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The dominant view in the recent literature on regional convergence seems to be that the evolution of regional incomes in the industrial countries is characterized by very slow but absolute beta convergence. This process of convergence is seen as reflecting the operation of decreasing returns to scale, and its slowness is interpreted as evidence that the technology is close to exhibiting constant returns to scale in a broad capital aggregate. In this paper we challenge this view on the basis of an analysis of the Spanish experience (1964-91). We develop and estimate a simple descriptive growth model which allows for factor accumulation, technological diffusion and rate effects from human capital and includes fixed regional effects to allow for unobserved factors. The estimated model is then used to quantify the sources of regional convergence. Our results indicate that technological catch-up, the equalization of educational levels and the redistribution of employment across regions account for most of the observed reduction of regional disparities. We also find that, even after controlling for factor stocks and flows and technological diffusion, there remain very significant cross-regional differences in estimated TFP levels which point to the omission of important variables and to the need for a more disaggregated analysis. Finally, we provide some preliminary evidence of the importance of sectoral factors in explaining the evolution of the regional income distribution. _____________________________________ * I would like to thank Rafael Doménech, Xavier Vives and the participants in the CEPR Workshop on Location and Regional Convergence/Divergence for useful comments and suggestions and J. A. Duro for his competent research assistance. Financial support from the Spanish Ministry of Education (DGICYT grant no. PB95-130) and the European Regional Development Fund (through the research project "Determinants of growth at the regional and national level") is gratefully acknowledged. Address: Instituto de Análisis Económico, Campus de la Universidad Autónoma de Barcelona, 08193, Bellaterra, Barcelona, Spain. Tel: 34-3-580-6612. Fax: 34-3-580-1452. E-Mail address: delafuente@cc.uab. es. Non-technical summary A host of papers have found a negative partial correlation between output per capita (or per worker) and subsequent growth. The strength of this correlation, which is often taken as a measure of the speed of convergence, varies considerably across papers reflecting differences in specification. Estimates of the rate of convergence obtained with unconditional convergence equations (at the regional level), or controlling for investment rates in physical and human capital (at the national level) are typically quite low and cluster around a central value of 2% per year. Recently, however, a number of authors have obtained much higher estimates of the speed of convergence using more flexible specifications which allow more room for regional or national specificities. From a theoretical perspective these recent estimates are somewhat problematic. Slow convergence can be given a sensible interpretation within a standard neoclassical model as an indication that the technology displays close to constant returns to scale in a broad capital aggregate which includes cumulative investment in education. Within the same framework, however, very fast convergence either takes us back to the old-fashioned neoclassical model with a narrow interpretation of capital (implying that investment in intangibles is not productive), or cannot be explained at all. This paper argues that in order to make sense of these recent empirical results we must depart from the standard neoclassical framework and think in terms of a broader model which allows for convergence mechanisms other than diminishing returns. Two such mechanisms come immediately to mind: one is technological diffusion across countries and regions (the so-called catch-up effect), and the second one is the reallocation of resources across sectors. One of the objectives of the paper will be to provide quantitative estimates of the contribution of these forces to observed productivity convergence. Another important implication of some recent studies is that regions (and probably countries) may be far more different from each other than we suspected up to now. Evidence of this, however, comes mostly from non-structural models which rely on dummy variables to pick up all crossregional differences except for initial income and cannot, therefore, give us any indication of even the proximate sources of what seem to be very subtantial productivity differentials. A second goal of this paper will be to determine the extent to which estimated long-term regional disparities may be explained by the forces identified by a further extension of the standard neoclassical model. To explore these issues we will use a rather comprehensive data set on output levels and factor stocks for the Spanish regions. Our research strategy will be the following. We start by estimating a non-structural, dummy-variable convergence model similar to the one proposed by Canova and Marcet (1995). While this specification is essentially a black box, it does allow us to estimate the distribution of regional productivities to which the sample may be expected to converge in the long run provided "things remain equal", and the speed of convergence of the regional economies towards their stationary relative productivity levels. We use the results of this dummy-variable model as a benchmark to evaluate the performance of an aggregate structural model which extends the standard neoclassical model by partially endogenizing the rate of technical progress to allow for technological diffusion and the impact of education on total factor productivity (TFP) growth. We proceed essentially by asking to what extent the introduction of the variables suggested by standard growth theory allows us to fit the data (i.e. to generate convergence rates and sustained productivity differentials comparable to those estimated using the benchmark model) without resorting to the use of regional dummies. The results of the exercise are mixed. On the positive side, our structural model yields very reasonable estimates of the parameters of the production function and we find evidence of a rapid process of technological diffusion across regions. These findings suggest that a suitably extended aggregate model may provide an adequate framework for a first approximation to the analysis of growth and convergence. On the other hand, a version of the model without fixed regional effects presents large and systematic regional residuals which point to important omitted variables and predicts convergence rates which are much lower than our benchmark estimate. Both problems can be "fixed" through the introduction of fixed regional effects to capture productivity differentials due to unobserved regional characteristics. This gives us a "hybrid" model which generates conditional convergence at just about the right speed and reproduces almost perfectly the observed pattern of relative productivity growth. This model is used to quantify the contribution to the reduction of regional inequality of technological diffusion and factor accumulation, and to provide an estimate of the amount of long-term inequality which is not explained by either of these factors. Our results indicate that technological catch-up, the equalization of educational levels and the redistribution of employment across regions account for most of the observed reduction of regional disparities. We also find that, even after controlling for factor stocks and flows and technological diffusion, there remain very significant cross-regional differences in estimated TFP levels. This last finding suggests that there is still a lot to do before we can claim a reasonable understanding of the determinants of regional income. Some of our results seem to indicate that sectoral factors may be responsible for at least part of the unexplained productivity differentials and point towards a more disaggregated analysis as a promising strategy for future research. The last part of the paper provides some preliminary evidence which is consistent with this hypothesis.