Static and dynamic externalities, industry composition, and state labor productivity: a panel study of states.

• Author: Partridge, Mark D.

1. Introduction

   The recent popularity of macroeconomic endogenous growth models has spurred interest in regional economic growth. A primary focus of the endogenous growth literature is the relationship between geographic concentration of production and regional productivity.(1) Geographic concentration of firms within an industry can facilitate spillovers of knowledge and innovations among them, increasing the industry's productivity in the area. These spillovers have become commonly referred to as localization or Marshall-Arrow-Romer (MAR) externalities (e.g., Romer 1986). Similarly, spillovers also may occur among firms of different industries that are located in close proximity, which are commonly referred to as urbanization or Jacobs externalities (Jacobs 1969). In addition, geographic proximity also may reduce costs of transporting intermediate inputs, representing a pecuniary spillover (Krugman 1991).

   Several empirical regional studies related to geographic concentration of economic activity and economic spillovers emphasize their relationship to employment growth, only indirectly testing the externality-productivity relationship (e.g., Glaeser et al. 1992; Henderson, Kuncoro, and Turner 1995; Partridge and Rickman 1996; Henderson 1997). Also, studies of regional productivity differences typically focus on static urbanization and localization economies and not on dynamic externality effects emphasized in the endogenous growth literature (e.g., Moomaw 1983, 1986). In addition, although Ciccone and Hall (1996) examined the relationship between density of production and state labor productivity, they relied on cross-sectional analysis. Cross-sectional analyses ignore unobserved fixed factors that may underlie the productivity differences, such as those arising from the region's history, leaving open the possibility that the estimated determinants of productivity are biased.(2)

   Previous regional productivity studies also did not isolate the two different ways that a region's productivity can be above the national average: (i) having a mix of industries that are highly productive and (ii) having existing industries more productive than their respective industry's national average. This distinction is important if the alternative sources of externalities affect the composition of industries differently than they affect productivity for all existing industries. For example, suppose industry concentration tends to attract a more productive concentration of industries, while industry diversity raises the productivity for all existing industries. The offsetting effects of industry concentration and industry diversity economies would be unobservable when only examining total productivity.

   In this paper, we use panel data for the contiguous states of the U.S. to examine directly the relationship between externalities and labor productivity. Although urban areas are thought to be most associated with economic externalities (Lucas 1988), there are advantages to using state data. Foremost, because production is reported annually at the state level, we can consider directly predictions of recent growth models that emphasize productivity, whereas county and metropolitan studies must rely on employment growth (an indirect test of the productivity-externality link). Likewise, if there are economic spillovers across county or metro borders, examining state data captures most of these effects. Finally, studies examining cities or metro areas omit rural areas. Yet if urbanization is an important phenomenon, a state like North Dakota would be at a significant productivity disadvantage, making it a valuable observation in a regional productivity study.(3)

   Our empirical approach involves fixed effects estimation of state panel data, which controls for the influence of omitted time-invariant state-level variables. This approach also allows us to distinguish between the effects of static externalities versus dynamic externalities.(4) Using a novel two-stage approach, we search for both contemporaneous static effects and dynamic effects that either persist or take longer to develop. In another innovation, we assess the influence of externalities on productivity in each industry as well as determine whether externality effects influence a state's composition of industries. The distinction has public policy implications in that states have choices related to attracting high-productivity industries versus increasing productivity in all existing industries.

2. Theoretical Framework

   Because of state policy makers' interest in wage rates and per capita income, we focused on the determinants of labor productivity. In so doing, we followed other studies (e.g., Ciccone and Hall 1996) by directly relating labor productivity to its determinants. This avoided estimating a production function, which typically involves imposing restrictions to derive total factor productivity estimates or estimates of returns to scale.(5) Nevertheless, the disadvantage of our approach was that we were unable to address the precise production channel through which variables influenced labor productivity. In addition, consistent with the literature on regional and national productivity, we examined productivity aggregates, which implies that caution should be exercised in interpreting the results.(6)

   Measuring Labor Productivity

   Because states differ in theft composition of industries, it is likely that some of the state differences in productivity are due to their relative concentrations of high- and low-productivity industries. To be sure, in a survey of the regional productivity literature, Gerking (1994, p. 182) suggests that future research on productivity adjust for industry mix to better understand "the forces that contribute to productivity growth rates." At best, past productivity studies have included one-digit industry shares in productivity regression equations (e.g., Carlino and Voith 1992) or examined the determinants for particular detailed industries (e.g., Moomaw 1986). As far as we know, no study has separated regional productivity differences into the portion due to regional differences in industry concentration and the portion due to productivity differences in each industry across regions. Also, it has been unexplored whether a state's composition of industries is related to dynamic externalities. The significance of this point is that it may be more difficult for states to contemporaneously alter their industrial compositions if dynamic externalities exist since dynamic externalities make state industrial compositions dependent on their histories (Henderson 1997).

   Therefore, using Bureau of Economic Analysis Gross State Product (GSP) data, we construct a measure of relative state labor productivity (PROD) as GSP or output (Q), divided by labor input (L), all divided by the same for the nation. An advantage of normalizing by the nation is that it nets out national business cycle effects and long-term productivity trends that are common across all states. We then decompose PROD into two components. The first component of relative state labor productivity relates to its concentration of industries (PROD_MIX). The second component is then calculated as the remaining productivity difference, which is the average relative productivity in each industry, or relative productivity competitiveness (PROD_COMP). The corresponding mathematical expressions are:

   [PROD.sub.k] = ([Q.sub.k]/[L.sub.k])/([Q.sub.u]/[L.sub.u]), (1)

   [PROD.sub.k] = PROD_[MIX.sub.k] x PROD_[COMP.sub.k], (2)

   [Mathematical Expression Omitted], (3)

   PROD_[COMP.sub.k] = [PROD.sub.k]/PROD_[MIX.sub.k], (4)

   where

   [Q.sub.ki] = [[Sigma].sub.j] [Q.sub.kij], (5a)

   [Q.sub.k] = [[Sigma].sub.i] [Q.sub.ki], (5b)

   [Q.sub.ui] = [[Sigma].sub.j] [Q.sub.uij], (5c)

   [Q.sub.u] = [[Sigma].sub.i] [Q.sub.ui], (5d)

   [L.sub.ui] = [[Sigma].sub.j] [L.sub.uij], (5e)

   subscripts k and u denote state and nation, respectively, subscript i indicates two-digit standard industrial classification (SIC) industry, and subscript j refers to a firm within industry i.(7)

   By normalizing relative to the nation, Equation 1 exceeds unity when a state has above-average productivity. Equation 2 decomposes total productivity differentials into industry mix differences and average productivity differences across all industries. Equation 3 shows that PROD. MIX is obtained by weighting U.S. industry productivity by the state share of output in that industry in the numerator, and the U.S. share of output in that industry in the denominator.(8) Equation 4 reveals that PROD_COMP is derived from the total level of productivity (PROD) and PROD_MIX. If a state has an above-average concentration of nationally high-productivity industries, PROD_MIX exceeds unity. Yet if all industries on average in the state have higher productivity than they do nationally (i.e., PROD [greater than] PROD_MIX), PROD_COMP will be greater than one.

   Taking natural logs of Equation 2, the log of relative productivity equals the sum of the log of productivity mix and the log of productivity competitiveness:

   ln[(PROD).sub.k]= ln[(PROD_MIX).sub.k] + ln(PROD_COMP).sub.k], (6)

   in which values above zero now reflect productivity advantages. From Equation 6, differences in state productivity depend on factors that increase its mix of high-productivity industries plus those that increase productivity in each industry above the industry's national average level. When multiplied by 100, PROD.MIX is approximately the percentage point difference in average productivity from the nation attributable to the state concentration of high-productivity industries. Likewise, PROD_COMP multiplied by 100 is the percentage point deviation attributable to the state's relative average productivity difference in all industries.

   Model

   Given a positive marginal product of capital, labor productivity is an increasing function of the capital-to-labor ratio (K/L). Similarly, if there are...