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【Stata】 Oster检验结果排版及描述

稳健性之遗漏变量检验

1 基本原理

  • 通过设定可达到的最大 $R^2 (Rmax)$ 和未观测变量的相对重要性 ($\delta $)来估计遗漏变量可能造成的影响，并判断处理效应估计值的稳定性。

  • 根据Oster (2019)的建议，我们假设$Rmax$是基准回归模型中$R^2$的1.3倍，而未观测变量对因变量的影响至少与已观测变量同等重要，即$\delta = 1$，进一步采用估计量$\beta^\star =\beta^\star (Rmax, \delta )$得到真实系数的一致估计。

2 操作代码

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//计算Uncontrolled结果
reghdfe Y X, noa vce(cl ind3#year) level(99.5)

//计算Controled结果与置信区间
reghdfe Y X $controls ,a( ind3#year ) vce(cl ind3#year) level(99.5)

//计算true beta与beta为0时的delta
local r = e(r2) * 1.3
psacalc2 beta X, delta(1) rmax(`r')
psacalc2 delta X, beta(0) rmax(`r')

3 结果排版

Dependent variable Y
Uncontrolled coefficients -0.0130
Uncontrolled R² 0.001
Controled coefficients 0.0073***
Controled R² 0.405
99.5% Confidence interval [-0.0005,0.0152]
Control variables YES
Industry-Year fixed effect YES
“True” $\beta$ 0.0192
$\delta$ for $\beta$ = 0 -0.8627

按顺序需要手动录入以下数据：

  • Uncontrolled下的X回归系数与R-squared
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. reghdfe Y X, noa vce(cl ind3#year) level(99.5)
(MWFE estimator converged in 1 iterations)

HDFE Linear regression                            Number of obs   =     16,752
Absorbing 1 HDFE group                            F(   1,    847) =       2.47
Statistics robust to heteroskedasticity           Prob > F        =     0.1167
                                                  R-squared       =     0.0013
                                                  Adj R-squared   =     0.0012
                                                  Within R-sq.    =     0.0013
Number of clusters (ind3#year) =        848       Root MSE        =     6.2419

                            (Std. err. adjusted for 848 clusters in ind3#year)
------------------------------------------------------------------------------
             |               Robust
           Y | Coefficient  std. err.      t    P>|t|   [99.5% conf. interval]
-------------+----------------------------------------------------------------
           X |  -.0130469   .0083091    -1.57   0.117    -.0364321    .0103383
       _cons |   8.291464   .2427002    34.16   0.000     7.608406    8.974521
------------------------------------------------------------------------------
  • Controled下的X回归系数、R-squared与置信区间
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. reghdfe Y X $controls ,a( ind3#year ) vce(cl ind3#year) level(99.5)
(MWFE estimator converged in 1 iterations)

HDFE Linear regression                            Number of obs   =     16,752
Absorbing 1 HDFE group                            F(  13,    847) =      46.08
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.4049
                                                  Adj R-squared   =     0.3727
                                                  Within R-sq.    =     0.0814
Number of clusters (ind3#year) =        848       Root MSE        =     4.9466

                            (Std. err. adjusted for 848 clusters in ind3#year)
------------------------------------------------------------------------------
             |               Robust
           Y | Coefficient  std. err.      t    P>|t|   [99.5% conf. interval]
-------------+----------------------------------------------------------------
           X |   .0073397   .0027781     2.64   0.008     -.000479    .0151585
         Lev |  -.1551993   .2676344    -0.58   0.562    -.9084319    .5980334
     firmage |  -.0206417   .1378441    -0.15   0.881    -.4085913    .3673078
        Size |   1.397631    .061951    22.56   0.000     1.223276    1.571987
        sfee |   1.895896   .5163247     3.67   0.000     .4427476    3.349045
        Dual |   .1007562   .0789137     1.28   0.202    -.1213394    .3228517
        Top1 |   -.012556   .0028019    -4.48   0.000    -.0204416   -.0046704
       Indep |  -.0170681   .0075772    -2.25   0.025    -.0383933    .0042572
      occupy |  -2.832035   2.223062    -1.27   0.203     -9.08864     3.42457
        Cash |   1.180776   .4373728     2.70   0.007    -.0501698    2.411722
         Soe |  -1.301147   .1252125   -10.39   0.000    -1.653546   -.9487476
         Gdp |   .6944393   .1217796     5.70   0.000     .3517018    1.037177
      People |   -.635223   .1217548    -5.22   0.000    -.9778907   -.2925554
       _cons |  -3.086463   .9588209    -3.22   0.001    -5.784976    -.387949
------------------------------------------------------------------------------
  • Estimate出的true Beta
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 psacalc2 beta X, delta(1) rmax(`r')

                 ---- Treatment Effect Estimate ----
             |     Estimate           Sq. difference      Bias changes
             |                      from controlled beta    direction
-------------+----------------------------------------------------------------
Beta         |       0.01920              .000141             
Alt. sol. 1  |      -2.18561                 4.81             Yes
Alt. sol. 2  |                                                
-------------+----------------------------------------------------------------

                 ---- Inputs from Regressions ----
             |      Coeff.            R-Squared
-------------+----------------------------------------------------------------
Uncontrolled |       -0.01305         0.001
Controlled   |        0.00734         0.405
-------------+----------------------------------------------------------------

                 ---- Other Inputs ----
-------------+----------------------------------------------------------------
R_max        |   0.526
Delta        |   1.000
Unr. Controls|   
-------------+----------------------------------------------------------------
  • Estimate出的delta
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 psacalc2 delta X, beta(0) rmax(`r')

                 ---- Bound Estimate ----
-------------+----------------------------------------------------------------
delta        |      -0.86273
-------------+----------------------------------------------------------------

                 ---- Inputs from Regressions ----
             |      Coeff.                      R-Squared
-------------+----------------------------------------------------------------
Uncontrolled |       -0.01305                   0.001
Controlled   |        0.00734                   0.405
-------------+----------------------------------------------------------------

                 ---- Other Inputs ----
-------------+----------------------------------------------------------------
R_max        |   0.526
Beta         |    0.000000
Unr. Controls|   
-------------+----------------------------------------------------------------

4 结果判断与描述

oster有多种判断方法，满足其一就可以：

  • true $\beta$ 与基准回归系数相比，绝对值更大，且符号相同
    • 表明X对Y的真实影响可能大于基准模型中的回归系数，且不会出现符号相反的情况
  • $\delta$ 大于1或小于0
    • 大于1表明：不可观测变量的重要性需要是可观测变量的 $\delta$ 倍时，才会产生零处理效果，这种情况较难成立，验证了系数的稳定性
    • 小于0表明：经偏差调整后的估计系数应大于基准回归中得到的系数
  • true $\beta$ 落在置信区间内
  • true $\beta$ 与Controled coefficients（基准回归中X的系数）形成的区间落在置信区间内
    • 说明并不存在与本文解释变量同等重要的遗漏变量影响本文结论
  • true $\beta$ 与Controled coefficients（基准回归中X的系数）构成的区间不包含0
    • 说明遗漏变量不太可能将处理效应的真实值推至0

作话：mark住下次不要再忘了…

【Stata】 Oster检验结果排版及描述

https://lxxcandy.github.io/2024/05/20/1-Oster检验结果排版及描述/

作者

LxxCandy

发布于

2024-05-20

更新于

2024-06-14

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