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

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.

Assessments of Some Simultaneous Equation Estimation Techniques with Normally and Uniformly Distributed Exogenous Variables

In each equation of simultaneous Equation model, the exogenous variables need to satisfy all the basic assumptions of linear regression model and be non-negative especially in econometric studies. This study examines the performances of the Ordinary Least Square (OLS), Two Stage Least Square (2SLS), Three Stage Least Square (3SLS) and Full Information Maximum Likelihood (FIML) Estimators of simultaneous equation model with both normally and uniformly distributed exogenous variables under different identification status of simultaneous equation model when there is no correlation of any form in the model. Four structural equation models were formed such that the first and third are exact identified while the second and fourth are over identified equations. Monte Carlo experiments conducted 5000 times at different levels of sample size (n = 10, 20, 30, 50, 100, 250 and 500) were used as criteria to compare the estimators. Result shows that OLS estimator is best in the exact identified equation except with normally distributed exogenous variables when . At these instances, 2SLS estimator is best. In over identified equations, the 2SLS estimator is best except with normally distributed exogenous variables when the sample size is small and large, and;and with uniformly distributed exogenous variables when n is very large, , the best estimator is either OLS or FIML or 3SLS.

Effect of Aqueous Extracts of Bitter Leaf Powder on the Corrosion Inhibition of Al-Si Alloy in 0.5 M Caustic Soda Solution

The effect of bitter leaf (Vernonia amygdalina) extract as an inhibitor for aluminium silicon alloy in 0.5 M solution of caustic soda using weight loss method has been investigated. The alloy of composition 9% Si and 91% Al was sand cast at the Foundry Shop of the National Metallurgical Development Centre, Jos, Nigeria. The cast alloy was cut and machined to corrosion coupons and immersed into 0.5 M NaOH solution containing varying inhibitor concentrations (0.1%, 0.2%, 0.3%, 0.5% v/v) within a period of fifteen days. From the result, it was found that the adsorption of Vernonia amygdalina reduced the corrosion rate of this group of alloy in the alkaline medium. The inhibitive action of this plant extract was explained using inhibition efficiency and degree of surface coverage. The most suitable inhibitor concentration was found to be 0.5% with inhibition efficiency of 87%. The mechanism of inhibition is by physical adsorption and the adsorbed molecules of the inhibitor lies on the surface of the alloy blocking the active corrosion sites on the alloy, hence, giving the alloy a higher corrosion resistance in the studied environment.