Title: A test of exogeneity in the functional linear regression model
Authors: Melanie Birke - University of Bayreuth (Germany) [presenting]
Manuela Dorn - University of Bayreuth (Germany)
Carsten Jentsch - TU Dortmund University (Germany)
Abstract: Models containing endogenous control variables often occur in econometrics, natural sciences and other disciplines. They usually require more complex estimation methods. If the endogeneity remains unnoticed, it may lead to inconsistent estimates. In multivariate statistics several methods for testing exogeneity are known yet. We, in contrast, focus on the functional linear regression model, where the slope parameter belongs to the Sobolev space of periodic functions. For the functional linear model there exist estimation methods for the exogenous as well as the endogenous case, but no test for exogeneity is known so far. Assuming that an optimal linear instrument for the endogenous control variable exists, there is literature about instrumental variable estimators which are consistent in the endogenous case, whereas the ordinary least-squares estimator also proposed in literature for the exogenous case, is inconsistent under endogeneity. Based on the idea of the Hausman test, we compare both estimators to introduce a test for exogeneity. However, some modifications on the test statistic are necessary, since a direct analogue of the one used in the original Hausman test is not applicable in the functional context. We show the asymptotic behavior of the test statistic as well as the consistency of the bootstrap analogue. Finally, the test's finite-sample performance is checked by a small simulation study.