Essays on nonparametric identification and production function estimation




Pan, Qingsong

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This dissertation consists of three chapters on applied econometrics and econometric theory. The first two chapters propose new estimating approaches to nonparametric production functions, and the third chapter studies the partial identification of treatment effects in a nonparametric setting. In the first chapter, we study the nonparametric identification of gross output production functions with a nonseparable productivity shock when output markets are perfectly competitive. Our nonseparable specification relaxes the traditional assumption of Hicks neutrality that has been shown to be inconsistent with a number of data sets. It can thus capture the bias in technical change, which recent research has found relevant to many important economic questions. We first generalize the identification approach of Gandhi et al. (2020) to nonseparable models and show the identification of output elasticities. To identify the entire production function, we then impose a homogeneity assumption, which is supported by the data. Given the fact that our nonseparable models nest Hicks-neutral models, we are able to document the misspecification bias of the latter. Using Chilean and Colombian plant-level data, our estimates suggest that Hicks-neutral models overestimate returns to scale, overestimate output elasticities of labor, and generate biased estimates of capital intensity. Our estimates also indicate that technological change is predominantly biased toward capital over labor and intermediate inputs. In the second chapter, we extend the identification approach in chapter 1 from perfect competition to imperfect competition. When physical quantities of output are observed, we follow Flynn et al. (2019) and replace the assumption of perfect competition with a constant-returns-to-scale (CRS) condition. When only revenue instead of physical output is observed, we follow Kasahara and Sugita (2020) and combine a first-order condition with a CRS condition to show identification of output elasticities and markups. In the third chapter, we derive a set of partial identification results for the mean treatment response and the average treatment effect when the μ-strong concavity assumption is combined with the monotone treatment response (MTR) assumption or the MTR-MTS (monotone treatment selection) assumption. μ-strong concavity is a generalization of the usual concavity assumption and the parameter μ can be seen as a measure of the strength of concavity. By tuning the value of the parameter μ, a practitioner can conduct sensitivity analyses with respect to the concavity assumption. We illustrate my findings by reanalyzing the return to schooling example of Manski and Pepper (2000).



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