A Monte Carlo study the effects of multicollinearity and cross equation restrictions on the efficiency of seemingly unrelated regression

Ekkaphon Nuysri, Purdue University

Abstract

In this dissertation, the conditions which determine the relative efficiency of ordinary least squares (OLS), seemingly unrelated regression (SUR), and restricted seemingly unrelated regression (RSUR) for a two-equation, two-variable model were examined. The results show that whether or not the error structure must be estimated has little effect on the relative efficiency of the estimators. Of course, for FSUR (SUR with an estimated error structure) a reasonable level of error correlation is needed. Restrictions ($\beta\sb1$ = $\beta\sb2$) bring a substantial gain under most conditions, including when the errors are autocorrelated, despite the fact that the restricted estimator suffers a greater penalty due to estimation of the error covariance matrix. When restrictions are incorrect, the efficiency of FRSUR relative to OLS or FSUR is greater when both equations have lower R$\sp2$ than higher R$\sp2$. Higher multicollinearity makes the consequences of incorrect restrictions less damaging. In most cases, whether or not the explanatory variables are fixed or stochastic probably makes little difference. For the model with the autocorrelated errors, the results suggest that autocorrelation tends to enhance the desirability of restricted estimation. On average, the more complex the estimator, the greater is the loss from ignoring autocorrelation. There is some slight suggestion that autocorrelation lowers the value of the error correlation, for which OLS becomes more efficient than FSUR. In estimating the error structure (including autocorrelation coefficients) for FRSUR, whether or not to use residuals from separate OLS or OLS which incorporates restrictions implied by the null hypothesis is a matter of convenience. A better estimate of the error structure does not lead to a significant improvement in the efficiency of FRSUR. Finally, in spite of the fact that the error covariance matrix must be estimated, FSUR and FRSUR provide trustworthy inferences except when the errors are autocorrelated, in which there is a greater tendency to reject a true null hypothesis at low levels of autocorrelation.

Degree

Ph.D.

Advisors

Binkley, Purdue University.

Subject Area

Economics

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