Then, the generalized least squares (GLS) estimator is run and the residuals will be homoskedastic
TABLE 2 Testing Heteroskedasticity in Presence of Instrumental Variables (Levels of IVs) Null Hypothesis (H0): Disturbance is Homoskedastic
Test 2(6) p-values Pagan-Hall General Test Statistic 1.388 0.967 Pagan-Hall Test w/assumed Normality 1.394 0.966 White/Koenker n Rc2 Test Statistic 19.572 0.003 Breusch-Pagan/Godfrey/Cook-Weisberg 19.256 0.004
A modified Wald test for group-wise heteroskedasticity (9) in the FE regression model found a high level of significance (chi-squared = 99459.7), strongly rejecting the null hypothesis that the error terms are homoskedastic
. The result of a Wooldridge test for autocorrelation in panel data indicated that the first-order autocorrelation is also present (F = 112.9) in the model.
As for the specification tests for the VAR model, the errors are found serially uncorrelated and homoskedastic
. However, the Jarque and Bera (1980) test rejects the null hypothesis of normality.
The null hypothesis of this test was that the error variance was Homoskedastic
. The Modified Wald test produced a chi-square value of 22000.31 with a p-value of 0.0000 for model ROA and a chi-square of 56834.15 with a p-value of 0.0000 for model ROE.
Given the stylized facts of financial time series, examining the weekday effect in mean and variance under the assumption that returns are normally distributed and/or homoskedastic
(as postulated in most prior studies) may not be appropriate.
[x.sub.i] represents the set of individual characteristics that explain both the probability of taking out a loan for education and the amount of the loan.(24) The vector of parameters to be estimated is represented by B and [[epsilon].sub.i] represents the normally and homoskedastic
distributed error term.
This fixed effects model assumes that the errors are homoskedastic
and spatially and temporally independent, obtaining biases estimators when there is dependence and heteroskedasticity problems in the term errors as shown by Beck (2001) and O'Connell (1998).
(34) Predicted values from the regression provide the basis for computing changes in a "quality-adjusted" composite price index [P.sub.t]: with a set of time dummies in the regression, the change in the composite index relative to the base period is given by exponentiation of the values of their estimated coefficients ([??]), Although E[exp(P)] [not equal to] exp(E[P]) and [[epsilon].sub.it] may not be homoskedastic
, suggesting a "smearing" adjustment of the type discussed in the medical costs literature, (35) with time dummies in the regression these adjustment factors will typically be small.
idiosyncratic component, same variance for the common and idiosyncratic component: [e.sub.ii] ~ N(0,1) and r = [theta].
Regarding the diagnostic checks, as shown in Arellano and Bond (1991), the Sargan test only has an asymptotic chi-squared distribution for a homoskedastic
[y.sub.t] is an I(1) dependent variable defined as the total health expenditures (HEXP), [x.sub.t] = [GDP, MD, POPA, EQ] i.e., per capita GDP (GDP), medical density (MD), population ageing(POPA) and environmental quality (EQ) is the vector matrix of 'forcing' I(0) and regressors as already defined with a multivariate identically and independently distributed (i.i.d) zero mean error vector [[epsilon].sub.t] = ([[epsilon].sub.1t], [[epsilon]'.sub.2t])', and a homoskedastic