ivreghdfe standard errors

[Frank Huang]

Dear all,

I am trying to use ivreghdfe to replicate the results from ivregress and ivreg2 (ssc install ivreg2).

ivreghdfe was installed from here: https://github.com/sergiocorreia/ivreghdfe#installation

sysuse auto
ivregress 2sls price weight (length=gear) i.rep78
ivreg2 price weight (length=gear) i.rep78
ivreghdfe price weight (length=gear), absorb(rep78)

We can obtain exactly the same estimates, but the standard errors from ivreghdfe differ from the others.
Could anyone explain why this difference occurs? Any suggestions would be appreciated.

[Andrew Musau]

By default, ivregress and ivreg2 report z-statistics, whereas ivreghdfe always reports t-statistics. When the sample size is small, you may notice some differences in the standard errors, since z-statistics rely on large-sample approximations. If you are working with a relatively small sample, you can add the option -small- to either ivregress or ivreg2 to report t-statistics.

sysuse auto, clear
ivregress 2sls price weight (length=gear) i.rep78, small
ivreg2 price weight (length=gear) i.rep78, small
ivreghdfe price weight (length=gear), absorb(rep78)

Res.:

. ivregress 2sls price weight (length=gear) i.rep78, small


Instrumental-variables 2SLS regression

      Source |       SS       df       MS         Number of obs   =         69
-------------+------------------------------      F(  6,    62)   =       3.84
       Model |   8799835.9     6  1466639.32      Prob > F        =     0.0025
    Residual |   567997123    62  9161243.92      R-squared       =     0.0153
-------------+------------------------------      Adj R-squared   =    -0.0800
       Total |   576796959    68  8482308.22      Root MSE        =     3026.8

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      length |   156.4453   345.4758     0.45   0.652    -534.1511    847.0417
      weight |  -1.899938   9.598611    -0.20   0.844    -21.08729    17.28741
             |
       rep78 |
          2  |   262.1144   2659.123     0.10   0.922    -5053.397    5577.626
          3  |   1460.595   2220.161     0.66   0.513    -2977.445    5898.634
          4  |    1721.87   2385.178     0.72   0.473    -3046.033    6489.772
          5  |   2815.746    2545.01     1.11   0.273    -2271.657    7903.148
             |
       _cons |  -19113.85   35683.95    -0.54   0.594    -90445.05    52217.35
------------------------------------------------------------------------------
Endogenous: length
Exogenous:  weight 2.rep78 3.rep78 4.rep78 5.rep78 gear_ratio

.
. ivreg2 price weight (length=gear) i.rep78, small

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only

                                                      Number of obs =       69
                                                      F(  6,    62) =     3.84
                                                      Prob > F      =   0.0025
Total (centered) SS     =  576796958.9                Centered R2   =   0.0153
Total (uncentered) SS   =   3183192639                Uncentered R2 =   0.8216
Residual SS             =    567997123                Root MSE      =     3027

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      length |   156.4453   345.4758     0.45   0.652    -534.1511    847.0417
      weight |  -1.899938   9.598611    -0.20   0.844    -21.08729    17.28741
             |
       rep78 |
          2  |   262.1144   2659.123     0.10   0.922    -5053.397    5577.626
          3  |   1460.595   2220.161     0.66   0.513    -2977.445    5898.634
          4  |    1721.87   2385.178     0.72   0.473    -3046.033    6489.772
          5  |   2815.746    2545.01     1.11   0.273    -2271.657    7903.148
             |
       _cons |  -19113.85   35683.95    -0.54   0.594    -90445.05    52217.35
------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic):           1.551
                                                   Chi-sq(1) P-val =    0.2130
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic):                1.425
Stock-Yogo weak ID test critical values: 10% maximal IV size             16.38
                                         15% maximal IV size              8.96
                                         20% maximal IV size              6.66
                                         25% maximal IV size              5.53
Source: Stock-Yogo (2005).  Reproduced by permission.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments):           0.000
                                                 (equation exactly identified)
------------------------------------------------------------------------------
Instrumented:         length
Included instruments: weight 2.rep78 3.rep78 4.rep78 5.rep78
Excluded instruments: gear_ratio
------------------------------------------------------------------------------

.
. ivreghdfe price weight (length=gear), absorb(rep78)
(MWFE estimator converged in 1 iterations)

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only

                                                      Number of obs =       69
                                                      F(  2,    62) =    11.08
                                                      Prob > F      =   0.0001
Total (centered) SS     =  568436416.2                Centered R2   =   0.0008
Total (uncentered) SS   =  568436416.2                Uncentered R2 =   0.0008
Residual SS             =    567997123                Root MSE      =     3027

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      length |   156.4453   345.4758     0.45   0.652    -534.1511    847.0417
      weight |  -1.899938   9.598611    -0.20   0.844    -21.08729    17.28741
------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic):           1.551
                                                   Chi-sq(1) P-val =    0.2130
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic):                1.425
Stock-Yogo weak ID test critical values: 10% maximal IV size             16.38
                                         15% maximal IV size              8.96
                                         20% maximal IV size              6.66
                                         25% maximal IV size              5.53
Source: Stock-Yogo (2005).  Reproduced by permission.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments):           0.000
                                                 (equation exactly identified)
------------------------------------------------------------------------------
Instrumented:         length
Included instruments: weight
Excluded instruments: gear_ratio
Partialled-out:       _cons
                      nb: total SS, model F and R2s are after partialling-out;
                          any small-sample adjustments include partialled-out
                          variables in regressor count K
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
       rep78 |         5           0           5     |
-----------------------------------------------------+

.