4. [6 points] The figure below represents the stylized impact of a shock (ie, natural experiment) on a set of treated units (in red). Blue markers represent the outcomes that are observed for a (adequate) control.

What are implied values for parameters in the below diff-in-diff equation?

Question

4.  [6 points] The figure below represents the stylized impact of a shock (ie, natural experiment) on a set of treated units (in red). Blue markers represent the outcomes that are observed for a (adequate) control.

What are implied values for parameters  in the below diff-in-diff equation?

BlackTom AI · Accepted Answer

To determine the implied values for the parameters in the diff-in-diff equation, we analyze the given data:

- Control group (blue markers):
  - Pre-treatment outcome = 33
  - Post-treatment outcome = 15

- Treated group (red markers):
  - Pre-treatment outcome = 22
  - Post-treatment outcome = 38

The diff-in-diff equation is:

Y = β0 + β1 Post + β2 Treated + β3 (Treated×Post) + ε

1. **β0 (Intercept):**
   - Represents the expected outcome for the control group before treatment.
   - β0 = E[Y|Control, Pre] = 33

2. **β1 (Post Indicator):**
   - Represents the change in the outcome for the control group from pre to post period.
   - β1 = E[Y|Control, Post] − E[Y|Control, Pre] = 15 − 33 = -18

3. **β2 (Treated Indicator):**
   - Represents the difference in the pre-treatment outcomes between treated and control groups.
   - β2 = E[Y|Treated, Pre] − E[Y|Control, Pre] = 22 − 33 = -11

4. **β3 (Interaction Term):**
   - Represents the difference-in-differences estimator, capturing the treatment effect.
   - β3 = (E[Y|Treated, Post] − E[Y|Treated, Pre]) − (E[Y|Control, Post] − E[Y|Control, Pre])
   - β3 = (38 − 22) − (15 − 33) = 16 − (-18) = 34

Thus, the parameters are:
- β0 = 33
- β1 = -18
- β2 = -11
- β3 = 34

These values reflect the baseline, control group change, treated group baseline difference, and the treatment effect, respectively.

4. [6 points] The figure below represents the stylized impact of a shock (ie, natural experiment) on a set of treated units (in red). Blue markers represent the outcomes that are observed for a (adequate) control. What are implied values for parameters in the below diff-in-diff equation? 论述题

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