Elasticity of substitution and technical progress: Is there a misspecification problem?

Abstract

In Saltari et al. (2012, 2013) we estimated a dynamic model of the Italian economy. The main result of those papers is that the weakness of the Italian economy in the last two decades is due to the total factor productivity slowdown. In those models the information and communication technology (ICT) capital stock plays a key role in boosting the efficiency of the traditional capital, and hence of the whole economy. The ICT contribution is captured in a multiplicative way through a weighting factor. The other key parameter to explain the Italian productivity decline is the elasticity of substitution. Recent literature provides estimates of the elasticity of substitution well below 1 -- thus rejecting the traditional Cobb-Douglas production function -- though there is no particular value on which consensus converges. In our opinion, however, these estimates are affected by a theoretical specification problem. More generally, the technological parameters are long run in nature but the estimates are based on short-run data. Our aim is to look more deeply into the estimation procedure of the technological parameters. The standard estimation results present a common fundamental problem of serially correlated residuals so that the standard errors will be under-estimated (i.e. biased downwards). We think that at the root of this problem there are two theoretical issues: the estimated models are static in nature and do not incorporate frictions and rigidities. Our modelling strategy takes into account, though implicitly, adjustment costs without leaving out the optimization hypothesis. Although we cannot in general say that this framework gets rid of the serial correlation problem, the correlation statistics for our model do show that residuals are not serially correlated. Recent literature provides estimates well below 1 -- thus rejecting the traditional Cobb-Douglas production function -- though there is no particular value on which the consensus converges. In our opinion, however, these estimates are affected by a specification problem, which has theoretical roots. The technological parameters are long run in nature but the estimates are based on short-run data: the "real" issue is to bridge this gap. Our aim is to look more deeply into the estimation procedure of the technological parameters. The standard estimation results present a common fundamental problem of serially correlated residuals so that the standard errors will be under-estimated (i.e. biased downwards). We think that at the root of this problem there are two theoretical issues: the estimated models are static in nature and do not incorporate frictions and rigidities. Our modelling strategy takes into account, though implicitly, adjustment costs without leaving out the optimization hypothesis. Although we cannot in general say that these properties get rid of the serial correlation problem, the correlation statistics for our model does show that residuals are not serially correlated