TITLE:
Empirical Determination of the Tolerable Sample Size for Ols Estimator in the Presence of Multicollinearity (ρ)
AUTHORS:
O. O. Alabi, T. O. Olatayo, F. R. Afolabi
KEYWORDS:
Regression Model, OLS Estimator Multicollinearity, Power Rate Value and Tolerable Sample Size
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.13,
July
7,
2014
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.