Econometrics Question: Consider the data generating process Y= β1+ β2Xi+β3Zi+β4Wi+β5Pi+β6Ti+e e~N(0, σ^2) i. Write the null hypothesis...

Econometrics Question:

Consider the data generating process

Y= β1+ β2Xi+β3Zi+β4Wi+β5Pi+β6Ti+e e~N(0, σ^2)

i. Write the null hypothesis H0: β4=5 and β2+β3=0 and 2β5-4β6=0 in Rβ-q notation.

ii. Discuss how would test these conjectures in practice assuming that the variance is known.

iv. Discuss how you would test the null-hypothesis Ho: β2/β3= β4 against Ha: β2/β3≠β4.

Expert Solution

Rahul Sunny answered 2 years ago

Consider 2 models: yi = β1 + β2xi + ei (1) Y = X0β + e;...

Consider 2 models: yi = β1 + β2xi + ei (1) Y = X0β + e; (2) where Equation (1) represents a system of n scalar equations for individuals i = 1; ...; n , and Equation (2) is a matrix representation of the same system. The vector Y is n x 1. The matrix X0 is n x 2 with the first column made up entirely of ones and the second column is x1; x2; ...; xn. a. Set...

lambda=c(.5,1,10);n=50;nboot=100 est=matrix(0,nboot,2) for(i in 1:3) { x=NULL;y=NULL;z=NULL x=rpois(n,lambda[i]) l1=mean(x) l2=log(n/length(x[x==0])) y = rpois(nnboot, l1);z=rpois(nnboot, l2) bootstrapsample1...

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