Substitutability and Accumulation of Information Technology Capital in U.S. Industries

Abstract

1. IntroductionFor the last couple of decades, the U.S. economy has invested in information technology (IT) equipment and software at an extraordinary rate relative to other types of inputs. This rapid accumulation of IT capital per hour worked, known as IT capital deepening, has become one of the major contributors to labor productivity growth in the U.S. economy at both the aggregate and industry levels.1Jorgenson (2001) points out that an essential source of IT capital deepening is the substitution of IT capital for other inputs, induced by a rapid decline in IT prices. As a factor of production, however, the demand for IT capital depends not only on its own price but also on the degree of substitutability between IT capital and other inputs. Thus, it is crucial to investigate the degree of substitutability between IT capital and other inputs in order to explain a rapid IT capital deepening.2In this article, we estimate the elasticities of substitution between IT capital and other factors of production using data on 41 U.S. industries for the period from 1984 to 1999. In a cost function framework, we measure the cross-price elasticity (CPE), the Allen elasticity of substitution (AES), and the Morishima elasticity of substitution (MES). Based on these elasticity estimates, we also explore the quantitative importance of IT substitution in IT capital deepening.We find that the substitutability of IT capital for other inputs was an essential component in explaining the shift in production technique toward IT capital for U.S. industries. Estimated elasticities of substitution indicate that IT capital is a substitute for other factors of production such as labor, non-IT equipment, structures, and intermediate inputs. In particular, the degree of substitutability between IT capital and other inputs is higher in the manufacturing sector than in the service sector and is higher in the less IT-intensive sector than in the IT-intensive sector.We also find that IT substitution is an important contributor to IT capital deepening (relative growth of IT capital to hours worked). We decompose IT capital deepening into a substitution effect, an output expansion effect, and a technical change effect. The results show that the substitution of IT capital for other inputs explains about 60% of total IT capital deepening in the U.S. economy for the period from 1985 to 1999.This article is organized as follows. Section 2 compares various measures of the elasticity of substitution in a cost function model and presents the method for the decomposition of IT capital deepening. Section 3 describes the data used in this study and presents the empirical framework. Section 4 reports estimation results on the elasticities of substitution between IT capital and other inputs and the results on the decomposition of IT capital deepening. Section 5 concludes the article.2. Elasticity of Substitution and IT Capital DeepeningElasticity of SubstitutionIn the case of only two inputs, the elasticity of substitution (σ) between the two inputs x1 and x2 is defined as(Formula Omitted. See article image.) where pi is the price of input i. Thus, the elasticity of substitution, originally introduced by Hicks (1932), shows the degree of input substitutability by measuring the elasticity of the input ratio with respect to the input price ratio (the marginal rate of technical substitution).3When there are more than two inputs used in production, there is no unique measure of substitutability. A conventional measure is the AES introduced by Allen (1938). As shown in Uzawa (1962), the AES between inputs i and j for a twice-differentiable cost function (C) is defined as(Formula Omitted. See article image.) where the subscripts denote partial derivatives with respect to input prices. …