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Nonlinear Econometric Models with Deterministically Trending Variables

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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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File URL: http://cowles.econ.yale.edu/P/cd/d10b/d1053.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, 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: 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

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  1. 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.
  2. 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.
  3. 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.
  4. 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..
  5. 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.
  6. 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.
  7. 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.
  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.
  9. 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.
  10. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  11. 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.
  12. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  13. Martin S. Eichenbaum & Lars Peter Hansen, 1991. "Estimating Models with Intertemporal Substitution Using Aggregate Time Series Data," NBER Working Papers 2181, National Bureau of Economic Research, Inc.
  14. Donald W.K. Andrews, 1990. "Generic Uniform Convergence," Cowles Foundation Discussion Papers 940, Cowles Foundation for Research in Economics, Yale University.
  15. repec:cup:etheor:v:8:y:1992:i:2:p:241-57 is not listed on IDEAS
  16. 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.
  17. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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Citations

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Cited by:
  1. Allan W. Gregory & Gregor W. Smith, 1994. "Measuring Business Cycles with Business-Cycle Models," Working Papers 901, Queen's University, Department of Economics.
  2. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
  3. Alexander Ludwig, 2005. "Aging and Economic Growth: The Role of Factor Markets and of Fundamental Pension Reforms," MEA discussion paper series 05094, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
  4. Kumhof, Michael, 2000. "A quantitative exploration of the role of short-term domestic debt in balance of payments crises," Journal of International Economics, Elsevier, vol. 51(1), pages 195-215, June.
  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.
  6. 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.
  7. ERIC HILLEBRAND & MArcelo Cunha Medeiros, 2010. "Asymmetries, breaks, and long-range dependence: An estimation framework for daily realized volatility," Textos para discussão 578, Department of Economics PUC-Rio (Brazil).
  8. Aue, Alexander & Horváth, Lajos & Hušková, Marie, 2012. "Segmenting mean-nonstationary time series via trending regressions," Journal of Econometrics, Elsevier, vol. 168(2), pages 367-381.
  9. Diego Comin & Bart Hobijn, 2010. "An Exploration of Technology Diffusion," American Economic Review, American Economic Association, vol. 100(5), pages 2031-59, December.
  10. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
  11. Ripatti, Antti & Saikkonen, Pentti, 1998. "Cointegrated Vector Autoregressive Processes with Continuous Structural Changes," Research Discussion Papers 29/1998, Bank of Finland.
  12. Chang, Yoosoon & Park, Joon Y., 2003. "Index models with integrated time series," Journal of Econometrics, Elsevier, vol. 114(1), pages 73-106, May.
  13. Liang, Zhongwen & Li, Qi, 2012. "Functional coefficient regression models with time trend," Journal of Econometrics, Elsevier, vol. 170(1), pages 15-31.
  14. 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.
  15. Haiqiang Chen, 2013. "Robust Estimation and Inference for Threshold Models with Integrated Regressors," SFB 649 Discussion Papers SFB649DP2013-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  16. Diego Comin & Bart Hobijn, 2004. "Neoclassical Growth and the Adoption of Technologies," NBER Working Papers 10733, National Bureau of Economic Research, Inc.

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