Productividad

The study established a link between demographic variables and various categories of government expenditures (capital and recurrent). The equations are based, on a base case expenditure scenario. The specification shown below was used to estimate equations for three expenditure categories: education expenditure (EXEDUC), economic services expenditure (EXECON) and health expenditure (EXHE). The equations served as a basis for projecting government expenditure.

The general specification of the expenditure equations is: Exp = f(Pop, Sa)

Where:

Exp = expenditure category

Pop = population variables (Pop 5+; Pop6-11; Pop12-17; Pop18-24; Pop25-34; Pop35-44; Pop45-54; Pop55-64; & Pop65-74)

SA = speed of adjustment (residual from the Cointegration Equation Model)

We estimated three (3) equations after treating for stationarity and cointegrating vectors. In our model, population dynamics were used as independent variables only to gauge the effects on the dependent varibles. In estimating the equations using this general specification, lagged dependent variables were introduced on the right-hand side to test for serial dependence in public spending. This was later dropped because of its insignificance. All equations are in a log-linear form.

4.1.1 Econometric Tests:

1. Unit Root Analysis

The Augmented Dickey-Fuller (ADF) test was used for stationarity analysis. According to Dickey and Fuller (1979), the unit root is the Null Hypothesis and is based on i.i.d. error. Another test for such analysis is the Phillips-Perron test (PP) (Perron, 1988). This test is nonparametric and allows for heterogeneity and serial

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correlation while the KPSS test (Kwiatkowski, Phillips, Schmidt and Shin, 1992) differ from both the ADF and PP tests. The ADF’s null hypothesis takes the form of stationarity, while the alternative hypotheses is the unit root. The ADF uses a baseline for variable integration. Its results indicate if the variables are integrated of order one or a zero. Evidence of non-stationarity series required differencing of some variables to attain stationarity. This is to avoid the problem of spurious correlation, or inconsistent regression that plagues econometric estimation when some or all of the individual series are non-stationary.

2. Co integration Analysis

The existence of a linear combination between the endogenous variables would suggest a long-run relationship. The Stationarity test of the residuals from the OLS I(I) variables were used to validate this point. This can be a particularly useful approach in unrestricted (non – normalized) equations that are consistent with long – run equilibrium, but may be characterized by considerable short –run dynamics.

The process refers to a situation where each component Xi,t, i=1,…,k, of a vector

time series Xt is a unit root process, but certain linear combinations of the Xi,t’s are

stationary. Thus Xt = Xt,1 + m + Vt,

Where Vt is a zero-mean K-variate stationary time series process and m is a K- vector of drift parameters, but there exists a k’ r matrix b with rank r < k such that b`Xt is (trend) stationary. In order to show that this is possible, let us assume that Vt can be written as an infinite order vector moving average process:

Vt = C(L)et,

Where et is i.i.d. k-variate white noise with unit variance matrix and C(L) is a

matrix-valued lag polynomial:

C(L) = Co + C1L + C2L2 + C3L3 + ……….,

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With the Cj`s k` k coefficient matrices and L the backshift lag operator (i.e., L = et-1). Now C(L) = C(1) + [C(L) – C(1)] = C(1) + (1 – L)D(L),

Where

D(L) = [C(L) – C(1)]/C(1- L).

This is always possible because C(L) – C(1) is a zero matrix for L =1, hence each element of this lag polynomial matrix has root 1 and thus these elements have a common factor 1 – L.

3. Exogeneity Tests and Diagnostic Checks

Exogeneity tests were also carried out on the variables while diagnostic checks such as autocorrelation, heteroskedasticity, Swartz-criterion, Hanna-Quinn tests, normality and re-specification tests were checked after the estimations. Furthermore, statistics such as adjusted R2, F-tests, and T-tests benchmarked the model and sensitivity to parameterization was also checked for model congruency.

N/b

In our analysis, we did not consider the inverse relationship between Population dynamics and government expenditure because it is out of the scope of the present study. No doubt, the inverse relationship would have some effect on the studies direct relationship. Furthermore, it should be noted that the evolution of an Age Class is not unconnected with the development of the previous Age Classes. However, we did not take into account of this dimension in our analysis, which could be studied further.

Also, we have not included Enrollment as a variable in the sensitivity analysis for government spending on Education because we are not interested in the singular effect of this, but rather how government expenditure adjusts to demographic changes in general. As a result of this, we also excluded the independent variables as dependent variables in the other equations. The issue of controlling the variables was not adjudged necessary in our estimations.

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Objective 2: Estimate the Benefit Incidence of Public Expenditure (Primary/Secondary/Tertiary) on Health, and Education in the South East (SE), using 2010 NHLSS Data

4.2 Beneficiaries’ and Marginal Odds of Health and Education Expenditure