逐年PSM - DID
2.3 逐年PSM DID
逐年PSM - DID的整个流程与截面PSM - DID大致相似，也是通过PSM获得匹配后样本，然后再将样本代入DID模型中参与回归，最后比较回归结果以验证稳健性。
首先还是进行1:2的卡尺最近邻匹配。
**# 二、逐年匹配
use psmdata.dta, clear
**# 2.1 卡尺最近邻匹配（1:2）
forvalue i = 1998/2007{
preserve
capture {
keep if year == `i'
set seed 0000
gen norvar_2 = rnormal()
sort norvar_2
psmatch2 treated $xlist , outcome(TFPQD_OP) logit neighbor(2) ///
ties common ate caliper(0.05)
save `i'.dta, replace
}
restore
}
clear all
use 1998.dta, clear
forvalue k =1999/2007 {
capture {
append using `k'.dta
}
}
save ybydata.dta, replace
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明显可以看出，与截面PSM - DID相比这里多了两个循环。
第一个循环的作用是逐年进行PSM，并将各年份PSM结果保存，最后获得1998年至2007年共10年的匹配后数据集。其中，
preserve和restore方便高效使用数据，即不用在循环中写入use psmdata.dta, clear。capture{}是为了避免某些年份数据缺失导致Stata报错并停止运行，当然，这里的年份都是连续的。第二个循环的作用是将各年份匹配后数据纵向合并至一个数据集中，生成我们回归需要的面板数据。
capture{}的作用同上。
之后是绘制倾向得分值的核密度图（当然，先进行平衡性检验也行）。
**# 2.2 倾向得分值的核密度图
sum _pscore if treated == 1, detail // 处理组的倾向得分均值为0.5698
*- 匹配前
sum _pscore if treated == 0, detail
twoway(kdensity _pscore if treated == 1, lpattern(solid) ///
lcolor(black) ///
lwidth(thin) ///
scheme(qleanmono) ///
ytitle("{stSans:核}""{stSans:密}""{stSans:度}", ///
size(medlarge) orientation(h)) ///
xtitle("{stSans:匹配前的倾向得分值}", ///
size(medlarge)) ///
xline(0.5698 , lpattern(solid) lcolor(black)) ///
xline(`r(mean)', lpattern(dash) lcolor(black)) ///
saving(kensity_yby_before, replace)) ///
(kdensity _pscore if treated == 0, lpattern(dash)), ///
xlabel( , labsize(medlarge) format(%02.1f)) ///
ylabel(0(1)3, labsize(medlarge)) ///
legend(label(1 "{stSans:处理组}") ///
label(2 "{stSans:控制组}") ///
size(medlarge) position(1) symxsize(10))
graph export "kensity_yby_before.emf", replace
discard
*- 匹配后
sum _pscore if treated == 0 & _weight != ., detail
twoway(kdensity _pscore if treated == 1, lpattern(solid) ///
lcolor(black) ///
lwidth(thin) ///
scheme(qleanmono) ///
ytitle("{stSans:核}""{stSans:密}""{stSans:度}", ///
size(medlarge) orientation(h)) ///
xtitle("{stSans:匹配后的倾向得分值}", ///
size(medlarge)) ///
xline(0.5698 , lpattern(solid) lcolor(black)) ///
xline(`r(mean)', lpattern(dash) lcolor(black)) ///
saving(kensity_yby_after, replace)) ///
(kdensity _pscore if treated == 0 & _weight != ., lpattern(dash)), ///
xlabel( , labsize(medlarge) format(%02.1f)) ///
ylabel(0(1)3, labsize(medlarge)) ///
legend(label(1 "{stSans:处理组}") ///
label(2 "{stSans:控制组}") ///
size(medlarge) position(1) symxsize(10))
graph export "kensity_yby_after.emf", replace
discard
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结果如图 6和图 7。
与截面PSM的结果类似，匹配前后两条核密度曲线偏差都比较大，但匹配后均值线距离缩短，两条曲线更加接近，因此一定程度上可以说明逐年匹配有效。
然后是逐年PSM的平衡性检验。
与截面PSM不同的是，由于逐年PSM是一年一年进行匹配的，因此考察各协变量在两组间是否存在系统性偏差只能在同一年份中进行比较，不同年份的匹配样本没有可比性，而且合并成面板数据后再进行平衡性检验Stata在技术上也不可行。这里参考谢申祥等（2021）的方法，比较匹配前后不同年份logit回归结果，即，如果匹配后各协变量的系数值减小、变得不显著和伪R方明显减小，则说明在不同年份两组的协变量不存在系统性偏差。
**# 2.3 逐年平衡性检验
*- 匹配前
forvalue i = 1998/2007 {
capture {
qui: logit treated $xlist i.ind3 if year == `i', vce(cluster prov)
est store ybyb`i'
}
}
local ybyblist ybyb1998 ybyb1999 ybyb2000 ybyb2001 ybyb2002 ///
ybyb2003 ybyb2004 ybyb2005 ybyb2006 ybyb2007
reg2docx `ybyblist' using 逐年平衡性检验结果_匹配前.docx, b(%6.4f) t(%6.4f) ///
scalars(N r2_p(%6.4f)) noconstant replace ///
indicate("Industry = *.ind3") ///
mtitles("1998b" "1999b" "2000b" "2001b" "2002b" ///
"2003b" "2004b" "2005b" "2006b" "2007b") ///
title("逐年平衡性检验_匹配前")
*- 匹配后
forvalue i = 1998/2007 {
capture {
qui: logit treated $xlist i.ind3 ///
if year == `i' & _weight != ., vce(cluster prov)
est store ybya`i'
}
}
local ybyalist ybya1998 ybya1999 ybya2000 ybya2001 ybya2002 ///
ybya2003 ybya2004 ybya2005 ybya2006 ybya2007
reg2docx `ybyalist' using 逐年平衡性检验结果_匹配后.docx, b(%6.4f) t(%6.4f) ///
scalars(N r2_p(%6.4f)) noconstant replace ///
indicate("Industry = *.ind3") ///
mtitles("1998a" "1999a" "2000a" "2001a" "2002a" ///
"2003a" "2004a" "2005a" "2006a" "2007a") ///
title("逐年平衡性检验_匹配后")
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以上代码的运行结果如下。
*- 匹配前
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
1998b 1999b 2000b 2001b 2002b 2003b 2004b 2005b 2006b 2007b
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
treated
ADM 2.2684*** 2.3222*** 2.0865*** 1.9288** 1.4294* 2.0740** 2.0784* 1.5288 2.3137 2.7268**
(2.7355) (2.5959) (2.8096) (2.4781) (1.9008) (2.0923) (1.9458) (0.9822) (1.3856) (2.1562)
PPE -0.5244** -0.3025 -0.7743*** -0.5716** -0.7099*** -0.6272** -1.0487*** -1.0451*** -0.8431* -0.9608**
(-2.2990) (-1.5852) (-3.4052) (-2.3569) (-2.6279) (-2.2244) (-3.5397) (-2.7774) (-1.9164) (-2.1682)
ADV 0.0000 0.0000 0.0000 13.4355 0.0000 0.0000 26.4667** 34.6121** 31.8339** 16.2578
(.) (.) (.) (1.0514) (.) (.) (2.4702) (2.2337) (2.2127) (1.2177)
RD 0.0000 0.0000 0.0000 10.9171 0.0000 0.0000 0.0000 -1.3296 14.1701 8.3546
(.) (.) (.) (1.2536) (.) (.) (.) (-0.1238) (1.5283) (0.7065)
HHI -1.6439* -1.6918** -1.1028 -1.2699 -1.0869 -0.6338 0.0072 0.0714 -0.0496 0.0429
(-1.7219) (-1.9652) (-1.3282) (-1.4922) (-1.4629) (-0.8633) (0.0148) (0.1513) (-0.0896) (0.0784)
INDSIZE 0.5445* 0.4829* 0.3557 0.3033 0.2376 0.1528 -0.2555 -0.0907 -0.1805 -0.2358
(1.7667) (1.8760) (1.4057) (1.1672) (0.9226) (0.6146) (-1.2398) (-0.4178) (-0.7170) (-0.9694)
NFIRMS -0.3930 -0.2420 0.0200 0.1023 0.2644 0.3734 0.9632*** 0.6899** 0.7769** 0.8697**
(-0.6612) (-0.4746) (0.0427) (0.2083) (0.5603) (0.8035) (2.7205) (1.9736) (2.0972) (2.4071)
FCFIRM 1.6635 0.7963 1.6429 1.1912 0.7410 0.6982 2.0390** 0.8335 1.1705 1.5674*
(0.9054) (0.4392) (1.1530) (0.6450) (0.5633) (0.6334) (2.1761) (0.6433) (1.3389) (1.6736)
MARGIN 1.5995*** 1.4034*** 1.0741*** 1.2462*** 0.4034 0.8745** 1.2484** -0.3829 0.7840 0.1712
(3.5296) (3.5031) (2.8690) (3.1566) (0.8275) (2.0900) (2.3096) (-0.3499) (0.6127) (0.1870)
LEVDISP -0.9378 -0.8800 -1.3296 -1.3270 -0.9001 -1.1339 -0.9631 -1.2057 -1.6036 -1.5013
(-0.4328) (-0.5331) (-0.7892) (-0.7769) (-0.5507) (-0.6717) (-0.5041) (-0.6542) (-0.9766) (-0.9726)
SIZEDISP -0.0741 0.0517 0.0790 0.1699 0.1840 0.1689 0.5612*** 0.3714 0.5487** 0.6102**
(-0.2874) (0.2080) (0.3297) (0.7125) (0.6938) (0.7498) (2.7553) (1.4051) (2.1442) (2.1618)
ENTRYR 0.0000 -0.0619 0.9535* 0.2964 0.0387 0.0183 0.0348 -0.6241 -0.6629** -0.6837**
(.) (-0.1157) (1.7572) (0.5243) (0.1305) (0.0435) (0.1230) (-0.6853) (-2.1473) (-2.3081)
EXITR -0.9139 0.7341 0.0460 -0.5761 -0.3070 0.2523 0.8344** 0.0524 -0.5910 -0.5330
(-1.1158) (1.1616) (0.0659) (-0.8138) (-0.6607) (0.4841) (2.0014) (0.1361) (-0.9383) (-0.7851)
_cons -8.6621*** -8.8834*** -7.3079*** -6.6187** -5.6780** -5.4720** -2.9528 -2.3179 -2.4977 -1.5174
(-2.7961) (-3.3483) (-2.6862) (-2.2210) (-2.1561) (-2.1240) (-1.0200) (-0.8532) (-0.7556) (-0.4968)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Industry Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
N 6303 6600 6656 6845 7187 7601 9057 9428 10221 11207
r2_p 0.1321 0.1301 0.1337 0.1368 0.1369 0.1351 0.1578 0.1351 0.1314 0.1368
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
t statistics in parentheses
* p<0.1, ** p<0.05, *** p<0.01
*- 匹配后
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
1998a 1999a 2000a 2001a 2002a 2003a 2004a 2005a 2006a 2007a
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
treated
ADM 0.8186 0.7099 1.0169 0.8462 0.1525 0.7434 0.0853 0.3600 0.8061 0.7568
(1.0061) (0.8124) (1.3867) (1.0619) (0.2048) (0.8235) (0.0714) (0.2385) (0.4899) (0.5814)
PPE 0.2349 0.3703* 0.1335 0.1864 0.2028 0.0637 -0.0651 -0.1128 -0.0983 -0.1607
(0.9089) (1.9154) (0.5660) (0.7556) (0.7784) (0.2231) (-0.2131) (-0.2964) (-0.2179) (-0.3868)
ADV 0.0000 0.0000 0.0000 6.5454 0.0000 0.0000 15.1587 4.7196 12.2655 -1.5428
(.) (.) (.) (0.6044) (.) (.) (1.3536) (0.2908) (0.8152) (-0.1188)
RD 0.0000 0.0000 0.0000 -8.3398 0.0000 0.0000 0.0000 -9.1278 -0.9288 -12.7757
(.) (.) (.) (-0.6978) (.) (.) (.) (-0.9596) (-0.0959) (-0.9324)
HHI -0.4786 -0.4828 -0.4323 -0.6529 -0.4950 -0.2469 -0.0630 -0.0505 0.2196 0.0863
(-0.5030) (-0.5685) (-0.5165) (-0.7708) (-0.6700) (-0.3173) (-0.1331) (-0.1042) (0.4048) (0.1496)
INDSIZE 0.2424 0.2039 0.0910 0.1361 0.1026 0.0569 -0.0786 0.0223 -0.0374 -0.1057
(0.7698) (0.8281) (0.3584) (0.5155) (0.3942) (0.2317) (-0.4091) (0.1061) (-0.1454) (-0.4386)
NFIRMS -0.1716 -0.0790 0.1095 0.0273 0.0924 0.1564 0.3901 0.2145 0.3206 0.4058
(-0.2827) (-0.1616) (0.2372) (0.0546) (0.1948) (0.3406) (1.1371) (0.6342) (0.8572) (1.1148)
FCFIRM 0.1643 -0.2306 -0.7050 -0.5302 -1.3960 -0.7499 -0.6088 -1.3333 -0.8095 -0.5513
(0.0941) (-0.1382) (-0.5092) (-0.3022) (-1.0856) (-0.7352) (-0.7719) (-1.0874) (-0.9200) (-0.6073)
MARGIN 1.1374** 0.7720* 0.7420* 0.5409 0.3343 0.4295 0.2948 -0.3597 0.3036 -0.0030
(2.3418) (1.7993) (1.9478) (1.2911) (0.6710) (1.0841) (0.5314) (-0.3368) (0.2356) (-0.0033)
LEVDISP -0.0022 0.2363 0.0725 0.5919 0.2944 0.4385 0.2644 0.2651 -0.0433 0.0963
(-0.0011) (0.1432) (0.0417) (0.3263) (0.1779) (0.2698) (0.1413) (0.1424) (-0.0264) (0.0619)
SIZEDISP -0.0387 0.0307 0.1642 0.1315 0.2040 0.2365 0.3054 0.1376 0.1875 0.2849
(-0.1369) (0.1286) (0.6774) (0.5625) (0.8189) (1.0679) (1.5141) (0.5676) (0.6690) (1.0209)
ENTRYR 0.0000 -0.0030 0.4019 0.0722 -0.2552 0.0391 -0.0099 -0.1736 -0.2510 -0.2626
(.) (-0.0054) (0.7407) (0.1290) (-0.8574) (0.0951) (-0.0325) (-0.2006) (-0.7387) (-0.9214)
EXITR -0.3475 0.1600 0.3100 -0.0141 -0.1314 0.2665 0.3176 0.1137 -0.0595 -0.1399
(-0.4376) (0.2422) (0.4429) (-0.0211) (-0.2864) (0.4944) (0.7820) (0.2809) (-0.0983) (-0.2001)
_cons -2.7021 -5.7169** -4.4212 -4.1241 -3.9158 -3.7323 -2.6553 -2.7141 -2.6220 -1.8506
(-0.9521) (-2.2631) (-1.6429) (-1.4217) (-1.4988) (-1.4734) (-0.9617) (-1.0106) (-0.7973) (-0.6046)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Industry Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
N 4576 4769 4813 4889 5168 5557 6418 6732 7387 8048
r2_p 0.0907 0.0934 0.0894 0.0931 0.0878 0.0917 0.0951 0.0836 0.0767 0.0797
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
t statistics in parentheses
* p<0.1, ** p<0.05, *** p<0.01
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可以看到，匹配后各年份绝大多数协变量的系数值减小（少数几个协变量因为共线性而被omitted），并且系数大多变得不显著，而且所有回归的伪R方明显减小，这说明在不同年份两组的协变量不存在系统性偏差。
最后是回归结果的对比。
**# 2.4 回归结果对比
use ybydata.dta, clear
*- 基准回归1（混合OLS）
qui: reg TFPQD_OP FB $xlist , cluster(city)
est store m1
*- 基准回归2（固定效应模型）
qui: reghdfe TFPQD_OP FB $xlist , $regopt
est store m2
*- PSM-DID1（使用权重不为空的样本）
qui: reghdfe TFPQD_OP FB $xlist if _weight != ., $regopt
est store m6
*- PSM-DID2（使用满足共同支撑假设的样本）
qui: reghdfe TFPQD_OP FB $xlist if _support == 1, $regopt
est store m7
*- PSM-DID3（使用频数加权回归）
gen weight = _weight * 2
replace weight = 1 if treated == 1 & _weight != .
qui: reghdfe TFPQD_OP FB $xlist [fweight = weight], $regopt
est store m8
*- 回归结果输出
local mlist_2 "m1 m2 m6 m7 m8"
reg2docx `mlist_2' using 逐年匹配回归结果对比.docx, b(%6.4f) t(%6.4f) ///
scalars(N r2_a(%6.4f)) noconstant replace ///
mtitles("OLS" "FE" "Weight!=." "On_Support" "Weight_Reg") ///
title("基准回归及逐年PSM-DID结果")
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运行结果如下。回归结果与截面PSM - DID基本一致，因此也同样可以说明基准回归结果在考虑到选择偏差问题之后依然稳健。
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(1) (2) (3) (4) (5)
OLS FE Weight!=. On_Support Weight_Reg
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FB -0.1243*** -0.0496*** -0.0493*** -0.0498*** -0.0466***
(-5.2480) (-3.6531) (-3.5125) (-3.6669) (-3.1779)
ADM 1.0682*** 0.8719*** 0.8917*** 0.8712*** 0.9117***
(17.6388) (18.0260) (15.3250) (17.9650) (11.4538)
PPE -0.1183*** -0.0845*** -0.0899*** -0.0848*** -0.1136***
(-4.3488) (-5.4869) (-4.8695) (-5.5008) (-4.9564)
ADV 3.4239* 0.4029 0.3887 0.3767 4.4924
(1.9284) (0.2547) (0.1959) (0.2374) (1.5339)
RD -1.1993 -3.5116*** -5.1446*** -3.5391*** -5.2116**
(-0.8120) (-2.6572) (-2.9252) (-2.6649) (-2.1192)
HHI -0.0284 0.1391*** 0.1510*** 0.1392*** 0.0911*
(-0.5123) (3.7371) (3.6121) (3.7313) (1.7278)
INDSIZE 0.1061*** 0.0398*** 0.0363*** 0.0397*** 0.0459***
(6.4798) (5.1231) (4.1622) (5.1027) (4.3791)
NFIRMS -0.2011*** -0.1012*** -0.0975*** -0.1011*** -0.1199***
(-7.0272) (-8.2637) (-6.9857) (-8.2429) (-6.8619)
FCFIRM 0.2561** -0.0343 -0.1043 -0.0388 0.0600
(2.5595) (-0.5604) (-1.3284) (-0.6256) (0.6081)
MARGIN 0.2333*** 0.2377*** 0.2238*** 0.2368*** 0.3077***
(6.6555) (8.2641) (6.8292) (8.2343) (7.1966)
LEVDISP 1.8228*** 1.1270*** 1.1647*** 1.1270*** 1.1589***
(15.3788) (20.1912) (18.2101) (20.1705) (14.0951)
SIZEDISP 0.1373*** 0.0678*** 0.0637*** 0.0678*** 0.0712***
(5.2810) (4.5861) (3.8471) (4.5825) (3.5551)
ENTRYR 0.0735*** 0.0732*** 0.0635*** 0.0743*** 0.0563**
(2.9277) (3.2806) (2.6220) (3.3212) (2.0777)
EXITR 0.0560* 0.0491* 0.0468 0.0483* 0.0201
(1.7687) (1.7444) (1.4509) (1.7128) (0.4843)
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N 81567 81567 58926 81507 116269
r2_a 0.0646 0.1613 0.1548 0.1612 0.1590
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t statistics in parentheses
* p<0.1, ** p<0.05, *** p<0.01
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