Anonymous
timer Asked: May 5th, 2020

Question Description

I want to get it done quickly and get it right 85 percent of the time。

For Q3, part "d"

"OLS will produce unbiased estimates for the above"

It is referring to estimating the parameters of the equation:
P_i= exp(Z_i)/1+exp(Z_i)

For question 3a, you are required to write down just the name of the probability distribution.

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Please read and signed before you begin the exam. Pledge: “As a student of the University of Miami, I commit myself to being an active member in the Academic Community of Trust By promoting the values of Honesty, Responsibility, and Integrity.” Moreover, I pledge, on my honor, that I have neither given nor received assistance on this Exam, (in particular I pledge that I will not communicate (this includes emailing) with anyone after the exam about the material on this exam until the professor gives me permission to do so). Signed, _____________________________________ Please write the following on your exam “I acknowledge that I have read and understand the pledge” Then sign it. Exam1 Directions: This is a take-home exam. Students are NOT allowed to collaborate. There are 3 questions with various parts. Make sure you write your name as it appears on your ID so that you can receive the correct grade. The exam due date is Wednesday, May 6 at 11:30am any exam return after this deadline will not be accepted. Student must sign the Pledge and upload it as the …rst page on the answer sheet. Good luck! NAME: ID: Some de…nitions are: xi n x2 i=1 i Let ki = where xi = Xi X (where the Xi are non-stochastic or treated as …x in repeated samplings, so are the ki too). 1. n i=1 ki =0 2. n 2 i=1 ki = 3. n i=1 ki xi 1 n x2 i=1 i = n i=1 ki Xi =1 4. E(aX) = aE(X) where "a" is constant 5. V ar(X) = E(X 6. V ar( n i=1 Xi ) = E(X))2 n i=1 V ar(Xi ) for independent random variables 7. V ar(a) = 0 8. Cov(X; Y ) = E[(X E(X))(Y E(Y ))] = E(XY ) E(X)E(Y ) 9. In general the variance of the partial regression coe¢ cient is given as: var( b j ) = 2 2 i=1 xj (1 Rj2 ) Rj2 is the R2 derive from regressing Xj on all the remaining regressors ..................................................................................................................................................... 1 where 0.1 Questions You must explain and show all workings in order to get full credit for each question. The solutions to all the questions should include technique/s that were discussed in class lectures. Other techniques will be given zero credit. Q1. (20 points) Suppose we are given the structural models, Qdt = 1 + 2 Pt + u1t (1) Qst = 1 + 2 Pt + u2t (2) Note that the u1t and u2t are IID (0; 2 ), Qdt and Qst are quantities demand and supply, respectively. Assume that covariance between the errors is zero i.e. cov(u1t ; u2t ) = 0: a. Derive equilibrium price Pt (hint set Qdt = Qst = Q) b. Derive the covariance between Pt and u2t i.e. Cov(Pt ; u2t ) c. Suppose you estimate supply equation using OLS what are the properties of the estimators, please explain/justify your answer using one or two sentences? .......................................................................................................................... Q2.(40 points) You are given the following structural models: Y3t = 11 Y4t + 12 Y5t Y4t = 21 Y3t + 41 X5t + + 13 Y6t + X3t 42 X6t 2 + u4t 31 + X4t 32 + u3t (3) (4) Assume that the X 0 s are the only exogenous variables in the system. a. Explain and show which equation/s is/are: not identi…ed, exactly identi…ed or over-identi…ed. b. OLS will always yield consistent estimates of the the equation that is identi…ed, true/false please explain using one or two sentences. c. Write down the reduce form for the equation/s which is/are identi…ed. (you may write the reduce form parameters using 0 and 1 etc.) d. Explain how you would conduct 2SLS on one of the equation which is identi…ed, (1. you must explain and write out the …rst stage procedure, 2. you must explain and write out the second stage procedure and 3. you must explain why in the second stage the new error term is uncorrelated with the RHS variables). .............................................................................................. Q3. (40 points) The regression model is: Yi = 1 + 2 X2i + 3 X3i + 4 X4i + ui where ui is the random error with E(ui ) = 0; for i = 1; :::; n. Assume that the dependent variable (Yi = 0; 1) is a dummy variable which takes the values Yi = 1 represent a family that owns an car (2020 Ferrari) and Yi = 0 represents a family who does not own a car. a. What is the probability distribution of ui ? b. Find the variance of ui c. Assume that LPM/OLS is used to estimate the equation above leading to, Ybi = b 1 + b 2 X2i + b 3 X3i + b 4 X4i what do the estimates of b 1 and b 3 , respectively, represent, (what are the interpretations)? 3 d. Suppose that we assume that the probability (pi ) of owning a car is given by, pi = where zi = 1 + 2 X2i + 3 X3i + 1 exp(zi ) = 1 + exp( zi ) 1 + exp(zi ) 4 X4i . i. OLS will produce unbiased estimates for the above, true/false explain using one or two sentences. ii. Explain how one would proceed to the estimate the model (assume that pi 6= 0 or pi 6= 1). In the explanation, you must include (1.The econometric method/technique, 2. Write down the formula on how to compute the probabilities and explain it. 3. Write down the formula for the marginal e¤ects and explain it). END OF EXAM .............................................................................................................................................................................................. 4 ...
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