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An Application of Bayesian Dynamic Linear Model to Okun’s Law
(Scienpress Ltd, 2017) Awe, O. O.; Sanusi, K.A.; Adepoju, A. A.
Many authors have used dynamic time series regression models to analyse Okun’s law. This type of models often require first differencing the dependent and independent variables, as well as investigating the maximum lag length required for the model to be efficient. In this paper, we propose a straight-forward time-varying parameter state space model for analyzing Okun’s law. In particular, as a case study, we investigate the validity and stability of Okuns law using a Bayesian Dynamic Linear Model which implicitly describes the time-varying relationship between Gross Domestic Product (GDP) and unemployment rate of a major economy in Africa for three decades. The time-varying parameters of this model are estimated via a modified recursive forward filtering, backward sampling algorithm. We find that Okuns law exhibited structural instability in Nigeria in the period 1970-2011, with the sensitivity of unemployment rate to movements in output growth loosing stability over time, which may have been a contributor to her recent economic decline
Application of ordinal logistic regression model to occupation data
(Duncan Science Company, 2009) Adepoju, A. A.; Adegbite, M.
People's occupational choices might be influenced by their parents' occupation, gender, previous experiences, ages, and their own education level. We can study the relationship of one's occupation choice with education level and father's occupation. The occupational choices will be the outcome variable which consists of categories of occupations. The regression methods are capable of allowing researchers to identify explanatory variables related to organizational programs and services that contribute to the overall staff status. These methods also permit researchers to estimate the magnitude of the effect of the explanatory variables on the outcome variable. Therefore, regression methods seem to be superior in studying the relationship between the explanatory and outcome variables. This study used ordinal logistic regression method to examine the relationship between the ordinal outcome variable, different levels of staff status in the Lagos State Civil Service of Nigeria, the explanatory variables are Gender, Indigenous status, Educational Qualification, Previous Experience and Age. The outcome variable was measured on an ordered, categorical, and three-point Likert scale as Junior staff Middle Management staff, and Senior Management staff. Within the complete models, the legit link was the better choice because of its satisfying parallel lines assumption and larger model- fitting statistics. The study revealed that two explanatory variables namely, Education Qualification and Previous Working Experience significantly predicted the probability of an individual staff being a member of any of the three levels of staff status
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 observation
Bayesian optimal filtering in dynamic linear models: an empirical study of economic time series data
(2015) Awe, O. O.; Adepoju, A. A.
This paper reviews a recursive Bayesian methodology for optimal data cleaning and filtering of economic time series data with the aim of using the Kalman filter to estimate the parameters of a specified state space model which describes an economic phenomena under study. The Kalman filter, being a recursive algorithm, is ideal for usage on time-dependent data. As an example, the yearly measurements of eight key economic time series data of the Nigerian economy is used to demonstrate that the integrated random walk model is suitable for modeling time series with no clear trend or seasonal variation. We find that the Kalman filter is both predictive and adaptive, as it looks forward with an estimate of the variance and mean of the time series one step into the future and it does not require stationarity of the time series data considered
Bootstrap approach for estimating seemingly unrelated regressions with varying degrees of autocorrelated disturbances
(2013) Ebukuyo, O. B.; Adepoju, A. A.; Olamide, E. I.
The Seemingly Unrelated Regressions (SUR) model proposed in 1962 by Arnold Zellner has gained a wide acceptability and its practical use is enormous. In this research, two methods of estimation techniques were examined in the presence of varying degrees of _rst order Autoregressive [AR(1)] coefficients in the error terms of the model. Data was simulated using bootstrapping approach for sample sizes of 20, 50, 100, 500 and 1000. Performances of Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) estimators were examined under a definite form of the variance-covariance matrix used for estimation in all the sample sizes considered. The results revealed that the GLS estimator was efficient both in small and large sample sizes. Comparative performances of the estimators were studied with 0.3 and 0.5 as assumed coefficients of AR(1) in the first and second regressions and these coefficients were further interchanged for each regression equation, it was deduced that standard errors of the parameters decreased with increase in the coefficients of AR(1) for both estimators with the SUR estimator performing better as sample size increased. Examining the performances of the SUR estimator with varying degrees of AR(1) using Mean Square Error (MSE), the SUR estimator performed better with autocorrelation coefficient of 0.3 than that of 0.5 in both regression equations with best MSE obtained to be 0.8185 using _ = 0:3 in the second regression equation for sample size of 50. Key words: Autocorrelation||Bootstrapping||Generalized least squares||Ordinary least squares||Seemingly unrelated regressions
Clinical efficacy and health implications of inconsistency in different production batches of antimycotic drugs in a developing country
(2011-03) Ogunshe, A. A. O.; Adepoju, A. A.; Oladimeji, M. E.
Objective: This study aimed at evaluating the in vitro efficacy and health implications of inconsistencies in different production batches of antimycotic drugs. Materials and Methods: In vitro susceptibility profiles of 36 Candida spp. – C. albicans (19.4%), C. glabrata (30.6%), C. tropicalis (33.3%), and C. pseudotropicalis (16.7%) – obtained from human endocervical and high vaginal swabs (ECS/HVS) to two different batches (B1 and B2) of six antimycotic drugs (clotrimazole, doxycycline, iconazole, itraconazole, metronidazole and nystatin) was determined using modified agar well-diffusion method. Results: None of the Candida strains had entirely the same (100%) susceptibility / resistance profiles in both batches of corresponding antimycotic drugs; while, different multiple antifungal susceptibility (MAS) rates were also recorded in batches 1 and 2 for corresponding antifungals. Only 14.3%, 27.3%, 16.7–33.3%, and 8.3–25.0% of C. albicans, C. glabrata, C. pseudotropicalis, and C. tropicalis strains, respectively, had similar susceptibility/resistance profiles toward coressponding antifungal agents in both batches; while up to 57.1% of C. albicans, 45.5% of C. glabrata, 66.7% of C. pseudotropicalis, and 50.0% of C. tropicalis strains were susceptible to one batch of antifungals but resistant to corresponding antifungals in the second batch. As high as about 71.4% (C. albicans), 73.0% (C. glabrata), 50.0% (C. pseudotropicalis), and 66.74% (C. tropicalis) strains had differences of ≥10.0 mm among corresponding antimycotic agents. Conclusions: Candida strains exhibited different in vitro susceptibility / resistance patterns toward two batches of corresponding antimycotic agents, which has clinical implications on the efficacy of the drugs and treatment of patients. The findings of the present study will be of benefit in providing additional information in support of submission for drug registration to the appropriate regulatory agencies.
Comparative performance of the limited information techniques in a two equation structural model
(2007) Adepoju, A. A.
The samples with which we deal in practice are rather small. seldom exceeding 80 observations and frequently much smaller. 'Thus, it is of great interest to inquire into the properties of estimators for the typical sample sizes encountered in practice. The performances of three simultaneous estimation method using a model consisting of a mixture of an identified and over identified equations with correlated error terms and compared. The result of the Monte Carlo study revealed that the Two Stage least Squares (2SLS) and the Limited Information Maximum Likelihood (LIML) estimates are similar and in most cases identical in respect of the just-identified equation. The Total Absolute Biases (TAB) of 2SLS and LIML revealed asymptotic behavior under (upper triangular matrix) P1 while those of Ordinary Least Squares (OLS) exhibited no such behavior. For both upper and lower triangular matrices (P, and P2), 2SI.S estimates showed asymptotic behavior in the middle interval. The OI.S is the only stable estimator with a stable behavior of Root Mean Square Error (RM3F.) as its estimates increase (decrease) consistently for equation 1(equation 2) for P, (for P2).
The effect of students' pre-admission performance on post-admission performance
(2008) Olayiwola, O. M.; Adepoju, A. A.; Okunlade, A.; Akomolafe, A.
This study uses canonical correlation analysis to investigate the effect of pre-admission performance (performance in SSCE/GCE and JAMB) on the post-admission performance (performance in 1OOlevel to 400 Level). The study population comprised of a set of students that were admitted in the same year in the department of computer science. University of Ibadan, Nigeria. The students’ SSCE/GC, JAMB. 100 Level to 400 level results were studied. The result shows that students ' pre-admission performance are highly correlated with their 100 level to 300 level, but uncorrelated with 400 level result. This may due to: complexity of the course as they are moving higher, effect of the project work. Strike, riot, lack of relevant textbooks, social activities. etc. This study then recommends that the University should introduce or assign level advisers to advice the students; they should ensure that they provide relevant textbooks to the library for the students.
Effects of atypical observations on the estimation of seemingly unrelated regression model
(Science and Education Publishing, 2017) Adepoju, A. A.; Akinwumi, A. O
The 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 OLS
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 estimators
Estimation of fertility rates for Bayelsa state; using brass p/f ratio technique and gompertz relational model
(Blackwell Educational Books, 2011) Adepoju, A. A.; Ipiteikumoh, B.; Obiene, E. A.; Loko, P. O.
The aim of this paper is lo examine fertility rate in the study area. The estimates presented in this research were sampled from secondary data extracted from records of three general hospitals in the three eco zones of the State using the Brass and Gompertz methods. From the analysis, it was observed that the estimated mean parities rise steadily with age reaching the peak in both methods. This observation is in line with the international standards that "data on lifetime fertility by the ages of women from most developing countries show that it rise steadily with age, reaching a maximum in the 45-49 age groups. " The estimated total fertility rates obtained from both methods in the State lies within the estimates reported for Nigeria. The study further show that fertility rate in the study area is high and varies relatively among the sampled zones. Since majority of the rural dwellers lack knowledge of family planning and with the absence of primary health care services, planners and policy makers in the health sector should formulate programs aimed at bringing these services closer to the people so as to dissuade them from child mortality. Furthermore. enlightenment campaigns should be put in place to educate them on the use of contraceptive and the importance of birth control.
Estimation of garch models for Nigerian exchange rates under non-gaussian innovations
(2013) Adepoju, A. A.; Yaya, O. S.; Ojo, O. O.
Financial series often displays evidence of leptokurticity and in that case, the empirical distribution often fails normality. GARCH models were initially based on normality assumption but estimated model based on this assumption cannot capture all the degree of leptokurticity in the return series. In this paper, we applied variants of GARCH models under non-normal innovations-t-distribution and Generalized Error Distribution (GED) on selected Nigeria exchange rates. The Berndt, Hall, Hall, Hausman (BHHH) numerical derivatives applied in the estimation of models converged faster and the time varied significantly across models. Asymmetric GARCH model with t-distribution (GARCH-t) was selected in most of the cases whereas for Nigeria-US Dollar exchange rate, GARCH-GED was specified. Both distributions showed evidence of leptokurticity in Naira exchange rate return series. The result is of practical importance to practitioners
Estimators of linear regression model with autocorrelated error terms and prediction using correlated uniform regressors
(2012-11) Ayinde, K.; Adedayo, D. A.; Adepoju, A. A.
Performances of estimators of linear regression model with autocorrelated error term have been attributed to the nature and specification of the explanatory variables. The violation of assumption of the independence of the explanatory variables is not uncommon especially in business, economic and social sciences, leading to the development of many estimators. Moreover, prediction is one of the main essences of regression analysis. This work, therefore, attempts to examine the parameter estimates of the Ordinary Least Square estimator (OLS), Cochrane-Orcutt estimator (COR), Maximum Likelihood estimator (ML) and the estimators based on Principal Component analysis (PC) in prediction of linear regression model with autocorrelated error terms under the violations of assumption of independent regressors (multicollinearity) using Monte-Carlo experiment approach. With uniform variables as regressors, it further identifies the best estimator that can be used for prediction purpose by averaging the adjusted co-efficient of determination of each estimator over the number of trials. Results reveal that the performances of COR and ML estimators at each level of multicollinearity over the levels of autocorrelation are convex – like while that of the OLS and PC estimators are concave; and that as the level of multicollinearity increases, the estimators perform much better at all the levels of autocorrelation. Except when the sample size is small (n=10), the performances of the COR and ML estimators are generally best and asymptotically the same. When the sample size is small, the COR estimator is still best except when the autocorrelation level is low. At these instances, the PC estimator is either best or competes with the best estimator. Moreover, at low level of autocorrelation in all the sample sizes, the OLS estimator competes with the best estimator in all the levels of multicollinearity
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 misspecification
Evaluation of small sample estimators of outliers infested simultaneous equations model: a monte carlo approach
(2012-01) Adepoju, A. A.; Olaomi, J. O.
In practice, data collected in a broad range of applications frequently contain one or more atypical observations called outlier. A single outlier can have a large distorting influence on a classical statistical method that is optimal under the assumption of normality or linearity. Many estimation procedures proposed by researchers to handle simultaneous equation models are based on the assumptions that give little consideration to atypical data, thus the need to investigate the distorting effects of outliers in simultaneous equations estimation methods. In this study, we compare the performance of five estimators (OLS, 2SLS, 3SLS, GMM and W2SLS) of simultaneous equations model parameters at small sample sizes (n) 15, 20 and 25; first order autocorrelation levels (ρ) 0.3, 0.6 and 0.9 of the error terms, when the series are perturbed (polluted) at zero, one and two times. The estimators are adjudged using the minimum criteria of Bias, Variance and RMSE criteria on the 135 scenarios, each replicated 10,000 times. Identical results were obtained for the 2SLS and W2SLS methods since there are no restrictions on the parameters. The system methods clearly performed better than the single equation counterparts. Generally, the estimates obtained for the just identified equation are better than those of the over identified counterpart. Surprisingly, the ranking of the various techniques on the basis of their small sample properties does not reveal any distinguishable feature according to whether there is outlier(s) in the data or not and at the different level of correlation. On the BIAS criterion, the best method is OLS in the just identified equation, followed by 3SLS in most cases especially where the pollution level is zero for all the three autocorrelation levels considered. The GMM and 2WSLS are struggled for the third and last positions. However, in the over identified case, 3SLS is leading closely followed by GMM in most cases (when rho is 0.9 for all sample sizes considered) and OLS in few other cases (especially at rho = 0.3 and 0.6 and for N = 20 and 25 with single/double pollution levels), it is expected that we would be able to identify or suggest the best method to use when we have the scenario depicted above
Fractional integration and structural breaks in bank share prices in Nigeria
(Elsevier, 2015) Gil-Alana, L. A.; Yaya, O.S.; Adepoju, A. A.
The paper employs both fractional integration and structural break techniques in studying the daily share prices structure of the banking sector in Nigeria. Our data span between 2001 and 2012, covers periods before and after the global financial crisis. The results obtained using both parametric and semi parametric methods indicate little evidence of mean reversion since most of the orders of integration are equal to or higher than1. Long memory is found in the absolute and squared return series. The possibility of structural breaks is also taken into account and the results show a different number of breaks depending on the bank examined. In general, an increase in the degree of dependence across time is noticed, and the most common break took place in December 2008, probably being related with the world financial crisis affecting also the banking system in Nigeria
Frequentist and bayesian estimation of parameters of linear regression model with correlated explanatory variables
(2017) Adepoju, A. A.; Adebajo, E. O; Ogundunmade, P. T.
This paper addressed the popular issue of collinearity among explanatory variables in the context of a multiple linear regression analysis, and the parameter estimations of both the classical and the Bayesian methods. Five sample sizes: 10, 25, 50, 100 and 500 each replicated 10,000 times were simulated using Monte Carlo method. Four levels of correlation p = 0.0,0.1,0.5, and 0.9 representing no correlation, weak correlation, moderate correlation and strong correlation were considered. The estimation techniques considered were; Ordinary Least Squares (OLS), Feasible Generalized Least Squares (FGLS) and Bayesian Methods. The performances of the estimators were evaluated using Absolute Bias (ABIAS) and Mean Square Error (MSE) of the estimates. In all cases considered, the Bayesian estimators had the best performance. It was consistently most efficient than the other estimators, namely OLS and FGLS
On the comparative study of estimators in seemingly unrelated regression equation
(2015) Adepoju, A. A.; Olamide, E. I.
This work examined the efficiencies of Ordinary Least Squares (OLS) and Seemingly Unrelated Regression (SUR) estimators in lagged and unlagged models. Literature has shown gain in efficiency of SUR estimator over OLS estimator when the errors are correlated across equations. This paper studied the efficiencies of these estimators in a lagged and unlagged models and also sought a comparative study of these estimators in both models. Data was simulated for sample sizes 50, 100 and 1000 with 5000 bootstrapped replicates in each case with the predictors having Gaussian distribution. Results from the study showed that both estimators were efficient in each model with the SUR estimator being consistently more efficient than the OLS estimator as the sample size increased. On the assessment of the models, the unlagged model was found to be more efficient than the lagged model in small sample but converged as sample size increased.
Performances of the full information estimators in a two-equation structural model with correlated disturbances
(Bachudo Science, 2009) Adepoju, A. A.
The performances of two full information techniques, Three Stage Least Squares (3SLS) and Full Information Maximum Likelihood (FIML) of simultaneous equation models with correlated disturbance terms are compared with the Ordinary Least Squares (OLS) method in small samples. Comparative performance evaluation of the estimators was done using Average of Estimates, Total Absolute Bias (TAB) of Estimates, Root Mean Squared Error (RMSE) and Sum of Squared Residuals (RSS) of parameter estimates. The results of the Monte Carlo experiment showed that OLS is best with large negative or positive correlation, while 3SLS is best with feebly correlated error terms in the case of replication-based averages. The total absolute biases increase consistently as the sample size increases for OLS while FIML estimates reveal no distinct pattern. The magnitudes of the estimates yielded by two estimators, OLS and 3SLS, exhibited fairly consistent reaction to changes in magnitudes and direction of correlations of error terms
Probability and Distribution Theory
(Ibadan University Press, 2014) Adepoju, A. A.