Empirical Economics 5

Videos and questions for Chapter 5 of the course "Empirical Economics with R" at Ulm University (taught by Sebastian Kranz)

A large scale job counseling experiment

Make a guess which percentage of the job seekers who got the option for intensive counselling accepted it?

31.7%

61.7%

91.7%

Consider the regression \[\text{job_6m}_i = \beta_0 + \beta_1 \text{treated}_i + u_i\] Is our estimator \(\hat \beta_1\) likely a consistent estimator of the effect of job counseling on those who received treatment?

Most economists would say yes, because a randomized experiment was conducted.

Most econmists would say no.

In the following two quizzes let us consider two stories that could yield a bias in \(\hat \beta_1\) in the regression:

\[\text{job_6m}_i = \beta_0 + \beta_1 \text{treated}_i + u_i\]

Assume the that only those job seekers reject intensive counseling who can easily find themselves a good new job.

\(\hat \beta_i\) would then have a negative bias.

\(\hat \beta_i\) would then have a positive bias.

Assume the that only those job seekers reject intensive counseling who are demotivated and generally have low chances to find a new job.

\(\hat \beta_i\) would then have a negative bias.

\(\hat \beta_i\) would then have a positive bias.

Instrumental Variable Estimation

Consider again our regression \[\text{job_6m}_i = \beta_0 + \beta_1 \text{treated}_i + u_i\]

and let the dummy variable \(\text{treat_option}_i\), which indicates whether subject \(i\) had the option for intensive counseling, be the instrument for \(\text{treated}_i\).

What is the exogeneity condition for the instrument in our example?

\(cor(\text{treated}_i,\text{treat_option}_i) =0\)

\(cor(\text{treated}_i,\text{treat_option}_i) \ne 0\)

\(cor(\text{treated}_i,u_i) = 0\)

\(cor(\text{treat_option}_i,u_i) = 0\)

Is the exogeneity condition for the instrument \(\text{treat_option}_i\) satisfied in our application if we assume that subjects' assignment to treatment and control group was perfectly randomized?

Yes

What can we say about the relevance condition for the instrument \(\text{treat_option}_i\) in our application?

Satisfied, since \(cor(\text{treated}_i,\text{treat_option}_i) < 0\)

Satisfied, since \(cor(\text{treated}_i,\text{treat_option}_i) > 0\)

Not satisfied, since \(cor(\text{treated}_i,\text{treat_option}_i) = 0\)

IV Estimation via Two-Stage Least Squares

Direct IV estimation

IV estimation with more than one instrument and with control variables

IV estimation in our job counseling application

We found an IV estimator of \(\hat \beta_1 = 0.102\) and a lower OLS estimator of just \(\hat \beta_1 = 0.079\).

Comparing the OLS estimator, which story seems on average more consistent with some subjects' decision to reject the intensive counseling?

Mainly those job seekers reject intensive counseling who can easily find themselves a good new job.

Mainly those job seekers reject intensive counseling who have low chances to find a new job.

Excursion: Should we worry about the small R-squared in the regressions?

Note: At around 5 minutes 30 seconds, I say "increase by 10 percent", where of course it should be "increase by 10 percentage points", one should always be careful with this distinction...

Which average treatment effect does our IV estimator estimate?

The Rubin causal model and average treatment effects

IV estimator estimates local average treatment effect (LATE)

Not perfectly randomized treatment allocation

Which condition would our instrument violate in the short IV regression given the problem explained in the video?

The exogeneity condition.

The relevance condition.

Could we, in principle, solve the problem by adding region specific fixed effects to our IV regression?

No, one cannot add fixed effects to an IV regression.

Yes, as least as long as we assume a homogeneous treatment effect.

Region fixed effects or "inverse probability weighting"?

An example to motivate inverse probability weighting

4 regressions for our inverse probability weighting example and discussion

Back to our job-counseling application

Great, you have finished the video lectures for Chapter 5. Now would be a good time to start with the RTutor problem set in order to perform some IV estimation yourself.