Different results for ivreghdfe and reghdfe when using predict after the same regression

[Bobby Wood]

Hi all,

I run two estimations

reghdfe y x1 x2, absorb(i t)
predict yhat1

and

ivreghdfe y x1 x2, absorb(i t)
predict yhat2

But the predictions are very different for yhat1 and yhat2. What could be the reason here and which gives correct predictions?

Thank you!
Bobby

[Bobby Wood]

Similarly, I get again different results for predict if I use xtreg

xtset i t
xtreg y x1 x2 i.t, fe
predict yhat3

Aren't they all supposed to be same?

[Andrew Musau]

There are different defaults for the prediction, e.g., if the prediction includes the individual effect. See

help xtreg postestimation

under -predict-

[Bobby Wood]

And which one is correct if I want to do an IV by hand?

[Andrew Musau]

Should be with the individual effects.

webuse nlswork
xtivreg ln_w age c.age#c.age not_smsa (tenure = union south), fe first
*BY HAND NOT CORRECTING STANDARD ERRORS
qui xtreg tenure age c.age#c.age not_smsa  union south, fe
predict tenurehat, xbu
xtreg ln_w tenurehat age c.age#c.age not_smsa, fe

Res.:

. xtivreg ln_w age c.age#c.age not_smsa (tenure = union south), fe first

First-stage within regression

Fixed-effects (within) regression               Number of obs     =     19,007
Group variable: idcode                          Number of groups  =      4,134

R-sq:                                           Obs per group:
     within  = 0.3019                                         min =          1
     between = 0.0578                                         avg =        4.6
     overall = 0.1289                                         max =         12

                                                F(5,14868)        =    1285.83
corr(u_i, Xb)  = -0.1871                        Prob > F          =     0.0000

------------------------------------------------------------------------------
      tenure |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0863031   .0343238     2.51   0.012     .0190241    .1535821
             |
 c.age#c.age |   .0039115    .000549     7.12   0.000     .0028353    .0049876
             |
    not_smsa |  -.3552488   .1269318    -2.80   0.005    -.6040507   -.1064468
       union |   .3896861   .0706568     5.52   0.000     .2511901    .5281821
       south |  -.4296172   .1349122    -3.18   0.001    -.6940618   -.1651726
       _cons |  -2.554764   .5293374    -4.83   0.000     -3.59233   -1.517197
-------------+----------------------------------------------------------------
     sigma_u |  3.1334845
     sigma_e |  2.5869529
         rho |  .59467598   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4133, 14868) = 6.40                 Prob > F = 0.0000

Fixed-effects (within) IV regression            Number of obs     =     19,007
Group variable: idcode                          Number of groups  =      4,134

R-sq:                                           Obs per group:
     within  =      .                                         min =          1
     between = 0.1304                                         avg =        4.6
     overall = 0.0897                                         max =         12

                                                Wald chi2(4)      =  147926.58
corr(u_i, Xb)  = -0.6843                        Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      tenure |   .2403531   .0373419     6.44   0.000     .1671643    .3135419
         age |   .0118437   .0090032     1.32   0.188    -.0058023    .0294897
             |
 c.age#c.age |  -.0012145   .0001968    -6.17   0.000    -.0016003   -.0008286
             |
    not_smsa |  -.0167178   .0339236    -0.49   0.622    -.0832069    .0497713
       _cons |   1.678287   .1626657    10.32   0.000     1.359468    1.997106
-------------+----------------------------------------------------------------
     sigma_u |  .70661941
     sigma_e |  .63029359
         rho |  .55690561   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F  test that all u_i=0:     F(4133,14869) =     1.44      Prob > F    = 0.0000
------------------------------------------------------------------------------
Instrumented:   tenure
Instruments:    age c.age#c.age not_smsa union south
------------------------------------------------------------------------------

.
. *BY HAND NOT CORRECTING STANDARD ERRORS

.
. qui xtreg tenure age c.age#c.age not_smsa  union south, fe

.
. predict tenurehat, xbu
(9,527 missing values generated)

.
. xtreg ln_w tenurehat age c.age#c.age not_smsa, fe

Fixed-effects (within) regression               Number of obs     =     19,007
Group variable: idcode                          Number of groups  =      4,134

R-sq:                                           Obs per group:
     within  = 0.1052                                         min =          1
     between = 0.1304                                         avg =        4.6
     overall = 0.0948                                         max =         12

                                                F(4,14869)        =     437.24
corr(u_i, Xb)  = -0.8478                        Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   tenurehat |    .240353    .015377    15.63   0.000     .2102122    .2704939
         age |   .0118437   .0037074     3.19   0.001     .0045767    .0191108
             |
 c.age#c.age |  -.0012145   .0000811   -14.98   0.000    -.0013733   -.0010556
             |
    not_smsa |  -.0167178   .0139694    -1.20   0.231    -.0440995    .0106639
       _cons |   1.678287    .066984    25.06   0.000      1.54699    1.809584
-------------+----------------------------------------------------------------
     sigma_u |  .70661939
     sigma_e |  .25954812
         rho |  .88112219   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4133, 14869) = 8.47                 Prob > F = 0.0000

.