Academic journal article Economic Inquiry

Estimation of the Depreciation Rate of Physical and R&D Capital in the U.S. Total Manufacturing Sector

Academic journal article Economic Inquiry

Estimation of the Depreciation Rate of Physical and R&D Capital in the U.S. Total Manufacturing Sector

Article excerpt


Numerous studies on production and cost, the sources of productivity, and endogenous growth have recognized the pivotal role of the physical capital stock. Studies at various levels of aggregation over assets and industries have emphasized the crucial role of investment in plant and equipment in the growth of demand and productive capacity. It is clearly recognized by economists and policymakers that knowledge capital, approximated by R&D capital, is crucial for productivity growth and the transformation of the industrial structure of an economy.

The distinction between net and replacement investment in these types of capital is important for policy purposes. Critical to an analysis of the contributions of physical and R&D capital is an accurate measurement of the stocks of physical and R&D capital, which in turn requires measuring their depreciation rates. However, measuring these depreciation rates provides a formidable challenge. In the following we present an approach that uses an econometric model and gross investment data to generate estimates of the depreciation rates and consistent series for the stocks of physical and R&D capital as well.

The conventional procedure for estimating the stock of physical capital is based on the perpetual inventory method. Unfortunately, the assumptions underlying this procedure are typically not subjugated to formal statistical testing. So far only a few econometric studies provide estimates for the depreciation rate of physical capital within the context of a behavioral model.(1) Very little effort has been made, except for Pakes and Schankerman [1978; 1986], to measure the depreciation rates of the stock of R&D. Researchers doing applied work typically assume an arbitrary depreciation rate of 0.10 to 0.15 percent to construct the stock of R&D capital using the perpetual inventory method.

In this paper we estimate the depreciation rates of both physical and R&D capital stocks for the U.S. total manufacturing sector within the framework of a factor demand model. We also generate, using our analytical framework, "capital" stock series for both types of capital, which are consistent with the estimated depreciation rates. We need only gross investment data to obtain the implied estimates of the depreciation rates and to generate consistent capital stock series.

The model considered here is a special case of the theoretical model in Prucha and Nadiri [1991], which allows for the estimation of variable depreciation rates for several types of capital stocks. In that modeling framework the firm is allowed to combine its beginning-of-period stocks of physical and R&D capital with other inputs to produce output as well as end-of-period stocks of both types of capital. Basic elements of that modeling framework date back to Hicks [1946] and Malinvaud [1953] and were recently discussed by Diewert [1977; 1980]. In the literature on dynamic demand models such an approach was first adopted by Epstein and Denny [1980] and more recently by Kollintzas and Choi [1985] for a single capital good, and on a theoretical level in Bernstein and Nadiri [1987a; 1987b].

The paper is organized as follows. The specification of the model is presented in section II. Section III is devoted to a discussion of the data and to the presentation of the parameter estimates of the model. In section IV we present the empirical results for the depreciation rates for physical and R&D capital and compare them with those reported in the literature. We compare the physical capital stock estimates generated by our model with the "official" capital stock estimates produced by U.S. Department of Commerce, Bureau of Economic Analysis. In this section we also present our estimates of the decomposition of gross investment into replacement and expansion investment for both physical and R&D capital. These decompositions are important from the vantage point of public policy analysis. …

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