README.md · 贾凯威/RCM

```

*========================================
          *           高级计量经济学
          *========================================
    
      
          *        计量经济学服务中心

*-------------------------------------------------------------------------------     
*        参考资料：
*        《初级计量经济学及Stata应用：Stata从入门到进阶》             
*        《高级计量经济学及Stata应用：Stata回归分析与应用》
*        《量化社会科学方法》
*        《社会科学因果推断》
*        《面板数据计量分析方法》
*        《时间序列计量分析方法》
*        《高级计量经济学及Eviews应用》
*        《R、Python、Mtalab初高级教程》
*        《空间计量入门：空间计量在Geoda、GeodaSpace中的应用》 
*        《零基础|轻松搞定空间计量：空间计量及GeoDa、Stata应用》
*        《空间计量第二部：空间计量及Matlab应用课程》
*        《空间计量第三部：空间计量及Stata应用课程》
*        《空间计量第四部：《空间计量及ArcGis应用课程》
*        《空间计量第五部：空间计量经济学》
*        《空间计量第六部：《空间计量及Python应用》
*        《空间计量第七部：《空间计量及R应用》
*        《空间计量第八部：《高级空间计量经济学》
*-------------------------------------------------------------------------------
```

# 1、简介
RCM有效地实现了回归控制方法(rcm)，即一种用于项目评估的面板数据方法(Hsiao et al., J. Ap. Met. 2012)，该方法利用横截面相关性，通过线性回归(OLS)、套索或套索后OLS构建单个治疗单元的反事实结果。协变量(indepvars)被允许进一步改进by Hsiao and Zhou(J. Ap. Met., 2019)。RCM也支持使用反事实和/或时间来进行统计推断的安慰剂试验。关于rcm使用的详细指南，请参阅Yan和Chen(2021)。

# 2、命令下载安装
```
rcm -- efficient implementation of regression control method (RCM), aka panel data approach (PDA) for program evaluation (Hsiao et al. 2012)
```

在Stata中实现“回归控制方法(RCM)”

安装方法命令为:
```
ssc install rcm, all replace
```
要求：Stata版本>= 16

安装文件包括:
rcm.ado and rcm.sthlp: Stata ado and help file

其他数据文件包括growth.dta 和repgermany.dta这两个数据

# 3、语法格式为：

```
 rcm depvar [indepvars] [if] [in] , trunit(#) trperiod(#) [options]

```
注意事项：
必须使用Xtset panelvar timevar来以通常的长形式声明面板数据集;参考xtset。

RCM自动重塑面板数据集从长到宽的形式，适合于实现回归控制方法。

depvar和indepvars必须是数值变量，不允许使用缩写。

**必选项包括**

Trunit(#)在xtset panelvar中指定的面板变量中给定的被处理单元(即受干预影响的单元)的单元号。注意，只能指定单个受影响的单元。

Trperoid(#)干预发生的时间周期。时间周期指的是xtset timevar中指定的时间变量，并且必须是一个整数(参见下面的示例)。注意，只有一个可以指定时间段。

**可选项包括如下**
```
Model
ctrlunit(numlist)   表示控制单元用作供体池
preperiod(numlist)  表示受干预前
postperiod(numlist) 表示受干预前

Optimization

criterion(sel_criterion) 用于选择最优模型的方法

estimate(est_method)                                        
method for estimating post-selection coefficients

Placebo Test
使用假治疗单位和/或时间的安慰剂试验

Reporting
frame(framename)   创建一个Stata数据框，以宽格式存储数据集和生成的变量

nofigure     不要显示图。默认是显示所有的图。
 
```

# 4、Stata操作案例

复制Hsiao et al.(2012)

考虑1997年7月1日回归对香港实际GDP增长率的影响

处理变量时间点:1997Q3

预处理期:1993Q1-1997Q2

后处理期:1997Q3-2004Q1

处理单位:香港

对照组:10个与香港经济有密切联系的国家/地区

###  4.1案例1  estimating the impact of political integration of Hong Kong with mainland China in 1997q3 (Hsiao et al., 2012)
```
. use growth, clear
        . xtset region time

```
结果为

```
        . xtset region time

Panel variable: region (strongly balanced)
 Time variable: time, 1993q1 to 2008q1
         Delta: 1 quarter

. 
end of do-file

. do "C:\Users\Metrics\AppData\Local\Temp\STD43e8_000000.tmp"

.         . label list
region:
           1 Australia
           2 Austria
           3 Canada
           4 China
           5 Denmark
           6 Finland
           7 France
           8 Germany
           9 HongKong
          10 Indonesia
          11 Italy
          12 Japan
          13 Korea
          14 Malaysia
          15 Mexico
          16 Netherlands
          17 NewZealand
          18 Norway
          19 Philippines
          20 Singapore
          21 Switzerland
          22 Taiwan
          23 Thailand
          24 UnitedKingdom
          25 UnitedStates

```
接下来进行RCM分析

```
 . rcm gdp, trunit(9) trperiod(150) ctrlunit(4 10 12 13 14 19 20 22 23 25) postperiod(150/175)
```

结果为：
```
    . rcm gdp, trunit(9) trperiod(150) ctrlunit(4 10 12 13 14 19 20 22 23 25) postperiod(150/175)

Step 1: Select the suboptimal models
(method best specified)
Note: If this takes too long, you may wish to try method(lasso)(recommended), method(forward) or method(backward).
      Alternatively, you may restrict indepvars, and/or the donor pool by the option ctrlunit().

Selecting the suboptimal model with number of predictors 1-10...

Step 2: Select the optimal model from the suboptimal models
(criterion aicc specified)

Comparing the suboptimal models containing different set of predictors:
-----------------------------------------------------
  K |    AICc         AIC         BIC      R-squared 
----+------------------------------------------------
  1 |  -144.7514   -146.4657   -143.7946      0.4034 
  2 |  -160.5063   -163.5832   -160.0217      0.7937 
  3 |  -170.6492   -175.6492   -171.1973      0.9056 
  4 |  -171.7725   -179.4088   -174.0666      0.9314 
  5 |  -169.7878   -180.9878   -174.7552      0.9438 
  6 |  -164.2937   -180.2937   -173.1707      0.9477 
  7 |  -156.6834   -179.1834   -171.1701      0.9503 
  8 |  -146.2921   -177.7207   -168.8169      0.9517 
  9 |  -131.7464   -175.7464   -165.9523      0.9518 
 10 |  -111.3603   -173.7603   -163.0758      0.9518 
-----------------------------------------------------
Among models with 1-10 predictors, the optimal model contains 4 predictors with AICc = -171.7725.

Fitting results in the pre-treatment periods using OLS:
-----------------------------------------------------------------------------------
 Mean Absolute Error      =   0.00611          Number of Observations  =         18
 Mean Squared Error       =   0.00003          Number of Predictors    =          4
 Root Mean Squared Error  =   0.00578          R-squared               =    0.93144
-----------------------------------------------------------------------------------
-----------------------------------------------------------------------------------
    gdp路HongKong | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
------------------+----------------------------------------------------------------
       gdp路Korea |    -0.4323     0.0634    -6.82   0.000      -0.5692     -0.2954
       gdp路Japan |    -0.6760     0.1117    -6.05   0.000      -0.9172     -0.4347
      gdp路Taiwan |     0.7926     0.3099     2.56   0.024       0.1231      1.4621
gdp路UnitedStates |     0.4860     0.2195     2.21   0.045       0.0118      0.9603
            _cons |     0.0263     0.0170     1.54   0.147      -0.0105      0.0631
-----------------------------------------------------------------------------------

Prediction results in the post-treatment periods using OLS:
---------------------------------------------
  Time  |   Treated    Predicted  Tr. Effect 
--------+------------------------------------
 1997q3 |     0.0610      0.0798     -0.0188 
 1997q4 |     0.0140      0.0810     -0.0670 
 1998q1 |    -0.0320      0.1294     -0.1614 
 1998q2 |    -0.0610      0.1433     -0.2043 
 1998q3 |    -0.0810      0.1319     -0.2129 
 1998q4 |    -0.0650      0.1390     -0.2040 
 1999q1 |    -0.0290      0.0876     -0.1166 
 1999q2 |     0.0050      0.0670     -0.0620 
 1999q3 |     0.0390      0.0400     -0.0010 
 1999q4 |     0.0830      0.0445      0.0385 
 2000q1 |     0.1070      0.0434      0.0636 
 2000q2 |     0.0750      0.0398      0.0352 
 2000q3 |     0.0760      0.0524      0.0236 
 2000q4 |     0.0630      0.0318      0.0312 
 2001q1 |     0.0270      0.0118      0.0152 
 2001q2 |     0.0150     -0.0177      0.0327 
 2001q3 |    -0.0010     -0.0177      0.0167 
 2001q4 |    -0.0170      0.0184     -0.0354 
 2002q1 |    -0.0100      0.0314     -0.0414 
 2002q2 |     0.0050      0.0500     -0.0450 
 2002q3 |     0.0280      0.0577     -0.0297 
 2002q4 |     0.0480      0.0346      0.0134 
 2003q1 |     0.0410      0.0538     -0.0128 
 2003q2 |    -0.0090      0.0251     -0.0341 
 2003q3 |     0.0380      0.0628     -0.0248 
 2003q4 |     0.0470      0.0761     -0.0291 
--------+------------------------------------
  Mean  |     0.0180      0.0576     -0.0396 
---------------------------------------------
Note: The average treatment effect over the post-treatment periods is -0.0396.

Finished.

. 
end of do-file

```

### 4.2Use post-lasso OLS with LOOCV and all control units, and create a Stata frame "growth_wide" storing dataset with generated variables in wide form

代码为
```
rcm gdp, trunit(9) trperiod(150) postperiod(150/175) method(lasso) criterion(cv) frame(growth_wide)

```
结果为

```
. rcm gdp, trunit(9) trperiod(150) postperiod(150/175) method(lasso) criterion(cv) frame(growth_wide)

Step 1: Select the suboptimal models
(method lasso specified)

Selecting the suboptimal model...

Step 2: Select the optimal model from the suboptimal models
(criterion cv specified for leave-one-out cross-validation)

Comparing the suboptimal models containing different set of predictors:
-------------------------------------------------------------------------------------------------------------
  K |    AICc         AIC         BIC       CV MSE     R-squared     lambda  |           Operation           
----+------------------------------------------------------------------------+-------------------------------
  1 |  -136.4018   -138.1161   -135.4450      0.0004      0.0513      0.0136 | add gdp路Mexico      
  2 |  -137.2575   -140.3344   -136.7729      0.0003      0.2495      0.0108 | add gdp路Japan       
  3 |  -135.5407   -140.5407   -136.0888      0.0003      0.3361      0.0098 | add gdp路Finland     
  4 |  -137.3309   -144.9673   -139.6250      0.0003      0.5354      0.0074 | add gdp路Korea       
  6 |  -129.9034   -145.9034   -138.7804      0.0002      0.6468      0.0062 | add gdp路Australia gdp路Italy 
  5 |  -138.0419   -149.2419   -143.0093      0.0002      0.6722      0.0059 | drop gdp路Finland    
  6 |  -143.4155   -159.4155   -152.2925      0.0002      0.8333      0.0032 | add gdp路Taiwan      
  5 |  -153.4700   -164.6700   -158.4374      0.0002      0.8609      0.0028 | drop gdp路Italy      
  6 |  -147.6414   -163.6414   -156.5184      0.0001      0.8682      0.0027 | add gdp路Malaysia    
  7 |  -153.9967   -176.4967   -168.4834      0.0001      0.9422      0.0011 | add gdp路UnitedStates 
  8 |  -145.5446   -176.9732   -168.0695      0.0001      0.9497      0.0008 | add gdp路Canada      
  7 |  -157.4199   -179.9199   -171.9065      0.0001      0.9522      0.0007 | drop gdp路UnitedStates 
  8 |  -146.7505   -178.1790   -169.2753      0.0001      0.9529      0.0007 | add gdp路Philippines 
  9 |  -133.3717   -177.3717   -167.5776      0.0001      0.9559      0.0006 | add gdp路UnitedStates 
 11 |   -84.8554   -175.8554   -164.2805      0.0001      0.9616      0.0004 | add gdp路France gdp路Germany 
 12 |   -35.5339   -175.5339   -163.0687      0.0001      0.9650      0.0004 | add gdp路Switzerland 
 11 |   -92.2461   -183.2461   -171.6713      0.0001      0.9745      0.0002 | drop gdp路UnitedStates 
 13 |    59.2679   -180.7321   -167.3766      0.0001      0.9766      0.0002 | add gdp路China gdp路UnitedStates 
 12 |   -44.0388   -184.0388   -171.5736      0.0001      0.9782      0.0002 | drop gdp路Canada     
 13 |    56.8234   -183.1766   -169.8211      0.0001      0.9795      0.0002 | add gdp路UnitedKingdom 
 12 |   -47.6918   -187.6918   -175.2266      0.0001      0.9822      0.0002 | drop gdp路UnitedStates 
 12 |   -54.1876   -194.1876   -181.7224      0.0001      0.9876      0.0001 | .                              
-------------------------------------------------------------------------------------------------------------
Among models with 1-24 predictors, the optimal model contains 12 predictors with CV MSE = 0.0001.

Fitting results in the pre-treatment periods using post-lasso OLS:
------------------------------------------------------------------------------------
 Mean Absolute Error      =   0.00404           Number of Observations  =         18
 Mean Squared Error       =   0.00001           Number of Predictors    =         12
 Root Mean Squared Error  =   0.00256           R-squared               =    0.99481
------------------------------------------------------------------------------------
------------------------------------------------------------------------------------
     gdp路HongKong | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------------+----------------------------------------------------------------
    gdp路Australia |     0.0293     0.0988     0.30   0.779      -0.2247      0.2833
        gdp路China |     0.3318     0.1115     2.98   0.031       0.0452      0.6184
       gdp路France |     0.4306     0.1858     2.32   0.068      -0.0469      0.9081
      gdp路Germany |     0.5107     0.1917     2.66   0.045       0.0180      1.0033
        gdp路Japan |    -0.8833     0.1007    -8.77   0.000      -1.1421     -0.6244
        gdp路Korea |    -0.6836     0.0753    -9.07   0.000      -0.8773     -0.4900
     gdp路Malaysia |     0.0400     0.0481     0.83   0.443      -0.0836      0.1636
       gdp路Mexico |     0.0667     0.0489     1.36   0.231      -0.0591      0.1925
  gdp路Philippines |    -0.6231     0.1339    -4.65   0.006      -0.9674     -0.2789
  gdp路Switzerland |     0.1001     0.1098     0.91   0.404      -0.1822      0.3824
       gdp路Taiwan |    -0.4112     0.4313    -0.95   0.384      -1.5198      0.6974
gdp路UnitedKingdom |     0.8364     0.2854     2.93   0.033       0.1027      1.5701
             _cons |     0.0881     0.0220     4.01   0.010       0.0317      0.1446
------------------------------------------------------------------------------------

Prediction results in the post-treatment periods using post-lasso OLS:
---------------------------------------------
  Time  |   Treated    Predicted  Tr. Effect 
--------+------------------------------------
 1997q3 |     0.0610      0.0896     -0.0286 
 1997q4 |     0.0140      0.0929     -0.0789 
 1998q1 |    -0.0320      0.2110     -0.2430 
 1998q2 |    -0.0610      0.2397     -0.3007 
 1998q3 |    -0.0810      0.2472     -0.3282 
 1998q4 |    -0.0650      0.2572     -0.3222 
 1999q1 |    -0.0290      0.1389     -0.1679 
 1999q2 |     0.0050      0.0670     -0.0620 
 1999q3 |     0.0390      0.0515     -0.0125 
 1999q4 |     0.0830      0.0395      0.0435 
 2000q1 |     0.1070      0.0063      0.1007 
 2000q2 |     0.0750      0.0448      0.0302 
 2000q3 |     0.0760      0.0377      0.0383 
 2000q4 |     0.0630      0.0571      0.0059 
 2001q1 |     0.0270      0.1183     -0.0913 
 2001q2 |     0.0150      0.1144     -0.0994 
 2001q3 |    -0.0010      0.1302     -0.1312 
 2001q4 |    -0.0170      0.1325     -0.1495 
 2002q1 |    -0.0100      0.0814     -0.0914 
 2002q2 |     0.0050      0.0722     -0.0672 
 2002q3 |     0.0280      0.0872     -0.0592 
 2002q4 |     0.0480      0.0271      0.0209 
 2003q1 |     0.0410      0.1020     -0.0610 
 2003q2 |    -0.0090      0.1192     -0.1282 
 2003q3 |     0.0380      0.0829     -0.0449 
 2003q4 |     0.0470      0.0950     -0.0480 
--------+------------------------------------
  Mean  |     0.0180      0.1055     -0.0875 
---------------------------------------------
Note: The average treatment effect over the post-treatment periods is -0.0875.

Finished.

```

### 4.3 Implement a placebo test using all fake treatment units in the donor pool

```
        . rcm gdp, trunit(9) trperiod(150) postperiod(150/175) method(lasso) criterion(cv) placebo(unit)

```

```
. rcm gdp, trunit(9) trperiod(150) postperiod(150/175) method(lasso) criterion(cv) placebo(unit)

Step 1: Select the suboptimal models
(method lasso specified)

Selecting the suboptimal model...

Step 2: Select the optimal model from the suboptimal models
(criterion cv specified for leave-one-out cross-validation)

Implementing placebo effects using fake treatment unit Australia...Austria...Canada...China...Denmark...Finland...France...Ge
> rmany...Indonesia...Italy...Japan...Korea...Malaysia...Mexico...Netherlands...NewZealand...Norway...Philippines...Singapore
> ...Switzerland...Taiwan...Thailand...UnitedKingdom...UnitedStates...

Placebo test results using fake treatment units:
--------------------------------------------------------------------------------------------------
      Unit     |        Pre MSPE        Post MSPE    Post/Pre MSPE   Pre MSPE of Unit/Treated Unit 
---------------+----------------------------------------------------------------------------------
      HongKong |          0.0000           0.0198        3009.7824           1.0000 
     Australia |          0.0000           0.0008          18.5015           6.4202 
       Austria |          0.0000           0.0004          28.6729           2.0841 
        Canada |          0.0000           0.0020        1039.6208           0.2995 
         China |          0.0000           0.0016          82.3533           2.8889 
       Denmark |          0.0000           0.0012          43.5217           4.3274 
       Finland |          0.0000           0.0039         207.2381           2.8796 
        France |          0.0000           0.0006          73.2262           1.1454 
       Germany |          0.0000           0.0003          16.0078           2.7504 
     Indonesia |          0.0000           0.0092         284.5697           4.9035 
         Italy |          0.0000           0.0014         228.5263           0.9062 
         Japan |          0.0000           0.0054         183.8924           4.4759 
         Korea |          0.0000           0.0068        3721.7026           0.2798 
      Malaysia |          0.0007           0.0060           9.0531         100.4546 
        Mexico |          0.0001           0.0032          30.5062          15.8926 
   Netherlands |          0.0000           0.0001           4.8597           4.3291 
    NewZealand |          0.0001           0.0032          26.6424          18.1849 
        Norway |          0.0001           0.0078          55.8595          21.2922 
   Philippines |          0.0000           0.0198        3757.4421           0.8045 
     Singapore |          0.0001           0.0072         137.8805           7.9428 
   Switzerland |          0.0000           0.0013          58.8820           3.3993 
        Taiwan |          0.0000           0.0011        2852.1634           0.0595 
      Thailand |          0.0002           0.0060          39.4678          23.0439 
 UnitedKingdom |          0.0000           0.0015         161.0820           1.4022 
  UnitedStates |          0.0000           0.0001         285.1185           0.0517 
--------------------------------------------------------------------------------------------------
Note: The probability of obtaining a post/pre-treatment MSPE ratio as large as HongKong's is 0.1200.

Placebo test results using fake treatment units (continued):
---------------------------------
  Time  |   Tr. Eff.    P-value  
--------+------------------------
 1997q3 |    -0.0286      0.1667 
 1997q4 |    -0.0789      0.0000 
 1998q1 |    -0.2430      0.0000 
 1998q2 |    -0.3007      0.0000 
 1998q3 |    -0.3282      0.0000 
 1998q4 |    -0.3222      0.0000 
 1999q1 |    -0.1679      0.0417 
 1999q2 |    -0.0620      0.2083 
 1999q3 |    -0.0125      0.8333 
 1999q4 |     0.0435      0.1250 
 2000q1 |     0.1007      0.0000 
 2000q2 |     0.0302      0.2917 
 2000q3 |     0.0383      0.1667 
 2000q4 |     0.0059      0.8333 
 2001q1 |    -0.0913      0.1250 
 2001q2 |    -0.0994      0.1667 
 2001q3 |    -0.1312      0.0833 
 2001q4 |    -0.1495      0.1250 
 2002q1 |    -0.0914      0.2083 
 2002q2 |    -0.0672      0.1667 
 2002q3 |    -0.0592      0.1250 
 2002q4 |     0.0209      0.3750 
 2003q1 |    -0.0610      0.1250 
 2003q2 |    -0.1282      0.0417 
 2003q3 |    -0.0449      0.1250 
 2003q4 |    -0.0480      0.0833 
---------------------------------
Note: The p-value of the treatment effect for a particular period is definded as the frequency that the absolute values of
      the placebo effects are greater or equal to the absolute value of treatment effect.

Finished.

```

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