Robust Confidence Intervals in Nonlinear Regression Under Weak Identification

In this paper, we develop a practical procedure to construct confidence intervals (CIs) in a weakly identified nonlinear regression model. When the coefficient of a nonlinear regressor is small, modelled here as local to zero, the signal from the respective nonlinear regressor is weak, resulting in weak identification of the unknown parameters within the nonlinear regression component. In such cases, standard asymptotic theory can provide a poor approximation to finite-sample behavior and failure to address the problem can produce misleading inferences. This paper seeks to tackle this problem in complementary ways. First, we develop a local limit theory that provides a uniform approximation to the finite-sample distribution irrespective of

the strength of identification. Second, standard CIs based on conventional normal or chi-squared approximations as well as subsampling CIs are shown to be prone to size distortions that can be severe. Third, a new confidence interval (CI) is constructed that has good finite-sample coverage probability. Simulation results show that when the nonlinear function is a Box-Cox type transformation, the nominal 95% standard CI and subsampling CI have asymptotic sizes

of 53% and 2.3%, respectively. In contrast, the robust CI has correct asymptotic size and a finite-sample coverage probability of 93.4% when sample size is 100.

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For more information, contact Frank Schorfheide.