ECON 488, Pset #5: Estimation of TEs with Observational Datain the presence of Unobserved ConfoundersPart 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 regressionspecialcation 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 unbiasedestimators 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 thisproof in steps:(a) (8 p) Prove that expression (9) is an equivalent parametrization of regression specialcation ((18) fromslides) 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).1Part 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 UnjustDismissal Doctrine to the Growth of Employment Outsourcing, Journal of Labor Economics, Vol. 21,no. 1, pp. 1-42.1. (5 p) Consider regression specialcation (8) at page 16 of the article. Why is the dependent variable the logof THS instead of the level of THS?2. (10 p) Consider Table 3 at page 18, column 1. The author writes that ìthe coe￠ cient of 0.112 in column1 indicates that after removing mean state THS levels and common year e§ects, THs employment grew byapproximaECON 488作业代做、代写Python/c++程序设计作业、代做Java语言作业、代写DD Estimator作业 tely 11.2 long points more in states adopting the implied contract exceptions than in nonadoptingstates?. What does this mean? How are log points to be interpreted?3. (5 p) Suppose that employers anticipate the introduction of exceptions in their states and pre-emptivelystart using more THS and fewer long term workers. Does this invalidate the DD design? Explain.4. (10 p) Consider Table 3 at page 18, column 2. The author adds ìState time trends? to the regressionspeci?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 growingrapidly? How would this invalidate or cause problem for identialcation and estimation of the ATT ofexceptions with the specialcation used in column 1?5. (10 p) Consider Table 7 at page 24. Explain how the author modi?es his baseline specialcation (fromTable 3) in order to explore whether the ATT changes over (event) time, in particular whether the impactaccelerates, stabilizes or mean reverts.6. (10 p) Consider Table 7 at page 24. Explain why the author writes that ìif temporary help employmentgrowth leads to the adoption of exceptions rather than viceversa, the previous estimates [Table 1] wouldobscure this reverse causuality?.7. (20 p) Summarize in 4 paragraphs the following: 1) the causal question posed by the author and why it isimportant to answer it; 2) the estimated impact as obtained by the author and its economic signialcanceand implications; 3) your opinion as to whether the estimates have a causal interpretation; and 4) youropinion as to what else the author might have done to convince you that he is uncovering the causale§ect of exceptions on temporary help employment i.e. that he has properly dealt with the presence ofconfounders.2转自：http://www.7daixie.com/2019052248576226.html
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