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Stochastic Process Methods with an Application to Budgetary Data

Published online by Cambridge University Press:  04 January 2017

Christian Breunig  and
Bryan D. Jones
Christian Breunig*
Affiliation:
Department of Political Science, University of Toronto, Sidney Smith Hall, Room 3018, 100 St. George Street, Toronto, Ontario M5S 3G3 Canada
Bryan D. Jones
Affiliation:
Department of Government, The University of Texas at Austin, 1 University Station A1800, Austin, TX 78712-0119. e-mail: [email protected]
*
e-mail: [email protected] (corresponding author)
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Abstract

Political scientists have increasingly focused on causal processes that operate not solely on mean differences but on other stochastic characteristics of the distribution of a dependent variable. This paper surveys important statistical tools used to assess data in situations where the entire distribution of values is of interest. We first outline three broad conditions under which stochastic process methods are applicable and show that these conditions cover many domains of social inquiry. We discuss a variety of visual and analytical techniques, including distributional analysis, direct parameter estimates of probability density functions, and quantile regression. We illustrate the utility of these statistical tools with an application to budgetary data because strong theoretical expectations at the micro- and macrolevel exist about the distributional characteristics for such data. The expository analysis concentrates on three budget series (total, domestic, and defense outlays) of the U.S. government for 1800–2004.

Type
Research Article
Information
Political Analysis , Volume 19 , Issue 1 , Winter 2011 , pp. 103 - 117
Copyright
Copyright © The Author 2010. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Footnotes

Authors' Note: The authors would like to thank Michael D. Ward, John Ahlquist, and Samuel Workman, our reviewers, and the editors of Political Analysis for helpful comments. Supplementary materials for this article as well as R and Stata code for implementing the presented methods are available on the authors' Web site.

References

Alvarez, R. Michael, and Brehm, John. 1995. American ambivalence towards abortion policy: Development of a heteroskedastic probit model of competing values. American Journal of Political Science 39: 1055–82.CrossRefGoogle Scholar
Alvarez, R. Michael. 2009. In Election fraud: Detecting and deterring electoral manipulation, eds. Hall, Thad E. and Hyde, Susan D. Washington, DC: Brookings Institution Press.Google Scholar
Barabási, Albert-László, and Albert, Réka. 1999. Emergence of scaling in random networks. Science 286: 509–12.Google Scholar
Baumgartner, Frank R., and Jones, Bryan D. 1993. Agendas and instability in American politics. Chicago, IL: University of Chicago Press.Google Scholar
Baumgartner, Frank R., Foucault, Martial, and François, Abel. 2006. Punctuated equilibrium and French budgeting processes. Journal of European Public Policy 13: 1086–103.CrossRefGoogle Scholar
Beinhocker, Eric D. 2006. Origin of wealth: Evolution, complexity, and the radical remaking of economics. Cambridge: Harvard Business School Press.Google Scholar
Biggs, Michael. 2005. Strikes as forest fires: Chicago and Paris in the late nineteenth century. American Journal of Sociology 110: 1684–714.Google Scholar
Breunig, Christian. 2006. The more things change, the more things stay the same: a comparative analysis of budget punctuations. Journal of European Public Policy 13(7): 1065–81.Google Scholar
Breunig, Christian, and Koski, Chris. 2006. Punctuated equilibria and budgets in the American States. Policy Studies Journal 34: 363–79.Google Scholar
Buchinsky, Moshe. 1994. Changes in the U.S. wage structure 1963-1987: Application of quantile regression. Econometrica 62: 405–58.Google Scholar
Cederman, Lars-Erik. 2003. Modeling the size of wars: From billiard balls to sandpiles. American Political Science Review 97: 135–50.Google Scholar
Clauset, Aaron, Shalizi, Cosma Rohilla, and Newman, M. E. J. 2007. Power-law distributions in empirical data. arXiv: 706.1062v1. Physics.Data.an. 7: 1–26.Google Scholar
DeCarlo, Lawrence T. 1997. On the meaning and use of kurtosis. Psychological Methods 2: 292–307.Google Scholar
Engel, Ernst. 1857. Die Produktions- und Konsumptionsverhältnisse des Königreichs Sachsen. Zeitschrift des Statistischen Bureaus des Koniglich Sächsischen Ministeriums des Innern 8: 1–54.Google Scholar
Gabaix, Xavier. 1999. Zipf's law for cities: An explanation. Quarterly Journal of Economics 114: 739–67.Google Scholar
Groneveld, Richard A. 1998. A class of quintile measures for kurtosis. American Statistician 51: 325–9.Google Scholar
Hacker, Jacob S., and Pierson, Paul. 2010. Winner-take-all politics: Public policy, political organization, and the precipitous rise of top incomes in the United States. Politics & Society 38: 152–204.Google Scholar
Handcock, Mark and Morris, Martina. 1999. Relative distribution methods in the social sciences. New York: Springer.Google Scholar
Hosking, Jonathan R. M. 1990. L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society B 52: 105–24.Google Scholar
Hosking, Jonathan R. M. 1998. L-moments. In Encyclopedia of statistical sciences. Vol. 2, eds. Kotz, S., Read, C., and Banks, D. L., 357–62. Hoboken, NJ: Wiley.Google Scholar
John, Peter, and Margetts, Helen. 2003. Policy punctuations in the UK. Public Administration 81(3): 411–32.CrossRefGoogle Scholar
Jones, Bryan D., Baumgartner, Frank, Breunig, Christian, Wlezien, Christopher, Soroka, Stuart, Foucault, Martial, Francois, Able, Green-Pederson, Christoffer, Koski, Chris, John, Peter, Mortensen, Peter, Varone, Frederic, and Walgrave, Steffan. 2009. A general empirical law of public budgets. American Journal of Political Science 53: 855–73.Google Scholar
Jones, Bryan D., and Baumgartner, Frank R. 2005. The politics of attention. Chicago, IL: University of Chicago Press.Google Scholar
Jones, Bryan D., and Breunig, Christian. 2007. Noah and Joseph effects in government budgets: Analyzing long-term memory. Policy Studies Journal 35: 329–48.Google Scholar
Jones, Bryan D., Sulkin, Tracy, and Larsen, Heather. 2003. Policy punctuations in American political institutions. American Political Science Review 97: 151–70.Google Scholar
Koenker, Roger. 2005. Quantile regression. Cambridge: Cambirdge University Press.Google Scholar
Koenker, Roger, and Jr, Gilbert Bassett. 1978. Regression quantiles. Econometrica 46: 33–50.CrossRefGoogle Scholar
Laherrère, J., and Sornette, D. 1998. Stretched exponential distributions in nature and economy: “fat tails” with characteristic scales. The European Physical Journal B 2(4): 525–39.CrossRefGoogle Scholar
Lorenz, Max O. 1905. Methods of measuring the concentration of wealth. Publications of the American Statistical Association 9: 209–19.Google Scholar
Mandelbrot, Benoit. 1963. The variation of certain speculative prices. Journal of Business 36: 294–419.Google Scholar
Mandelbrot, Benoit. 1997. Fractals and scaling in finance. New York: Springer.Google Scholar
Mandelbrot, Benoit, and Hudson, Richard L. 2004. The (Mis)behavior of markets. New York: Basic Books.Google Scholar
Mantegna, Rosario N., and Eugene Stanley, H. 2000. An introduction to econophysics. Cambridge: Cambridge University Press.Google Scholar
Mortensen, Peter. 2005. Policy punctuations in Danish local budgeting. Public Administration 83: 931–50.CrossRefGoogle Scholar
Padgett, John F. 1980. Bounded rationality in budgetary research. American Political Science Review 74: 354–72.Google Scholar
Paolino, Philip. 2001. Maximum likelihood estimation of models with beta-distributed dependent variables. Political Analysis 9: 325–46.CrossRefGoogle Scholar
Pareto, Vinferdo. 1897. The new theories of economics. Journal of Political Economy 5: 485–502.Google Scholar
Piketty, Thomas, and Saz, Emmanuel. 2003. Income inequality in the United States, 1913-1998. Quarterly Journal of Economics 118: 1–39.CrossRefGoogle Scholar
Podobnik, B., Horvatic, D., Petersen, A. M., Njavro, M., and Stanley, H. E. 2009. Common scaling behavior in finance and macroeconomics. The European Physical Journal B 76(4): 487–90.Google Scholar
Poole, Keith T., and Rosenthal, Howard. 1985. A spatial model for legislative roll call analysis. American Journal of Political Science 29: 357–84.Google Scholar
R Development Core Team. 2008. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. http://www.R-project.org.Google Scholar
Richardson, Lewis F. 1948. Variation of the frequency of fatal quarrels with magnitude. Journal of the American Statistical Association 43: 523–46.Google Scholar
Sheather, S. J., and Jones, M. C. 1991. A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society series B 53: 683–90.Google Scholar
Simonoff, Jeffrey. 1996. Smoothing methods in statistics. New York: Springer.Google Scholar
Sornette, Didier. 2003. Why stock markets crash. Princeton, NJ: Princeton University Press.Google Scholar
Sornette, Didier. 2006. Critical phenomena in natural sciences. Berlin, Germany: Springer.Google Scholar