Academic journal article Economic Inquiry

Estimating Capital Efficiency Schedules within Production Functions

Academic journal article Economic Inquiry

Estimating Capital Efficiency Schedules within Production Functions

Article excerpt


The appropriate method for aggregating capital goods of different vintages into a single measure of capital stock has long been a contentious issue.(1) The works of Leontief [1947], Fisher [1965] and Diewert [1980] explore the theoretical conditions under which an aggregate capital stock exists and when it may be expressed as a weighted sum across all vintages of capital in use. These weights reflect the relative efficiency of capital as it ages, and the series of these weights is referred to as an efficiency schedule. The empirical literature on capital efficiency schedules includes studies that estimate economic depreciation, from which efficiency schedules can be obtained, for specific classes of capital goods (e.g., Hall [1971] and Hulten and Wykoff [1981]), dynamic factor demands that explicitly estimate a geometric capital efficiency rate (e.g., Epstein and Denny [1980], Kim [1988], and Prucha and Nadiri [1993]), and models that measure the effects of a distributed lag of investments on current profit (e.g., Pakes and Griliches [1984]).

This paper presents a methodology that estimates capital efficiency schedules by using a parameterized investment stream as a capital variable in a production function. The parameters of the production function are then simultaneously estimated with the parameters of the investment stream. In order to perform this exercise, data on inputs, output, and previous investments for a group of manufacturing plants that employ a common technology are required. I chose to estimate efficiency schedules for a group of steelmaking plants that employ electric arc furnace technology, also known as minimills. These plants are ideal to study capital efficiency since they possess a common technology and produce a similar product.(2) The data are from a plant-level panel data set from the Census Bureau's Longitudinal Research Database.(3) I view this study as an exploratory exercise, testing whether the rich panel data in the Census Bureau's database can be used to obtain precise estimates of the relationship between capital age and capital efficiency.

I test several hypotheses regarding efficiency schedules and fundamental questions regarding capital accumulation. Jorgenson [1989] reviews some of the differing opinions regarding the form of efficiency schedules. A point of contention is whether most production machinery is able to perform close to original standards over time before rapidly deteriorating (e.g. one-hoss stray), or whether machines become gradually more inefficient (e.g. geometric). These issues are not only important for obtaining accurate productivity measures, but also for the specification of a wide range of dynamic models that contain capital accumulation equations. For instance, one of the more frequently used capital accumulation equations is [K.sub.t] = (1-[lambda]) [K.sub.t-1] + [I.sub.t-1], where [K.sub.t] is capital at time t, I is investment, and [lambda] is the geometric rate of decay. One of my primary goals is to test whether the data support this frequently used model.

My primary finding is that when efficiency schedules are estimated within a translog production function, the estimated efficiency schedules follow a near geometric pattern, with efficiency declining by 4 to 5 percent per year. However, these estimates are somewhat imprecise, so that efficiency schedules that are concave cannot be rejected.(4) I also test whether the efficiency of capital goods initially increases, due to learning or other phenomena, as Pakes and Griliches [1984] and Hulten and Wykoff [1981] find. The results suggest that increases in the efficiency schedule do not occur after the first year. When plant fixed effects are introduced, the estimates for the efficiency schedule become even more imprecise.

Do these results imply that capital goods in mini-mills physically deteriorate at a rate of 4 to 5 percent a year? There is no doubt that older machines are more likely to suffer breakdowns than newer machines. …

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