断点回归设计方法应用的研究综述
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摘要
近年来,国内经济学界颇为关注断点回归设计(RDD)方法,运用RDD的文章日益增多。首先概述Lee和Lemieux (2010)提出的运用RDD的规范,然后基于2011-2017年五大英文顶级经济学期刊发表的RDD应用研究论文,归纳出运用RDD的三个新动作:新的最优带宽确定方法、甜甜圈RDD和参数估计中最高只能使用二次多项式。以国外的RDD用法为参照,我们发现,国内熟悉Lee和Lemieux (2010)提出的规范,也在吸收国外文献中出现的新动作,但运用RDD时存在如下几个突出问题:不做适用性检验、不重视描述统计图和不交代清楚非参数估计的关键细节。建议国内运用RDD时需要增加如下动作:非参数估计应该同时尝试CV、IK和CCT三种带宽确定方法;在配置变量存在堆积现象或被操纵的可能时,使用甜甜圈RDD;尝试到四次多项式。
Recent years has witnessed increasing interest of China's economic scholars on Regression Discontinuity Design(RDD) and fast expansion of empirical papers using RDD. This paper summarizes the roadmap of using RDD advocated by Lee and Lemieux(2010) at first, and then extracts three advancements from the empirical papers using RDD published on the top five economic journals between 2011 and 2017: new methods of selecting optimal bandwidth, donut-hole RDD, and using up to second-order polynomials in parametric estimation. Compared to literature in English, we find that Chinese economic scholars are familiar with the roadmap advocated by Lee and Lemieux(2010) and some of them have used the advancements stated above in their research. However, generally speaking, Chinese papers are characterized by three obvious drawbacks: lack of validity test, neglect of descriptive figure, and ambiguity on the key details when using non-parametric estimation. Our suggestion for using RDD are as follows: try different methods such as CV, IK, and CCT to select optimal bandwidth when employing non-parametric estimation; use donut-hole RDD when the assignment variable is possibly heaped or precisely manipulated; try up to quartic order polynomials when employing parametric estimation.
Recent years has witnessed increasing interest of China's economic scholars on Regression Discontinuity Design(RDD) and fast expansion of empirical papers using RDD. This paper summarizes the roadmap of using RDD advocated by Lee and Lemieux(2010) at first, and then extracts three advancements from the empirical papers using RDD published on the top five economic journals between 2011 and 2017: new methods of selecting optimal bandwidth, donut-hole RDD, and using up to second-order polynomials in parametric estimation. Compared to literature in English, we find that Chinese economic scholars are familiar with the roadmap advocated by Lee and Lemieux(2010) and some of them have used the advancements stated above in their research. However, generally speaking, Chinese papers are characterized by three obvious drawbacks: lack of validity test, neglect of descriptive figure, and ambiguity on the key details when using non-parametric estimation. Our suggestion for using RDD are as follows: try different methods such as CV, IK, and CCT to select optimal bandwidth when employing non-parametric estimation; use donut-hole RDD when the assignment variable is possibly heaped or precisely manipulated; try up to quartic order polynomials when employing parametric estimation.
引文
[1]Angrist J D, Pischke J. The credibility revolution in empirical economics: How better research design is taking the con out of econometrics[J]. Journal of Economic Perspectives, 2010, 24(2): 3-30.
[2]Lee D S, Lemieux T. Regression discontinuity designs in economics[J]. Journal of Economic Literature, 2010, 48(2): 281-355.
[3]Thistlethwaite D L, Campbell D T. Regression-discontinuity analysis: An alternative to the ex post facto experiment[J]. Journal of Educational Psychology, 1960, 51(6):309-317.
[4]雷晓燕,谭力,赵耀辉.退休会影响健康吗?[J].经济学(季刊),2010,(04):1539-1558.
[5]余静文,赵大利.城市群落的崛起、经济绩效与区域收入差距——基于京津冀、长三角和珠三角城市圈的分析[J].中南财经政法大学学报,2010,(04):15-20,142.
[6]Imbens G W, Lemieux T. Regression discontinuity designs: A guide to practice[J]. Journal of Econometrics, 2008, 142(2): 615-635.
[7]Der Klaauw W V. Regression-discontinuity analysis: A survey of recent developments in economics[J]. Labour, 2008, 22(2): 219-245.
[8]Nyhan B, Skovron C, Titiunik R. Differential registration bias in voter file data: A sensitivity analysis approach[J]. American Journal of Political Science, 2017, (61): 744-760.
[9]Hausman C, David S. Rapson. Regression discontinuity in time: Considerations for empirical applications[J]Annual Review of Resource Economics, 2018,10(1): 533–552.
[10]余静文,王春超.新“拟随机实验”方法的兴起——断点回归及其在经济学中的应用[J].经济学动态,2011,(02):125-131.
[11]Papay J P, Willett J B, Murnane R J. Extending the regression-discontinuity approach to multiple assignment variables[J]. Journal of Econometrics, 2011, 161(2):203-207.
[12]Frandsen B R, Frolich M, Melly B, Quantile treatment effects in the regression discontinuity design[J]. Journal of Econometrics, 2012, 168(2): 382-395.
[13]Card D, Giuliano L. Can tracking raise the test scores of high-ability minority students?[J]. The American Economic Review, 2016, 106(10): 2783-2816.
[14]Cattaneo M D, Keele L, Titiunik R.Interpreting regression discontinuity designs with multiple cutoffs[J]. The Journal of Politics, 2016, 78(4): 1229-1248.
[15]Wing C, Cook T D. Strengthening the regression discontinuity design using additional design elements: A within-study comparison[J]. Journal of Policy Analysis and Management, 2013, 32(4): 853-877.
[16]Angrist J D, Rokkanen M. Wanna get away? Regression discontinuity estimation of exam school effects away from the cutoff[J]. Journal of the American Statistical Association, 2015, 110(512): 1331-1344.
[17]Kolesar M, Rothe C. Inference in regression discontinuity designs with a discrete running variable[J]. The American Economic Review, 2018, 108(8): 2277-2304.
[18]Imbens G W, Kalyanaraman K. Optimal bandwidth choice for the regression discontinuity estimator[J]. The Review of Economic Studies, 2012, 79(3): 933-959.
[19]Calonico S, Cattaneo M D, Titiunik R. Robust nonparametric confidence intervals for regression-discontinuity designs[J]. Econometrica, 2014, 82(6): 2295-2326.
[20]Justin McCrary. Manipulation of the running variable in the regression discontinuity design: A density test[J]. Journal of Econometrics, 2008, (142): 698-714.
[21]Frandsen, Brigham R. Party bias in union representation elections: Testing for manipulation in the regression discontinuity design when the running variable is discrete[Z]. Unpublished Manuscript, Brigham Young University, Provo Utah, USA, 2013.
[22]Barreca A I, Guldi M, Lindo J M. Saving Babies? Revisiting the effect of very low birth weight classification[J]. Quarterly Journal of Economics, 2011, 126(4): 2117-2123.
[23]Gelman A, Imbens G W. Why High-order Polynomials Should not be Used in Regression discontinuity designs[J]. Journal of Business & Economic Statistics, 2017,(05): 1-10.
[24]Dell M. Trafficking networks and the Mexican drug war[J]. The American Economic Review, 2015, 105(6): 1738-1779.
[25]Pinotti P. Clicking on heaven's door: The effect of immigrant legalization on crime[J]. The American Economic Review, 2017, 107(1): 138-168.
[26]Malamud O, Popeleches C. Home computer use and the development of human capital[J]. Quarterly Journal of Economics, 2011, 126(2): 987-1027.
[27]Chetty R, Friedman J N, Lethpetersen S. Active vs. passive decisions and crowd-out in retirement savings accounts: Evidence from Denmark[J]. Quarterly Journal of Economics, 2014, 129(3): 1141-1219.
[28]Meng K C. Using a free permit rule to forecast the marginal abatement cost of proposed climate policy [J]. The American Economic Review, 2017, 107(3): 748-784.
[29]Clark D, Martorell P. The signaling value of a high school diploma[J]. Journal of Political Economy, 2014, 122(2): 282-318.
[30]Deshpande, Manasi. Does welfare inhibit success? The long-term effects of removing low-income youth from the disability rolls[J]. The American Economic Review,2016, 106(11) : 3300-3330.
[31]Auffhammer M, Kellogg R. Clearing the air? The effects of gasoline content regulation on air quality [J]. The American Economic Review, 2011, 101(6): 2687-2722.
[32]王骏,孙志军.重点高中能否提高学生的学业成绩——基于F县普通高中的一个断点回归设计研究[J].北京大学教育评论,2015,(04):82-109,186.
[33]李宏彬,施新政,吴斌珍.中国居民退休前后的消费行为研究[J].经济学(季刊),2015,(01):117-134.
[34]张川川,John Giles,赵耀辉.新型农村社会养老保险政策效果评估——收入、贫困、消费、主观福利和劳动供给[J].经济学(季刊),2015,(01):203-230.
[35]张明.税收征管与企业全要素生产率——基于中国非上市公司的实证研究[J].中央财经大学学报,2017,(01):11-20.
[36]马光荣,郭庆旺,刘畅.财政转移支付结构与地区经济增长[J].中国社会科学,2016,(09):105-125.
[37]何文剑,徐静文,张红霄.森林采伐限额管理制度能否起到保护森林资源的作用[J].中国人口·资源与环境,2016,(07):128-136.
[38]李江一,李涵.新型农村社会养老保险对老年人劳动参与的影响——来自断点回归的经验证据[J].经济学动态,2017,(03):62-73.
[39]王家庭,毛文峰,臧家新,等.节约集约用地政策对城市蔓延的遏制效应[J].城市问题,2017,(05):9-16.
[40]曹静,王鑫,钟笑寒.限行政策是否改善了北京市的空气质量?[J].经济学(季刊),2014,(03):1091-1126.
[41]杨小聪,彭飞,康丽丽.绿色地铁:轨道交通对空气污染的净化效果评估——基于南京地铁3号线的实证研究[J].甘肃行政学院学报,2017,(04):82-94,129-130.
[42]张英,陈绍志.产权改革与资源管护——基于森林灾害的分析[J].中国农村经济,2015,(10):15-27.
[43]陈强,孙丰凯,徐艳娴.冬季供暖导致雾霾?来自华北城市面板的证据[J].南开经济研究,2017,(04):25-40.
[44]黄新飞,杨丹.产业转移促进区域经济协调发展了吗——基于广东省县域数据的断点回归分析[J].国际经贸探索,2017,(02):101-112.
[45]高彦彦,王逸飞.熔断制度可以降低中国股市波动吗?——基于断点回归设计的实证分析[J].华东经济管理,2017,(06):104-112.
[46]王旭光.新型农村养老保险政策提升农民消费水平了吗——来自CFPS数据的实证研究[J].南方经济,2017,(01):1-12.
[47]邹红,喻开志.退休与城镇家庭消费:基于断点回归设计的经验证据[J].经济研究,2015,(01):124-139.
[48]邓婷鹤,何秀荣.退休对男性老年人健康的影响——基于断点回归的实证研究[J].人口与经济,2016,(06):82-91.
[49]Crost B, Felter J H, Johnston P B, et al. Aid under fire: Development projects and civil conflict[J]. The American Economic Review, 2014, 104(6): 1833-1856.
(1)分别为American Economic Review(AER)、Econometrica(ECMA)、Journal of Political Economy(JPE)、Quarterly Journal of Economics(QJE)和Review of Economic Studies(RES)。
(2)不包括五大上关于RDD方法的理论研究论文。我们在Jstor数据库中用全文任一地方出现“regression discontinuity”这个关键词检索,然后剔除不是运用RDD做的经验研究论文,譬如RDD的理论研究论文、仅论文文献综述或脚注中出现“regression discontinuity”的论文等。
(1)这方面的一个表现是,大量行政管理数据(administrative data)被用于经济学经验研究。根据英国《经济学人》(The Economist)的报道, NBER(National Bureau of Economic Research)工作论文摘要里出现“administrative data”的论文数,2000年是0篇,之后快速增长,2017年达到28篇。报道链接为:https://www.economist.com/international/2018/05/26/government-data-are-ever-more-important-to-economic-research。
(2)中文核心期刊论文数的检索方法如下:在中国知网检索出主题包含“断点回归”、发表年度为2011年至2017年的中文社会科学引文索引(CSSCI)期刊论文,然后逐一检查、剔除非经验研究论文,最后剩下46篇。将检索限定在中文社会科学引文索引期刊,是为了保证检索到的论文的质量。英文五大期刊论文数的检索方法如下:在Jstor数据库中用全文任一地方出现“regression discontinuity”这个关键词、发表年度为2011至2017年、期刊为五大期刊检索到50篇,然后逐一检查、剔除非经验研究论文,最后剩下39篇。
(3)Imbens和Kalyanaraman(2009)是工作论文,后来于2012年发表在《Review of Economic Studies》上。
(4)用Stata软件实现这些新进展的操作命令可以参考Cattaneo et al.(2018),更详细的操作命令细节可参考本文所引用文献的网上附件。这些网上附件可在发表各引用文献的期刊官网上下载。
(5)作者文中用的都是4次多项式,没解释不用其他次数多项式的原因。
(6)作者说这是经验上的做法,没解释这样做的原因。
(7)Lee和Lemieux (2010)在脚注中提到了之后应用广泛的IK法(Imbens和Kalyanaraman, 2009),但是文中举例只使用拇指规则法和交叉验证法,没使用IK法。
(8)实际上,甜甜圈RDD也可以克服数据操纵问题对估计结果的影响。
(9)分别来自美国、巴西、挪威、意大利等17个国家。
(10)为方便讨论,使用矩形核密度函数的非参数估计虽然等同于参数估计,但此处只将其归为非参数估计。
(11)运用IV必需的技术环节是报告第一阶段回归的F统计量取值,运用DID必需的技术环节是做平行趋势假设检验。
[2]Lee D S, Lemieux T. Regression discontinuity designs in economics[J]. Journal of Economic Literature, 2010, 48(2): 281-355.
[3]Thistlethwaite D L, Campbell D T. Regression-discontinuity analysis: An alternative to the ex post facto experiment[J]. Journal of Educational Psychology, 1960, 51(6):309-317.
[4]雷晓燕,谭力,赵耀辉.退休会影响健康吗?[J].经济学(季刊),2010,(04):1539-1558.
[5]余静文,赵大利.城市群落的崛起、经济绩效与区域收入差距——基于京津冀、长三角和珠三角城市圈的分析[J].中南财经政法大学学报,2010,(04):15-20,142.
[6]Imbens G W, Lemieux T. Regression discontinuity designs: A guide to practice[J]. Journal of Econometrics, 2008, 142(2): 615-635.
[7]Der Klaauw W V. Regression-discontinuity analysis: A survey of recent developments in economics[J]. Labour, 2008, 22(2): 219-245.
[8]Nyhan B, Skovron C, Titiunik R. Differential registration bias in voter file data: A sensitivity analysis approach[J]. American Journal of Political Science, 2017, (61): 744-760.
[9]Hausman C, David S. Rapson. Regression discontinuity in time: Considerations for empirical applications[J]Annual Review of Resource Economics, 2018,10(1): 533–552.
[10]余静文,王春超.新“拟随机实验”方法的兴起——断点回归及其在经济学中的应用[J].经济学动态,2011,(02):125-131.
[11]Papay J P, Willett J B, Murnane R J. Extending the regression-discontinuity approach to multiple assignment variables[J]. Journal of Econometrics, 2011, 161(2):203-207.
[12]Frandsen B R, Frolich M, Melly B, Quantile treatment effects in the regression discontinuity design[J]. Journal of Econometrics, 2012, 168(2): 382-395.
[13]Card D, Giuliano L. Can tracking raise the test scores of high-ability minority students?[J]. The American Economic Review, 2016, 106(10): 2783-2816.
[14]Cattaneo M D, Keele L, Titiunik R.Interpreting regression discontinuity designs with multiple cutoffs[J]. The Journal of Politics, 2016, 78(4): 1229-1248.
[15]Wing C, Cook T D. Strengthening the regression discontinuity design using additional design elements: A within-study comparison[J]. Journal of Policy Analysis and Management, 2013, 32(4): 853-877.
[16]Angrist J D, Rokkanen M. Wanna get away? Regression discontinuity estimation of exam school effects away from the cutoff[J]. Journal of the American Statistical Association, 2015, 110(512): 1331-1344.
[17]Kolesar M, Rothe C. Inference in regression discontinuity designs with a discrete running variable[J]. The American Economic Review, 2018, 108(8): 2277-2304.
[18]Imbens G W, Kalyanaraman K. Optimal bandwidth choice for the regression discontinuity estimator[J]. The Review of Economic Studies, 2012, 79(3): 933-959.
[19]Calonico S, Cattaneo M D, Titiunik R. Robust nonparametric confidence intervals for regression-discontinuity designs[J]. Econometrica, 2014, 82(6): 2295-2326.
[20]Justin McCrary. Manipulation of the running variable in the regression discontinuity design: A density test[J]. Journal of Econometrics, 2008, (142): 698-714.
[21]Frandsen, Brigham R. Party bias in union representation elections: Testing for manipulation in the regression discontinuity design when the running variable is discrete[Z]. Unpublished Manuscript, Brigham Young University, Provo Utah, USA, 2013.
[22]Barreca A I, Guldi M, Lindo J M. Saving Babies? Revisiting the effect of very low birth weight classification[J]. Quarterly Journal of Economics, 2011, 126(4): 2117-2123.
[23]Gelman A, Imbens G W. Why High-order Polynomials Should not be Used in Regression discontinuity designs[J]. Journal of Business & Economic Statistics, 2017,(05): 1-10.
[24]Dell M. Trafficking networks and the Mexican drug war[J]. The American Economic Review, 2015, 105(6): 1738-1779.
[25]Pinotti P. Clicking on heaven's door: The effect of immigrant legalization on crime[J]. The American Economic Review, 2017, 107(1): 138-168.
[26]Malamud O, Popeleches C. Home computer use and the development of human capital[J]. Quarterly Journal of Economics, 2011, 126(2): 987-1027.
[27]Chetty R, Friedman J N, Lethpetersen S. Active vs. passive decisions and crowd-out in retirement savings accounts: Evidence from Denmark[J]. Quarterly Journal of Economics, 2014, 129(3): 1141-1219.
[28]Meng K C. Using a free permit rule to forecast the marginal abatement cost of proposed climate policy [J]. The American Economic Review, 2017, 107(3): 748-784.
[29]Clark D, Martorell P. The signaling value of a high school diploma[J]. Journal of Political Economy, 2014, 122(2): 282-318.
[30]Deshpande, Manasi. Does welfare inhibit success? The long-term effects of removing low-income youth from the disability rolls[J]. The American Economic Review,2016, 106(11) : 3300-3330.
[31]Auffhammer M, Kellogg R. Clearing the air? The effects of gasoline content regulation on air quality [J]. The American Economic Review, 2011, 101(6): 2687-2722.
[32]王骏,孙志军.重点高中能否提高学生的学业成绩——基于F县普通高中的一个断点回归设计研究[J].北京大学教育评论,2015,(04):82-109,186.
[33]李宏彬,施新政,吴斌珍.中国居民退休前后的消费行为研究[J].经济学(季刊),2015,(01):117-134.
[34]张川川,John Giles,赵耀辉.新型农村社会养老保险政策效果评估——收入、贫困、消费、主观福利和劳动供给[J].经济学(季刊),2015,(01):203-230.
[35]张明.税收征管与企业全要素生产率——基于中国非上市公司的实证研究[J].中央财经大学学报,2017,(01):11-20.
[36]马光荣,郭庆旺,刘畅.财政转移支付结构与地区经济增长[J].中国社会科学,2016,(09):105-125.
[37]何文剑,徐静文,张红霄.森林采伐限额管理制度能否起到保护森林资源的作用[J].中国人口·资源与环境,2016,(07):128-136.
[38]李江一,李涵.新型农村社会养老保险对老年人劳动参与的影响——来自断点回归的经验证据[J].经济学动态,2017,(03):62-73.
[39]王家庭,毛文峰,臧家新,等.节约集约用地政策对城市蔓延的遏制效应[J].城市问题,2017,(05):9-16.
[40]曹静,王鑫,钟笑寒.限行政策是否改善了北京市的空气质量?[J].经济学(季刊),2014,(03):1091-1126.
[41]杨小聪,彭飞,康丽丽.绿色地铁:轨道交通对空气污染的净化效果评估——基于南京地铁3号线的实证研究[J].甘肃行政学院学报,2017,(04):82-94,129-130.
[42]张英,陈绍志.产权改革与资源管护——基于森林灾害的分析[J].中国农村经济,2015,(10):15-27.
[43]陈强,孙丰凯,徐艳娴.冬季供暖导致雾霾?来自华北城市面板的证据[J].南开经济研究,2017,(04):25-40.
[44]黄新飞,杨丹.产业转移促进区域经济协调发展了吗——基于广东省县域数据的断点回归分析[J].国际经贸探索,2017,(02):101-112.
[45]高彦彦,王逸飞.熔断制度可以降低中国股市波动吗?——基于断点回归设计的实证分析[J].华东经济管理,2017,(06):104-112.
[46]王旭光.新型农村养老保险政策提升农民消费水平了吗——来自CFPS数据的实证研究[J].南方经济,2017,(01):1-12.
[47]邹红,喻开志.退休与城镇家庭消费:基于断点回归设计的经验证据[J].经济研究,2015,(01):124-139.
[48]邓婷鹤,何秀荣.退休对男性老年人健康的影响——基于断点回归的实证研究[J].人口与经济,2016,(06):82-91.
[49]Crost B, Felter J H, Johnston P B, et al. Aid under fire: Development projects and civil conflict[J]. The American Economic Review, 2014, 104(6): 1833-1856.
(1)分别为American Economic Review(AER)、Econometrica(ECMA)、Journal of Political Economy(JPE)、Quarterly Journal of Economics(QJE)和Review of Economic Studies(RES)。
(2)不包括五大上关于RDD方法的理论研究论文。我们在Jstor数据库中用全文任一地方出现“regression discontinuity”这个关键词检索,然后剔除不是运用RDD做的经验研究论文,譬如RDD的理论研究论文、仅论文文献综述或脚注中出现“regression discontinuity”的论文等。
(1)这方面的一个表现是,大量行政管理数据(administrative data)被用于经济学经验研究。根据英国《经济学人》(The Economist)的报道, NBER(National Bureau of Economic Research)工作论文摘要里出现“administrative data”的论文数,2000年是0篇,之后快速增长,2017年达到28篇。报道链接为:https://www.economist.com/international/2018/05/26/government-data-are-ever-more-important-to-economic-research。
(2)中文核心期刊论文数的检索方法如下:在中国知网检索出主题包含“断点回归”、发表年度为2011年至2017年的中文社会科学引文索引(CSSCI)期刊论文,然后逐一检查、剔除非经验研究论文,最后剩下46篇。将检索限定在中文社会科学引文索引期刊,是为了保证检索到的论文的质量。英文五大期刊论文数的检索方法如下:在Jstor数据库中用全文任一地方出现“regression discontinuity”这个关键词、发表年度为2011至2017年、期刊为五大期刊检索到50篇,然后逐一检查、剔除非经验研究论文,最后剩下39篇。
(3)Imbens和Kalyanaraman(2009)是工作论文,后来于2012年发表在《Review of Economic Studies》上。
(4)用Stata软件实现这些新进展的操作命令可以参考Cattaneo et al.(2018),更详细的操作命令细节可参考本文所引用文献的网上附件。这些网上附件可在发表各引用文献的期刊官网上下载。
(5)作者文中用的都是4次多项式,没解释不用其他次数多项式的原因。
(6)作者说这是经验上的做法,没解释这样做的原因。
(7)Lee和Lemieux (2010)在脚注中提到了之后应用广泛的IK法(Imbens和Kalyanaraman, 2009),但是文中举例只使用拇指规则法和交叉验证法,没使用IK法。
(8)实际上,甜甜圈RDD也可以克服数据操纵问题对估计结果的影响。
(9)分别来自美国、巴西、挪威、意大利等17个国家。
(10)为方便讨论,使用矩形核密度函数的非参数估计虽然等同于参数估计,但此处只将其归为非参数估计。
(11)运用IV必需的技术环节是报告第一阶段回归的F统计量取值,运用DID必需的技术环节是做平行趋势假设检验。