ECON 3039 Labor Economics By Elliott Fan Economics, NTU Elliott Fan: Labor 2015 Fall Lecture 61

A little jumpy here 2Elliott Fan: Labor 2015 Fall Lecture 6

A little jumpy here 3Elliott Fan: Labor 2015 Fall Lecture 6 Mortality risk shoots up on and immediately following a twenty-first birthday This spike adds about 100 deaths to a baseline level of about 150 per day. The age-21 spike doesn’t seem to be a generic party-hardy birthday effect. If this spike reflects birthday partying alone, we should expect to see deaths shoot up after the twentieth and twenty-second birthdays as well, but that doesn’t happen. There’s something special about the twenty-first birthday.

A little jumpy here 4Elliott Fan: Labor 2015 Fall Lecture 6

Define the terms 5Elliott Fan: Labor 2015 Fall Lecture 6 Forcing variable (or running variable): age Cutoff point: the 21 st birthday Treatment variable: legal privilege for drinking alcohol Outcome variable: mortality rate

Jumpy here and there -- examples 6Elliott Fan: Labor 2015 Fall Lecture 6

Jumpy here and there -- examples 7Elliott Fan: Labor 2015 Fall Lecture 6

Jumpy here and there -- examples 8Elliott Fan: Labor 2015 Fall Lecture 6

What can we do to use the jump? 9Elliott Fan: Labor 2015 Fall Lecture 6 Recall that removing selection bias demands random assignment of the treatment Observations just on the right of the cutoff point and those just on the left of the cutoff point are very similar except for for the likelihood of treatment taking up So the key requirement is that people cannot precisely control the exact position along the forcing variable around the cutoff point But there are different degree of “control”

Methodologies – the RD design The RD design utilizes the randomness from incomplete manipulation of a characteristic around the threshold point for the treatment. From Lee and Lemieux (2009): Elliott Fan: RDPEE Lecture 1110

Sharp RD 11Elliott Fan: Labor 2015 Fall Lecture 6 Go back to the case of legal access to alcohol on death rates. The treatment variable in this case can be written Da, where Da = 1 indicates legal drinking and is 0 otherwise. Da is a function of age a : the MLDA transforms 21-year-olds from underage minors to legal alcohol consumers. We capture this transformation in mathematical notation by writing: In sharp RD designs, treatment switches cleanly off or on as the running variable passes a cutoff.

Running a regression 12Elliott Fan: Labor 2015 Fall Lecture 6 1.Ma is the death rate in month a (again, month is defined as a 30-day interval counting from the twenty-first birthday). 2.Da, the treatment dummy, is defined as in the previous slide 3.a is a linear control for age in months.

Linear or non-linear? 13Elliott Fan: Labor 2015 Fall Lecture 6

Linear or non-linear? 14Elliott Fan: Labor 2015 Fall Lecture 6

Linear or non-linear? 15Elliott Fan: Labor 2015 Fall Lecture 6

Linear or non-linear? 16Elliott Fan: Labor 2015 Fall Lecture 6

Running a regression – normalized form 17Elliott Fan: Labor 2015 Fall Lecture 6 1.Ma is the death rate in month a (again, month is defined as a 30-day interval counting from the twenty-first birthday). 2.Da, the treatment dummy, is defined as in the previous slide 3.a is a linear control for age in months 4. a 0 refers to the cutoff point

Running a regression – making it more flexible 18Elliott Fan: Labor 2015 Fall Lecture 6

Compare the results 19Elliott Fan: Labor 2015 Fall Lecture 6

Which function form is best? 20Elliott Fan: Labor 2015 Fall Lecture 6 1.There are no general rules here, and no substitute for a thoughtful look at the data. 2.When different forms provide varied estimates, caution is needed.

The next question: how do you know it is MLDA? Elliott Fan: RDPEE Lecture 821

The next question: how do you know it is MLDA? 22Elliott Fan: Labor 2015 Fall Lecture 6