Specialization

Empirical Motivation and Evidence

In a growth-accounting exercise using constant returns to scale and perfect competition assumptions, Jorgenson and Griliches (1967) show that, when inputs are properly measured, growth in total input may account for 96.7 per cent of the growth in total output. Griliches and Jorgenson (1966) have shown similar results. In the 1967 paper, they show that, without making their adjustments, growth in total input explains 52.4 per cent of the growth in total output; the remainder is the residual (or total factor productivity). After aggregation by summing quantities in constant prices has been changed to using Divisia indexing procedures, total input explains 54.3 per cent of the growth in total output. After the prices of investment goods have been adjusted, total input explains 61.0 per cent of the rate of growth in output. After capital hours have been taken into account, total input explains 71.6 per cent of the rate of growth in output. After different depreciation weights for different capital goods have been taken into account, total input explains 82.7 per cent of the growth in output. After the labor (which, in their case, includes human capital) aggregate has been adjusted using a Divisia index, total input explains 96.7 per cent of the growth in total output. The capital hours and the depreciation adjustments contribute about 50% to the increased ability of growth in total input to explain the growth in total output.

In order to adjust for capital hours, they follow Foss's (1963) use of data on electric power consumption. Foss (1963, 1997) finds that capital hours in manufacturing has increased over time. As we will see explicitly in Section 3, increasing capital utilization may not increase total output in a constant-returns-to- scale model. However, persistent increase in capital hours in the data may point to something else that is changing. Foss (1963, 1997) also finds that, although capital hours in manufacturing have increased over time, labor hours have decreased over time and that shiftwork has increased over time.¹ Foss (1997) also reports Bureau of Labor Statistics estimates that wage differentials for shiftwork have declined over time and have never exceeded 6 percent on average.²
We think that the measurement methods used by Griliches and Jorgenson (1966) and Jorgenson and Griliclies (1967) are able to measure the technological change “embodied” in the measured capital inputs.³ Griliches (1990, p. 192) summarizes that “the difficulty with the available capital measures then, was, and to a great extent is still now, in my view, the fact that they were being overdeflated and overdepreciated, that items with different expected lives were being added together in a wrong way, and that no allowance was being made for changes in the utilization of such capital.” The overdeflation issue has to do with adjusting for quality changes or vintage effects that are embodied (Solow 1960, Jorgenson 1966) in the capital stock. We now think that the overdepreciation issue and the capital utilization issue have to do with measuring increased capital inputs due to the increased ability of different individuals to time-share the use of the same set of specialized capital by shiftwork within the firm or in the market. If the same set of specialized capital is used by different sets of labor as in shiftwork or rental services, then some kind of “double counting” pointed out by Denison (1966, p.77) may be appropriate. It is therefore important to get the depreciation rates right so that the amount of capital input used by each set of labor is properly measured. Griliches (1963a, 1963b) explains that most depreciation methods have very little economic justification except for accounting convenience or tax purposes and (1963a, p.121) that “for many purposes, in particular for productivity comparisons, the one-hoss-shay assumption seems to be reasonable, or at least less extreme than some of the more commonly used assumptions (e.g., declining balance).”
Both Denison (1966) and Griliches (1990) agree that the long-run aspect of capital utilization is due to the long-run trend in shiftwork. Denison (1966, pp.77-8) states that “longer machine hours were not at all the consequence of increased saving and investment. They look to me like the result of capital-saving organizational and technical innovation, with perhaps a dash of improved quality of management thrown it. But however we classify their effects, it is interesting to isolate them.” Griliches (1990, pp.195-6) points out that, when capital utilization increases, “if capital is not measured in machine hours, we would show a rise in productivity even though there has been no ‘technological’ change in methods of production. I would prefer not to include such changes in the definition of productivity since I interpret them as movements along (or toward) a stable production possibilities frontier.⁴ But there did occur an organizational change that allowed us to get more ‘flow, more hours per day or year, from a given stock of equipment or other resources.” They both may be right if we can show that the organizational change may be “embodied” in some measures of capital inputs.
Economic historians have independently observed the fact that organizational or institutional change may be important for economic growth. In particular, North and Thomas (1973, p.1) concludes generally that “efficient economic organization is the key to growth; the development of an efficient economic organization in Western Europe accounts for the rise of the West.” North (1990, p.3) maintains that “that the differential performance of economies over time is fundamentally influenced by the way institutions evolve is also not controversial.” Winston's (1971) study of capital utilization in “the typical underdeveloped country” West Pakistan may be suggestive on this point. Winston (1971, p.38) finds that “in West Pakistan in 1965-1966, for instance, the average industrial firm operated its equipment only 33% of the time industrial capacity sat idle and unproductive two-thirds of the time in a country where capital is assumed to be critically scarce.” Another significant finding is that, ceteris paribus, higher capital utilization is associated with lower labor productivity. In addition, Winston (1971, p.54) reports that, even with widespread unemployment, “the shift differentials paid by manufacturers (or at least legislated) in underdeveloped countries are a great deal larger — 25-50% above day-time wage- rates — than they are in advanced countries — about 10%.” These findings together seem puzzling because they seem to be saying that, particularly in poor countries, “industrial capacity is unused in large part because people don't want to use it” (Winston, 1971, p.52). We suggest another interpretation. If shiftwork and rental services require costly coordination, organization, and market institutions, then perhaps capital is underutilized in poor countries because people there cannot afford the costly institutions necessary for higher capital utilization.
Aside from coordination and institutions, localization may also be required for the use of shiftwork and rental services. The reason for localization may be simple — it reduces the costs of commuting to and from the same sets of capital shared by different shifts of people or the costs of transporting the same sets of capital around to different users. See Chan (1999) for more discussion of this idea. Adam Smith (1976), Marshall (1949), and Jacobs (1969) may have all observed that specialized services are localized in cities. The US Bureau of the Census (1992) shows that, in 1992, 74.6% of all service industry receipts in the United States came from the forty largest metropolitan areas; and over 25% came from New York, Los Angeles, and Chicago. Segal (1975) has shown convincingly that any economies of localization do not come from increasing returns to scale; he shows that constant returns to scale obtain across cities of different size. Without adjusting for capital utilization and differences in depreciation weights, he finds the total productivity parameter of a constant-returns-to-scale aggregate urban production function to be larger in bigger cities. The results in this paper imply that this shift in the total productivity parameter across cities may go away if the Griliches-Jorgenson adjustments are used in measuring the capital inputs.

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