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Estimation of Models with Variable Coefficients

  • John E. Jackson


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.



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Brady, Henry E. 1988. “The Perils of Survey Research: Interpersonally Incomparable Responses.” Political Methodology 11 (3-4): 269–91.
Dent, Warren T., and Hildreth, Clifford. 1977. “Maximum Likelihood Estimation in Random Coefficient Models.” Journal of the American Statistical Association 72: 6972.
Dubin, Jeffrey A., and Douglas Rivers, R. 1987. Statistical Software Tools. Pasadena: Dubin/Rivers Research.
Friedrich, Robert J. 1982. “In Defense of Multiplicative Terms in Multiple Regression Equations.” American Journal of Political Science 26 (40): 797833.
Froehlich, B. R. 1973. “Some Estimators for a Random Coefficient Regression Model.” Journal of the American Statistical Association 68: 329–35.
Hanushek, Eric A., and Jackson, John E. 1977. Statistical Methods for Social Scientists. New York: Academic Press.
Hildreth, Clifford, and Houck, James. 1968. “Some Estimators for a Linear Model with Random Coefficients.” Journal of the American Statistical Association 63: 584–95.
Jackson, John E., and King, David C. 1989. “Public Goods, Private Interests, and Representation.” American Political Science Review 83 (4): 1143–64.
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.
Key, V. O. Jr. 1949. Southern Politics. New York: Vintage Books.
Rivers, Douglas R. 1988. “Heterogeneity in Models of Electoral Choice.” American Journal of Political Science 32 (3): 737–57.
Shively, W. Phillips. 1969. “Ecological Inference: The Use of Aggregate Data to Study Individuals.” American Political Science Review 63 (4): 1183–96.
Shively, W. Phillips. 1988. “A Strategy for Cross-Level Inference Under an Assumption of Breakage Effects.” Political Methodology 11 (3-4): 167–80.
Stokes, Donald E. 1969. “Cross-Level Inference as a Game Against Nature.” In Mathematical Applications in Political Science, vol. 4, ed. Bernd, Joseph L., 6283. Charlottesville: University of Virginia Press.
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Estimation of Models with Variable Coefficients

  • John E. Jackson


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