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Moment-bases estimation of smooth transition regression models with endogenous variables

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Author Info

  • Areosa, W.D.
  • McAleer, M.J.
  • Medeiros, M.C.

Abstract

Nonlinear regression models have been widely used in practice for a variety of time series and cross-section datasets. For purposes of analyzing univariate and multivariate time series data, in particular, Smooth Transition Regression (STR) models have been shown to be very useful for representing and capturing asymmetric behavior. Most STR models have been applied to univariate processes, and have made a variety of assumptions, including stationary or cointegrated processes, uncorrelated, homoskedastic or conditionally heteroskedastic errors, and weakly exogenous regressors. Under the assumption of exogeneity, the standard method of estimation is nonlinear least squares. The primary purpose of this paper is to relax the assumption of weakly exogenous regressors and to discuss moment based methods for estimating STR models. The paper analyzes the properties of the STR model with endogenous variables by providing a diagnostic test of linearity of the underlying process under endogeneity, developing an estimation procedure and a misspecification test for the STR model, presenting the results of Monte Carlo simulations to show the usefulness of the model and estimation method, and providing an empirical application for inflation rate targeting in Brazil. We show that STR models with endogenous variables can be specified and estimated by a straightforward application of existing results in the literature.

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File URL: http://repub.eur.nl/pub/14154/ei2008-36.pdf
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Bibliographic Info

Paper provided by Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute in its series Econometric Institute Research Papers with number EI 2008-36.

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Date of creation: 16 Dec 2008
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Handle: RePEc:ems:eureir:14154

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Keywords: endogeneity; generalized method of moments; inflation targeting; nonlinear instrumental variables; nonlinear models; smooth transition;

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References

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  1. Mayte Suarez Farinãs & Carlos Eduardo Pedreira & Marcelo C. Medeiros, 2003. "Local-global neural networks: a new approach for nonlinear time series modelling," Textos para discussão 470, Department of Economics PUC-Rio (Brazil).
  2. Martin Cerisola & Gaston Gelos, 2005. "What Drives Inflation Expectations in Brazil? An Empirical Analysis," IMF Working Papers 05/109, International Monetary Fund.
  3. Newey, W.K., 1989. "Efficient Instrumental Variables Estimation Of Nonlinear Models," Papers 341, Princeton, Department of Economics - Econometric Research Program.
  4. Jordi Gali & Mark Gertler, 2000. "Inflation Dynamics: A Structural Econometric Analysis," NBER Working Papers 7551, National Bureau of Economic Research, Inc.
  5. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
  6. Nobay, A. R. & Peel, D. A., 2000. "Optimal monetary policy with a nonlinear Phillips curve," Economics Letters, Elsevier, vol. 67(2), pages 159-164, May.
  7. Sergio A. L. Alves & Waldyr D. Areosa, 2005. "Targets and Inflation Dynamics," Working Papers Series 100, Central Bank of Brazil, Research Department.
  8. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  9. Frederic S. Mishkin & Klaus Schmidt-Hebbel, 2001. "One decade of inflation targeting in the world : What do we know and what do we need to know?," Working Papers Central Bank of Chile 101, Central Bank of Chile.
  10. Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
  11. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, September.
  12. Medeiros, Marcelo & Veiga, Alvaro, 2000. "A Flexible Coefficient Smooth Transition Time Series Model," Working Paper Series in Economics and Finance 360, Stockholm School of Economics, revised 10 Feb 2000.
  13. Li, W K & Ling, Shiqing & McAleer, Michael, 2002. " Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 245-69, July.
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Citations

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Cited by:
  1. 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.
  2. Kunitomo, N. & McAleer, M.J. & Nishiyama, Y., 2010. "Moment Restriction-based Econometric Methods: An Overview," Econometric Institute Research Papers EI 2010-61, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  3. Donald W.K. Andrews & Xu Cheng, 2011. "GMM Estimation and Uniform Subvector Inference with Possible Identification Failure," Cowles Foundation Discussion Papers 1828, Cowles Foundation for Research in Economics, Yale University.
  4. Massacci, Daniele, 2013. "A variable addition test for exogeneity in structural threshold models," Economics Letters, Elsevier, vol. 120(1), pages 5-9.
  5. Massacci, Daniele, 2012. "A simple test for linearity against exponential smooth transition models with endogenous variables," Economics Letters, Elsevier, vol. 117(3), pages 851-856.
  6. Line Elvstrøm Ekner & Emil Nejstgaard, 2013. "Parameter Identification in the Logistic STAR Model," Discussion Papers 13-07, University of Copenhagen. Department of Economics.
  7. Olivier Damette, 2013. "Mixture distribution hypothesis and the impact of a Tobin tax on exhange rate volatility : a reassessment," Working Papers of BETA 2013-07, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  8. Asai, Manabu & Brugal, Ivan, 2013. "Forecasting volatility via stock return, range, trading volume and spillover effects: The case of Brazil," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 202-213.

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