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Abstract
In this article, we examine whether variations in the level of public capital across Spain's Provinces affected productivity levels over the period 1996 to 2005. The analysis is motivated by contemporary urban economics theory, involving a production function for the competitive sector of the economy (‘industry’) which includes the level of composite services derived from ‘service’ firms under monopolistic competition. The outcome is potentially increasing returns to scale resulting from pecuniary externalities deriving from internal increasing returns in the monopolistic competition sector. We extend the production function by also making (log) labour efficiency a function of (log) total public capital stock and (log) human capital stock, leading to a simple and empirically tractable reduced form linking productivity level to density of employment, human capital and public capital stock. The model is further extended to include technological externalities or spillovers across provinces. Using panel data methodology, we find significant elasticities for total capital stock and for human capital stock, and a significant impact for employment density. The finding that the effect of public capital is significantly different from zero, indicating that it has a direct effect even after controlling for employment density, is contrary to some of the earlier research findings which leave the question of the impact of public capital unresolved.
Notes
1 See Boscá et al. (2002), Moreno et al. (Citation2002), Avilés et al. (Citation2003), Cohen and Morrison (Citation2004), Matmazakis (Citation2007).
2 See Maudos et al. (Citation1998), Martín and Suárez (Citation2000), Pedraja et al. (Citation2002), Salinas-Jiménez (Citation2004) and Delgado and Álvarez (Citation2007).
3 There are very few countries where regional public investment data are available. Exceptions are Germany and Italy, where recently Marrocu and Paci (Citation2010) obtained a positive and significant but variable public investment effect on production.
4 The Dixit-Stiglitz theory of monopolistic competition provides the reason why an increase in service labour maps to an increase in service variety, rather than more of the same variety. Monopolistic competition envisages a large number of services firms producing differentiated services and firms freely entering the sector until profits go to zero. The existence of fixed costs means that firms prefer to concentrate on a single variety and reap internal economies of scale; there is no advantage in a variety's production being split between two or more firms. On the other hand, if there were no fixed costs, average costs would not decrease with increasing output so that no internal economies of scale would be realized. Since each firm is the producer of its own differentiated services, the ensuing monopoly power allows prices to be a mark up on marginal cost. The number of firms supplying services is an endogenous variable in the model instead of being an ad hoc restriction. There is an equilibrium level of output and therefore equilibrium labour requirement per service firm that is a constant, and as will be stated later we have an equilibrium number of firms. These equilibrium values depend on exogenous parameters.
5 This is the substitution parameter of the CES production function, which determines the elasticity of substitution, the price elasticity of demand and the internal returns to scale given by the average cost to marginal cost for producer services in equilibrium.
6 Note that as i becomes large, W i tends to a matrix in which each cell in a column contains the same value, columns differ, and each row of W i is identical. This means that the matrix products tend to constant vectors.
7 See Fingleton (Citation2003a) for further discussion of alternative assumptions about W.
8 The elements of the main diagonal are set to zero by convention.
9 If the basic theoretical model was New Economic Geography rather than our urban economics specification, then that would automatically capture spatial dependencies based on the size of economies, similar to those embodied in our W matrix as defined below.
10 This way of capturing interactions weighted by distance is used very often in spatial econometrics literature. Fingleton (Citation2003b) hypothesized that the efficiency of the labour force employed within an area will be in part determined by commuting, the frequency of which falls as distance increases. The rate at which this fall-off in commuting frequency occurs is embodied within the matrix W, which is determined by the varying rate of decline-with-distance of commuting in each individual area. So a scalar that reflects the commuting of people between different regions is selected to weight distances. As this information is not available for the Spanish provinces, we weighted using the square to make relation more intense as the distance becomes shorter. Additionally, controlling for distance, we assume that the grater the commuting between provinces will be, the larger the provincial economies.
11 We use, somewhat arbitrarily, the GDP in 1971, but other years could have been used with very little impact on the outcome. Using a previous year ensures that the resulting W matrix comprises fixed exogenous quantities with no possibility of feedback from the level of productivity.
12 The estimation results were similar when we used different W matrices, the coefficient varied slightly and all the signs were as expected from theory. The alternative Ws were obtained using and
.
13 Specifically we use the xtivreg available in Stata for estimating panel data models with endogenous variables.
14 The range of ρ is automatically bounded in Maximum Likelihood (ML) estimator but under 2SLS can fall outside this stable range and thus encounter singular points. Fortunately, in our estimates the estimated ρ lies within the stable bounds.
15 Spanish provinces correspond to level 3 of the Nomenclature of Territorial Units for Statistics (NUTS) of EUROSTAT, the Statistical Office of the EU. The average surface of a representative province is 10 120 km2 (range 1980 to 21 766 km2).
16 During the period analysed, Spain has received a sustained increasing amount of funding from the Structural and Cohesion Funds. During the period 1994 to 1999, Spain received the ‘Delors II’ package and during 2000 to 2006 the ‘Agenda 2000’ package, receiving a yearly average amount of 5.900 and 8.900 million of Euros, respectively.
17 Eurostat reported an average rate of growth of public investment of 3.37% in Spain for the period 1995 to 2005, while in the euro area it was of 2.5%. This higher rate has been sustained throughout the decade even though public expenditure has reduced as a proportion of GDP. At the same time provincial differences have also been reduced during the period, thanks to the Structural and Cohesion Funds. Most of the Spanish regions were Objective 1 regions and received European funds to finance infrastructure projects.
18 In order to make the gross value added and employment series homogeneous, we took the rates of growth of the variable in FUNCAS database and applied it to the variable produced by FBBVA. Previously, we had to transform the valued added into constant euros of 1995 using the Implicit Index Prices facilitated by both organizations.
19 To satisfy the diagnostic tests described below, the matrix product W ln K has been dichotomized, being equal to 1 for values exceeding the median value, and 0 otherwise.
20 After having eliminated the spatial lag of log total capital as an instrument, as is necessary in order to pass the test of over-identifying restrictions.
21 This is an option (endog) available within Stata's xtivreg2 command (Schaffer, Citation2010), and under conditional homoscedasticity, the test statistic is equal to that provided by a Hausman test.
22 Option orthog in xtivreg2.
23 Also obtained by the Stata command xtoverid, see Schaffer and Stillman (Citation2010).
