Guadalupe Serrano-Domingo

Francisco Requena-Silvente

Guadalupe Serrano+
email: guadalupe.serrano@uv.es

Francisco Requena
email: francisco.requena@uv.es

Joan Martin-Montaner

Factor Movements and International Business < F -International Economics, R11 -Regional Economic Activity: Growth, Development, and Changes

Keywords: Rybczynski effect, immigration, production specialisation, technological Rybczynski Effect, immigration, production specialisation, technological change F22, R11, R13

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Guadalupe Serrano+, Francisco Requena**, Joan Martin-Montaner * Resumen. La participación de los inmigrantes en el mercado de trabajo español aumentó desde menos de un 3% en 1996 hasta más de un 13% en 2005. En el marco del modelo de producción de proporciones factoriales, analizamos el impacto de este shock de oferta de trabajo en la estructura productiva de las regiones españolas. Los resultados apuntan que: las diferencias en las dotaciones factoriales regionales determinan los patrones regionales de especialización industrial; los inmigrantes y los nativos actúan como factores complementarios en muchos sectores; y en la explicación de los cambios en la estructura productiva, la importancia de la inmigración es relativamente pequeña comparada con la de los cambios tecnológicos y de las características idiosincrásicas sectoriales. Large migration flows can be viewed as labour supply shocks which affect the relative factor endowments in both the source and the host economy. If the skill endowments of migrant workers strongly differ from those of native workers in the host countries, then it is likely that the factor intensities in different sectors may be affected.

This could be one explanation for the observed differences in wages of more-skilled relative to less-skilled workers in the developed countries over the nineties (Davis and Reeve, 2004). This migratory phenomenon may also induce (or prevent) technological adjustments, as the adoption of new capital-intensive technologies could be delayed when low-skilled labour is a relative abundant factor (Lewis, 2004; Gandal et al., 2004).

In this paper we analyse the impact of immigration on Spanish regions' industrial compositions by quantifying the extent to which the rise of the immigrant labour force has caused a shift in the industrial specialisation pattern of the regional economies. To do so, we adopt a general equilibrium approach -the factor proportions model of production-to explain up to which point changes in industrial structure of economies are driven by shifts in factor endowments, with independence of those specific changes happening in each industry. 1 This approach was popularised by Harrigan (1995) as an empirical tool for investigating the shifts in production composition in an economy over time. Harrigan found that relative factor endowments had a large influence on industrial specialisation across OECD countries over the period 1970-1985. 2 Bernstein and Weinstein (2002) evaluate the prediction capacity of the standard factor proportions theory using both regional and international data. They observed that prediction errors using intra-national data were much larger than using international data and concluded that the standard factor proportions model of production does a poor job of explaining production patterns at regional level. Redding and Vera-Martin (2006) analyse the regional pattern of output specialisation in Europe and find that it is necessary to account for technological differences and price differences across countries in the standard factor proportion model to predict accurately the pattern of industrial specialisation of the European regions. Based on previous research we adopt the standard factor proportion model of production in our analysis of the pattern of specialization of Spanish regions and check for technological and price differences across regions.

A novelty of the paper is the incorporation of immigrants as an additional production factor. The underlying assumption is that immigrants and native workers are imperfect substitutes. Recent papers by Carrasco et al. (2008), Izquierdo et al. (2009) and De la Rica and Dorantes (2009) provide empirical support in the case of Spain. First, there is evidence of important occupational segregation, in line with the popular idea that immigrants are employed in jobs that native workers do not want. Second, there are important institutional barriers (such as the existence of regional languages and the need for public recognition of the educational degree) that limit the access of foreign workers to be employed in certain jobs (professional services with a university degree, jobs in the public sector). Third, the arrival of immigrants is recent and has occurred very quickly so there has been insufficient time for complete assimilation. The foreign labour force in Spain increased from 2.7% of the total labour force in 1996 to an astonishing 13.3% in 2005. The existence of important institutional barriers, the lack of sufficient time for cultural assimilation and the fact that there are vacancies which require skills that foreign workers have, are three reasons that explain why immigrant workers with Finally, and despite the strong efforts made by both private and public agents to increase the level of R&D expenditures, the adoption of new technologies in certain manufacturing and services activities in Spain has been slow compared to other European countries (OECD, 2005). A plausible reason is the type of technologies required to accommodate the new inflows of workers in sectors that use the new production factor more intensively. Therefore, knowing whether production in each sector varies because of changes in endowments or because of the adoption of new technologies becomes a key point in the analysis.

The rest of the paper is structured as follows. First, we formalise the production side of the factor proportions model and its extensions to accommodate differences in prices and technology across regions. Second, we present the data and describe the evolution of the foreign and native labour force in the period 1996-2005. Third, we estimate the model using different levels of regional and sectoral aggregation and interpret the Rybczynski coefficients. Fourth, we allow the Rybczynski coefficients to change over time and assess the relative importance of changes in factor endowments and changes in production techniques in explaining changes in industrial specialisation.

Finally, we summarize our results in the conclusions section.

THE PRODUCTION SIDE OF THE FACTOR PROPORTIONS MODEL

In this section we describe the factor endowment production function, originally proposed by Harrigan (1995) and extended recently by Harrigan and Zakrajšek (2000),

Theoretical foundations

The core insight of the factor proportions model is that regions tend to produce relatively more of those goods that intensively use the factors of production that the region has in abundance. Thus, relative factor endowments become the determinant of industrial structure and the source of comparative advantage.

Under constant-returns-to-scale technology and perfect competition in goods and factor markets, a country's national product is given by its revenue function

{ } (V) Y PY max ) V P, ( Y Y ∈ = Π
where P is an (N × 1) vector of goods prices, V is an (M × 1) vector of inelastic factor supplies, Y is an (N × 1) vector of net outputs, and (V) Y is a compact production set. Assuming Π (P, V) is twice continuously differentiable, the gradient with respect to P gives the net supply vector, ( )

V P, Π Y p = .
Differentiating again with respect to factor supplies gives the matrix of Rybczynski derivatives, ( )

V P, Π R PV =
. Since the supply function is homogeneous of degree one in

V, RV Y = (1)
and net output is a linear function of factor endowments. 3 The underlying condition that allows the R matrix to be identical across regions and thus equation (1) to be used as a model of interregional location of production is that regions must be able to produce the same set of goods with the same techniques.

Producing the same set of goods requires relative factor endowments not to be "too" 4 The fact that regions use the same techniques of production depends on common technologies and factor prices. Good prices will be equalized across regions with free trade and zero transport costs. A crucial condition for factor price equalization is that the number of goods exceeds the number of factors, N ≥ M.

However, in order for the supply function to be singly-valued, there must be at least as many factors as goods, M ≥ N. Thus, what is left is the "square" model in which there are equal numbers of goods and factors, N = M. In this case, equation (1) holds for each region and forms the basis for the empirical work to follow. Obviously there are more goods than factors and therefore there does not exist a unique mapping between factor endowments and production. Nevertheless, the existence of a structural relationship between factor endowments and production is all that really matters for the present analysis. 5

A final point is that the use of a general equilibrium relationship between production structure, relative prices, technology and factor endowments holds irrespective of the degree of factor mobility. 6

2.2 Empirical model.

Equation ( 1) can be rewritten for each industry in each year with an additive error term as

i ct i t ct i ct R v Y ε + = (2)
Here, i ct Y is region c's value added in industry i in year t and ct v is region c's (1 × M) vector of factor endowments in year t. The (M × 1) vector

i i i R V Y ε + = (
          ∴ +           ∴ =           ∴ i i i ε ε R V R V Y Y 1 1 1 (4)
The main advantage of this approach is the ability to test homogeneity hypotheses across equations, i.e. across industrial branches belonging to the same sector.

Moreover, since it is likely that the disturbances across equations are correlated, the multivariate approach may lead to efficiency gains and account for inter-industry externalities, an issue that has not been addressed in previous studies.

Next we allow for a more flexible specification that relaxes the assumptions on identical prices and technology among regions. In order to do so the model becomes (4a).

          ∴ +           ∴ +           ∴ =           ∴ i i i i D D R V R V Y Y ε ε φ φ τ τ τ τ 1 1 1 1 (4a)
Where τ refers to "periods of time": the 1996-2000 period of low immigration in The model can also be extended to accommodate time-invariant regional differences in relative prices and technology, by adding a time-invariant regional fixed effect, Z D , with dimension [(CxT) x Z], and its correspondent vector of [Z x 1] parameters, Z φ , where C denotes the spatial dimension of the data that we are using -NUTS-2 Spanish Autonomous Communities or NUTS-3 Spanish provinces -while Z always is referred to NUTS-II Spanish Autonomous Communities. 7 This is illustrated in model (4b).

          ∴ +           ∴ +           ∴ +           ∴ =           ∴ i i Z Z Z Z i i i D D D D R V R V Y Y ε ε φ φ φ φ τ τ τ τ 1 1 1 1 1 (4b)
A final extension consists on allowing region-specific differences in prices and technology to vary over time, by including a set of region-time dummy variables, τ Z D , with dimension [(CxT) x (Zx2)], and its correspondent vector of [(Zx2) x 1] parameters, τ φ Z , as shown in model (4c).

          ∴ +           ∴ +           ∴ +           ∴ =           ∴ i i Z Z Z Z i i i D D D D R V R V Y Y ε ε φ φ φ φ τ τ τ τ τ τ τ τ 1 1 1 1 1 (4c)
We estimate equations (4a), 4(b) and (4c) and test for the best specification using different geographic units and levels of industry aggregation. The dependent variable in our study is annual production by geographical unit and industry. Industry's output is measured by means of sector GVA (gross value added) at current basic prices from the homogeneous series of INE's Regional Accounts base year 2000. The database provides regional value added at two different geographical levels: 17 regions (NUTS-2) 8 which can be disaggregated into 52 provinces (NUTS-3). The number of industries varies depending on the level of geographical aggregation. There are 21 sectors (S-21) for NUTS-2, which are grouped into 5 sectors (S-5) for NUTS-3: Agriculture, Energy, Manufacturing, Building and Services. Immigrants increased their participation in the Spanish labour market from less than 3 percent in 1996 to more than 13 percent in 2005. Table 1 shows that the newly

MODEL SPECIFICATION AND ESTIMATION

We conduct the analysis from the two different data-sets referring to different geographic units in the Spanish economy. As we can also aggregate Spanish provinces from NUTS-3 to NUTS-2, we can perform our analysis both for S-5 and S-21 classifications. This latter possibility allows us to explore differences in the estimates due to different levels of spatial and industrial aggregation. 9 Models (4a)-(4c) are estimated considering the eight productive factors described in the previous section. When data correspond to S-5 disaggregation, we estimate two five-equation SUR models both for provincial and regional data. 10 Nevertheless, computational capabilities do not allow the estimation of a 21-equation SUR model. Because of this, we estimate a single equation model for Agriculture and Building whereas SUR specifications are estimated for Energy (two equations), Industry (ten equations) and Services (seven equations).

Through the analysis, sector Gross Value Added (GVA) for each region and the regional gross capital stock are measured in current prices. To control scale effects due to differences in the size of region, sectoral outputs and regional inputs are expressed in relative terms with respect to regional GDP, which is measured in current prices.

Moreover, to avoid heteroskedasticity problems in each equation, we specify a SUR We start selecting the best model specification. Table 2 reports the mean absolute percent errors (MAPE) by industry and regional units for the models (4a), ( 4b) and (4c) in columns (ii), (iv) and (v) respectively. 11 As a crude benchmark for comparison, these percent errors are contrasted with those based on the estimation of relative production using the cross-sectional mean. This naïve estimator in the estimation without dummy variables, column (i), has an overall mean absolute percent error of 66.5 and 66.4 percent for provinces and for regions, respectively; that is 30 percentage points larger than the average error based on the factor proportions model. In addition, the naïve estimator percent error is larger than the overall mean absolute percent error in all sectors. 12 As was expected, the factor proportion model of production performs better at a regional level (NUTS-2) than at a province level (NUTS-3). Thus, in the estimation without regional dummies, column (i), the MAPE is 35.3 percent for provinces higher than the one in the specification for regions (27.2 percent). Following the same trend, the MAPE is smaller across regions than across provinces in those models including time and regional dummies. Our results contrast with those of Bernstein and Weinstein (2002), which report a MAPE of 310 percent using data on Japanese regions. More striking is the fact that our largest MAPE, 35.3 percent in the provincial model without dummies, is smaller than any other percent error reported by papers using international data. 13 (Insert According to this last criterion, the better specification is (4c) in both S-5 and S-21 cases. This specification, which corresponds to an augmented factor proportion model of production, is such that regional dummies capture differences in technology and prices that are not permanent but change over time. This conclusion is confirmed by three additional tests. First, we always reject the null hypothesis that the coefficients of the regional dummies are zero. Second, we reject the homogeneity of regional effects obtaining evidence supporting the fixed effects model specification. Finally, we test whether the coefficients for the regional dummy variables are constant over time (model 4b vs 4c), being that the hypothesis is always rejected.

Finally, we analyse the validity of the SUR specification by testing the null hypothesis of no correlation of the residuals between equations independently estimated. The results of the Breusch-Pagan test do reject the null hypothesis, confirming the adequacy of the SUR estimation of the model (being the exception Energy in the specifications (i) and (ii) with 21 sectors).

The analysis of the MAPE obtained in the S-5 model and in the S-21 model shows negligible differences, which does not support the idea that production indeterminacy is mainly due to the fact that the number of goods is larger than the number of factors. We perform a last test to choose between S-5 (Table A-2 in the Appendix) and S-21 (Table A-3 in the Appendix) using regional level data. Using the S-5 and S-21 sectoral correspondence in Table A-1 in the Appendix, we test the equality of Rybczynski parameters across those S-21 branches belonging to the same S-5 sector. Because of that, we selected model (4c) using regional data (NUTS 2) and 21 sectors as our best specification. Estimates are displayed in Table A-3 and the findings are explained in the next section.

The test results displayed in the last row of

IMMIGRATION IN THE FACTOR PROPORTION MODEL OF PRODUCTION.

In this section we use the Rybczynski coefficients to investigate the impact of immigration on the production structure of Spanish regions. The sign and significance of the coefficients can be interpreted in terms of comparative advantage (Leamer, 1984).

Profit-maximizing firms adapt to changes in relative endowments, according to the differences in benefits that can be drawn from an increase in the endowment of each factor. Thus, productive factors are reallocated across sectors and that reallocation might imply increases and reductions of production depending on the sector. Therefore, a positive sign for the corresponding Rybczynski coefficient means that the increase in one region's endowment of a certain factor translates into an increase in production in that sector (or, in other words, represents a source of comparative advantage), whereas a negative sign means that the accumulation of that factor leads to a reduction of the production of the sector (representing, therefore, a comparative disadvantage). 14 The coefficient on capital is significant in most sectors, although only displays a positive sign in branches 3 (Electricity, gas and water), 4 (Food, drink and tobacco), 14 (Building), 19 (Renting and business services) and 20 (Education, health and other services). The coefficient on land is also significant in most branches, playing a positive impact in branch 1 (Agriculture), 6 (Wood Products), 14 (Building), 18 (Financial Services), 19 (Renting and business services) and 20 (Education, health and other services). With regard to the native labour force, the coefficient on medium-educated workers appears to be positive and significant in most sectors (17 branches out of 21).

For high-educated workers the coefficient is positive and significant in Energy and Services branches, whereas for low-educated workers the coefficient exhibits mixed signs across sectors.

With regard to immigrants, our results display a high degree of heterogeneity in terms of significance. The coefficient on medium-skilled immigrants is significant in 14 branches (in most cases negative), whereas for high-skilled immigrants it shows a statistically significant coefficient only in 6 branches. Low-skilled immigrants are in an intermediate position, with a statistically significant coefficient in 9 branches, most of them in the Industry sector. The significant, unexpected absence of less-skilled immigrants in Agriculture and Building can be explained by the fact that our data do not include undocumented workers which would likely enlarge the amount of foreign workers in that sector. Another striking result comes from the Industry sectors, where the impact of low and medium-educated foreign workers is negative in all its branches. This negative impact can be interpreted as foreign workers constituting a source of comparative disadvantage. This could explain both the small number of overall immigrants in Industry and the fact that they tend to be medium-level educated (some qualifications are required, but not as many as to require high-qualified workers).

We analyse next the kind of relationship, if any, that exists between foreign and native workers. Table 4 shows the results of testing the equality of the parameters for native and immigrant workers at different skill levels. The results are mixed. The hypothesis of equal parameters for high-qualified workers is only rejected in two cases: sectors 7 (Paper and printing) and 13 (Miscellaneous). This is not surprising as the coefficients of both native and foreign high-qualified workers are the only significant ones in these two sectors. The equality of the parameters for medium-qualified workers is rejected in all the cases in which both native and foreign workers exhibit statistically significant coefficients (sectors 1, 2, 4, 5, 6, 7, 10, 13, 15 and 17) and it is not rejected in two cases: 3 (Electricity, gas and water) and 20 (Education, health and other services).

In these two cases the coefficient of both types of workers is positive. Finally, in the case of low-qualified workers, equality is only rejected in three sectors: branches 4 (Food, drink and tobacco), 9 (Plastic and Rubber) and 10 (Metal industries and nonmetallic products).

(Insert Table 4 approximately here)

In general, it can be observed that the coefficient on immigrant workers is not significant unless the coefficient on native workers is also significant. We observe that only in 9 out of 63 cases the coefficient for a type of immigrant worker is statistically significant when the coefficient of the native counterpart is not statistically significant.

This outcome is partly explained by the high standard errors in the estimated coefficients associated with the immigrant worker variables (see Tables A-2 and A-3).

Given the asymmetry of estimated effects for native and foreign workers in most sectors, it is not possible to point to any accumulation or compensation effect of foreign workers relative to native ones, but there is a sort of interrelation between both types of labour, especially for medium-qualified workers.

FACTOR ACCUMULATION AND INDUSTRIAL STRUCTURE CHANGES FROM 1996 TO 2005

Although factor endowments have been proved to be significant in determining the value added for the different sectors, changes in the productive structure can also be caused by both changes in the level of those endowments or in the way they are combined to produce. In order to incorporate the possibility of changes in production techniques, we need to test the stability of the Rybczynski parameters over the period analysed. Table 3 reports In order to identify the relative importance of the forces acting on production structures, the estimation results from Equation (4) can be used to decompose the change in output from t-n to t as:

( ) ( ) ( ) n t i t i n t i t i i n t t n t i t i R R V R V V Y Y - - - - ε - ε + - + - = - ˆ ( 5
)
where V is the average value of factor endowments in years t and t-n, and i R ˆ is the average estimated coefficient matrix in periods t and t-n for industry i. The first term, V ∆ can also be interpreted as the Rybczynski effect. The second term in Equation ( 5),

i n R V ∆
, is the effect that changes in production techniques have on shifts in production, holding fixed endowments. Here, "technique" refers to factor usage which depends on technology (i.e. the production function) as well as relative factor prices. 16 The final term, i n ε ∆ ˆ, is the difference in the residuals.

Table 5 shows the decomposition analysis in equation ( 5) used to determine the percentage contribution of changes in factor endowments and technology to variations in value added between 1996-2000 and 2001-2005. The values reported are the percentage contributions of the terms in equation ( 5), expressed as cross-country averages. 17 The overall contribution of factor accumulation, across all industries and years, is about 7.2 percent. Changes in the techniques of production contribute about 47.5 percent. The residual term comprises the remaining 45.4 percent. In general terms, these results give little room for changes in factor endowments to play a relevant role. In fact, they factor endowments are the dominant source of change only in the case of branch 14 (Building), and represent more than 10 percent in branches 20 (Education, health and other services) and 21 (Household services). Nevertheless, changes in techniques appear to have contributed more in most cases, followed by the regionspecific changes of each sector which are included in the residual term. The residual term in Table 5 represents a high share of the change in sector output in most cases. This term includes all regional issues beyond technology and endowments which may affect the regional value added per sector. In order to reduce this residual term and put on the front some of these regional issues, an alternative decomposition has been attempted.

(Insert

In our estimates, we controlled scale effects due to differences in the size of the region by expressing sectoral output and regional inputs in relative terms with respect to regional GDP. Therefore model ( 2) can be rewritten for each industry in each year

as i ct ct i t ct ct i ct Q R v Q Y ε + =
, where Q ct is the aggregate region c output. Following the same methodology as in ( 5), we decompose the change in output from t-n to t as:

( ) ( ) ( ) n t i t i i n t t n t i t i i n t t n t i t i Q Q R R V R V V Y Y - - - - - - + - + - + - = - ε ε ε ) ( ˆ (6)
The new term,

i n Q ε ∆
, stands for a regional effect that captures the contribution of changes in regions' relative relevance (in regions' scale) on shifts in sector production.

As shown in Table 6, the scale effect is relevant. All three initial effects are smaller than in Table 5, although the mean for the technological effect and the residual are those which decrease more. Once the scale effect is taken into account, the factor endowment effects in Building becomes smaller (accounting for just a 10.4% of total VAB variation), whereas it becomes more important in the case of Mechanical Machinery and Electric and Electronic Equipment and Transport Equipment and, even more so, in Wood Products. Finally, the "regional scale effect" represents a high share in the total variation in value added in the case of Chemical Products, Reparation and (Insert Table 6 approximately here)

7. FINAL REMARKS.

This paper provides the first evidence of the impact of immigration in the pattern of production specialisation across Spanish regions in the period 1996-2005. The extent to which an increase in the immigrant labour force could induce shifts in the industrial structure of regional economies is also quantified. Based on the factor proportions model of international trade, foreign and native labour force are introduced as two separate inputs in an augmented supply production function to estimate how much sectoral output varies with changes in factor endowments (the so-called Rybczynski coefficients).

The results show that both the effects of factor endowments and specific timevarying regional characteristics in each industry appear to be important in understanding industrial structure. While a higher spatial disaggregation reveals a production indeterminacy problem and a poor performance of the model, the higher sector disaggregation does not seem to generate this indeterminacy problem.

Our first finding is that the data reject the hypothesis of equality in the impact of native and foreign labour by educational type on industrial shares across Spanish regions. This result holds even when we examine those sectors in which the Rybczynski coefficients for natives and immigrants have the same sign. This can be interpreted that natives and immigrants are not perfect substitutes in the production function. In terms of the impact of factor endowments and its role as a source of comparative advantage across industries within Spain, the results point to a small effect caused by the presence of foreign workers. Only medium-educated foreign workers present a statistically significant impact in most of the sectors, whereas the impact of low and high-educated foreign workers appears to differ from zero in less than half of the branches considered.

If we connect these results to those showing complementarities between native and foreign labour, we can conclude that the presence of immigrants never implies the leaving of native workers from a sector, as shown by the fact that immigrant work is never statistically significant without native work also being so. In general, results

suggest a sort of complementarity between natives and immigrants at the different levels of qualification, especially among the medium-educated workers.

To conclude, factor accumulation has tended to be the least important gross force acting on production. In contrast, shifts in the national techniques of production have been the more relevant source of changes in relative outputs in Spanish regions.

That immigration has been one of the most important sources of change in factor endowments in Spain in recent years, a strong conclusion stems from our results:

although immigration has changed the factor endowment mix across Spanish regions, it has had little impact on the changes observed in the industrial structure in Spain between 1996 and 2005.

F

Data sources and variable computations.

Data on Gross Value Added (GVA) have been obtained from INE's Spanish

Regional Accounts Base-year 2000 information (www.ine.es). We use 1996-2005 homogenous information on current GVA, both for Spanish provinces (NUTS-3) and regions (NUTS-2), for 5 aggregated production sectors (S-5). Data on current GVA for 25 production branches is only available from the year 2000 onwards. Because of this, the need for estimating homogeneous information on current GVA for activity branches implied the reduction of activity branches considered to 21 (S-21). See Table A1.

We obtain the current GVA of the 21 branches (S-21) from the period 1996-1999, splitting the S-5 current GVA data, by using sector shares from information from INE's Spanish Regional Accounts Base-year 1995 data, once those shares have been corrected according to Base 2000 database revision. The main problem with sector branch classification in current Euros is found in the services sector. While the Baseyear 1995 database distinguishes between market and non-market service branches, the Base-year 2000 database does not distinguish the non-market services. Then, in order to reduce branch share differentials among both databases, we considered an aggregated "Education health, public administration and other services" branch which is obtained as a rest.

(Insert The key assumption for the present analysis is the existence of a structural relationship between factor endowments and outputs, but for our purposes, we do not need to go further into testing the factor proportion model's assumptions against alternatives or address any of its critics. Thus, the factor proportion model is a good theoretical framework to base our analysis on. 3 Equation (1) can also be derived in a monopolistic competition model with increasing returns to scale (see Harrigan, 1995). The assumption of constant returns to scale is supported by the work by Goerlich and Orts (1994) in the case of Spain.

4 Regions will produce a different set of goods in the case of "lumpiness" (i.e. an excessive uneven distribution of factors across Spanish provinces). Artal et al. (2008) applied the "lens condition" test and rejects the existence of lumpiness in the case of Spain.

5 The structural relationship goes in one direction since factor endowments are exogenous in the model. However, as far as accumulation depends primarily on broad forces that are largely external to a given sector, this assumption should not be a serious problem. For example, educational attainment seems to be driven largely by demographic characteristics and domestic educational policy and capital accumulation depends on aggregate forces such as life-cycle behaviour, macroeconomic conditions, and tax policy. From a more pragmatic point of view, there are no good instruments available for factor supplies. Indeed many empirical papers use factor endowments as "good" instruments of production output, when this variable is included in the regression as an explanatory variable, under the assumption that they are exogenous.

6 Redding and Vera-Martín (2006) show that the production-factor endowment relationship holds without factor price equalisation given that both differences in relative prices and technology are controlled in the model, and hold under factor 7 As we explain in more detail later, we use both EUROSTAT NUTS-2 (17 Spanish Autonomous Communities) and NUTS-3 (52 Spanish provinces) in our analysis. Then, for NUTS-2, C=Z, and for NUTS-3, C>Z.

8 The Spanish Autonomous Communities (EUROSTAT NUTS-2 classification) represent the most important administrative units at the regional level and 11 out of 17 include more than one province. 9 In their study of regional production specialisation across European regions, Redding and Vera-Martin (2006) find larger, within-sample-average absolute-percent errors in disaggregated manufacturing industries, and relate it to the production indeterminacy problem given the larger number of industries relative to production factors. They also refer to the Bernstein and Weinstein (2002) explanation of production indeterminacy, "which is likely to be larger for the lower values of trade costs observed across regions within a country" (page 4).

10 See Table A-2 for estimated coefficients using regional data. Estimated coefficients using provincial data are available on request from the authors. 14 Notice that the values of Rybczynski coefficients do not indicate differences in marginal value productivity. Rather the value of the coefficients indicates differences in the benefit that can be drawn from an increase in the endowment of each factor, after optimal reallocation of all factors, given the endowments of other factors. 15 Standardised or beta coefficients, discussed in Leamer (1984), are formed by multiplying the regression slope by the standard deviation of the explanatory variable and dividing by the standard deviation of the dependent variable. The actual coefficient estimates are reported in Table A-3 in Appendix. 16 Techniques can change for a wide variety of reasons. These include changes in technology and preferences. Other sources of change include trade liberalization with the rest of the world, the emergence of new industrialized trading partners, overall factor accumulation within the sample, and even industry-specific shocks. Whatever the reasons for change in techniques, they cannot be distinguished in the present framework.

However, explaining the changes in the techniques is not our goal, but merely distinguishing them from the factor endowment effect. 17 Since the terms in Equation ( 5) can be of either sign, a simple average obscures their true contributions. Therefore, the averages are reported in terms of absolute values.

Moreover, these components have been normalized to sum to 100 percent.

(i) (ii) (iii) (iv) (v) (i) (ii) (iii) (iv) (v) (i) (ii) (iii) (iv) (v
( ) i n t t R V V - - ( ) n t i t i R R V - -ˆ( ) n t i t i - ε - ε î n t t Q Q ε )

  of education as their native colleagues are not being employed in the same occupations.

  and Redding and Vera-Martín (2006) to accommodate differences in technology and factor prices across countries and regions.

  Spanish regions and the 2001-2005 period of high immigration in Spain. Here, D τ -specific impact of changes in prices and technology over the period τ.

  Figure1shows the map of Spain where NUTS-3 provinces (left map) and NUTS

  equations, in which each weight is obtained from the equation's robust estimation. Then, the estimates of the cross-equation covariance matrix are based upon GLS parameter estimates of the weighted system.

  regional dummy variables, show that the equality of Rybczynski coefficients is rejected for branches belonging to Energy, Industry and Services.

  the Wald test statistics for the null hypothesis of equality of coefficient estimates for the periods of 1996-2000 and 2001-2005. The null hypothesis of constant coefficients can be rejected at standard levels of significance in all the cases. Therefore changes in the techniques of production over the entire period 1996-2005 could be an important source of change in industrial structure.

  the contribution of changes in factor endowments, holding fixed i R ˆ, of production. The Rybczynski theorem characterises how output responds to changes in endowments at fixed prices and technology, i.e. at fixed techniques of production. Hence, the term i n R

  and Transport and Communication Services, whereas it is negligible for other service activities such as Financial Services, Renting and Business Services, Education and Health and Household Services.

  conclusions are shown to be robust to alternative model specifications and estimation techniques byHarrigan (1999),Harrigan and Zakrajšek (2000) andReeve (2006).

  , the interpretation of this general equilibrium relationship changes depending on the mobility of factors. When factor immobility holds, the model can be interpreted in supply-side terms (external changes in factor endowments cause production structure changes). When factors are perfectly mobile across regions, there is also a demand-side interpretation (external changes in demand and production cause endogenous changes in factor endowments).

  report absolute percent errors of 40 percent, 67 percent, and 52 percent, respectively.

Figure 1 .Figure 2 .

 12 Figure 1. Participation of foreign labour (% total labour force). Year 2005

  indicate the cross-region average percentage contributions of the three effects normalised to sum to 100 percent (aside from rounding).

  Table A-1 in the Appendix displays the correspondence between S-21 and S-5.

	The period of analysis is 1996-2005.
	Endowment data includes three primary factors: arable land, capital stock and
	labour. Labour is split into native and foreign workers and into three educational
	categories: low, medium, and high-educated workers, to account for differences in
	human capital in the labour force. Data on arable land is provided by INE's Statistical
	Yearbook of Spain and data on capital stock is provided by the BBVA Foundation and
	IVIE (http://www.ivie.es/banco/stock2.php). Labour endowments come from INE's
	Economically Active Population Survey (EPA, 2005 methodology). Low-educated
	workers include illiterates and workers with only primary education. Medium-educated
	workers have completed secondary school. High-educated workers have at least
	enrolled in a high education degree. The Appendix provides a detailed explanation of
	the construction of the variables.
	(Insert Table 1 approximately here)

  Table 2 approximately here)

	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

  Table 2 also reports an LR test for the global significance of estimates and the AIC criterion for model selection.

Table A

 A

-2 for model (4c), which includes

Table 3

 3 reports the beta coefficient estimates. Beta coefficients indicate the relevance of the explanatory variable in the regression, since they measure the expected change in the standardised dependent variable induced by a unitary change in the standardised independent variable, which is conditional on the other standardised regressors.15 (Insert Table3approximately here)

	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

Table 5

 5

	approximately here)

Table A

 A that arrived in Spain from the second half of the nineties. In order to extrapolate population data from sample data, the EPA compute an "elevation factor" variable (so-called 'facele') from the 2001 population census data. The elevation factor captures the representativeness of each individual in the EPA sample in the total population. The use of the 2005 EPA methodology over the period 1996-2005 is especially relevant for our immigrants' population database because the INE considers that, due to the unexpected fast increase of such population in Spain, the elevation factor, computed using the previous population census (1991), severely underestimates the immigrant population within the total Spanish population. Data on arable land is provided by INE's Statistical yearbook of Spain and interpolated when a specific year is missing. Finally data on the gross capital stock in current Euros is obtained from estimations provided by the BBVA Foundation and IVIE. Concretely, we use the gross capital stock in current Euros for the period 1995-2005, which is valued at restoration prices.

	F o r P e e r R e wave of immigrants Additional Tables. v (Insert Table A-2 approximately here) i e w (Insert Table A-3 approximately here)
	NOTES 1	O l n
		y
	-1 approximately here)
	We use data from INE's Economically Active Population Survey (EPA, 2005
	methodology) to measure native and foreign labour endowments. We use data on the
	second quarter of each year from 1996 to 2005, given its possibility of actualization
	using the new 2005 methodology, which is adopted explicitly to account for the large
		25

Table 1 .

 1 Composition of Labour Supply by Education Levels and Nationality.

	Baleares
	Madrid
	C Valenciana
	Murcia		Natives Low-edu
	Canarias		Natives Med-edu
			Natives High-edu
	Rioja		Immigrants Low-edu
	Cataluña		Immigrants Med-edu
			Immigrants High-edu
	Aragón
	Navarra
	Cast la Mancha
	Andalucía
	Galicia
	Cantabria
	País Vasco
	Cast y León
	Asturias
	Extremadura
	0%	20%	40%	60%	80%	100%
	Source: INE's Economically Active Population Survey.

http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nl

Table 2 .

 2 Model Specification and evaluation.

	GLS & SUR ESTIM. 5 SECTORS. PROV. DATA	GLS & SUR ESTIM. 5 SECTORS. CCAA DATA	GLS & SUR ESTIM. 21 SECTORS. CCAA DATA

Table 3 .

 3 Standardised Coefficient Estimates (1996-2005). Beta Coefficients.

	)

http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nl

Table 4 .

 4 Hypotheses Tests for Equality in the Marginal Effects of Native and Foreign Actives by Education Categories.

		Sector	Hig-edu. Medium-edu.	Low-edu
	1 Agriculture	0,33	4,5	0,04
			(0,5672)	(0,0358)	(0,8427)
	2 Extractive energy	1,1	5,94	9,04
			(0,2945)	(0,0148)	(0,0026)
	3 Electricity, gas and water	1,43	0,57	8,24
			(0,2323)	(0,4496)	(0,0041)
	4 Food, beberages and tobacco	0,14	24,32	55,69
			(0,7093)	(0,000)	(0,000)
	5 Textiles, clothing, leather, fur	0,72	75,13	9,71
			(0,3966)	(0,000)	(0,0018)
	6 Wood products, excl. Furniture	1,59	11,34	6,62
			(0,2072)	(0,0008)	(0,0101)
	7 Paper, printing & publishing	4,15	10,83	5,03
			(0,0417)	(0,001)	(0,0249)
	8 Chemical products	0,25	3,43	2,44
			(0,6145)	(0,0638)	(0,1179)
	9 Plastic & rubber	0,82	6,84	35,68
			(0,3648)	(0,0089)	(0,000)
	10	Metal basic and other non-metallic mineral prod.	0,15	38,64	28,35
			(0,6988)	(0,000)	(0,000)
	11	Mechanical & Electric and electronic equip.	1,53	3,88	1,52
			(0,2162)	(0,0489)	(0,2179)
	12 Transport equipment	0,25	1,53	0,01
			(0,6194)	(0,2161)	(0,9206)
	13 Miscellaneous	6,88	8,9	0,01
			(0,0087)	(0,0029)	(0,9249)
	14 Building	2,62	11,46	4,66
			(0,1082)	(0,0009)	(0,0327)
	15 Reparation and commerce	0,5	6,27	0,7
			(0,4789)	(0,0123)	(0,4016)
	16 Hotels	0,05	3,72	0,95
			(0,8274)	(0,0537)	(0,329)
	18 Transport & communi.serv.	2,26	24,65	0,37
			(0,1326)	(0,000)	(0,5448)
	18 Financial services	3,21	0,12	7,83
			(0,073)	0,7254)	0,0051)
	19 Renting and business services	0,2	8,7	3,22
			(0,6566)	(0,0032)	(0,0727)
	20	Education, health and other services	2,48	0,26	1,65
			(0,1153)	(0,6123)	(0,1996)
	21 Household services	2,74	6,8	0,95
			(0,0978)	(0,0091)	(0,3286)

Note: Wald tests. P-values in parentheses.

Table 5 .

 5 Decomposition of Output Change between 1996 and 2005 Values indicate the cross-region average percentage contributions of the three effects in terms of relative magnitudes, normalised to sum to 100 percent (aside from rounding).

	Sector	Techniques ( ) n t i t i R R V --ˆ( Factor Endowments ( ) i n t t R V V --ε Residual n t i t i -ε -ˆ	)
	1	47,5	6,7	45,8
	2	50,4	0,9	48,7
	3	44,5	8,9	46,5
	4	40,8	14,7	44,5
	5	49,9	9,8	40,3
	6	46,2	29,8	24,0
	7	50,8	2,0	47,2
	8	52,1	3,8	44,1
	9	51,1	1,9	47,0
	10	41,2	8,5	50,3
	11	53,8	1,8	44,4
	12	42,8	8,9	48,3
	13	47,3	20,5	32,2
	14	31,9	57,4	10,8
	15	37,6	5,0	57,4
	16	26,9	18,9	54,1
	17	36,1	11,4	52,4
	18	47,7	2,3	50,0
	19	47,8	2,2	50,0
	20	46,8	3,1	50,1
	21	47,0	3,2	49,8
	Mean	44,8	10,6	44,7

Note:

Table 6 .

 6 Alternative Decomposition of Output Change between 1996 and 2005

		Techniques Factor Endowments	Regional Scale	Residual
	Sector
	1	42,9	3,2	8,2	45,7
	2	40,7	1,2	4,9	53,1
	3	55,6	11,1	14,4	18,8
	4	19,8	0,9	22,0	57,4
	5	32,2	8,5	11,0	48,4
	6	29,8	55,0	7,7	7,5
	7	49,4	0,5	35,6	14,4
	8	36,6	3,8	38,1	21,5
	9	44,4	7,5	8,0	40,1
	10	10,9	5,7	32,0	51,4
	11	35,8	12,4	19,7	32,2
	12	29,0	13,0	17,4	40,5
	13	11,7	17,6	28,8	41,9
	14	13,2	10,4	26,3	50,1
	15	15,1	6,8	54,3	23,7
	16	17,6	3,0	40,6	38,8
	17	25,6	9,2	35,2	30,0
	18	40,8	9,3	0,1	49,9
	19	40,8	9,2	0,1	49,9
	20	40,8	8,8	1,9	48,5
	21	39,1	9,3	0,3	51,4
	Mean	32,0	9,8	19,4	38,8

Table A -

 A 1. Geographic units and Sector classification.

	Geographic unit Provinces (NUTS 3) Period 1996-2005 Sectors S-5 1. Agriculture 2. Energy 3. Manufactures F o r Autonomous Communities (NUTS 2) 1996-2005 S-21 1 Agriculture 2 Extractive energy and other energetic minerals, oil and nuclear 3 Electricity, gas and water 4 Food, drink and tobacco 5 Textiles, clothing, leather, fur 6 Wood products, excl. furniture 7 Paper, printing and publishing 8 Chemical products 9 Plastic, rubber 10 Metal basic industries and other non-metallic mineral products 11 Mechanical mach. & electric and electronic equipment P e e r R e F o r P e e r R e v i e w	O n l y
	4. Building	12 Transport equipment 13 Miscellaneous 14 Building v i e
	5. Services	15 Reparation and commerce 16 Hotels 17 Transport and communication services w
		18 Financial services 19 Renting and business services 20 Education, health and other services 21 Household services n l O	43
		y

Table A -

 A 3. Coefficient Estimates. GLS and SUR estimates. (1996-2005).[Continues]

	Regional dummies	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21

The exceptions are Wood Products in all the specifications and Financial Services in the estimation without regional dummies.

Using OECD country-level data,[START_REF] Harrigan | Factor endowments and the international location of production: econometric evidence for the OECD, 1970-1985[END_REF],[START_REF] Bernstein | Do endowments determine the location of production? Evidence from national and international data[END_REF]

Acknowledgements. The authors thank the two anonymous referees for valuable comments. Financial support from the Instituto Valenciano de Investigaciones

< R1 -General Regional Economics < R -Urban, Rural, and Regional Economics, R13 -General Equilibrium, Welfare Econ.

Note: ***, **,* significant at 1%, 5% and 10% respectively. Standard errors are in parentheses.


Enrique López-Bazo

Rosina Moreno
email: rmoreno@ub.edu

IN EDUCATION. EVIDENCE FROM SPANISH REGIONS

Keywords: economic development, education, productivity, rate of return JEL: O180, O470, R110

The objective of this paper is to furnish new evidence concerning the aggregate profitability of the accumulation of educational human capital. In addition to the traditional measure of the return to human capital, combining the information on its shadow price with the social cost of providing education allows us to confirm the profitability of investments in education as a tool for promoting economic growth. The possibility of obtaining estimations of these effects for each Spanish region enables us to empirically evaluate the amount of heterogeneity across regions in the effects of human capital.

INTRODUCTION

The effect that education can have on a society, as a mechanism that generates human capital, has meant that today the principal motivation underpinning human capital theory has been extended from simply accounting for wage differentials between individuals to that of explaining economic growth [START_REF] Willis R | Wage determinants: A survey and reinterpretation of human capital earning functions[END_REF]. Predictions of a range of theoretical models of economic growth (e.g. [START_REF] Lucas R | On the mechanics of economic development[END_REF] has given rise to many empirical exercises linking aggregate productivity and growth with the endowment of human capital (e.g. Mankiw, Romer & Weil, 1992;[START_REF]The role of human capital in economic development: evidence from aggregate cross-country data[END_REF][START_REF] Bils | Does schooling cause growth?[END_REF][START_REF] Krueger | Education and growth: why and for whom?[END_REF]. Despite recent findings that lend support to a positive effect of human capital based on the use of what is more refined human capital data (de la Fuente and Doménech, 2006), and to the link between economic performance and non-traditional measures of human capital such as the matching of educational supply and local labor market needs (Rodríguez-Pose and Vilalta-Bufí, 2005), the debate on the real contribution of human capital investments in promoting economic growth is by no means settled, and the evidence from an aggregate perspective on the effects of human capital on growth remains unclear [START_REF] Temple | Generalizations that aren't? Evidence on education and growth[END_REF]).

Many studies have not only identified human capital as being a major factor in determining a significant part of the levels and growth rates of productivity and per capita income (Mankiw et al., 1992;Barro, 2001), but they have also identified human capital as being a key element in strengthening the effect of other factors considered essential for economic growth, such as investment in technology (Romer, 1990;[START_REF] Aghion | Endogenous growth theory[END_REF] and trade openness (Miller et al, 2000;[START_REF] Serrano G | Complementarity between local knowledge and internationalization in regional technological progress[END_REF]. As a result, recent contributions have stressed the role of human capital in explaining growth differences across countries [START_REF] Krueger | Education and growth: why and for whom?[END_REF][START_REF]Does human capital matter for growth in OECD countries? A pooled mean-group approach[END_REF][START_REF] Engelbrecht H | Human capital and economic growth: cross-section evidence for OECD countries[END_REF] and across regions within countries (Cheshire and Magrini, 2000;[START_REF] Fingleton | Some alternative geo-economics for Europe's regions[END_REF]Di Liberto, 2008). It 3 is of little surprise then that financing the accumulation of human capital in the least developed economies through the educational system has been suggested as one of the main measures of development policy.

In this context, the first aim of this paper is to check whether human capital is a profitable investment once the cost of providing it is taken into account. With this purpose, we show how the use of the dual framework [START_REF] Berndt | Modelling the interrelated demands for factors of production: estimation and inference in equation systems[END_REF], through the specification of a cost system, can provide with this additional evidence concerning the contribution of human capital, acquired in the formal education system, to regional economic growth. 1 In this sense, the first step we give is to compute the return to human capital obtained with the estimates of a cost function aggregated with human capital, and compare it with the returns previously obtained in the literature estimating production functions. In a second step and thanks to the estimation of a cost system, we obtain the shadow price of human capital, defined as the price that the firms in the region would have been willing to pay for an additional year of education of all the employees in the economy. Combining the information on the shadow price with the social cost of providing education in each regional economy allows us to confirm the profitability of human capital investments as a tool for promoting economic growth. This second step is the major value added of this paper, since such measure of profitability can not be obtained through a production framework. Morrison and Siegel (1997) is one of the only studies to analyze some of the effects of human capital endowment on production activity by adopting the duality approach, in a more general context of the study of the effects of the accumulation of knowledge. 2 Yet, such study does not explore the possibility of obtaining an estimate of the return to human capital, or, for that matter, of any other measures of interest in the study of the effect of this capital such as the shadow price. As far as we know this analysis has not been previously addressed in the literature, and it is possible to deal with it in our case due to the use of the dual approach and the availability of data on the public and private costs of a year of education in the formal educational system in each of the Spanish regions. 3 In addition to that, the evidenced obtained from Spain might be paradigmatic when it comes to evaluating the contribution of this type of factor to economic development and to the evolution of regional imbalances. The level of education experienced a spectacular increase in all the Spanish regions in the last decades, though significant interregional differences in the level of education still remain. Interestingly, following the accession to the European Union, the country as a whole and, to a greater or lesser extent, all the regions opened to competition, and underwent a process of modernization of the productive and institutional structures. These processes have been shown to enhance the positive effect of human capital investments on productivity as they allow high-skilled individuals to obtain the appropriate return from the investments they made in education (Miller and Upadhyay, 2000;[START_REF] Serrano G | Complementarity between local knowledge and internationalization in regional technological progress[END_REF]. . We thus consider that the setting is adequate for assessing whether human capital can really promote economic growth, especially when this occurs in combination with other elements that might allow both individuals and regions to use this capital in productive activities for which they receive their corresponding return. Actually, we would expect the effect of human capital to be homogenous in all regions in the case that they were also homogenous in other aspects, such as in their productive structure, in their propensity to generate and adopt innovations and in their engagement in trade. Were this not the case, it is possible that the return to human capital would differ between regions, which means that an appraisal of its value as a tool for use in development policy would be particularly useful if information about the distribution of this effect across regions was available. Our empirical approach allows The rest of this paper is organized as follows. In the second section we present the model based on the duality theory that includes the human capital stock as a factor that influences the technology of production in an economy, and describe the empirical specification from which the effects of educational human capital will be estimated. The third section describes the dataset and the major variables in the empirical analysis, paying special attention to the accumulation of human capital in the Spanish regions over the last decades, while the results are reported in the fourth. The fifth section concludes.

EMPIRICAL FRAMEWORK

The aggregate variable cost function corresponding to an aggregate production function expanded with human capital can be expressed as follows:

) H , K , Y , P , P ( VC VC M L = (1)
where we consider two variable inputs, labor (L) and intermediates (M) which appear in the cost function through their prices, P L and P M respectively; a quasi-fixed input, physical

L LT M L LH M L LK M L LY 2 TT 2 HH 2 KK 2 YY M L 2 LL T H K Y M L L 0 M β + β + β + β β + β + β + β + β β +       β + β + β β β + β + β + β β + β + β = (3)
where t is a time trend which summarizes technological change. For ease of notation, variables in equation (3) onwards do not carry subscripts referring to the observations. This functional form permits the consideration of a wide range of substitution possibilities and can be accommodated within any production technology without the need to impose a priori restrictions on returns to scale. Intermediate prices are included as a relative factor to ensure that the function is homogeneous of degree one in factor prices and symmetry conditions are imposed [START_REF] Berndt | Modelling the interrelated demands for factors of production: estimation and inference in equation systems[END_REF]. Besides, no kind of a priori returns to scale is imposed.

The share equations for variable inputs on variable costs are obtained through the differentiation of equation ( 3

• P S YT YH YK M L LY YY Y Y Y β β β β β β ∂ ∂ ≡ (5)
The set of expressions (3)-( 5) would comprise the framework of the partial static equilibrium, that is used in the rest of the paper to obtain the measures of the effects of human capital.

DATABASE

The spatial units considered here correspond to the 17 Spanish NUTS II regions 5 and the period analyzed runs from 1980 to 1995. Thus, as stated in the introductory section we shall consider the influence of human capital in the private productive sector of the Spanish regions during a period in which there was a marked accumulation of human capital in all the regions, in conjunction with the modernization of the Spanish economy and its opening up to the exterior following integration into the European Union.

The measure used for human capital in this study combines the average number of years in each level of education with the percentage of the population in each of these levels, thereby producing an attractive synthetic indicator of educational human capital, like that of the average number of years of education of an economy. This type of indicator has been constructed for various samples of economies by, among others, [START_REF] Kyriacou G | Level and growth effects of human capital, Working paper C. Starr Center[END_REF], [START_REF] Barro R And | International comparisons of educational attainment[END_REF], 1996, 2001), and has been used to analyze the contribution of this factor to growth [START_REF]The role of human capital in economic development: evidence from aggregate cross-country data[END_REF], [START_REF] Temple | The new growth evidence[END_REF]), DiLiberto (2008) and Pereira and Aubyn (2009). 6 The information required for constructing the indicator was drawn from Mas, Pérez, Uriel, Serrano & Soler (2002).

We have information for five levels of education: no schooling, primary education, secondary education, first level of higher education, and second level of higher education. Given that this information is tabulated for, among other groups, the workers employed in each period, it is possible to obtain the percentage of workers for each of these levels of education, for the period 1964 to 2001. We have followed [START_REF] Serrano L | Indicadores de capital humano y productividad[END_REF] by designating 0 years to workers with no schooling, 3.5 years to the group with primary education studies, 11 years to those having completed secondary education, 16 years to those workers with a first level of higher education and 17 years to those with a second level of higher education.

Figure 1 illustrates the evolution in the education of the working population engaged in the private productive sector of the Spanish economy as a whole. It clearly reveals the important growth in the level of education of the working population described above. The group of workers with no schooling virtually disappears and primary education -the preponderant level for much of this period for which data are available-is supplanted by secondary education. Although smaller in number, the increase in the percentage of workers with university studies is notable as well.

[Insert Figure 1 around here] Correspondingly, the average years of schooling of workers in the private productive sector of the Spanish economy increased notably throughout the period (Figure 2). In particular, the 9 increase during the period in which this study is focused was even more intense than in earlier periods. Thus, in a decade and a half there was an increase of more than three years, reaching 8.34 years in 1995. Although the period following this year is not included in the analysis undertaken here, it should be pointed out that this trend shows no sign of weakening.

[Insert Figure 2 around here]

The results obtained for Spain as a whole are reproduced in the case of all the regions, although marked differences persist in the regional endowment of human capital at the end of the period. Specifically, Figure 3 shows the average years of education of those employed in the private sector in 1980 and in 1995, i.e. the first and last years of the period analyzed in our subsequent study. It can be seen how, despite the convergence in the levels of human capital over the period, marked differences persist across regions. Thus, compared to 9.6 years in Madrid in 1995, Galicia and Extremadura do not reach 7 years.

[Insert Figure 3 around here] Therefore, the increase in the education stock in all the regions and the existence of marked variability among them should provide us with substantial information for comparing the effect that educational attainment has on aggregate productivity and economic growth which, as discussed above, will enable us to draw conclusions as to the aggregate return to investment in human capital.

The remaining statistical information has been taken from the BD.MORES database prepared by the Spanish Ministry of Economy and Finance [START_REF] Dabán | La base de datos BD.MORES, Dirección General de Análisis y Programación Presupuestaria[END_REF]. 10 Specifically, of the data provided by the BD.MORES database, we have used the series relating to Gross Added Value at factor prices, employment, wages, private physical capital stock and its cost. Similarly, the data referring to the intermediates, quantity and price, are taken from Díaz (1998), so that the output variable chosen is the production value, which is obtained by summing intermediates to value added. The time period for all these series runs from 1980 to 1995.

RESULTS

Estimate of the coefficients of the cost system

For purposes of empirical implementation the models discussed in section 2 have to be embedded within a stochastic framework. In order to do this we consider errors in variable costs -eq. 3-and variable factor demands -eq. 4-as being due to errors in optimization in the short-run, while that for the equilibrium in the output market -eq. 5-represents unanticipated information that becomes available once the decision on the amount to produce has been taken. To allow for separate elasticities across groups of regions we have included two dummy variables interacting with the linear terms of the variable factor prices, the stock of physical capital and output. Correspondingly, those dummies have been included as well in the factor share equations and in those for the equilibrium condition of output. The first of these dummies (D1) controls for the size of the regional economy, in terms of the share of its output over the one of the country. The second (D2) is included to account for the situation in some regions in which the ratio of physical to human capital was fairly low. 7 The unknown coefficients in the model were estimated using the iterative Zellner technique for seemingly unrelated regression equations, which converge to the maximum likelihood estimator for models of this type. In this regard, it should be mentioned that in addition to the 3) to ( 5), the estimated cost system included an additional equation for the short-run demand of physical capital. This is so to account for the likely correlation between the shocks that affect this quasi-fix factor and the other variables in the system. However, according to the partial static equilibrium framework, no constraints between the coefficients of that additional equation and the set of coefficients in the variable cost system in (3) to (5) were imposed in the estimation. 8 The results of the estimation are shown in Table 1. The restrictions between the parameters of equation 3 and those of equations 4 and 5 are imposed (column i, where we only give the estimates of equation 3 to avoid repetition), whereas as indicated above the equation for the short-run demand of physical capital is estimated in the model without imposing restrictions between its parameters and the others from the cost system (column ii). In addition, we show the results obtained from the likelihood-ratio test of the null hypothesis of which the matrix of covariances of the disturbance of the system of equations is diagonal -in other words, the contrast of the fit of the cost system as a model of apparently unrelated equations. The value obtained for the test statistic (108.8) lies clearly within the rejection zone of the null hypothesis, so that the Zellner estimation for the SURE-type estimation is adequate.

[Insert Table 1 around here] It should be pointed out that it is unreasonable to undertake any kind of interpretation or structural analysis directly from the estimated parameters, given that we are using the translog approximation of the unknown functional form underlying the cost system. Similarly, it is worth stressing that convergence in the estimation was reached with a relatively small number of iterations and, more importantly from an economic point of view, that the coefficients of 12 the terms that involve the dummy variables on the one hand, as well as all the variables that describe the effect of human capital, are together significant. Consequently, the Wald test confirms the existence of a significant effect of human capital on costs.

Aggregate returns to human capital

There are various measures easily derived from the estimation of the cost system defined in section 2 that allow us to quantify and evaluate the contribution of investments in human capital to economic growth. The first one is the change in production costs due to a marginal addition to the stock of human capital, the cost elasticity of human capital, defined as:

SC H H VC SC H H SC H ln SC ln H , SC ∂ ∂ = ∂ ∂ = ∂ ∂ ≡ ε (6)
The elasticity in ( 6) is negative when additions to the stock of educational human capital save costs of production in a given economy. That is, when they contribute to improve productivity. In connection with the cost elasticity is the traditional elasticity of output to human capital usually obtained in growth studies analyzing the effects of human capital. 9 This measure can be recovered from the dual approach thanks to the envelope theorem (see Chambers, 1988):

Y H Y SC H VC = H ln Y ln = H , Y ∂ ∂ ∂ ∂ - ∂ ∂ ε (7)
This relationship provides the connection between the primal (via the production function)

and the dual (via the cost function) measurement of the productivity impact of capital stocks.

However, in the case of educational human capital it is more intuitive to analyze the impact of an additional year of education on output. We can define the return to human capital as the increase in output given an increase of one year in the average level of education of the labor force. This semi-elasticity of output with respect to human capital is given by:

F o r P e e r R e v i e w O n l y 13 H 1 = H Y ln R H , Y H ε ∂ ∂ ≡ (8)
The cost elasticity in (6) and the return to human capital in (8) can be estimated for each region and year by using the parameters estimated in the cost system and the corresponding values for the variables involved. Table 2 summarizes the results, providing the average for each region throughout the period considered and the global average for a representative Spanish region. 10 It can be seen in the first column that the improvements in the endowment of human capital gave rise to a saving in total production costs (ε SC,H < 0), which is true in all the Spanish regions. This confirms that the improvement in educational attainment of the working population contributed positively to the returns to scale of the private productive sector. Accordingly, the estimation of the returns to human capital is positive and of a sizeable magnitude in all the regions under analysis, with an average return slightly greater than 9%. In other words, for the mean of the period under consideration and in a typical Spanish region, an increase in one year in the average level of education of the labor force gave rise to an increase of 9% in output. At this point, it should be born in mind that the estimation of the return to human capital in a cost framework is parallel to the one obtained through using a production function aggregated with the stock of human capital. In this sense, we observe that the magnitude of our estimate for the aggregate return to human capital is of the same order of magnitude as that reported in [START_REF]Does human capital matter for growth in OECD countries? A pooled mean-group approach[END_REF] for a sample of OECD countries from a growth equation setting. It is also quite similar to the return estimated for the Spanish economy by Serrano (1996) using the production framework, and by [START_REF] Arrazola | Three measures of returns to education: An illustration for the case of Spain[END_REF] using individual data on wages and school attainment.

The positive and non-negligible return for human capital obtained in this paper would therefore justify subsidies being made to estimulate the education of individuals, as an effective tool of development policy given that the resources that are diverted for this purpose 14 would be effectively spent, even in comparison with the return obtained from alternative investments. 11 Yet this global result hides an important regional heterogeneity. Indeed, the mean return to human capital over the period under analysis is very high in the cases of the regions of Aragon, Castilla-Leon, Castilla-La Mancha, Extremadura and Cantabria. By contrast, in Andalucia, Galicia, Catalunya, Valencia, Madrid, Murcia, Navarra and La Rioja the return on human capital was considerably lower. Note, for example, that the return in the region in which investments in human capital were most productive (Extremadura) more than double the region with the lowest return (La Rioja).

[Insert Table 2 around here]

In short, the investments in education in all the regions of Spain presented far from negligible aggregate impact, given that they contributed significantly to reducing production costs, that is, to increasing the returns of the private productive sector. But the magnitude of this effect was far from homogenous throughout all the regions. This suggests that the return could be related to the level of development attained by each regional economy as well as the existing endowment of educational human capital. In order to analyze these questions, Figures 4 and5 show the relationship between the estimation of the return on human capital in each region and year, and its productivity and stock of human capital respectively. A trend is noted for the regions with the lowest levels of productivity to benefit most from the accumulation of this factor (Figure 4). 12 This result supports the idea that, in general terms, investments in human capital might be an effective tool in enhancing productivity in the less developed regions, and that the social or aggregate return to investments in human capital in those regions might even be larger than in the most productive ones. As expected, the estimated return is negatively related to the existing relative stock of human capital. This is derived from Figure 5 in which the estimated return for each region and year is related to the corresponding ratio of human to physical capital. The negative relationship confirms that the return was higher in those regions in which there was a shortage of human capital in relation to the stock of physical capital, and suggests that investments in educational human capital should be supported up to the level in which the ratio of human to physical capital is in its equilibrium. That way, the process of regional convergence will be reinforced as the endowment of a factor that has been shown to have a positive influence on growth will be increased in regions with levels of development below the average.

[Insert Figures 4 and5 around here]

Time profile of the returns to human capital

From the above results it can be deduced that, for the whole period under review, investments in human capital were on average profitable in all the Spanish regions, though their effect might have been stronger in those with low initial endowments of such type of capital and low levels of productivity. This evidence points to the presence of decreasing returns to the accumulation of educational human capital. Actually, under the assumption of diminishing returns for the accumulation of this capital, the continuous increase in its stock throughout the period and in all the regions, as described in Section 3 (Figures 2 and3), could have brought about a decreasing trend in returns, which could even have led to the exhaustion of this resource as a factor that strengthens growth in the Spanish regional economies at the end of this period. In order to verify this, we have calculated the return for each region in each of the years under consideration and that corresponding to the average of all the Spanish regions.

For reasons of space, Table 2 only provides information about the latter. 13 As expected under the assumption of decreasing returns, the most notable feature in the results in the third and fourth columns of Table 2 is the large fall in the returns to human capital. Thus, at the end of the period these returns represented slightly more than 50% of those observed in 1980. However, the return of an extra year of education at the end of the period in a representative Spanish region maintained its importance (almost 7%). But interestingly, at the end of the period, the return in some of the regions is rather low (4.5% in La Rioja, around 6% in Catalunya and Madrid) while in some others it remains large enough (10.25% and 8.4% in Extremadura and Castilla La Mancha respectively) to strongly support additional investments. Therefore, the lower return of an extra year of education in some of the most economically developed regions in Spain (such as Catalunya and Madrid), compared to those less developed, can be a signal of the existence of diminishing returns for the accumulation of this capital. Given the higher levels of the stock of human capital in those advanced regions, an increase of one extra year of education in their population has lower, although still important, benefits.

Hence, it could be said that while educational human capital in the Spanish regions has played a significant role during the period analyzed, this significance has decreased over time in line with the continuous increase in its stock, and its importance is unlikely to persist with the same strength into the future. Thus, investments in human capital seemed to be a highly effective means of increasing productivity and, hence, promoting economic growth even in the mid-nineties, when the Spanish economy already achieved a substantial degree of economic development. And considering the trend in returns and the current existing stocks, we predict that there is still room for significant returns to human capital investments, particularly in those regions with the smallest endowments.

The shadow price and the cost of provision of human capital

Results described so far point to positive aggregate returns to investments in human capital.

However, to confirm the effectiveness of human capital as a tool for promoting economic growth it would be interesting to relate its effect on productivity, i.e. in saving production costs, with the social cost of provision of additional years of education of the labor force. As far as we know this analysis has not been previously addressed in the literature from an aggregate point of view, and it is possible to deal with it in our case due to the use of the dual approach and the availability of data on the public and private costs of a year of education in the formal educational system in each of the Spanish regions. This analysis therefore comes to complement the measure of the return to human capital, which is the traditional measure obtained in the literature, and can be considered as the main value added of this paper.

In brief, we will state that investments in educational human capital will be socially profitable in a given region when its shadow price, that is the cost saving it causes to the productive sector of that region, exceeds the cost of provision of a year of education for the labor force in the region. We will firstly describe the way in which we compute the above mentioned measures, and then we will discuss the major results for our sample of regions.

If firms in the economy obtain cost reductions due to its aggregate stock of human capital, it can be considered that they will be willing to pay for it up to an amount equal to the savings in cost that this endowment implies. Hence, it is possible to obtain a measure of the implicit willingness of all firms in the economy to pay for educational human capital -that is, the shadow price of human capital: ). The shadow price is defined as the reduction in variable costs due to an increase in the stock of human capital. As long as this value is positive, human capital will maintain, to a greater or lesser extent, a net substitutability relationship with variable factors, so that investments in this type of capital will imply improvements in efficiency, the latter understood as net savings as a result of decreases in variable input utilization and thus in variable costs. For the sake of convenience we define the shadow price by worker as Z H /L, where L is the number of workers.

      - ε = ∂ ∂ - ≡ H VC H VC Z H ,
To compare the shadow price of human capital investments with their cost we define a q-Tobin type of measure as q H ≡ Z H /P H , where P H is the cost of an additional year of education for the workers in the region. Given that we are using the average years of schooling of the labor force as the measure of human capital, we are actually considering that workers accumulated it throughout the formal system of education. The cost of one year in the educational system financed by the government and the households is the measure used to proxy for P H . Data for the cost of education comes from the report of Uriel, Moltó, Pérez, [START_REF] Uriel E | Las cuentas de la educación en España y sus comunidades autónomas: 1980-1992[END_REF]. It includes the cost per student in the public educational system in the NUTS II Spanish regions for the period 1980 to 1991. It is obtained by adding to the amount financed by different governmental agencies the expenditure made by households in connection with the education (fees, books, transportation, and so on). The cost in the private educational centers is available as well from the same source, but in this case we have decided not to use this information as it was obtained by an indirect estimation, and its quality is much lower than in the case of the public system, as stressed by the authors of the above-mentioned report. Anyway, the cost of the public system is higher for all regions and years, basically due to higher labor costs in the public versus the private centres. [Insert Table 3 around here]

The first column in Table 3 shows the estimates for the shadow price per worker, whereas the cost of one year of education in each region relative to the Spanish average cost is given in the second column, and finally the results for the q H are in the third column. It should be noted that, to save space, these figures refer to the average over the period 1980 to 1991 in each of the regions. We find that on average over the period under analysis the firms on a representative Spanish region would have been willing to pay more than 3,000 € for an additional year of education of its labor force. This figure represents the savings in variable costs for an additional year of education. However, and as occurred with the return, we should highlight the significant regional variability in the shadow price of human capital (its standard deviation being greater than 570€). Thus, while Aragon, Cantabria and Extremadura exceeded 4,000 €, Galicia did not reach 2,100 €.

However, figures in the second column of Table 3 show how the cost of education in the Spanish regions is far from homogeneous as well. For instance, the lowest cost is observed in the lagged regions of Andalucia and Castilla La Mancha with an 87% of the average cost in Spain, while the cost in some other regions is more than 10% over the national average. This makes it necessary to relate the shadow price of human capital in each region to the cost for its provision. In accordance with the results in the previous sections, the value for the q H -Tobin measure suggests that investments in educational human capital were very profitable in all the regions. On average, the shadow price more than triplicates the cost of the investment, which suggests that, from a social point of view, human capital was in a shortage over the period under analysis. Actually, regional estimates indicate that this was so in all the regions, although heterogeneity in both the shadow price and the cost of education causes important regional variation in the q H measure. The largest profitability of investments was reached in the lagged regions of Extremadura and Castilla La Mancha, which combined a high shadow price and a relatively low cost. Interestingly, profitability was below the average in some other less-advanced regions, such as Galicia, Andalucía and Canarias.

Summing up, investments in human capital, made through the formal system of education, not only contributed to enhance productivity growth in Spain but were also socially profitable, in the sense that the social return they provided were clearly superior to their cost. But this general result should not hide another important feature, that is the existence of noticeable heterogeneity across regions in the aggregate return and social profitability of human capital.

Such heterogeneity should be considered when supporting and financing human capital as a tool for regional development policy.

CONCLUSIONS

This paper provides a new insight in the analysis of the impact of human capital on regional economic growth through the use of the duality framework to give evidence concerning the aggregate profitability of the accumulation of human capital. We have described an analytical strategy based on the framework supplied by the duality theory that in addition to the return to human capital also allows us to compute the shadow price of investments in this type of capital. Combining the information on the shadow price with the social cost of providing education in each region allows us to assess the profitability of investments in human capital as a tool for promoting economic growth. From a purely economic perspective, the identification of a positive effect would justify the use of public resources for financing We have shown that the return to human capital in Spain was positive throughout the period studied. And this aggregate return is obtained to be superior to the cost of the investments in human capital, made through the formal system of education. This finding would justify the subsidizing of human capital through financing the education of individuals, given that the resources devoted to this purpose would prove profitable. We can affirm, therefore, that it is socially justifiable to dedicate resources to the financing of education given that it results in increases in productivity and, consequently, in greater economic growth.

However, our results confirm that the magnitude of the effect of human capital is far from homogenous across regional economies, even in the case of regions within a country. This result agrees with the recent evidence in Di Liberto (2008) which only obtains a significant positive effect of human capital in the lagging regions of the Italian South. Relating this effect to the level of development attained by each regional economy as well as the existing endowment of human capital, a trend is observed for the regions with the lowest levels of productivity to benefit most from the accumulation of this factor. Similarly, the negative relationship of the return with the existing stock of human capital suggests that no conflict was caused when using the stimulus for investment in human capital in the less developed regions as a development policy measure, given that the objectives of efficiency and equity are simultaneously met. Thus, such heterogeneity in the aggregate return and social profitability of human capital should be considered when supporting and financing human capital as a tool for development policy. The conclusion from a social perspective is undoubtedly the confirmation that educational policy can really play a key role in regional economic development. Used correctly and in combination with other incentives, it should allow greater levels of productivity and income, together with a greater development of the least favored economies. If so, investments in human capital made in such regions would positively contribute to the process of regional convergence.

Whatever the case, there are a number of aspects arising from this study which need to be analyzed in greater detail in future studies. First, one could obtain measures of the profitability of investment at different levels of education, following for instance the suggestion in Di Liberto ( 2008) and Pereira and Aubyn (2009). Here, we have considered the shadow price as being homogenous for all levels of education; however, it would be interesting to check whether the effects may differ significantly from one level to another. On the other hand, as we have not included the opportunity cost of school attendance (foregone wages), our measure of the cost of education might be underestimating the real price of human capital investments. It might be of interest to include this opportunity cost as well as to consider some other elements linked to the level of education that have not been taken into account in the present analysis such as the change in the probability of being employed and the increase in taxes associated to higher wages. Undoubtedly, they might have a role when measuring the aggregate profitability of human capital investments. in each region relative to the Spanish average cost. q H -Ratio is a Tobin type measure obtained as the ratio of the shadow price of education and the cost of an additional year of education. 2 The use of the dual approach has been much more frequent in analyzing the effects of investments in infrastructure and public capital (e.g. Nadiri and Mamuneas, 1994;Morrison and Schwartz, 1996;Moreno, López-Bazo & Artís, 2002).

3 The macroeconomic evidence on the impact of educational human capital presented to-date has been based on the analysis of the aggregate return to human capital obtained through the application of a range of specifications centered on a primal approach -in other words, basing the analysis within a production function framework (see the survey in [START_REF] Krueger | Education and growth: why and for whom?[END_REF]. As said above, an alternative and complementary approach to analyze the effect of human capital at the aggregate level -and one that is virtually unexploredis the one based on the duality theory.

4 This corresponds to a partial static equilibrium model where physical capital cannot be instantaneously adjusted to the optimum stock in every time period. A full static equilibrium can also be defined in which that type of capital is assumed to be always in equilibrium (see for instance Brown and Christensen, 1981 for further details). Our preference for the partial static equilibrium model lies in the result of the formal test proposed by Schankerman and Nadiri (1986) to the data used in the empirical section of this paper. Detailed results are available upon request.

5 NUTS is the French acronym for Nomenclature of Territorial Units for Statistics, a hierarchical classification established by EUROSTAT to provide comparable regional breakdowns of EU Member States. In the case of Spain, the NUTS II regions correspond to the 17 Autonomous Communities, historical and administrative regions with a high level of political and financial autonomy.

6 Alternatives, such as the rate of schooling or the literacy rate have been subjected to considerable criticism due to their clear limitations when approximating an economy's human capital stock. They have, however, been used in several studies because of the impossibility of obtaining detailed information about the levels of education of the population. 7 Comparable regional dummies were considered when estimating an aggregate cost system for the Spanish regions in [START_REF] Boscá | The Effect of Public Infrastructure on the Private Productive Sector of Spanish Regions[END_REF]. 8 We follow Morrison and Schwartz (1996) in taking this decision. To identify the impact of the aggregate stock of education in the economy, we follow the idea in Morrison and Siegel (1997) that human capital, as an external factor, can cause downward shifts of cost curves, so that their effect on aggregate productivity can be examined through a cost-function approach. It should then be noted that our approach differs from the one based on estimating human capital externalities from a Mincerian approach (see among others Rauch, 1993;[START_REF] Acemoglu | How large are human capital externalities? Evidence from compulsory schooling laws?[END_REF][START_REF] Fields B | Identifying Human Capital Externalities: Theory with Applications[END_REF][START_REF] Heuermann D | Human capital externalities and the urban wage premium: Two literatures and their interrelations[END_REF] for a recent survey). The use of a cost function to analyse the effect of human capital must be understood therefore as parallel to the common practice in economic growth literature of using a production function aggregated with the stock of human capital (see for instance Topel, 1999). Both frameworks lie on the same idea that a higher endowment of human capital in the economy may imply higher productivity growth. In the duality framework, this result implies that additional investment in human capital results in a downward shift in the aggregate cost function.

10 The set of effects for each of the regions in each of the years is available upon request.

11 By way of example, estimations of the return on investments in public productive capital on the Spanish economy in a similar period stand at around 3% (e.g. 2.8% in Moreno, López-Bazo & Artís, 2003, and 2.6%

in [START_REF] Boscá | The Effect of Public Infrastructure on the Private Productive Sector of Spanish Regions[END_REF].

12 A similar trend is observed when the yearly average for each region is plotted against its average level of productivity over the period. 13 The same temporal profile was recorded in each of the Spanish regions. Results are available upon request.

  -mentioned effect for each of the regions under analysis and, thus, assessing the particular contribution of human capital to economic growth in each of them. To provide evidence of the heterogeneous profitability of human capital in the Spanish regions constitutes the second main objective of this paper.

  Similarly, our results should enable us to assess the use of education as a tool in regional development policy.

Figure 5 .

 5 Figure 1. Educational attainment of the Spanish labour force

  paper we use indiscriminately the terms human capital and education since we are referring specifically to the human capital acquired in the formal educational system.

Table 1 . Estimates of the partial static equilibrium model

 1 SURE estimation of equations 3 4, 5 and the equation for the physical capital share as described in the main text of section 4. The restrictions between the parameters of equation 3 and those of equations 4 and 5 are imposed (column i), whereas the equation of the share of physical capital is estimated in the SURE model without imposing restrictions with parameters of the other equations, in accordance with the framework of the partial static equilibrium (column ii).

	Page 32 of 37

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Table 2 . Regional and time effects of education

 2

		Cost elasticity of	Return to		Cost elasticity of	Return to
		education	education		education	education
		(ε SC ,H )	(R H )		(ε SC ,H )	(R H )
	ANDALUCIA	-0.496	0.081	1980	-0.708	0.131
	ARAGON	-0.791	0.106	1981	-0.676	0.121
	ASTURIAS	-0.637	0.091	1982	-0.672	0.115
	BALEARES	-0.678	0.092	1983	-0.686	0.112
	CANARIAS	-0.620	0.092	1984	-0.638	0.100
	CANTABRIA	-0.767	0.100	1985	-0.628	0.095
	CAST -LEON	-0.668	0.104	1986	-0.649	0.096
	CAST-LA MANCHA	-0.668	0.114	1987	-0.629	0.089
	CATALUNYA	-0.729	0.085	1988	-0.632	0.086
	VALENCIA	-0.599	0.085	1989	-0.632	0.082
	EXTREMADURA	-0.726	0.144	1990	-0.630	0.079
	GALICIA	-0.404	0.078	1991	-0.640	0.078
	MADRID	-0.800	0.080	1992	-0.633	0.076
	MURCIA	-0.508	0.081	1993	-0.671	0.078
	NAVARRA	-0.748	0.086	1994	-0.664	0.074
	PAIS VASCO	-0.795	0.091	1995	-0.632	0.069
	RIOJA	-0.439	0.062
	Average for Spain	-0.652	0.093

Table 3 . Shadow price of education and its cost of provision

 3

		Shadow price per worker (Z H /L)	Relative cost of education (P H )	q H -Ratio
	ANDALUCIA	2.603	0.871	2.907
	ARAGON	4.042	1.121	3.643
	ASTURIAS	3.324	1.055	3.005
	BALEARES	3.329	0.941	3.514
	CANARIAS	2.883	1.003	2.863
	CANTABRIA	4.028	1.099	3.497
	CAST -LEON	3.520	1.107	3.088
	CAST-LA MANCHA	3.580	0.889	4.076
	CATALUNYA	3.329	0.958	3.558
	VALENCIA	2.712	0.890	3.034
	EXTREMADURA	4.001	0.983	4.037
	GALICIA	2.075	0.959	1.971
	MADRID	3.143	1.073	2.923
	MURCIA	2.575	0.899	2.944
	NAVARRA	3.582	1.045	3.464
	PAIS VASCO	3.876	1.125	3.630
	RIOJA	3.059	0.982	2.941
	Average for Spain	3.274	1.000	3.240

Note: Shadow price per worker (Z H /L) is given in thousands of euros. Relative P H is the cost of education

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Acknowledgements:

The authors acknowledge financial support from Ministerio de Educación y Ciencia, Programa Nacional de I+D+I, ECO2008-05314 as well as from the project "Intangible Assets and Regional Economic Growth (IAREG)" financed by the European Union under the 7 th Framework Programme (FP7-SSH-2007-1. 216813).

Development < O -Economic Development, Technological Change, and Growth, O47 -Measurement of Economic Growth|Aggregate Productivity < O4 -Economic Growth and Aggregate Productivity < O -Economic Development, Technological Change, and Growth, R11 -Regional Economic Activity: Growth, Development, and Changes < R1 -General Regional Economics < R -Urban, Rural, and Regional Economics