STATE‐LEVEL CAPITAL AND INVESTMENT: UPDATES AND IMPLICATIONS

I. INTRODUCTION U.S. states provide a ready-made laboratory to test macroeconomic theories of production and growth. Compared to cross-country studies, state-level analysis benefits from uniform data collection and similar institutional backgrounds which reduces measurement and omitted variable bias. Accordingly, researchers have used state-level data to estimate Cobb--Douglas production function (Garcia-Mild, McGuire, and Porter 1995); stochastic production frontier (Domazlicky and Weber 1998); employment growth (Taylor and Brown 2006); foreign direct investment (Brock 2009; Mullen and Williams 2005); tax policy (Reed 2008); neoclassical growth (Yamarik 2006); and macro-Mincerian (Yamarik 2008) models. One obstacle to state-level analysis is a lack of an up-to-date series on physical capital and investment. The Bureau of Economic Analysis (BEA) provides net capital stock data for the nation, but not for individual states. Garofalo and Yamarik (2002) (hereafter GY) produce state-level capital stock estimates for 1947-2000 by apportioning the BEA national total. Unfortunately, the switch from the SIC classification system to the NAICS by the BEA makes the estimates of GY difficult to extend. (1) In this paper, I create state-by-state capital stock and investment estimates for 1990-2007. I use the same procedure of GY of apportioning the national capital stock to the individual states. For each NAICS one-digit industry, I divide up the national capital stock estimate based on the relative income generated within each state. I then add up the industrial estimates to generate capital stock and investment data for each U.S. state. I test the soundness of the state-level capital and investment data by estimating a Cobb--Douglas production function and a Solow growth model. Under both models, the output elasticity for physical capital is predicted to equal the observed income share paid to capital. In the production function, the output elasticity is obtained directly from the estimated coefficient for the physical capital stock. In the Solow growth model, the output elasticity is derived algebraically from the estimated coefficients for the initial level of real income per worker and net investment per worker. I estimate each model using a variety of estimators to examine the potential impact of unobserved heterogeneity, measurement error, and endogeneity. I obtain estimates of the output elasticity for capital that are plausible and close to the observed national income share of one-third. For the production function, the output elasticity is 0.35 to 0.42 under the preferred estimators. I also compare the fixed-effects estimates to time-differenced estimates and find little evidence of measurement error in the capital stock series. For the Solow growth model, the implied output elasticity is 0.23 to 0.34 under the preferred estimators. However, the lower estimate of the output elasticity under first-differences can be attributed more to measurement error in the real income data rather than the investment data. Nevertheless, the results indicate that the updated capital stock and investment data contain real and legitimate information of state differences in the stocks and accumulation rates of physical capital across U.S. states. The remainder of the paper is organized as follows. Section II discusses the data methodology. Section III presents the Cobb--Douglas production function and the Solow growth model. Section IV provides the estimation results and Section V concludes. II. DATA METHODOLOGY I use the same procedure of GY to create state-by-state capital stock and investment estimates for 1990-2007. The procedure apportions the national capital stock estimates to the states using industry-level income data. The difference in implementation is that GY uses one-digit SIC industry data for 1945-2001, while I use one-digit NAICS industry data for 1990-2007. …