三重差分法运行和示例

1、三重差分法及运行双重差分法的关键假设是实验组与对照组的时间效应一样。这个假设只有通过足够长的时间序列数 据才能检验。需要指出的一点是，即使干预发生之前两组时间序列一致，也不能保证干预发生后两组时间序列是一致的。有可能在干预发生的同时在实验组或者对照组中又发生了其他影响产出的事件，则干预发生后两组的时间趋势是不一致的。简单的双重差分估计是有偏的。如图 3所示，如果对照组是虚线所示，则双重差分估计是无偏的。但如果对照组是上方的实线，则双重差分估计法是有偏的，偏差部分是在 打时刻，该实线与虚线之间的距离。解决这个问题有两个思路：第一个是寻找更多的对照组，把多个对照组加权构造成一个虚拟的对照组, 使得

2、虽然每个对照组都与实验组的时间趋势不一样， 但加权后的虚拟对照组的时间趋势与实验组的一 样。这个方法被称作综合控制法 (synthetic control method) 。abadie & gardeazabal(2003)(14) 用这个方法研究了恐怖冲突对经济发展的影响。解决这个问题的第二个思路是估算出这个因为时间趋势不同而带来的偏差，然后从双重差分结果中减去这个偏差即可。这被称作三重差分法(difference-in-differences-in-differences, ddd)。三重差分法的思路是，既然两个地区(分别指实验组和对照组)的时间趋势不一样，那么我们可以分别在两个地区寻找

3、一个没有受到干预影响的人群/行业，通过对这两组的双重差分估算出时间趋势的差异，然后再从原来实验组和对照组的双重差分估算值中减去这个时间趋势差异。gruber(15)就使用了这种方法。图3 时间趋势差异造成的估计偏差三重差分法例证：two towns, x and y in each town: pool cross-sections of male and female hourly wages, one from the year before a wage- discnmmation policy took effect and one from the year afterconside

4、r the following mcdel =或）+ 为&针工 + 例mm/ 4 %尤 + bgftd1尤 +female40xjfemale +用值上加6先抽出.工十u；where ajtrn rf date after gander-wage d iscrirrination policy; 0 if date before genderwagediscn mi nation policy. the g&nder wage discrimination policy only applies to females in town x. /rmnlg=】if temple; 0 it mal

5、e xi i if town x; 0 if town y.the treatment group is females from town xoes this model measure the effect of a g&ndenwago discrrmination policy on the average wage of women relative to nwn in town x compared to the average wa-ge of women relative to men in town y1in this model, the affect of the pol

6、icy is captured by /57:the difference-in-difference-in-differences1 estimator.afor 仇 to be interpreted as the causal effect of the policy on wages in town x, e(uifemaleilafterxi) = 0 has to be assumed.does this mean that once gender, date of policy, and town have been controlled fort there exist no

7、unobserved factors which change over both town and time that affect wages?what you propose here is actually difference in difference in differences (ddd) instead of the usual difference in differences (see these lecture notes by 川)l a)( icuii： ： i2i : on the first two pages). this method can potenti

8、ally account for the unobserved trends in wages of women across your two towns and the wage changes of both male and female workers in the treatment town. in this sense ddd is a more robust approach to the dd approach you had in mind previously.3 = ,f2 -)一(方匕f.2 -mu )let y be average income and inde

9、x periods 1,2. females and men f m. and towns x、y. then your ddd coefficient gives youthe time change in y for women in town xthe time change in y fbr women in town y the time chaiigo in y fbr men in town xso your treatment effect will still be the effect of the policy on female wages relative to ma

10、le wages in town x. ttie second term subtracts the potential wage trend of females that has nothing to do with the policy. this relate$ to what i mentioned in my response to your other question that you would need to know the common trends between male and female wages this was to exclude the possib

11、ility that male and female wages are subject to systematically different changes that have nothing to do with the policy. having untreated females in another town allows to you take out this potential female wage trend that might be different from the male wage trend.read the imbens and wooldridge i

12、 ecure very carefully because they do a great job on explaining this (especially see page 2 after equation 14).even though this method is more robust, it does not mean that there is nothing left which can bias your estimates if there is another policy at the same time, for instance a law for motherc

13、are that affects female wages, this might still be picked up by your regression. in your work it will be your job to show tliat nothing else is going on in town x besides your discrimination policy.the key identifying assumption in dd models is that the treatment states have similar trends to the co

14、ntrol states in the absence of treatment.# with only one beatment and contol group, graph your results, and look at trends in periods with before the treatment. with many treatment and control groups:。 and a binary treatment, estimate treatment impacts at different datesq wr = 7s + &istwhere dt is n

15、ow an indicator for whether the treatment got switched on in year 匕 this estimates q kads and m lags of the treatment. the leads should all be zero,* include state specific trends.三重差分法回归及运行命令the did method can bo implemend according to the tabla below, wtiere the tawer nght cell is the did estimatc

16、r机tjs = 2= idifferencet 2ynvl2 u22t = 1如yusni -。灯chang*v* 一 gvii - im(v” 一 si) 一 幅12 - vt3)running a regression analysis gives the same res it. consider the 0l5 modelv =员+为丁+凡$ +为(，$)+名11kr . zw川单* & t sit ufuny ndim.细工 th.wtahf (t s1. ihn1 . 1mwm1* g t .allhough kift ml show n 闻 0rg吟 twa. (urnfr ou

17、t that ifw eslirra tmm if* model 审附正如上面的二重差分法实际上运用的是 ols做的回归，我们之前说过，倍差法是相当于 two-way fixed effect model ,里面包括个体效应时间效应，而对于一个这样的 panel data ,我们可以运 用lsdv通过添加个体和时间虚拟变量来回归，或者运用 demeaned variables 回归来消除个体和时间效应，再加上那些交互效应后就可以像其他fixed effect回归一样。二重差分法一般是在同一个省（地区）区分treatment和control组的，而三重差分法则包括另一个未受到政策冲击的省（地区）

18、，来区分treatment和control组的，当然三重差分法要稳健得多。empirical methods in applied economics lecturejorn-steffen pischke接下来，我们来区分一下二重差分和三重差分在stata的运行过程1992年，美国新泽西州通过法律将最低工资从每小时4.25美元提高到5.05美元，但在相邻的宾夕法尼亚州最低工资却保持不变。card and krueger收集了两个州的快餐店在实施新法前后雇佣人数 的数据，并使用双重差分法进行估计。注：fte ： full time employment 人数；treated=1 ,表示快餐店在

19、新泽西州，否则在宾夕法尼亚 州；t=1 ,表示时间为1992年11月， 否则为1992年2月；bk=1 ,表示burger king 快餐品 牌；kfc=1 ,表示肯彳惠基快餐品牌；roys=1 ,表示roy rogers快餐品牌；wendys=1 ,表示 wendys快餐品牌。以下黑色字体的code可以直接在stata上执行1 .读取数据：use repec/bocode/c/cardkrueger1994.dta”idtreatedfeebkkf eroysvendys_df f1qnj31100011nj401000 ril-20mj131000021mjlz 51q0q30nj12.50100c31nj7.501004gnji.60d工004-ik j.nj2d00100$nj20q01cc51nj2500100cdj300l0061njq0ql0qb0nj-00010g3wj27. 5qq102 .简单的二重差分：diff fte, t(treated) p(t)difference-in-dieferences estimation