Jörg Breitung | Searcharxiv

arXiv2023

Asymptotic Properties of Endogeneity Corrections Using Nonlinear Transformations

This paper considers a linear regression model with an endogenous regressor which arises from a nonlinear transformation of a latent variable. It is shown that the corresponding coefficient can be consistently estimated without external instruments by adding a rank-based transformation of the regressor to the model and performing standard OLS estimation. In contrast to other approaches, our nonparametric control function approach does not rely on a conformably specified copula. Furthermore, the approach allows for the presence of additional exogenous regressors which may be (linearly) correlated with the endogenous regressor(s). Consistency and asymptotic normality of the estimator are proved and the estimator is compared with copula based approaches by means of Monte Carlo simulations. An empirical application on wage data of the US current population survey demonstrates the usefulness of our method.

econ.EM↗

arXiv2022

Backward CUSUM for Testing and Monitoring Structural Change with an Application to COVID-19 Pandemic Data

It is well known that the conventional cumulative sum (CUSUM) test suffers from low power and large detection delay. In order to improve the power of the test, we propose two alternative statistics. The backward CUSUM detector considers the recursive residuals in reverse chronological order, whereas the stacked backward CUSUM detector sequentially cumulates a triangular array of backwardly cumulated residuals. A multivariate invariance principle for partial sums of recursive residuals is given, and the limiting distributions of the test statistics are derived under local alternatives. In the retrospective context, the local power of the tests is shown to be substantially higher than that of the conventional CUSUM test if a break occurs in the middle or at the end of the sample. When applied to monitoring schemes, the detection delay of the stacked backward CUSUM is found to be much shorter than that of the conventional monitoring CUSUM procedure. Furthermore, we propose an estimator of the break date based on the backward CUSUM detector and show that in monitoring exercises this estimator tends to outperform the usual maximum likelihood estimator. Finally, an application of the methodology to COVID-19 data is presented.

econ.EM↗