An investigator estimates the

An investigator estimates the following equation using OrdinaryLeast Squares from time series data: Y1 = a0 + a1X1t + a2X2t + UtThe following scenarios represent violations of the CLRMassumptions. For each scenario, state the underlying assumptionbeing referred to and state the null hypothesis of that assumption.i- There is another important variable, which has been omitted. ii-X1 and X2 are correlated iii- Ui is correlated with its own pastvalues. iv- The mean value of the residual from the regression isequal to 1 Please help


i) there is another important variable which has been omitted.say that is X3

i.e. the true model will beyt=a0+a1x1t+a2x2t​​​​+a3x3t​​​​+ut

But if we will use theprevious model, then E(ut)is not equal to zero, so thatassumption will be violated.


which is not equal to zero as x3 is a importantvariable.

null hypothesis will be H0:a3=0

ii) x1 and x2 are correlated. i.e. these two regressors can beexpressed by each other.

i.e. there is a problem of multicollinearity involved in thedata,so that assumption is violated in this case.

null hypothesis will be H0:cov(x1,x2)=0

iii)Ui is correlated with its own past values. that means Ui’sare not independent .

i.e. there is a problem of auto correlation in the data. thatassumption is violated.

null hypothesis will be H0:cov(ui,uj)=0,for all i ≠k

iv) E(ut)=1

but we know mean value of residual should be 0; that assumptionis violated here.

null hypothesis will be H0:E(ut)=0,

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