Hostname: page-component-6766d58669-mzsfj Total loading time: 0 Render date: 2026-05-14T19:23:58.345Z Has data issue: false hasContentIssue false
  • English
  • Français

Error Correction Methods with Political Time Series

Published online by Cambridge University Press:  04 January 2017

Taylor Grant  and
Matthew J. Lebo
Taylor Grant
Affiliation:
Stony Brook University, e-mail: Taylor.Grant@stonybrook.edu
Matthew J. Lebo*
Affiliation:
Stony Brook University
*
e-mail: matthew.lebo@stonybrook.edu (corresponding author)
Get access Rights & Permissions [Opens in a new window]

Abstract

While traditionally considered for non-stationary and cointegrated data, DeBoef and Keele suggest applying a General Error Correction Model (GECM) to stationary data with or without cointegration. The GECM has since become extremely popular in political science but practitioners have confused essential points. For one, the model is treated as perfectly flexible when, in fact, the opposite is true. Time series of various orders of integration–stationary, non-stationary, explosive, near- and fractionally integrated–should not be analyzed together but researchers consistently make this mistake. That is, without equation balance the model is misspecified and hypothesis tests and long-run-multipliers are unreliable. Another problem is that the error correction term's sampling distribution moves dramatically depending upon the order of integration, sample size, number of covariates, and the boundedness of Yt. This means that practitioners are likely to overstate evidence of error correction, especially when using a traditional t-test. We evaluate common GECM practices with six types of data, 746 simulations, and five paper replications.

Information

Type
Time Series Symposium
Information
Political Analysis , Volume 24 , Issue 1 , Winter 2016 , pp. 3 - 30
Copyright
Copyright © The Author 2016. Published by Oxford University Press on behalf of the Society for Political Methodology 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

Authors' note: Previous versions of this article were presented at the 2014 meeting of the Midwest Political Science Association, the 2014 meeting of the European Political Science Association, and the 2014 PolMeth conference. We are grateful for helpful comments from Neal Beck, Matthew Blackwell, Janet Box-Steffensmeier, Patrick Brandt, Justin Esarey, Stanley Feldman, Paul Kellstedt, Suzanna Linn, Vera Troeger, and seminar participants at Rice University and Stony Brook University. Replication materials are available online as Grant and Lebo (2016). Supplementary materials for this article are available on the Political Analysis Web site and at: https://sites.google.com/a/stonybrook.edu/matthew-lebo/about/resume/papers.

References

Baillie, Richard T., and Bollerslev, Tim. 1994. Cointegration, fractional cointegration, and exchange rate dynamics. Journal of Finance 49(2): 737–45.CrossRefGoogle Scholar
Baillie, Richard T. 1996. Long memory processes and fractional integration in econometrics. Journal of Econometrics 73(1): 5–59.CrossRefGoogle Scholar
Baillie, R., and Kapetanios, George. 2007. Semiparametric estimation of long memory: The holy grail or a poisoned chalice. In International Symposium on Financial Econometrics, pp. 1–2.Google Scholar
Banerjee, Anindya, Dolado, Juan, and Mestre, Ricardo. 1998. “Error-Correction Mechanism Tests for Cointegration in a Single-Equation Framework.” Journal of Time Series Analysis 19(3): 267–283.Google Scholar
Banerjee, Anindya, Dolado, Juan J., Galbraith, John W., and Hendry, David. 1993a. Co-integration, error correction, and the econometric analysis of non-stationary data. OUP Catalogue. CrossRefGoogle Scholar
Banerjee, Anindya, Dolado, Juan J., Galbraith, John W., and Hendry, David. 1993b. Integration, error correction, and the econometric analysis of non-stationary data. Oxford: Oxford University Press.CrossRefGoogle Scholar
Bårdsen, Gunnar. 1989. Estimation of long run coefficients in error correction models. Oxford Bulletin of Economics and Statistics 51(3): 345–350.CrossRefGoogle Scholar
Bauwens, Luc, Lubrano, Michel, and Richard, Jean-Francois. 2000. Bayesian inference in dynamic econometric models. New York: Oxford University Press.CrossRefGoogle Scholar
Beck, Nathaniel. 1992. Comparing dynamic specifications: The case of presidential approval. Political Analysis 3:27–50.Google Scholar
Beran, Jan. 1994. Statistics for long-memory processes, Vol. 61. Boca Raton, FL: CRC Press.Google Scholar
Bernhard, William, and Leblang, David. 2002. Democratic processes, political risk, and foreign exchange markets. American Journal of Political Science 46:316–33.CrossRefGoogle Scholar
Box, George E.P., and Pierce, David A. 1970. Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association 65(332): 1509–26.CrossRefGoogle Scholar
Box, George E.P., and Jenkins, Gwilym M. 1976. Time series analysis: Forecasting and control. San Francisco: Holden-Day.Google Scholar
Box-Steffensmeier, Janet M., and Smith, Renée M. 1996. The dynamics of aggregate partisanship. American Political Science Review 90:567–80.CrossRefGoogle Scholar
Box-Steffensmeier, Janet M., and Smith, Renée M. 1998. Investigating political dynamics using fractional integration methods. American Journal of Political Science 42:661–89.CrossRefGoogle Scholar
Box-Steffensmeier, Janet M., and Tomlinson, Andrew R. 2000. Fractional integration methods in political science. Electoral Studies 19(1): 63–76.CrossRefGoogle Scholar
Brandt, Patrick T., and Freeman, John R. 2006. Advances in Bayesian time series modeling and the study of politics: Theory testing, forecasting, and policy analysis. Political Analysis 14(1): 1–36.CrossRefGoogle Scholar
Büthe, Tim, and Milner, Helen V. 2014. Foreign direct investment and institutional diversity in trade agreements: Credibility, commitment, and economic flows in the developing world, 1971–2007. World Politics 66(1): 88–122.CrossRefGoogle Scholar
Byers, David, Davidson, James, and Peel, David. 2000. The dynamics of aggregate political popularity: Evidence from eight countries. Electoral Studies 19(1): 49–62.CrossRefGoogle Scholar
Casillas, Christopher J., Enns, Peter K., and Wohlfarth, Patrick C. 2011. How public opinion constrains the US Supreme Court. American Journal of Political Science 55(1): 74–88.CrossRefGoogle Scholar
Cavaliere, Giuseppe. 2005. Limited time series with a unit root. Econometric Theory 21:907–45.CrossRefGoogle Scholar
Cavaliere, Giuseppe, and Xu, Fang. 2014. Testing for unit roots in bounded time series. Journal of Econometrics 178(2): 259–72.CrossRefGoogle Scholar
Cheung, Yin-Wong, and Lai, Kon S. 1993. A fractional cointegration analysis of purchasing power parity. Journal of Business & Economic Statistics 11(1): 103–12.Google Scholar
Clarke, Harold D., and Stewart, Marianne C. 1994. Prospections, retrospections and rationality: The “Bankers” model of presidential approval reconsidered. American Journal of Political Science 38:1104–23.CrossRefGoogle Scholar
Clarke, Kevin A. 2003. Nonparametric model discrimination in international relations. Journal of Conflict Resolution 47(1): 72–93.CrossRefGoogle Scholar
Clarke, Harold D., and Lebo, Matthew. 2003. Fractional (co)integration and governing party support in Britain. British Journal of Political Science 33(2): 283–301.CrossRefGoogle Scholar
Davidson, James E.H., Hendry, David F., Srba, Frank, and Yeo, Steven. 1978. Econometric modelling of the aggregate time-series relationship between consumer's expenditure and income in the United Kingdom. Economic Journal 88:661–92.CrossRefGoogle Scholar
DeBoef, Suzanna. 2001. Modeling equilibrium relationships: Error correction models with strongly autoregressive data. Political Analysis 9(1): 78–94.CrossRefGoogle Scholar
DeBoef, Suzanna, and Granato, Jim. 1997. Near-integrated data and the analysis of political relationship. American Journal of Political Science 41:619–40.CrossRefGoogle Scholar
DeBoef, Suzanna, and Granato, Jim. 1999. Testing for cointegrating relationships with near-integrated data. Political Analysis 8(1): 99–117.CrossRefGoogle Scholar
DeBoef, Suzanne, and Keele, Luke. 2008. Taking time seriously. American Journal of Political Science 52(1): 184–200.CrossRefGoogle Scholar
Dickinson, Matthew J., and Lebo, Matt J. 2007. Reexamining the growth of the institutional presidency, 1940–2000. Journal of Politics 69(1): 206–19.CrossRefGoogle Scholar
Dueker, Michael, and Startz, Richard. 1998. Maximum-likelihood estimation of fractional cointegration with an application to US and Canadian bond rates. Review of Economics and Statistics 80(3): 420–26.CrossRefGoogle Scholar
Durr, Robert H. 1992. Of forests and trees. Political Analysis 4:255–58.CrossRefGoogle Scholar
Durr, Robert H. 1993. What moves policy sentiment? American Political Science Review 87:158–70.CrossRefGoogle Scholar
Durr, Robert H., Martin, Andrew D., and Wolbrecht, Christina. 2000. Ideological divergence and public support for the Supreme Court. American Journal of Political Science 44:768–76.CrossRefGoogle Scholar
Enders, Walter. 2004. Applied econometric time series. 2nd ed. New York: Wiley.Google Scholar
Enders, Walter. 2010. Applied econometric time series. 3rd ed. New York: Wiley.Google Scholar
Engle, Robert F., and Granger, C.W.J. 1987. Co-integration and error correction: Representation, estimation, and testing. Econometrica 55:251–76.CrossRefGoogle Scholar
Enns, Peter K. 2014. The public's increasing punitiveness and its influence on mass incarceration in the United States. American Journal of Political Science 58:857–72.Google Scholar
Enns, Peter K., Kelly, Nathan J., Morgan, Thomas Volscho, Janna, and Witko, Christopher. 2014. Conditional status quo bias and top income shares: How U.S. political institutions have benefitted the rich. Journal of Politics 76:289–303.Google Scholar
Ericsson, Neil R., and MacKinnon, James G. 2002. Distributions of error correction tests for cointegration. Econometrics Journal 5(2): 285–318.CrossRefGoogle Scholar
Faricy, Christopher. 2011. The politics of social policy in America: The causes and effects of indirect versus direct social spending. Journal of Politics 73(1): 74–83.CrossRefGoogle Scholar
Fuller, Wayne A. 2009. Introduction to statistical time series, Vol. 428, Wiley.com.Google Scholar
Granger, Clive W.J. 1980. Long memory relationships and the aggregation of dynamic models. Journal of Econometrics 14(2): 227–38.CrossRefGoogle Scholar
Granger, Clive W.J., and Newbold, Paul. 1974. Spurious regressions in econometrics. Journal of Econometrics 26:1045–66.Google Scholar
Granger, Clive W.J., and Joyeux, Roselyne. 1980. An introduction to long-memory time series models and fractional differencing. Journal of Time Series Analysis 1(1): 15–29.CrossRefGoogle Scholar
Granger, C.W.J. 2010. Some thoughts on the development of cointegration. Journal of Econometrics 158:3–6.CrossRefGoogle Scholar
Grant, Taylor, and Lebo, Matthew J. 2016. Replication data for: Error correction methods with political time series. Harvard Dataverse, V1 http://dx.doi.org/10.7910/DVN/VAKZ2G.CrossRefGoogle Scholar
Hansen, Bruce E. 1995. Rethinking the univariate approach to unit root testing. Econometric Theory 11(5): 1148–71.CrossRefGoogle Scholar
Hendry, David F., and Anderson, G.J. 1977. Testing dynamic specification in small simultaneous systems: An application to a model of building society behaviour in the United Kingdom. New Haven, CT: Yale University.Google Scholar
Hendry, David F., Srba, Frank, and Yeo, Stephen. 1978. Econometric modelling of the aggregate time-series relationship between consumers’ expenditure and income in the United Kingdom. Economic Journal 88(352): 661–92.Google Scholar
Hosking, Jonathan R.M. 1981. Fractional differencing. Biometrika 68(1): 165–76.CrossRefGoogle Scholar
Jennings, Will, and John, Peter. 2009. The dynamics of political attention: Public opinion and the queen's speech in the United Kingdom. American Journal of Political Science 53(4): 838–54.CrossRefGoogle Scholar
Kayser, Mark Andreas. 2009. Partisan waves: International business cycles and electoral choice. American Journal of Political Science 53(4): 950–70.CrossRefGoogle Scholar
Keele, Luke. 2007. Social capital and the dynamics of trust in government. American Journal of Political Science 51(2): 241–54.CrossRefGoogle Scholar
Kelly, Nathan J., and Enns, Peter K. 2010. Inequality and the ynamics of public opinion: The self-reinforcing link between economic inequality and mass preferences. American Journal of Political Science 54(4): 855–70.CrossRefGoogle Scholar
Kono, Daniel Yuichi. 2008. Democracy and trade discrimination. Journal of Politics 70(4): 942–55.CrossRefGoogle Scholar
Kremers, Jeroen J.M., Ericsson, Neil R., and Dolado, Juan J. 1992. The power of cointegration tests. Oxford Bulletin of Economics and Statistics 54(3): 325–48.CrossRefGoogle Scholar
Layman, Geoffrey C., Carsey, Thomas M., Green, John C., Herrera, Richard, and Cooperman, Rosalyn. 2010. Activists and conflict extension in American party politics. American Political Science Review 104(2): 324–46.CrossRefGoogle Scholar
Leblang, David, and Bernhard, William. 2006. Parliamentary politics and foreign exchange markets: The world according to GARCH. International Studies Quarterly 50(1): 69–92.CrossRefGoogle Scholar
Lebo, Matthew J., Walker, Robert W., and Clarke, Harold D. 2000. You must remember this: Dealing with long memory in political analyses. Electoral Studies 19(1): 31–48.CrossRefGoogle Scholar
Lebo, Matthew J., and Moore, Will H. 2003. Dynamic foreign policy behavior. Journal of Conflict Resolution 47(1): 13–32.Google Scholar
Lebo, Matthew J., McGlynn, Adam J., and Koger, Greg. 2007. Strategic party government: Party influence in Congress, 1789–2000. American Journal of Political Science 51(3): 464–81.CrossRefGoogle Scholar
Lebo, Matthew J., and Young, Everett. 2009. The comparative dynamics of party support in Great Britain: Conservatives, Labour and the Liberal Democrats. Journal of Elections, Public Opinion and Parties 19(1): 73–103.CrossRefGoogle Scholar
MacKinnon, James G. 1994. Approximate asymptotic distribution functions for unit-root and cointegration tests. Journal of Business & Economic Statistics 12(2): 167–76.Google Scholar
Narayan, Paresh Kumar. 2005. The saving and investment nexus for China: Evidence from cointegration tests. Applied Economics 37(17): 1979–90.CrossRefGoogle Scholar
Nicolau, Joao. 2002. Stationary processes that look like random walks: The bounded random walk process in discrete and continuous time. Econometric Theory 18(1): 99–118.CrossRefGoogle Scholar
Ostrom, Charles W. Jr., and Smith, Renée. 1993. Error correction, attitude persistence, and executive rewards and punishments: A behavioral theory of presidential approval. Political Analysis 4:127–84.Google Scholar
Pesaran, M. Hashem, Shin, Yongcheol, and Smith, Richard J. 2001. Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics 16(3): 289–326.CrossRefGoogle Scholar
Phillips, A William. 1954. Stabilization policy in a closed economy. Economic Journal 64(254): 290–323.CrossRefGoogle Scholar
Phillips, A William. 1957. Stabilization policy and the time-forms of lagged responses. Economic Journal 67(266): 265–77.CrossRefGoogle Scholar
Pickup, Mark. 2009. Testing for fractional integration in public opinion in the presence of structural breaks: A comment on Lebo and Young. Journal of Elections, Public Opinion and Parties 19(1): 105–16.CrossRefGoogle Scholar
Ramirez, Mark D. 2009. The dynamics of partisan conflict on congressional approval. American Journal of Political Science 53(3): 681–94.CrossRefGoogle Scholar
Rickard, Stephanie J. 2012. Welfare versus subsidies: Governmental spending decisions in an era of globalization. Journal of Politics 74(4): 1171–83.CrossRefGoogle Scholar
Robinson, Peter M. 1995. Gaussian semiparametric estimation of long range dependence. Annals of Statistics 23(5): 1630–61.CrossRefGoogle Scholar
Urribarri, Sanchez, Raul, A., Schorpp, Susanne, Randazzo, Kirk A., and Songer, Donald R. 2011. Explaining changes to rights litigation: Testing a multivariate model in a comparative framework. Journal of Politics 73(2): 391–405.CrossRefGoogle Scholar
Sargan, John Denis. 1964. Wages and prices in the United Kingdom: A study in econometric methodology. Econometric Analysis for National Economic Planning 16:25–54.Google Scholar
Stimson, James A. 1991. Public opinion in America: Moods, cycles, and swings. Boulder, CO: Westview Press.Google Scholar
Stock, James H., and Watson, Mark W. 2011. Introduction to econometrics, 3/E. Instructor 10.Google Scholar
Tsay, Wen-Jay, and Chung, Ching-Fan. 2000. The spurious regression of fractional integrated processes. Journal of Econometrics 96:155–82.CrossRefGoogle Scholar
Ura, Joseph Daniel. 2014. Backlash and legitimation: Macro political responses to Supreme Court decisions. American Journal of Political Science 58(1): 110–26.CrossRefGoogle Scholar
Ura, Joseph Daniel, and Ellis, Christopher R. 2012. Partisan moods: Polarization and the dynamics of mass party preferences. Journal of Politics 74(1): 277–91.Google Scholar
Ura, Joseph Daniel, and Wohlfarth, Patrick C. 2010. “An appeal to the people”: Public opinion and congressional support for the Supreme Court. Journal of Politics 72(4): 939–56.CrossRefGoogle Scholar
Volscho, Thomas W., and Kelly, Nathan J. 2012. The rise of the super-rich power resources, taxes, financial markets, and the dynamics of the top 1 percent, 1949 to 2008. American Sociological Review 77(5): 679–99.CrossRefGoogle Scholar
Williams, John T. 1992. What goes around comes around: Unit root tests and cointegration. Political Analysis 4:229–35.CrossRefGoogle Scholar
Young, Everett, and Lebo, Matthew J. 2009. Long memory methods and structural breaks in public opinion time series: A reply to pickup. Journal of Elections, Public Opinion and Parties 19(1): 117–24.CrossRefGoogle Scholar
Yule, G. Udny. 1926. Why do we sometimes get nonsense-correlations between time-series? A study in sampling and the nature of time-series. Journal of the Royal Statistical Society 89(1): 1–63.CrossRefGoogle Scholar
Zivot, Eric. 2000. The power of single equation tests for cointegration when the cointegrating vector is prespecified. Econometric Theory 16(3): 407–39.CrossRefGoogle Scholar
Supplementary material: PDF

Grant and Lebo supplementary material

Appendices

Download Grant and Lebo supplementary material(PDF)
PDF 984.9 KB