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Summary Triple difference has become a widely used estimator in empirical work. A close reading of articles in top economics journals reveals that the use of the estimator to a large extent rests on intuition. The identifying assumptions are neither formally derived nor generally agreed on. We give a complete presentation of the triple difference estimator, and show that even though the estimator can be computed as the difference between two difference-in-differences estimators, it does not require two parallel trend assumptions to have a causal interpretation. The reason is that the difference between two biased difference-in-differences estimators will be unbiased as long as the bias is the same in both estimators. This requires only one parallel trend assumption to hold.

Early evaluation of the Affordable Care Act's Medicaid expansion demonstrated persistent disparities among Medicaid beneficiaries in use of high-volume hospitals for pancreatic surgery. Longer-term effects of expansion remain unknown. This study evaluated the impact of expansion on the use of high-volume hospitals for pancreatic surgery among Medicaid and uninsured patients.State inpatient databases (2012-2017), the American Hospital Association Annual Survey Database, and the Area Resource File from the Health Resources and Services Administration, were used to examine 8,264 non-elderly adults who underwent pancreatic surgery in nine expansion and two non-expansion states. High-volume hospitals were defined as performing 20 or more resections/year. Linear probability triple differences models measured pre- and post-Affordable Care Act utilization rates of pancreatic surgery at high-volume hospitals among Medicaid and uninsured patients versus privately insured patients in expansion versus non-expansion states.The Affordable Care Act's expansion was associated with increased rates of utilization of high-volume hospitals for pancreatic surgery by Medicaid and uninsured patients (48% vs 55.4%, P = .047) relative to privately insured patients in expansion states (triple difference estimate +11.7%, P = .022). A pre-Affordable Care Act gap in use of high-volume hospitals among Medicaid and uninsured patients in expansion states versus non-expansion states (48% vs 77%, P.0001) was reduced by 15.1% (P = .001) post Affordable Care Act. A pre Affordable Care Act gap between expansion versus non-expansion states was larger for Medicaid and uninsured patients relative to privately insured patients by 24.9% (P.0001) and was reduced by 11.7% (P = .022) post Affordable Care Act. Rates among privately insured patients remained unchanged.Medicaid expansion was associated with greater utilization of high-volume hospitals for pancreatic surgery among Medicaid and uninsured patients. These findings are informative to non-expansion states considering expansion. Future studies should target understanding referral mechanism post-expansion.

In the present paper, we extend the notion of rough ideal lacunary statistical quasi Cauchy triple difference sequence of order α using the concept of ideals, which automatically extends the earlier notions of rough convergence and rough statistical convergence. We prove several results associated with this notion.

Background This paper re-evaluates the impacts of China’s New Cooperative Medicine Scheme (NCMS), a social health insurance program targeting China’s rural population, on the incidences of chronic diseases among its enrollees. Although coverage under the NCMS expanded rapidly following its implementation in 2003, previous studies have failed to reach a consensus on its health impacts. Existing conflicting results may be due to methodological problems such as implausible identification assumptions and the failure to focus on the most relevant beneficiaries. Methods Drawing on data from a longitudinal sample from the China Health and Nutrition Survey (CHNS), we focus on a subgroup of patients over the age of 55 years to re-estimate the NCMS’s impact on incidences of chronic disease among enrollees. We adopt a triple-difference (difference-in-difference-in-differences) method, relaxing the parallel-trend assumption commonly invoked in the previous double-difference (difference-in-differences) studies. Results Our triple-difference estimates suggest that the NCMS has significantly reduced the incidences of apoplexy and diabetes among rural residents aged 55 years or older. The impacts of the NCMS on chronic disease are underestimated by the commonly adopted double-difference method. The triple-difference method allows evaluations to focus on the most relevant subgroups for detecting program impacts. Conclusion Our findings that the NCMS has significantly positive impacts on elderly enrollees’ incidences of chronic diseases also suggest the need for examining its impacts on other vulnerable groups, such as low-income individuals, young children, and individuals with poor health conditions.

This paper focuses on the effects of a 2005 health insurance reform in Vietnam. Through this reform, public health insurance was newly offered to nonpoor children under 6 years old, but it required the use of community health facilities. This requirement potentially limited the value of the insurance. Employing difference-in-discontinuities and triple-difference methods and using data from 2002, 2004, and 2006, I show that, despite health coverage among nonpoor children increasing by nearly three times, there is little or no evidence that the reform significantly increased health care utilization, changed care locations from private to public sites, lowered out-of-pocket costs, or improved health status for nonpoor young children. My results suggest a "bypassing" phenomenon whereby nonpoor families skipped free health care at low-quality facilities.

Hiring subsidies are widely used to create (stable) employment for the long-term unemployed. This paper exploits the abolition of a hiring subsidy targeted at long-term unemployed jobseekers older than 45 years of age in Belgium to evaluate its effectiveness in the short and medium run. Based on a triple-difference methodology, the hiring subsidy is shown to increase the job-finding rate by 13% without any evidence of spillover effects. This effect is driven by a positive effect on individuals with at least a bachelor's degree. However, the hiring subsidy mainly creates temporary short-lived employment: eligible jobseekers are not more likely to find employment that lasts at least 12 consecutive months compared with ineligible jobseekers.

Hiring subsidies are widely used to create (stable) employment for the long-term unemployed. This paper exploits the abolition of a hiring subsidy targeted at long-term unemployed jobseekers over 45 years of age in Belgium to evaluate its effectiveness in the short and medium run. Based on a triple difference methodology the hiring subsidy is shown to increase the job finding rate by 13% without any evidence of spill-over effects. This effect is driven by a positive effect on individuals with at least a bachelor’s degree. However, the hiring subsidy mainly created temporary short-lived employment: eligible jobseekers were not more likely to find employment that lasted at least twelve consecutive months than ineligible jobseekers.

Hiring subsidies are widely used to create (stable) employment for the long-term unemployed. This paper exploits the abolition of a hiring subsidy targeted at long-term unemployed jobseekers over 45 years of age in Belgium to evaluate its effectiveness in the short and medium run. Based on a triple difference methodology the hiring subsidyis shown to increase the job finding rate by 13% without any evidence of spill-over effects. This effect is driven by a positive effect on individuals with at least a bachelor’sdegree. However, the hiring subsidy mainly created temporary short-lived employment: eligible jobseekers were not more likely to find employment that lasted at least twelveconsecutive months than ineligible jobseekers.

The Clean Water Act (CWA) significantly improved surface water quality, but at a cost exceeding the estimated benefits. We quantify the effect of the CWA on a direct measure of health and incorporate health benefits into a cost-benefit analysis. Using a difference-in-differences framework, we compare health upstream and downstream from wastewater treatment facilities before and after CWA grant receipt. Pollution only decreased downstream from facilities required to upgrade their treatment technology, and we leverage this additional variation with a triple difference. CWA grants increased average birth weight by 8 grams. A back-of-the-envelope calculation bounds infant health benefits below $29 billion.

BACKGROUND In 2012, the Korean government expanded dental insurance for the elderly to promote improved access to dental care. We examined the causal effect of this policy on dental care needs, focusing on low-income older adults. METHODS We compared data before and after policy implementation using double difference (DD) and triple difference (DDD) analyses. We used the nationally representative data from the Korea National Health and Nutrition Examination Survey from 2010 and 2016-2018. Individuals aged ≥65 years were included in the treatment group, and individuals aged

In 2007, approximately one in five children in Zambia lived with an HIV positive adult. We identify the effect of adult antiretroviral therapy (ART) availability at scale on children’s educational outcomes by combining data on the expansion of ART availability with two national household surveys that include HIV testing. Through a triple difference specification, we find that the availability of ART increased the likelihood that children in households with HIV positive household heads started school on time and were the appropriate grade-for-age. Two mechanisms were likely decreased incidental infections in the household and related care giving duties.

Colleges are experimenting with integrating technology into the classroom to improve student learning and reduce costs. While fully online models appear to have negative effects on student learning compared to in-person instruction, there is less evidence about models that blend elements of online and in-person instruction. In this study, I estimate the effect of adopting a blended approach to teaching called the emporium model in which students complete online work in an on-campus lab with instructors onsite to assist. Using a triple difference identification strategy, I find that using the emporium model compared to traditional instruction in remedial math courses in a state community college system reduces course pass rates, retention, and degree attainment. Effects were generally consistent across all three levels of remediation, suggesting there was little variation by students’ incoming placement test score.

This paper examines the relationship between maternal employment and infant health in the context of a large workfare program that explicitly prioritizes female participation, India's National Rural Employment Guarantee Scheme. Using multiple estimation strategies including a triple difference strategy that exploits a discontinuity in program eligibility at age 18, we find that the program had negative impacts on newborn infant survival, increasing newborn mortality among women who were eligible to participate in the program.

Schools across the United States and the world have been closed in an effort to mitigate the spread of COVID-19. However, the effect of school closure on COVID-19 transmission remains unclear. We estimate the causal effect of changes in the number of weekly visits to schools on COVID-19 transmission using a triple difference approach. In particular, we measure the effect of changes in county-level visits to schools on changes in COVID-19 diagnoses for households with school-age children relative to changes in COVID-19 diagnoses for households without school-age children. We use a data set from the first 46 weeks of 2020 with 130 million household-week level observations that includes COVID-19 diagnoses merged to school visit tracking data from millions of mobile phones. We find that increases in county-level in-person visits to schools lead to an increase in COVID-19 diagnoses among households with children relative to households without school-age children. However, the effects are small in magnitude. A move from the 25th to the 75th percentile of county-level school visits translates to a 0.3 per 10,000 household increase in COVID-19 diagnoses. This change translates to a 3.2 percent relative increase. We find larger differences in low-income counties, in counties with higher COVID-19 prevalence, and at later stages of the COVID-19 pandemic.

Planning for the research and development (R&D) of renewable energy resources (RERs) has not received enough attention. This paper aims to study the planning for the R&D of RERs in order to avoid bottlenecks and ensure sustainable development in developing marine economies. We have established a triple difference model (DDD) model and a wise pig game model between the theoretical government and enterprise. The data on RERs come from the World Bank and International Energy Agency databases. We have three contributions on the basis of distinguishing between mature and immature marine RERs technologies. First, it emphasizes the importance of developing R&D planning for marine RERs immature technology in the future. Second, the DDD model is used to empirically establish whether RERs planning has a significant positive impact on RERs’ output, which explains the importance of existing RERs planning. Third, the wise pig game model is used to analyze the welfare benefits to the government brought by the R&D planning of marine RERs which proves the importance of future RERs R&D planning.

This study examines the relationship between the 2004 introduction of California’s paid family leave (PFL) program on food security. While previous work has shown that PFL laws affect employment, poverty and health, there is no evidence so far whether such policies affect food security levels of families after the birth of a child. Estimating difference-in-differences (DD) and triple difference (DDD) models, this is the first study to evaluate potential effects on food security, which could be a potential mechanism explaining improvements in health outcomes for both infants and mothers found in previous studies. My analysis shows that California’s PFL implementation reduced the incidence of very low household food security by 2.29 (DD) and 1.98 percentage points (DDD) in the year following a birth. I find that the effects are driven improvements in food security among children who are 1.41 percentage points less likely to be food insecure after the PFL introduction. Subgroup analysis shows that the effects are largest for low-income households, a group that has been shown to highly value PFL benefits, as well as for families with more than one child.

How do politicians benefit from a policy? Politicians create and maintain policies even when beneficiaries do not reciprocate electorally, but existing research rarely explores alternative feedback channels. In this paper, we assess both direct and indirect political dividends of public policies by examining Minha Casa, Minha Vida (MCMV), a programmatic housing policy in Brazil. We surveyed 2,119 MCMV lottery participants and found that winners do not hold incumbents or the benefactor party in higher regard than non-winners. But MCMV is not politically barren. Non-beneficiaries, who lack direct experience with the program but are a much larger group than beneficiaries, are aware of the program and evaluate it very well. Based on a triple difference design, we find that MCMV contractor firms and their owners donate to political campaigns significantly more than would otherwise be expected. This shows that politicians reap political returns indirectly both through “audience” and “insider” channels.

This study investigates the effects of compulsory military service on adolescent crime. I exploit the reduction in the duration of Taiwan’s compulsory military service from one year to four months, which started in 2013. Using a triple difference approach, I find that the shorter service duration has led to a 36% increase in the number of adolescent male suspects and a 30% increase in crime rates. In particular, by enacting a 67% reduction in the time adolescents are incapacitated by military service, the reform has allowed adolescent males to engage in more criminal activities. My findings indicate that military service helps reduce crime; specifically, they suggest that the incapacitation effect of compulsory military service rather than the positive values (discipline, obedience, and collaboration) cultivated in a military camp has the most substantial impact on crime rates.

This paper measures the change in US unemployment and participation rates by gender due to the onslaught of the COVID-19 pandemic. It uses a triple difference estimation, DiDiD, and time series generated synthetic controls to compare these rates. The results suggest, thought not strongly, that the effects of the pandemic on male and female unemployment and participation rates do not differ statistically. This paper encourages the use of time series methods to complement the traditional impact evaluation approaches, which to date have leaned mostly on cross-section and panel observations.

We study the effect of an Iranian educational policy implemented in 2012 that restricted access to higher education for women in 30% of Iran’s public universities, mostly in sciences and engineering. To analyze the effect of the policy, we use a triple difference strategy across gender, cohorts and regions. We find that the admission cap was binding, as it significantly reduced university attendance by women relative to men. Additionally, we find that the policy had a negative impact on female labor force participation and employment, and a positive impact on marrying at a young age. Furthermore, we explore heterogeneous treatment effects for urban and rural areas and show that most observed effects are driven by individuals in urban areas.

Journal of environmental economics and management : JEEM 108, 102452 (2021). doi:10.1016/j.jeem.2021.102452, Published by Elsevier, Amsterdam [u.a.]

Recent homelessness figures in the United States show a puzzling trend of aggregate decline but lopsided changes across states. This study examines the puzzle through healthcare access and provides the first causal evidence of the Medicaid expansion’s impact on homeless adults’ location. Using the state and county-level data on the homeless population from 2010-2017, the estimates from a difference-in-differences model show a significant 10 % post-expansion increase in homeless individuals per capita in states that adopted Medicaid expansion. Furthermore, utilizing the difference in homeless individuals’ coverage status vis-a-vis homeless people in families, estimates from a triple difference (DDD) model also confirm the post-expansion increase in homelessness in expansion states. This study contributes further by uniquely utilizing county-level data to provide subsample analysis on metropolitan counties and counties located at state borders. Results from the state, county, and border-county-discontinuity design reveal the evidence of homeless individuals’ migration from non-expansion to expansion states. Two mechanisms explain the migration process: post-expansion coverage eligibility of previously uninsured homeless individuals and the increased ability of homeless service providers in expansion states in offering healthcare and housing-related services. This paper concludes by measuring the state spending on Medicaid to demonstrate the implications of these findings on state welfare policymaking and fiscal expenditure.

There have been stark differences in the ability of low-income and high-income individuals to protect themselves during the COVID-19 pandemic. Using a triple difference specification, we document that debt burdens contribute to this inequity by disproportionately increasing the cost to low-income individuals of reducing their mobility after the start of the pandemic. This effect is stronger in counties located in states with residential mortgage recourse. Furthermore, the debt burden channel is exacerbated for Black/African-American and Hispanic/Latino borrowers. Additionally, we provide suggestive evidence that this debt burden channel could have contributed to 2.71% more COVID-19 cases.

Triple difference has become a widely used estimator in empirical work. A close reading of articles in top economics journals reveals that the use of the estimator to a large extent rests on intuition. The identifying assumptions are neither formally derived nor generally agreed on. We give a complete presentation of the triple difference estimator, and show that even though the estimator can be computed as the difference between two difference-in-differences estimators, it does not require two parallel trend assumptions to have a causal interpretation. The reason is that the difference between two biased difference-in-differences estimators will be unbiased as long as the bias is the same in both estimators. This requires only one parallel trend assumption to hold.

In response to strong rental price increases, Germany's Federal Government introduced a rent control in 2015 aiming to disburden low-income households. Beside the general effectiveness of rent control, this study analyses temporal dynamics of the obtained effect and the effectiveness for the target group. Applying a triple difference event study approach on rental offer price data, we find that the rent control indeed has significant success, dampening rental prices by up to 5% for all dwellings (up to 9% for specific types). However, the effect vanishes about one year after the implementation, causing basically no effect on rental prices afterwards. Moreover, the rent control mostly benefits areas inhabited by high-income households, missing its original policy goal. Despite the poor persistent effectiveness on rental prices, quality of the offered dwellings suffers from the rent control.