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Moment-Based Estimation of Smooth Transition Regression Models with Endogenous Variables

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Author Info

  • Waldyr Dutra Areosa

    (Department of Economics, Pontifical Catholic University of Rio de Janeiro and Banco Central do Brasil)

  • Michael McAleer

    (Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute and Center for International Research on the Japanese Economy (CIRJE), Faculty of Economics, University of Tokyo)

  • Marcelo C. Medeiros

    (Department of Economics Pontifical Catholic University of Rio de Janeiro)

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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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-671.

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Length: 29pages
Date of creation: Sep 2009
Date of revision:
Handle: RePEc:tky:fseres:2009cf671

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References

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  1. Mayte Suarez -Farinas & Carlos E. Pedreira & Marcelo C. Medeiros, 2004. "Local Global Neural Networks: A New Approach for Nonlinear Time Series Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1092-1107, December.
  2. 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?," NBER Working Papers 8397, National Bureau of Economic Research, Inc.
  3. 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.
  4. Jordi Gali & Mark Gertler, 2000. "Inflation Dynamics: A Structural Econometric Analysis," NBER Working Papers 7551, National Bureau of Economic Research, Inc.
  5. 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.
  6. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
  7. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  8. Newey, W.K., 1989. "Efficient Instrumental Variables Estimation Of Nonlinear Models," Papers 341, Princeton, Department of Economics - Econometric Research Program.
  9. Martin Cerisola & Gaston Gelos, 2009. "What drives inflation expectations in Brazil? An empirical analysis," Applied Economics, Taylor & Francis Journals, vol. 41(10), pages 1215-1227.
  10. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
  11. Sergio A. L. Alves & Waldyr D. Areosa, 2005. "Targets and Inflation Dynamics," Working Papers Series 100, Central Bank of Brazil, Research Department.
  12. Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
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Cited by:
  1. Naoto Kunitomo & Michael McAleer & Yoshihiko Nishiyama, 2010. "Moment Restriction-based Econometric Methods: An Overview," KIER Working Papers 734, Kyoto University, Institute of Economic Research.
  2. 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.
  3. 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.
  4. Line Elvstrøm Ekner & Emil Nejstgaard, 2013. "Parameter Identification in the Logistic STAR Model," Discussion Papers 13-07, University of Copenhagen. Department of Economics.
  5. 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.
  6. 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, revised Jan 2013.
  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. Massacci, Daniele, 2013. "A variable addition test for exogeneity in structural threshold models," Economics Letters, Elsevier, vol. 120(1), pages 5-9.

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