Help me solve the followings. Show your work step-by-step .,,,

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Consider the instrumental variable regression model Yi = ?0 + ?1Xi + ?2Wi + ui where Zi is an instrument. Suppose that data on Wi are not available and the model is estimated omitting Wi from the regression (a) Suppose that Zi and Wi are uncorrelated. Is the IV estimator consistent? (b) Suppose that Zi and Wi are correlated. Is the IV estimator consistent?d. If Z, = X,, it will not be exogenous as X is correlated with the error term and thus it will violate the exogeneity of the instrument.3. Consider the general regression model given as below: Y, = Bo + B,X, + B,W, + u, Here, Wis the exogenous independent variable, X is an independent variable correlated with the error u, and Y is dependent variable. And, 's are the coefficients. If Z was used as an instrument but it is independent of X, Y, and W, then there will be no correlation between Z and X, which makes Z an irrelevant variable.b. If Z, = W , it means that Z is not a valid instrument. Then, the first stage regression should be written as below: A Xi = not MW Here, , are the estimations used for estimating the X variable. This means the estimated X variable y will be perfectly correlated or collinear with W. Thus, making the regression equation: Y, = Bo + B, Xi + B,W, + u, This above equation is perfectly collinear with W. It can also be said alternatively that the first stage regression is suffering from perfect multicollinearity.Consider the short-run equilibrium in a closed economy. Desired consumption is Cd = 2000 + 0.9 Y - 100,000r - 7, and desired investment is /d = 1000 - 45,000r. Real money demand is Mad/P = Y - 6000i. Other variables are we = 0.03, G= 500, M =700, and P=1. The government does not run a balanced budget. How much should taxes 7 be in order to obtain Y = 1006