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

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 (internal) increasing returns to scale in all inputs, increased firm size increases labor productivity. So at the aggregate level, average firm size may be positively related to aggregate productivity. Firm size also may affect productivity if it is related to market power (Glaeser et al. 1992). The effect of market power is a priori ambiguous. On the one hand, a large monopolistic firm may have more incentive to conduct research and development because of a higher probability of appropriating the returns (Romer 1990). Alternatively, smaller competitive firms may face more market pressures to innovate (Porter 1990).

Scale at the industry level that is external to firms, but internal within an industry, may also influence labor productivity. Increasing scale that is internal within an industry but not the firm can result from what are commonly known as MAR externalities in a dynamic sense, or localization economies in a static sense. Localization economies will occur if there are scale economies from intraindustry specialization (Moomaw 1986) or labor market economies from reduced search costs for workers with specific skills. Correspondingly, MAR externalities may result from a buildup of local firms in an industry (Romer 1986), which raises future productivity of firms within that industry. To be sure, Ellison and Glaeser (1997) found that all U.S. industries were somewhat geographically concentrated. In addition to the potential role of natural advantages, they argue that the concentration suggests the presence of localization/MAR economies. The existence of localization or MAR externalities can both increase average productivity in all industries (PROD_COMP) or induce a greater concentration in nationally productive industries if externalities particularly occur in them.

Labor productivity also may be enhanced by urbanization economies in a static sense, and by what are commonly referred to as Jacobs economies in a dynamic sense (Jacobs 1969). Urbanization and Jacobs economies are external to the firm and industry but internal within a region. For example, they can result from knowledge or innovation spillovers between industries that may occur with the greater diversity of industries in more populated areas. Closer geographic proximity also may produce pecuniary spillovers through lowering transportation costs of intermediate inputs (e.g., Krugman 1991).

Taken together, we write productivity competitiveness (PROD_COMP) and productivity mix (PROD.MIX) as:

ln[(PROD_COMP).sub.k] = g[((K/L).sub.k], [FIRM.sub.k], [INDUSTRY.sub.k], [URBAN.sub.k], [Z.sub.k]), (7a)

ln[(PROD_MIX).sub.k] = h[((K/L).sub.k], [FIRM.sub.k], [INDUSTRY.sub.k], [URBAN.sub.k], [Z.sub.k]), (7b)

where FIRM, INDUSTRY, and URBAN denote variables representing firm size, economies of scale to industry size, and urbanization economies, respectively, and Z denotes control variables.

3. Empirical Implementation

One concern of previous studies is the difficulty of separating static externality effects from dynamic effects. For example, many studies regress initial levels of the independent variables (e.g., total population) on measures of long-term economic activity and characterize the coefficients as the effects of dynamic externalities (e.g., Glaeser et al. 1992). Yet, contemporaneous values of the independent variables are often correlated with initial values of these variables, making it difficult to sort out static from dynamic effects (a fact that is usually acknowledged in the literature, e.g., Henderson [1997]).(9)

We approach this issue in a two-step fashion. We first regress contemporaneous labor productivity on contemporaneous values of the independent variables using fixed effects estimation. The fixed effects slope estimates derive from within-state time series (or year-to-year) changes in the variables. Thus, the slope estimates should primarily reflect short-term static effects of urbanization, localization, or other factors that affect current levels of productivity. This is most akin to the traditional technique used in regional productivity studies (e.g., Moomaw 1986). Yet, the estimated state fixed effects (dummy coefficients) contain information on persistent productivity differences across states that result from long-run effects of various factors. These effects may relate to resource endowments, cultural influences, and proximity to neighboring states. More importantly, because dynamic externalities (either MAR or Jacobs) are long-term, the fixed effects also may reflect the existence of dynamic externality effects. To explore this, we secondly regress the estimated state fixed effects on the initial values of the independent variables.

Static Externality Equations

Using Equations 7a-b, we write our panel (first-step) regressions as:

[Mathematical Expression Omitted], (8a)

[Mathematical Expression Omitted], (8b)

where t denotes time period; c and m denote competitiveness and mix; [Alpha] represents the intercept; [Beta] a slope parameter; [Gamma], [Phi], [Delta], [Theta] denote vectors of slope parameters; [[Sigma].sub.t] and [[Sigma].sub.l] represent year and state fixed effects; and e and v are stochastic terms. The year fixed effects control for national cyclical and trend effects common across all states in the independent variables (the dependent variables are centered around the national average).(10) The state fixed effects are then used as dependent variables in the second-step regressions discussed below.

Equations 8a, b are estimated using data for the 48 contiguous states from 1972-1986. Capital (K) is total private nonfarm capital, and labor (L) is total private nonfarm employment. Included in FIRM is the natural log of average nonfarm private sector establishment size in the state (Log Avg Firm Size). Included in URBAN is the percent of a state's population that resides in a metropolitan area (%Metro). If urbanization economies are associated with urban population (Moomaw 1983), then an increase in the urban share would be expected to increase labor productivity. For example, increased urban share may be associated with increased density of economic activity, which has been found to explain cross-sectional differences in labor productivity in the U.S. (Ciccone and Hall 1996).

Knowledge spillovers between industries may be particularly associated with the high-tech sector, which may occur when high-tech firms represent best-practice technology. Therefore, we also include in INDUSTRY the percent of private nonfarm employment in high-tech manufacturing (%High-Tech Manu).(11) In Equation 8a, high-tech share is intended to capture innovations or knowledge that spill over from the high-tech sector to other sectors. Note that these spillover effects are separate from a greater effect of the high-tech share in directly changing the productivity mix of the state's industries (i.e., PROD_MIX in Eqn. 8b).

Following Glaeser et al. (1992) and Henderson (1997), a Herfindahl index variable is used to reflect the influence of either within-industry spillovers (INDUSTRY) or between industry spillovers (URBAN). Specifically, the Herfindahl index is a measure of industry diversity or concentration and is calculated as the sum of squares of the percentage of employment in each two-digit private sector industry. Increased diversity (lower Herfindahl) may lead to greater knowledge spillovers between industries, whereas increased concentration (larger Herfindahl) may lead to greater within-industry spillovers. Thus, the sign of the Herfindahl index coefficient indicates whether within-industry spillovers are more prevalent than between-industry spillovers in a static sense.

Control variables (Z) include the percentage of the population over the age of 24 that are high school graduates but not four-year college graduates (%HS Grad), and four-year college graduates (%College Grad). Besides the productivity effects directly associated with a better educated worker, there also may be positive externalities associated with concentrations of educated workers. For example, there may be sharing of knowledge and skills between workers that occurs through formal and informal interactions, making human capital accumulation a group activity (Lucas 1988; Rauch 1993).

Several variables are included as static or cyclical determinants of productivity. First, the percentage of the civilian labor force that are union members is included (%Union). Unions reduce PROD_COMP in Equation 8a if they are associated with rigid work rules; however, if there are union voice effects, productivity is enhanced (Freeman and Medoff 1984). Similarly, by changing relative business costs and altering industry composition, unions may change PROD_MIX in Equation 8b. As a measure of structural change, we include the variance of two-digit employment growth rates each year (Industry Var). A larger variance is likely associated with increased costs of adjusting capacity utilization and labor utilization, reducing productivity. Finally, we include the total annual criminal offenses per 100,000 people (Crime Rate). Higher crime is likely to cause firms to devote significant resources to protection, decreasing total labor productivity. Higher crime also may lead to reduced worker productivity for related reasons or through a psychological toll. In Equation 8b, higher crime may repel high-productivity industries.

Dynamic Externality Equations

The estimated state fixed effects in Equations 8a, b are used as dependent variables in a second set of regressions to examine potential dynamic externality effects:

[Mathematical Expression Omitted], (9a)

[Mathematical Expression Omitted], (9b)

where 72 denotes beginning of period 1972 values. The coefficients in these equations will reveal whether there are persistent growth effects associated with beginning of period conditions (i.e., dynamic externality effects). Most of the same variables used in Equations 8a, b as contemporaneous values to examine static externalities are used as initial values in Equations 9a, b to examine dynamic externalities.

However, the education variables are the only Z variables included because they have the potential for dynamic effects on productivity in addition to contemporaneous effects. In addition, while we account for static urbanization effects (aside from industry diversity) using the percentage of the state's population living in metropolitan areas, we partition this factor into two separate categories in the fixed effect regressions to better identify the sources of dynamic externalities.(12) First, we add the log of the 1972 state population to account for urbanization scale effects, market-size threshold effects, and urban hierarchy effects.(13) Second, the 1972 log state employment per square mile is included to measure employment density or concentration factors (Ciccone and Hall 1996), which may proxy for both closer proximity to different inputs and better information exchange.

4. Empirical Results

Table 1 shows the results of fixed effects estimation of the panel data, which we use to assess static externality effects on productivity. Column 1 contains the unweighted descriptive statistics. For example, it shows that over the 1972-1986 period, the average metropolitan share of the population was

about 60.3%, and the average share of nonfarm employment in high-tech manufacturing was 7.7%. Columns 2-4 present the pooled cross-sectional regression results (using fixed effects estimation) for the log competitiveness productivity index (from Eqn. 8a), and columns 5 and 6 contain the corresponding results for the log industry mix productivity index (from Eqn. 8b). Preliminary analysis suggested significant (within-state) first-order autocorrelation of the residuals (0.5 [less than] [Rho] [less than] 0.6). Hence, all five reported regressions are corrected for first-order autocorrelation using the Cochrane-Orcutt procedure in LIMDEP 7.0, resulting in the loss of the first observation for each state.

Static Externality Results

Competitiveness Productivity

Column 2 of Table 1 shows that the competitiveness productivity index is positively related to capital intensity with a corresponding static elasticity of 0.07. Thus, an increase of one standard deviation in the capital/labor ratio increases the state's competitiveness component of productivity by about 2.5%.(14) Conversely, average firm size was statistically insignificant, suggesting no strong internal return-to-scale productivity effects or possible benefits from more competitive small firms.

There is evidence that static externalities increase the productivity levels of all existing industries. First, regarding urbanization effects, a greater share of the population living in metropolitan areas is positively related to competitiveness productivity. With economic diversity or concentration accounted for with the Herfindahl index, the metropolitan coefficient reflects other effects, such as product market size, closer proximity to markets, or density of production. Yet, the positive and significant Herfindahl coefficient suggests that positive static localization externalities (i.e., within industry) dominate urbanization externalities that result from a diverse range of industries and input suppliers.

The insignificant high-tech coefficient implies that productivity levels of existing firms are not influenced by a greater share of high-tech employment. That is, once industry mix effects are taken into account (PROD_MIX), there is no evidence of information transfers from the high-tech sector that raises productivity for other industries (in a static sense).

Both educational attainment coefficients are positively related to average state productivity in each industry at the 1% level of significance. Unionization, variation in growth rates across industries, and crime rates are statistically insignificant. However, the industry variance coefficient is negative and nearly significant at the 10% level, weakly suggesting that reallocating labor across sectors may produce training problems or create imperfect labor force utilization rates (Lilien 1982).

Although not always considered in productivity studies, the model in column 3 of Table 1 considers whether employment growth influences contemporaneous levels of productivity. For example, faster economic growth may allow firms to fully utilize both their capital resources and publicly provided capital (or over-utilize them). Correspondingly, faster growth may be associated with increased market size and improved access to markets (Mullen and Williams 1990). Notwithstanding, greater hiring may reduce the average quality of the applicant pool, reducing current productivity levels.

[TABULAR DATA FOR TABLE 1 OMITTED]

An empirical concern with the model, shown in column 3 of Table 1, is that above (below) average levels of productivity can in turn affect business location and employment growth, which could bias the coefficients. This possibility is tested with a Hausman test. The null hypothesis is that any potential endogeneity of employment growth is not biasing the coefficients. The bottom of column 3 shows that the null hypothesis can be rejected (5% level), suggesting that two-stage least squares (2SLS) should be used. Thus, the results in column 3 reflect the use of 2SLS treating employment growth as endogenous.(15)

The 2SLS results show that employment growth is positively related to labor productivity. The positive coefficient suggests that in a tight labor market characterized by strong employment growth, productivity gains could somewhat offset wage increases to moderate price effects, which may be one explanation for the relatively low inflation rates during the latter 1990s. Most of the other results are basically unchanged except for the college graduate coefficient losing some statistical significance and the variance of industry growth measure becoming significant at the 10% level.

Another possible concern is that the capital/labor ratio may be endogenous. If so, it is not clear in which direction its coefficient is biased. For example, higher average worker productivity due to human capital may reduce the demand for capital, but a more productive labor force may attract more capital to a state. Yet, given that we do not have suitable exogenous instruments for capital, we re-estimated the model shown in column 4 of Table 1 by omitting the capital/labor ratio from the equation. Regarding capital intensity, this model is akin to treating capital/labor in a reduced-form fashion.(16) Generally, the coefficients in column 4 are similar to those in column 3, suggesting little if any bias (although there were modest changes in the values of some of the t-statistics).

Industry Mix Productivity

The log industry mix productivity index for each state is the dependent variable in the models shown in columns 5 and 6 of Table 1. Except for the omission of the capital/labor ratio due to endogeneity concerns, the model in column 5 corresponds to the competitiveness model in column 2.(17) Likewise, the model in column 6 corresponds to the competitiveness model in column 4.

Because both sets of productivity mix results are similar, the 2SLS findings in column 6 of Table 1 will be emphasized.(18) The support for static externality effects on industry composition is weaker, which is not surprising since industry composition likely changes more gradually (suggesting more of a dynamic process) than the time it takes productivity effects to be realized in existing industries. Nevertheless, if one is willing to accept the 20% statistical significance level (two-tail test) as evidence, there is some indication that larger average firm size leads to a more productive mix of industries. Likewise, the negative coefficient on the metropolitan share coefficient suggests that certain urbanization effects do not play a role in attracting a productive industry mix (in a static sense), where perhaps urban congestion effects dominate. However, the negative coefficient on the Herfindahl index weakly suggests that industry diversity is conducive to attracting a productive industry composition, which is consistent with certain urbanization effects overwhelming localization effects. Finally, even at the 20% level, there are no static advantages of having a greater share of high-tech manufacturing employment.

The educational attainment variables are positively and significantly related to a state's productive mix at the 1% level. The crime rate was negatively and significantly related to industry mix productivity, suggesting that industries with high average levels of productivity avoid locating in areas with high crime rates. Finally, productivity mix is positively related to employment growth (at the 1% level), perhaps due to market proximity effects. Thus for expanding areas, there may be a virtuous cycle of faster employment growth increasing productivity, which in turn stimulates further employment growth.

Given that a state's log total productivity equals the sum of the mix and competitiveness components (see Eqn. 6), adding the coefficients in columns 4 of Table 1 to those in 6 illustrates each variable's total static effect on average labor productivity. Some variables have a reinforcing effect on total productivity, whereas other variables have an offsetting effect. For example, the metropolitan results suggest that static urbanization effects raise productivity for all of the state's existing industries (column 4), but these urbanization effects tend to (weakly) attract a mix of industries with lower than average productivity (column 6). Likewise, the offsetting Herfindahl results are consistent with competitiveness productivity being favorably influenced by localization economies (column 4), but the productivity mix of industries being more affected by diversity effects (column 6). Perhaps the offsetting effects for urbanization and localization economies explain the ambiguous results found when only considering total productivity (or employment) in the previous literature, which points to the advantage of our productivity decomposition.

Dynamic Externality Results

The state fixed effects associated with the models in Table 1 reflect persistent differences in productivities (over the 1973-1986 period) that result from long-run processes (since short-term static effects should be netted out in the first-step regressions). Endogenous growth models with dynamic externalities hypothesize that particular historical or initial conditions should influence productivity for long periods of time, especially those conditions associated with MAR and Jacobs externalities (Glaeser et al. 1992; Henderson, Kuncoro, and Turner 1995). To examine this possibility, Table 2 presents results using the state fixed effects from the models [TABULAR DATA FOR TABLE 2 OMITTED] shown in columns 3 and 6 of Table 1 as dependent variables. For ease of comparison, each state's fixed effect is differenced from the national average fixed effect. The corresponding independent variables are the initial 1972 measures associated with dynamic externalities.(19)

Column 1 of Table 2 shows the descriptive statistics. For example, the standard deviation of competitiveness productivity across states are about 9% due to state fixed effects, whereas the corresponding standard deviation for industry mix productivity is about 12%. Column 2 presents the competitiveness state fixed effect results using the state fixed effect regression coefficients from the model reported in column 3 of Table 1. Column 3 of Table 2 presents the industry composition state fixed effect results using the state fixed effect regression coefficients from the model shown in column 6 of Table 1. Table 2 reports White heteroscedasticity-corrected t-statistics because the dependent variable consists of predicted state fixed effects, which can introduce heteroscedasticity of an unknown form.

The results in Table 2 suggest that those states with a greater initial capital/labor ratio had a higher concentration of more productive industries (column 3) and higher long-run labor productivity in all industries (column 2) (significant at the 1% level). The high-tech manufacturing share coefficient is negative and insignificant (at the 10% level) in the competitiveness state fixed effect model (column 2), but positive and significant in the industry mix state fixed effect model (column 3). This suggests that a greater initial high-tech concentration is conducive to attracting more high-productivity industries in the long run, perhaps due to a threshold or cluster effect in the labor market. Yet, a greater initial high-tech share did not increase relative long-term productivity for all industries, suggesting few long-term knowledge spillovers to other industries. Taken together with the insignificant (static) high-tech coefficients in Table 1, it appears that there are little short-term gains from government policies aimed at attracting high-tech industries, but there may be long-term gains in attracting high-productivity industries if a state can achieve a certain threshold (consistent with Henderson, Kuncoro, and Turner 1995).

The insignificant Herfindahl coefficients in columns 2 and 3 of Table 2 suggest that neither MAR localization economies nor (Jacobs) diversity economies dominate in a dynamic sense. Similarly, average firm size does not dynamically affect productivity. The college education coefficients are both insignificant. The high school coefficients are both negative, but only significant in the productivity mix fixed effects model. This somewhat surprising pattern suggests that education's positive effects on productivity are more immediate, without any persistent residual effects.

The log state population coefficient is positive and significant in the competitiveness model in column 2, but insignificant in the mix model in column 3. Thus, greater initial population appears to have persistent average productivity effects over all industries but does not have any long-term influence on the productivity mix of industries that locate in the state. This market-size result generally accords with the findings of Henderson, Kuncoro, and Turner (1995). The initial employment per square mile is positive and significant (at least at the 10% level) in both models. That is, greater employment density raises the long-run productivity of all industries, as well as attracting a more productive mix of industries in the long-term. With industry diversity and concentration accounted for (Herfindahl), these results are consistent with positive productivity effects resulting from increased contacts between workers, greater access to specialized labor, and reduced transportation costs (Krugman 1991). Summing the two model's population size and employment density coefficients together suggests that employment density has a greater effect on long-term total productivity than state size. This supports the findings of Ciccone and Hall (1996). Yet the benefit of our approach is that we determined that employment density's primary advantage - compared to state size - is through attracting a productive mix of industries.

The high [R.sup.2] coefficients (respectively, 0.52 and 0.77) support our interpretation of the state fixed effects reflecting persistent factors such as dynamic externalities. Nevertheless, for further support we included three public policy variables in both models to see if government policies explain the fixed effects results (not shown). Specifically, we included a dummy variable for right-to-work state, average 1973-1986 state and local welfare expenditures as a share of personal income, and average 1973-1986 state and local taxes as a share of personal income. These variables are often viewed as indicators of a business-friendly environment. Except for the tax variable in the competitiveness regression, the policy variables were nowhere near statistically significant, supporting our contention that dynamic externalities primarily underlie the state fixed effects.

5. Conclusion

Using panel data for the 48 contiguous U.S. states, we examined the potential link between externalities and state labor productivity. In the analysis, we separated state productivity differences into those due to its composition of industries and those due to average productivity differences in each industry. Moreover, we separated externalities into static externalities (those that have more immediate effects) and dynamic externalities (those that persist or take longer to unfold).

A primary finding is that static localization externalities, as measured by industry specialization, dominated static economic diversity externalities. Also in a static sense, increased urbanization through a higher metropolitan population share led to increased average productivity across all industries (effects not related to diversity of urban areas), but this was offset by a less productive composition of industries.

In the long run, consistent with the conclusions of Glaeser et al. (1992), Jacobs dynamic externalities appear more important than MAR dynamic externalities. Dynamic externalities across all industries appeared related to employment density and population size. However, only initial employment density was associated with a more productive long-run industry composition. Neither initial-period industry diversity nor initial-period industry specialization dominated regarding dynamic effects. Despite no evidence of high-tech productivity spillovers to other industries in the near- or long-term, a state's initial share of high-tech industries appeared to influence its composition of productive industries in the long run.

Appendix

Crime Rate: Various issues of the Statistical Abstract of the United States.

Employment-based Variables - Total private nonfarm employment, Employ Grth, Labor (L), Industry Var, Herfindahl: U.S. Bureau of Economic Analysis.

Gross State Product: For years 1977-1986, see Trott, Dunbar, and Friedenberg (1991), and for the earlier years, see Renshaw, Trott, and Friedenberg (1988).

%High-Tech Manu: Manufacturing industries classified as high-tech are from the U.S. Department of Commerce classification given in the 1993 Statistical Abstract of the United States. Employment in these sectors are used to calculate the high-tech employment shares.

%HS Grad, %College Grad: U.S. Department of Commerce Census of Population 1970, 1980, and 1990. Values for years between censuses are obtained through linear interpolation.

Log Avg Firm Size: U.S. Department of Commerce County Business Patterns Data.

%Metro, 1972 Log State Pop: U.S. Department of Commerce.

Private Capital (K), Public Capital: Munnell (1990).

State Land Area: 1993 Statistical Abstract of the United States.

%Union: U.S. Department of Commerce and Hirsch and Macpherson (1993).

This paper benefitted from comments by an anonymous referee and individuals attending presentations at the Federal Reserve Bank of Dallas, Oklahoma State University, the Southern Regional Science Association Meetings in Savannah, Georgia, the University of Strathclyde, and the University of Wyoming. Particular thanks go to Steve Brown, Shelby Gerking, Chuck Mason, Ron Moomaw, Edward Nissan, Jamie Partridge, and Lori Taylor.

1 Romer (1994) contains a discussion of the endogenous growth literature.

2 Henderson (1997) refers to these unobserved factors as location fixed effects that arise from the region's history. He lists such effects as regional resource endowments; cultural influences on legal, political, and institutional arrangements; and skill-specific immobile portions of the labor force.

3 National and international studies have additional difficulties in observing externalities associated with geographic concentration (Pack 1994).

4 There is ambiguity in the literature regarding the terminology for dynamic and static externalities. In what follows, we generally follow the terminology used by Glaeser et al. (1992) and Henderson, Kuncoro, and Turner (1995), although even here some ambiguity remains.

5 As Moomaw (1983) notes, regional comparisons of productivity either assume constant returns to scale and attribute the labor productivity differences to total factor productivity differences or assume uniform total factor productivity and attribute the labor productivity differences to differences in returns to scale. Similarly, growth accounting studies (e.g., Hulten and Schwab 1984) assume that inputs are paid their marginal revenue products and constant returns-to-scale to estimate total factor productivity.

6 National and regional productivity studies have relied exclusively on industry aggregations of firms and often national or regional aggregations of industries. Yet as Fisher (1969) demonstrates, conditions required for aggregation of firm production functions are extremely restrictive and unlikely to be met in reality. For example, even the case of homogeneity of outputs and inputs across firms does not necessarily allow aggregation. With heterogeneity, aggregation is theoretically supported if all firms are restricted to additively separable production functions. And given heterogeneous capital and nonadditively separable production, aggregation can occur if constant returns to scale are assumed and technical differences across firms augment capital. Despite the restrictive nature in these examples, Fisher (1969) acknowledges that aggregate production functions often give good results, possibly because other unidentified factors reduce the dimensionality of the problem.

7 Moomaw (1998) shows that two-digit-level data do not exaggerate estimated regional productivity differences when compared to three-digit-level data, such that estimates of localization and urbanization are not sensitive to the level of industry aggregation.

8 This is akin to the commonly used shift-share decompositions of regional aggregates, such as employment and wage rates, found in other studies (e.g., Partridge and Rickman 1995). In this manner, we also employ shift-share terminology by referring to industry mix and competitiveness effects.

9 A related problem in growth studies occurs when attempting to estimate the rate of convergence between low-income and high-income states and nations (Evans 1997).

10 Note that K/L is not included in Equation 8b because it is likely to be influenced by industry mix (i.e., Eqn. 8b is a reduced form). For example, both the capital/labor ratio and average productivity are greater in a state with a large aircraft industry than in a state with a large beautician industry. Because K/L and PROD_MIX are so closely interrelated, including K/L would cause endogeneity problems in econometric estimation, although we relax this assumption in sensitivity analysis.

11 Manufacturing industries classified as high-tech are from the U.S. Department of Commerce classification given in the 1993 Statistical Abstract of the United States.

12 In both cases, the initial 1972 capital/labor ratio is included to control for persistent effects of capital intensity, which may include "embodied" technological progress. Unlike the pooled time series cross-sectional models, we are less concerned with direct endogeneity in the state fixed effects models because the 1972 capital/labor ratio was determined prior to the 1973-1986 fixed effect.

13 We also experimented with the log of the 1972 population of the state's largest SMSA. Generally, the results for this variable were similar to the results for state population, but using state population resulted in a better fit.

14 Experiments were also conducted by adding the log of per capita highway public capital and the log of per capita public capital net of highways. Highway public capital was negatively related to competitiveness productivity and positively related to industry mix productivity, where it was statistically significant in both cases. Other public capital was statistically insignificant in the competitiveness regression and negative and significant in the productivity mix regression. Given this counterintuitive pattern, we did not pursue public capital effects further, although it should be noted that negative public capital effects on productivity have been found in other studies (e.g., Holtz-Eakin 1994).

15 The Hausman test uses the predicted value of employment growth from the first-stage regression, where the test statistic is the t-statistic on the predicted employment growth variable when it is included as an additional variable in the productivity ordinary least squares regression. The exogenous instrument is the industry mix employment growth rate, which is the state's employment growth rate if all its industries grew at their respective national average growth rates (i.e., it shows whether the state has a fast or slow growing mix of industries and has often been used as an exogenous instrument for employment growth [Bartik 1991]). As expected, the industry mix coefficient t-statistic in the first-stage regression was 13.8 (not shown), suggesting it

is a good instrument (Bound, Jaeger, and Baker 1995). We also examined whether industry mix is improperly omitted as a variable in the second-stage regression by using an artificial regression technique (MacKinnon 1992). These tests suggested that the industry mix employment growth rate was properly omitted in the second stage.

16 By comparison, Ciccone and Hall (1996) substituted capital out of their state labor productivity model by assuming that the price of capital was identical across states. More typically, the influence of capital is ignored in recent regional studies of "new" growth models.

17 To examine the sensitivity of the results, we re-estimated an industry mix productivity model that included the capital/labor ratio, in which the capital/labor coefficient and t-statistic were almost zero, and the other results were virtually unchanged.

18 The Hausman test statistic at the bottom of column 6 of Table 1 indicates that potential endogeneity of employment growth also may bias the productivity mix results. Thus, we utilize 2SLS, where industry mix employment growth is the exogenous instrument. The artificial regression technique discussed in footnote 15 suggested that the industry mix employment growth rate was properly omitted in the second-stage model.

19 It is possible that the control variable coefficients in Table 1 may have captured some of the long-term effect of the state fixed effects. This suggests that the fixed effect regressions in Table 2 may understate the influence of dynamic externalities. Likewise, using the estimated fixed effects introduces measurement error in the dependent variable of the regressions in Table 2. This does not bias the resulting variable coefficients, yet it can bias the t-statistics toward zero.

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Mark D. Partridge, Associate Professor of Economics, Department of Economics, Stewart Hall, St. Cloud State University, St. Cloud, MN 56301-4498, USA; E-mail [e-mail].

Dan S. Rickman, Professor of Economics and OG&E Chair in Regional Economic Analysis, Department of Economics and Legal Studies, 303 College of Business Administration, Oklahoma State University, Stillwater, OK 74078, USA; E-mail [e-mail]; corresponding author.