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

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  • 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.

Suggested Citation

  • Areosa, W.D. & McAleer, M.J. & Medeiros, M.C., 2008. "Moment-bases estimation of smooth transition regression models with endogenous variables," Econometric Institute Research Papers EI 2008-36, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  • Handle: RePEc:ems:eureir:14154
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    References listed on IDEAS

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    Cited by:

    1. Damette, Olivier, 2016. "Mixture Distribution Hypothesis And The Impact Of A Tobin Tax On Exchange Rate Volatility: A Reassessment," Macroeconomic Dynamics, Cambridge University Press, vol. 20(06), pages 1600-1622, September.
    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. repec:fgv:epgrbe:v:67:n:4:a:8 is not listed on IDEAS
    4. 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.
    5. Phiri, Andrew, 2015. "Examining asymmetric effects in the South African Philips curve: Evidence from logistic smooth transition regression (LSTR) models," MPRA Paper 64487, University Library of Munich, Germany.
    6. Naoto Kunitomo & Michael McAleer & Yoshihiko Nishiyama, 2010. "Moment Restriction-based Econometric Methods: An Overview," Working Papers in Economics 10/65, University of Canterbury, Department of Economics and Finance.
    7. Massacci, Daniele, 2013. "A variable addition test for exogeneity in structural threshold models," Economics Letters, Elsevier, vol. 120(1), pages 5-9.
    8. 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.
    9. Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(02), pages 287-333, April.
    10. Line Elvstrøm Ekner & Emil Nejstgaard, 2013. "Parameter Identification in the Logistic STAR Model," Discussion Papers 13-07, University of Copenhagen. Department of Economics.
    11. repec:spr:empeco:v:53:y:2017:i:4:d:10.1007_s00181-016-1195-0 is not listed on IDEAS
    12. Otilia Boldea & Alastair R. Hall, 2013. "Testing structural stability in macroeconometric models," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 9, pages 206-228 Edward Elgar Publishing.
    13. Sachsida, Adolfo, 2013. "Inflação, Desemprego e Choques Cambiais: Uma Revisão da Literatura sobre a Curva de Phillips no Brasil," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 67(4), November.

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    Keywords

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

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