ECON 628: Final (Take Home) Exam

Instructor: Thomas Lemieux

December 2nd 2005

 

INTRUCTIONS:

1.               Answer all four questions (total grade of 100).

2.               You have until Saturday December 3rd at 12:00 noon to complete your exam.

3.               There are three ways to hand in your exam:

a.      Slide it under the door of my office

b.     Send it by email to tlemieux@interchange.ubc.ca. 

c.      Hand it in to my personally on Friday (I will be in until about 5 pm) or Saturday (I will be at the entrance of Buchanan Tower between 11:30 am and 12:00 noon).

4.               If you hand in the exam using option a or b I will send you an email acknowledging that I have received it.  If you don’t receive the acknowledgement by 12:00 noon on Saturday contact me by email immediately.  

5.               Exams handed in after the 12:00 noon deadline will still be graded but expect a stiff grade penalty.  If you are late for whatever reason, please hand in your exam in the Economics main office and get it stamped so that I know when it was handed in when I come back.

6.               The same ethical standards are expected as for an in-class open book exam.  This means that you can consult and use any resources you want (papers, books, computer lab, web) but that all communications with your classmates of other individuals about the content of the exam are prohibited.

7.               I will be available for questions in my office from 1 pm to 5 pm on Friday.  I will also check my email regularly until Saturday at noon.

 

Question 1: (30 points)

 

In the second assignment, you were provided with several data sets from the Labour Force Survey to estimate a “wage curve” for Canada.  In this question, you now have to focus instead on the effect of unions (represented by a dummy variable in the data set) on log wages using data from the 2004 cross-section available at lfs04.raw . 

           

a.                Report OLS estimates of the effect of unions on log wages and test whether the estimated effect is significantly different from zero.  Are the results of the test affected by the way you compute the standard errors?

b.               Report estimates of the effect of unions on log wages using two alternative estimation procedures of your choice.  These estimation procedures can either be procedures we discussed in class or other procedures available in the literature.

c.                Briefly discuss why you think that the results turn out to be different (or not different) using the three different estimation methods. 

 

 

 

 

Question 2: (25 points)

 

In the third assignment, you had to estimate the propensity score using PSID-1 as the non-experimental control group.  Let’s now see what happens when we use the experimental control group instead.  In other words, estimate the same logit or probit model using a) the PSID-1 and b) the experiment control group as alternative control groups, and then answer the following questions:

 

a.                Compare the estimates logit or probit coefficients in the two cases, focusing on whether coefficients tend to be statistically different from zero. 

b.               Someone tells you that a joint test that the coefficients in the model for the propensity score are all equal to zero is equivalent to a test of random assignment.  Do you agree with this claim? Why? [You will a higher mark the more formally you manage to illustrate your point] What is the result of such a test in the Lalonde data?

c.                The same person that you that when the test fails, this means that there is a selection bias and that you need to estimate a Heckman selection model.  Do you agree? Explain.

 

Question 3: (25 points)

 

Consider the abstract of the paper “Estimating Average and Local Average Treatment Effects When Compulsory Schooling Laws Really Matter” by Phil Oreopoulos that is now forthcoming in the American Economic Review:

 

The change to the minimum school-leaving age in the UK from 14 to 15 had a powerful and immediate effect that redirected almost half the population of 14 year olds in the mid-20th century to stay in school for one more year. The magnitude of this impact provides a rare opportunity to 1) estimate local average treatment effects (LATE) of high school that come close to population average treatment effects (ATE) and 2) estimate returns to education using a regression discontinuity design instead of previous estimates that rely on difference in differences methodology or relatively weak instruments. Comparing LATE estimates for the U.S. and Canada, where very few students were affected by compulsory school laws, to the UK estimates provides a test to whether IV returns to schooling often exceed OLS because gains are high only for small and peculiar groups among the more general population. I find instead that the gains from compulsory schooling are very large – between 10 and 14 percent – whether these laws impact a majority or minority of those exposed.

 

As a reference, the full version of the paper is available at

 

http://www.economics.utoronto.ca/oreo/research/ATE_LATE/average%20treatment%20effects%20of%20education%20June%2005.pdf

 

The two key points in this abstract seem to imply that 1) it is more desirable to get an ATE than a LATE, and 2) a regression discontinuity design is more “credible” that typical IV estimates.  These two observations raise a number of interesting issues that also apply to other studies we have covered in class.  Discuss these issues by answering the following questions

 

  1. What would it take to literally get the ATE in Oreopoulos setting (for the UK)? In other words, what would the distribution of school leaving age have to be before and after compulsory schooling increased?
  2.  Should we think of the main estimates in Angrist (1990) as ATE or LATE estimates of the impact of military service on earnings? List two scenarios under which Angrist’s Wald estimates (or corresponding regression models that also adjust for other characteristics) would literally yield the ATE.
  3. How could one estimate the effect of social assistance of Lemieux and Milligan (2005) using an IV or difference-in-difference approach instead of a regression discontinuity approach?  Do you think that, as in Oreopoulos, the regression discontinuity estimates are more “credible” than these alternative estimates?

Question 4: (20 points)

 

One of the most influential difference-in-differences study was a paper on employment effects of the minimum wage by Card and Krueger published in the American Economic Review in 1994.  The study compares the evolution of employment in fast-food restaurants in the state of New Jersey where the (state) minimum wage increased in April 1992 to the evolution of employment in fast-food restaurants in Pennsylvania where the minimum wage did not change.  Pennsylvania is arguably a good “control” for New Jersey as the two states share a common, and densely populated border.  Note also that the minimum wage went up form $4.25 to $5.05 in New Jersey while remaining constant at $4.25 in Pennsylvania.

 

Comparing employment before and after the increase in the minimum wage, Card and Krueger reached the controversial conclusion that the minimum wage had no adverse effect on employment.  If anything, it even appears that the increase in the minimum wage in New Jersey increased employment.

 

In the paper, they report the following mean employment (per store)

 

                                    New Jersey     Pennsylvania

Before change             20.4                 23.3    

(early 1992)                (.51)                (1.35)

 

After change                21.0                 21.2

(late 1992)                  (.52)                (.94)

 

where the numbers in parenthesis are the standard errors. 

 

a.                Compute the difference-in-difference estimate of the effect of minimum wage on employment using the number above.

b.               Under some specific assumptions, the standard errors above provide all the necessary information to compute the standard error of the difference-in-differences estimate.  State what these assumptions are and compute the standard error of the difference-in-difference estimate accordingly.

c.                Discuss why the assumptions you used in b. are not likely to hold in a case like the one considered by Card and Krueger.  Briefly explain the step you would go through to get correct standard errors if you were give access to the Card and Krueger data.