1. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. Lecture 23 Supplement: Local Average Treatment Effects (Chapter 15.5)

2. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 23S-2 Randomized Experiments Not every voucher recipient uses the voucher. There are probably systematic differences between voucher-users and non-users. The Moving to Opportunity study estimates the effect of the treatment on those we intend to treat. It is useful for assessing the effects of a voucher program.

3. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 23S-3 Randomized Experiments (cont.) What if we want to assess the benefit of living in a good neighborhood instead of a bad neighborhood? We cannot simply compare the Treatment and Control groups. However, the experiment provides an Instrumental Variable.

4. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 23S-4 Randomized Experiments (cont.) However, the experiment provides an Instrumental Variable. Being randomly assigned to the Treatment group IS correlated with moving to a good neighborhood (some of the recipients do use the vouchers). Being randomly assigned to the Treatment group is NOT correlated with any component of

5. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 23S-5 Randomized Experiments (cont.) By combining randomized experiments and instrumental variables, we can estimate the effect of moving to a good neighborhood. However, this effect may not be the same for everyone. Some people may benefit more from moving than others.

6. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 23S-6 Randomized Experiments (cont.) There may be heterogeneity in the treatment effect itself. In this case, IV methods estimate NOT the average treatment effect in the entire population, but the average treatment effect for individuals who move because they receive a voucher.

7. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 23S-7 Randomized Experiments (cont.) In general, when there exists heterogeneity in the effect of X, instrumental variables methods estimate the average effect of X for those observations affected by the instrument. We call such a specialized estimate the local average treatment effect.

8. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 23S-8 Review If the entire Treatment group does not respond to the Treatment, we can estimate only the average effect of the treatment on those we intend to treat. Those who respond to the treatment will differ systematically from those who do not respond. However, the random assignment of the Treatment provides an instrumental variable.

9. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 23S-9 Review (cont.) If the heterogeneity also extends to the effect of the treatment itself, then the IV method estimates only the effect of the treatment on those who respond to the instrument. We estimate the Local Average Treatment Effect.