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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}? + MHz71 “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 ﬂizzri + ’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 + Ogztwl + 91: (6)
Z: Z 38314 + 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 nonstationary 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'rcIm 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 zeroone 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 ...
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This note was uploaded on 03/23/2012 for the course ECON 201 taught by Professor Cowell during the Spring '10 term at LSE.
 Spring '10
 Cowell

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