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Changepoint Analysis of Binary and Ordinal Probit Models: An Application to Bank Rate Policy Under the Interwar Gold Standard

Published online by Cambridge University Press:  04 January 2017

Jong Hee Park*
Affiliation:
Department of Political Science, The University of Chicago, 5828 S. University Ave., Chicago, IL 60637 e-mail: [email protected]

Abstract

In this paper, I introduce changepoint models for binary and ordered time series data based on Chib's hidden Markov model. The extension of the changepoint model to a binary probit model is straightforward in a Bayesian setting. However, detecting parameter breaks from ordered regression models is difficult because ordered time series data often have clustering along the break points. To address this issue, I propose an estimation method that uses the linear regression likelihood function for the sampling of hidden states of the ordinal probit changepoint model. The marginal likelihood method is used to detect the number of hidden regimes. I evaluate the performance of the introduced methods using simulated data and apply the ordinal probit changepoint model to the study of Eichengreen, Watson, and Grossman on violations of the “rules of the game” of the gold standard by the Bank of England during the interwar period.

Type
Regular Articles
Copyright
Copyright © The Author 2011. Published by Oxford University Press on behalf of the Society for Political Methodology 

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References

Agresti, Alan. 2010. Analysis of ordinal categorical data. Hoboken, NJ: John Wiley & Sons.Google Scholar
Albert, James H., and Chib, Siddhartha. 1993. Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association 88: 669–79.CrossRefGoogle Scholar
Albert, James H., and Chib, Siddhartha. 2001. Sequential ordinal modeling with applications to survival data. Biometrics 57: 829–36.Google Scholar
Andrews, Donald W. K. 1993. Tests for parameter instability and structural change with unknown change point. Econometrica 61: 821–56.Google Scholar
Bai, Jushuan, and Perron, Pierre. 1998. Estimating and testing linear models with multiple structural changes. Econometrica 66: 4778.Google Scholar
Baum, Leonard E., Petrie, Ted, Soules, George, and Weiss, Norman. 1970. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Annals of Mathematical Statistics 41: 164–71.CrossRefGoogle Scholar
Brandt, Patrick T., and Sandler, Todd. 2009. Hostage taking: Understanding terrorism event dynamics. Journal of Policy Modeling 31(5): 758–78.Google Scholar
Brown, R. L., Durbin, J., and Evans, J. M. 1975. Techniques for testing the constancy of regression relationships over time. Journal of the Royal Statistical Society, Series B 35: 149–92.Google Scholar
Carlin, Bradley P., Gelfand, Alan E., and Smith, Adrian F. M. 1992. Hierarchical Bayesian analysis of changepoint problems. Applied Statistics 41: 389405.Google Scholar
Carlin, Bradley P., and Louis, Thomas A. 2000. Bayes and empiricalBayes methods for data analysis. Boca Raton, FL: Chapman and Hall/CRC.Google Scholar
Chernoff, Herman, and Zacks, Shelemyahu. 1964. Estimating the current mean of a normal distribution which is subject to changes in time. Annals of Mathematical Statistics 35: 9991018.Google Scholar
Chib, Siddhartha. 1995. Marginal likelihood from the Gibbs output. Journal of the American Statistical Association 90: 1313–21.Google Scholar
Chib, Siddhartha. 1996. Calculating posterior distributions and modal estimates in Markov mixture models. Journal of Econometrics 75: 7998.CrossRefGoogle Scholar
Chib, Siddhartha. 1998. Estimation and comparison of multiple change-point models. Journal of Econometrics 86: 221–41.Google Scholar
Chib, Siddhartha, and Jeliazkov, Ivan. 2001. Marginal likelihood from the Metropolis-Hastings output. Journal of the American Statistical Association 96: 270–81.Google Scholar
Chow, Gregory C. 1960. Tests of equality between sets of coefficients in two linear regressions. Econometrica 28: 591605.Google Scholar
Cowles, Mary Kathyrun 1996. Accelerating Monte Carlo Markov chain convergence for cumulative-link generalized linear models. Statistics and Computing 6: 101–11.Google Scholar
Eichengreen, Barry, Watson, Mark W., and Grossman, Richard S. 1985. Bank Rate policy under the interwar gold standard: A dynamic probit model. Economic Journal 95: 725–45.Google Scholar
Freeman, John R., Hays, Jude C., and Stix, Helmut. 2000. Democracy and markets: The case of exchange rates. American Journal of Political Science 44: 449–68.Google Scholar
Frühwirth-Schnatter, Sylvia. 2006. Finite mixture and Markov switching models. New York: Springer-Verlag.Google Scholar
Geweke, John. 1989. Bayesian inference in econometric models using Monte Carlo integration. Econometrica 57: 1317–39.Google Scholar
Geweke, John. 1991. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Federal Reserve Bank of Minneapolis Staff Report No. 148.Google Scholar
Green, Peter J. 1995. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82: 711–32.Google Scholar
Hamilton, James D. 1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57: 357–84.Google Scholar
Hyndman, Rob J. 1996. Computing and graphing highest density regions. American Statistician 50: 120–6.Google Scholar
Kass, Robert E., and Raftery, Adrian E. 1995. Bayes factors. Journal of the American Statistical Association 90: 773–95.CrossRefGoogle Scholar
Kim, Chang-Jin. 2004. Markov-switching models with endogenous explanatory variables. Journal of Econometrics 122: 127–36.CrossRefGoogle Scholar
Kim, Chang-Jin, and Nelson, Charles R. 1999. State-space models with regime-switching: Classical and Gibbs-sampling approaches with applications. Cambridge, MA: The MIT Press.Google Scholar
Long, J. Scott. 1997. Regression models for categorical and limited dependent variables. Thousand Oaks, CA: Sage Publications.Google Scholar
Martin, Andrew D., Quinn, Kevin M., and Park, Jong Hee. 2011. MCMCpack, version 1.0-9. http://CRAN.R-project.org/package=MCMCpack.Google Scholar
Meng, Xiao-Li, and Wong, Wing Hung. 1996. Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statistica Sinica 6: 831–60.Google Scholar
Newton, Michael A., and Raftery, Adrian E. 1994. Approximate Bayesian inference with the weighted likelihood bootstrap. Journal of the Royal Statistical Society, Series B 56: 348.Google Scholar
Nyblom, Jukka. 1989. Testing for the constancy of parameters over time. Journal of the American Statistical Association 84: 223–30.Google Scholar
Park, Jong Hee. 2010. Structural change in U. S. presidents' use of force. American Journal of Political Science 54: 766–82.Google Scholar
Park, Jong Hee. 2011. Analyzing preference changes using hidden Markov item response theory models. In Handbook of Markov chain Monte Carlo: Methods and applications, eds. Jones, Galin, Brooks, Steve, Gelman, Andrew, and Meng, Xiao-Li. Boca Raton, FL: Chapman and Hall/CRC.Google Scholar
Quandt, Richard E. 1958. The estimation of the parameters of a linear regression system obeying two separate regimes. Journal of the American Statistical Association 53: 873–80.CrossRefGoogle Scholar
Scheve, Kenneth, and Stasavage, David. 2009. Institutions, partisanship, and inequality in the long run. World Politics 61: 215–53.Google Scholar
Simmons, Beth A. 1994. Who adjusts? Domestic sources of foreign economic policy during the interwar years 1923-1939. Princeton, NJ: Princeton University Press. Spirling, Arthur. 2007a. Bayesian approaches for limited dependent variable change point problems. Political Analysis 15: 387405.Google Scholar
Spirling, Arthur. 2007a. Bayesian approaches for limited dependent variable change point problems. Political Analysis 15: 387405.Google Scholar
Spirling, Arthur. 2007b. “Turning points” in Iraq: Reversible jump Markov chain Monte Carlo in political science. American Statistician 61: 315–20.CrossRefGoogle Scholar
Svolik, Milan. 2009. When and why democracies consolidate: Coups, incumbent takeovers, and democratic survival. Unpublished manuscript.Google Scholar