The four estimation methods yielded the following results given in Table 1. Heteroskedasticity robust standard errors

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

This part of the test asks a series of questions about the relationship between dthrte, tra¢c death rates (number of tra¢c deaths per million miles driven), unem, unemployment rates, and admn, a dummy variable that equals 1 if a State in a given year has administrative laws such as driver licenses can be suspended for drunk driving. Data was gathered for these variables for the 48 contiguous States of the United States (Hawaii, Alaska and Washington D.C. are not included) for the years 1980 and 2004. The average death rate across all states was 3.55 in 1980 and was 1.51 in 2004.

Suppose we are interested in the following regression relationship

dthrteit = β0 + δ0d2t + β1admnit + β2unemit + ai + uit,

where t = 1 is 1980 and t = 2 is 2004. The variable d2t is a dummy variable that equals 1 if t = 2 (2004). The total error depends on the State specific heterogeneity, ai, and an idiosyncratic error, uit. We would expect ai to be correlated with admnit because states with higher than normal tra¢c death rates may be under pressure to pass drunk driving laws. You can assume that uit is not correlated with admnit and unemit.

Consider four options for estimating the parameters β1 and β2. For the first two options we estimate separate regressions for 1980 (t = 1) and 2004 (t = 2) using OLS:

dthrtei1 = β0 + β1admni1 + β2unemi1 + ai + ui1, dthrtei2 = α0 + β1admni2 + β2unemi2 + ai + ui2.

For the third option we can pool the data from both years and estimate the panel model

dthrteit = β0 + δ0d2t + β1admnit + β2unemit + ai + uit,

using OLS (i.e. the Pooled-OLS estimators). Finally, we can apply the first di§erence transforma- tion to the panel model and estimate the transformed model

∆dthrtei = δ0 + β1∆admni + β2∆unemi + ∆ui.

by OLS (i.e. the First-Di§erences estimators).

a) What are the interpretations of the δ0, β1 and β2 parameters? (6 points) If you used First- Di§erences to estimate these parameters, would this change the interpretation? Why or why not? (2 points)

The four estimation methods yielded the following results given in Table 1. Heteroskedasticity robust standard errors are given in parentheses.

Table 1: Estimates for Death Rate Model Using the Years 1980 and 2004 

βb1  (admn). 

1.56

βb2  (unem) -.070

bδ0 (d2) NA

b) Provide an explanation for why the estimates of β1 are so di§erent across the four estimation methods. (6 points)

c) Which estimator of β1 do you prefer and why?  (4  points) Is your preferred estimator of β1 statistically significant at the 10% level? Why or why not? (2 points) Is it practically significant? Why or why not? (2 points)

d) Using the First Diferences estimator, test the null hypothesis that mean tra¢c death rates did NOT fall from 1980 to 2004 (holding admn and unemp constant) against the hypothesis that mean tra¢c death rates did fall.  Write down the null and alternative hypotheses in terms of the relevant parameter and carry out your test at the 5% level.  (6  points) What do you conclude? (1 point)

e) From the Table we see that First Di§erences is based on only one year’s worth of data (obs = 48). Someone suggests that Fixed-E§ects is a better estimation option than First Di§erences because there is unlikely to be much, if any, correlation between uit at years 1980 and 2004 because shocks to tra¢c death do not last for 25 years. Suppose it is true that ui1 (1980) is uncorrelated with ui2 (2004). Can Fixed-E§ects be better than First Di§erences? Why or why not? (6 points)

An intern was hired to collect data for all the years between 1980 and 2004 increasing the sample size of the panel from 96 to 1,200 observations. We now have T = 25 rather than T = 2. The model of interest is the same except that dummy variables are included for the additional time periods:

dthrteit = β0 + δ2d2t + δ3d3t + ... + δ25d25t + β1admnit + β2unemit + ai + uit, (1)

Model (1) was estimated using Pooled-OLS, First Di§erences, Fixed-E§ects and Random E§ects. The results are in given in the following table.  Time dummy parameter estimates are only reported for  every  5th  year.  The  estimated  value  of  θ used  for  the  random  e§ects  transformation  was θ = .749. All standard errors are robust to heteroskedasticity and correlation across time (serial correlation).

Table 2: Estimates for Death Rate Model Using the Years 1980 through 2004

f) Assuming that cov(admnit, ai) = 0, which estimation methods of model (1) could be LUE? Why? (3 points) Which estimation methods are biased? Why? (3 points)

g) For each of the potentially LUE estimators, under what assumptions will that estimator be BLUE? (4 points)

h) The Pooled-OLS estimator of β1 has the opposite sign as the First-Di§erence and Fixed- E§ects estimators. Provide a theoretical explanation for this fact. (4 points) The Random E§ects estimator of β1 is very similar to Fixed-E§ects. Are you surprised by this? Why or why not? (2 points)

i) Calculate 95% confidence intervals for β1 using the First Di§erence and Fixed-E§ects esti- mators. (4 points) Can you reject the null hypothesis that β1 = 0 with either confidence interval? (2 points) Which estimator would you use for measuring the impact of adminis- trative laws on tra¢c death rates? Why? (2 points)

j) Go back to Table 1 that only uses the 1980 and 2004 data and compute a 95% confidence interval for β1 using the First Di§erence estimator. (2 points) You should find that this confidence interval is substantially wider than the confidence intervals using all the data from 1980 to 2004. What accounts for this di§erence in confidence interval widths? (2 points) What do you conclude about using just the 1980 and 2004 data compared to using all the years from 1980 to 2004? (2 points)

k) Using the First Di§erences estimator from Table 2 (all years from 1980 to 2004), test the null hypothesis that mean tra¢c death rates did NOT fall from 1980 to 2004 (holding admn and unemp constant) against the hypothesis that mean tra¢c death rates did fall. Write down the null and alternative hypotheses in terms of the relevant parameter and carry out your test at the 5% level. (2 points) How do your results compare to what you found in part (d)? (2 points) Provide an explanation for any di§erences you see. (2 points)

l) Using the Fixed-E§ects estimated parameters, holding admn and unem constant, over what 5 year period did tra¢c death rates fall more:  1984 to 1989, 1989 to 1994, 1994 to 1999, or 1999 to 2004? Provide details on your calculations. (4 points)

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