Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models
نویسنده
چکیده
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(1) > 0 versus K: 1 E RK. We extend these results to consider local hypotheses tests of the form H: hI(1) ? 0 and h2(3) = 0 versus K: 1 E RK. For each test we derive the asymptotic distribution for any size test as a weighted sum of x2-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.
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