Question

In: Economics

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.

Solutions

Expert Solution


Related Solutions

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(n*nboot, l1);z=rpois(n*nboot, l2) bootstrapsample1...
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(n*nboot, l1);z=rpois(n*nboot, l2) bootstrapsample1 = matrix(y, nrow=nboot, ncol=n) bootstrapsample2 = matrix(z, nrow=nboot, ncol=n) for(j in 1:nboot) { est[j,1]=mean(bootstrapsample1[j,]) est[j,2]=log(length(bootstrapsample1[j,][bootstrapsample1[j,]>0])) } }
2. Consider the stochastic process {Xn|n ≥ 0}given by X0 = 1, Xn+1 = I{Xn =...
2. Consider the stochastic process {Xn|n ≥ 0}given by X0 = 1, Xn+1 = I{Xn = 1}Un+1 + I{Xn 6= 1}Vn+1, n ≥ 0, where {(Un, Vn)|n ≥ 1} is an i.i.d. sequence of random variables such that Un is independent of Vn for each n ≥ 1 and U1−1 is Bernoulli(p) and V1−1 is Bernoulli(q) random variables. Show that {Xn|n ≥ 1} is a Markov chain and find its transition matrix. Also find P{Xn = 2}.
Consider the model: yi = βxi + ei, i = 1,...,n where E(ei) = 0 and...
Consider the model: yi = βxi + ei, i = 1,...,n where E(ei) = 0 and Variance(ei) = σ2 and ei(s) are non-correlated errors. a) Obtain the minimum-square estimator for β and propose an unbiased estimator for σ2. b) Specify the approximate distribution of the β estimator. c) Specify an approximate confidence interval for the parameter β with confidence coefficient γ, 0 < γ < 1.
Write PYTHON CODE to answer the following question: Consider the following data: x = [0, 2,...
Write PYTHON CODE to answer the following question: Consider the following data: x = [0, 2, 4, 6, 9, 11, 12, 15, 17, 19] y = [5, 6, 7, 6, 9, 8, 8, 10, 12, 12] Using Python, use least-squares regression to fit a straight line to the given data. Along with the slope and intercept, compute the standard error of the estimate and the correlation coefficient. Best fit equation y = ___ + ___ x Standard error, Sy/x =...
Consider the following ARMA(1,1) process (1 − 0.3B)Xt = (1 − 0.2B)Zt where{Zi}∼WN(0,σ^2)withE(Z1)=0andVar(Z1)=σ^2 <∞. (i) Discuss...
Consider the following ARMA(1,1) process (1 − 0.3B)Xt = (1 − 0.2B)Zt where{Zi}∼WN(0,σ^2)withE(Z1)=0andVar(Z1)=σ^2 <∞. (i) Discuss if the process has a causal stationary solution. (ii) Find an MA(∞) representation for Xt. (iii) Find the autocorrelation function for the process {Xt}.
Data Structure: 1. Write a program for f(n) = 1^2+2^3+…+n^2. (i^2 = i*i) 2. If you...
Data Structure: 1. Write a program for f(n) = 1^2+2^3+…+n^2. (i^2 = i*i) 2. If you have the following polynomial function f(n)=a0 +a1 x + a2x2+…+an xn , then you are asked to write a program for that, how do you do? 3. Write a function in C++ to sort array A[]. (You can assume that you have 10 elements in the array.) 4. Analyze the following program, tell us what does it do for each location of “???” (...
Use the data set below to answer the question. x −2 −1 0 1 2 y...
Use the data set below to answer the question. x −2 −1 0 1 2 y 2 2 4 5 5 Find a 90% prediction interval for some value of y to be observed in the future when x = −1. (Round your answers to three decimal places.)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT