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


  • Wolak, Frank A.


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 null R . 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 null R . 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.

Suggested Citation

  • Wolak, Frank A., 1989. "Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(01), pages 1-35, April.
  • Handle: RePEc:cup:etheor:v:5:y:1989:i:01:p:1-35_01

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