This paper considers the problem of estimating a nonparametric stochastic frontier model with shape restrictions and when some or all regressors are endogenous. We discuss three estimation strategies based on constructing a likelihood with unknown components. One approach is a three-step constrained semiparametric limited information maximum likelihood, where the first two steps provide local polynomial estimators of the reduced form and frontier equation. This approach imposes the shape restrictions on the frontier equation explicitly. As an alternative, we consider a local limited information maximum likelihood, where we replace the constrained estimation from the first approach with a kernel-based method. This means the shape constraints are satisfied locally by construction. Finally, we consider a smooth-coefficient stochastic frontier model, for which we propose a two-step estimation procedure based on local GMM and MLE. Our Monte Carlo simulations demonstrate attractive finite sample properties of all the proposed estimators. An empirical application to the US banking sector illustrates empirical relevance of these methods.
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