4.2.3Capital

Authors studying the productivity effects of IT have considered distinct definitions of total and IT capital. Total capital is here represented by fixed private nonresidential capital, equipment and structures. Capital can be measured as a stock or a flow of services (also called capital input) concept. Ideally, capital services are used in productivity studies involving production functions with capital and labor inputs. Jorgenson and Stiroh (1995) noticed that capital stock underestimates the growth of capital input because it ignores quality adjustments. However, data on capital services are not directly available at the state and industry level. Still, as noted by Norsworthy and Jang (1992), neoclassical theory assumes that “the quantity of capital services that each asset type contributes to capital input is proportional to the stock of that asset.” Thus, I will use data on capital stocks as a measure of capital input. Furthermore, Oliner and Sichel (2000) considered productive stocks instead of wealth stocks, arguing it is more appropriate to consider “how much computers and other assets produce each period” and not “tracking their market value.” Still, I have to consider wealth stocks because of data availability reasons.

Real 1992 values of capital stocks are available for the 52 industries nationally from the Bureau of Economic Analysis (1999a). BEA considers “net stock,” which means the perpetual inventory method and Tornqvist aggregations were applied to gross stocks of capital [detailed explanation in Norsworthy and Jang (1992)]. Capital stocks data are decomposed into 57 types of assets. This detailed description of assets allows the decomposition of total capital (K) into IT capital (KIT) and non-IT capital (KNIT). Table 4.4, a different version of Figure 2.1, shows the distribution of nonresidential equipment and structures. Variable KIT measures the stock of Information Processing Equipment (IPE), which is constituted of assets #1 to #11: mainframe computers, personal computers, direct access storage devices, computer printers, computer terminals, computer tape drives, computer storage devices, other office equipment, communication equipment, instruments and photocopy and related equipment. Note that BEA recently added the stock of software to this category, but it was not available when I constructed my dataset. Thus, the variable KIT might be underestimated. The variable KNIT is constituted of all other nonresidential equipments and structures containing assets #12 to #57 (Table 4.3).

Thus, data on aggregate industry variables K it, KIT it and KNIT it were obtained from BEA for all 52 industries (at the national level), for the years between 1977 and 1997 (in real 1992 dollars). Data for aggregate national variables K t ,KIT t and KNIT t were obtained by simple aggregation across industries for each year, according to the following definitions

K t ≅ Σi K it ; KIT t ≅ Σi KIT it ; KNIT t ≅ Σi KNIT it(4.20)

Data for the remaining state and state industries capital variables (K st, KIT st, KNIT st, K its, KIT its and KNIT its) are not directly available and had to be estimated. Next I describe the procedure used to estimate these variables.

Marcus (1964) discussed the capital to output and capital to labor ratios in 2-digit industries by states. For each 2-digit industry, he assumes: (1) all states use the same production function which is homogeneous of degree one and is well-behaved, that is, has convex isoquants; (2) labor, measured in manhours, is homogeneous; (3) similarly, capital (measured in net stock of fixed private nonresidential equipment and structure) represents homogenous physical inputs, and (4) value-added represents homogenous physical output. Then, productivity differences across states are mainly due to differences in states’ industry mixes. Based on these assumptions, Marcus noticed that the state 2-digit industry capital to output ratio (Kits / Yits) differs from the national 2-digit ratio (Kit / Yit) only through 3-digit weights. Assuming these weights are negligible (this hypothesis is tested next), I can then calculate the state industry variables using aggregate industry variables.

Thus, I need to test if the following hypothesis is true

Kit / Yit ≅ Kits / Yits (4.21)

This equation means that the capital to output ratios are equal across states within the same 2-digit industry and for the same year. For instance, if the capital to output ratio in the Food & kindred products industry is 2 at the aggregate national level in 1990, then this ratio is also 2 in the Food & kindred products industry at the aggregate state level in 1990, for any of the 51 states. To empirically test hypothesis 4.21, I had to find a proxy for Kits since it was the only variable in equation 4.21 for which I did not have data. I obtained capital stock data for the manufacturing industry (1-digit level) for the year 1992 from the U.S. Bureau of the Census (1994). Indeed, the Annual Census of Manufactures reports annually the “gross book value of depreciable assets, capital expenditures, retirements, depreciation, and rental payments by state: 1992” for the manufacturing sector only, by state⁵. Hence, these data concern variable K its at the level of aggregate manufacturing data (industries ind1 = 5 according to Table 4.2) for 1992, for each of the 51 states. Calling this variable KCENS

KCENC ≅ Σi K its (4.22)

Where i = 521,...,5310, t=1992, s =1,...,51. Thus, equation 4.19 is equivalent to

KCENC / Y its ≅ K it / Y it, (4.23)

Where i = 521,...,5310, t=1992 and s = 1,...,51. Creating the variable KYSTATE, which represents the capital-to-output ratio at the state level in a given industry (left-hand side of equation 4.23), and KYNAT, which represents this ratio at the national level for that industry (right-hand side of equation 4.23), the relationship to be tested becomes

KYSTATE ≅ KYNAT(4.24)

Using the data available, I calculated the variable KYNAT and found a value of 1.11, which represents the value of the capital to output ratio for the manufacturing 1-digit sector nationally in 1992. Then, I performed a t-test on variable KYSTATE to check if it was significantly different from 1.11. The results appear in Table 4.4. The hypothesis of equality between state industry and national industry capital to output ratio (equation 4.24) can be rejected at the 15% level, but cannot be rejected at the 10% level. Note that this test was established at the 1-digit industry level (aggregate manufacturing), and it can safely be assumed that the t-statistic would have been greater if the test had been realized at the more detailed 2-digit industry level. Indeed, if the test of capital to output ratio defined in equation 4.21 is “almost” true for 1-digit industries, it is more likely to be true at the more detailed 2-digit industry level where the amplitude of errors is limited. Since no capital stock data for 2-digit industry are available by state, the test, unfortunately, cannot be done at this level.

Based on this evidence and the work of Marcus, I cannot reject the null hypothesis stated in equation 4.21, and I assume this relationship is valid. This equation can also be written as

Kits / Kit ≅ Yits / Yit(4.25)

A state’s proportion of a given industry’s capital is equal to this state’s proportion of that industry’s output. In other words, I assume the total aggregate capital used in industry i can be distributed among states proportionally to states’ shares of output from that industry. This crucial hypothesis allows me to estimate the capital stocks at the detailed industries level by state, for each year, according to the following equation:

Kits ≅ Kit Yits / Yit(4.26)

Following the same procedure, I can compute the states’ industries’ IT capital (KIT its) and non-IT capital stocks (KNIT its) according to the following relationships:

KITits ≅ KITit .Yits / Yit(4.27)

KNITits ≅ KNITit .Yits / Yit(4.28)