Seemingly unrelated regressions

In econometrics, the seemingly unrelated regressions (SUR)[1]: 306 [2]: 279 [3]: 332  or seemingly unrelated regression equations (SURE)[4][5]: 2  model, proposed by Arnold Zellner in (1962), is a generalization of a linear regression model that consists of several regression equations, each having its own dependent variable and potentially different sets of exogenous explanatory variables. Each equation is a valid linear regression on its own and can be estimated separately, which is why the system is called seemingly unrelated,[3]: 332  although some authors suggest that the term seemingly related would be more appropriate,[1]: 306  since the error terms are assumed to be correlated across the equations.

The model can be estimated equation-by-equation using standard ordinary least squares (OLS). Such estimates are consistent, however generally not as efficient as the SUR method, which amounts to feasible generalized least squares with a specific form of the variance-covariance matrix. Two important cases when SUR is in fact equivalent to OLS are when the error terms are in fact uncorrelated between the equations (so that they are truly unrelated) and when each equation contains exactly the same set of regressors on the right-hand-side.

The SUR model can be viewed as either the simplification of the general linear model where certain coefficients in matrix are restricted to be equal to zero, or as the generalization of the general linear model where the regressors on the right-hand-side are allowed to be different in each equation. The SUR model can be further generalized into the simultaneous equations model, where the right-hand side regressors are allowed to be the endogenous variables as well.

  1. ^ a b Davidson, Russell; MacKinnon, James G. (1993). Estimation and inference in econometrics. Oxford University Press. ISBN 978-0-19-506011-9.
  2. ^ Hayashi, Fumio (2000). Econometrics. Princeton University Press. ISBN 978-0-691-01018-2.
  3. ^ a b Greene, William H. (2012). Econometric Analysis (Seventh ed.). Upper Saddle River: Pearson Prentice-Hall. pp. 332–344. ISBN 978-0-273-75356-8.
  4. ^ Zellner, Arnold (1962). "An efficient method of estimating seemingly unrelated regression equations and tests for aggregation bias". Journal of the American Statistical Association. 57 (298): 348–368. doi:10.2307/2281644. JSTOR 2281644.
  5. ^ Srivastava, Virendra K.; Giles, David E.A. (1987). Seemingly unrelated regression equations models: estimation and inference. New York: Marcel Dekker. ISBN 978-0-8247-7610-7.