Labour market effects of public capital stock: evidence for the Spanish private sector

Abstract

This paper provides a new rationale for the positive effect of public capital stock on employment and wages. We show that higher levels of public capital reduce wages along the wage equation and enhance employment due to the resulting larger elasticity of labour demand with respect to wages. The estimation of a structural model for the Spanish private sector reveals that this wage channel is empirically relevant. We use the estimated parameters to simulate the recent incidence of the ratio of public to private capital stock on the private sector economic performance. We find (i) sizeable effects on employment, capital stock and gross domestic product, and (ii) that the wage channel is particularly important for employment.

Keywords:

• public capital stock
• wage setting
• employment
• economic growth

JEL classifications:

• E24
• J23
• J38

Acknowledgements

Raurich, Sala and Sorolla acknowledge financial support from the Spanish Ministry of Education, Science and Technology through grants, respectively, SEJ2006‐05441, SEJ2006‐14849 and SEJ2006‐03879. Raurich acknowledges financial support from the Generalitat of Catalonia through the Barcelona Economics program (CREA) and grant SGR2005‐00984. We thank Juan Francisco Jimeno, Marika Karanassou, Victor Montuenga, Howard Petith and Dennis J. Snower for their helpful comments on earlier versions of this paper.

Notes

1. See Bean and Pissarides (1993), Aghion and Howitt (1994), Eriksson (1997) or Daveri and Tabellini (2000). More recently, Ventelou and Bry (2006) have used the DEA method to re‐evaluate the effects of public spending on economic growth.

2. Our results hold even under the assumption of an elastic labour supply.

3. See also Van Ommeren and Rietveld (2005). Their main finding is that when productivity grows, average commuting costs and average wages both increase in the long run.

4. This is a necessary condition in the long run, since, otherwise, the unemployment benefit would either converge to zero or diverge to infinite.

5. This theoretical result is obtained in a more specific setting by Raurich and Sorolla (2003), where this elasticity is shown to increase or decrease with the ratio of public to private capital stock depending on the assumptions made on the production function.

6. Note that if φ(G_t ,N_t ) is a constant elasticity of substitution production function and the elasticity of substitution is non‐unitary then F_N does not coincide with β(Y_t /N_t ) unless we consider a more general production function with externalities. As an example, consider that where N _t and K _t are externalities accruing from the average level of employment and capital, respectively. This production function allows for sustained growth and zero profits, the marginal product of labour is a constant fraction of production at the firm level, and the elasticity of the labour demand increases with the stock of public capital at the aggregate level. For simplicity, we have not introduced externalities in the theoretical exposition.

7. Since the 1990s, the IVIE (Instituto Valenciano de Investigaciones Económicas) supplies data to the Fundación BBVA on the capital stock for the Spanish economy. See Mas, Pérez and Uriel (2000, 2005) for methodological details on this database. We use the latest data made available in 2005 and running up to 2002.

8. Note that the variables in lower‐case letters correspond to the logarithm of the variables in upper‐case letters.

9. To allow a closer connection with the theoretical equations, we present these results in the form of traditional autoregressive distributed lag models, rather than in their error correction form. For an example of the latter type of presentation see Sala (2008). Further, for the sake of brevity we do not show the following information, which is available upon request: (i) results on the misspecification and the structural stability tests of the individual equations; (ii) the long run estimated parameters and their standard errors computed with the delta method; (iii) results on the Sargan test validating the instruments for the 3SLS estimation.

10. The analysis has been limited to the private sector because the labour demand in the public sector may not be related to the labour marginal product. Hence, the introduction of the public sector in the analysis would distort the results.

11. Note that the estimated production function does not correspond exactly to the one proposed in Section 3. The discrepancy is due to the existence of externalities (for simplicity not taken into account in Section 3). However, we can also consider the following production function , where K _t and N _t are externalities. Equation (8) emerges from this function.

12. In the production function, a Wald test on the restriction (γ ₂+γ ₃)/−γ ₁ = 1 cannot be rejected. This test gives a value of 0.83, which has to be compared with a = 3.84. In the labour demand equation, the Wald test on the restriction α ₃/(1 − α ₁) = 1 cannot be rejected either. This test gives a value of 0.42, also below the standard 5% critical value.

13. It can be shown that past period wages are a fraction of current production in the long run. As past wages account for the unemployment benefit in equation (7), the unemployment benefit is a constant fraction of production. This is assumed in both Sections 3 and 5.

14. Since there is no homogeneous long time series for unemployment benefits as a specific component of Social Security benefits, the estimated wage equation does not consider the former – even though it is a relevant variable in the wage equation (4) – but the latter. Sala (2008) shows that this variable does in fact capture the global effect of different labour market institutional variables among which the unemployment protection legislation.

15. The influence of employment on wages arises from an insider–outsider argument by which, the higher the number of new employees (entrants) in past year, the higher the number of insiders in this year (see Lindbeck and Snower (1989) for a justification of this upward influence). Though relevant, this relationship has not been considered in Section 3 because of the static nature of the model. Karanassou and Snower (2000) report empirical estimates of this sort. Empirical analyses commonly report the effect of unemployment on wages. However, in this paper we are just concerned with employment and economic growth. We do not consider a labour supply equation because data on the labour supply is not available by institutional sectors (private and public) and, thus, we cannot make the unemployment rate endogenous.

16. This rationale is also developed in Raurich and Sorolla (2003). As stated, Sala (2008) provides an additional rationale based on the effects of g on working conditions (via commuting costs) and, thereby, on wage bargaining.

17. Note that Δ, Δ, Δ, Δ and Δ are the growth rates of Y_t , K_t , N_t , W_t and B_t respectively.

18. Recall that this is the empirical counterpart of the production function in the theoretical model, where the TFP only depends on the ratio of public to private capital stock.

19. These equations pass the misspecification and structural stability tests. Again, the results on these tests are available upon request.

20. Note that we could also have assumed that the increase in public capital is financed by means of taxes on the interest rate since, because of the homotheticity of the utility function, taxes on the interest rate do not distort agents’ decisions on savings. With this assumption, the government budget constraint is X_t = τ_tr_tK_t , which can be rewritten as follows G_t = τ_tr_t .

21. Of course we do not claim to be capturing actual responses to changes in g. This exercise should be taken as a dynamic accounting analysis to illustrate the economic incidence of public capital stock.