We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.

Evolution and Rationality Some Recent Game-Theoretic Results. Identification and Estimation of Local Average Treatment Effects

All Our Kin: Strategies for Survival in a Black Community. C. B. Stack. New York: Harper & Row. 1974. Carol Stack wrote one of the most powerful books of the last half century about African American families. The book's power derived from its focus on the stories and the lives of persons who were struggling to manage with limited resources and who had evolved seamless methods of survival and coping strategies. Stack was not content to view the problems of impoverished African American families from an outside perspective, as had been done in the past, but chose instead to present her work from the view of the participants. She presented a sensitive view of families that has not been duplicated to this day. Stack put specific emphasis on being accepted by the families before she began interviewing them. She and her son took a long time to be accepted by the families as they gradually became participants in the day-to-day lives of the "Flats." She was sensitive to the patterns of interactions among the networks of family and friends that would have been overlooked by almost any other researcher or method of observation. The book showed how a person from another racial and economic group was able, with skill, to become an intimate part of the experience and the lives of very poor families. Her anthropological approach stands in sharp contrast to the countless attempts of others to quickly go in and pull out slices of families' lives with a preexisting conceptual framework. The African American families of the Flats were presented as they were, not from a White academic theoretical perspective that was not based on reality. Stack made many observations that allowed one to see the intricate workings of the families that "outsiders" had not been documented before. Participants were allowed to make observations about their own families' patterns of interaction and to uncover truths of family functioning based on the reality of their lives. Important data on these second-generation urban dwellers are presented in such a calm manner that one could overlook their significance to the field. The impact of the economic pressures on the men and women in the African American community show how persons can have mainstream values but are prevented from achieving them because of the lack of employment and economic security within the community. In response to the reality, Stack found that African Americans have cooperated to produce an adaptive strategy of exchanging goods and trading resources, as well as offering child care or temporary fosterage. Kinship boundaries were more elastic than they were in more affluent families because these individuals immersed themselves in a domestic network of kinfolk and fictive kin, or those who became as kin. The participants in Stack's study moved around and had loyalties to more than one household grouping at a time, making their family networks unlike the "household" structures of most American families. These networks were diffused over several kin-based households that changed frequently. The usual method of arbitrarily specifying widely accepted definitions of the family as nuclear or matrilocal may block one from seeing the world as it exists in very poor communities. Stack's observations refuted the "culture of poverty" position that had seen African Americans as having no culture or totally negative qualities of family disorganization, personal disorganization, and fatalism. Unfortunately, too many current writings on African Americans still take these same positions. The views may be the result of ignorance, naivete, or complex levels of racism that insidiously make their way into present family literature. Stack continued to reflect on the poverty of the participants' situations. By doing so, she avoided another position that is all too common-assumption that all African American families are the same, regardless of their levels of poverty or affluence. …

All Our Kin: Strategies for Survival in a Black Community

Difference-in-Differences with multiple time periods

In this article, we consider identification, estimation, and inference procedures for treatment effect parameters using Difference-in-Differences (DiD) with (i) multiple time periods, (ii) variation in treatment timing, and (iii) when the "parallel trends assumption" holds potentially only after conditioning on observed covariates. We show that a family of causal effect parameters are identified in staggered DiD setups, even if differences in observed characteristics create non-parallel outcome dynamics between groups. Our identification results allow one to use outcome regression, inverse probability weighting, or doubly-robust estimands. We also propose different aggregation schemes that can be used to highlight treatment effect heterogeneity across different dimensions as well as to summarize the overall effect of participating in the treatment. We establish the asymptotic properties of the proposed estimators and prove the validity of a computationally convenient bootstrap procedure to conduct asymptotically valid simultaneous (instead of pointwise) inference. Finally, we illustrate the relevance of our proposed tools by analyzing the effect of the minimum wage on teen employment from 2001--2007. Open-source software is available for implementing the proposed methods.

Difference-in-Differences with Multiple Time Periods

To estimate the dynamic effects of an absorbing treatment, researchers often use two-way fixed effects regressions that include leads and lags of the treatment. We show that in settings with variation in treatment timing across units, the coefficient on a given lead or lag can be contaminated by effects from other periods, and apparent pretrends can arise solely from treatment effects heterogeneity. We propose an alternative estimator that is free of contamination, and illustrate the relative shortcomings of two-way fixed effects regressions with leads and lags through an empirical application.

Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects

https://www.nber.org/system/files/working_papers/w25018/w25018.pdf

Difference-in-Differences with Variation in Treatment Timing

The canonical difference-in-differences (DD) model contains two time periods, “pre” and “post”, and two groups, “treatment” and “control”. Most DD applications, however, exploit variation across groups of units that receive treatment at different times. This paper derives an expression for this general DD estimator, and shows that it is a weighted average of all possible two-group/two-period DD estimators in the data. This result provides detailed guidance about how to use regression DD in practice. I define the DD estimand and show how it averages treatment effect heterogeneity and that it is biased when effects change over time. I propose a new balance test derived from a unified definition of common trends. I show how to decompose the difference between two specifications, and I apply it to models that drop untreated units, weight, disaggregate time fixed effects, control for unit-specific time trends, or exploit a third difference.

This paper uses the rollout of the first Community Health Centers (CHCs) to study the longer-term health effects of increasing access to primary care. Within ten years, CHCs are associated with a reduction in age-adjusted mortality rates of 2 percent among those 50 and older. The implied 7 to 13 percent decrease in one-year mortality risk among beneficiaries amounts to 20 to 40 percent of the 1966 poor/non-poor mortality gap for this age group. Large effects for those 65 and older suggest that increased access to primary care has longer-term benefits, even for populations with near universal health insurance. (JEL H75, I12, I13, I18, I32, I38, J14).

/pdf/the-war-on-poverty-s-experiment-in-public-medicine-community-4me2i1805x.pdf

The War on Poverty's Experiment in Public Medicine: Community Health Centers and the Mortality of Older Americans

This paper provides new evidence that Medicaid’s introduction reduced infant and child mortality in the 1960s and 1970s. Mandated coverage of all cash welfare recipients induced substantial cross-state variation in the share of children immediately eligible for the program. Before Medicaid, higher- and lower-eligibility states had similar infant and child mortality trends. After Medicaid, public insurance utilization increased and mortality fell more rapidly among children and infants in high-Medicaid-eligibility states. Mortality among nonwhite children on Medicaid fell by 20 percent, leading to a reduction in aggregate nonwhite child mortality rates of 11 percent.

/pdf/public-insurance-and-mortality-evidence-from-medicaid-368j8om7s5.pdf

Public Insurance and Mortality: Evidence from Medicaid Implementation

Policymakers have implemented a wide range of non-pharmaceutical interventions to fight the spread of COVID-19. Variation in policies across jurisdictions and over time strongly suggests a difference-in-differences (DD) research design to estimate causal effects of counter-COVID measures. We discuss threats to the validity of these DD designs and make recommendations about how researchers can avoid bias, interpret results accurately, and provide sound guidance to policymakers seeking to protect public health and facilitate an eventual economic recovery.

https://www.econstor.eu/bitstream/10419/222454/1/Goodman-Bacon_2020_Using%20Di%ef%ac%80erence-in-Di%ef%ac%80erences.pdf

Andrew Goodman-Bacon

Papers

Difference-in-Differences with Variation in Treatment Timing

Difference-in-Differences with Variation in Treatment Timing

The War on Poverty's Experiment in Public Medicine: Community Health Centers and the Mortality of Older Americans

Public Insurance and Mortality: Evidence from Medicaid Implementation

Using difference-in-differences to identify causal effects of COVID-19 policies