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Article Excerpt
This article develops a theory of how capital, skilled labor, and unskilled labor interact at the plant level. The theory has implications for the relationship between factor allocation and plant size and the effects of trade and growth on the skill premium. The theory is consistent with certain facts about factor allocation and factor price changes in the 19th and 20th centuries.
1. Introduction
* This article develops a theory of how capital, skilled labor, and unskilled labor interact at the plant level. In the equilibrium of the model, the allocation of factors at the plant level depends upon plant size. One outcome in the model is for larger plants to employ a larger fraction of skilled workers than small plants do, what we call a positive size-skill relationship. As documented below, there is strong evidence that such a positive relationship has existed in recent decades. It is also possible in the model for there to be a negative size-skill relationship where larger plants employ a smaller fraction of skilled workers. As discussed further below, a century ago, the size-skill relationship was actually negative. The assembly lines in the large factories opened by industrialists such as Henry Ford were operated by legions of unskilled workers. In contrast, small plants during this time period tended to hire skilled artisans.
Our main result connects the size-skill relationship--a property of the cross-section of plants at a point in time--with changes over time in the skill premium, an aggregate relationship. We consider the effects of forces over time that enable firms to increase plant size. The expansion of markets made possible through reductions in transportation costs and other trade barriers is one such factor that we consider. Chandler (1990) has emphasized the important role this factor played a century ago with the expansion of railroads and the advent of new communication techniques. This process continues to this day.
We show that if the size-skill relationship in the cross-section is negative, then an expansion of markets necessarily leads to a reduction in the skill premium. If, alternatively, the size-skill relationship is positive, then an expansion of markets might increase the skill premium. We show in numerical examples that an expansion of markets raises the skill premium only when the size-skill relationship is sufficiently pronounced. These implications are consistent with the historical record, including work by Goldin and Katz (1999) on the time pattern of the skill premium. A century ago, the skill premium was falling while the size-skill relationship was negative. In recent years, the skill premium has been rising and the size-skill relationship has been significantly positive.
In our model, there is an analogy between the way capital relates to unskilled labor and the way unskilled labor relates to capital. Capital can do relatively simple mechanical tasks that unskilled labor would otherwise do, but only if high setup costs are incurred. Analogously, unskilled labor can do complex brain tasks skilled labor would otherwise do, but only if high setup costs are incurred. (1) To explain, consider a simple mechanical task such as emptying the trash or moving a box from point A to point B. Unskilled labor has general ability to undertake such simple tasks. An unskilled worker hired just five minutes ago could first empty the trash and then move a box with virtually no training. It may be possible to obtain a machine to take out the trash, but this would in general require extensive setup costs, namely to construct a conveyor belt that would have to be designed to fit a particular space. Moreover, we expect that a different machine would have to be obtained to move the box. Machines tend to be specific in tasks they can be used for, at least as compared to the general ability of the human body to undertake simple mechanical tasks. Although advances in robotics and computer-controlled machinery have certainly made capital more flexible, it is still not as flexible as the human body.
Next consider a more complex task such as the management of the production process in an assembly line. A skilled worker with a degree in engineering can be put in charge of the production line; this worker has general knowledge to make appropriate decisions when problems arise. Alternatively, fixed costs can be incurred to redesign the production process to reduce the number of problems that arise. In conjunction with this redesign of the production process, manuals can be developed and protocols devised to make it possible for an unskilled worker managing the line to know what to do in the event of a (now rare) problem. The tradeoff here is that by paying fixed costs, it may be possible to design out the need for skill. Perhaps the most famous example of designing out skill is what Henry Ford did with the production process of automobiles. Following the principles of Frederick Taylor, he paid fixed costs to design a system that routinized tasks so that skilled craftsmen could be replaced by unskilled laborers. This de-skilling through Taylorist principles that took place early in the 20th century has attracted much attention in the literature. See, for example, Brown and Philips (1986). There is a literature in sociology that emphasizes de-skilling. See, in particular, Braverman (1974).
To incorporate these ideas, we develop a model with the following features. To produce output at any plant, a variety of tasks needs to be performed. The firm must decide which inputs (capital, unskilled labor, or skilled labor) should do which tasks. Tasks vary in complexity, and more complicated tasks require more setup costs. Skilled workers, with their high level of general-purpose knowledge, have low setup costs. The setup costs of unskilled workers are higher, and the setup costs of capital are higher still. Thus, capital can be thought of as an extreme form of unskilled labor.
In the optimal assignment of tasks, there is a partition. Skilled workers are assigned complex tasks that would require extensive setup if undertaken by unskilled workers or capital. Capital is assigned the relatively easy-to-master tasks such as those that involve the movement of objects. Unskilled labor is assigned the in-between tasks. Thus, on one margin, capital substitutes for unskilled labor, whereas on the second margin, unskilled labor substitutes for skilled labor.
Historians know well that the size-skill relationship was negative in 1900. And labor economists know well that the size-skill relationship is positive today. But no previous analysis has tried to address both facts at the same time as we do here. In our theory, the relationship can go either way. Larger plants tend to substitute capital for unskilled labor and unskilled labor for skilled labor, because the larger scale makes it more worthwhile to pay fixed costs to lower marginal costs. Thus, the net effect of plant size on the skilled labor share is ambiguous. We are able to derive a simple condition determining the direction of the net effect. What makes our result have content is that we relate the condition to how an expansion of markets or productivity growth affects the skill premium.
Our analysis of changes over time in the skill premium is closely related to previous work. Goldin and Katz (1998), Caselli (1999), Mobius and Schoenle (2006), and Mitchell (2001) all have models where changes in technology lead first to a reduction and then to an increase in the skill premium. And there is a large literature about capital skill complementarity. (See Griliches, 1969; Krusell et al., 2000; Goldin and Katz, 1998; and Autor, Levy, and Murnane, 2003.) What distinguishes our work from these papers is our attempt to connect changes in the skill premium to cross-section relationships between plants of varying size. Furthermore, we show how the observed U-shaped pattern of the skill premium can be generated in a model even when there is no technological change. Expansion of markets and capital deepening, forces that raise plant size, are sufficient to obtain this result.
We note that an expansion of markets in our model is the same thing as an increase in trade. The channel through which increased trade affects the skill premium in our model is very different from the channel in the standard model, which is based on Hecksher-Ohlin arguments. In our article, we interpret trade as simply the merging of multiple, identical countries, so it is simply a scaling up of market size. As a result, trade has no effect on the skill premium through the conventional channel. Here, trade allows plants to enjoy scale economies, and as plants expand, relative factor demands are affected. This is consistent with the plant-level evidence from Berman, Bound, and Griliches (1994), who find that the increase in demand for skilled labor is within industries and not due to a reallocation across industries, as in Hecksher-Ohlin. Our analysis of the effect of trade between similar countries is similar in spirit to Acemoglu (2003), who also identifies a channel (in his case, endogenous technological change) through which increases in market size affect the skill premium.
2. Supporting evidence
* This section provides supporting evidence for assertions made in the Introduction.
** The size-skill relationship. Suppose for now that an individual's pay can be used as a proxy for his or her skill. It is a well-known and robust fact that in today's economy, larger plants have higher-paid employees (Brown and Medoff, 1989). See also Oi and Idson (1999) for a survey of the literature. It is not as well appreciated that the size-pay relationship has changed over time. Using micro data from the Census of Manufactures over the 1963-1986 period, Davis et al. (1991) show there was a sharp upward trend in the relationship over this period. Idson (2001) also reports recent increases. Atack, Bateman, and Margo (2004) analyze Census micro data from the late 19th century and report a fundamentally different relationship between size and pay. In a simple linear regression of log wage on log size, they find a negative relationship. In a regression with a quadratic term, they find an inverted U-shaped relationship that is first increasing and then decreasing.
These results are illustrated in Table 1. Whereas output size is our preferred size measure because we use it in our theory, here we use employment to measure plant size because of data availability. The Census has published tabulations by employment size class in a consistent way over a long period, enabling us to examine the long-run trend. To construct the table, we first calculated average pay for each plant size category by dividing total payroll in the category by total employment. For example, in the 1997 Census, average pay calculated this way for plants with 2,500 employees or more equaled $52,100. We then normalized by dividing by average pay in the entire manufacturing sector. The mean in 1997 was $33,900, so the normalized wage in 1997 in the 2,500 plus size category is 1.54 = 52.1/33.9, which is the figure reported in the table. Thus, average pay in the largest size category is 54% higher than the average wage, a substantial premium.
Going from left to right in the table, we move forward in time. Observe that for the largest two size classes, the premium increases monotonically with time. Thus, the table replicates Davis...
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