ABSTRACT
For valid statistical inference there is a need to take account of pos;;ible lag dependence while we test for error dependence, and vice versa. In Anselin ( 198Bc) two different approaches are suggested. One i!:' to test jointly for H0 : A = p = 0 in (73) using the HS principle so that the test can be implemented with OLS residuals (see Ansel in 1988c). The resulting joint test statistic is given by
(77)
whereE=(Dja 2)Tzz-(TJz) 2 .Notethatthisjointtestnotonlydependsond;. anddpbutalsoontheirinteractionfactorwithacoefficientTJz.Expression(77)appearstobesomewhatcomplicatedbutcanbecomputedquiteeasilyusingonlyOLS residuals.Alsotheexpressionsimplifiesgreatlywhenthespatialweightsmatrices W1andW2areassumedtobethesamewhichisthecaseinmostapplications.Under W1=Wz=W,f)1=721=T22=T=tr[(W'+W)W],and(77)reducesto
(78)
UnderHo:'A=p=0,RS;.pwillconvergetoacentralx2withtwodegreesof freedom.Becauseofthistwodegreesoffreedom,thestatisticwillresultinlossof powercomparedtotheproperone-directionaltestwhenonlyoneofthetwoforms ofmisspecificationispresent.Toseethisconsiderthepresenceofonly).=rj.Jli, withp=0.InthiscasethenoncentralityparameterforbothRS;.andRS;.pis thesamer 2NT.DuetothehigherdegreesoffreedomofthejointtestRS;.p,we canexpectsomelossofpower(DasguptaandPerlman1974).Anotherproblem withRS~cpisthatsinceitisanomnibustest,ifthenullhypothesisisrejected, itisnotpossibletoinferwhetherthemisspecificationisduetolagorerrordependence.
