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Department of Economics
W3412
Columbia University
Spring 2010
SOLUTION TO
Problem Set 9
Introduction to Econometrics
Prof. Marcelo J. Moreira and Seyhan E Arkonac, PhD
for all sections
Spring 2010
Question I:
SW Exercise 13.5 (page 512)
(a) This is an example of attrition, which poses a threat to internal validity. After the male
athletes leave the experiment, the remaining subjects are representative of a population that
excludes male athletes. If the average causal effect for this population is the same as the average
causal effect for the population that includes the male athletes, then the attrition does not affect
the internal validity of the experiment. On the other hand, if the average causal effect for male
athletes differs from the rest of population, internal validity has been compromised.
(b) This is an example of partial compliance which is a threat to internal validity. The local area network
is a failure to follow treatment protocol, and this leads to bias in the OLS estimator of the average causal
effect.
(c) This poses no threat to internal validity. As stated, the study is focused on the effect of dorm room
Internet connections. The treatment is making the connections available in the room; the treatment is not
the use of the Internet. Thus, the art majors received the treatment (although they chose not to use the
Internet).
(d) As in part (b) this is an example of partial compliance. Failure to follow treatment protocol leads to
bias in the OLS estimator.
Question II:
1.
Estimate the ownprice elasticity of demand by using OLS to regress the log of the quantity of
grain shipped on the log of the price of shipping grain and the full set of month binary
indicators.
. reg lquantity lprice $months, r;
Regression with robust standard errors
Number of obs =
328
F( 13,
314) =
11.42
Prob > F
=
0.0000
Rsquared
=
0.2819
Root MSE
=
.40542


Robust
lquantity 
Coef.
Std. Err.
t
P>t
[95% Conf. Interval]
+
lprice 
.6620433
.0754213
8.78
0.000
.8104383
.5136484
seas1 
.0955314
.0901446
1.06
0.290
.2728952
.0818324
seas2 
.1064381
.0844977
1.26
0.209
.0598151
.2726913
seas3 
.1510242
.0916339
1.65
0.100
.0292699
.3313182
seas4 
.1286241
.1236321
1.04
0.299
.1146279
.3718761
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View Full Documentseas5 
.1166274
.1206273
0.97
0.334
.3539673
.1207125
seas6 
.3666743
.0978573
3.75
0.000
.5592132
.1741354
seas7 
.2919127
.1338223
2.18
0.030
.5552145
.0286108
seas8 
.6490938
.095055
6.83
0.000
.8361191
.4620685
seas9 
.4108652
.0904551
4.54
0.000
.5888399
.2328905
seas10 
.2473659
.0898223
2.75
0.006
.4240957
.0706362
seas11 
.1993899
.0906922
2.20
0.029
.3778311
.0209488
seas12 
.1926615
.0870309
2.21
0.028
.3638989
.021424
_cons 
9.2401
.1172646
78.80
0.000
9.009376
9.470823

a.
What is the estimated demand elasticity and its standard error?
The estimated demand elasticity is the coefficient on
lprice
, which is .662 (
SE
= .075)
b.
Explain why the interaction of supply and demand plausibly makes this estimator of
the elasticity biased.
Price and quantity are simultaneously determined by the interaction of supply and demand, so
that there is simultaneous causality bias.
As depicted in SW Fig. 12.1, if there are shifts in the
demand curve then the points resulting from the intersection of supply and demand will not trace
out the demand curve, and in general neither the demand nor supply elasticity are estimated
consistently by OLS.
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 Fall '11
 SeyhanArkonac
 Econometrics

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