Exercise: Understanding first-differences and de-meaning
- Q: How would you calculate the \(\Delta y_{it}\), \(\Delta d_{it}\) (first differences), \(y_{it}-{\overline {y_{i}}}\) and \(d_{it} - {\overline {d_{i}}}\) (de-meaned) for Brittany in Table 11.1 below? (same logic for covariates!)
Table 11.1: Some wide format panel data
|
Name
|
trust.2006
|
trust.2007
|
trust.2008
|
threat.2006
|
threat.2007
|
threat.2008
|
|
Brittany
|
4
|
4
|
2
|
0
|
0
|
1
|
|
Ethan
|
5
|
6
|
4
|
1
|
0
|
0
|
|
Kyle
|
0
|
7
|
5
|
0
|
0
|
0
|
|
Jacob
|
5
|
3
|
6
|
0
|
1
|
1
|
|
Jessica
|
7
|
9
|
4
|
0
|
0
|
0
|
- Q: What happens to variables that are stable over time?
- Q: In a normal linear reg. model we would compare the average of the outcome between treatment and control. What are we comparing here (Hint: Change/Deviation)?
- Q: Thinking back to the controversy around what variables can be causes (see Section 4.31) would you say that investigating changes (panel data etc.) is more consistent with the idea of searching for causal effects?
- Q: What should we control for here since stable covariates drop out of the equation?
- Remember to conceptualize controlling as estimating causal effect in/averaging it across subsets of the data defined by values on covariates
- Q: If we look at change for both treatment & outcome between t0 and t1, what additional assumptions are we making (Hint: Temporal order)?