This week, we’re going think about selection bias and exogeneity in study design. We’ll also continue our discussion of the connection between economic theory and empirics!
Selection bias: Bias introduced when individuals in the groups being studied differ systematically. For example, exit polls in the week of November 3rd suffered from selection bias: the respondents were systematically more likely to have voted in person and, consequently, have been supporters of President Trump.
Exogeneity: A change which comes from outside the system being studied. For example, bad weather in Colorado (where the weather is notoriously unpredictable) on November 3rd could have exogenously depressed in-person turnout. While this change might disproportionately impact certain voting subgroups, the weather was not caused by people’s choices of when and how to vote.
Discuss the following questions as a group. Professor Rao will visit each group to help clarify any questions you may have.
Each of you will be selected randomly, without replacement, to share your thoughts/questions from your small-group discussions for (up to) 1.5 minutes. You can use your time to share your thoughts and questions, respond to others, or both.
When your time is up, the alert will flash and Professor Rao will say it’s time to move on. You can skip your turn if you’d like by saying “skip”, and you can also finish early if you’d like.
You’ll each choose to read sections of a different article from the following set:
Card 1991, The Mariel Boatlift and the Miami Labor Market : Another highly-impactful David Card paper. Read the introduction, “Overview of the Miami Labor Market Before the Boatlift”, “Interpretation of the Findings”, and “Conclusions”. Look over Tables 3-7 and match what you see there against the interpretation Card gives. Skim the bits you don’t follow and make notes on your questions.
Shierholz 2010, Immigration and Wages : A more recent summary of what we’ve learned about immigration and wages study design. Read carefully the Executive summary, the Introduction, the first 6 paragraphs of “A brief look at the recent advancements in the research” (up to the paragraph ending “…the wages of dispatchers).”), and then the conclusion. Where tables are referenced, look over them and match what you see there against the interpretation Shierholz gives. Skim the bits you don’t follow and make notes on your questions.
Make sure each article gets read.
\[ wages_i = \alpha + \beta immigration_i + \epsilon_i \] where \(i\) represents different counties. What would this bias do to the estimate of \(\beta\) and why?
What kind of exogenous variation does Card use to overcome selection issues? How does Card know/argue this variation is in fact exogenous?
Card focuses on the effect of the Mariel Boatlift on Cubans and non-Cubans. Why is this distinction meaningful for this study?
Shierholz focuses on the long-run effect of immigration on wages. What is the key economic assumption she needs to make?
What are the relative advantages and disadvantages of studying the effect of immigration on native-born workers’ wages in a narrow place and time (the area approach) vs studying it nationally over a potentially larger time horizon (the national approach)? Focus your answer on selection issues—ignore sample size for now.
How could you make sense of the findings Card and Shierholz present using economic theory?
How would you measure how much elasticities of substitution matter here? What kinds of issues would you worry about?