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ECON 488, Pset #5: Estimation of TEs with Observational Data
in the presence of Unobserved Confounders
Part 1: On The DD Estimator with Repeated Cross-Sections (30 p)
Objective We refer to the lecture slides CAUS_4_Observational.pdf, page 45. You consider the regression
specialcation in expression (18), which implements DD estimation using repeated cross-sections, namely:
, i = 1; :::; N1 + N2. ((18) from slides)
In the slides we make two claims. First, we claim that the OLS estimators of the regression coe￠ cients
(;
;
; ) in specialcation ((18) from slides) are:
Second, we claim that, under the DD design spelled out at slide 6, the above OLS estimators are unbiased
estimators of the following population data moments:

1. (15 p) Prove the rst claim, namely verify expressions (1)-(4). Speci cally, you are asked to provide this
   proof in steps:
   (a) (8 p) Prove that expression (9) is an equivalent parametrization of regression specialcation ((18) from
   slides) i.e. derive the relationship between 
   (b) (3 p) Obtain the OLS estimators of.
   (c) (4 p) Use the OLS estimators of to write out the OLS estimators of 
2. (15 p) Prove the second claim, namely verify expressions (5)-(8).
   1
   Part 3: An Application of DD Methods to Panel Data (70 p)
   Objective You want to read the 2003 article by D. Autor: ìOutsourcing at Will: The Contribution of Unjust
   Dismissal Doctrine to the Growth of Employment Outsourcing, Journal of Labor Economics, Vol. 21,
   no. 1, pp. 1-42.
3. (5 p) Consider regression specialcation (8) at page 16 of the article. Why is the dependent variable the log
   of THS instead of the level of THS?
4. (10 p) Consider Table 3 at page 18, column 1. The author writes that ìthe coe￠ cient of 0.112 in column
5. indicates that after removing mean state THS levels and common year e§ects, THs employment grew by
   approximately 11.2 long points more in states adopting the implied contract exceptions than in nonadopting
   states?. What does this mean? How are log points to be interpreted?
6. (5 p) Suppose that employers anticipate the introduction of exceptions in their states and pre-emptively
   start using more THS and fewer long term workers. Does this invalidate the DD design? Explain.
7. (10 p) Consider Table 3 at page 18, column 2. The author adds ìState time trends? to the regression
   speci?cation. What does this mean in practice? Also, why does he add these extra right-end side terms?
   Hint: Is the author worried that exceptions were adopted in states whose THS was already growing
   rapidly? How would this invalidate or cause problem for identialcation and estimation of the ATT of
   exceptions with the specialcation used in column 1?
8. (10 p) Consider Table 7 at page 24. Explain how the author modi?es his baseline specialcation (from
   Table 3) in order to explore whether the ATT changes over (event) time, in particular whether the impact
   accelerates, stabilizes or mean reverts.
9. (10 p) Consider Table 7 at page 24. Explain why the author writes that ìif temporary help employment
   growth leads to the adoption of exceptions rather than viceversa, the previous estimates [Table 1] would
   obscure this reverse causuality?.
10. (20 p) Summarize in 4 paragraphs the following: 1) the causal question posed by the author and why it is
    important to answer it; 2) the estimated impact as obtained by the author and its economic signialcance
    and implications; 3) your opinion as to whether the estimates have a causal interpretation; and 4) your
    opinion as to what else the author might have done to convince you that he is uncovering the causal
    e§ect of exceptions on temporary help employment i.e. that he has properly dealt with the presence of
    confounders.