Empirical Determination of the Tolerable Sample Size for Ols Estimator in the Presence of Multicollinearity (&amp;lt;i&amp;gt;ρ&amp;lt;/i&amp;gt;)

O O Alabi,F R Afolabi,T O Olatayo

doi:10.4236/am.2014.513180

Empirical Determination of the Tolerable Sample Size for Ols Estimator in the Presence of Multicollinearity (&lt;i&gt;ρ&lt;/i&gt;)

O O Alabi, F R Afolabi + Show 1 more

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https://doi.org/10.4236/am.2014.513180

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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.

Highlights

There has been a serious argument between the researchers that multicollinearity problem could be solved with the increase of the sample size while some researchers say that Multicollinearity problem will increase withHow to cite this paper: Alabi, O.O., Olatayo, T.O. and Afolabi F.R. (2014) Empirical Determination of the Tolerable SampleSize for Ols Estimator in the Presence of Multicollinearity (ρ)
Likewise, when the true values of β 0 and β 2 are maintained and that of β1 is allowed to change, The summary of the tolerable sample sizes required for the parameter β1 to have a power rate value of 0.99 or 1 was determined at different levels of multicollinearity and hypothesized values
When the true values of β 0 and β1 are maintained and that of β 2 is allowed to change, The summary of the tolerable sample sizes required for the parameter β 2 to have a power rate value of 0.99 or 1 was determined at different levels of multicollinearity and hypothesized values

Summary

Introduction

There has been a serious argument between the researchers that multicollinearity problem could be solved with the increase of the sample size while some researchers say that Multicollinearity problem will increase withHow to cite this paper: Alabi, O.O., Olatayo, T.O. and Afolabi F.R. (2014) Empirical Determination of the Tolerable SampleSize for Ols Estimator in the Presence of Multicollinearity (ρ). [1] stated that Multicollinearity problem could be solved by increase of the size of the sample if the presence of multicollinearity is due to errors of measurement as well as when intercorrelation happens to exist only in our original sample but not in the population [2]. Because of these arguments this paper investigates the tolerable sample size needed for Ordinary Least Square Estimator to be used when there is presence of Multicollinearity among the exogenous variables of a linear regression model before we can say that multicollinearity problem could be solved with increase of the sample size method. When this assumption is violated, it results into multicollinearity problem [3]

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