Empirical Determination of the Tolerable Sample Size for Ols Estimator in the Presence of Multicollinearity (ρ)

O. O. Alabi, T. O. Olatayo, F. R. Afolabi

Department of Mathematical Sciences, Federal University of Technology, Akure, Ondo State, Nigeria.
Department of Mathematical Sciences, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria.
Department of Mathematics and Statistics, Bowen University, Bowen, Iwo Osun State, Nigeria.

DOI: 10.4236/am.2014.513180                

Abstract

This paper investigates the tolerable sample size needed for Ordinary Least Square (OLS) Estimator to be used when there is presence of Multicollinearity among the exogenous variables of a linear regression model. A regression model with constant term (β₀) and two independent variables (with β₁ and β₂ as their respective regression coefficients) that exhibit multicollinearity was considered. A Monte Carlo study of 1000 trials was conducted at eight levels of multicollinearity (0, 0.25, 0.5, 0.7, 0.75, 0.8, 0.9 and 0.99) and sample sizes (10, 20, 40, 80, 100, 150, 250 and 500). At each specification, the true regression coefficients were set at unity while 1.5, 2.0 and 2.5 were taken as the hypothesized value. The power value rate was obtained at every multicollinearity level for the aforementioned sample sizes. Therefore, whether the hypothesized values highly depart from the true values or not once the multicollinearity level is very high (i.e. 0.99), the sample size needed to work with in order to have an error free estimation or the inference result must be greater than five hundred.

Keywords

Regression Model, OLS Estimator Multicollinearity, Power Rate Value and Tolerable Sample Size

Conflicts of Interest

The authors declare no conflicts of interest.

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