Al-Hikmah University Journal

In practice, virtually all form of Gross Domestic Products are usually difference stationary

series of order one {I(1)} except Real GDPwhich is often difference stationary series of order

two {I(2)}.Since no Traditional Time Series Models (TTSM) cannot adequately capture the

dynamics of an I(2) variable in a multivariable time series settings, the system equation

techniques(single or system estimators) such as the Indirect Least Squares (ILS), Two-Stage

Least Squares (2SLS), Three-Stage Least Squares (3SLS)Seemingly Unrelated Regression

(SUR) and Full Information Maximum Likelihood (FIML) estimators are desirable.

However, comparison among these estimators using suitable selection criteria in order to

determine the best estimator(s) for estimating the regression coefficients in the formulated

model is crucial. To demonstrate this assertion empirically, this study therefore apply a

Simultaneous Equation Model (SEM) to examine the Tax-Real GDPrelationship under mixed

order of integrations such as I(2) and I(1)s. Results from unit root tests established that Real

GDP (Ly1t )is I(2)while Company Income Tax (Ly2t ), Petroleum Profit Tax (Ly3t ), Personal

Income Tax (Lx1t ) and Value Added Tax (Lx2t ) are all I(1). Endogeneity tests carried out on the

series further confirmed that there is no two-way causation among the three endogenous

variables (i.e. Ly1t , Ly2t and Ly3t ) in the model. The findings show that despite the absence of

simultaneity in the model, the Ordinary Least Squares (OLS) and Two-Stage Least Squares

(2SLS) estimators though produced identical estimates which are spurious. The Three Stage

Least Squares (3SLS) outperformed the Seemingly Unrelated Regression (SUR) reported the

least values of the standard errors of the regression parameters. Projections using the 3SLS

estimates further revealed that for every one percent increase in Lx1t , Lx2t and Lx(t-1), Ly1t is

expected to increase by 14.4%, 11.6% and 6.93% respectively.