Motivated by the long-standing interest of economists in understanding the nexus between firm productivity and export behavior, this paper develops a novel structural framework for control-function-based nonparametric identification of the gross production function and latent firm productivity in the presence of endogenous export opportunities that is robust to recent unidentification critiques of proxy estimators. We provide a workable identification strategy, whereby the firm's degree of export orientation provides the needed (excluded) relevant independent exogenous variation in endogenous freely varying inputs, thus allowing us to identify the production function. We estimate our fully nonparametric instrumental variable model using the Landweber-Fridman regularization with the unknown functions approximated via artificial neural network sieves with a sigmoid activation function, which are known for their superior performance relative to other popular sieve approximators, including the polynomial series favored in the literature. Using our methodology, we obtain robust productivity estimates for manufacturing firms from 28 industries in China during the 1999-2006 period to take a close look at China's exporter productivity puzzle, whereby exporters are found to exhibit lower productivity levels than nonexports.
