120_spring08_pset2_solutions

120_spring08_pset2_solutions - ECO 120 Problem Set 2...

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ECO 120 Problem Set 2 Solutions Prof. Jon Robinson 1. malaria = b a 1 + b b 1 used + e 1 (1) To answer the second, we would run used = b a 2 + b b 2 given + e 2 (2) and to answer the third, we would run malaria = b a 3 + b b 3 given + e 3 (3) (b) Each equation will give an unbiased estimate if the independent variable is not cor- related with any important variables that have been omitted from the regression. In this case, since being given a net is completely random, equations (2) and (3) will be unbiased estimates of the e/ect of being given a net on the probability of using a net and on the probability of getting malaria, respectively. Equation (1) is likely to be biased, however. This is because actually using the net is a choice and so is non-random: people that use the nets are di/erent than people that don±t, so b b 1 is likely to be biased. More concretely, assume that we±re particularly worried that income is omitted from each equation. The true relationships of interest are malaria = b a 1 + b b 1 used + b c 1 income + e 1 used = b a 2 + b b 2 given + b c 2 income + e 2 1
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and malaria = b a 3 + b b 3 given + b c 3 income + e 3 The bias for Equation (1) is of the sign b c 1 corr ( income; used ) . We might expect that b c 1 6 = 0 (income might have an independent e/ect on the probability of getting malaria) and that corr ( income; used ) 6 = 0 (richer and poorer people might have di/erent rates of bednet usership), so this equation might be biased. However, the bias in Equation (2) is of the sign b c 2 corr ( income; given ) and the bias in Equation (3) is of the sign b c 3 corr ( income; given ) . Since the nets were given out randomly, corr ( income; given ) with the randomization). 4, and the last 2 come from Column 3. group percentage that had malaria control group 0 : 416 treatment group 0 : 416 ± 0 : 114 = 0 : 302 control group individuals that did use a net 0 : 407 + 0 : 077 = 0 : 484 control group individuals that did not use a net 0 : 407 treatment group individuals that did use a net 0 : 407 + 0 : 012 + 0 : 077 ± 0 : 347 = 0 : 149 treatment group individuals that did not use a net 0 : 407 + 0 : 012 = 0 : 419 all individuals that did use a net 0 : 411 ± 0 : 191 = 0 : 220 all individuals that did not use a net 0 : 411 2
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(d) The regression of interest is malaria = b a 3 + b b 3 given + e 3 (3) From this regression, b b 3 is the di/erence in the probability of getting malaria between
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This note was uploaded on 05/04/2008 for the course ECON 120 taught by Professor Robinson during the Spring '08 term at UCSC.

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120_spring08_pset2_solutions - ECO 120 Problem Set 2...

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