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A Nonlinear IV Likelihood-Based Rank Test for Multivariate Time Series and Long Panels

A test for the rank of a vector error correction model (VECM) or panel VECM based on the well-known trace test is proposed. The proposed test employs instrumental variables (IV's) generated by a class of nonlinear functions of the estimated stochastic trends of the VECM under the null. The test improves the standard trace test by replacing the non-standard critical values with chi-squared critical values. Extending the result to the panel VECM case, the test is robust to cross-sectional correlation of the disturbances. With this test, I extend earlier research using nonlinear IV's for unit root testing. However, the optimal instrument in the univariate case is not admissable in the more general multivariate case. The chi-squared result suggests that IV tests may be used to replace limits of other standard tests with integrated time series that are given by nonstandard stochastic integrals, even without a panel with which to pool tests.

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File URL: https://economics.missouri.edu/working-papers/2010/wp1001_zmiller.pdf
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Paper provided by Department of Economics, University of Missouri in its series Working Papers with number 1001.

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Length: 22 pgs.
Date of creation: 30 Jan 2010
Publication status: Published in Journal of Time Series Econometrics 2010
Handle: RePEc:umc:wpaper:1001
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  1. Shintani, Mototsugu, 2001. "A simple cointegrating rank test without vector autoregression," Journal of Econometrics, Elsevier, vol. 105(2), pages 337-362, December.
  2. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, April.
  3. Pedroni, Peter, 2004. "Panel Cointegration: Asymptotic And Finite Sample Properties Of Pooled Time Series Tests With An Application To The Ppp Hypothesis," Econometric Theory, Cambridge University Press, vol. 20(03), pages 597-625, June.
  4. Demetrescu Matei, 2009. "Panel Unit Root Testing with Nonlinear Instruments for Infinite-Order Autoregressive Processes," Journal of Time Series Econometrics, De Gruyter, vol. 1(2), pages 1-30, December.
  5. Groen, Jan J J & Kleibergen, Frank, 2003. "Likelihood-Based Cointegration Analysis in Panels of Vector Error-Correction Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(2), pages 295-318, April.
  6. P. Jeganathan, 2008. "Limit Theorems for Functionals of Sums that Converge to Fractional Brownian and Stable Motions," Cowles Foundation Discussion Papers 1649, Cowles Foundation for Research in Economics, Yale University.
  7. Osterwald-Lenum, Michael, 1992. "A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 461-472, August.
  8. Kao, Chihwa, 1999. "Spurious regression and residual-based tests for cointegration in panel data," Journal of Econometrics, Elsevier, vol. 90(1), pages 1-44, May.
  9. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(03), pages 710-738, June.
  10. Zivot, Eric, 2000. "The Power Of Single Equation Tests For Cointegration When The Cointegrating Vector Is Prespecified," Econometric Theory, Cambridge University Press, vol. 16(03), pages 407-439, June.
  11. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, April.
  12. Wang, Zijun & Bessler, David A., 2005. "A Monte Carlo Study On The Selection Of Cointegrating Rank Using Information Criteria," Econometric Theory, Cambridge University Press, vol. 21(03), pages 593-620, June.
  13. Yoosoon Chang & Wonho Song, 2009. "Testing for Unit Roots in Small Panels with Short-run and Long-run Cross-sectional Dependencies," Review of Economic Studies, Oxford University Press, vol. 76(3), pages 903-935.
  14. So, Beong Soo & Shin, Dong Wan, 1999. "Cauchy Estimators For Autoregressive Processes With Applications To Unit Root Tests And Confidence Intervals," Econometric Theory, Cambridge University Press, vol. 15(02), pages 165-176, April.
  15. Aznar, Antonio & Salvador, Manuel, 2002. "Selecting The Rank Of The Cointegration Space And The Form Of The Intercept Using An Information Criterion," Econometric Theory, Cambridge University Press, vol. 18(04), pages 926-947, August.
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