Estimating Production Function And Productivity Impact Of Export Persistence In Presence Of Market Imperfections

This paper develops a new method to estimate a production function and the total factor productivity (TFP)impact of persistence in exporting. Certain “proxymethods” for estimating the production function invert the demand for flexible inputs with respect to TFP to obtain a proxy for the unobserved TFP. When markets are imperfectly competitive, the demand for inputs depends on unobserved demand shifters (UDS), which violates the “scalar unobservability” required for inversion. We write the production function as a partially linear model,where the nonparametric part, the proxy for productivity, depends on the UDS. Identification rests on postulating (i) a law of motion for the UDS, which evolves endogenously, and(ii) distributional restrictions to control for the correlation between the UDS and the variables of interest. Output elasticities and productivity impact of endogenous treatments are identified. Using Estonian firm-level data, we find that revenue per employee and the amount, in physical units, of goods exported per employee generally increase with the number of years of exporting activities (NYrEx). However, we find limited evidence of the TFP impact of exporting, with only the most persistent of exporters experiencing such gains. In comparison, the estimated productivity impact of NYrEx from analternative estimator, which assumes perfect competition, closely matches the way revenue per employee varies with the NYrEx. Finally, exporters charge lower markups than non-exporters, where the difference between the exporters’and the non-exporters’ markups increases with NYrEx.