Heteroscedasticity

The problem of autocorrelation is usually predicted in time series data. Conversely, heteroscedasticity is generally found in the cross-sectional data. The classic linear regression model assumes that disturbances (εj) of the observation regression function

are homoscedastic. If homoscedasticity is rejected, there is a sign that the estimates of the parameters obtained by the OLS technique are no longer minimum variance unbiased estimators over time and the estimate explanatory variables becomes inefficient (Gujarati, 2003).

To solve the problem of heteroscedasticity, the tool used is the White Heteroscedasticity Consistent Variance, which is available in the statistical and econometric software. This study employed E-Views Software for the Statistical and Econometrics Analysis. There is an important test if the model obtains a heteroscedasticity problem. It provides correct estimates for the coefficient covariances in the existence of heteroscedasticity of unknown form. Hence, we can employ the White’s General Heteroscedasticity Test (Gujarati, 2003: 413-14).

In order to find the consistent variance of disturbance-terms (ε^j2) this test is done by

using the equations (4.1), (4.2), (4.3), (4.4) and (4.5) as the followings:

Model 1: Auxiliary regression of equation (4.1): ε^

j2= Φ0 + Φ1CSRD + Φ2CSRD2 + Φ3CSRD*BETA + Φ4CSRD*LEV + Φ5CSRD*LSIZE + Φ6CSRD*LSALES + Φ7CSRD*ATR + Φ8CSRD*EPS + Φ9BETA + Φ10BETA2 + Φ11BETA*LEV + Φ12BETA*LSIZE + Φ13BETA*LSALES + Φ14BETA*ATR + Φ15BETA*EPS + Φ16LEV + Φ17LEV2 + Φ18LEV*LSIZE + Φ19LEV*LSALES + Φ20LEV*ATR Φ21LEV*EPS + Φ22LSIZE + Φ23LSIZE2 + Φ24LSIZE*LSALES + Φ25LSIZE*ATR + Φ26LSIZE*EPS + Φ27LSALES + Φ28LSALES2 + Φ29LSALES*ATR + Φ30LSALES**EPS + Φ31ATR + Φ32ATR2 + Φ33ATR* EPS + Φ34EPS + Φ35EPS2 + εjt (4.7)

160 Model 2: Auxiliary regression of equation (4.2):

ε^

j2 = Ω0 + Ω1EMPL + Ω2EMPL2 + Ω3EMPL*COM + Ω4EMPL*PROD + Ω5EMPL*ENV + Ω6EMPL*BETA + Ω7EMPL*LEV + Ω8EMPL*LSIZE + Ω9EMPL*LSALES + Ω10EMPL*ATR + Ω11EMPL*EPS + Ω12COM + Ω13COM2 + Ω14COM*PROD + Ω15COM*ENV + Ω16COM*BETA + Ω17COM*LEV + Ω18COM*LSIZE + Ω19COM*LSALES + Ω20COM*ATR + Ω21COM*EPS + Ω22PROD +Ω23PROD2 + Ω24PROD*ENV + Ω25PROD*BETA + Ω26PROD*LEV + Ω27PROD*LSIZE + Ω28PROD*LSALES + Ω29PROD*ATR + Ω30PROD*EPS + Ω31ENV + Ω32ENV2 + Ω33ENV*BETA + Ω34ENV*LEV + Ω35ENV*LSIZE + Ω36ENV*LSALES +Ω37ENV*ATR + Ω38ENV*LSALES +Ω39BETA +Ω40BETA2 + Ω41BETA*LEV + Ω42BETA*LSIZE + Ω43BETA*LSALES + Ω44BETA*ATR + Ω45BETA*EPS + Ω46LEV + Ω47LEV2 + Ω48LEV*LSIZE + Ω49LEV*LSALES + Ω50LEV*ATR + Ω51LEV*EPS + Ω52LSIZE + Ω53LSIZE2 + Ω54LSIZE*LSALES + Ω55LSIZE*ATR + Ω56LSIZE*EPS + Ω57LSALES + Ω58LSALES2 + Ω59LSALES*ATR + Ω60LSALES*EPS + Ω61ATR + Ω62ATR2 + Ω63ATR*EPS + Ω64EPS + Ω65EPS2 + εjt (4.8)

Model 3: Auxiliary regression of equation (4.3): ε^

j2 = Χ0 + Χ1CSRD + Χ2CSRD2 + X3CSRD*X + Χ4CSRD*BETA + Χ5CSRD*LEV + Χ6CSRD*LSIZE + Χ7CSRD*LSALES + X8CSRD*ATR + Χ9CSRD*EPS + Χ10X + X11X2 + Χ12X*BETA + Χ13X*LEV + X14X*LSIZE + X15X*LSALES + X16X*ATR + X17X*EPS + X18BETA + X19 BETA2 + Χ20BETA*LEV + Χ21BETA*LSIZE + Χ22BETA*LSALES + Χ23BETA*ATR + X24BETA*EPS + Χ25LEV + Χ26LEV2 + Χ27LEV*LSIZE + Χ28LEV*LSALES + Χ29LEV*ATR + Χ30LEV*EPS + Χ31LSIZE + Χ32LSIZE2 + Χ33LSIZE*LSALES + Χ34LSIZE*ATR + Χ35LSIZE*EPS + Χ36LSALES + Χ37LSALES2 + Χ38LSALES*ATR + Χ39LSALES*EPS + Χ40ATR + X41ATR2 + X42ATR*EPS + Χ43EPS + Χ44EPS2 + εjt (4.9)

Model 4: Auxiliary regression of equation (4.4): ε^

j2 = Ϋ0 + Ϋ1EMPL + Ϋ2EMPL2 + Ϋ3EMPL*COM + Ϋ4EMPL*PROD + Ϋ5EMPL*ENV + Ϋ6EMPL*X + Ϋ7EMPL*BETA + Ϋ8EMPL*LEV + Ϋ9EMPL*LSIZE + Ϋ10EMPL*LSALES + Ϋ11EMPL*ATR + Ϋ12EMPL*EPS + Ϋ13COM + Ϋ14COM2 + Ϋ15COM*ENV + Ϋ16COM*X + Ϋ17COM*BETA + Ϋ18ENV*LEV + Ϋ20ENV*LSIZE + Ϋ21ENV*LSALES + Ϋ22ENV*ATR + Ϋ23ENV*EPS + Ϋ24X + Ϋ25X2 + Ϋ26X*BETA + Ϋ27X*LEV + Ϋ28X*LSIZE + Ϋ29X*LSALES +Ϋ30X*ATR +Ϋ31X*EPS +Ϋ32BETA +Ϋ33BETA2 +Ϋ34BETA*LEV + Ϋ35BETA*LSIZE +Ϋ36BETA*LSALES +Ϋ37BETA*ATR +Ϋ38BETA*LSALES + Ϋ39LEV + Ϋ40LEV2 + Ϋ41LEV*LSIZE + Ϋ42LEV*LSALES + Ϋ43LEV*ATR + Ϋ44LEV*LSALES + Ϋ45LEV*ATR + Ϋ46LEV*EPS + Ϋ47LSIZE + Ϋ48LSIZE2 + Ϋ49LSIZE*LSALES + Ϋ50LSIZE*ATR + Ϋ51LSIZE*EPS + Ϋ52LSALES + Ϋ53LSALES2 + Ϋ54LSALES*ATR + Ϋ55LSALES*EPS + Ϋ56ATR + Ϋ57ATR2 +

Ϋ58ATR*EPS +Ϋ59EPS +Ϋ60EPS2 + + εjt (4.10)

161 Model 5: Auxiliary regression of equation (4.5):

ε^

j2 = Ψ0 + Ψ1CSRD + Ψ2CSRD2 + Ψ3CSRD*PERCIO + Ψ4CSRD*BETA + Ψ5CSRD*LEV + Ψ6CSRD*LSIZE + Ψ7CSRD*LSALES + Ψ8CSRD*ATR + Ψ9CSRD*EPS + Ψ10PERCIO + Ψ11PERCIO2 + Ψ12PERCIO*BETA + Ψ13PERCIO*LEV + Ψ14PERCIO*LSIZE + Ψ15PERCIO*LSALES + Ψ16PERCIO*ATR + Ψ17PERCIO*EPS + Ψ18BETA + Ψ19BETA2 + Ψ20BETA*LEV + Ψ21BETA*LSIZE + Ψ22BETA*LSALES + Ψ23BETA*ATR + Ψ24BETA*EPS + Ψ25LEV + Ψ26LEV2 + Ψ27LEV*LSIZE + Ψ28LEV*LSALES + Ψ29LEV*ATR + Ψ30LEV*EPS + Ψ31LSIZE + Ψ32LSIZE2 + Ψ33LSIZE*LSALES + Ψ34LSIZE*ATR + Ψ35LSIZE*EPS + Ψ36LSALES + Ψ37LSALES2 + Ψ38LSALES*ATR + Ψ39 LSALES*EPS + Ψ40ATR + Ψ41 ATR2 + Ψ42 ATR*EPS + Ψ43EPS + Ψ44EPS2 + εjt

(4.11)

where:

ε^j2 = variance of disturbances of multiple regression model in equations (4.1), (4.2),

(4.3), (4.4) and (4.5).

In additional, from the auxiliary regression above, R2 is obtained. Under the null hypothesis, there is homoscedasticity. It can be shown that the number of observations (n) times the R2 obtains the chi-square distribution:

n.R2 ≈ χ2df (4.12) asy

The conclusion is that there is heteroscedasticity if the chi-square value obtained in equations (4.12) exceeds the critical chi-square value at the chosen level of significance.