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Item Effects of atypical observations on the estimation of seemingly unrelated regression model(Science and Education Publishing, 2017) Adepoju, A. A.; Akinwumi, A. OThe Seemingly Unrelated Regression Equation model is a generalization of a linear regression model that consists of several regression equations in order to achieve efficient estimates. Unfortunately, the assumptions underlying most SUR estimators give little/no consideration to outlying observations which may be present in the data. These atypical observations may have some apparent distorting effects on the estimates produced by these estimators. This study thus examined the effect of outliers on the performances of SUR and OLS estimators using Monte Carlo simulation method. The Cholesky method was used to partition the variance-covariance matrix by decomposing it into the upper and lower non-singular triangular matrices. Varying degree of outliers; 0%, 5%, and 10% were each introduced into five sample sizes; 20, 40, 60, 100 and 500 respectively. The performances of the estimators were evaluated using Absolute Bias (ABIAS) and Mean Square Error (MSE). The results showed that at 0% outliers (when outliers were absent), the ABIAS and MSE of the SUR and OLS estimators showed similar results. At 5% and 10% outliers, the magnitude in ABIAS and MSE for both estimators increased but the SUR estimator showed better performance than the OLS estimator. As the sample size increases, ABIAS and MSE of the estimators decreased consistently for the various degrees of outliers considered with SUR consistently better than OLSItem Evaluation of simultaneous equation techniques in the presence of misspecification error: a Monte Carlo approach(2014) Ojo, O. O.; Adepoju, A. A.One of the assumptions of Classical Linear Regression Model (CLRMA), is that the regression model be ‘correctly’ specified. If the model is not ‘correctly’ specified, the problem of model misspecification error arises. The objective of the study is to know the performances of the estimator and also the estimator that is greatly affected by misspecification error due to omission of relevant explanatory variable. Four simultaneous equation techniques (OLS, 2SLS, 3SLS, LIML) were applied to a two-equation model and investigated on their performances when plagued with the problem of misspecification error. A Monte Carlo method simulation method was employed to investigate the effect of these estimators due to misspecification of the model. The findings revealed that the estimates obtained by 2SLS and 3SLS are similar and variances by all the estimates reduced consistently as the sample size increases. The study had revealed that 2 3 SLS performed best using average of parameter criterion while OLS generated the least variances. LIML is mostly affected by misspecificationItem Simultaneous equation estimation with first order auto correlated disturbances(2013-08) Ojo, Y. O.; Adepoju, A. A.The estimation of the parameters of simultaneous equation problem is usually affected by the existence of mutual correlation between pairs of random deviates, which is a violation of the assumption of no autocorrelation between the error terms. In practice the form of correlation between the pairs of random deviates is not known. This study therefore examined a two-equation model in which the correlation between the random deviates is assumed to follow a first-order Autoregressive [AR (1)] process. Data was simulated using Monte Carlo approach with varying sample sizes each replicated 1000 times. The behaviour of OLS, 2SLS, LIML and 3SLS were evaluated using Variance, Root Mean Square Error (RMSE) and Absolute Bias (AB). The absolute bias estimates decrease in most cases as the sample size increases. The variances obtained by all the estimators reduced consistently as the sample size increases. There was no clear pattern in the behaviour of the RMSE across sample sizes. The results for = 0.3 were better than when = 0.0 with respect to each criterion but retained the same pattern. This work established that when was different from zero, the estimators performed better, hence the choice of should be carefully made as this may significantly affect the performances of the estimatorsItem Estimating seemingly unrelated regressions with first order autoregressive disturbances(CSCanada, 2013-05) Olamide, E. I.; Adepoju, A. A.In Seemingly Unrelated Regressions (SUR) model, disturbances are assumed to be correlated across equations and it will be erroneous to assume that disturbances behave independently, hence, the need for an efficient estimator. Literature has revealed gain in efficiencyof the SUR estimator over the Ordinary Least Squares (OLS) estimator when the errors are correlated across equations. This work, however, considers methods of estimating a set of regression equations when disturbances are both contemporaneously and serially correlated. The Feasible Generalized Least Squares (FGLS), OLS and Iterative Ordinary Least Squares (IOLS) estimation techniques were considered and the form of autocorrelation examined. Prais-Winstein transformation was conducted on simulated data for the different sample sizes used to remove autocorrelations. Results from simulation studies showed that the FGLS was efficient both in small samples and large samples. Comparative performances of the estimators were investigated on the basis of the standard errors of the parameter estimates when estimating the model with and without AR(1) and the results showed that the estimators performed better with AR(1) as the sample size increased especially from 20. On the criterion of the Root Mean Square, the FGLS was found to have performed better with AR(1) and it was revealed that bias reduces as sample size increases. In all cases considered, the SUR estimator performed best. It was consistently most efficient than the OLS and IOLS estimatorsItem Ranking of simultaneous equation estimators to outliers from heavy-tailed quasi-uniform distribution(2012-11) Oseni, B.M.; Adepoju, A. A.; Olubusoye, O. E.In this work, the ranking of the performances of two-equation simultaneous models when outliers are presumed present in a convoluted exogenous variable is carried out. The exogenous variable is a convolution of normal and uniform distribution. Monte Carlo experiment was carried out to investigate the performances of four estimators namely: Ordinary Least Squares (OLS), Two Stage Least Squares (2SLS), Limited Information Maximum Likelihood (LIML) and Three Stage Least Squares (3SLS). Five sample sizes were used to allow for measure of asymptotic properties of these estimators. The experiment was replicated 1000 limes and the results were evaluated using Total Absolute Bias (TAB), Variance and Root Mean Squared Error (RMSE). It is observed that the performances of the estimators when lower triangular matrix is used are better than that of upper triangular matrix. OLS using TAB as evaluation criterion is better than the other estimators when an exogenous variable is convoluted for the just-identified equation. The performance of 2SLS is best for the over-identified equation. OLS possesses the least variance for both equations and both matrices while LIML has the worst variance in most crises. OLS possesses the smallest RMSE for both matrices and equations except with the over-identified equation using lower triangular matrix when an exogenous variable is convolutedItem Assessment of simultaneous equation techniques under the influence of outliers(2011) Oseni, B. M.; Adepoju, A. A.Most simultaneous equations estimation techniques are based on the assumptions of normality which gives little consideration to some atypical data often called outliers which may be present in the observations. The outliers may have some obvious distorting influence on the estimates produce by these techniques. This study investigates the distorting effect of outliers on four simultaneous equation estimation techniques through Monte Carlo method. Outliers of various degrees were introduced into observations of different sizes. The estimators were ranked based on their ability to absorb the shock due to outliers in the observations. The Total Absolute Bias (TAB), Variance and Root Mean Square Error (RMSE) were used in ranking the performances of the estimators. Based on the criterion of tab, two stages least squares (2SLS) ranked the best, closely followed by three stage least squares (3SLS) and ordinary least squares (OLS) in that order, while limited information maximum likelihood (LIML) was the poorest when outliers of not more than 5% are present in the observation. It is however, not strange to observe that OLS outperformed the other estimators when variance was used. This could be misleading since variance may be measured around a wrong parameter. Based on the criterion of RMSE, ordinary least squares yields estimates with the least value of RMSE while LIML yields the greatest when outliers of not more than 10% are present in the observation. Also it was established that OLS has the greatest capacity to absorb the shock due to the presence of outliers in the observationItem Robustness of simultaneous estimation methods to varying degrees of correlation between pairs of random deviates(International Research Publication House, 2010) Oyamakin, O.; Adepoju, A.A.This study examined how six estimation methods of a simultaneous equation model cope with varying degrees of correlation between pairs of random deviates using the Variance and Total Absolute Bias (TAB). A two-equation simultaneous system was considered with assumed covariance matrix. The model was structured to have a mutual correlation between pairs of random deviates which is a violation of the assumption of mutual independence between pairs of such random deviates. The correlation between the pairs of normal deviates were generated using three scenarios of r = 0.0, 0.3 and 0.5. The performances of various estimators considered were examined at various sample sizes, correlation levels and 50 replications. The sample size, N = 20,25,30 each replicated 50 times was considered. OLS is performed best when the variance is used to study the finite sample properties of the estimators in that it produces the least variances in all the cases considered and at all sample sizes. All the estimators revealed an asymptotic pattern under CASE I.Item Ranking of simultaneous equation techniques to small sample properties and correlated random deviates(Science Publications, 2009) Adepoju, A.A; Olaomi, J.OProblem statement: All simultaneous equation estimation methods have some desirable asymptotic properties and these properties become effective in large samples. This study is relevant since samples available to researchers are mostly small in practice and are often plagued with the problem of mutual correlation between pairs of random deviates which is a violation of the assumption of mutual independence between pairs of such random deviates. The objective of this research was to study the small sample properties of these estimators when the errors are correlated to determine if the properties will still hold when available samples are relatively small and the errors were correlated. Approach: Most of the evidence on the small sample properties of the simultaneous equation estimators was studied from sampling (or Monte Carlo) experiments. It is important to rank estimators on the merit they have when applied to small samples. This study examined the performances of five simultaneous estimation techniques using some of the basic characteristics of the sampling distributions rather than their full description. The characteristics considered here are the mean, the total absolute bias and the root mean square error. Results: The result revealed that the ranking of the five estimators in respect of the Average Total Absolute Bias (ATAB) is invariant to the choice of the upper (P1) or lower (P2) triangular matrix. The result of the FIML using RMSE of estimates was outstandingly best in the open-ended intervals and outstandingly poor in the closed interval (- 0.05