Evaluation of Two Stage Modified Ridge Estimator and Its Performance

Abstract

Biased estimation methods are more desirable than two stage least squares estimation for simultaneous equations models suffering from the problem of multicollinearity. This problem is also handled by using some prior information. Taking account of this knowledge, we recommend two stage modified ridge estimator. The new estimator can also be evaluated as an alternative to the previously proposed two stage ridge estimator. The widespread performance criterion, mean square error, is  taken into consideration to compare the two stage modified ridge, two stage ridge and two stage least squares estimators. A real life data analysis is investigated to prove the theoretical results in practice. In addition, the intervals of the biasing parameter which provide the superiority of the two stage modified ridge estimator are determined   with the help of figures. The researchers who deal with simultaneous systems with multicollinearity can opt for the two stage modified ridge estimator.

Keywords

• Modified ridge estimator,Multicollinearity,Simultaneous equations model,Two stage least squares

References

1. A. E. Hoerl and R. W. Kennard, “Ridge regression: biased estimation for nonorthogonal problems”, Technometrics, vol. 12, no. 1, pp. 55-67, 1970.
2. H. D. Vinod and A. Ullah, “Recent advances in regression methods”, Marcel Dekker, New York, Inc., 1981.
3. B. F. Swindel, “Good Ridge Estimators Based on Prior Information”, Communications in Statistics-Theory and Methods, vol. A5, pp. 1065-1075, 1976.
4. G. Trenkler, “Generalized mean squared error comparisons of biased regression estimators”, Communications in Statistics-Theory and Methods, vol. A9, no. 12, pp. 1247-1259, 1980.
5. J. L. Pliskin, “A ridge type estimator and good prior means”, Communications in Statistics-Theory and Methods, vol. 16, no. 12, pp. 3429–3437, 198.
6. A. E. Hoerl, R. W. Kennard and K. F. Baldwin, “Ridge regression: some simulations”, Communications in Statistics-Simulation and Computation, vol. 4, pp. 105–123, 1975.
7. B. M. G. Kibria, “Performance of some new ridge regression estimators”, Communications in Statistics-Simulation and Computation, vol. 32, no. pp. 419–435, 2003.
8. J. F. Lawless and P. A. Wang, “Simulation study of ridge and other regression estimators”, Communications in Statistics-Theory and Methods , vol. 5, no. 4, pp. 307-323, 1976.

9. W. E Griffiths, R.C. Hill and G.G. Judge, “Learning and Practicing Econometrics”, John Wiley&Sons Inc., New York, 1993.