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Algorithm is Experiment: Machine Learning, Market Design, and Policy Eligibility Rules. (2021). Narita, Yusuke ; Yusuke, Narita ; Kohei, Yata.
In: Discussion papers.
RePEc:eti:dpaper:21057.

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  1. A Theory of Quasi-Experimental Evaluation of School Quality. (2021). Narita, Yusuke.
    In: Management Science.
    RePEc:inm:ormnsc:v:67:y:2021:i:8:p:4982-5010.

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  27. Confirmed ICU Patients (d) # Confirmed COVID Patients in ICU Notes: The figure shows the results of estimating our main 2SLS specification about the effect of $1mm of relief funding on weekly hospital outcomes from 07/31/2020 to 04/02/2021. The outcomes record the 7-day sum of the number of hospitalized patients with the specified condition. We compute the Approximate Propensity Score with S = 10, 000 and δ = 0.05. The estimates from the uncontrolled OLS, uncontrolled 2SLS, and 2SLS with the Approximate Propensity Score controls are plotted on the y-axis. Standard error ribbons are given in grey.
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  40. Funding We calculate the projected funding using the formula on the CARES ACT website. Hospitals that do not qualify on any of the three dimensions are not given any funding. Each eligible hospital is assigned an individual facility score, which is calculated as the product of disproportionate patient percentage and number of beds in that hospital. We calculate cumulative facility score as the sum of all individual facility scores in the dataset. Each hospital receives a share of $10 billion, where the share is determined by the ratio of individual facility score of that hospital to the cumulative facility score. The amount of funding received by hospitals is bounded below at $5 million and capped above at $50 million. 43 For the precise definition, see https://www.cms.gov/Medicare/Medicare-Fee-for-Service-Payment/ AcuteInpatientPPS/dsh. 44 The precise definition can be found at https://www.aha.org/fact-sheets/2020-01-06-fact-sheetuncompensated -hospital-care-cost.
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  41. Furthermore, for every x ∈ N(∂S, ) \ ∂S, Π∂S(x) is a singleton as shown in the proof of Theorem 4.16 of Crasta and Malusa (2007). Let π∂S(x) be the unique element in Π∂S(x). By Lemma 4.3 of Crasta and Malusa (2007), for every x ∈ N(∂S, ) \ ∂S, ∇ds S(x) = νS(π∂S(x)) ρK(νS(π∂S(x))) = νS(π∂S(x)) kνS(π∂S(x))k = νS(π∂S(x)), where the last equality follows since νS(π∂S(x)) is a unit vector. It then follows that k∇ds S(x)k = kνS(π∂S(x))k = 1 for every x ∈ N(∂S, ) \ ∂S.
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  47. νS(x0) kνS(x0)k = νS(x0), where the last equality follows since νS(x0) is a unit vector. It then follows that k∇ds S(x0)k = kνS(x0)k = 1 for every x0 ∈ ∂S. Also, it is obvious that, for every x0 ∈ ∂S, Π∂S(x0) = {x0} and x0 = x0 + ds S(x0)νS(x0), since ds S(x0) = 0. In addition, as stated in the proof of Theorem 4.16 of Crasta and Malusa (2007), is chosen so that (4.7) in Proposition 4.6 of Crasta and Malusa (2007) holds for every x0 ∈ ∂S and every t ∈ (−, ). That is, Π∂S(x0 + t∇ρK(νS(x0))) = {x0} for every x0 ∈ ∂S and every t ∈ (−, ). Since ∇ρK(νS(x0)) = νS(x0) kνS(x0)k = νS(x0), Π∂S(x0 + tνS(x0)) = {x0} for every x0 ∈ ∂S and every t ∈ (−, ).
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  50. It then follows from Theorem 4.16 of Crasta and Malusa (2007) that ds S is twice continuously differentiable on N(∂S, ) for some > 0, and for every x0 ∈ ∂S, ∇ds S(x0) = νS(x0) ρK(νS(x0)) =
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  61. One version of their approach constructs a linear estimator by choosing the weight (γi)n i=1 greedily to make the inference as precise as possible. Although their estimator is favorable in terms of precision, it is not obvious what estimand the estimator estimates, without assuming a constant treatment effect. The other version of Imbens and Wager (2019)’s approach and some other existing approaches (Zajonc, 2012; Keele and Titiunik, 2015) consider nonparametric estimation of the conditional average treatment effect E[Yi(1)−Yi(0)|Xi = x] for a specified boundary point x. The estimand has a clear interpretation, but “when curvature is nonnegligible, equation (6) can effectively make use of only data near the specified focal point c, thus resulting in relatively long confidence intervals” (Imbens and Wager, 2019, p. 268), where equation (6) defines their estimator.
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  64. Proof. We apply results from Crasta and Malusa (2007). Let K = {x ∈ Rp : kxk ≤ 1}. K is nonempty, compact, convex subset of Rp with the origin as an interior point. The polar body of K, defined as K0 = {y ∈ Rp : y x ≤ 1 for all x ∈ K}, is K itself. The gauge functions ρK, ρK0 : Rp → [0, ∞] of K and K0 are given by ρK(x) ≡ inf{t ≥ 0 : x ∈ tK} = kxk, ρK0 (x) ≡ inf{t ≥ 0 : x ∈ tK0} = kxk. Given ρK0 , the Minkowski distance from a set S ⊂ Rp is defined as δS(x) ≡ inf y∈S ρK0 (x − y), x ∈ Rp . Note that we can write ds S(x) = ( δ∂S(x) if x ∈ cl(S) −δ∂S(x) if x ∈ Rp \ cl(S).
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  70. The data is available from financial year 1996 to 2019. As the coverage is higher for 2018 (compared to 2019), we utilize the data corresponding to the 2018 financial year. Hospitals are uniquely identified in a financial year by their CMS (Center for Medicaid and Medicare Services) 41 We use the RAND cleaned version of this dataset, which can be accessed https://www.hospitaldatasets. org/ 42 We use the methodology detailed in the CARES ACT website to project funding based on 2018 financial year cost reports.
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  31. Dissonant Conclusions When Testing the Validity of an Instrumental Variable. (2014). Small, Dylan S. ; Lorch, Scott ; Rosenbaum, Paul R. ; Zubizarreta, Jos R. ; Yang, Fan.
    In: The American Statistician.
    RePEc:taf:amstat:v:68:y:2014:i:4:p:253-263.

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  32. Finite Population Causal Standard Errors. (2014). Wooldridge, Jeffrey ; Imbens, Guido ; Athey, Susan ; Abadie, Alberto.
    In: NBER Working Papers.
    RePEc:nbr:nberwo:20325.

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  33. Instrumental Variables: An Econometricians Perspective. (2014). Imbens, Guido.
    In: NBER Working Papers.
    RePEc:nbr:nberwo:19983.

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  34. A Permutation Test and Estimation Alternatives for the Regression Kink Design. (2014). Jäger, Simon ; Ganong, Peter ; Jager, Simon.
    In: IZA Discussion Papers.
    RePEc:iza:izadps:dp8282.

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  35. Instrumental Variables: An Econometricians Perspective. (2014). Imbens, Guido.
    In: IZA Discussion Papers.
    RePEc:iza:izadps:dp8048.

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  36. A Permutation Test and Estimation Alternatives for the Regression Kink Design. (2014). Ganong, Peter Nathan ; Jaeger, Simon C.
    In: Scholarly Articles.
    RePEc:hrv:faseco:34222894.

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  37. Do Judges Vary in Their Treatment of Race?. (2012). Mullainathan, Sendhil ; Bertrand, Marianne ; Abrams, David S..
    In: The Journal of Legal Studies.
    RePEc:ucp:jlstud:doi:10.1086/666006.

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  38. From Correlation to Granger Causality. (2011). Stern, David.
    In: Crawford School Research Papers.
    RePEc:een:crwfrp:1113.

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  39. The WTO trade effect. (2011). Lee, Myoung-jae ; Chang, Pao-Li.
    In: Journal of International Economics.
    RePEc:eee:inecon:v:85:y:2011:i:1:p:53-71.

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  40. Does school time matter?—On the impact of compulsory education age on school dropout. (2011). De Witte, Kristof ; Cabus, Sofie J..
    In: Economics of Education Review.
    RePEc:eee:ecoedu:v:30:y:2011:i:6:p:1384-1398.

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  41. The WTO Trade Effect. (2010). Lee, Myoung-jae ; Chang, Pao-Li.
    In: Working Papers.
    RePEc:siu:wpaper:31-2010.

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  42. Season of Birth and Later Outcomes: Old Questions, New Answers. (2008). Hungerman, Daniel ; Buckles, Kasey.
    In: NBER Working Papers.
    RePEc:nbr:nberwo:14573.

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  43. Symmetry-based inference in an instrumental variable setting. (2008). Lawford, Steve ; Bekker, Paul A..
    In: Journal of Econometrics.
    RePEc:eee:econom:v:142:y:2008:i:1:p:28-49.

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  44. Exactly distribution-free inference in instrumental variables regression with possibly weak instruments. (2008). Marmer, Vadim ; Andrews, Donald.
    In: Journal of Econometrics.
    RePEc:eee:econom:v:142:y:2008:i:1:p:183-200.

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  45. The WTO Trade Effect. (2008). Lee, Myoung-jae ; Chang, Pao-Li.
    In: DEGIT Conference Papers.
    RePEc:deg:conpap:c013_027.

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  46. The Impact of Damage Caps on Malpractice Claims: Randomization Inference with Difference?in?Differences. (2007). Ho, Daniel E ; Donohue, John J.
    In: Journal of Empirical Legal Studies.
    RePEc:wly:empleg:v:4:y:2007:i:1:p:69-102.

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  47. SENSITIVITY ANALYSIS OF JOB-TRAINING EFFECTS ON REEMPLOYMENT FOR KOREAN WOMEN. (2007). Lee, Myoung-jae.
    In: Discussion Paper Series.
    RePEc:iek:wpaper:0720.

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  48. The WTO Trade Effect. (2007). Lee, Myoung-jae ; Chang, Pao-Li.
    In: Trade Working Papers.
    RePEc:eab:tradew:22063.

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  49. Exactly Distribution-free Inference in Instrumental Variables Regression with Possibly Weak Instruments. (2005). Marmer, Vadim ; Andrews, Donald.
    In: Cowles Foundation Discussion Papers.
    RePEc:cwl:cwldpp:1501.

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