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DYNAMIC TIME SERIES BINARY CHOICE

Published online by Cambridge University Press:  03 March 2011

Robert M. de Jong  and
Tiemen Woutersen
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Abstract

This paper considers dynamic time series binary choice models. It proves near epoch dependence and strong mixing for the dynamic binary choice model with correlated errors. Using this result, it shows in a time series setting the validity of the dynamic probit likelihood procedure when lags of the dependent binary variable are used as regressors, and it establishes the asymptotic validity of Horowitz’s smoothed maximum score estimation of dynamic binary choice models with lags of the dependent variable as regressors. For the semiparametric model, the latent error is explicitly allowed to be correlated. It turns out that no long-run variance estimator is needed for the validity of the smoothed maximum score procedure in the dynamic time series framework.

Type
Research Article
Information
Econometric Theory , Volume 27 , Issue 4 , August 2011 , pp. 673 - 702
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

We thank Stephen Cosslett, James Davidson, Jon Faust, Lung-Fei Lee, Benedikt Pötscher, Jim Stock, and Jeff Wooldridge for helpful discussions.

References

REFERENCES

Andrews, D.W.K. (1987) Consistency in nonlinear econometric models: A generic uniform law of large numbers. Econometrica 55, 1465–1471.10.2307/1913568CrossRefGoogle Scholar
Andrews, D.W.K. (1988) Laws of large numbers for dependent non-identically distributed random variables. Econometric Theory 4, 458–467.10.1017/S0266466600013396CrossRefGoogle Scholar
Azuma, K. (1967) Weighted sums of certain dependent random variables. Tokohu Mathematical Journal 19, 357–367.Google Scholar
Bierens, H.J. (1981) Robust Methods and Asymptotic Theory in Nonlinear Econometrics. Springer-Verlag.10.1007/978-3-642-45529-2CrossRefGoogle Scholar
Bierens, H.J. (2004) Introduction to the Mathematical and Statistical Foundations of Econometrics. Cambridge University Press. Available at http://econ.la.psu.edu/∼hbieress/chaper7.pdf.CrossRefGoogle Scholar
Cosslett, S.R. (1983) Distribution-free maximum likelihood estimator of the binary choice model. Econometrica 51, 765–782.CrossRefGoogle Scholar
Davidson, J. (1994) Stochastic Limit Theory. Oxford University Press.CrossRefGoogle Scholar
de Jong, R.M. (1995) Laws of large numbers for dependent heterogeneous processes. Econometric Theory 11, 347–358.CrossRefGoogle Scholar
de Jong, R.M. (1997) Central limit theorems for dependent heterogeneous random variables. Econometric Theory 13, 353–367.10.1017/S0266466600005843CrossRefGoogle Scholar
Dueker, M.J. (1997) Strengthening the case for the yield curve as a predictor of U.S. recessions. Federal Reserve Bank of St. Louis Review in Business & Finance 2, 41–51.Google Scholar
Eichengreen, B., Watson, M., & Grossman, R. (1985) Bank rate policy under the interwar gold standard: A dynamic probit model. Economic Journal 95, 725–745.CrossRefGoogle Scholar
Engle, R.F. & Russell, J.R. (1998) Autoregressive conditional duration: A new model for irregularly spaced transaction data. Econometrica 66, 1127–1162.10.2307/2999632CrossRefGoogle Scholar
Gallant, A.R. & White, H. (1988) A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models. Basil Blackwell.Google Scholar
Hahn, J. & Kuersteiner, G. (2005) Bias Reduction for Dynamic Nonlinear Panel Models with Fixed Effects. Working paper, Boston University.Google Scholar
Hamilton, J.D. & Jorda, O. (2002) A model of the Federal Funds target. Journal of Political Economy 110, 1135–1167.CrossRefGoogle Scholar
Horowitz, J. (1992) A smoothed maximum score estimator for the binary response model. Econometrica 60, 505–531.CrossRefGoogle Scholar
Horowitz, J. (1993) Optimal rates of convergence of parameter estimators in the binary response model with weak distributional assumptions. Econometric Theory 9, 1–18.10.1017/S0266466600007301CrossRefGoogle Scholar
Hu, L. & Phillips, P.C.B. (2004) Nonstationary discrete choice. Journal of Econometrics 120, 103–138.CrossRefGoogle Scholar
Ichimura, I. (1993) Semiparametric least squares (SLS) and weighted SLS estimation of single-index models. Journal of Econometrics 58, 71–120.CrossRefGoogle Scholar
Imbens, G.W. (1992) An efficient method of moment estimator for discrete choice models with choice-based sampling. Econometrica 60, 1187–1214.CrossRefGoogle Scholar
Kauppi, H. & Saikkonen, P. (2008) Predicting U.S. recession with dynamic binary response models. Review of Economics and Statistics 90, 777–791.10.1162/rest.90.4.777CrossRefGoogle Scholar
Kim, J. & Pollard, D. (1990) Cube root asymptotics. Annals of Statistics 18, 191–219.10.1214/aos/1176347498CrossRefGoogle Scholar
Manski, C.F. (1975) Maximum score estimation of the stochastic utility model of choice. Journal of Econometrics 3, 205–228.10.1016/0304-4076(75)90032-9CrossRefGoogle Scholar
Manski, C.F. (1985) Semiparametric analysis of discrete response: Asymptotic properties of the maximum score estimator. Journal of Econometrics 27, 313–333.CrossRefGoogle Scholar
Matzkin, R.L. (1992) Nonparametric and distribution-free estimation of the binary threshold crossing and the binary choice models. Econometrica 60, 239–270.CrossRefGoogle Scholar
McLeish, D.L. (1974) Dependent central limit theorems and invariance principles. Annals of Probability 2, 620–628.CrossRefGoogle Scholar
Moon, H.R. (2004) Maximum score estimation of a nonstationary binary choice model. Journal of Econometrics 120, 385–403.CrossRefGoogle Scholar
Newey, W.K. & McFadden, D. (1994) Large sample estimation and hypothesis testing. In Engle, R.F. & MacFadden, D. (eds.). Handbook of Econometrics, vol. 4. North-Holland .Google Scholar
Park, Y. & Phillips, P.C.B. (2000) Nonstationary binary choice. Econometrica 68, 1249–1280.CrossRefGoogle Scholar
Poirier, D. & Ruud, P. (1988) Probit with dependent observations. Review of Economic Studies 55, 593–614.CrossRefGoogle Scholar
Pötscher, B.M. & Prucha, I.R. (1997) Dynamic Nonlinear Econometric Models. Springer-Verlag.CrossRefGoogle Scholar
Robinson, P.M. (1982) On the asymptotic properties of estimators of models containing LDV. Econometrica 50, 27–41.10.2307/1912527CrossRefGoogle Scholar
Ruud, P. (1981) Conditional Minimum Distance Estimation and Autocorrelation in Limited Dependent Variable Models, Ch. 3. Ph.D. thesis, MIT.Google Scholar
White, H. (2001) Asymptotic Theory for Econometricians. Academic Press.Google Scholar
Wooldridge, J. (1994). Estimation and inference for dependent processes. In Engle, R.F. & MacFadden, D. (eds.), Handbook of Econometrics, vol. 4. North-Holland.Google Scholar