# ps9_sol - Department of Economics Columbia University...

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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 own-price 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 R-squared = 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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seas5 | -.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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## This note was uploaded on 02/05/2012 for the course ECON W3412 taught by Professor Seyhanarkonac during the Fall '11 term at Columbia College.

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ps9_sol - Department of Economics Columbia University...

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