Applied Econometrics

━━HW3

徐韧锋 Xu Renfeng
UID:2012970544

E10.2 a [pic]

For the coefficient on the sb_useage term,t=3.30, p-value=0.001, which is smaller than 5%, we can reject the null hypothesis. The estimated coefficient on seat belt useage is positive and statistically significant. One the face of it, this suggests that seat belt useage leads to an increase in the fatality rate.

b.

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The results change. The coefficient on seat belt useage is now negative and the coefficient is statistically significant. The estimated value of .. βsb_useage is.0.00577, so that a 10% increase in seat belt useage (so that sb_useage increases by 0.10) is estimated to lower the fatality rate by .000577 fatalities per million traffic miles. States with more dangerous drving conditions (and a higher fatality rate) also have more people wearing seat belts. Thus (1) suffers from omitted variable bias.

c.

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The results change. The coefficient on seat belt useage is now negative and the coefficient is statistically significant. The estimated value of βsb_useage=-0.0037

d.

The time effects are statistically significant .. the F-statistic .. 10.91 with a p-value of 0.00.
The results in (3) are the most reliable.

e.

A 38% increase in seat belt useage from 0.52 to 0.90 is estimated to lower the fatality rate by
0.00372* 0.38= 0.0014 fatalities per million traffic miles. The average number of traffic miles per year per state in the sample is 41,447. For a state with the average number of traffic miles, the number of fatalities prevented is 0.0014 *41,447 =58 fatalities.

f.

sb_useage= 0.206 * primary + 0.109 *secondary + (speed65, speed70, ba08, drinkage21, ln(income), age, time effects, state effects) where the coefficients on the other regressors are not reported to save space. The coefficients on primary and secondary are positive and significant. Primary enforcement is estimated to increase seat belt useage by 20.6% and secondary enforcement is estimated to increase seat belt useage by
10.9%.

g.

This results in an estimated increase in seatbelt useage of 0.206-0.109 =0.094 or 9.4% from (f).
This is predicted to reduce the fatality rate by 0.00372 * 0.094 = 0.00035 fatalities per million traffic miles. The data set shows that there were 63,000 million traffic miles in 1997 in New
Jersey, the last year for which data is available. Assuming the same number of traffic miles in
2000 yields 0.00035 * 63,000 = 22 lives saved.

E11.1
a.
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Estimated probability of smoking (mean of smoker)

All Workers P- 0.242 SE-0.004
No Smoking Ban P-0.290 SE- 0.007
Smoking Ban P- 0.212 SE-0.005

b.

From model (1), the difference in ..0.078 we a standard error of 0.009. The resulting t-statistic is ..8.66, so the coefficient is statistically significant.

c.

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From model (2) the estimated difference is ..0.047, smaller than the effect in model (1).
Evidently (1) suffers from omitted variable bias in (1). That is, smkban may be correlated with the education/race/gender indicators or with age. For example, workers with a college degree are more likely to work in an office with a smoking ban than high-school dropouts, and college graduates are less likely to smoke than high-school dropouts.

d.

The t-statistic is ..5.27, so the coefficient is statistically significant at the 1% level.

e.

The F-statistic has a p-value of 0.00, so the coefficients are significant. The omitted education status is “Masters degree or higher”. Thus the coefficients show the increase in probability relative to someone with a postgraduate degree. For example, the coefficient on Colgrad is 0.045, so the probability of smoking for a college graduate is 0.045 (4.5%) higher than for someone with a postgraduate degree. Similarly, the coefficient on HSdrop is 0.323, so the probability of smoking for a college graduate is 0.323 (32.3%) higher than for someone with a postgraduate degree. Because the coefficients are all positive and get smaller as educational attainment increases, the probability of smoking falls as educational attainment increases.

f.

The coefficient on age1(age*age) is statistically significant. This suggests a nonlinear relationship between age and the probability of smoking. The figure below shows the estimated probability for a white, non-Hispanic male college graduate with no workplace smoking ban.

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E11.2
a.

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b.

The t-statistic is -5.47, very similar to the value for the linear probability model.

c.

The F-statistic is significant at the 1% level, as in the linear probability model.

d.

To calculate the probabilities, take the estimation results from the probit model to calculate z and calculate the cumulative standard normal distribution at z i.e., Prob(smoke) =φ(z). The probability of Mr. A smoking without the workplace ban is 0.464 and the probability of smoking with the workplace bans is 0.401. Therefore the workplace bans would reduce the probability of smoking by 0.063 (6.3%).
e.

To calculate the probabilities, take the estimation results from the probit model to calculate z and calculate the cumulative standard normal distribution at z i.e., Prob(smoke) =φ(z). The probability of Ms. B smoking without the workplace ban is 0.143 and the probability of smoking with the workplace ban is 0.110. Therefore the workplace bans would reduce the probability of smoking by .033 (3.3%).

f.

For Mr. A, the probability of smoking without the workplace ban is 0.449 and the probability of smoking with the workplace ban is 0.402. Therefore the workplace ban would have a considerable impact on the probability that Mr. A would smoke. For Ms. B, the probability of smoking without the workplace ban is 0.145 and the probability of smoking with the workplace ban is 0.098. In both cases the probability of smoking declines by 0.047 or 4.7%.

g.

The linear probability model assumes that the marginal impact of workplace smoking bans on the probability of an individual smoking is not dependent on the other characteristics of the individual. On the other hand, the probit model’s predicted marginal impact of workplace smoking bans on the probability of smoking depends on individual characteristics. Therefore, in the linear probability model, the marginal impact of workplace smoking bans is the same for
Mr. A and Mr. B, although their profiles would suggest that Mr. A has a higher probability of smoking based on his characteristics. Looking at the probit model’s results, the marginal impact of workplace smoking bans on the odds of smoking are different for Mr. A and Ms. B, because their different characteristics are incorporated into the impact of the laws on the probability of smoking. In this sense the probit model is likely more appropriate.
Are the impacts of workplace smoking bans “large” in a real-world sense? Most people might believe the impacts are large. For example, in (d) the reduction on the probability is 6.3%.
Applied to a large number of people, this translates into a 6.3% reduction in the number of people smoking.

h.

An important concern is two-way causality. Do smokers seek employment with employers that do not have a smoking ban?