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Nonlinear Econometric Models with Deterministically Trending Variables

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Author Info
Donald W.K. Andrews () (Cowles Foundation, Yale University)
C. John McDermott

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Abstract

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 non-trending 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.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1053.

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Length: 25 pages
Date of creation: Aug 1993
Date of revision:
Publication status: Published in Review of Economic Studies (1005), 62: 343-360
Handle: RePEc:cwl:cwldpp:1053

Note: CFP 907.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Asymptotics; deterministic trend; generalized method of moments estimator; hypothesis test; nonlinear econometric model; time trend;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  2. 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. [Downloadable!] (restricted)
  3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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  5. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July. [Downloadable!] (restricted)
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  6. Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
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  7. Benedikt Pötscher & Ingmar Prucha, 1991. "Basic structure of the asymptotic theory in dynamic nonlinear econometric models," Econometric Reviews, Taylor and Francis Journals, vol. 10(3), pages 253-325. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. repec:cup:etheor:v:8:y:1992:i:2:p:241-57 is not listed on IDEAS
  10. 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.. [Downloadable!] (restricted)
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  11. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Statistical Inference in Instrumental Variables," Cowles Foundation Discussion Papers 869R, Cowles Foundation, Yale University, revised Apr 1989. [Downloadable!]
  12. 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.
  13. Eichenbaum, Martin & Hansen, Lars Peter, 1990. "Estimating Models with Intertemporal Substitution Using Aggregate Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 53-69, January.
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  14. Donald W.K. Andrews, 1990. "Generic Uniform Convergence," Cowles Foundation Discussion Papers 940, Cowles Foundation, Yale University. [Downloadable!]
  15. 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. [Downloadable!] (restricted)
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  16. 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. [Downloadable!] (restricted)
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Alexander Ludwig, 2005. "Aging and Economic Growth: The Role of Factor Markets and of Fundamental Pension Reforms," MEA discussion paper series 05094, Mannheim Research Institute for the Economics of Aging (MEA), University of Mannheim. [Downloadable!]
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  2. Jonathan Treussard, 2005. "On the Validity of Risk Measures over Time: Value-at-Risk, Conditional Tail Expectations and the Bodie-Merton-Perold Put," Boston University - Department of Economics - Working Papers Series WP2005-029, Boston University - Department of Economics. [Downloadable!]
  3. Yoosoon Chang & Joon Y. Park & Peter C.B. Phillips, 1999. "Nonlinear Econometric Models with Cointegrated and Deterministically Trending Regressors," Cowles Foundation Discussion Papers 1245, Cowles Foundation, Yale University. [Downloadable!]
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  4. Mynbaev, Kairat, 2003. "Asymptotic properties of OLS estimates in autoregressions with bounded or slowly growing deterministic trends," MPRA Paper 18448, University Library of Munich, Germany, revised 2005. [Downloadable!]
  5. Olympia Bover & Manuel Arellano, 1995. "Female labour force participation in the 1980s: the case of Spain," Investigaciones Economicas, Fundación SEPI, vol. 19(2), pages 171-194, May. [Downloadable!]
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  6. Diego Comin & Bart Hobiijn, 2006. "An Exploration of Technology Diffusion," NBER Working Papers 12314, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  7. Diego Comin & Bart Hobijn, 2004. "Neoclassical Growth and the Adoption of Technologies," NBER Working Papers 10733, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  8. Alexander Ludwig, 2005. "Moment estimation in Auerbach-Kotlikoff models: How well do they match the data?," MEA discussion paper series 05093, Mannheim Research Institute for the Economics of Aging (MEA), University of Mannheim. [Downloadable!]
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  9. Joon Y. Park & Peter C.B. Phillips, 1998. "Nonlinear Regressions with Integrated Time Series," Cowles Foundation Discussion Papers 1190, Cowles Foundation, Yale University. [Downloadable!]
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