Skip to main content

Stochastic Process Methods with an Application to Budgetary Data

  • Christian Breunig (a1) and Bryan D. Jones (a2)

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.

Corresponding author
e-mail: (corresponding author)
Hide All

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.

Hide All
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.
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.
Barabási, Albert-László, and Albert, Réka. 1999. Emergence of scaling in random networks. Science 286: 509–12.
Baumgartner, Frank R., and Jones, Bryan D. 1993. Agendas and instability in American politics. Chicago, IL: University of Chicago Press.
Baumgartner, Frank R., Foucault, Martial, and François, Abel. 2006. Punctuated equilibrium and French budgeting processes. Journal of European Public Policy 13: 1086–103.
Beinhocker, Eric D. 2006. Origin of wealth: Evolution, complexity, and the radical remaking of economics. Cambridge: Harvard Business School Press.
Biggs, Michael. 2005. Strikes as forest fires: Chicago and Paris in the late nineteenth century. American Journal of Sociology 110: 1684–714.
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.
Breunig, Christian, and Koski, Chris. 2006. Punctuated equilibria and budgets in the American States. Policy Studies Journal 34: 363–79.
Buchinsky, Moshe. 1994. Changes in the U.S. wage structure 1963-1987: Application of quantile regression. Econometrica 62: 405–58.
Cederman, Lars-Erik. 2003. Modeling the size of wars: From billiard balls to sandpiles. American Political Science Review 97: 135–50.
Clauset, Aaron, Shalizi, Cosma Rohilla, and Newman, M. E. J. 2007. Power-law distributions in empirical data. arXiv: 706.1062v1. 7: 126.
DeCarlo, Lawrence T. 1997. On the meaning and use of kurtosis. Psychological Methods 2: 292307.
Engel, Ernst. 1857. Die Produktions- und Konsumptionsverhältnisse des Königreichs Sachsen. Zeitschrift des Statistischen Bureaus des Koniglich Sächsischen Ministeriums des Innern 8: 154.
Gabaix, Xavier. 1999. Zipf's law for cities: An explanation. Quarterly Journal of Economics 114: 739–67.
Groneveld, Richard A. 1998. A class of quintile measures for kurtosis. American Statistician 51: 325–9.
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: 152204.
Handcock, Mark and Morris, Martina. 1999. Relative distribution methods in the social sciences. New York: Springer.
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.
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.
John, Peter, and Margetts, Helen. 2003. Policy punctuations in the UK. Public Administration 81(3): 411–32.
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.
Jones, Bryan D., and Baumgartner, Frank R. 2005. The politics of attention. Chicago, IL: University of Chicago Press.
Jones, Bryan D., and Breunig, Christian. 2007. Noah and Joseph effects in government budgets: Analyzing long-term memory. Policy Studies Journal 35: 329–48.
Jones, Bryan D., Sulkin, Tracy, and Larsen, Heather. 2003. Policy punctuations in American political institutions. American Political Science Review 97: 151–70.
Koenker, Roger. 2005. Quantile regression. Cambridge: Cambirdge University Press.
Koenker, Roger, and Jr, Gilbert Bassett. 1978. Regression quantiles. Econometrica 46: 3350.
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.
Lorenz, Max O. 1905. Methods of measuring the concentration of wealth. Publications of the American Statistical Association 9: 209–19.
Mandelbrot, Benoit. 1963. The variation of certain speculative prices. Journal of Business 36: 294419.
Mandelbrot, Benoit. 1997. Fractals and scaling in finance. New York: Springer.
Mandelbrot, Benoit, and Hudson, Richard L. 2004. The (Mis)behavior of markets. New York: Basic Books.
Mantegna, Rosario N., and Eugene Stanley, H. 2000. An introduction to econophysics. Cambridge: Cambridge University Press.
Mortensen, Peter. 2005. Policy punctuations in Danish local budgeting. Public Administration 83: 931–50.
Padgett, John F. 1980. Bounded rationality in budgetary research. American Political Science Review 74: 354–72.
Paolino, Philip. 2001. Maximum likelihood estimation of models with beta-distributed dependent variables. Political Analysis 9: 325–46.
Pareto, Vinferdo. 1897. The new theories of economics. Journal of Political Economy 5: 485502.
Piketty, Thomas, and Saz, Emmanuel. 2003. Income inequality in the United States, 1913-1998. Quarterly Journal of Economics 118: 139.
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.
Poole, Keith T., and Rosenthal, Howard. 1985. A spatial model for legislative roll call analysis. American Journal of Political Science 29: 357–84.
R Development Core Team. 2008. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
Richardson, Lewis F. 1948. Variation of the frequency of fatal quarrels with magnitude. Journal of the American Statistical Association 43: 523–46.
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.
Simonoff, Jeffrey. 1996. Smoothing methods in statistics. New York: Springer.
Sornette, Didier. 2003. Why stock markets crash. Princeton, NJ: Princeton University Press.
Sornette, Didier. 2006. Critical phenomena in natural sciences. Berlin, Germany: Springer.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Political Analysis
  • ISSN: 1047-1987
  • EISSN: 1476-4989
  • URL: /core/journals/political-analysis
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed