PSM 倾向得分匹配

PSM 倾向得分匹配是什么？

PSM 先问处理组和对照组在处理前能不能变得可比。它不是直接估计因果效应，而是先用处理前协变量估计被处理的概率，再在相近概率的人之间比较结果。

先用一句话理解

把 PSM 想成先找相似同学再比较成绩。处理组和对照组原本可能差很多，PSM 要做的是在对照组里找到处理前看起来足够像处理组的人。

什么时候用

把它和相近方法分清楚

核心直觉和模型公式

倾向得分和 ATT

PSM 的第一步是估计被处理的条件概率：

第二个式子里的 Y_i(0) 对处理组不可观察，所以要用匹配后的对照组近似。

公式里的符号怎么读

专业使用口径

PSM 的正文不能只写“做了匹配”，必须交代匹配质量。

一步一步做：从问题到结果的五步

结果怎么读：先读口径，再读数字

本页案例读表时，先记住这个口径：本案例匹配方法是 nn1，状态为 ok；处理变量按 dfi_index 的 median_high_exposure 构造。

初学者最容易错在哪里

先看这个案例的结论

• 本案例匹配方法是 nn1，状态为 ok；处理变量按 dfi_index 的 median_high_exposure 构造。
• 匹配后的 ATT 是 0.7725，标准误是 0.1270；这比只说“做了 PSM”更有信息量。
• PSM 页要同时看处理效应和协变量平衡。页面下方补充输出里会展示 psm_balance、候选矩阵和 trim sensitivity。

变量要求和案例口径

实际代码

下面是本页案例里的最小 Stata 代码。它的作用是帮助你看清变量怎么进入模型、结果文件怎么生成，而不是要求你在网页里手动运行。

log using "/root/workspace/empirical-wizard/workspace/dc2c4126/analysis.log", replace text
global JOB_DIR "/root/workspace/empirical-wizard/workspace/dc2c4126"
set more off
adopath + "/root/ado/plus"
global DATA_PATH "/root/workspace/empirical-wizard/workspace/test_e2e/csmar_innovation.csv"
import delimited "/root/workspace/empirical-wizard/workspace/test_e2e/csmar_innovation.csv", clear case(preserve)
capture confirm global JOB_DIR
if _rc global JOB_DIR "."
* 自动去除完全重复行（同列同值），避免 N 虚增与 xtset 失败
quietly duplicates drop
local idvar ""
local timevar ""
capture confirm variable stkcd
if !_rc {
    capture confirm numeric variable stkcd
    if _rc {
        tempvar __ewiz_id
        capture encode stkcd, gen(`__ewiz_id')
        if !_rc local idvar "`__ewiz_id'"
    }
    else {
        local idvar "stkcd"
    }
}
else {
    di as text "面板ID变量不存在，跳过 xtset ID：stkcd"
}
capture confirm variable year
if !_rc {
    capture confirm numeric variable year
    if _rc {
        tempvar __ewiz_time
        capture encode year, gen(`__ewiz_time')
        if !_rc local timevar "`__ewiz_time'"
    }
    else {
        local timevar "year"
    }
}
else {
    di as text "时间变量不存在，跳过 xtset time：year"
}
if "`idvar'" != "" & "`timevar'" != "" {
    capture xtset `idvar' `timevar'
}
capture confirm numeric variable dfi_index
if _rc {
    tempname fh_badpsm
    capture file close `fh_badpsm'
    file open `fh_badpsm' using "$JOB_DIR/psm_results.csv", write replace
    file write `fh_badpsm' "指标,值" _n
    file write `fh_badpsm' "状态,degenerate" _n
    file write `fh_badpsm' "处理变量定义,核心解释变量 dfi_index 无法作为数值变量构造高暴露组" _n
    file close `fh_badpsm'
    exit 0
}
capture drop __ewiz_psm_treat
quietly summarize dfi_index if !missing(dfi_index), detail
local __ewiz_psm_med = r(p50)
gen byte __ewiz_psm_treat = (dfi_index >= `__ewiz_psm_med') if !missing(dfi_index)
label variable __ewiz_psm_treat "High dfi_index exposure (>= median)"
capture which psmatch2
if _rc {
    tempname fh
    capture file close `fh'
    file open `fh' using "$JOB_DIR/psm_results.csv", write replace
    file write `fh' "指标,值" _n
    file write `fh' "状态,unavailable" _n
    file write `fh' "说明,psmatch2 ADO 未安装或 Stata 找不到，建议 ssc install psmatch2 后重跑。" _n
    file close `fh'
    tempname cf_unavail
    capture file close `cf_unavail'
    file open `cf_unavail' using "$JOB_DIR/psm_candidate_matrix.csv", write replace
    file write `cf_unavail' "candidate,treatment_var,source,rule,method,status,ATT,ATT_se,N,note" _n
    file write `cf_unavail' "high_dfi_index_median_nn1,__ewiz_psm_cand1,dfi_index,median_high_exposure,nn1,unavailable,.,.,.,psmatch2 ADO 未安装" _n
    file write `cf_unavail' "high_dfi_index_p75_nn1,__ewiz_psm_cand2,dfi_index,p75_high_exposure,nn1,unavailable,.,.,.,psmatch2 ADO 未安装" _n
    file write `cf_unavail' "high_dfi_index_median_nn4,__ewiz_psm_cand3,dfi_index,median_high_exposure,nn4,unavailable,.,.,.,psmatch2 ADO 未安装" _n
    file write `cf_unavail' "high_dfi_index_median_kernel,__ewiz_psm_cand4,dfi_index,median_high_exposure,kernel,unavailable,.,.,.,psmatch2 ADO 未安装" _n
    file write `cf_unavail' "high_dfi_index_within_time_median_nn1,__ewiz_psm_cand5,dfi_index,within_time_median_high_exposure,nn1,unavailable,.,.,.,psmatch2 ADO 未安装" _n
    file write `cf_unavail' "high_dfi_index_within_industry_median_nn1,__ewiz_psm_cand6,dfi_index,within_industry_median_high_exposure,nn1,unavailable,.,.,.,psmatch2 ADO 未安装" _n
    file close `cf_unavail'
    di as error "psmatch2 未安装；已写入 psm_results.csv 的 unavailable 状态。"
    exit 0
}
capture psmatch2 __ewiz_psm_treat roa lev size growth cashflow tobinq top1 dual board indep soe age, outcome(patent_count) neighbor(1) common logit
local __psm_rc = _rc
tempname fh
capture file close `fh'
file open `fh' using "$JOB_DIR/psm_results.csv", write replace
file write `fh' "指标,值" _n
file write `fh' "处理变量,high_dfi_index_median" _n
file write `fh' "处理变量来源,dfi_index" _n
file write `fh' "处理变量规则,median_high_exposure" _n
file write `fh' "匹配方法,nn1" _n
local att "."
local att_se "."
if `__psm_rc' != 0 {
    file write `fh' "状态,degenerate" _n
    file write `fh' "ATT,." _n
    file write `fh' "标准误,." _n
    file write `fh' "t 值,." _n
    file write `fh' "说明,PSM 估计退化：可能由于处理变量分布过于不平衡、logit 完美预测或匹配样本不足。已如实披露，不得解读为已完成。" _n
    di as error "PSM 估计退化，已写入 degenerate 状态。rc=`__psm_rc'"
}
else {
    local att : display %9.4f r(att)
    local att_se : display %9.4f r(seatt)
    file write `fh' "状态,ok" _n
    file write `fh' "ATT,`att'" _n
    file write `fh' "ATT 标准误,`att_se'" _n
}
file close `fh'
if `__psm_rc' == 0 {
    capture pstest roa lev size growth cashflow tobinq top1 dual board indep soe age, both
    local _pstest_rc = _rc
    capture local _meanbias_b = r(meanbiasbef)
    capture local _meanbias_a = r(meanbiasaft)
    capture local _medbias_b  = r(medbiasbef)
    capture local _medbias_a  = r(medbiasaft)
    capture local _rubin_b_b  = r(Bbef)
    capture local _rubin_b_a  = r(Baft)
    capture local _var_r_b    = r(Rbef)
    capture local _var_r_a    = r(Raft)
    capture local _pseudo_b   = r(Pbef)
    capture local _pseudo_a   = r(Paft)
    capture graph export "$JOB_DIR/psm_balance.png", replace width(1800)
    if `_pstest_rc' == 0 {
        tempname bh
        file open `bh' using "$JOB_DIR/psm_balance.csv", write replace
        file write `bh' "指标,匹配前,匹配后" _n
        file write `bh' "MeanBias(%),`_meanbias_b',`_meanbias_a'" _n
        file write `bh' "MedBias(%),`_medbias_b',`_medbias_a'" _n
        file write `bh' "Rubin B,`_rubin_b_b',`_rubin_b_a'" _n
        file write `bh' "Variance Ratio R,`_var_r_b',`_var_r_a'" _n
        file write `bh' "Pseudo R²,`_pseudo_b',`_pseudo_a'" _n
        file close `bh'
    }
    else {
        tempname bh2
        file open `bh2' using "$JOB_DIR/psm_balance.csv", write replace
        file write `bh2' "指标,匹配前,匹配后" _n
        file write `bh2' "状态,unavailable,pstest 估计失败" _n
        file close `bh2'
    }
}
if `__psm_rc' == 0 & "`att'" != "." {
    tempname tfh
    capture file close `tfh'
    file open `tfh' using "$JOB_DIR/psm_trim_sensitivity.csv", write replace
    file write `tfh' "trim_阈值,ATT,标准误,t,N_treated,N_control,说明" _n
    foreach _trim_t in 0.00 0.05 0.10 0.15 0.20 {
        preserve
            capture quietly drop if _pscore < `_trim_t' | _pscore > (1 - `_trim_t')
            quietly count if !missing(_pscore)
            local _n_trim = r(N)
            if `_n_trim' < 20 {
                file write `tfh' "`_trim_t',.,.,.,.,.,trim 后样本不足 (N<20)" _n
            }
            else {
                capture noisily psmatch2 __ewiz_psm_treat roa lev size growth cashflow tobinq top1 dual board indep soe age, outcome(patent_count) neighbor(1) common logit
                if _rc == 0 {
                    capture local _att_t : display %9.4f r(att)
                    capture local _se_t  : display %9.4f r(seatt)
                    capture local _t_t   : display %9.4f r(att)/r(seatt)
                    capture quietly count if _treated == 1
                    local _nt = r(N)
                    capture quietly count if _treated == 0
                    local _nc = r(N)
                    file write `tfh' "`_trim_t',`_att_t',`_se_t',`_t_t',`_nt',`_nc',ok" _n
                }
                else file write `tfh' "`_trim_t',.,.,.,.,.,psmatch2 在 trim 后估计失败 rc=`=_rc'" _n
            }
        restore
    }
    file write `tfh' "解读说明,—,—,—,—,—,主 ATT 与曲线一致 → overlap 充足；曲线随 trim 翻转或显著放大 → propensity 极端尾巴主导主结论，应在限制段披露 LaLonde 类敏感性。" _n
    file close `tfh'
    di "PSM trim 敏感性曲线已写入 psm_trim_sensitivity.csv"
}

* ── PSM 候选处理定义/匹配方法矩阵（披露用，不自动替代主结论）──
tempname cf
capture file close `cf'
file open `cf' using "$JOB_DIR/psm_candidate_matrix.csv", write replace
file write `cf' "candidate,treatment_var,source,rule,method,status,ATT,ATT_se,N,note" _n
capture drop __ewiz_psm_cand1
capture confirm numeric variable dfi_index
if !_rc {
    quietly summarize dfi_index if !missing(dfi_index), detail
    gen byte __ewiz_psm_cand1 = (dfi_index >= r(p50)) if !missing(dfi_index)
}
capture confirm variable __ewiz_psm_cand1
if _rc {
    file write `cf' "high_dfi_index_median_nn1,__ewiz_psm_cand1,dfi_index,median_high_exposure,nn1,missing_treatment,.,.,.,候选 treatment 未生成或不存在" _n
}
else {
    quietly count if !missing(__ewiz_psm_cand1)
    local __cand_N = r(N)
    capture drop _pscore _weight _treated _support _id _n1 _nn _pdif
    capture psmatch2 __ewiz_psm_cand1 roa lev size growth cashflow tobinq top1 dual board indep soe age, outcome(patent_count) neighbor(1) common logit
    local __cand_rc = _rc
    if `__cand_rc' == 0 {
        local __cand_att : display %9.4f r(att)
        local __cand_se : display %9.4f r(seatt)
        file write `cf' "high_dfi_index_median_nn1,__ewiz_psm_cand1,dfi_index,median_high_exposure,nn1,ok,`__cand_att',`__cand_se',`__cand_N',exploratory disclosed candidate" _n
    }
    else {
        file write `cf' "high_dfi_index_median_nn1,__ewiz_psm_cand1,dfi_index,median_high_exposure,nn1,degenerate,.,.,`__cand_N',psmatch2 failed rc=`__cand_rc'" _n
    }
}
capture drop __ewiz_psm_cand2
capture confirm numeric variable dfi_index
if !_rc {
    quietly summarize dfi_index if !missing(dfi_index), detail
    gen byte __ewiz_psm_cand2 = (dfi_index >= r(p75)) if !missing(dfi_index)
}
capture confirm variable __ewiz_psm_cand2
if _rc {
    file write `cf' "high_dfi_index_p75_nn1,__ewiz_psm_cand2,dfi_index,p75_high_exposure,nn1,missing_treatment,.,.,.,候选 treatment 未生成或不存在" _n
}
else {
    quietly count if !missing(__ewiz_psm_cand2)
    local __cand_N = r(N)
    capture drop _pscore _weight _treated _support _id _n1 _nn _pdif
    capture psmatch2 __ewiz_psm_cand2 roa lev size growth cashflow tobinq top1 dual board indep soe age, outcome(patent_count) neighbor(1) common logit
    local __cand_rc = _rc
    if `__cand_rc' == 0 {
        local __cand_att : display %9.4f r(att)
        local __cand_se : display %9.4f r(seatt)
        file write `cf' "high_dfi_index_p75_nn1,__ewiz_psm_cand2,dfi_index,p75_high_exposure,nn1,ok,`__cand_att',`__cand_se',`__cand_N',exploratory disclosed candidate" _n
    }
    else {
        file write `cf' "high_dfi_index_p75_nn1,__ewiz_psm_cand2,dfi_index,p75_high_exposure,nn1,degenerate,.,.,`__cand_N',psmatch2 failed rc=`__cand_rc'" _n
    }
}
capture drop __ewiz_psm_cand3
capture confirm numeric variable dfi_index
if !_rc {
    quietly summarize dfi_index if !missing(dfi_index), detail
    gen byte __ewiz_psm_cand3 = (dfi_index >= r(p50)) if !missing(dfi_index)
}
capture confirm variable __ewiz_psm_cand3
if _rc {
    file write `cf' "high_dfi_index_median_nn4,__ewiz_psm_cand3,dfi_index,median_high_exposure,nn4,missing_treatment,.,.,.,候选 treatment 未生成或不存在" _n
}
else {
    quietly count if !missing(__ewiz_psm_cand3)
    local __cand_N = r(N)
    capture drop _pscore _weight _treated _support _id _n1 _nn _pdif
    capture psmatch2 __ewiz_psm_cand3 roa lev size growth cashflow tobinq top1 dual board indep soe age, outcome(patent_count) neighbor(4) common logit
    local __cand_rc = _rc
    if `__cand_rc' == 0 {
        local __cand_att : display %9.4f r(att)
        local __cand_se : display %9.4f r(seatt)
        file write `cf' "high_dfi_index_median_nn4,__ewiz_psm_cand3,dfi_index,median_high_exposure,nn4,ok,`__cand_att',`__cand_se',`__cand_N',exploratory disclosed candidate" _n
    }
    else {
        file write `cf' "high_dfi_index_median_nn4,__ewiz_psm_cand3,dfi_index,median_high_exposure,nn4,degenerate,.,.,`__cand_N',psmatch2 failed rc=`__cand_rc'" _n
    }
}
capture drop __ewiz_psm_cand4
capture confirm numeric variable dfi_index
if !_rc {
    quietly summarize dfi_index if !missing(dfi_index), detail
    gen byte __ewiz_psm_cand4 = (dfi_index >= r(p50)) if !missing(dfi_index)
}
capture confirm variable __ewiz_psm_cand4
if _rc {
    file write `cf' "high_dfi_index_median_kernel,__ewiz_psm_cand4,dfi_index,median_high_exposure,kernel,missing_treatment,.,.,.,候选 treatment 未生成或不存在" _n
}
else {
    quietly count if !missing(__ewiz_psm_cand4)
    local __cand_N = r(N)
    capture drop _pscore _weight _treated _support _id _n1 _nn _pdif
    capture psmatch2 __ewiz_psm_cand4 roa lev size growth cashflow tobinq top1 dual board indep soe age, outcome(patent_count) kernel common logit
    local __cand_rc = _rc
    if `__cand_rc' == 0 {
        local __cand_att : display %9.4f r(att)
        local __cand_se : display %9.4f r(seatt)
        file write `cf' "high_dfi_index_median_kernel,__ewiz_psm_cand4,dfi_index,median_high_exposure,kernel,ok,`__cand_att',`__cand_se',`__cand_N',exploratory disclosed candidate" _n
    }
    else {
        file write `cf' "high_dfi_index_median_kernel,__ewiz_psm_cand4,dfi_index,median_high_exposure,kernel,degenerate,.,.,`__cand_N',psmatch2 failed rc=`__cand_rc'" _n
    }
}
capture drop __ewiz_psm_cand5
capture confirm numeric variable dfi_index
if !_rc & "`timevar'" != "" {
    tempvar __psm_wt_med
    bysort `timevar': egen double `__psm_wt_med' = median(dfi_index)
    gen byte __ewiz_psm_cand5 = (dfi_index >= `__psm_wt_med') if !missing(dfi_index, `__psm_wt_med')
}
capture confirm variable __ewiz_psm_cand5
if _rc {
    file write `cf' "high_dfi_index_within_time_median_nn1,__ewiz_psm_cand5,dfi_index,within_time_median_high_exposure,nn1,missing_treatment,.,.,.,候选 treatment 未生成或不存在" _n
}
else {
    quietly count if !missing(__ewiz_psm_cand5)
    local __cand_N = r(N)
    capture drop _pscore _weight _treated _support _id _n1 _nn _pdif
    capture psmatch2 __ewiz_psm_cand5 roa lev size growth cashflow tobinq top1 dual board indep soe age, outcome(patent_count) neighbor(1) common logit
    local __cand_rc = _rc
    if `__cand_rc' == 0 {
        local __cand_att : display %9.4f r(att)
        local __cand_se : display %9.4f r(seatt)
        file write `cf' "high_dfi_index_within_time_median_nn1,__ewiz_psm_cand5,dfi_index,within_time_median_high_exposure,nn1,ok,`__cand_att',`__cand_se',`__cand_N',exploratory disclosed candidate" _n
    }
    else {
        file write `cf' "high_dfi_index_within_time_median_nn1,__ewiz_psm_cand5,dfi_index,within_time_median_high_exposure,nn1,degenerate,.,.,`__cand_N',psmatch2 failed rc=`__cand_rc'" _n
    }
}
capture drop __ewiz_psm_cand6
capture confirm numeric variable dfi_index
if !_rc {
    tempvar __psm_ind_med
    bysort ind: egen double `__psm_ind_med' = median(dfi_index)
    gen byte __ewiz_psm_cand6 = (dfi_index >= `__psm_ind_med') if !missing(dfi_index, `__psm_ind_med')
}
capture confirm variable __ewiz_psm_cand6
if _rc {
    file write `cf' "high_dfi_index_within_industry_median_nn1,__ewiz_psm_cand6,dfi_index,within_industry_median_high_exposure,nn1,missing_treatment,.,.,.,候选 treatment 未生成或不存在" _n
}
else {
    quietly count if !missing(__ewiz_psm_cand6)
    local __cand_N = r(N)
    capture drop _pscore _weight _treated _support _id _n1 _nn _pdif
    capture psmatch2 __ewiz_psm_cand6 roa lev size growth cashflow tobinq top1 dual board indep soe age, outcome(patent_count) neighbor(1) common logit
    local __cand_rc = _rc
    if `__cand_rc' == 0 {
        local __cand_att : display %9.4f r(att)
        local __cand_se : display %9.4f r(seatt)
        file write `cf' "high_dfi_index_within_industry_median_nn1,__ewiz_psm_cand6,dfi_index,within_industry_median_high_exposure,nn1,ok,`__cand_att',`__cand_se',`__cand_N',exploratory disclosed candidate" _n
    }
    else {
        file write `cf' "high_dfi_index_within_industry_median_nn1,__ewiz_psm_cand6,dfi_index,within_industry_median_high_exposure,nn1,degenerate,.,.,`__cand_N',psmatch2 failed rc=`__cand_rc'" _n
    }
}
file close `cf'
di "PSM 估计完成 ATT=`att'"
log close

实际输出表

这张表是本方法页配套案例的输出结果，用来把前面的公式、变量口径和代码对应到实际数字。

补充输出

下面这些文件来自同一次案例生成流程，用来补齐主表之外的诊断信息。

psm_balance.csv

psm_candidate_matrix.csv

psm_trim_sensitivity.csv

案例图

这是一张由同一份案例数据生成的页面内诊断图。

论文里怎么写

本文进一步采用PSM 倾向得分匹配检验数字普惠金融变化对企业创新的影响。处理组、对照组和政策后变量均基于同一 firm-year 样本构造，结果报告在 psm_results.csv 中。若处理效应方向与基准回归一致，可作为政策评估维度的补充证据；若不一致，应优先解释识别假设和样本切分差异。

检查清单

• 先读匹配前后协变量平衡，再读 ATT；匹配不平衡时 ATT 不可信。
• 说明 caliper、邻居数、共同支撑和被丢弃样本，否则匹配过程不可审查。
• PSM 只能处理可观测协变量差异，不能解决不可观测内生性。

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