Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-07T04:24:04.499Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimation of Models with Variable Coefficients

Published online by Cambridge University Press:  04 January 2017

John E. Jackson
Get access Rights & Permissions [Opens in a new window]

Abstract

The ordinary least squares (OLS) estimator gives biased coefficient estimates if coefficients are not constant for all cases but vary systematically with the explanatory variables. This article discusses several different ways to estimate models with systematically and randomly varying coefficients using estimated generalized least squares and maximum likelihood procedures. A Monte Carlo simulation of the different methods is presented to illustrate their use and to contrast their results to the biased results obtained with ordinary least squares. Several applications of the methods are discussed and one is presented in detail. The conclusion is that, in situations with variables coefficients, these methods offer relatively easy means for overcoming the problems.

Type
Research Article
Information
Political Analysis , Volume 3 , 1991 , pp. 27 - 49
Copyright
Copyright © by the University of Michigan 1992 

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.)

References

Brady, Henry E. 1988. “The Perils of Survey Research: Interpersonally Incomparable Responses.” Political Methodology 11 (3-4): 269–91.Google Scholar
Dent, Warren T., and Hildreth, Clifford. 1977. “Maximum Likelihood Estimation in Random Coefficient Models.” Journal of the American Statistical Association 72: 69–72.Google Scholar
Dubin, Jeffrey A., and Douglas Rivers, R. 1987. Statistical Software Tools. Pasadena: Dubin/Rivers Research.Google Scholar
Friedrich, Robert J. 1982. “In Defense of Multiplicative Terms in Multiple Regression Equations.” American Journal of Political Science 26 (40): 797–833.CrossRefGoogle Scholar
Froehlich, B. R. 1973. “Some Estimators for a Random Coefficient Regression Model.” Journal of the American Statistical Association 68: 329–35.Google Scholar
Hanushek, Eric A., and Jackson, John E. 1977. Statistical Methods for Social Scientists. New York: Academic Press.Google Scholar
Hildreth, Clifford, and Houck, James. 1968. “Some Estimators for a Linear Model with Random Coefficients.” Journal of the American Statistical Association 63: 584–95.Google Scholar
Jackson, John E., and King, David C. 1989. “Public Goods, Private Interests, and Representation.” American Political Science Review 83 (4): 1143–64.Google Scholar
Judge, George G., Griffiths, W. E., Carter Hill, R., Lütkepohl, Helmut, and Lee, Tsoung-Chao. 1985. The Theory and Practice of Econometrics. 2d ed. New York: Wiley.Google Scholar
Key, V. O. Jr. 1949. Southern Politics. New York: Vintage Books.Google Scholar
Rivers, Douglas R. 1988. “Heterogeneity in Models of Electoral Choice.” American Journal of Political Science 32 (3): 737–57.Google Scholar
Shively, W. Phillips. 1969. “Ecological Inference: The Use of Aggregate Data to Study Individuals.” American Political Science Review 63 (4): 1183–96.CrossRefGoogle Scholar
Shively, W. Phillips. 1988. “A Strategy for Cross-Level Inference Under an Assumption of Breakage Effects.” Political Methodology 11 (3-4): 167–80.Google Scholar
Stokes, Donald E. 1969. “Cross-Level Inference as a Game Against Nature.” In Mathematical Applications in Political Science, vol. 4, ed. Bernd, Joseph L., 62–83. Charlottesville: University of Virginia Press.Google Scholar