双重差分法的假定，为了使用OLS一致地估计方程，需要作以下两个假定。

假定1：此模型设定正确。特别地，无论处理组还是控制组，其时间趋势项都是。此假定即“平行趋势假定”（parallel trend assumption）。DID最为重要和关键的前提条件：共同趋势（Common Trends）

双重差分法并不要求实验组和控制组是完全一致的，两组之间可以存在一定的差异，但是双重差分方法要求这种差异不随着时间产生变化，也就是说，处理组和对照组在政策实施之前必须具有相同的发展趋势。

假定2：暂时性冲击与政策虚拟变量不相关。这是保证双向固定效应为一致估计量（consist estimator）的重要条件。在此，可以允许个体固定效应与政策虚拟变量相关（可通过双重差分或组内变换消去，或通过LSDV法控制）。

DID允许根据个体特征进行选择，只要此特征不随时间而变；这是DID的最大优点，即可以部分地缓解因 “选择偏差”（selection bias）而导致的内生性（endogeneity）。

2、DID操作案例

Difference in differences (DID) Estimation step‐by‐step双重差分操作步骤

首先我们读入所需数据，生成政策前后以及控制组虚拟变量，并将它们相乘产生交互项。

方法一：

Getting sample data调用数据

use "http://dss.princeton.edu/training/Panel101.dta", clear

Create a dummy variable to indicate the time when the treatment started. Lets assume that treatment started in1994. In this case, years before 1994 will have a value of 0 and 1994+ a 1. If you already have this skip this step.设置虚拟变量，政策执行时间为1994年

gen time = (year>=1994) & !missing(year)

*Create a dummy variable to identify the group exposed to the treatment. In this example lets assumed that countries with code 5,6, and 7 were treated (=1). Countries 1-4 were not treated (=0). If you already have this skip this step生成地区的虚拟变量

gen treated = (country>4) & !missing(country)

* Create an interaction between time and treated. We will call this interaction ‘did’ 产生交互项

gen did = time*treated

Estimating the DID estimator随后将这三个变量作为解释变量，y作为被解释变量进行回归：

reg y time treated did, r

结果为：

. gen time = (year>=1994) & !missing(year)

.

.

. gen treated = (country>4) & !missing(country)

.

.

. gen did = time*treated

. reg y time treated did, r

Linear regression Number of obs = 70

F(3, 66) = 2.17

Prob > F = 0.0998

R-squared = 0.0827

Root MSE = 3.0e+09

------------------------------------------------------------------------------

| Robust

y | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

time | 2.29e+09 9.00e+08 2.54 0.013 4.92e+08 4.09e+09

treated | 1.78e+09 1.05e+09 1.70 0.094 -3.11e+08 3.86e+09

did | -2.52e+09 1.45e+09 -1.73 0.088 -5.42e+09 3.81e+08

_cons | 3.58e+08 7.61e+08 0.47 0.640 -1.16e+09 1.88e+09

------------------------------------------------------------------------------

. reg y time treated did, r

Linear regression Number of obs = 70

F(3, 66) = 2.17

Prob > F = 0.0998

R-squared = 0.0827

Root MSE = 3.0e+09

------------------------------------------------------------------------------

| Robust

y | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

time | 2.29e+09 9.00e+08 2.54 0.013 4.92e+08 4.09e+09

treated | 1.78e+09 1.05e+09 1.70 0.094 -3.11e+08 3.86e+09

did | -2.52e+09 1.45e+09 -1.73 0.088 -5.42e+09 3.81e+08

_cons | 3.58e+08 7.61e+08 0.47 0.640 -1.16e+09 1.88e+09

------------------------------------------------------------------------------

.

did的系数显著为负，表明政策实施对Y有显著的（10%显著性水平下）负效应

方法二：diff

The command diff is user‐defined for Stata，To install type

ssc install diff下载外部命令方法

**diff y, t(treated) p(time)**

结果为：

. diff y, t(treated) p(time)

DIFFERENCE-IN-DIFFERENCES ESTIMATION RESULTS

Number of observations inthe DIFF-IN-DIFF: 70

Before After

Control: 16 24 40

Treated: 12 18 30

28 42

--------------------------------------------------------

Outcome var. | y | S. Err. | |t| | P>|t|

----------------+---------+---------+---------+---------

Before | | | |

Control | 3.6e+08| | |

Treated | 2.1e+09| | |

Diff (T-C) | 1.8e+09| 1.1e+09| 1.58 | 0.120

After | | | |

Control | 2.6e+09| | |

Treated | 1.9e+09| | |

Diff (T-C) | -7.4e+08| 9.2e+08| 0.81 | 0.422

| | | |

Diff-in-Diff | -2.5e+09| 1.5e+09| 1.73 | 0.088*

--------------------------------------------------------

R-square: 0.08

* Means and Standard Errors are estimated by linear regression

**Inference: *** p F = .

R-squared = 0.7212

Root MSE = 10.808

(Std. Err. adjusted for49 clusters instfips)

------------------------------------------------------------------------------

| Robust

asmrs | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

pcinc | -.0011046 .0004136 -2.67 0.010 -.0019363 -.000273

asmrh | 1.08064 .6064578 1.78 0.081 -.1387247 2.300006

cases | -190.3716 136.6556 -1.39 0.170 -465.136 84.39279

|

year |

1965 | 5.225278 2.119377 2.47 0.017 .9639841 9.486572

1966 | 2.803378 2.269053 1.24 0.223 -1.75886 7.365615

1967 | 4.61116 2.338898 1.97 0.054 -.0915108 9.31383

1968 | 5.596837 2.514211 2.23 0.031 .5416775 10.652

1969 | 8.574786 3.158377 2.71 0.009 2.224444 14.92513

1970 | 10.65894 3.821476 2.79 0.008 2.975344 18.34253

1971 | 17.6067 3.585572 4.91 0.000 10.39743 24.81598

1972 | 14.0683 4.136396 3.40 0.001 5.751524 22.38509

1973 | 16.16345 4.772027 3.39 0.001 6.568642 25.75825

1974 | 17.01009 4.575588 3.72 0.001 7.810252 26.20992

1975 | 20.48743 4.720196 4.34 0.000 10.99684 29.97802

1976 | 16.76032 5.32978 3.14 0.003 6.044076 27.47656

1977 | 18.8125 4.946074 3.80 0.000 8.867751 28.75725

1978 | 15.53648 5.404453 2.87 0.006 4.670103 26.40286

1979 | 13.97376 6.075092 2.30 0.026 1.758968 26.18855

1980 | 11.16642 5.34852 2.09 0.042 .4125048 21.92034

1981 | 13.86874 5.929315 2.34 0.024 1.947052 25.79043

1982 | 10.84654 5.143604 2.11 0.040 .5046313 21.18845

1983 | 10.26562 5.662058 1.81 0.076 -1.118707 21.64996

1984 | 13.14376 5.892586 2.23 0.030 1.295919 24.9916

1985 | 9.251855 6.348267 1.46 0.152 -3.51219 22.0159

1986 | 14.41652 6.246341 2.31 0.025 1.857413 26.97563

1987 | 15.65435 6.059627 2.58 0.013 3.470651 27.83805

1988 | 13.44858 6.610391 2.03 0.047 .1574946 26.73966

1989 | 12.80977 7.303105 1.75 0.086 -1.874109 27.49364

1990 | 14.06857 7.146289 1.97 0.055 -.3000028 28.43715

1991 | 13.22049 7.084524 1.87 0.068 -1.023902 27.46488

1992 | 12.87047 7.475258 1.72 0.092 -2.159543 27.90048

1993 | 15.34731 7.739088 1.98 0.053 -.2131671 30.90779

1994 | 15.13629 7.863552 1.92 0.060 -.6744393 30.94702

1995 | 13.79803 8.179808 1.69 0.098 -2.648576 30.24464

1996 | 13.98251 8.506622 1.64 0.107 -3.1212 31.08622

|

stfips |

4 | 36.9288 1.924405 19.19 0.000 33.05952 40.79807

5 | -4.461478 3.095326 -1.44 0.156 -10.68505 1.762091

6 | 60.38981 5.349018 11.29 0.000 49.63489 71.14473

8 | 50.05651 3.608116 13.87 0.000 42.80191 57.31111

9 | 17.08357 6.756787 2.53 0.015 3.498137 30.669

10 | 20.5695 5.507517 3.73 0.000 9.495893 31.64311

11 | 12.56921 7.996852 1.57 0.123 -3.50954 28.64796

12 | 35.74881 2.233152 16.01 0.000 31.25876 40.23887

13 | 13.61893 1.454427 9.36 0.000 10.69461 16.54325

16 | 18.44103 2.264297 8.14 0.000 13.88836 22.99371

17 | 11.29719 5.409254 2.09 0.042 .4211582 22.17323

18 | 10.4168 2.696812 3.86 0.000 4.994492 15.8391

19 | 10.28096 3.304845 3.11 0.003 3.636126 16.9258

20 | 15.3332 2.936976 5.22 0.000 9.42801 21.23838

21 | 11.01473 1.716834 6.42 0.000 7.562801 14.46665

22 | 6.137733 3.045236 2.02 0.049 .0148753 12.26059

23 | 16.7276 3.137669 5.33 0.000 10.41889 23.03631

24 | 12.89125 5.953918 2.17 0.035 .9200967 24.8624

25 | 12.10367 5.718826 2.12 0.040 .6052007 23.60214

26 | 21.57043 3.800149 5.68 0.000 13.92972 29.21114

27 | 13.77685 4.183384 3.29 0.002 5.365598 22.18811

28 | -5.819917 3.34078 -1.74 0.088 -12.53701 .8971724

29 | 15.73647 2.563135 6.14 0.000 10.58294 20.88999

30 | 24.89907 2.293199 10.86 0.000 20.28828 29.50985

31 | 7.785651 3.439078 2.26 0.028 .8709211 14.70038

32 | 78.63681 3.694747 21.28 0.000 71.20802 86.0656

33 | 20.4206 4.235537 4.82 0.000 11.90448 28.93672

34 | 6.52651 5.834313 1.12 0.269 -5.204163 18.25718

35 | 30.08897 1.257066 23.94 0.000 27.56147 32.61648

36 | 4.890387 6.564132 0.75 0.460 -8.307686 18.08846

37 | 3.285438 3.225977 1.02 0.314 -3.200823 9.771699

38 | -.5794964 3.058447 -0.19 0.851 -6.728916 5.569923

39 | 20.46251 3.613936 5.66 0.000 13.19621 27.72882

40 | 11.7639 3.582965 3.28 0.002 4.559865 18.96793

41 | 30.98784 3.101588 9.99 0.000 24.75168 37.224

42 | 11.86828 4.25983 2.79 0.008 3.30332 20.43325

44 | 15.73751 4.480252 3.51 0.001 6.729364 24.74567

45 | 4.63611 .4879704 9.50 0.000 3.65498 5.61724

46 | .1719819 3.504933 0.05 0.961 -6.875158 7.219122

47 | 5.709774 3.396845 1.68 0.099 -1.120042 12.53959

48 | 16.48494 1.94482 8.48 0.000 12.57461 20.39526

49 | 11.92987 4.052823 2.94 0.005 3.781118 20.07861

50 | 14.00645 4.839034 2.89 0.006 4.276916 23.73597

51 | 9.583616 4.912417 1.95 0.057 -.2934614 19.46069

53 | 35.6558 4.270496 8.35 0.000 27.06939 44.2422

54 | .321997 3.730593 0.09 0.932 -7.178863 7.822857

55 | 19.1378 3.921319 4.88 0.000 11.25346 27.02214

56 | 31.20661 3.447895 9.05 0.000 24.27415 38.13907

|

lead21 | -22.92073 4.075373 -5.62 0.000 -31.11481 -14.72664

lead20 | -12.08418 11.17267 -1.08 0.285 -34.54834 10.37998

lead19 | 8.842727 6.053351 1.46 0.151 -3.328351 21.01381

lead18 | -.5159513 4.753964 -0.11 0.914 -10.07444 9.042533

lead17 | -4.434874 6.310563 -0.70 0.486 -17.12311 8.253363

lead16 | -1.022577 3.651244 -0.28 0.781 -8.363896 6.318742

lead15 | .8477567 4.262787 0.20 0.843 -7.72315 9.418664

lead14 | 4.327995 5.301677 0.82 0.418 -6.33174 14.98773

lead13 | -1.388568 4.708948 -0.29 0.769 -10.85654 8.079407

lead12 | -.0434501 7.023583 -0.01 0.995 -14.16531 14.07841

lead11 | -9.381948 4.044052 -2.32 0.025 -17.51306 -1.250836

lead10 | -1.150666 5.011109 -0.23 0.819 -11.22618 8.924843

lead9 | -5.000702 3.645503 -1.37 0.177 -12.33048 2.329073

lead8 | -2.73765 3.965503 -0.69 0.493 -10.71083 5.235528

lead7 | -1.256434 4.40995 -0.28 0.777 -10.12323 7.610363

lead6 | -.7505582 3.038754 -0.25 0.806 -6.860382 5.359266

lead5 | -2.775423 2.662771 -1.04 0.302 -8.129282 2.578436

lead4 | .2283574 2.435786 0.09 0.926 -4.669119 5.125834

lead3 | -2.312587 3.017688 -0.77 0.447 -8.380055 3.754881

lead2 | -.5157397 2.555229 -0.20 0.841 -5.653371 4.621892

lag0 | .2507466 2.765789 0.09 0.928 -5.310244 5.811737

lag1 | -1.619351 2.988699 -0.54 0.590 -7.628534 4.389831

lag2 | -1.687107 3.960678 -0.43 0.672 -9.650584 6.27637

lag3 | -.7444709 2.908468 -0.26 0.799 -6.592338 5.103396

lag4 | -2.956354 2.878044 -1.03 0.309 -8.743049 2.830342

lag5 | -2.377841 2.798907 -0.85 0.400 -8.00542 3.249739

lag6 | -3.311888 3.625365 -0.91 0.366 -10.60117 3.977398

lag7 | -5.136502 3.45649 -1.49 0.144 -12.08624 1.813237

lag8 | -6.991146 3.135858 -2.23 0.031 -13.29621 -.6860805

lag9 | -4.82321 3.139015 -1.54 0.131 -11.13462 1.488201

lag10 | -8.814158 3.733515 -2.36 0.022 -16.32089 -1.307423

lag11 | -7.27331 3.689987 -1.97 0.054 -14.69253 .1459062

lag12 | -6.151559 4.15508 -1.48 0.145 -14.50591 2.202789

lag13 | -8.276837 4.00952 -2.06 0.044 -16.33852 -.2151567

lag14 | -6.593221 3.929278 -1.68 0.100 -14.49356 1.307121

lag15 | -7.850839 4.136105 -1.90 0.064 -16.16703 .465356

lag16 | -7.234422 4.339311 -1.67 0.102 -15.95919 1.490348

lag17 | -8.516898 4.413931 -1.93 0.060 -17.3917 .3579043

lag18 | -9.991582 3.819046 -2.62 0.012 -17.67029 -2.312876

lag19 | -11.53613 3.923685 -2.94 0.005 -19.42523 -3.647036

lag20 | -9.219165 4.574047 -2.02 0.049 -18.4159 -.0224257

lag21 | -10.79088 4.488696 -2.40 0.020 -19.81601 -1.765756

lag22 | -10.65478 4.682235 -2.28 0.027 -20.06905 -1.240518

lag23 | -12.08658 5.376989 -2.25 0.029 -22.89774 -1.275415

lag24 | -10.67796 6.246086 -1.71 0.094 -23.23655 1.880642

lag25 | -10.26777 7.578635 -1.35 0.182 -25.50564 4.970098

lag26 | -16.69255 10.71136 -1.56 0.126 -38.22919 4.844089

lag27 | -.4344752 8.27773 -0.05 0.958 -17.07797 16.20902

_cons | 56.23195 5.941966 9.46 0.000 44.28483 68.17908

------------------------------------------------------------------------------

. #delimit cr

delimiter now cr

.

end of do-file

该命令存储所有事件延迟、它们的下界、点估计和上界。例如，如果我们希望可视化整个滞后集的估计，以及它们的上置信区间和下置信区间，我们可以简单地检查返回的滞后矩阵:

. mat list e(lags)

e(lags)[28,4]

Lag LB Est UB

r1 0 -5.3102441 .25074664 5.8117375

r2 1 -7.6285343 -1.6193515 4.3898311

r3 2 -9.6505833 -1.6871067 6.27637

r4 3 -6.5923381 -.74447083 5.1033964

r5 4 -8.7430496 -2.9563539 2.8303416

r6 5 -8.0054207 -2.3778408 3.2497389

r7 6 -10.601172 -3.3118875 3.9773974

r8 7 -12.086242 -5.1365023 1.813237

r9 8 -13.296212 -6.9911461 -.68608052

r10 9 -11.134622 -4.8232102 1.4882015

r11 10 -16.320892 -8.8141575 -1.3074229

r12 11 -14.692526 -7.2733097 .14590624

r13 12 -14.505907 -6.1515589 2.2027895

r14 13 -16.338516 -8.2768364 -.21515673

r15 14 -14.493564 -6.5932212 1.3071214

r16 15 -16.167034 -7.8508396 .46535599

r17 16 -15.959191 -7.2344217 1.4903481

r18 17 -17.391701 -8.5168982 .35790426

r19 18 -17.670288 -9.9915819 -2.312876

r20 19 -19.42523 -11.536133 -3.6470358

r21 20 -18.415903 -9.2191648 -.02242574

r22 21 -19.816011 -10.790884 -1.7657557

r23 22 -20.069046 -10.654782 -1.240518

r24 23 -22.897739 -12.086576 -1.2754151

r25 24 -23.236555 -10.677957 1.8806419

r26 25 -25.505636 -10.267769 4.9700985

r27 26 -38.229191 -16.692551 4.8440886

r28 27 -17.077967 -.43447518 16.209017

检验领先和滞后的联合显著性。

． estat eventdd

使用野蛮自举法检验领先和滞后的联合显著性。

estat eventdd, wboot seed(1303)

结果为：

. estat eventdd

Joint significance testfor

leads and lags

----------------------------------------

LEADS

----------------------------------------

F-stat: 31.1251

P-value: 0.0000

Degrees of freedom (20,48)

----------------------------------------

LAGS

----------------------------------------

F-stat: 4.0011

P-value: 0.0000

Degrees of freedom (28,48)

----------------------------------------

5、论文应用

下面以《专利质押、融资约束与企业劳动雇佣》为例讲解一下如何使用该命令进行平行趋势检验。

政策背景：专利质押融资试点政策是研究专利质押影响企业劳动雇佣的一个良好的准自然实验。本文借助于专利质押融资试点政策的外生冲击，采用广义双重差分法，检验专利质押对企业劳动雇佣的影响。

变量介绍：

其中，被解释变量Y为企业劳动雇佣规模，用企业员工人数取自然对数进行度量。企业高技术水平员工规模，用企业技术人员取自然对数进行度量。

主要解释变量 Policy 为专利质押融资试点政策施行与否的虚拟变量。当上市公司所在地区为知识产权质押融资试点地区且时间为政策颁布的下一年及以后时，Policy 取1，否则取0。

控制变量向量X中包括企业层面和地区层面的控制变量。

企业层面控制变量主要包括企业规模(Size)、资产负债室(Ler)、资产收益率(Roa)以及股权性质(Soe)。

地区层面控制变量主要包括地级市人均GDP(P_CDP)、地级市第二产业比重(Second_ind)。λ和n分别表示企业和年度固定效应。我们对企业层面进行了聚类，以控制整个样本期内企业层面的任意结构依存性。

其中，被解释变量Y为企业劳动雇佣规模，用企业员工人数取自然对数进行度量。企业高技术水平员工规模，用企业技术人员取自然对数进行度量。

主要解释变量 Policy 为专利质押融资试点政策施行与否的虚拟变量。当上市公司所在地区为知识产权质押融资试点地区且时间为政策颁布的下一年及以后时，Policy 取1，否则取0。

控制变量向量X中包括企业层面和地区层面的控制变量。

企业层面控制变量主要包括企业规模(Size)、资产负债室(Ler)、资产收益率(Roa)以及股权性质(Soe)。

地区层面控制变量主要包括地级市人均GDP(P_CDP)、地级市第二产业比重(Second_ind)。λ和n分别表示企业和年度固定效应。我们对企业层面进行了聚类，以控制整个样本期内企业层面的任意结构依存性。

use 数据, clear

xtset code year

qui xtreg Labor Policy i.year,fe vce(cluster code) // 不带控制变量 //

est store m1

qui xtreg Labor Policy $ci.year ,fe vce(cluster code)

est store m2

qui xtreg Hlabor Policy i.year ,fe vce(cluster code)

est store m3

qui xtreg Hlabor Policy $ci.year ,fe vce(cluster code)

est store m4

lxhreg m1 m2 m3 m4 using 基准回归结果1.rtf, replace t(%13.3f) b(%13.3f) drop( *year* )

结果为：

7 平行趋势检验

采用双重差分法的前提是，实验组与控制组在专利质押融资试点政策施行前企业的劳动雇佣规模、高技术水平员工规模的趋势是保持平行的，若政策试点前的趋势不平行，则政策试点后的趋势也可能不平行，从而导致有偏的结果。由于政策试点在在多个时期，本文借鉴 Clarke 和Tapia-Schythe(2021)、Barrios(2021)的思路，利用当前处理交错型 DID 的较为新颖的事件研究法(Event Study Method)检验政策的动态处理效应。

绘制平行趋势检验图的命令为：

** # 4、**********3.2 DID有效性检验与其他稳健性测试**********

************平行趋势检验-图2******

use 数据,clear

xtset code year

replace Policy_year=. ifPolicy_year==0

gen yeardif=year-Policy_year

xtset code year

eventdd Labor $ci.year, timevar(yeardif) method(fe) cluster(code) level(95) baseline(0) ///

graph_op( yline(0,lcolor(edkblue*0.8) ) ///

xlabel(-6 "- 6"-5 "- 5"-4 "- 4"-3 "- 3"-2 "-2"-1 "-1"0 "0"1 "1"2 "2"3 "3"4 "4"5 "5"6 "6") ///

ylabel(-0.1(0.1)0.4,format (%7.1f)) ///

xline(0 ,lwidth(vthin) lpattern(dash) lcolor(teal)) ///

xtitle(` "{fontface "宋体 ": 政策时点}"', size(medium small)) ///

ytitle(`"{fontface "宋体": 回归系数}{stSerif: (Labor)}"' , size(medium small)) ///

legend(order(2 ` "{fontface "宋体 ": 回归系数}"' 1 "95% confidence interval" )) scheme(s1mono))

graph export "平行趋势Labor.png", replace

eventdd Hlabor $c i.year, timevar(yeardif) method(fe) cluster(code) level(95) baseline(0) ///

graph_op( yline(0,lcolor(edkblue*0.8) ) ///

xlabel(-6 "- 6" -5 "- 5" -4 "- 4" -3 "- 3" -2 "-2" -1 "-1" 0 "0" 1 "1" 2 "2" 3 "3" 4 "4" 5 "5" 6 "6") ///

ylabel(-0.2(0.2)1,format (%7.1f)) ///

xline(0 ,lwidth(vthin) lpattern(dash) lcolor(teal)) ///

xtitle(`"{fontface "宋体": 政策时点}"' , size(medium small)) ///

ytitle(` "{fontface "宋体 ": 回归系数}{stSerif: (HLabor)}"', size(medium small)) ///

legend(order(2 `"{fontface "宋体": 回归系数}"' 1 "95% confidence interval")) scheme(s1mono))

graph export"平行趋势HLabor.png", replace

结果为：

图1：平行趋势Labor.png

图2：平行趋势HLabor.png

结果解释：图2绘制了在95%置信水平的专利质押融资政策试点的平行趋势图。图平行趋势Labor.png表明，在专利质押政策实施前，试点地区与非试点地区的劳动雇佣并不存在显著差异，而政策试点对劳动雇佣的影响出现在政策实施一年及以后。图平行趋势HLabor.png显示，专利质押政策出台前，试点地区与非试点地区的高技术水平员工规模并不存在显著差异，在政策实施后，企业高技术员工规模的增长存在一定持续性。以上结果支持了平行趋势假设。返回搜狐，查看更多