The impact of private, public and human capital on the US states' economies: Theory, extensions and evidence

The last decade has seen an upsurge of estimations of regional production functions stimulated by the desire to identify the factors at the origin of economic growth in general1 and the role of public investments in particular. A large amount of empirical work focusing on these issues relies on a Cobb–Douglas production framework to estimate the impact of labor, physical and human capital on output level and output growth. The extensive use of Cobb–Douglas production functions started in the growth accounting literature (Solow, 1956) as a framework to explain wide differences in economic performances across countries. Despite its age and the criticisms related to aggregating firm-level Cobb–Douglas production functions to the regional or national level (see, e.g., Felipe and McCombie, 2012), it is still one of the most popular ways to estimate factor productivity and technological progress, the so-called Solow residual. An extension of the growth accounting framework is the level accounting decomposition, whose goal is to estimate factor productivity and efficiency levels instead of growth rates and technological changes (Hall and Jones, 1999). The parametric equivalent of the growth accounting methods is the growth regression literature (Islam, 1995; Barro and Sala-i- Martin, 1991, 2004), where technological progress is estimated as opposed to being treated as a residual from a calibration exercise, as in the former literature. A recent development based on this approach would be the non-stationary panel methodologies that assume cross-section dependence (Marrocu et al., 2000; Costantini and Destefanis, 2009). The literature also offers the frontier models approach where, unlike former models, the factors of production are not assumed to always operate in full efficiency. The appeal of this approach relies on its capacity to disentangle the role of technological progress and technical efficiency change in productivity growth. Empirically, frontier models can be measured deterministically by a data envelopment analysis (Farrell, 1957) or econometrically in the frame of a stochastic frontier analysis (Lovell and Schmidt, 1988; Coelli et al., 2005). A more detailed description of the production function methods is available in Del Gatto et al. (2012).