Regression discontinuity design and its applications to Science of Science: A survey

Li, Meiling; Zhang, Yang; Wang, Yang

doi:10.2478/jdis-2023-0008

Figures & Tables

Illustrations of RDD. (a) The continuity framework, and (b) the local randomization framework. The figure depicts the expected outcomes conditional on the running variable Xi, denoted by E[Yi(1)│Xi=x] and E[Yi(0)│Xi=x]. τSRD and τSLR represent the causal effect using these two frameworks at the cutoff c in the window [c−Δ, c+Δ], respectively. This figure is adapted from (Cattaneo & Titiunik, 2022).

Data collection procedure. (a) Illustration of data collection procedure. Specifically, we manually collect 3,387 RDD papers from Web of Science through keyword searching, and we obtain 2,061 RDD papers in the MAG by matching their DOIs with the Web of Science data. (b) The number of RDD papers in 19 MAG categories as the function of time. The main plot is smoothed using a three-year sliding window. The inset figure shows the total number of RDD papers from 1960 to 2021.

The RDD keyword network and emergent words in WOS. (a) We illustrate the RDD keyword network, where nodes represent keywords and links indicate that two keywords appear in the same paper. The modularity Q is 0.37, indicating a strong community structure. Here, we display only the largest eight clusters, excluding small clusters. (b) Top 15 emergent words of RDD papers, which indicate research frontiers. Year indicates the year when the keyword first appeared, while Begin and End represent the starting and ending years of the keyword as the research frontier. The graph on the rightmost displays the research frontiers in different time periods. For example, air pollution is the research frontier of RDD between 2021 and 2023.

The citation behaviors between RDD and other academic domains over time. (a) The fraction of references made by RDD papers to certain scientific domains. (b) The fraction of references made to RDD papers by papers in various scientific domains. (c) Reference strength from RDD papers to papers in other academic fields. (d) Reference strength from other academic fields to RDD papers. Black dashed lines in c,d represent φ= 1, and other dashed lines in c, d indicate that the strength of references from certain academic fields is lower than the average value cross fields in 2016.

The results of the analysis conducted in (Ludwig & Miller, 2007). (a) - (b) show the linear and quadratic fits, respectively, using rdplot for county mortality of children aged 5 to 9 in 1973-1983. (c) shows the quadratic fit using rdplot for county mortality of people ages 25 and older in 1973-1983. The data used in the analysis come from (Matias D. Cattaneo, 2021).

Regression discontinuity estimation of the effect of HS funding on mortality_ Robust standard errors are in parentheses,

		(1)	(2)	(3)	(4)	(5)
Variable	Mean	Nonparametric estimator			Parametric
Variable	Mean	Nonparametric estimator			Flexible linear	Flexible quadratic
Bandwidth or poverty range		9	18	36	8	16
Main results
Number of countries		524	954	2,161	482	858
Mortality, Ages 5-9 (%)	2.252	−1.895*(0.984)	−1.198*(0.662)	−1.114**(0.501)	−2.201**(1.058)	−2.558**(1.096)
Mortality, Ages 25+(%)	132.626	2.204(5.645)	6.016(4.025)	5.872(3.600)	2.091(5.872)	2.574(6.370)

The survey of studies that utilize RDD_ Context reveals the settings of the focal paper_ Outcome(s) means the dependent variable of the focal paper_ Treatment(s) is the treatment variable in the focal paper_ In practice, the treatment variable is a binary variable_ Running variable(s) is the forcing variable for individuals_

	Context	Outcome(s)	Treatment(s)	Running Variable(s)
Economics
Yi et al. (Yi et al., 2022)	Great Famine in China	Risk tolerance and entrepreneurship in adulthood	Experiencing early-life hardship	Location
García-Jimeno et al. (García-Jimeno et al., 2022)	Women’s Temperance Crusade in American	Collective action decisions	Affective information networks	Location
Akhtari et al. (Akhtari et al., 2022)	The politically motivated replacement of personnel in the schools in Brazil	The quality of public education provision by the government	Political turnover	Share of Votes
Van Der Klaauw (Van Der Klaauw, 2002)	East Coast college’s aid	College enrollment	Offering financial aid	Aid allocation decisions
Education
Davies et al. (Davies et al., 2018)	Reform of increasing the minimum school leaving age in England	Risk of diabetes and mortality	Remaining in school	Time
Huang et al. (Huang & Zhou, 2013)	Great Famine in China	Cognition estimated by episodic memory survey	Completion of primary school	Year of birth and entering primary schooling
Clark et al. (Clark & Royer, 2013)	Reform of increasing the minimum school leaving age in England	Adult mortality and health	Remaining in school	Time
Science of Science or Innovation Studies
Seeber et al. (Seeber et al., 2019)	Scientists’ promotion in Italian higher Education system	Scientists’ number of self-citations	Undergoing the introduction of the habilitation procedure	Time
Wang et al. (Y. Wang et al., 2019)	Early-career setback, NIH R01 grant applications	Future Career outcomes	Receiving the R01 grant	Priority score
Bol et al. (Bol et al., 2018)	Innovation Research Incentives Scheme for early career scientists, Netherlands	Winning a midcareer grant	Winning the early career award	Evaluation scores
Bronzini et al. (Bronzini & Iachini, 2014)	Firms’ R&D subsidy in northern Italy	Investment spending of firms	Receiving funding	Priority score
Jacob et al. (Jacob & Lefgren, 2011b)	NIH R01 grant applications	Subsequent publications and citations	Receiving an NIH research grant	Priority score
Jacob et al. (Jacob & Lefgren, 2011a)	NIH postdoctoral training grants	Subsequent publications and citations	Receiving an NIH postdoctoral training grant	Priority score

Counties Characteristic_ Column 1 represents county-level data, including the county poverty rate in 1960, mortality of children aged 5 to 9, and people aged 25 and older in 1973-1983_ Counties with a 1960 poverty rate of 49_198% to 59_198% are the control group, while counties with a 1960 poverty rate of 59_1984% to 69_1984% are the treatment group, i_e_, the poorest counties funded by the HS funding program_

County-level data	Counties with 1960 poverty 49.198% to 59.198		Counties with 1960 poverty 59.1984% to 69.1984
No. of observations (counties)	347		228
	Mean	Std	Mean	Std.
County Poverty Rate 1960 (%)	54.08	2.861	63.40	2.644
Mortality, Ages 5-9, 1973-1983 (%)	3.044	5.897	2.316	4.566
Mortality, Ages 25+, 1973-1983 (%)	132.5	30.96	135.7	30.53

Regression discontinuity design and its applications to Science of Science: A survey

Figures & Tables

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Regression discontinuity estimation of the effect of HS funding on mortality_ Robust standard errors are in parentheses,

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