Quiz 4 - Lahore School of Economics MPHIL Advanced...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lahore School of Economics MPHIL Advanced Econometrics Winter 2011 Quiz 4 Question 1. Suppose that you have a simple Vector Autoregression (VAR) of the form: I"? : bl!) * Efizz: +l’113’t—1 +l’123r—1 + 53x (1‘) Z: : E32o — 3321}? + MHz-71 “I” “Peggy—1 + £2: (2) which can also be written in matrix form as: 1 2 3"; __ 1V ii“ 2 7 €393": i i {a — [a a M 1 M 3 1HE J m i”: 1 he 5:71 z? 1 (312 Suppose that B: [ and that {331 = {J 3’} (A) Calculate 8'1 and use this to solve e nation 3 for C1 Zr . (10 points) (B) Suppose that you wanted to estimate the system of equations represented by equations (1) and (2) using OLS. In order to do this, you estimate the equation: 3:": = 5516 + ems—1 t flizzr-i + ’31: (4) 3r I 5520 + flzil’t—i '+ 55:23:71 + 532: (5) Using your answers to part (A) express am an and £122 in terms of b’s and y’s. (10 points) (C) Identification of the VAR above required the restriction that 332.1 = 0. How many restrictions would you require if you had a simple VAR with four variables, y, 2t, Wt and q; (instead of just yt and 2t which is the case above)? (5 points) (D) Suppose that you estimated the OLS and obtained the following equation: 33: : 32311371 + O-gztwl + 91: (6) Z: Z 3-8314 + 0232—1 + 92: (7) Draw the impulse response function of ya in response to a one unit shock in en and em. (10 points) MPHIL Advanced Econometrics - Winter 20] 1 — Quiz 4 1 Question 2. (A) Explain what an autocorrelation function (ACE) or correlogram is. Below are three ACFS (labeled (i)j (ii) and (iii)). Explain which of these ACES may be a white noise process, which one may be a stationary process and which one may be a non-stationary process. Make sure to give a explanation for each one of your answers. (10 points) (i) (ii) (iii) E m i E g . 6 ms unnm nuumum \HUWUI Whitman rucllwmm - Lag»; ' (B) Explain what a partial autocorrelation function (PACF) is. Below are three PACFs (labeled (i), (ii) and (iii)). Explain which of these PACFS may be a white noise process, which one may be a stationary process and which one may be a non—stationary process. Make sure to give a explanation for each one of your answers. (10 points) (i) (ii) (iii) Hi} Emmmw........._... Gris? figflifiéfifilffilifié: fiat dimmer.ng neefiiffi . 7WWWWW; \ mocmra'cl'ii €4er 0w régaifiwaug‘ek‘e E E'm'iuu \ Ill nwn'rc-Im run I m‘liu Ti‘iH< i‘rn'lmé Lugs A ..3 . . . . . . MPHIL Advanced Econometrics ~ Winter 2011 - Quiz 4 2 Question 3. [PLEASE NOTE THAT THIS IS AN EXTENSION OF A QUESTION THAT YOU HAVE ATTEMPTED PREVIOUSLY] This question revolves around an experiment run in Minnesota to try and examine the efficacy of various police responses to domestic violence calls. Essentially, when police respond to a call they have some leeway in what they do they can arrest the offender, take the offender away for a cooling off period, or attempt to talk sense into the offender. But which is best? The experimental setup involved randomly assigning one of these three responses when called to a domestic violence situation. The randomization was undertaken using color—coded notepads. Officers used this to determine the response. The outcome variable of interest was a binary variable, simply whether or not they were called again to the same problem later. So an outcome of zero is good (no return call), one not so good. The regression to determine the effect was: : ii: r 1311':- r if: — i135- Wi; + fr if}: t 8r:- where X n = l for taking away for a cooling off period (zero otherwise), ng : l for talking to the offender (zero otherwise), W“ : 1 if there was a gun involved, and “bi = 1 if there was evidence of substance abuse (both zero otherwise). (Note that although the Y variable is a zero-one variable, we do not need to use binary dependent variable methods since all the right hand side variables are also binary, there are no functional form issues in this very special case). (A) Explain how the randomization in the experimental setup helps ensure that the OLS estimates for B] and B; are unbiased. Give a reason why it is useful to include the additional variables W“, ng. Is there a problem if we omit them? Why is there no variable for the cases where the officers arrest the perpetrator? (5 points) (B) It turns out that the police did not always do what the color—coded pad suggested W110 surprise since it would be quite unethical to give a “good talking to” to someone who appeared very likely to commit an act of violence. This means that we have data on both the treatment assigned (dummy variables Z” and Zgi, which are dummies for assigning a cooling off period or a talking to respectively) and the actual treatment given (KM and Xzi as above). Why does this lead to a bias in the OLS estimates for BI and [52. (5 points) (C) Suppose that officers always made an arrest when it appeared to them that violence was likely regardless of the random assignment. In what direction do you think the bias in the OLS estimates would be? (5 points) (D) The actual random assignments (Zn , Zgj) could be used as instruments to estimate the regression using two—stage least squares. Do these variables make for good instruments? Why or why not? (5 points) (E) Explain the two OLS regressions that would need to be run to obtain the two—stage least squares estimates for B] and fig. (10 points) MPHIL Advanced Econometrics — Winter 201 l — Quiz 4 3 Question 4. Consider the ARCHG) process: Effigy; : 5.50 + (alga-£1 + 91355;: + 5235513 (A) Suppose the residuals come from the model )6; : a9 + aljxtfl -l— 3;. Find the unconditional variance of yt in terms of (11, 0:3, 5:1, azand a3. (5 points) (B) Suppose that y is an ARCH—M process such that the level of yI is positively related to its owu conditional variance. For simplicity let: E¥3+ 5: 3’; ~ :20 + 6:15:24 + 9:38:32 + £2.35 Trace out the impulse response function ofyt to an a; shock. You may assume that the system has been in long run equilibrium (€3_3=Ef_ 1:0) but now 51 = 1.. Thus the issue is to find the values of y]. y2_,y3_,y4 and y5 given that 53:53:. . . =0. (10 points) MPHIL Advanced Econometrics — Winter 20'] 1 « Quiz 4 ...
View Full Document

This note was uploaded on 03/23/2012 for the course ECON 201 taught by Professor Cowell during the Spring '10 term at LSE.

Page1 / 4

Quiz 4 - Lahore School of Economics MPHIL Advanced...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online