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Varying Responses to Common Shocks and Complex Cross-Sectional Dependence: Dynamic Multilevel Modeling with Multifactor Error Structures for Time-Series Cross-Sectional Data

Published online by Cambridge University Press:  04 January 2017

Xun Pang
Xun Pang*
Affiliation:
School of Social Sciences, Tsinghua University, 314 Minzhai Hall, Haidian District, Beijing 100084, China. e-mail: xpang@tsinghua.edu.cn
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Abstract

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Multifactor error structures utilize factor analysis to deal with complex cross-sectional dependence in Time-Series Cross-Sectional data caused by cross-level interactions. The multifactor error structure specification is a generalization of the fixed-effects model. This article extends the existing multifactor error models from panel econometrics to multilevel modeling, from linear setups to generalized linear models with the probit and logistic links, and from assuming serial independence to modeling the error dynamics with an autoregressive process. I develop Markov Chain Monte Carlo algorithms mixed with a rejection sampling scheme to estimate the multilevel multifactor error structure model with a pth-order autoregressive process in linear, probit, and logistic specifications. I conduct several Monte Carlo studies to compare the performance of alternative specifications and approaches with varying degrees of data complication and different sample sizes. The Monte Carlo studies provide guidance on when and how to apply the proposed model. An empirical application sovereign default demonstrates how the proposed approach can accommodate a complex pattern of cross-sectional dependence and helps answer research questions related to units' sensitivity or vulnerability to systemic shocks.

Information

Type
Research Article
Information
Political Analysis , Volume 22 , Issue 4 , Autumn 2014, pp. 464 - 496
Copyright
Copyright © The Author 2014. Published by Oxford University Press on behalf of the Society for Political Methodology 

References

Ahn, S. C., Lee, Y. H., and Schmidt, P. 2001. GMM estimation of linear panel data models with time-varying individual effects. Journal of Econometrics 101(2): 219–55.Google Scholar
Alston, C., Kuhnert, P., Choy, L. S., McVinish, R., and Mengersen, K. 2005. Bayesian model comparison: Review and discussion. International Statistical Institute, 55th session.Google Scholar
Andrews, F. D., and Mallows, C. L. 1974. Scale mixtures of normal distributions. Journal of the Royal Statistical Society: Series B (Methodological) 36(1): 99–102.Google Scholar
Anselin, L. 1988a. Spatial econometrics: Methods and models. Dordrecht, The Netherlands: Kluwer Academic Publishers.Google Scholar
Anselin, L. 1988b. Spatial econometrics: Methods and models. Dordrecht, The Netherlands: Kluwer Academic Publishers.CrossRefGoogle Scholar
Anselin, L. 2003. Spatial externalities, spatial multipliers, and spatial econometrics. International Regional Science Review 26(2): 153–66.Google Scholar
Anselin, L., Gallo, J. L., and Jayet, H. 2007. Spatial panel econometrics. In The econometrics of panel data: Fundamentals and recent developments in theory and practice, 3rd ed, eds. Mátyás, László and Sevestre, Patrick, 625–18. Dordrech: Kluwer.Google Scholar
Arbia, G., and Fingleton, B. 2008. New spatial econometric techniques and applications in regional science. Regional Science 87(3): 311–7.Google Scholar
Archer, C. C., Biglaiser, G., and DeRouen, K. 2007. Sovereign bonds and the “democratic advantage”: Does regime type affect credit rating agency ratings in the developing world? International Organization 61: 341–65.Google Scholar
Bai, J. 2009. Panel data models with interactive fixed effects. Econometrica 77(4): 1229–79.Google Scholar
Bai, J. 2013. Fixed-effects dynamic panel models: A factor analytical method. Econometrica 81(1): 285–314.Google Scholar
Bai, J., and Li, K. 2012. Statistical analysis of factor models of high dimension. Annuals of Statistics 40(1): 436–65.CrossRefGoogle Scholar
Baliga, S., Lucca, D. O., and Sjöström, T. 2009. Domestic political survival and international conflict: Is democracy good for peace? Unpublished manuscript.Google Scholar
Balkan, E. M. 1992. Political instability, coutry risk, and probability of default. Applied Economics 24: 999–1008.Google Scholar
Banerjee, S., Gelfand, A. E., and Carlin, B. P. 2003. Hierchical modeling and analysis for spatial data. 1st ed. New York: Chapman & Hall/CRC.Google Scholar
Beaulieu, E., Cox, G. W., and Saiegh, S. 2012. Sovereign debt and regime type: Reconsidering the democratic advantage. International Organization 66(4): 709–38.Google Scholar
Beck, N., and Katz, J. N. 2007. Random coefficient models for time-series-cross-section data: Monte Carlo experiments. Political Analysis 15: 182–95.Google Scholar
Beck, N., Katz, J. N., and Tucker, R. 1998. Taking time seriously: Time-series-cross-section analysis with a binary dependent variable. American Journal of Political Science 42(4): 1260–88.Google Scholar
Berger, S. 2000. Globalization and politics. Annual Review of Political Science 3: 43–62.Google Scholar
Berger, J. O., and Pericchi, L. 1998. Accurate and stable Bayesian model selection: The median intrinsic Bayes factor. Sankhaya B 60: 1–18.Google Scholar
Beron, K. J., and Vijverberg, W. P. M. 2004. Probit in a spatial context: A Monte Carlo analysis. In Advance in spatial econometrics: Methodology, tools, and applications, eds. Anselin, L. and Florax, R. J. G. M. Berlin: Springer.Google Scholar
Botcheva, L., and Martin, L. L. 2001. Institutional effect on state behavior: Convergence and divergence. International Studies Quarterly 45(1): 1–26.Google Scholar
Breslow, N. E. 1991. Statistics in epidemiology: The case-control study. Journal of the American Statistical Association 91(433): 14–28.Google Scholar
Chang, R. 2002. Financial crises and political crises. Working paper.Google Scholar
Chaudoin, S., Milner, H., and Pang, X. Forthcoming. International systems and domestic politics: Linking complex interactions with empirical models in international relations. International Organization.Google Scholar
Chib, S. 1993. Bayes regression with autoregressive errors: A Gibbs sampling approach. Journal of Econometrics 58(3): 275–94.Google Scholar
Chib, S. 1995. Marginal likelihood from the Gibbs output. Journal of the American Statistical Association 90: 1313–21.CrossRefGoogle Scholar
Chib, S., and Jeliazkov, I. 2001. Marginal likelihood from the Metropolis-Hastings output. Journal of the American Statistical Association 96: 270–81.Google Scholar
Chib, S., and Jeliazkov, I. 2006. Inference in semiparametric dynamic models for binary longitudinal data. Journal of the American Statistical Association 101(474): 685–700.Google Scholar
Christensen, W. F., and Amemlya, Y. 2002. Latent variable analysis of multivariate spatial data. Journal of the American Statistical Association 97(457): 302–17.Google Scholar
Coakley, J., Fuertes, A.-M., and Smith, R. 2002. A principal components approach to cross-section dependence in panels. Birkbeck College Discussion Paper.Google Scholar
Conley, T. G. 1999. GMM estimation with cross sectional dependence. Journal of Econometrics 92: 1–45.Google Scholar
Conley, T. G., and Topa, G. 2002. Socio-economic distance and spatial patterns in unemployment. Journal of Applied Econometrics 17: 303–27.CrossRefGoogle Scholar
Cowles, M. K., Carlin, B. P., and Connett, J. E. 1996. Bayesian Tobit modeling of longitudinal ordinal clinical trial compliance data with nonignorable missingness. Journal of the American Statistical Association 91: 86–98.Google Scholar
Cox, G. W. 2011. Sovereign debt, political stability, and bargaining efficiency. Unpublished manuscript.Google Scholar
Davis, C. L. 2005. Food fights over free trade: How international institutions promote argricultural trade liberalization. Princeton, NJ: Princeton University Press.Google Scholar
Demir, F. 2006. Volatility of short-term capital flows and socio-political instability in Argentina, Mexico, and Turkey. MPRA Paper No. 1943.Google Scholar
Devroye, L. 1981. The series method in random variate generation and its application to the Kolmogorov-Smirnov distribution. American Journal of Mathematical and Management Science 1(4): 359–79.Google Scholar
Devroye, L. 1986. Non-uniform random variate generation. New York: Springer.Google Scholar
Elhorst, J. P. 2010. Spatial panel data models. In Handbook of applied spatial analysis, eds. Fischer, M. M. and Getis, A., chapter 2, 377–407. Berlin: Springer.CrossRefGoogle Scholar
Franzese, R. J., and Hays, J. C. 2007. Spatial econometric models of cross-sectional interdependence in political science panel and time-series-cross-section data. Political Analysis 15: 140–64.Google Scholar
Franzese, R. J., and Hays, J. C. 2008. Interdependence in comparative politics. Comparative Political Studies 41 (4–5): 742–80.Google Scholar
Franzese, R. J., Hays, J. C., and Schaelffer, L. M. 2010. Spatial, temporal, and spatiotemporal autoregressive probit models of binary outcomes: estimation, interpretation, and presentation.Google Scholar
Frieden, J. A., and Rogowski, R. R. 1996. The impact of the international economy on national policies: An analytical overview. In Internationalization and domestic politics, eds. Robert, R. and Milner, H., 25–47. New York: Cambridge University Press.Google Scholar
Geweke, J. 1991. Efficient simulation from the multivariate normal and student-t distributions subject to linear constaints. In Computing science and statistics: Proceedings of the twenty-third symposium on the interface, ed. Keramidas, E. M., 571–8. Fairfax, VA: Interface Foundation of North America.Google Scholar
Geweke, J., and Zhou, G. 1996. Measuring the pricing error of the arbitrage pricing theory. Review of Financial Studies 9(2): 557–87.Google Scholar
Ghosh, J., and Dunson, D. B. 2008. Bayesian model selection in factor analysis. In Random effect and latent variable model selection, ed. Dunson, David B., 151–64. New York: Springer.Google Scholar
Gill, J. 2008. Is partial-dimension convergence a problem for inferences from MCMC algorithms? Political Analysis 16(2): 153–78.Google Scholar
Goetze, C., and Guzina, D. 2008. Peacebuilding, statebuilding, nationbuilding: Turtles all the way down. Civil Wars 10(4): 319–47.Google Scholar
Gourevitch, P. 1978. The second image reversed: The international sources of domestic politics. International Organization 32(4): 881–911.Google Scholar
Gourevitch, P. 1986. Politics in hard times: Comparative responses to international economic crises. Ithaca, NY: Cornell University Press.Google Scholar
Green, W. 2002. Econometric analysis. 5th ed. Prentice Hall.Google Scholar
Hamilton, J. D. 1994. Time series analysis. Princeton, NJ: Princeton University Press.Google Scholar
Han, C., and Carlin, B. 2001. Markov Chain Monte Carlo methods for computing Bayes factors: A comprehensive review. Journal of the American Statistical Association 96(455): 1122–32.Google Scholar
Hogan, J. W., and Tchernis, R. 2004. Bayesian factor analysis for spatially correlated data, with application to summarizing area-level material deprivation from census data. Journal of the American Statistical Association 99(466): 314–24.Google Scholar
Holmes, C. C., and Held, L. 2006. Bayesian auxiliary variable models for binary and multinomial regression. Bayesian Analysis 1(1): 145–68.Google Scholar
Holtz-Eakin, D., Newey, W. K., and Rosen, H. 1988. Estimating vector autoregressions with panel data. Econometica 56: 1371–95.Google Scholar
Ibrahim, J. G., and Klainman, K. 1998. Bayesian inference for random effect models. In Practical nonparametric and semiparametric Bayesian statistics, eds. Dey, D., Mueller, P., and Sinha, D. New York: Springer.Google Scholar
Jervis, R. 1997. System effects: Complexity in political and social life. Princeton, NJ: Princeton University Press.Google Scholar
Kahler, M. 1986. The politics of international debt. Ithaca, NY: Cornell University Press.Google Scholar
Kapetanios, G., Pesaran, M. H., and Yamagata, T. 2011. Panels with nonstationary multifactor error structures. Journal of Econometrics 160(2): 326–48.Google Scholar
Kapstein, E. B. 2000. Review: Winners and losers in the global economy. International Organization 54(2): 359–84.Google Scholar
Kass, R. E., and Raftery, A. E. 1995. Bayes factors. Journal of the American Statistical Association 90(430): 773–95.Google Scholar
Kelejian, H., Kapoor, M., and Prucha, I. 2007. Panel data models with spatial correlation error components. Journal of Econometrics 140: 97–130.Google Scholar
Keohane, R., and Milner, H. 1996. The political economy and economic regionalism. New York: Cambridge University Press.Google Scholar
Keohane, R. O., and Nye, J. S. 1977. Power and interdependence: World politics in transition. Boston: Little, Brown.Google Scholar
King, G., and Zeng, L. 2001. Improving forecasts of state failure. World Politics 53: 623–58.Google Scholar
Kohlscheen, E. 2006. Sovereign risk: constitutions rule. Warwick Economic Research Papers, No. 731.Google Scholar
Kraay, A., and Nehru, V. 2006. When is external debt sustainable? World Bank Economic Review 20: 341–65.Google Scholar
Lacy, M. G. 1997. Efficiently studying rare events: Case-control methods for sociologists. Sociological Perspectives 40: 129–54.Google Scholar
LeSage, J. P., and Pace, R. K. 2009. Introduction to spatial econometrics. Boca Raton, FL: CRC Press.Google Scholar
LeSage, J. P., and Pace, R. K. 2012. The biggest myth in spatial econometrics. Working paper.Google Scholar
Lord, F. M., and Novick, M. R. 1968. Statistical theories of mental test scores. Reading, MA: Addison Wesley.Google Scholar
Marshall, M. G., and Jaggers, K. 2007. Polity IV project: Political regime charateristics and transitions, 1800–2008: Dataset users' manual. Center for Systemic Peace.Google Scholar
Martin, A. D., Quinn, K. M., and Park, J. H. 2011. MCMCpack: Markov Chain Monte Carlo in R. Journal of Statistical Software 42(9): 1–21.Google Scholar
Mei, J., and Guo, L. 2004. Political uncertainty, financial crisis, and market volatility. European Financial Management 10(4): 639–57.Google Scholar
Moser, C. 2006. The impact of political risk on sovereign bond spreads: Evidence from Latin America. Working paper.Google Scholar
Mulaik, S. A. 1988a. A brief history of the philosophical foundations of explanatory factor analysis. Multivariate Behavioral Research 23: 267–305.Google Scholar
Pang, X. 2010. Modeling heterogeneity and serial correlation in binary time-series cross-sectional data: A Bayesian multilevel model with AR(p) errors and non-nested cluterings. Political Analysis 18(4): 470–98.Google Scholar
Pang, X. 2014. Replication data for: Varying responses to common shocks and complex cross-sectional dependence: Dynamic multilevel modeling with multifactor error structures for time-series cross-sectional data. http://dx.doi.org/10.7910/DVN/25430UNF:5:CJFgK1PHYQztfyhPOCAh+w==IQSSDataverseNetwork[Distributor]V1[Version].Google Scholar
Pesaran, M. H. 2006. Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74(4): 967–1012.Google Scholar
Pesaran, M. H., and Tosetti, E. 2011. Large panels with common factors and spatial correlations. Journal of Econometrics 161: 182–202.Google Scholar
Pesaran, M. H., Schuermann, T., and Weiner, S. M. 2004. Modeling regional interdependencies using a global error-correcting macroeconometric model. Journal of Business & Economic Statistics 22: 129–62.Google Scholar
Pesaran, M. H., Smith, L. V., and Yamagata, T. 2013. Panel unit root test in the presence of a multifactor error structure. Journal of Econometrics 175(2): 94–115.Google Scholar
Pierson, P. 1996. The new politics of the welfare state. World Politics 48(2): 143–79.Google Scholar
Plümper, T., and Neumayer, E. 2010. Model specification in the analysis of spatial dependence. European Journal of Political Research 49(3): 418–42.Google Scholar
Plümper, T., and Neumayer, E. 2012. Conditional spatial policy dependence: Theory and model specification. Comparative Political Studies 45(7): 819–49.Google Scholar
Reinhart, C. M., Rogoff, K. S., and Savastano, M. A. 2003. Debt Intolerance. NBER Working Paper 9908.Google Scholar
Robertson, D., and Symons, J. 2000. Factor residuals in SUR regressions: Estimating panel allowing for cross sectional correlation. Unpublished manuscript.Google Scholar
Rost, N., Schneider, G., and Kleibl, J. 2009. A globle risk assessment model for civil wars. Social Science Research 38: 921–33.Google Scholar
Rudra, N. 2002. Globalization and the decline of the welfare state in less-developed countries. International Organization 56(2): 411–45.Google Scholar
Saiegh, S. M. 2008. Coalitions governments and sovereign debt crises. Working paper.CrossRefGoogle Scholar
Schmukler, S. L. 2004. Financial globalization: Gain and pain for developing countries. Economic Review (Federal Reserve Bank of Atlanta) 2: 39–66.Google Scholar
Shor, B., Bafumi, J., Keele, L., and Park, D. 2007. A Bayesian multilevel modeling approach to time-series cross-sectional data. Political Analysis 15: 165–81.CrossRefGoogle Scholar
Simmons, B. A. 2000. International law and state behavior: Commitment and compliance in international monetary affairs. American Political Science Review 94(4): 819–36.Google Scholar
Simmons, B. A., and Elkins, Z. 2004. The globalization of liberalization: Policy diffusion in the international political economy. American Political Science Review 98(1): 171–89.Google Scholar
Skrondal, A., and Laake, P. 2001. Regression among factor scores. Psychometrika 66: 563–76.Google Scholar
Skrondal, A., and Rabe-Hesketh, S. 2004. Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models. New York: Chapman & Hall/CRC.CrossRefGoogle Scholar
Srivastava, V. K., and Giles, D. E. A. 1987. Seemingly unrelated regression equations models: Estimation and inference. New York: Marcel Dekker.Google Scholar
Stallings, B. 1995. Global change, regional response: A new international context of development. New York: Cambridge University Press.Google Scholar
Tomz, M., and Wright, M. L. J. 2007. Do countries default in bad times?. Journal of the European Economic Association 5 (2–3): 1–9.Google Scholar
van Rijicheghem, C., and Weder, B. 2004. The politics of debt crises. London: Center for Economic Policy Research.Google Scholar
Vreeland, J. R. 2008. The effect of political regime on civil war: Unpacking anocracy. Journal of Conflict Resolution 52: 401–25.Google Scholar
Waltz, K. N. 1979. Theory of international politics. Reading, MA: Addison-Wesley.Google Scholar
Weerahandi, S. 2004. Generalized inference in repeated measures: Exact methods in manova and mixed models. Hoboken, NJ: Wiley & Sons.Google Scholar
Wendt, A. 1999. Social theory of international politics. Cambridge, UK: Cambridge University Press.Google Scholar
West, M. 2003. Bayesian factor regression models in the “Large p, Small n” paradigm. Bayesian Statistics 7: 723–32.Google Scholar
Wibbels, E. 2006. Dependency revisited: International markets, business cycles, and social spending in the developing world. International Organization 60: 433–68.Google Scholar
Wibbels, E., and Arce, M. 2003. Globalization, taxation, and burden-shifting in Latin America. International Organization 57(1): 111–36.Google Scholar
Wilhelm, S., and de Matos, M. G. 2013. Estimating spatial probit models in R. R Journal 5(1): 130–43.Google Scholar
Williamson, J. A. 1997. Globalization and inequality, past and present. World Bank Research Observer 12: 117–35.Google Scholar