Moment-based estimation of smooth transition regression models with endogenous variables
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.
|Date of creation:||Mar 2010|
|Contact details of provider:|| Postal: Rua Marquês de São Vicente, 225, 22453-900 Rio de Janeiro, RJ|
Phone: 021 35271078
Fax: 021 35271084
Web page: http://www.econ.puc-rio.br
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
- Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002.
"Smooth Transition Autoregressive Models — A Survey Of Recent Developments,"
Taylor & Francis Journals, vol. 21(1), pages 1-47.
- van Dijk, D.J.C. & Terasvirta, T. & Franses, Ph.H.B.F., 2000. "Smooth transition autoregressive models - A survey of recent developments," Econometric Institute Research Papers EI 2000-23/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- van Dijk, Dick & Teräsvirta, Timo & Franses, Philip Hans, 2000. "Smooth Transition Autoregressive Models - A Survey of Recent Developments," SSE/EFI Working Paper Series in Economics and Finance 380, Stockholm School of Economics, revised 17 Jan 2001.
- 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.
- 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).
- Caner, Mehmet & Hansen, Bruce E., 2004. "Instrumental Variable Estimation Of A Threshold Model," Econometric Theory, Cambridge University Press, vol. 20(05), pages 813-843, October.
- Douglas Laxton & Guy Meredith & David Rose, 1995. "Asymmetric Effects of Economic Activity on Inflation: Evidence and Policy Implications," IMF Staff Papers, Palgrave Macmillan, vol. 42(2), pages 344-374, June.
- Douglas Laxton & Guy M Meredith & David Rose, 1994. "Asymmetric Effects of Economic Activityon Inflation; Evidence and Policy Implications," IMF Working Papers 94/139, International Monetary Fund.
- Cukierman, Alex & Wachtel, Paul, 1979. "Differential Inflationary Expectations and the Variability of the Rate of Inflation: Theory and Evidence," American Economic Review, American Economic Association, vol. 69(4), pages 595-609, September.
- Lundbergh, Stefan & Teräsvirta, Timo, 1998. "Modelling economic high-frequency time series with STAR-STGARCH models," SSE/EFI Working Paper Series in Economics and Finance 291, Stockholm School of Economics.
- Amemiya, Takeshi, 1975. "The nonlinear limited-information maximum- likelihood estimator and the modified nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 3(4), pages 375-386, November.
- Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-837, July.
- Newey, W.K., 1989. "Efficient Instrumental Variables Estimation Of Nonlinear Models," Papers 341, Princeton, Department of Economics - Econometric Research Program.
- Logue, Dennis E & Willett, Thomas D, 1976. "A Note on the Relation between the Rate and Variability of Inflation," Economica, London School of Economics and Political Science, vol. 43(17), pages 151-158, May.
- Galí, Jordi & Gertler, Mark, 1999. "Inflation Dynamics: A Structural Economic Analysis," CEPR Discussion Papers 2246, C.E.P.R. Discussion Papers.
- Alberto Musso & Livio Stracca & Dick van Dijk, 2009. "Instability and Nonlinearity in the Euro-Area Phillips Curve," International Journal of Central Banking, International Journal of Central Banking, vol. 5(2), pages 181-212, June.
- Stracca, Livio & Musso, Alberto & van Dijk, Dick, 2007. "Instability and nonlinearity in the euro area Phillips curve," Working Paper Series 811, European Central Bank.
- Michael Woodford, 2004. "Inflation targeting and optimal monetary policy," Review, Federal Reserve Bank of St. Louis, issue Jul, pages 15-42.
- Frederic S. Mishkin, 2004. "Can Inflation Targeting Work in Emerging Market Countries?," NBER Working Papers 10646, National Bureau of Economic Research, Inc.
- 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.
- Martin Cerisola & R. G Gelos, 2005. "What Drives Inflation Expectations in Brazil? An Empirical Analysis," IMF Working Papers 05/109, International Monetary Fund.
- Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
- Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-529, October.
- 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 245-269, July.
- Medeiros, Marcelo & Veiga, Alvaro, 2000. "A Flexible Coefficient Smooth Transition Time Series Model," SSE/EFI Working Paper Series in Economics and Finance 360, Stockholm School of Economics, revised 29 Apr 2004.
- Dionísio Dias Carneiro, 2000. "Inflation targeting in Brazil: what difference does a year make?," Textos para discussão 429, Department of Economics PUC-Rio (Brazil).
- Saikkonen, Pentti & Choi, In, 2004. "Cointegrating Smooth Transition Regressions," Econometric Theory, Cambridge University Press, vol. 20(02), pages 301-340, April.
- In Choi & Pentti Saikkonen, 2004. "Testing linearity in cointegrating smooth transition regressions," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 341-365, December.
- Gali, Jordi & Gertler, Mark, 1999. "Inflation dynamics: A structural econometric analysis," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 195-222, October.
- Jordi Galí & Mark Gertler, 1998. "Inflation dynamics: A structural econometric analysis," Economics Working Papers 341, Department of Economics and Business, Universitat Pompeu Fabra.
- Jordi Gali & Mark Gertler, 2000. "Inflation Dynamics: A Structural Econometric Analysis," NBER Working Papers 7551, National Bureau of Economic Research, Inc.
- Sergio A. L. Alves & Waldyr D. Areosa, 2005. "Targets and Inflation Dynamics," Working Papers Series 100, Central Bank of Brazil, Research Department.
- Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
- McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
- 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.
- 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.
- 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.
- Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
- Amemiya, Takeshi, 1977. "The Maximum Likelihood and the Nonlinear Three-Stage Least Squares Estimator in the General Nonlinear Simultaneous Equation Model," Econometrica, Econometric Society, vol. 45(4), pages 955-968, May. Full references (including those not matched with items on IDEAS)