Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models

This paper considers a general nonlinear econometric model framework that contains a large class of estimators defined as solutions to optimization problems. For this framework we derive several asymptotically equivalent forms of a test statistic for the local (in a way made precise in the paper) multivariate nonlinear inequality constraints test H : h (β) ≥ 0 versus K : β ∈ R K . We extend these results to consider local hypotheses tests of the form H : h 1 (β) ≥ 0 and h 2 (β) = 0 versus K : β ∈ R K . For each test we derive the asymptotic distribution for any size test as a weighted sum of χ 2 -distributions. We contrast local as opposed to global inequality constraints testing and give conditions on the model and constraints when each is possible. This paper also extends the well-known duality results in testing multivariate equality constraints to the case of nonlinear multivariate inequality constraints and combinations of nonlinear inequality and equality constraints.