A SPATIAL AUTORREGRESIVE PANEL MODEL TO ANALYZE ROAD NETWORK SPILLOVERS ON PRODUCTION. Inmaculada C. Álvarez * José L. Zofío **

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1 A SPATIAL AUTORREGRESIVE PANEL MODEL TO ANALYZE ROAD NETWORK SPILLOVERS ON PRODUCTION Abstract Inmaculada C. Álvarez * José L. Zofío ** Universidad Autónoma de Madrid The production function approach is used to introduce the impact of public infrastructure on economic growth. As regressors we incorporate new concepts related to the internally used and imported transport infrastructure capal stock, which are actually used in commercial flows, calculated by network analysis performed in GIS. The internally used capal stock represents own infrastructure that benefs accessing markets whin a given region, while the imported capal stock characterizes the spillover effect associated to the use of other neighboring regions. From an econometric perspective, we introduce spatial interdependence in these type of models, extending Baltagi and Liu s (2011) method based on instrumental variables estimation in spatial autoregressive panel models wh random effects. We also define and estimate the spatial direct and indirect marginal effects associated to the explanatory variables capal stock variables. We illustrate the methodology wh Spanish provincial panel data for the period Results support the hypothesis that the imported capal has a posive effect on production both for the whole economy and the manufacturing sector. KEYWORDS: Transport spillovers; Market access; Network analysis; GIS (Geographic Information Systems); Production function; Panel Data Econometrics. JEL CODES: E22, H54, R49 * Corresponding author: Departamento de Análisis Económico: Teoría Económica e Historia Económica, Universidad Autónoma de Madrid, C/ Francisco Tomás y Valiente, 5, E-28049, Madrid, Spain Voice: , Fax: , inmaculada.alvarez@uam.es ** Departamento de Análisis Económico: Teoría Económica e Historia Económica, Universidad Autónoma de Madrid, C/ Francisco Tomás y Valiente, 5, E-28049, Madrid, Spain Voice: , Fax: , jose.zofio@uam.es We are grateful to Professor Badi H. Baltagi for his helpful comments and suggestions and Carlos Llano and the C-intereg project team for sharing the data on the Spanish interregional trade ( Authors acknowledge financial support from Madrid s Directorate-General of Universies and Research: under grant S2007-HUM-0467 ( the Spanish Ministry of Transportation, P42/08, and the Spanish Ministry of Science and Innovation, ECO and TRA

2 1. Introduction We analyze the impact (spillovers) of transport infrastructure on economic activy, following the production function approach, extended so as to account for spatial effects by way of an autoregressive panel data model. In the lerature, numerous studies take into account the spillover effects understood as the benefs obtained by a region when using the infrastructures existing in other regions for trading (Pereira and Roca-Sagalés, 2003). Some of these studies (García-Milá and McGuire, 1992; Cantos et al., 2005; Delgado and Álvarez, 2007) evaluate the importance of spillovers differentiating by levels of terrorial disaggregation. Following this thread these studies usually quantify the spillover through a crerion of proximy, incorporating the public capal corresponding only to adjacent neighbors. Based on this analytical framework, in this study we contribute in two distinctive ways. In first place, we consider a new concept of transport capal stock used in commercial relations, corresponding to the internally used and imported capal stocks as discussed in Alvarez et al. (2012). A given geographical level of aggregation, e.g., countries, regions, provinces, the internally used capal stock corresponds to the road infrastructure suated whin an area, that is used in trade flowsexports and importsto access markets. Complementing this internal stock, the imported capal stock represents the spillover effects derived from using the road network capal stock suated in neighboringadjacent and non-adjacentareas. Secondly, we apply novel estimation methods pertaining to the spatial econometrics lerature; particularly we employ a spatial autoregressive panel data model that allows us to determine the marginal direct and indirect effects associated to the explanatory variables, including the internal and imported capal stocks. Spatial econometric techniques allow us to capture de spatial interdependence in empirical analyses. Baltagi and Liu (2011) develop a method of estimation for autoregressive spatial panel models wh random effects based on an instrumental scheme. These authors obtain the best two stage least squares estimator (SEC-B2SLS). In our empirical application, the estimation of the production function at the provincial level in Spain introducing road transport infrastructurecapal stocksis developed considering the SEC-B2SLS introduced by these authors. Addionally, we follow Lesage and Pace (2009) to introduce the partial derivatives effects associated wh changing explanatory variables. The own partial derivative represents the direct effect, while the cross partial measures the effect on other regions or indirect effect. 2

3 The paper is structured as follows. In the next section we briefly present well-known methodological approach corresponding to the production function framework. In section 3 we present the relevant variables, databases and statistical sources, paying a special attention to the new definions of internal and imported capal stocks. In section 4 we perform regression analyses, and in section 5 we determine the direct and spillover effects of transport infrastructure on production. In the last section we present the main conclusions. 2. Methodological approach. Following Alvarez and Delgado (2012) and Alvarez et al. (2012), we analyze the impact of transport infrastructure on regional production by embedding our new stock variables whin the existing regional production function models. We measure the magnude of the spillovers between regions and compare these results wh the ones obtained using spatial econometrics techniques. Particularly, this analysis is developed applying the instrumental variable estimation in spatial autoregressive panel models, introduced by Baltagi and Liu (2011). Our analysis departs from the standard production function model, for a regional panel data for N observations along T periods: i v X ; e, i 1,..., N, t 1 T Y f,..., (1) Where Y is the output of the i-th province in the t-th period; X is a (1 x k) vector of explanatory variables, is a (k x 1) vector of parameters to be estimated, i is the vector of province effects and v is the remainder error term. It is assumed that independent of each other and the regressor matrix X. i and v are The usual input variables include the amount of labor ( L ), private capal ( K ), and the public capal stock incorporating the road infrastructure. Using this structure, we introduce a new concept of used capal stock to determine s contribution to production. This allows us to differentiate between the internally used capal stock ( INTKP ) capturing direct effects, and the imported capal stock from other locations ( IMPKP ) to which we associate the spillover effects, and the rest of the public capal stock ( KP ). In order to do 3

4 so, we extend the production function (1) so as to include these new variables as regressors: Y f i v L K ; g( KP, INTKP, IMPKP ; ) e, (2) The empirical model to be estimated is based on the log-linear Cobb-Douglas (CD) aggregate production function: log Y log L L K log K KP log KP INT log INTKP IMP IMPKP v (3) Most studies use the production function approach to estimate the elasticy of inputs. Under the assumption of separabily of the production function and the CD specification, the vector of coefficients represents the elasticies of the different public capal stocks in i road infrastructure. The sign and magnude of the INT parameter represent the effect of own public road capal stock that is really used at the national, regional or provincial level internal capal stock, while IMP allows us to determine the importance of the spillover effectsimported capal stock. As for this latter concept, the nature of the transport infrastructure results in benefs that transcend the borders of the regions where they are located, and the use of a region s capal by neighboring regions can be though as an import of capal stock, hence the name. These spillovers effects are scarcely studied in the lerature and, as far as we know, have not been analyzed in the context of a spatial autoregressive panel data model. For the Spanish case, some studies (García-Milá and McGuire (1992), Cantos et al. (2005), Delgado and Alvarez (2007) and Alvarez and Delgado (2012)) show the direct posive effects of infrastructure transport and confirm the significance of the spillover effect. Otherwise, the majory of the studies endeavoring to quantify the effects of transport infrastructure on private production are focused on high capacy roads in the U.S. (see Cohen and Morrison (2002) and Pereira et al. (2004)). Following this lerature, we consider as spillover effect the road infrastructure existing in all the rest of provinces, not only in neighboring ones, weighted by commercial trade flows, which constutes the imported capal stock. Next, we introduce spatial interdependence in our model. Baltagi and Liu (2011) propose a method based on instrumental variables estimation in spatial autoregressive 4

5 panel models. To introduce the spillover effects we are able to control for spatial interdependence in the production equation, considering an extended version of the approach proposed by these authors and therefore we adopt the following autoregressive spatial panel model: Y WY X WX Z v (4) Y X u Z v Particularly, considering the CD specification in (3), we estimate the following specification incorporating spatial interdependence in the dependent variable and in some explanatory variables: ln Y INT W ln Y ln L 1 ln INTKP IMP L ln K ln IMPKP W ln L K 2 KP ln KP i Z v (5) where W I T W and W N ( NxN ) is a spatial weight matrix which defines dependence N across N provinces. We refer to WY and variable and the labor input, respectively. 1 WL as the spatial lag of the dependent output The common approach in the lerature to capture and measure the spatial interdependence is based on the consideration of a physical contiguy matrix, in which s elements would be 1, for two bordering provinces and 0 for all others. These matrices treat physical proximy as the main driver for the presence of spillovers. In our study W N collects the regional weights that reflect proximy between provinces, based on four alternative measures of distance: (i) the log of trade flows in real million euros in year , as commercial relations are more intense wh the nearest provinces (Baltagi et al. (2008)), and; (iia) the inverse of the log of optimal distances in kilometers, (iib) time (minutes) and (iic) monetary costs (generalized transport costs, GTC) averaged over the period from 1980 to We note that these optimal accessibily values 1 In principle, one may apply the spatial matrix to any production factor, eher capal or labor; nevertheless, in the empirical application is labor the one showing spatial dependence. 2 In our empirical application, commercial flows in Euros between Spanish provinces (NUTS 3) are obtained from the C-intereg database (see Llano et al., 2008 and Llano et al., 2010), and referred to 16 economic sectors whose goods are shipped by road. 5

6 take into account the best road routes considering economic costs 3. This weighting scheme implies that there is spatial interdependence among all provinces, reflecting less correlation as the commercial relations decrease as the distance increases. The diagonal elements of WN are 0. The off-diagonal elements of our application, WN are defined as * w jk w, for j, k = 1,, N. In wjk corresponds eher to the log trade flows (exports from j to k) in real million euros in year 2005, the inverse of log distances, time (minutes), or monetary costs (GTC). The row-normalization of corresponding row of W. W N, N w jk k 1 The Spatial Autoregressive model in (5) can be expressed as: * w is the sum of the elements in the ( I NT W )lny INT 1 ln INTKP ln L IMP L ln K ln IMPKP W ln L K 2 KP ln KP i Z v (6) In our panel model, changes to an explanatory variable will have direct and indirect effects on self and other regions dependent variables values. We follow Lesage and Pace (2009) to estimate these direct and indirect or spatial spillover effects. These authors propose taking the sum of the rows (or columns) of these matrices and using the average to obtain a measure of the total impact. The direct impact is summarized using the average of the diagonal elements, while the difference between the total and direct effects reflects the indirect or spatial spillover effects. The own- and cross-partial derivatives for this suation on average for the T periods are shown in the following expression: ln Y ln L 1 I ˆ W I ˆ W N ln Y 1 N 1 N ln K ˆ 1 N N L N 2 I ˆ W I ˆ ln Y 1 N 1 N ln KP I ˆ W I ˆ ln Y 1 N ln INTKP N N K, (7.a), (7.b) KP I ˆ W I ˆ MI ˆ 1 N N INT, (7.c) N IMP, (7.d) 3 See Zofío et al. (2011) for further details about the elaboration of Generalized Transport Costs and matrices of distance and time between origins and destinations in the Spanish case. 6

7 where M is a NxN matrix that presents the proportion of road network capal stock imported wh respect to the internally used capal stock. The results in (7) are NxN matrices that show how changes in each region s explanatory variable value will impact the own and all other regions. In the cross-section spatial autoregressive model, Kelejian and Prucha (1998) suggested a two- stage least square estimator (2SLS). Applying the 2SLS to the panel autoregressive spatial model transformed in deviations from means or multiplied by 1/ 2, where E(uu' ) is the variance-covariance of u, we get the fixed effects spatial 2SLS (FE-S2SLS) and random effects spatial 2SLS (RE-S2SLS), respectively. More recently, Baltagi and Liu (2011) extend Baltagi s (1981) error component two-stage least square estimator, following the method introduced by Kelejian and Prucha (1998) and using Lee s (2003) optimal instruments to this spatial autoregressive panel model. They obtain the spatial error component best two stage least squares estimator (SEC-B2SLS). In our empirical application, the estimation of the production function at the provincial level in Spain introducing transport infrastructure, we consider the SEC-B2SLS, following Baltagi and Liu (2011). For robustness, we employ other different standard methods in the lerature of spatial models, the Kelejian and Prucha (1998) 2SLS and the most extended estimator in spatial panel models, the FE-S2SLS. A Hausman test allows us to test the consistency of SEC-B2SLS. 3. Data: sources and description The proposed production function was estimated using individual information on the Spanish provinces from 1980 to Data came from two main statistical sources. Gross Value Added (GVA) and private labor (number of employees, L) from the Spanish National Instute of Statistics (Instuto Nacional de Estadística, INE). The series of productive (i.e., non-residential) private capal (K) and public capal (KP) are taken from the database compiled by Mas et al. (2010) 4 at the Instuto Valenciano de Investigaciones Economicas (IVIE). All variables are expressed in 2000 constant values. Regarding the public capal stocks of road transport infrastructure we use the database estimated by Alvarez et al. (2012) at the provincial level. This study introduces a new concept of transport infrastructure capal stock reflecting the real benef obtained by a 4 The public capal stock id net of the road network stock, as this latter variable is the key variable resulting in the internal and imported stocks. The remaining capal stock KP includes the rest of infrastructures and social capal (health and education). 7

8 region when using s own infrastructure in commercial flows, making possible to perform an analysis of the effects on production of the internally used road network infrastructure (direct effect). Addionally, these authors introduce a concept of spillover effect derived from the road network infrastructure that is imported from the rest of the provinces and regions when exporting goods. Both, the internal and imported infrastructure stocks are calculated by network analysis performed in a Geographical Information Systems (GIS), which enables us to account exclusively for the public capal stock used in trading activies; mainly high capacy roads. The stock that is actually used corresponds to those specific ineraries consistent wh a minimizing cost behavior on the part of transport firms, and therefore comprises the specific arcs used for exporting production- (i.e., those ineraries considered when calculating generalized transport cost). The value of each arc is distributed among all provinces using the relative value of the trade flows as weights, giving rise to the internal and imported capal stock when the allocation is whin the same province or assigned to other different province, respectively. Figure 1 shows that the provinces making use of larger values of their neighbors infrastructure when developing commercial relations are those wh larger export flows: Madrid, Barcelona, Valencia, Zaragoza, etc., i.e., those where economic activy locates to a larger extent both in absolute and relative values. Therefore they use (import) the stock in all surrounding regions and main corridors so as to reach all potential markets. The case of Madrid is interesting, since allows us to portra two counterbalancing forces simultaneously. By locating in the center of the Iberian Peninsula, Madrid is a key corridor in all commercial flows, a suation that induces capal stock exports, but Madrid has grown also into an economic hub wh a large share of the Spanish export flows, resulting in a demand for s neighbor s capal stocks (imports). In fact, Madrid is the province wh the highest GDP in Spain, thereby accounting for the second largest share in the overall Spanish export flows after Barcelona. 8

9 Figure 1. Imported capal stock, 2007 (thousand Euros). Source: own elaboration As the rest of the variables, including the ancillary values of trade flows employed to estimate the used capal stock of infrastructure, we express the road network capal stock (both internal and imported) in monetary terms. Therefore, we estimate a production function introducing inputs on homogeneous monetary uns and prove the robustness of the results using our database. Table 1 shows the descriptive statistics corresponding to variables used in the production function analysis. Data corresponds to the total economic activy, GVA (economy) and the major non-agricultural business sector (industry). 9

10 Table 1 - Descriptive statistics Variable Mean Std. Dev. Min. Max. Total Economy Gross Value Added (millions of euro in 10,100 16, , constant prices) Labour (thousands of employees) ,465 Private Capal (millions of euro in ,000 19,100 1, ,000 constant prices) Public Capal (millions of euro in ,491 4, ,300 constant prices) Used Capal Stock (thousands of euro in 947, ,359 94,691 6,753, constant prices) Industry Gross Value Added (millions of euro in 2,784 4, , constant prices) Labour (thousands of employees) Private Capal (millions of euro in ,065 4, ,200 constant prices) Public Capal (millions of euro in ,491 4, ,300 constant prices) Used Capal Stock (thousands of euro in 947, ,359 94,691 6,753, constant prices) Source: Own elaboration 4. Spillover effects of transport infrastructure in production We analyze inially the contribution of the used internal and imported capal stock as specified in the basic model corresponding to eq. (3). The period of time used is of special interest given that coincides wh an increase in the decentralization of public functions as Spain joined the European Communy. Both events gave rise to substantial growth in public investment intended to improve road infrastructure. Results following panel data analysis techniques are shown in Table 2. F statistics of joint significance and R 2 show that all equations estimated are significant. Addionally, the model has been estimated by means of the fixed effects estimator, because both the F test of individual effects and Hausman s test (Hausman, 1978) reject the null hypothesis, so we can capture unobservable heterogeney (Baltagi, 2008). If we look at the results shown in the first column (total economy), the estimated coefficients for private labor (0.29) and private capal (0.48) are consistent wh other production function studies which, as expected, tend to match the share of these two inputs in aggregate output (GVA). In the second column, corresponding to the industry, the value of the coefficients for private labor (0.66) and private capal (0.23) varies considerably, increasing the share of labor. The public capal coefficient is posive and statistically significant, wh a value of 0.02 for the total economy, as well as for industry. This result is similar to other estimates reported for the Spanish economy (e.g., Goerlich and Mas (2001) analyze the impact of productive public capal on private province production and obtain an elasticy of ). However, the coefficient of the internally used capal stock is posive and significant for 10

11 the total economy and for the industry, wh a value of 0.06 in both cases, whereas the coefficient values of imported used capal stock in the total economy and the industry are 0.08 and 0.17, respectively. Table 2: Production function wh spatial spillovers ( ) Independent Variable ( N = 329 ) Total Economy Industry Fixed Effects Model Constant (c) 4.29 (8.64)** 4.99 (9.74)** Employment ( ln L ) 0.29 (5.99)** 0.66 (11.40)** Private Capal ( ln K ) 0.48 (8.51)** 0.23 (4.03)** Public Capal ( ln KP ) 0.02 (2.99)** 0.02 (2.66)** Internal Used Capal Stock ( ln INTKP ) 0.06 (3.21)** 0.06 (2.32)** Imported Used Capal Stock ( ln IMPKP ) 0.08 (3.13)** 0.17 (5.84)** Joint Significance Test F F(5,46) = F(5,46) = R Individual Effects Test F F(46,277) = F(46,277) = 6.26 Hausman Test 2 (5) (5) T-statistic in parenthesis. *Parameter significant at 95%. **Parameter significant at 99%. Source: Own elaboration Therefore, we can inially conclude that wh our basic specification the benefs of the internally used capal stock are less important than the spillover effects, being more intensive in the industry sector, which is the sector that benefs more of the road network in commercial relations. These results are in line wh those obtained in Delgado and Alvarez (2007), when consider spillover effects of High capacy road network between provinces wh similar socio-demographics features, and are coherent wh studies carried out on the Spanish industrial sector, which suggest broader measures for spillover based on public capal in the rest of the regions (Avilés et al. (2003) and Cantos et al. (2005)). As a result, we can conclude that the road network capal stock contributing to the accesibilty between similar centers of economic activy has a posive impact on the production of this sector. 5. Main results on the production function accounting for spatial effects Next, we continue analyzing the impact of the internal and imported capal stocks as addional inputs in the production function, but allowing for the possibily of spatial dependence, whose existence would render the standard regression model inconsistent. For this purpose we rely on the spatial autoregressive panel model presented in eq. (5) that 11

12 introduces lag spatial dependence in the dependent variable as well as in labor, in order to analyze the impact of the nearest provinces infrastructure on the employment. For robustness, we use different spatial weighting schemes described above. One of them is based on commercial relations between provinces and the rest on the optimal distances. The results wh these different matrices are shown in tables 3-6. The Hausman s test based on the difference between FE-S2SLS and SEC-S2SLS yields values in all the cases that do not reject the null hypothesis that SEC-B2SLS provides consistent estimators. Addionally, we can observe in tables 3 through 6 that the variation of the estimated coefficients for SEC-S2SLS wh respect to the Kelejian and Prucha (1998) estimator fluctuates between 0.07 and 0.10 for the significant coefficients in the total economy dataset, and the range of variation in the industry sector is 0.02 to 0.04 in absolute terms. Wh respect to the FE-S2SLS estimator, the range of variation for the parameters is from 0.15 to 0.18, and 0.08 to 0.3 for the whole economy and the industry sector, respectively, while keeping the sign and significance for the totaly of parameters. These results prove the robustness of the estimation applying SEC-B2SLS method using different weight matrices. 12

13 Table 3: Estimates for production function wh spatial spillover and weighting matrix of exports ( ) Independent Variable ( N = 329 ) Total Economy Industry Two-Stage Least Squares Estimator(2SLS) Kelejian and Prucha (1998) Constant (c) 0.96 (1.56) 0.92 (1.64) Spatial Lagged dependent variable ( ln WY ) 0.57 (7.86)** 0.48 (6.52)** Employment ( ln L ) 0.67 (26.39)** 0.65 (25.87)** Private Capal ( ln K ) 0.33 (11.71)** 0.30 (13.74)** Public Capal ( ln KP ) (0.77) (0.13) Internal Used Capal Stock ( ln INTKP ) (-1.36) 0.03 (1.75)* Imported Used Capal Stock ( ln IMPKP ) 0.09 (7.26)** 0.06 (3.24)** Spatial Lagged Employment ( ln ) (-8.24)** (-4.09)** WL Fixed Effects Spatial 2SLS (FE-S2SLS) Constant (c) (-0.67) (-0.56) Spatial Lagged dependent variable ( ln WY ) 0.79 (2.78)** 0.73 (1.83)* Employment ( ln L ) 0.67 (26.05)** 0.64 (21.83)** Private Capal ( ln K ) 0.34 (12.28)** 0.29 (11.26)** Public Capal ( ln KP ) 0.01 (1.27) (0.06) Internal Used Capal Stock ( ln INTKP ) (0.08) 0.05 (2.46)** Imported Used Capal Stock ( ln IMPKP ) 0.08 (6.60)** 0.08 (3.88)** Spatial Lagged Employment ( ln ) (-2.97)** (-1.35) WL Spatial Error Component Best Two Stage Least Squares estimator (SEC-B2SLS) Baltagi and Liu (2011) Constant (c) 1.83 (1.65)* 0.99 (1.72)* Spatial Lagged dependent variable ( ln WY ) 0.38 (2.02)* 0.49 (6.18)** Employment ( ln L ) 0.65 (2.55)** 0.68 (6.68)** Private Capal ( ln K ) 0.35 (1.85)* 0.28 (5.49)** Public Capal ( ln KP ) 0.01 (0.20) (-0.03) Internal Used Capal Stock ( ln INTKP ) (-0.10) 0.04 (2.42)** Imported Used Capal Stock ( ln IMPKP ) 0.09 (1.94)* 0.06 (2.39)** Spatial Lagged Employment ( ln ) (-1.74)* (-3.84)** WL Hausman s test for (FE S2SLS SEC B2SLS) T-statistic in parenthesis. P-value in brackets *Parameter significant at 95%. **Parameter significant at 99%. Source: Own elaboration 2.08 [0.96] 1.68 [0.98] 13

14 Table 4: Estimates for production function wh spatial spillover and weighting matrix of distances in kilometers ( ) Independent Variable ( N = 329 ) Total Economy Industry Two-Stage Least Squares Estimator(2SLS) Kelejian and Prucha (1998) Constant (c) 1.39 (2.30)* 0.83 (1.47) Spatial Lagged dependent variable ( ln WY ) 0.52 (7.42)** 0.52 (6.97)** Employment ( ln L ) 0.65 (25.74)** 0.66 (25.94)** Private Capal ( ln K ) 0.35 (12.42)** 0.29 (13.53)** Public Capal ( ln KP ) (0.72) (0.11) Internal Used Capal Stock ( ln INTKP ) (-1.32) 0.03 (1.69)* Imported Used Capal Stock ( ln IMPKP ) 0.09 (7.49)** 0.06 (3.37)** Spatial Lagged Employment ( ln ) (-7.89)** (-4.84)** WL Fixed Effects Spatial 2SLS (FE-S2SLS) Constant (c) (-0.08) (-0.95) Spatial Lagged dependent variable ( ln WY ) 0.73 (2.02)* 1.16 (2.42)** Employment ( ln L ) 0.65 (25.91)** 0.64 (21.93)** Private Capal ( ln K ) 0.35 (12.39)** 0.28 (10.72)** Public Capal ( ln KP ) 0.01 (1.04) (-0.17) Internal Used Capal Stock ( ln INTKP ) (-0.22) 0.04 (2.17)* Imported Used Capal Stock ( ln IMPKP ) 0.09 (7.22)** 0.08 (3.76)** Spatial Lagged Employment ( ln ) (-2.45)** (-2.40)** WL Spatial Error Component Best Two Stage Least Squares estimator (SEC-B2SLS) Baltagi and Liu (2011) Constant (c) 2.03 (3.25)** 1.32 (1.94)* Spatial Lagged dependent variable ( ln WY ) 0.39 (3.71)** 0.45 (4.73)** Employment ( ln L ) 0.64 (4.56)** 0.67 (5.87)** Private Capal ( ln K ) 0.36 (3.38)** 0.28 (4.88)** Public Capal ( ln KP ) 0.01 (0.38) (0.08) Internal Used Capal Stock ( ln INTKP ) (-0.29) 0.04 (2.08)* Imported Used Capal Stock ( ln IMPKP ) 0.09 (3.72)** 0.07 (2.15)* Spatial Lagged Employment ( ln ) (-3.87)** (-2.84)** WL Hausman s test for (FE S2SLS SEC B2SLS) T-statistic in parenthesis. P-value in brackets *Parameter significant at 95%. **Parameter significant at 99%. Source: Own elaboration 1.23 [0.99] 3.08 [0.88] 14

15 Table 5: Estimates for production function wh spatial spillover and weighting matrix of distances in time ( ) Independent Variable ( N = 329 ) Total Economy Industry Two-Stage Least Squares Estimator(2SLS) Kelejian and Prucha (1998) Constant (c) 1.38 (2.27)* 0.86 (1.52) Spatial Lagged dependent variable ( ln WY ) 0.52 (7.45)** 0.52 (6.92)** Employment ( ln L ) 0.65 (25.79)** 0.66 (25.89)** Private Capal ( ln K ) 0.35 (12.36)** 0.29 (13.49)** Public Capal ( ln KP ) (0.74) (0.15) Internal Used Capal Stock ( ln INTKP ) (-1.36) 0.03 (1.69)* Imported Used Capal Stock ( ln IMPKP ) 0.09 (7.46)** 0.06 (3.39)** Spatial Lagged Employment ( ln ) (-7.89)** (-4.78)** WL Fixed Effects Spatial 2SLS (FE-S2SLS) Constant (c) (-0.39) (-0.99) Spatial Lagged dependent variable ( ln WY ) 0.79 (2.21)* 1.13 (2.34)** Employment ( ln L ) 0.65 (25.90)** 0.65 (22.05)** Private Capal ( ln K ) 0.35 (12.49)** 0.28 (10.81)** Public Capal ( ln KP ) 0.01 (1.03) (-0.10) Internal Used Capal Stock ( ln INTKP ) (-0.19) 0.04 (2.16)* Imported Used Capal Stock ( ln IMPKP ) 0.09 (7.21)** 0.08 (3.76)** Spatial Lagged Employment ( ln ) (-2.42)** (-2.19)* WL Spatial Error Component Best Two Stage Least Squares estimator (SEC-B2SLS) Baltagi and Liu (2011) Constant (c) 2.05 (3.11)** 1.31 (1.97)* Spatial Lagged dependent variable ( ln WY ) 0.39 (3.50)** 0.45 (4.86)** Employment ( ln L ) 0.64 (4.32)** 0.67 (5.98)** Private Capal ( ln K ) 0.36 (3.19)** 0.28 (4.98)** Public Capal ( ln KP ) 0.01 (0.36) (0.09) Internal Used Capal Stock ( ln INTKP ) (-0.28) 0.04 (2.11)* Imported Used Capal Stock ( ln IMPKP ) 0.09 (3.52)** 0.07 (2.19)* Spatial Lagged Employment ( ln ) (-3.58)** (-2.93)** WL Hausman s test for (FE S2SLS SEC B2SLS) T-statistic in parenthesis. P-value in brackets *Parameter significant at 95%. **Parameter significant at 99%. Source: Own elaboration 1.22 [0.99] 2.30 [0.94] 15

16 Table 6: Estimates for production function wh spatial spillover and weighting matrix of distances in Generalized Transport Cost ( ) Independent Variable ( N = 329 ) Total Economy Industry Two-Stage Least Squares Estimator(2SLS) Kelejian and Prucha (1998) Constant (c) 1.41 (2.34)** 0.85 (1.51) Spatial Lagged dependent variable ( ln WY ) 0.52 (7.41)** 0.52 (6.94)** Employment ( ln L ) 0.65 (25.73)** 0.66 (25.94)** Private Capal ( ln K ) 0.35 (12.42)** 0.29 (13.55)** Public Capal ( ln KP ) (0.79) (0.15) Internal Used Capal Stock ( ln INTKP ) (-1.31) 0.03 (1.70)* Imported Used Capal Stock ( ln IMPKP ) 0.09 (7.51)** 0.06 (3.39)** Spatial Lagged Employment ( ln ) (-7.88)** (-4.79)** WL Fixed Effects Spatial 2SLS (FE-S2SLS) Constant (c) (-0.06) (-0.87) Spatial Lagged dependent variable ( ln WY ) 0.69 (1.93)* 1.09 (2.27)* Employment ( ln L ) 0.65 (25.81)** 0.64 (21.89)** Private Capal ( ln K ) 0.35 (12.44)** 0.29 (10.76)** Public Capal ( ln KP ) 0.01 (1.18) (-0.07) Internal Used Capal Stock ( ln INTKP ) (-0.19) 0.04 (2.17)* Imported Used Capal Stock ( ln IMPKP ) 0.09 (7.25)** 0.08 (3.79)** Spatial Lagged Employment ( ln ) (-2.27)* (-2.17)* WL Spatial Error Component Best Two Stage Least Squares estimator (SEC-B2SLS) Baltagi and Liu (2011) Constant (c) 2.04 (3.26)** 1.31 (1.85)* Spatial Lagged dependent variable ( ln WY ) 0.39 (3.73)** 0.44 (4.51)** Employment ( ln L ) 0.64 (4.58)** 0.67 (5.64)** Private Capal ( ln K ) 0.36 (3.38)** 0.28 (4.72)** Public Capal ( ln KP ) 0.01 (0.39) (0.09) Internal Used Capal Stock ( ln INTKP ) (-0.31) 0.04 (1.98)* Imported Used Capal Stock ( ln IMPKP ) 0.09 (3.75)** 0.07 (2.07)* Spatial Lagged Employment ( ln ) (-3.89)** (-2.68)** WL Hausman s test for (FE S2SLS SEC B2SLS) T-statistic in parenthesis. P-value in brackets *Parameter significant at 95%. **Parameter significant at 99%. Source: Own elaboration 0.78 [0.99] 2.43 [0.93] 16

17 Focusing on the SEC-B2SLS estimation, the results for both the total economy and the industry sector show coefficients for labor and private capal that are again similar to those found in the lerature on production functions. The estimations of the output elasticies of the rest of public capal, which includes social capal and other infrastructures, are not significant. Moreover, regarding the road network capal stock, the internally used capal stock shows a coefficient that is not significant for the whole economy, while for the industry sector exhibs a posive and significant effect on private production but less intensive than in the base model ignoring spatial interdependence. These results are in line wh studies that estimate the effect of infrastructure in the context of spatial production functions. This is the case of Holtz-Eakin and Schwartz (1995) and Kelejian and Robinson (1997), who also adopt a production function framework wh a spatial econometric model in order to estimate the spatial spillover effects of transportation. They argue that the models including spatial effects quantify smaller magnudes related to the influence of infrastructure. The presence of spillover effects for road network capal stock is tested through the use of the imported capal stock variable. The sign of the estimated coefficient is posive and significant, wh a value of 0.09 for the whole economy and between 0.06 and 0.07 for the industry sector, depending on the weight matrix that is included in the estimation. Note that the impact of transport spillovers is larger than the effect of the internally used capal stock in the industry sector. In accordance wh most papers using Spanish provincial data, as in the case of Delgado and Alvarez (2007) considering a stochastic frontier approach. More recently, Baños et al. (2012) find strong evidence of the posive impact of transport spillovers adopting econometric models that apply the spatial lag to public capal. The coefficient accompanying the spatial lag of the dependent variable is posive and significant, wh values that suate in the interval and for the total economy and the industry sector, respectively. Therefore, the output of the rest of provinces weighted by the degree of proximy in terms of commercial relations and distances affects posively the production, more intensively in the industry sector. This can be explained by the fact that having richer neighbor regions will foster economic activy since neighbor regions will buy products and services from his neighbor regions. Another interesting result is obtained by incorporating the variable that measures the spatial effects on labor. It worth noting that s coefficient value is significant, but negative, and adopts the same value for the whole economy and the industry sector when using exports for the weight matrix. Consequently, proximy in terms of commercial relations affects labor and 17

18 wh the same intensy. Furthermore, in the case of using the weight matrices based on distance s magnude is negative and the impact is even larger for the whole economy. So, the nearest provinces wh locational advantages attract employment, more intensively for the whole total economy. We calculate the partial derivative effects describing how the dependent variable in this model responds to changes in explanatory variable values. The estimates for these effects are shown in Tables 7 and 8 for each variable in the model. We also report the decomposion into direct and total effects following the expressions in (7). Table 7: Summary estimates of the effects (Total Economy) Weighting Matrix of exports Weighting Matrix of distances in Kms Weighting Matrix of distances in time Weighting Matrix of distances in Generalized Transport Costs (GTC) Employment Variable Direct Indirect Total Effects Private Capal Variable Direct Indirect Total Effects Public Capal Variable Direct Indirect Total Effects Used Capal Stock Variable Direct Indirect Total Effects Source: Own elaboration Table 8: Summary estimates of the effects (Industry) Weighting Matrix of exports Weighting Matrix of distances in Kms Weighting Matrix of distances in time Weighting Matrix of distances in Generalized Transport Costs (GTC) Employment Variable Direct Indirect Total Effects Private Capal Variable Direct Indirect Total Effects Public Capal Variable Direct e Indirect e e e Total Effects e Used Capal Stock Variable Direct Indirect Total Effects Source: Own elaboration 18

19 These estimates for total economy are reported in Table 7. In comparison wh the coefficients estimates from Tables 3 through 6 for employment, the total effects estimated in Table 7 include the direct and the indirect spatial effects. We can observe small differences between them. So, the employment variable shows posive direct effects and negative indirect or spillover effects. These results indicate that the nearest provinces wh local and economic advantages attract employment. Regarding private capal the direct effects are very similar to those obtained by estimations, showing posive indirect effects from the rest of provinces. For the case of public capal the results show posive effects wh a spillover benef smaller than the direct own-province benef. All these effects are much lower due to the fact that we are considering the rest of public capal, which include remaining infrastructure along wh social capal. As we have mentioned, in the context of production functions, the public capal effects on production including spatial effects reflect lower magnudes, in line wh the lerature. Another interesting result is that the total effects associated wh used capal stock are posive suggesting that public investment in road network used in commercial flows contributes to regional growth. We note that the spillover benefs from the rest of provinces in comparison wh the direct effect captured by own-province infrastructure increasing road network expendures. Furthermore, Table 8 shows the results for industry sector. Private productive factors, employment and private capal, as well as public capal stocks effects, own-province and cross-partial derivatives, are very similar to those of the in total economy. Regarding the used capal stock we observe that the direct effect is lower than the indirect or spillover effect, although both are posive, as their corresponding estimates reported in tables 3 through 6. In summary, the estimated coefficients along wh partial derivatives, show interesting results that are worth highlighting. These results constute an indirect corroboration of the existence of agglomeration economies drawing production factors to locations wh larger economic activy and whose growth is thereby reinforced; which constutes the main proposion of theories explaining core-periphery patterns, e.g., the postulates of the new economic geography. Since regions that have a locational advantage will tend to attract more economic activy, being a close neighbor of one of those regions can have a negative impact due to the fact that workers will move to the richer and better posioned region seeking for higher real wages, Barbero and Zofío (2012). Thus, having a richer neighbor 19

20 region will produce two oppose effects in our income. First, a posive impact in production since richer neighbors import products from our region. Second, a negative impact since workers will move from our region to the richer neighbors. 6. Summary and concluding remarks The objective of this paper is to analyze the effects of road infrastructure on economic activy at a spatial level using a production function approach, and taking into account the spillover effects associated to the use of the public transport infrastructure localized in other regions. In doing so, this study incorporates the concept of road network capal stock of the region analyzed internal as well as the rest of the other regional networks imported as addional inputs. Given statistics availabily, we employ Spanish data at provincial level to illustrate our methodology, and focus on the road network between 1980 and Regarding the public capal stocks, we use the database estimated by Alvarez et al. (2012), which enables us to identify the internally used capal stock effect on economic activy, and compare to the elasticy of the spillover effects through the imported capal stock from other provinces whose infrastructure is used in exporting goods. Our study departs from the estimation of the production function based in standard panel data analysis in that we use spatial econometrics methods. In the second stage estimation we consider a spatial autoregressive panel model, following a specification that introduces spatial lag dependence in the dependent variable and also in labor. This allows us to analyze the impact of the nearest provinces infrastructure on the employment. The spatial lag model is estimated considering the SEC-B2SLS method proposed by Baltagi and Liu (2011). There are several interesting findings. In the first place, for the spatial autoregressive panel model, the rest of public capal, which includes social capal and other infrastructures, is not significant, and the internally used capal stock of infrastructure has a posive effect on the production of the industrial sector. These results are in line wh related studies that obtain a smaller influence of infrastructure in the context of the production function model. Furthermore, the imported capal stock impact is posive for total economy as well as for the industry sector. So, we find strong evidence of the spillover effects in road infrastructures. Secondly, other interesting results are obtained when incorporating the spatial lag in both the dependent variable and labor. When these spatial relations are included we observe that economic activy in other provinces favor 20

21 production for the whole economy as well as for the industrial sector. In contrast, the parameter associated to the spatial lag in labor is negative. This result implies that the nearest provinces exhibing a favorable economic posion attract employment, more intensively for total economy. 21

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