Errors in variables and panel data: the labour demand response to permanent changes in output

This paper examines panel data modelling with latent variables in analyzing log-linear relations between inputs and output of firms. Our particular focus is on (i) the "increasing returns to scale puzzle" for labour input and (ii) the GMM estimation in the context of errors-in-variables and panel data. The IV's used for the observed log-differenced output are log output (in level form) for other years than those to which the difference(s) refer. Flexible assumptions are made about the second order moments of the errors, the random coefficients, and other latent variables, allowing, inter alia, for arbitrary heteroskedasticity and autocorrelation up to the first order of the errors-in-variables. We compare OLS, 2SLS, and GMM estimates of the average input response elasticity (which in some cases can be interpreted as an average inverse scale elasticity), and investigate whether year specific estimates differ substantially from those obtained when data for all years are combined. The results confirm the "increasing returns to scale puzzle" for labour input (measured in three different ways), but indicate approximately constant returns to scale when we consider the material input response. This indicates non-homotheticity of the production technology.