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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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  • Donald W.K. Andrews & C. John McDermott, 1993. "Nonlinear Econometric Models with Deterministically Trending Variables," Cowles Foundation Discussion Papers 1053, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1053
    Note: CFP 907.
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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. 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.
    3. 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 333-364, Oct.-Dec..
    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 1276-1294, December.
    5. 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.
    6. 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.
    7. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
    8. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "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?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    9. 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 157-178, March.
    10. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    11. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    12. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    13. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    14. 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.
    15. repec:cup:etheor:v:8:y:1992:i:2:p:241-57 is not listed on IDEAS
    16. 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.
    17. 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.
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    Cited by:

    1. 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.
    2. Hillebrand Eric & Medeiros Marcelo C. & Xu Junyue, 2013. "Asymptotic Theory for Regressions with Smoothly Changing Parameters," Journal of Time Series Econometrics, De Gruyter, vol. 5(2), pages 133-162, April.
    3. Liang, Zhongwen & Li, Qi, 2012. "Functional coefficient regression models with time trend," Journal of Econometrics, Elsevier, vol. 170(1), pages 15-31.
    4. Chang, Yoosoon & Park, Joon Y., 2003. "Index models with integrated time series," Journal of Econometrics, Elsevier, vol. 114(1), pages 73-106, May.
    5. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    6. Li, Zheng & Su, Li & Zhang, Daiqiang, 2014. "Profile least squares estimation of a partially linear time trend model with weakly dependent data," Economics Letters, Elsevier, vol. 125(3), pages 404-407.
    7. Diego Comin & Bart Hobijn, 2010. "An Exploration of Technology Diffusion," American Economic Review, American Economic Association, vol. 100(5), pages 2031-2059, December.
    8. Diego Comin & Bart Hobijn, 2004. "Neoclassical Growth and the Adoption of Technologies," NBER Working Papers 10733, National Bureau of Economic Research, Inc.
    9. Masao Ogaki & Carmen M. Reinhart, 1998. "Measuring Intertemporal Substitution: The Role of Durable Goods," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 1078-1098, October.
    10. Chen, Haiqiang, 2015. "Robust Estimation And Inference For Threshold Models With Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 31(04), pages 778-810, August.
    11. Gregory, Allan W. & Smith, Gregor W., 1996. "Measuring business cycles with business-cycle models," Journal of Economic Dynamics and Control, Elsevier, vol. 20(6-7), pages 1007-1025.
    12. Mira, Santiago & Escribano, Álvaro, 1995. "Nonlinear time series models: consistency and asymptotic normality of nls under new conditions," DES - Working Papers. Statistics and Econometrics. WS 6202, Universidad Carlos III de Madrid. Departamento de Estadística.
    13. 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.
    14. 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.
    15. repec:wyi:journl:002203 is not listed on IDEAS
    16. 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).
    17. 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.
    18. Michael Kumhof, "undated". "A Quantative Exploration of the Role of Short-Term Domestic Debit in Balance of Payments Crises," Working Papers 00017, Stanford University, Department of Economics.
    19. 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.
    20. 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.
    21. 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.
    22. Saikkonen, Pentti & Choi, In, 2000. "Cointegrating smooth transition regressions with applications to the Asian currency crisis," SFB 373 Discussion Papers 2000,98, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

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