Fuzzy Differences-in-Differences

Chaisemartin, Clément de; D’Haultfœuille, Xavier

doi:10.1093/restud/rdx049

Cited by 230 publications

(135 citation statements)

References 17 publications

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“…Specifically, we find a significant and positive effect of SC activation on Hispanics in sanctuary cities relative to non-sanctuary cities, such that SC activation has a net null effect on Hispanics in sanctuary jurisdictions. 40 Appendix Figure A8 presents corresponding event study estimates of the differential effect of SC activation on program take-up in sanctuary versus non-sanctuary jurisdictions.…”

Section: A Fearmentioning

confidence: 99%

“…The higher the share non-citizen in a county, the easier information could spread regarding the heightened risk of deportation under SC (see Figure 6). The greater the share of mixed-status households in the area, the more salient that 40 See the Online Appendix for institutional details of sanctuary cities. 41 See https://www.brookings.edu/opinions/census-data-blacks-and-hispanics-take-different-segregation-paths/.…”

Section: A Fearmentioning

confidence: 99%

See 1 more Smart Citation

Fear and the Safety Net: Evidence from Secure Communities

Alsan¹,

Yang²

2018

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This paper studies how changes in deportation fear induced by the roll-out of Secure Communities (SC), a far-reaching immigration enforcement program, affected the demand for safety net programs in the United States. We estimate the spillover effect of SC on the take-up of federal means-tested programs by Hispanic citizens, who are not themselves eligible for removal. We find significant declines in SNAP and SSI enrollment, particularly among mixed-citizenship status households. The response is muted for Hispanic households residing in sanctuary cities. Our results are most consistent with network effects that perpetuate fear rather than lack of benefit information or stigma.

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Section: A Fearmentioning

confidence: 99%

Section: A Fearmentioning

confidence: 99%

Fear and the Safety Net: Evidence from Secure Communities

Alsan¹,

Yang²

2018

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“…In fact, a preliminary version of our main result appeared in a working paper version of de Chaisemartin and D'Haultfoeuille (2018) (see Theorems S1 and S2 in deChaisemartin and D'Haultfoeuille, 2015).…”

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confidence: 98%

Two-way Fixed Effects Estimators with Heterogeneous Treatment Effects

Chaisemartin

D’Haultfœuille

2019

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Linear regressions with period and group fixed effects are widely used to estimate treatment effects. We show that they estimate weighted sums of the average treatment effects (ATE) in each group and period, with weights that may be negative. Due to the negative weights, the linear regression coefficient may for instance be negative while all the ATEs are positive. We propose another estimator that solves this issue. In the two applications we revisit, it is significantly different from the linear regression estimator.D g,t denotes the average treatment in group g at period t, while Y g,t (0), Y g,t (1), and Y g,t respectively denote the average potential outcomes without and with treatment and the average observed outcome in group g at period t.Throughout the paper, we maintain the following assumptions.Assumption 1 requires that no group appears or disappears over time. This assumption is often satisfied. Without it, our results still hold but the notation becomes more complicated as the denominators of some of the fractions below may then be equal to zero.Assumption 2 (Sharp design) For all (g, t) ∈ {1, ..., G} × {1, ..., T } and i ∈ {1, ..., N g,t },Assumption 2 requires that units' treatments do not vary within each (g, t) cell, a situation we refer to as a sharp design. This is for instance satisfied when the treatment is a group-level variable, for instance a county-or a state-law. This is also mechanically satisfied when N g,t = 1. In our survey in Section 6.1, we find that almost 80% of the papers using two-way fixed effects regressions and published in the AER between 2010 and 2012 consider sharp designs. We focus on sharp designs because of their prevalence, but in Section ?? of the Web Appendix, we show that all the results in Sections 3-4 below can be extended to fuzzy designs.Assumption 3 (Independent groups) The vectors (Y g,t (0), Y g,t (1), D g,t ) 1≤t≤T are mutually independent.We consider D g,t , Y g,t (0), Y g,t (1) as random variables. For instance, aggregate random shocks may affect the average potential outcomes of group g at period t. The treatment status of group g at period t may also be random. The expectations below are taken with respect to the distribution of those random variables. Assumption 3 allows for the possibility that the treatments and potential outcomes of a group may be correlated over time, but it requires that the potential outcomes and treatments of different groups be independent.

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“…It is worth mentioning a recent paper by De Chaisemartin and D'Haultfoeuille () that investigates identification in DiD applications where the introduction of a policy is used as an instrument for the treatment of interest. That is, individuals in the group under the policy regime as well as in the control group can receive the same treatment but the share of treated individuals is larger in the policy group.…”

Section: Introductionmentioning

confidence: 99%

“… De Chaisemartin and D'Haultfoeuille () refer to compliers in the policy group and in the control group as ‘treatment group switchers’ and ‘control group switchers’, respectively. …”

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confidence: 99%

Identification Based on Difference‐in‐Differences Approaches with Multiple Treatments

Fricke

2017

Oxf Bull Econ Stat

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This paper discusses identification based on difference‐in‐differences (DiD) approaches with multiple treatments. It shows that an appropriate adaptation of the common trend assumption underlying the DiD strategy for the comparison of two treatments restricts the possibility of effect heterogeneity for at least one of the treatments. The required assumption of effect homogeneity is likely to be violated because of non‐random assignment to treatment based on both observables and unobservables. However, this paper shows that, under certain conditions, the DiD estimate comparing two treatments identifies a lower bound in absolute values on the average treatment effect on the treated compared to the unobserved non‐treatment state, even if effect homogeneity is violated. This is possible if the treatments have ordered treatment effects, that is, in expectation, the effects of both treatments compared to no treatment have the same sign, and one treatment has a stronger effect than the other treatment on the respective recipients. Such assumptions are plausible if treatments are ordered or vary in intensity.

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Fuzzy Differences-in-Differences

Cited by 230 publications

References 17 publications

Fear and the Safety Net: Evidence from Secure Communities

Fear and the Safety Net: Evidence from Secure Communities

Two-way Fixed Effects Estimators with Heterogeneous Treatment Effects

Identification Based on Difference‐in‐Differences Approaches with Multiple Treatments

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