Internal versus external economies in European countries

Abstract

In this paper sectoral production functions are estimated with a two digit disaggregation for eight European countries corresponding to the period 1978–1992, distinguishing between internal economies of scale and intersectoral external effects. In order to avoid the possibility that the regressions, carried out by way of panel data techniques, are spurious, the integration order of each variable has been identified using unit root. Similarly, the Hausman procedure has been applied to test the exogeneity of the variables and determine whether the most appropriate estimations should be SUR or three stage least squares.

Acknowledgements

This study has been financed by University of Zaragoza and Government of Aragón Project 269–67.

Notes

Two important theoretical approaches have been developed in order to explain the presence of increasing returns in the production function. The first of these focuses on technological change (in learning economies) and on R&D activities. The second, which is the approach followed in this paper, considers the effects of the presence of external economies.

For Smolny (2000) this fact allows that the returns to scale are constant in the individual firms and increasing when aggregating these by sectors or regions to be accepted.

The exclusion of the sector itself avoids the situation where there is a variable that is equal for all the sectors in the same time period and, as a consequence, that might function simply as a set of time dummies, as Oulton (1996) points out. At the same time Vecchi (2000) demonstrates that this adjustment avoids an overestimation of the parameters. Knarvik and Steen (1999), following the same procedure, consider that the model is more consistent with economic theory and reduces the problem of endogeneity.

A panorama of recent developments in this prolific literature can be found in works such as those of Phillips and Moon (2000) and Banerjee (1999), where the mutual enrichment of the econometrics of panel data and of unit roots and cointegration in time series is made clear.

From amongst the remaining proposals, attention should particularly be drawn to the tests proposed by Levin and Lin (1992, 1993), Im et al. (1997) and, more specifically, for testing cointegration, to Pedroni (1999), McCoskey and Kao (1998) and Kao (1999).

Goerlich and Orts (1994) maintain that in the specific case of the estimation of production functions the correlation depends both on the particular form of the technology and on considerations of intertemporal substitution between production factors; that is to say, on the expectations of the economic agents as to whether the productivity shocks have a permanent or transitory character.

Assuming that Lx (Le) is determined endogenously with the level of output, the OLS estimations will be biased and inconsistent. To test this hypothesis, it is necessary to find a set of instrumental variables that are correlated with the ‘suspect’ variable Lx but not with the error term of the equation. The choice of the appropriate instrument is a crucial step. Here, the natural logarithm of labour and private capital in previous periods has usually been taken as instruments. To carry out the Hausman test by artificial regression, two OLS regressions were run. In the first, the suspect variable (Lx, Le) has been regressed on all exogenous variables and instruments and the residuals retrieved. Then, in the second, the production function including the residuals from the first regression were re-estimated as additional regressors. If the OLS estimates are consistent, then the coefficient on the first stage residuals should not be significantly different from zero (in the second regression). To be more precise, this is an asymptotic where the t-statistic should be compared with the critical values from the standard normal.

In the estimations reflected in Tables 2 and 3, the physical capital and the labour of the sectors, as well as their lags, have been used as instruments.

The importance of the sectoral differences is a result upon which emphasis has been placed by authors such as Burnside (1996).

On the difficulties of measuring the factor utilization, the different alternatives and the distinct national behaviour under a transaction costs approach, see Vecchi (2000) who completes the work of Caballero and Lyons (1992) precisely by following such an approach.

Data available at the following electronic address http://w3.grupobbva.com/TLFB/tlfb/TLFBindex_pub.jsp