Estimation and Inference of Threshold Regression Models with Measurement Errors

Chong, Terence Tai Leung and Chen, Haiqiang and Wong, Tsz Nga and Yan, Isabel K. (2015): Estimation and Inference of Threshold Regression Models with Measurement Errors.

Abstract

An important assumption underlying standard threshold regression models and their variants in the extant literature is that the threshold variable is perfectly measured. Such an assumption is crucial for consistent estimation of model parameters. This paper provides the first theoretical framework for the estimation and inference of threshold regression models with measurement errors. A new estimation method that reduces the bias of the coefficient estimates and a Hausman-type test to detect the presence of measurement errors are proposed. Monte Carlo evidence is provided and an empirical application is given.

• Item Type: MPRA Paper
• Language: English
• Keywords: Threshold Model; Measurement Error; Hausman-type Test.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Amemiya, Y. (1985). Instrumental Variable Estimator for the Nonlinear Errors in Variables Model. Journal of Econometrics 28(3), 273-289.

Amemiya, Y. (1990). Two Stage Instrumental Variable Estimators for the Nonlinear Errors-in-Variables Model. Journal of Econometrics 44(3), 311-332.

Armstrong, B. (1985). Measurement Error in Generalized Linear Models, Communications in Statistics: Simulation and Computation 14(3), 529-544.

Astatkie, T., D. G. Watts and W. E. Watt (1997). Nested Threshold Autoregressive (NeTAR) Models. International Journal of Forecasting 13(1), 105-116.

Bai, J., H. Chen, T. T. L. Chong and X. Wang (2008). Generic Consistency of the Break-Point Estimator under Specification Errors in a Multiple-Break Model. Econometrics Journal 11(2), 287-307.

Chan, K. S. and H. Tong (1986). On Estimating Thresholds in Autoregressive Models. Journal of Time Series Analysis 7(3), 179-190.

Chen, R. and S. Tsay (1993). Functional-Coefficient Autoregressive Models. Journal of the American Statistical Association 88, 298-308.

Chen, H., T. T. L. Chong and J. Bai (2012). Theory and Applications of TAR Model with Two Threshold Variables, Econometric Reviews 31(2), 142-170.

Chong, T. T. L. (2001). Structural Change in AR(1) Models. Econometric Theory 17(1), 87-155.

Chong, T. T. L. (2003). Generic Consistency of the Break-Point Estimator under Specification Errors. Econometrics Journal 6(1), 167-192.

Gonzalo, J. and J. Pitarakis (2002). Estimation and Model Selection Based Inference in Single and Multiple Threshold Models. Journal of Econometrics 110(2), 319-352.

Hansen, B. E. (2000). Sample Splitting and Threshold Estimation. Econometrica 68(3), 575-603.

Hansen, B.E. (2011). Threshold Autoregression in Economics. Statistics and Its Interface, 4, 123-127.

Hausman, J. A. (1978). Specification Tests in Econometrics. Econometrica 46(6), 1251-1271.

Hausman, J. A. (2001). Mismeasured Variables in Econometric Analysis: Problems from the Right and Problems from the Left. Journal of Economic Perspectives 15(4), 57-67.

Jeong, J. and G. S. Maddala (1991). Measurement Errors and Tests for Rationality. Journal of Business and Economic Statistics 9(4), 431-439.

Madansky, A. (1959). The Fitting of Straight Lines when Both Variables are subject to Error. Journal of the American Statistical Association 54, 173-205.

Li, C. W. and W. K. Li (1996). On a Double-threshold Autoregressive Heteroscedastic Time Series Model. Journal of Applied Econometrics 11(3), 253-274.

Li, W. K. and K. Lam (1995). Modeling Asymmetry in Stock Returns by a Threshold Autoregressive Conditional Heteroscedastic Model. The Statistician 44(3), 333-341.

Newey, W. K. and K. D. West (1987). A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica 55(3), 703-708.

Schennach, S. M. (2004). Estimation of Nonlinear Models with Measurement Error. Econometrica 72(1), 33-75.

Tong, H. and K.S. Lim (1980). Threshold Autoregression, Limit Cycles and Cyclical Data. Journal of the Royal Statistical Society, Series B 42(3), 245-292.

Tong, H. (1983). Threshold Models in Nonlinear Time Series Analysis: Lecture Notes in Statistics 21. Berlin: Springer.

Tong, H. (2011). Threshold Models in Time Series Analysis-30 Years on. Statistics and Its Interface 4(2), 107-118.

Tsay, R. S. (1998). Testing and Modeling Multivariate Threshold Models. Journal of the American Statistical Association 93, 1188-1202.

Wong, S.T. and W.K. Li (2010). A Threshold Approach for Peaks-over-threshold Modelling Using Maximum Product of Spacings. Statistica Sinica 20, 1257-1572.

Xia, Y. and Tong, H. (2011) Feature Matching in Time Series Modeling (with discussion), Rejoinder. Statistical Science 26(1), 21-61.