry. Household survey data are used to disaggregate total hours into hours worked by different types of workers classified by demographic variables such as sex, age, and education. Assuming that workers are paid proportionately to the value of their marginal products, Jorgenson and Fraumeni calculate labor input as a weighted sum of hours worked by different types of workers, weighted by relative wage rates. Annual growth in the labor input for the economy as a whole from 1947-1985 averaged 1.81 percent; hours grew an average 1.18 percent per year; and labor quality increased an average of 0.63 percent.

Jorgenson and Fraumeni also adjust capital input stocks by their relative efficiencies in order to account for quality changes. In order to perform this quality adjustment, the rental sales of various types of capital are needed. Because the rental price is not directly observable, they obtain total payments to capital as property compensation, a residual after all other inputs have been paid (see Fernald (1992)). Using this data, they derive the implied rental rates for each type of capital based on knowledge of this stock and the depreciation rates for each type, and tax parameters such as the corporate income tax and investment tax credits.

The construction of data on intermediate inputs of energy and materials by industry is difficult. The problems arise from the low quality of the underlying data. Intermediate inputs into any one sector include inputs from other sectors. To obtain the proper measure of intermediate inputs, the disaggregated intermediate inputs must be weighted by their marginal products in order to calculate the composite intermediate input. This requires consistent annual input-output tables in current and constant prices that are not available. The Bureau of Economic Analysis (BEA) compiles comprehensive input-output tables only about every five years. The most recent provides data for 1987. Jorgenson and Fraumeni, adjust the data for these benchmark years to make them consistent over time and then they aggregate them to the 35-industry level. The benchmarks are then connected into shares of industry output and the shares are then interpolated from benchmark to benchmark. This gives an estimated input-output table for each year which in turn allows creation of an appropriate price deflator for nominal payments to intermediate factors in each year.

Data on net highway capital stock are from Apogee Research, Inc., and are based on Federal Highway Administration expenditure data from 1921 to 1990. Total net highway capital is constructed using the perpetual inventory method with economic decay and an efficiency factor equal to 0.9.12 Capital expenditures are distributed as follows: 52 percent to paving, 26.5 percent to grading, and 21.5 percent to structures. The average lives of paving, grading, and structures are assumed to be 14, 80, and 50 years, respectively. After an initial decline between 1950 and 1951, the growth rate of highway capital surged, growing at an average rate of 6.2 percent during 1952-1959. From 1960, the growth rate declined continuously until 1979. It grew very little during 1979-1981. Since 1982, the highway capital stock has been growing at an average rate of 1.2 percent per annum.

To construct the aggregate infrastructure capital stock, we use annual data on fixed nonresidential government net capital stock (federal, state and local) obtained from the BEA. The total net government physical capital stock is measured as the sum of federal, state, and local net capital stock of structures and equipment, excluding military capital, at constant 1982 prices.13 The acquisition price of capital is constructed as a Tornqvist index from the government's gross investment series on structures and equipment, also obtained from the BEA. The series for the other infrastructure capital stock is derived as the difference between the aggregate infrastructure capital stock and the highway capital stock series.

We present certain selective descriptive statistics on the cost and prices of the 35 industries in our data. In Table 4, we provide the average levels and average growth rates of costs, output, prices of inputs and cost shares for the period 1950-1991 for the two-digit industries and various sectors of the economy. The growth rates of highway capital Mathematical Formula, gross national product Mathematical Formula, population Mathematical Formula, and the GNP price deflator Mathematical Formula are also listed in this table.

As is clear from the descriptive statistics, the size of the industries, measured by total cost or total output, varies considerably. Food and kindred products, construction, transportation and warehousing, trade, finance and particularly other services which includes water supply, hotels, business services, health, social services, and agriculture are among the largest sectors in the economy. Other industries such as mining, tobacco, furniture and fixtures, and leather and leather products are relatively small.

In addition, factor cost shares vary considerably among the 35 industries. For example, labor's share ranges from a low of about 0.065 in petroleum refining (16)14 to a high of 0.53 in trade (32). Capital's share of total cost also varies considerably across industries, ranging from 0.046 in Apparel and other Textile Products (10) to 0.438 in Crude Petroleum and Natural Gas (4). Generally, capital's share of total cost, with a few exceptions, is less than labor's share. Material inputs on the other hand, have the largest share in total cost in almost all sectors and industries, ranging from 0.87 in Petroleum Refining (16) to 0.30 in Other Transportation Equipment (25).

The rates of growth of output Mathematical Formula and inputs Mathematical Formula shown in Table 4 also vary among industries over the period 1950-1991. In Leather and Leather Products (18) the growth of output was negative, while in Tobacco and Tobacco Products (8) and Primary Metals (20) output grew less than 1%. A number of industries experienced output growth rates ranging between 1% to over 2%. Some industries in manufacturing and service sectors experienced impressive gains in output; the growth rates for these industries ranged from approximately 3.4% in Paper and Allied Product (13) to about 0.6% in Other Services (34). The diversity in the growth pattern of output and factors of production across industries suggests that different industries have experienced different degrees of change in their input mix and output and productivity growth. Similar patterns of negative, small and rapid growth rates are visible in the growth rates of labor, capital and materials. The growth rates of output price Mathematical Formula and input prices Mathematical Formula with few exceptions were generally positive but varied considerably across industries. The growth rate of total highway capital, real GNP, and population growth are shown at the bottom of Table 1. Highway capital grew at an average of 3.4%, GNP's growth rate was 3.3% and that of the population almost 1.3% in the period 1950-1991.

The substantial diversity in the size of output and structure of costs among the industries over the period 1950-1991 provide a rich body of data to test econometrically the impact of different policies and variables on growth of output and productivity. The diversity pattern noted here would certainly imply that the response of various industries to changes in variables such as highway capital, other infrastructure capital, real GNP and population growth are likely to be very diverse. Therefore, we would expect the estimated elasticities, marginal benefits of highway capital and TFP growth rates calculated for different industries using the parameter estimates of our econometric model will vary considerably across industries which in turn will affect the results for the aggregate economy.

Chapter 4 | Chapter 6

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