Estimation of endogenous firm productivity without instruments: an application to foreign investment

We consider identification and estimation of the firm-level gross production function with a controlled productivity evolution process and endogenous contemporaneous productivity determinants in the absence of instrumental variables (IVs). We allow the joint determination of firm productivity and its determinants, such as research and development, exports, and foreign direct investment, which is motivated by the recognition that certain unobserved confounders, such as CEO ability and managerial strategies, may simultaneously affect both productivity and these determinants. This assumption is in sharp contrast to those used in previous studies on proxy-variable estimation of production functions, in which productivity processes without determinants or with exogenous/predetermined determinants are often assumed. Since IVs for endogenous productivity determinants are in general difficult to obtain in the production context, we propose an IV-free generalized method of moments (GMM) estimator based on Lewbel et al. (2023) and use higher-order moments for unobserved errors in addition to conventional orthogonality conditions. We demonstrate the finite sample performance of the proposed estimator through Monte Carlo simulations. We also apply the methodology to investigate the impact of foreign equity on the productivity of Chinese manufacturing firms.