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Nonlinear Econometric Models with Deterministically Trending Variables

  • Andrews, Donald W K
  • McDermott, C John

This paper considers an alternative asymptotic framework to standard sequential asymptotics for nonlinear models with deterministically trending variables. The asymptotic distributions of generalized method of moments estimators and corresponding test statistics are derived using this framework. The asymptotic distributions are shown to be the same with deterministically trending variables as with nontrending variables. That is, the distributions are normal and chi-squared respectively. The asymptotic covariance matrices of the estimators, however, are found to depend on the form of the trends. These findings provide a justification for the use of standard asymptotic approximations in nonlinear models even when the variables have deterministic trends. Copyright 1995 by The Review of Economic Studies Limited.

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Article provided by Wiley Blackwell in its journal Review of Economic Studies.

Volume (Year): 62 (1995)
Issue (Month): 3 (July)
Pages: 343-60

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Handle: RePEc:bla:restud:v:62:y:1995:i:3:p:343-60
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  1. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  2. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  3. Martin S. Eichenbaum & Lars Peter Hansen, 1987. "Estimating Models with Intertemporal Substitution Using Aggregate Time Series Data," NBER Working Papers 2181, National Bureau of Economic Research, Inc.
  4. Fair, Ray C & Dominguez, Kathryn M, 1991. "Effects of the Changing U.S. Age Distribution on Macroeconomic Equations," American Economic Review, American Economic Association, vol. 81(5), pages 1276-94, December.
  5. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-64, Oct.-Dec..
  6. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  7. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  8. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  9. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
  10. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  11. DeJong, David N. & Whiteman, Charles H., 1991. "Reconsidering 'trends and random walks in macroeconomic time series'," Journal of Monetary Economics, Elsevier, vol. 28(2), pages 221-254, October.
  12. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
  13. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  14. Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
  15. repec:cup:etheor:v:8:y:1992:i:2:p:241-57 is not listed on IDEAS
  16. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Statistical Inference in Instrumental Variables," Cowles Foundation Discussion Papers 869R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1989.
  17. Hamilton, James D, 1992. "Was the Deflation during the Great Depression Anticipated? Evidence from the Commodity Futures Market," American Economic Review, American Economic Association, vol. 82(1), pages 157-78, March.
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