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
Answer:
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.
hereE(ut)=E(yt-a0+a1x1t+a2x2t)=E(yt)-a0+a1x1t+a2x2t=a0+a1x1t+a2x2t+a3x3t-(a0+a1x1t+a2x2t)=a3x3t
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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