Local Economic Structure and Growth

Transcription

1 Local Economic Structure and Growth Rita Almeida World Bank Research Department 21 September 2006 Abstract This paper tests how the local economic structure - measured by local sector specialization, competition and diversity - affects growth of manufacturing sectors. Most of the empirical literature assumes that in the long run more productive regions will attract more workers and use employment growth as a measure of local productivity growth. However, this approach is based on strong assumptions, such as those of national labor markets and homogenous labor. This paper shows that if we relax these assumptions, regional adjusted wage growth is a better measure of productivity growth than employment growth. I use this measure to study regional growth in Portuguese regions between 1985 and I find evidence of MAR externalities in some sectors and no evidence of Jacobs or Porter externalities in most of the sectors. These results are at odds with the findings for employment based regressions, which show that regional concentration and the region s size have a negative effect in most of the sectors. I also show that simply using regional wage growth would overstate the effect of regional concentration and competition on long-run growth. Keywords: Local Growth, Knowledge spillovers and Productivity. JEL Classification codes: R11, R12, O47. I am very grateful to Antonio Ciccone for his guidance and to Pedro Carneiro for several comments. I also thank an anonymous referee for several comments that significantly improved the paper. I thank the Economics Department at Universidade do Minho, Braga, and the Ministry of Employment for access to the data and to Ignácio Garcia, Jaume Garcia, Adriana Kugler and Rosella Nicolini for useful comments. I acknowledge the financial support of Fundação para a Ciência e Tecnologia and of the CEPR Research Training Network Specialization versus Diversification. Address: 1818 H Street, NW, Washington DC US. ralmeida@worldbank.org. 1

2 1 Introduction An important topic in economics is understanding the contribution of agglomeration economies and competition for local growth. Even though this is an old debate, most of the empirical work on this topic is fairly recent. The importance of scale economies in explaining the agglomeration of economic activity was first recognized by Marshall (1890). The idea behind this concept is that it would be beneficial to locate where other firms in the same sector already produce, for reasons such as the availability of intermediate goods, of specialized labor force, the existence of a large product demand or the diffusion of knowledge in the local environment. Recently, the literature on endogenous growth models emphasizes the role of dynamic information externalities as a driving force for technological innovations and, hence, for economic growth. According to this literature, the accumulation of knowledge in the geographical area, is a key driving factor for current productivity growth. Marshall (1890), Arrow (1962) and Romer (1986) argue that the most important externality derives from a buildup of knowledge associated with communications among local firms in the same sector (MAR externalities). Sector concentration in a region helps knowledge spillovers between firms and, therefore, that sector s growth in the region. This theory also predicts that local monopoly benefits growth as it restricts the flow of ideas to others and allows externalities to be internalized by the innovator. Alternative theories such as Jacobs (1969) have focused on the importance of the cross-fertilization of ideas across different sectors to promote innovation and growth (Jacobs externalities). According to this theory, more diversity in the region causes higher sector growth. Porter (1990) argues that local competition speeds up the adoption of technology. Several firms located together will intensely compete to innovate since the alternative to innovation is demise (Porter externalities). Since productivity growth is not directly observed, economists have tried to find proxies for it. Most of the empirical literature that tried to assess which type of externalities would be more favorable to local productivity growth has used employment growth to proxy for productivity growth. This measure is based on the assumption that labor is an homogeneous input and that it can freely move across the country so that, in the long-run, the more productive regions would attract more workers. These are reasonably strong assumptions since labor is a very heterogeneous input and, during this period, migration costs tend to be higher in Europe than in the US. The findings in these papers using employment growth as a proxy for productivity growth are mixed. Glaeser et al. (1992) and Peri (1992) find that 2

3 local competition and urban diversity, but not regional concentration, foster employment growth in the U.S. and Italy, respectively. Combes (2000), finds evidence for France that concentration and diversity negatively affect employment growth in several sectors. Henderson et al. (1995) find evidence of MAR externalities for the traditional capital goods industries, and of Jacobs and MAR externalities for new high-tech industries using data for the U.S. 1. However, using employment growth to proxy for productivity growth requires strong assumptions since employment and productivity growth need to positively covary across regions. For example, if there are local labor markets and labor supply shifts differently across regions (caused, for example, by labor migration), employment and productivity growth do not necessarily covary. Moreover, if in some sectors technological growth is labor biased, productivity growth may not translate into employment growth. 2 A more direct approach to this problem is to estimate total factor productivity growth from firm or regional level data. This approach is implemented with micro data by Henderson (2003) and Cingano and Schivardi (2004). 3 Henderson (2003) finds that increasing sector concentration in the region where a plant is located increases productivity in high tech sectors (though not in machinery industries). Cingano and Schivardi (2004) also find evidence of MAR externalities for productivity growth and no evidence of a positive effect of competition or diversity on local growth. This finding is at odds with the results obtained with employment regressions, which show that sector concentration is associated with higher local growth. However, the scarcity of time series data for the stock of capital with a sector and regional disaggregation for a sufficiently long period make this approach difficult to implement. 4 In this paper I assume local labor markets and heterogeneous labor and derive an alternative measure of productivity growth. Assuming that technological change is labor biased, this measure can be easily computed adjusting the regional wage growth with some weights which are a function of the regional 1 Glaeser et al. (1992) and Henderson et al. (1995) both use data for the US and reach different conclusions. However, they analyze different time periods and the samples are constructed in different ways. In Glaeser et al. (1992) the sample includes only the six largest sectors for each city and, therefore, all sectors included have an initially high degree of concentration. Furthermore, non-manufacturing sectors such as wholesale and retail trade are heavily represented, while in Henderson et al. (1995), these are not included. 2 The change in employment growth might also be smaller than the increase in labor demand if there are congestion externalities such as air pollution shifting labor supply and labor demand simultaneously. Also, if the demand for output is very inelastic in some sectors, increases in productivity may translate into a small increase in labor demand since firms become able to produce more output with the same labor, and there may be reductions in the sector s employment in that region. I thank Antonio Ciccone for pointing this out. 3 Henderson (2003) estimates a plant level production function including concentration measures as explanatory variables. On the other hand, Cingano and Schivardi (2004) estimate total factor productivity growth from the Solow residual and aggregate it to the regional level. This measure is then regressed on variables capturing different types of externalities. 4 Some papers have used alternative measures of productivity (e.g., labor productivity). In general, the evidence tends to be favorable to the importance of MAR externalities (e.g., Lucio et al., 2002). One exception is Gao (2003) that uses output growth has a measure of productivity growth. 3

4 skill composition. When the skill composition is constant across regions, this measure becomes simply the regional wage growth. Unfortunately, not all the problems of using regional employment growth as a proxy for productivity growth are addressed with the measure proposed in the paper. These are the problems generated by congestition externalities arising from agglomeration economies (e.g. pollution) or from the low demand elasticity in some product markets. I use the Portuguese census of manufacturing plants between 1985 and This data collects information for each plant on employment and wages for different types of workers. With the regional adjusted wage growth I find evidence of MAR externalities in some sectors and no evidence of Jacobs or Porter externalities in most of the manufacturing sectors. 5 Furthermore, simply using the regional wage growth (and hence neglecting the adjustment that comes from the assumption of heterogeneous labor) wouldleadustooverestimatetheeffect of regional concentration and competition on growth. Finally, these results are at odds with those for employment based regressions where concentration and region size has a negative and significant effect in most of the sectors. The paper is organized as follows. In section 2, I analyze different models where employment and productivity growth do not necessarily covary and I derive proxies for productivity growth. Sections 2.1 and 2.2 discuss the implications of having a local labor market and heterogenous labor, respectively, and Section 2.3 considers a constant return to scale technology with labor biased technological change. Section 3 describes the data. Section 4 describes the indices used to measure the local economic structure and presents the reduced form equation that is estimated. The empirical findings for alternative measures of productivity growth are presented and discussed in section 5. Section 6 concludes. 2 Theoretical Models As seen above, different theories argue that different local characteristics (as sector concentration, diversity or competition) are important in driving local knowledge accumulation. I follow most of the empirical literature and assume that the impact of the local economic structure on growth works mainly through knowledge spillovers (externalities). Nevertheless, the reduced form equation that will be estimated is also compatible with alternative explanations. In particular, some agglomeration forces operate directly 5 I find evidence that concentration fosters productivity growth for Food, Beverages and Tobacco, Basic Metals and Equipment. Regional competition increases productivity only in Chemical Products. 4

5 through markets. Krugman (1991), Krugman and Venables(1995), Fujita and Thisse (1996) present models where natural advantages and local market conditions, together with transportation costs and increasing returns to scale, generate regional specialization Local Labor Markets For simplicity, I assume that there is only one sector of activity. The good produced in region r, Y r, is sold in a national market and is produced with a sector specific labor input, L r. 7 The production function for each region is Cobb-Douglas with decreasing returns to labor: Y r = A r L α r, where A r is total factor productivity in region r and α is constant across regions (α < 1). 8 Labor is an homogeneous input and labor markets are competitive so that each firm takes the real wage, w r, as given (infinitely elastic labor supply curve). 9 The first order condition with respect to labor is given by: αa r L α 1 r = w r L r = αar w r 1 1 α Taking growth rates, A r = w r +(1 α) L r. (1) A standard assumption in the empirical literature is that labor can freely move across regions so that in the long run wage growth is equalized across regions (national labor market) even though initial wage levels might differ (e.g., Glaeser et al., 1992). The regional difference in wage levels is meant to capture that individuals might trade-off lower wages for being in regions with less crime or pollution. Under this assumption, w r = w, and(1)canbewrittenas: L r = 1 Ar w 1 α (2) 6 Ciccone and Hall (1996) show how different models (knowledge spillovers and market based forces) can result in the same reduced form equation. 7 For simplicity I assume that the stock of physical capital does not enter the production function. I relax this assumption in section For simplicity I start from a regional level production function instead of a firm level production function. As long as the tecnhology is constant returns to scale, every firm has the same tecnhology and all the firms in the same regions face thesamefactorpricesthisprocedureisvalid. 9 This is the assumption in most of this literature that models only the demand side of the labor market. 5

6 In this case, local employment growth is proportional to local productivity growth. 10 Figure 1 illustrates this point for the case where initial wage levels are thesameacrossregionsandwagegrowthispositive and constant across regions ( w r = w = 0) 11. Let different regions have initially the same A r = A and, therefore, the same labor demand schedule, D(A). Assume that all the regions face the same labor supply so that (L, W ) is the initial equilibrium for all the regions. Suppose that labor supply shifts from W to W in all the regions and that in some regions labor demand is higher because there is technological growth (labor demand shifts from D(A) to D (A )) and in other regions labor demand is lower because there is a technological contraction (labor demand shifts from D(A) to D (A )). This figure shows that even though there is a common shift in labor supply across regions and both regions have a reduction in employment, the A region has a smaller employment reduction than the A region. Under these assumptions, A and L will be positively correlated across regions. However, the assumption that labor can freely move across regions so that in the long run wage growth is equalized across regions is quite strong. If migration costs are sufficiently high ( e.g., high transportation costs or a stagnant real estate market) labor will not move to equalize wage growth across regions. Figures 2a to 2c illustrate that the simple one-to-one link between A and L is broken if wage growth is not constant across regions. Assume the initial equilibrium is the same across regions, (L, W ). Let the labor supply shift differently across regions, from W to W. I assume that there is technological growth in regions I and III and a technological contraction in region II. Thefinal equilibrium in regions with a technological expansion is characterized by either more employment (region I) or less employment (region III). In region II the technological contraction generates more employment. In this case, there is no longer a positive correlation between A and L. Hence, under the assumption of local labor markets, a better measure of productivity growth is given by equation (1), where both employment and wage growth capture the change in A. 2.2 Heterogeneous Labor I now introduce in the previous model different types of labor. I still assume that the production function for the region-sector is Cobb-Douglas and that there are decreasing returns to two types of labor, L 1r 10 Wage growth is constant across regions and would be captured by the intercept of a regression of L r different local characteristics. 11 The argument does not depend on the assumption that wage levels are constant across regions but it simplifies the intuition. 6

7 and L 2r : Y r = A r L α 1 1r Lα 2 2r,withα 1 + α 2 < 1. Aggregate labor in the region is L r = L 1r + L 2r. L 1r and L 2r are hired at wages w 1r and w 2r. This implies that the average wage in the region is given by: w r = L1r L r w 1r + L2r L r w 2r. The maximization problem of the firm is given by: Max L1rL 2r A r L α 1 1r Lα2 2r w 1r L 1r w 2r L 2r (3) Taking growth rates from the first order conditions with respect to L 1r and L 2r we get that: Â r =(1 α 2 )ŵ 1 + α 2 ŵ 2 +(1 α 1 α 2 )ˆL 1r (4) Â r =(1 α 1 )ŵ 2 + α 1 ŵ 1 +(1 α 1 α 2 )ˆL 2r (5) If wage growth is constant across regions (w 1r = ŵ 1 and w 2r = ŵ 2 ) these two equations are similar to equation (2). In this case, employment growth of either L 1r or L 2r can be used to proxy for productivity growth. However, notice that using the aggregate employment growth, instead of ˆL 1r or ˆL 2r, would generate a different measure. Recall that ˆL r = L1r L r L 1r + L2r L r L 2r. Replacing the value for L 1r and L 2r from equation (4) and (5) into L r we get: 1 ˆL r = 1 α 1 α 2 Â r ŵ 1r (1 α 2 ) L 1r L r L 2r L 1r + α 1 ŵ 2r α 2 L r L r +(1 α 1 ) L 2r L r From the expression above it is clear that, even if wage growth is constant across regions, aggregate employment growth is not a good proxy for productivity growth as long as regions differ in their skill composition. If regions differ in their relative wages between the two types of labor, they will end up with a different skill mix. In this case, wage growth needs to be adjusted by a term that depends on these regional skill differences. The intuition for the adjustment in in the regional wage growth that I will use in the empirical section is already present in this model. 2.3 Labor Biased Technological Change As argued above, one of the reasons why employment growth may be a misleading measure of productivity growth is because technology growth might be labor biased. Under this assumption, a positive 7

8 productivity shock in a region might lead to a reduction in the total labor demand, so that productivity growth and employment growth do not necessarily covary. 12 In this section, I develop a measure for productivity growth under the assumptions of labor biased technological change and assuming, as before, local labor markets and labor is an heterogeneous input, imperfectly substitute in the production function. Let the production function be given by Y r = F (K r,g(a 1r L 1r,A 2r L 2r,..., A Nr L Nr ), where F (.) and G(.) are constant returns to scale functions, L rk are different types of labor, and A k are different types of technological change. 13 The first order conditions for capital and labor and the assumption of constant returns to scale in G(.) and K yields: F 1 (K r,g r )=i K r G r = h(i) (6) F 2 (K r,g r )=w r F 2 ( K r G r, 1) = F 2 (h(i), 1) = w r (7) where w r is the minimum cost of producing one unit of G r, i.e. is the solution to the problem: w r = Min L1r,L 2r,...,L Nr w r1 L r1 + w r2 L r w rn L rn s.t. G(A 1r L 1r,A 2r L 2r,..., A Nr L Nr ) 1 This minimum cost function can be written as: w r = w r ( w 1r A 1r, w 2r A 2r,..., w Nr A Nr ) where w r (.) has constant returns to scale and the elasticities with respect to each argument equal to the cost share, i.e., the wage payments to workers of type k over total wage payments: α kr = w krl kr w rl r, where L r = L 1r + L 2r L Nr and w r = K L w kr kr L r. Differentiating the minimum cost function and using equation (6) yields, k=1 α 1r ( w 1r A 1r )+α 2r ( w 2r A 2r ) α Nr ( w Nr A Nr )=φ( i) (8) 12 In appendix A I derive this result. 13 I specify a production function at the regional level. The implicit assumption is that there may be agglomeration economies at the regional level but that these are not internalized by firms. In their maximization problem, firms take A as given so technology is constant returns to scale. At the regional level though, there are increasing returns to scale because A is a function of regional labor. There is an externality, common in the models implicit in most of the empirical work, which is not internalized by the firm. Alternatively, in Krugman (1991) like models firms decide based on the agglomeration economies and have an incentive for agglomeration. 8

9 α 1r A 1r + α 2r A 2r α Nr A Nr =[α 1r w 1r + α 2r w 2r α Nr w Nr ] φ( i) (9) where φ( i) = i F 2 (h(i),1) F 2(h(i),1) h(i) h i î. Differentiating w r with respect to time yields: w r = K k=1 w kr w kr L kr w r L r + K k=1 L kr L r w kr L kr w r L r w r = K w kr α kr + K k=1 k=1 L kr L r α kr. where α kr = w krl kr w rl r. Replacing this expression into equation (9) yields, α 1 A 1 + α 2 A α N A N = w r K k=1 L kr α kr φ( i). (10) L r where by assumption, the growth in the real interest rate is constant across regions. The expression above shows that, if the technology is constant returns to scale and has a labor biased technological change, regional productivity growth can be proxied by regional wage growth adjusted by a term that is a function of the skill mix across regions. 14. This measure can be easily computed with regional information on wages and employment of different labor types. As long as regions have different wage K L levels (and hence different skill compositions), the adjustment term, kr L r α kr, in equation (10) will not be constant across regions, and the measure proposed will differs from the regional wage growth. However, if the skill mix is the same across regions or if labor is an homogeneous input (α r = α =1), productivity growth is simply given by the regional wage growth. As seen in section 2.1, the hypothesis implicit in those models that use employment growth as a proxy for productivity growth, is that labor is mobile across regions so that w r = w. Thisimpliesthat, if wage growth is higher in one region than in other, labor would migrate until regional wage growth is equalized. It is worth stressing that the theoretical model developed is consistent with several migration models. The labor migration flows might, or not, equalize regional wage growth. Notice that when k=1 14 I thank an anonymous referee for pointing out that this measure cannot be easily computed under the assumption of constant returns to scale with factor neutral technological change. I develop this case in annex B. There φ(.) is also a function of productivity growth and the equivalent to equation (10) becomes non-linear in  r. 9

10 deriving equation (10), I never use the hypothesis that w kr = w k. However, in my empirical application, wage growth differs across regions in the period considered. This finding is consistent with significant restrictions to labor mobility across regions. 3 Data Iusethedataset,Quadros do Pessoal, that is based on an annual mandatory survey for all the firms operating in Portugal. The survey is conducted by the Portuguese Ministry of Labor. Each firm reports information on their plants and workers. 15 For each plant there is information on the sector of activity, regional location and its total size (measured by the number of employees). There is also information on the labor costs and some labor force characteristics for each worker in the plant. 16 The analysis will cover the period The sector classification used is the three-digit ISIC sectors. 18 The original data has 123, 294 and 214, 047 plants and 1, 8 million and 2, 2 million workers in 1985 and 1994, respectively. Due to the well known problems of estimating productivity in nonmanufacturing I restrict the analysis to manufacturing sectors (e.g., Griliches, 1994). To account for labor heterogeneity in the construction of the productivity measure, I construct different labor categories based on education and potential experience in the labor market (computed for each individual as age-years of schooling-6). I consider 8 education groups - workers with 1 or less years of schooling, 1-4 years, 4-6 years, 6-9 years, 9-12 years,12-14 years, years and 16 or more years - and 4 experience groups - less than 1, 1-5 years, 5-15 years and more than 15 years of schooling. This gives me a total of 32 different labor categories. For a given year, I classify each worker into one of the labor categories defined. Then I compute the average wage and the total labor size of each labor category in the region-sector Except those firms without wage-earnings employees and Public Administration. 16 Even though the survey collects information at the plant and firm level, the analysis in this paper is performed at the plant level. The objective is to estimate the effect of the local economic structure on regional growth. Using information on firms rather than plants, would misleadingly attribute all the changes in employment to the region where the firm headquarters is located. 17 In 1994 the classification of economic activities changed to match the European Community criteria and the correspondence between the two classifications is not unique. 18 These three-digit sectors can be grouped into the following two-digit sectors: Food, Beverages and Tobacco, Textiles and Clothing (includes textiles, clothing and leather products), Wood and Pulp (includes wood, pulp and furniture), Paper and Publishing, Chemicals (includes chemicals, oil and coal derivatives, rubber and plastic), Non-Metallic Mineral Products (includes porcelain, clay and glass), Basic Metals (includes steal and iron), Equipment (includes machinery, electronics, high-precision instruments, transports and transport material). 19 Notice that, over the period of 10 years, each individual will change categories simply because he/she become older and with higher potential experience. Nevertheless, all the analysis is performed at the regional level. 10

11 An important issue is the choice of the geographical unit. The location specific knowledge of a firm can be specific to the city, to the district or to another geographical unit, depending on the type of knowledge considered. Knowledge can range from being very location specific to being more general (possibly crossing international borders). However, there is evidence that knowledge spillovers are geographically localized (Jaffe et al., 1993). Most of the empirical literature has focused on metropolitan areas, based on the fact that communication is more intensive there (e.g. Lucas, 1988). To widen the scope of the study to non-urban areas I use concelhos as the geographic unit. 20 The Portuguese Administrative Law establishes that the division of Portugal s mainland is done into 275 concelhos, grouped together in 18 distritos. Aconcelho is an ensemble of persons resident in a certain geographical area. It is a juridical entity with its own independent administrative bodies. Their average area is square kilometers (standard deviation of 283.3), approximately 10% of the US county. Figure 3 illustrates the evolution of unemployment rate and the cyclical component of GDP for the Portuguese economy during this period. The period goes from bottom to bottom of the business cycle, and is sufficiently long to capture long term growth without being too much affected by cyclical considerations. Also these years are nearly equivalent with respect to the unemployment rate. During this period, national employment rose 16.5% and the Portuguese employment structure also registers a reasonably fast change. Figure 4 shows that the share of industrial employment is falling while agricultural employment is almost unchanged. In industry employment increases slightly 1.8%, but total employment in manufacturing falls by 2.5%. Figure 5 decomposes the change in the employment structure for three-digit manufacturing sectors. Wearing apparel and footwear, both with a large tradition in the Portuguese economy, were the sectors registering larger growth. They went from 9.6% and 4.1% of national manufacturing employment to 15% and 7.2%, respectively. Textiles and transport equipment registered the overall worst performances in manufacturing. These aggregate sector trends in employment growth hide the spatial disparity that each sector registered during this period. The dispersion of employment growth rates within each sector is very large. In more than 80% of the three-digit sectors, the coefficient of variation is above 100% while 53% of the sectors still have coefficients above the 200%. There is also a lot of dispersion in the sector 20 Other papers have also used different units of observations: Peri (1992) uses a data set with information at the city and province level which cover all Italian territory and Combes (2000) uses zones d emploi for France, which is the most similar unit to the one used in this study. 11

12 productivity growth rates across regions. The coefficients of variation within three-digit sectors are always above 100%. On average, each concelho grew 53% (standard deviation of 63%). 4 Empirical Implementation 4.1 Measuring the Local Economic Structure Since the seminal paper of Glaeser et al. (1992), the empirical literature has used employment based indices to measure dynamic externalities 21. I follow the literature and construct employment based indices. Throughout the text the subscript r stands for the geographic unit of concelho and r for the three-digit ISIC sector. The concentration index used in this paper is the same as in Glaeser et al. (1992), i.e., the employment share of sector s in region r. CON rs = L rs L r (11) where L rs and L r are the total employment in the sector-region and in the region, respectively. Following Henderson et al. (1995) and Combes (2000), I use a measure of diversity given by the inverse of a Hirschman-Herfindhal index of sector concentration based on the employment share of other sectors on the total manufacturing employment of the region. 1 DIV rs = (12) L rs ( ) L r L 2 rs s =s The index is maximum if the regional employment in the remaining sectors is evenly distributed. It is possible that for a given region, a sector has both a high concentration and a high diversity. This happens if there is a high concentration of employment in that sector but there are several remaining sectors all with approximately the same size. As in Combes (2000) sector competition in region r is measured by the inverse of a Hirschman- Herfindhal index of productive concentration: 21 One exception in this is Gao (2003) that uses output based indeces. 12

13 COMP rs = i (rs) 1 ( L irs L rs ) 2 (13) where L irs is the employment of plant i operating in sector s and located in region r and L rs is the total employment in sector s and in region r. Increases in the employment share of plant i in total employment in region r reflect less competition in the region and, therefore, a decrease in the index. This index also tendstoincreasewiththenumberofplantsineachsector-region. 4.2 Local Economic Structure and Growth The model that I estimate is of the following form: A rs,t+m = β CON CON rs,t + β DIV DIV rs,t + β COMP COMP rs,t + β EMP EMP r,t + β W W rs,t + S µ s + rs (14) where A rs,t+s is the aggregate productivity growth in region r and sector s between t + m and t (where m is sufficiently long to capture long-run growth), CON rs,t, DIV rs,t and COMP rs,t are the logarithms s=1 of the sector-regional indices in year t, EMP r,t is the log of total employment in region r in year t, W rs,t is the log of the average wage in the region-sector in year t, µ s is a time invariant effect for the three-digit sector s and rs is an unobserved sector-regional shock. I include in the model W rs,t to capture for the fact that more productive plants may move to low wage regions. Glaeser et al. (1992) and Henderson et al.(1995) also control for the initial sector employment in the region arguing that it might capture measurement error. However, in this context, β CON does not capture the effect of the relative sector size in the region but rather differences across the region s size (Combes, 1999). I follow Combes (2000) and control for the total employment in the region instead, EMP r,t. To account for unobservable sector time invariant characteristics, I also include dummy variables for the three-digit ISIC sector. Under the assumptions of the model in section (2.3), Ars can be computed using expression (10). This requires information on regional wage and employment growth for different types of labor. I use the 32 labor categories described in the previous section. I compute the growth rate between 1985 and 13

14 1994, sothattheperiodissufficiently long to capture long-run growth. All the indices are computed in The pooled sample of all the manufacturing sectors has approximately 2, 500 observations. I exclude 20 observations (0.83% of the sample) because the regional productivity growth rate was more than 3 standard deviations from the sample average. Table 1 characterizes the distribution of the main variables in the sample 22. To the extent that the explanatory variables are predetermined (uncorrelated with the sector-region shocks), they can be treated as exogenous and equation (14) can be estimated with least squares. The errors are corrected for heteroskedasticity using the White correction. Since the effects of the local characteristics on growth could differ across sectors (for example due to the stage of the industry life cycle) I estimate equation (14) poling all the manufacturing sectors together and separately within twodigit ISIC sectors Empirical Findings 5.1 Wage Adjusted Growth Table 2 presents the results for the sample pooling all the manufacturing sectors together. Columns (1) to (3) run the productivity growth regression entering each index at a time. Column (4) presents the results for all the indices. There is evidence of MAR externalities in columns (1) and (4), i.e., regions with a higher sector concentration tend to have higher productivity growth rates. My point estimate in column (4) implies that an increase in sector concentration that where to shift concentration from the median to the third quartile (raising sector employment 3.4 time),wouldbeassociatedtoanincreasein local productivity by 19%, i.e. approximately 2% per year between 1985 and The effect of sector concentration is positive and statistically significant for some sectors in table 3 as Food, Beverages and Tobacco, Nonmetallic Mineral Products and Basic Metals. There is also a robust positive effect of the initial region s size on productivity growth in table 2. The point estimate in column (4) implies that doubling a region s initial size is associated with a productivity increase that is approximately 2.5% per year. The positive effect of the region s size in local productivity is present for all the manufacturing 22 Notice that the magnitudes of the estimated productivity growth rate presented in the table can not be directly interpreted as the productivity growth in equation (10) because it excludes φ( i). 23 I prefer to report the estimates for two-digits ISIC sectors instead of three-digit because the coefficients in the latter where mostly insignificant due to the small number of observations in each group. 14

15 sectors in table There is no evidence that sector diversity or competition foster regional productivity growth when all the indices are included in the model, even though these variables have positive and significant effects in columns (2) and (3) of table 2. Furthermore, the sector regressions in table 3 show that this finding holds for most of the sectors. 25 It is also a robust finding across sectors, that regions where the average labor cost is higher tend to growth less during this period in Portugal. Overall, I find robust evidence in favor of a positive effect of sector concentration on productivity growth and, therefore, evidence of MAR externalities, and no effect of sector competition and sector diversity in manufacturing sectors in Portugal during this period. To check the robustness of the results reported in tables 2 and 3, I perform several robustness checks. One possible concern could be related to the omission in the model of other regional variables that affect long-run growth. For example, following the Portuguese entry into the European Union in 1986, several regional programs where specifically targeted to the low income regions. To the extent that these programs affected the long-run regional productivity growth and are not correlated with the variables included in the model (e.g., region s size or average wage) the least squares estimates reported could be biased. Columns (1) to (4) of table 4 report the results of including in the model concelhos and distritos time invariant effects. 26 It is reassuring to see that the positive effect of sector concentration on productivity growth is statistically significant independently of the number of regional controls and of the indices included. The main difference for the two-digit sector level regressions is that concentration has a positive and significant effect on productivity growth also in the Equipment sector (results not reported). This sector category includes the manufacturing of specialized high tech sectors, as electrical and optical equipment. So far, I have looked at long run growth. However, it is also informative to check whether the main findings of the paper are robust to shorter time periods. Table A1 in the annex reports the results for productivity growth between 1985 and 1988 and between 1985 and 1991, respectively. The findings show that for both sub-periods of the sample there is still evidence of MAR externalities in Portuguese regions and no effect of sector competition on medium-run growth. The major difference is that in column (3) 24 It just fails to be statisticaly significant in the Textiles and Clothing sectors. 25 The only exceptions are the Paper and Publishing and Chemicals. An increase in region s competition is associated with higher productivity growth for Chemicals and a lower productiivty growth for Paper and Publishing. Also, an increase in the sectoral diversity is associated with an increase in productivity for Paper and Publishing. 26 In the specifications (1) and (2), controlling for concelho dummies, it is not possible to identify the effect of regional size on growth since they are perfectly correlated. 15

16 the effect of sectoral diversity on productivity growth becomes strong, while in tables 2 and 4 the effect was mostly positive although it failed to be statistically significant. I interpret these findings as being suggestive that regions with a larger sectoral concentration, tend to have higher productivity growth in the medium-run (three to six years) as well as in the long-run. Another concern that could be raised refers to the wide range of sector-regional sizes who, nevertheless, contribute equally to the least squares identification. For example, the textile industry in the region of Guimaraes, which employed 28, 797 workers in 1985, is as important for identification as a much smaller concelho. To address this concern, I reestimate equation (14), weighting each observation with the employment in the region-sector in It is reassuring to see that the findings (not reported) are very similar to those reported in tables 2 to Finally, I also test the robustness of the results to the exclusion of the smallest concelhos from the sample. This robustness test is motivated by the fact that most of the papers using data for the US restrict their attention to the metropolitan areas (e.g., Glaeser et al, 1992). This could raise a possible econometric problem due to the selection of particular units. For my sample, the results obtained by reestimating the models reported in tables 2 to 4 but excluding concelhos with less than 53 persons (10% of the sample) were again very similar to those reported in tables 2 to 4. The main difference is that the effect of diversity on long-run growth in specification (4) of table 2 would became statistically strong, even though the effect is not robust to the inclusion of the time invariant regional effects (as in specifications (2) and (4) of table 4). 5.2 Wage and Employment Growth As discussed above, if labor is an homogeneous input or regions have the same skill composition, the wage adjusted measure proposed in expression (10) becomes the regional wage growth. Tables 5 and 6 report the results of estimating equation (14) with least squares using simply regional wage growth. The empirical findings show two main differences. First, in columns (3) and (4) of table 5 I find a positive and statistically strong effect of regional competition on long-run growth. This implies that regional wage growth in sectors where competition is tighter tend to be higher than in regions with less competition The main difference concerns the magnitude of the effects for sector concentration. In the specifications equivalent to column (4) of table 2 and 4 they become (0.028) and 0.10 (0.023), respectively. 28 This effect was also positive (though not strong) using productivity growth in columns (3) and (4) of table 2. 16

17 Second, the findings in table 6, comparedwiththoseintable3, show that there are more sectors for which an increase in the sector s concentration increases long-run regional growth. This positive effect is present in Food, Beverages and Tobacco, Textiles and Clothing, Wood and Pulp, Chemicals, Nonmetallic and Mineral Products and for Basic Metals. Since in my sample region s differ in their skill composition, I interpret these findings as being suggestive that heterogeneous labor should be accounted for when accessing the effects of the local economic structure on growth. Not accounting for it would overstate the positive effects of regional competition and concentration on the long-run growth. In the previous sections, I have showed that if technology is labor biased and labor is an heterogeneous input employment growth would be a bad proxy for productivity growth in spite of its widely use. To access how important are the differences between the two measures, tables 7 and 8 present the results of estimating equation (14) using employment growth. The effect of sector concentration and of the region s size in table 7 are opposite to those found for productivity growth in table 2. Regions with a higher sector concentration have lower employment growth and regions with initially more employment tend to have lower employment growth rates. These findings are robust to the inclusion of sector controls at the concelho and distrito level (results not reported) and are in line with what has been found by others (e.g., Glaeser et al., 1992, Combes, 2000, and Cingano and Schivardi, 2002). 29 The negative effect of concentration on growth is present for all the sectors of activity in table 8. There is a negative and significant effect of sector diversity on growth on column (2) of table 7 that is not robust to the inclusion of the other indices in column (4). At the sector level this effect is still not significant for all the sectors except for Textiles and for Chemicals, where regions with a higher sector diversity have lower employment growth. The effect of sector competition on employment growth is positive and statistically significant in column (4) of table 7 for the pooled sample. This positive effect of sector competition is present for all the manufacturing sectors except for Paper and Publishing and Equipment where it fails to be statistically significant. 30 I interpret these findings to suggest that using employment growth to proxy for long run productivity growth might be based on too restrictive hypothesis. 29 The coefficient of sector concentration ranges from (0.01) with 275 concelhos and no other indeces are included to (0.01) with 18 distritos and the competition and diversity indeces included. 30 I have also tested the robustness of the findings using employment growth to a weighted regression and to excluding the smaller concelhos from the sample. Again, the results were not significantly different from those reported (available on request). 17

18 6 Conclusion This paper assumes that local characteristics affect the accumulation of location specific knowledge and, therefore, of local technological growth. I test how the local economic structure, measured by local sector specialization, competition and diversity, affect the technological growth of Portuguese regions between 1985 and The previous literature on this topic assumed that in the long run more productive regions will attract more workers and, therefore, the growth rate of employment was used as a measure of local productivity growth. However, productivity growth is proportional to employment growth only under strong assumptions. In particular these two variables will not be positively correlated if labor is heterogeneous and labor markets are segmented. This paper derives an alternative measure of productivity growth under these assumptions. When technological change is labor biased, this measure can simply be computed by adjusting the regional wage growth by a function of the different types of labor. My empirical findings support the existence of MAR externalities in Portuguese regions between 1985 and 1994 for some manufacturing sectors and no effect of sector competition and sector diversity for most of the sectors. Furthermore, simply using the regional wage growth would overstate the effect of regional concentration and competition on growth. Moreover, the results are at odds with those found with the employment based regressions where, as in most of this literature, there is evidence that sector concentration has a negative effect and sector competition a positive effect on local employment growth. 18

19 References [1] Ciccone, A., Hall, R. (1996) Productivity and the Density of Economic Activity, American Economic Review, 86: [2] Cingano, F. and Schivardi, F. (2004) Identifying the Sources of Local Productivity Growth. Journal of the European Economic Association, MIT Press, vol. 2(4), pages , 06. [3] Combes, P. (1999) Marshall-Arrow-Romer externalities and city growth: A methodological note. Working Paper 99-06, CERAS. [4] Combes P. (2000) Economic Structure and Local Growth: France , Journal of Urban Economics, 47: [5] De Lucio, J., Herce, J. and Goicolea, A. (2002) The Effects of Externalities on Productivity Growth in Spanish Industry, Regional Science and Urban Economics, 32: [6] Fujita, M. and Thisse, J. (1996) Economics of agglomeration, Journal of the Japanese and International Economies, 10: [7] Gao, T. (2003) Regional industrial growth: evidence from Chinese industries, Regional Science and Urban Economics, forthcoming. [8] Glaeser, E., Kallal H.,Sheikman, J. and Shleifer, A. (1992) Growth in cities, Journal of Political Economy, 100: [9] Griliches, Zvi. (1994) Productivity, R&D, and the Data Constraint, American Economic Review: 84, [10] Henderson, J.V. (2003) Marshall s Scale Economies, Journal of Urban Economics, 53 (1), [11] Henderson, J., Kuncoro A. and Matthew M. (1995) Industrial Development in cities, Journal of Political Economy, 103: [12] Jaffe, A., Trajtenberg, M., Henderson, R. (1993) Geographic localization of knowledge spillovers as evidenced by patent citations. Quarterly Journal of Economics, 108: [13] Lucas, R. (1988) On the mechanics of economic development, Journal Monetary Economics, 22: [14] Marshall, A. (1890) Principles of economics. London: Macmillan. [15] Krugman, P. (1991) Increasing returns and economic geography, Journal of Political Economy, 99: [16] Krugman, P. and Venables A. (1995) Globalization and the inequality of nations, Quarterly Journal of Economics, 110: [17] Peri, G. (1992) Local characteristics and growth in Italian cities and provinces: , mimeo University of California, Berkeley. [18] Porter, P. (1990) The competitive advantage of nations. New York: Free Press. [19] Banco de Portugal, Relatório e contas,

20 Appendices A. Implications of Labor Biased Technical Change for Employment Growth Suppose the production function for each region is constant returns to scale and technological progress is labor biased: Y = F (K, G) where G = AL and F is homogeneous of degree 1. problem are: Then the first order conditions for the region s Totally differentiating this system we obtain: F K = i A F L = w 2 F K 2 dk + 2 F [AdL + LdA] K G = 0 A 2 F G K dk + F F A 2 [AdL + LdA]+ G2 G da = 0 Then dk da = 2 F K G 2 F K 2 A dl da + L Solving this expression for dl da yields: dl da = F G A[ ( 2 F G K ) 2 2 F K 2 A + 2F G 2 ] L 0 Again, the term within brackets will be negative so that A dl dl da + L>0. But da F G ϕ = (. Therefore, if technical change is labor biased then L can increase or decrease 2 F A[ + 2F G 2 ] G K ) 2 2 F K 2 when A increases. = ϕ L A 0, where 20

21 B. Productivity Measure with Factor Neutral Technological Change Assume that the and technology is factor neutral and that output is produced with capital and more than two types of labor. The production function in each region is assumed to be a general constant returns to scale in the inputs, and technology is factor neutral (Cobb-Douglas is just a particular case): Y r = A r F (K r,g r ),whereg r = G(L 1r,..., L Nr ) and is constant returns to scale, K r is physical capital and L kr is the number of workers of type k (total of N different types of labor). I allow for different types of labor that are imperfectly substitutes in the production. The first order conditions of the maximization problem for the region are given by: A r F 1 (K r,g r )=i K r G r = h( i A r ) (15) A r F 2 (K r,g r )=w r A r F 2 ( K r G r, 1) = A r F 2 (h( i A r ), 1) = w r (16) where i is the real interest rate, F 1 = F K r, F 2 = F G r of G r, i.e., is the solution to the problem: and w r is the minimum cost of producing one unit v r = Min L1r,L 2r,...,L Nr w 1r L 1r + w 2r L 2r w Nr L Nr s.t. G(L 1r,L 2r,..., L Nr ) 1 This minimum cost function can be written as: w r = c(w 1r,w 2r,..., w Nr ), where w r (.) is constant returns to scale. It can be shown that the elasticities with respect to each argument equal the cost share, i.e., the wage payments to workers of type k over total wage payments: α kr = w krl kr w rl r,where L r = L 1r + L 2r L Nr and w r = K equation (16) yields, F 2 (.) h k=1 L w kr kr L r. Differentiating the minimum cost function and α 1 w 1r + α 2 w 2r α N w Nr = A r + φ(î,  r ) (17) h F 2 (.) h h i î. where φ(î,  r )= Ar F 2 (.) A r  r + i F 2 (.) Differentiating w r with respect to time and replacing into equation (17) yields: A r = w r K k=1 L kr α kr φ(î,  r ). (18) L r In the expression above, φ(.) is no longer only a function of the interest rate growth (constant across regions) but it is also a function of Âr. As long as the specification for the production function is such that φ(î,â r ) > 0, thisdoesnotmaketheexerciseimpossiblesince the left hand side of equation (18) is Âr still monotonic in A r. 21