Hall, Alastair R. and Han, Sanggohn and Boldea, Otilia (2008): Inference regarding multiple structural changes in linear models estimated via two stage least squares.

PDF
MPRA_paper_9251.pdf Download (415kB)  Preview 
Abstract
In this paper, we extend Bai and Perron’s (1998, Econometrica, p.4778) framework for multiple break testing to linear models estimated via Two Stage Least Squares (2SLS). Within our framework, the break points are estimated simultaneously with the regression parameters via minimization of the residual sum of squares on the second step of the 2SLS estimation. We establish the consistency of the resulting estimated break point fractions. We show that various Fstatistics for structural instability based on the 2SLS estimator have the same limiting distribution as the analogous statistics for OLS considered by Bai and Perron (1998). This allows us to extend Bai and Perron’s (1998) sequential procedure for selecting the number of break points to the 2SLS setting. Our methods also allow for structural instability in the reduced form that has been identified a priori using databased methods. As an empirical illustration, our methods are used to assess the stability of the New Keynesian Phillips curve.
Item Type:  MPRA Paper 

Original Title:  Inference regarding multiple structural changes in linear models estimated via two stage least squares 
Language:  English 
Keywords:  unknown break points; structural change; instrumental variables; endogenous regressors; structural stability tests; new Keynesian Phillips curve 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models 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  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  9251 
Depositing User:  Otilia Boldea 
Date Deposited:  21. Jun 2008 02:26 
Last Modified:  11. Mar 2015 15:47 
References:  Amemiya, T. (1985). Advanced Econometrics. Harvard University Press, Cambridge, MA, U.S.A. Andrews, D. W. K. (1993). ‘Tests for parameter instability and structural change with unknown change point’, Econometrica, 61: 821–856. Andrews, D. W. K., and Fair, R. (1988). ‘Inference in econometric models with structural change’, Review of Economic Studies, 55: 615–640. Bai, J. (1994). ‘Least squares estimation of a shift in linear processes’, Journal of Time Series Analysis, 15: 453–472. Bai, J., and Perron, P. (1998). ‘Estimating and testing linear models with multiple structural changes’, Econometrica, 66: 47–78. (2001). ‘Additional critical values for multiple structural change tests’, Discussion paper, Department of Economics, Boston University, Boston, MA. Bhattacharya, P. K. (1987). ‘Maximum Likelihood estimation of a changepoint in the distribution of independent random variables: general multiparameter case’, Journal of Multivariate Analysis, 23: 183–208. de Jong, R. M., and Davidson, J. (2000). ‘THE Functional Central Limit Theorem and Weak Convergence to Stochastic Integrals I’, Econometric Theory, 16: 621–642. Ghysels, E., and Hall, A. R. (1990). ‘A test for structural stability of Euler condition parameters estimated via the Generalized Method of Moments’, International Economic Review, 31: 355– 364. Hahn, J., and Inoue, A. (2002). ‘A Monte Carlo comparison of various asymptotic approximations to the distribution of instrumental variables estimators’, Econometric Reviews, 21: 309–336. Hall, A. R. (2005). Generalized Method of Moments. Oxford University Press, Oxford, U.K. Hall, A. R., Han, S., and Boldea, O. (2007). ‘A distribution theory for change point estimators in models estimated by Two Stage Least Squares’, Discussion paper, Department of Economics, North Carolina State University, Raleigh, NC. Hall, A. R., and Sen, A. (1999). ‘Structural stability testing in models estimated by Generalized Method of Moments’, Journal of Business and Economic Statistics, 17: 335–348. Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press, Princeton, NJ, U. S. A. Han, S. (2006). ‘Inference regarding multiple structural changes in linear models estimated via Instrumental Variables’, Ph.D. thesis, Department of Economics, North Carolina State University, Raleigh, NC. Hawkins, D. L. (1986). ‘A simple least square method for estimating a change in mean’, Communications in Statistics  Simulation, 15: 655–679. Ortega, J. M. (1987). Matrix Theory: a Second Course. Plenum Press, New York, NY, U.S.A. Perron, P., and Qu, Z. (2006). ‘Estimating restricted structural change models’, Journal of Econometrics, 134: 373–399. Picard, D. (1985). ‘Testing and estimating change points in time series’, Journal of Applied Probability, 20: 411–415. Qu, Z., and Perron, P. (2007). ‘Estimating and testing structural changes in multivariate regressions’, Econometrica, 75: 459–502. Sowell, F. (1996). ‘Optimal tests of parameter variation in the Generalized Method of Moments framework’, Econometrica, 64: 1085–1108. Yao, Y.C. (1987). ‘Approximating the distribution of the ML estimate of the chnage point in a sequence of independent r.v.’s’, Annals of Statistics, 4: 1321–1328. Zhang, C., Osborn, D. R., and Kim, D. H. (2007). ‘The new Keynesian Phillips curve: from sticky inflation to sticky prices’, Journal of Money, Credit and Banking, forthcoming. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/9251 