Specialization

The Specialization of Capital
and Economic Growth

Louis M. Chan*

Last Revised: May 2020 First Draft: September 1997

Abstract

This paper presents a neoclassical-growth model in which long-run growth is driven by the continuous specialization of capital. The specialization of capital is the allocation of capital into sets of specialized capital and the coordination required for different individuals to use the same set of specialized capital. The specialization of capital may be implemented by shiftwork within firms or by rental services in rental markets. This paper shows that the specialization of capital is endogenous labor-augmenting and capital-augmenting organizational change and that this organizational change may be “embodied” in the measured capital inputs.

*SUNY, Suffolk County Community College, Southhampton H224, 533 College Rd, Selden, NY 11784. Email: [e-mail]. I thank Paul Evans, Sherwin Rosen, Lester Telser, and anonymous referees for helpful comments. This paper was HKU Economics Discussion Paper No.274. This work was supported in part by RGC Grant HKU546/95H.

1. Introduction

This paper presents a neoclassical-growth model in which long-run growth is driven by the continuous specialization of capital. Narrowly defined, the specialization of capital is the allocation of capital into specialized tasks or into sets of specialized capital. We broadly define the specialization of capital to include the coordination that is required for different individuals to use the same set of specialized capital. The specialization of capital may be implemented by shiftwork within firms or by rental services in rental markets. This paper shows that the specialization of capital is endogenous labor-augmenting and capital-augmenting organizational or technological change and that this organizational change may be “embodied” in the measured capital inputs.
There are empirical and theoretical motivations for this work. We present three main sources of empirical motivation and evidence that will be discussed in greater detail in Section 2. The first empirical motivation comes from Griliches and Jorgenson (1966) and Jorgenson and Griliches (1967). They find that, when inputs are properly measured, growth in total inputs may account for 96.7 per cent of the growth in total output. They point out that the amount of capital inputs/services should be measured directly, instead of assuming them to be proportional to capital stocks. They especially argue that, if a capital stock is used for more hours, then the capital inputs/services measure should be larger. They also point out that service prices should be measured directly, instead of assuming them to be proportional to asset prices. They include different depreciation and capital gains rates for different capital goods. Denison (1966) points out that there is no conceptual basis for the

capital utilization effect, except perhaps for increases in shiftwork which he attributes to organizational and technical progress. Denison also points out that their adjustment of depreciation introduces the “increasing double counting of investment in GNP” into capital input accounting. We provide in this paper a theoretical foundation for these two related effects that Griliches and Jorgenson have introduced into capital input accounting.

Both Denison (1966) and Griliches (1990) agree that the increased utilization of capital that Foss (1963) has found in the data may be due to the increased use of shiftwork — an organizational change. The fact that organizational or institutional change may be important for economic growth has also been independently observed by economic historians. See, for example, North and Thomas (1973) and North (1990). Another source of empirical motivation and evidence comes from Segal's (1975) empirical study of returns to scale in city size; he finds constant returns to scale in production across cities and that larger cities have a larger total productivity parameter.
The theoretical motivation for this paper is to find an endogenous source of technological change that is consistent with the empirical evidence cited above and within Solow's (1956) constant-returns-to-scale neoclassical growth model. Our approach is to ask how changes in the organization of work may increase total factor productivity.
To see how the organization of work may matter, let us hold capital utilization constant and introduce shiftwork or rental services (if shiftwork is contracted outside the firm or out-sourced). The introduction of shiftwork increases labor productivity since, with shiftwork, each set of labor may work with the same set of capital for a shorter period of time, thus decreasing task-specific fatigue. Thus, shiftwork may be

labor-augmenting. In fact, within the constant-returns-to-scale neoclassical model, increasing capital utilization — increasing capital inputs — may not be profitable without augmenting labor; and so the increased use of shiftwork may be responsible for the increased capital utilization. Of course, shiftwork and rental services require costly coordination; and coordination costs may limit the amount of shiftwork and therefore the level of capital utilization. Coordination activities may be performed by various levels of management within firms and by various intermediaries in the market; see Williamson (1975, 1985) and North (1990) for more discussions on this topic. In order to make shiftwork meaningful, capital must be made specialized. If every set of capital is the same, then there is no point shifting labor around. Therefore, broadly defined, the specialization of capital is a coordination technology that involves the allocation of capital into sets of specialized capital and the coordination such that many sets of individuals may use the same set of capital, such as in shiftwork.

There is more to the specialization of capital. Because of their specialized nature, specialized capital goods are quasi-public goods — rivalrous if used at the same time but non-rivalrous if used at different times. When one individual is not using some set of capital, he may lend it to another individual in return for using another set of capital. This kind of borrowing and lending at the same time depends on the fact that some goods are specialized and are capital goods. The fact that specialized capital inputs are quasi-public goods may justify the “double counting” of capital inputs. Thus, the specialization of capital may be capital-augmenting as well.
The specialization of capital may be increased continuously to generate growth in the long run. As per-capita capital increases, wealth effect increases each individual's demand for coordination and increases the specialization of capital, as represented by

more shiftwork or more rental services. Thus the amount of coordination is endogenous. By increasing the number and variety of sets of specialized capital, each set of increasingly specialized capital may be used by more number of individuals, with each individual spending less time with each set of capital. With labor being augmented, the amount of labor that works with each set of capital may remain the same (or may even increase); thus the marginal product of capital may stay constant (or may even increase) even as per-capita capital inputs increase.

Rental services may have been observed by Marshall (1949, p.225) when he writes that “subsidiary industries devoting themselves each to one small branch of the process of production, and working it for a great many of their neighbours, are able to keep in constant use machinery of the most highly specialized character, and to make it pay its expenses.” Rosen (1977) studies similar issues and finds that specialization within the team allows the team to have more capital of each type. See Foss (1997), Marris (1964), and Deardorff and Stafford (1976) for the early studies of shiftwork. See Becker (1965) for a seminal study of the allocation of time.
Our work is related to endogenous-growth models that, following Marshall's (1949) own interpretations and Young (1928), have emphasized various forms of increasing returns. Arrow (1962), Uzawa (1965), Romer (1986, 1990), and Lucas (1988) use models with human-capital spillover effects to generate endogenous growth. Romer (1987) and Grossman and Helpman (1990) use the Ethier (1982) formulation in which increases in the variety of intermediate inputs exogenously increase total productivity. They attribute this increase in productivity also to externalities. In these models the private return to capital is lower than the social return; and the standard growth-accounting method may not apply. See Jorgenson and Griliches (1967) and Barro and Sala-i-Martin (1995) for more discussions on
these models and growth accounting. Other growth models that use increasing returns and coordination include Yang and Borland (1991) and Becker and Murphy (1992). Increasing-returns models are ultimately related to Adam Smith's discussion of the division of labor in the Wealth of Nations, see Stigler (1951), Becker (1993, Chapter 2), Rosen (1977, 1982, 1983), Barzel and Yu (1984), Edwards and Starr (1987), and Baumgardner (1988). Our modeling of coordination costs in a competitive equilibrium is similar in some ways to that of Greenwood and Jovanovic (1990).
Section 3 presents a simple model of the specialization of capital to show how it works. Section 4 presents extended static models of the specialization of capital that explicitly include coordination and coordination costs. Section 5 presents a dynamic model and shows how the increasing specialization of capital may generate long-run growth in the neoclassical-growth model. Section 6 concludes the paper.

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