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# Re: st: RE: Difference in Difference vs. Fixed Effects

 From Joerg Lang <[email protected]> To [email protected] Subject Re: st: RE: Difference in Difference vs. Fixed Effects Date Thu, 3 Oct 2013 10:41:11 +0200

```Hey Mustafa,

thanks for your response. I think that my sentence with the treatment
was kind of misleading. Treatment is the dummy for treatment but what
I really want to know is the Difference in Difference dummy (did).
I have the results below:

reg gender_decision did treatment followup, cluster (h1)

Linear regression                                      Number of obs =     636
F(  3,   317) =    5.77
Prob > F      =  0.0007
R-squared     =  0.0233
Root MSE      =   .3456

(Std. Err. adjusted for 318 clusters in h1)
------------------------------------------------------------------------------
|               Robust
gender_dec~n |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
did |   .0913309   .0678396     1.35   0.179    -.0421419    .2248037
treatment |  -.0164835   .0396981    -0.42   0.678    -.0945886    .0616215
followup |   .0864469   .0292938     2.95   0.003      .028812    .1440818
_cons |   .2387057   .0157684    15.14   0.000     .2076819    .2697296
------------------------------------------------------------------------------

xtreg gender_decision treatment did followup, fe vce(cluster h1)
note: treatment omitted because of collinearity

Fixed-effects (within) regression               Number of obs      =       636
Group variable: h1                              Number of groups   =       318

R-sq:  within  = 0.0465                         Obs per group: min =         2
between = 0.0016                                        avg =       2.0
overall = 0.0230                                        max =         2

F(2,317)           =      8.59
corr(u_i, Xb)  = -0.0067                        Prob > F           =    0.0002

(Std. Err. adjusted for 318 clusters in h1)
------------------------------------------------------------------------------
|               Robust
gender_dec~n |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
treatment |          0  (omitted)
did |   .0913309    .067786     1.35   0.179    -.0420364    .2246982
followup |   .0864469   .0292707     2.95   0.003     .0288575    .1440363
_cons |   .2363732   .0132882    17.79   0.000      .210229    .2625174
-------------+----------------------------------------------------------------
sigma_u |  .25124096
sigma_e |  .33511619
rho |  .35982364   (fraction of variance due to u_i)
------------------------------------------------------------------------------

reg gender_decision did treatment followup log_hhsize h16_hoh
h16_hohsp hohdum_edu_no_imp sphohdum
> _edu_no_imp asset_Index_imp women_groupmember log_hexp, cluster (h1)

Linear regression                                      Number of obs =     636
F( 11,   317) =    2.64
Prob > F      =  0.0030
R-squared     =  0.0379
Root MSE      =  .34518

clusters in h1)
-------------------------------------------------------------------------------------
|               Robust
gender_decision |      Coef.   Std. Err.      t    P>|t|     [95%
Conf. Interval]
--------------------+----------------------------------------------------------------
did |   .0775325   .0689252     1.12   0.261
-.0580762    .2131412
treatment |  -.0422406   .0423164    -1.00   0.319
-.125497    .0410158
followup |   .0816601   .0315261     2.59   0.010
.0196332     .143687
log_hhsize |  -.0050365      .0308    -0.16   0.870
-.0656347    .0555617
h16_hoh |   .0002403   .0019649     0.12   0.903
-.0036256    .0041061
h16_hohsp |   -.000707   .0023795    -0.30   0.767
-.0053886    .0039746
hohdum_edu_no_imp |    .015657   .0364541     0.43   0.668
-.0560656    .0873795
sphohdum_edu_no_imp |   .0712825   .0410581     1.74   0.084
-.0094982    .1520633
asset_Index_imp |   .0650232   .0761579     0.85   0.394
-.0848155     .214862
women_groupmember |   .0290404     .03097     0.94   0.349
-.0318924    .0899731
log_hexp |   .0190211   .0207127     0.92   0.359
-.0217307    .0597728
_cons |   .0026582   .2046481     0.01   0.990
-.3999819    .4052984
-------------------------------------------------------------------------------------

xtreg gender_decision treatment did followup log_hhsize h16_hoh
h16_hohsp hohdum_edu_no_imp sphohd
> um_edu_no_imp asset_Index_imp women_groupmember log_hexp, fe vce(cluster h1)
note: treatment omitted because of collinearity

Fixed-effects (within) regression               Number of obs      =       636
Group variable: h1                              Number of groups   =       318

R-sq:  within  = 0.0723                         Obs per group: min =         2
between = 0.0005                                        avg =       2.0
overall = 0.0140                                        max =         2

F(10,317)          =      2.80
corr(u_i, Xb)  = -0.2809                        Prob > F           =    0.0024

clusters in h1)
-------------------------------------------------------------------------------------
|               Robust
gender_decision |      Coef.   Std. Err.      t    P>|t|     [95%
Conf. Interval]
--------------------+----------------------------------------------------------------
treatment |          0  (omitted)
did |   .0944656   .0685701     1.38   0.169
-.0404444    .2293756
followup |   .0637825   .0348781     1.83   0.068
-.0048393    .1324043
log_hhsize |  -.0601096   .0553426    -1.09   0.278
-.1689948    .0487756
h16_hoh |  -.0014844   .0055086    -0.27   0.788
-.0123225    .0093537
h16_hohsp |    .005337   .0047125     1.13   0.258
-.0039347    .0146088
hohdum_edu_no_imp |   .1778034   .0849698     2.09   0.037
.0106275    .3449793
sphohdum_edu_no_imp |   .0998635   .0816447     1.22   0.222
-.0607705    .2604975
asset_Index_imp |   .0307611   .1463719     0.21   0.834
-.257222    .3187443
women_groupmember |   .0098729   .0503457     0.20   0.845
-.0891811    .1089268
log_hexp |  -.0025051   .0278105    -0.09   0.928
-.0572215    .0522113
_cons |   .1998801   .3670395     0.54   0.586
-.5222612    .9220215
--------------------+----------------------------------------------------------------
sigma_u |  .26714979
sigma_e |  .33481165
rho |  .38900009   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------

2013/10/2 Hussein, Mustafa (Mustafa Hussien) <[email protected]>:
> Hi Joerg,
>
> Can you post your results? You say that "treatment" was omitted from xtreg output. So what are you comparing your reg coefficients to then? In fixed effects I think you should be able specify a dummy for treatment.
>
> Mustafa
>
> ________________________________________
> From: [email protected] [[email protected]] on behalf of Joerg Lang [[email protected]]
> Sent: Wednesday, October 02, 2013 1:26 AM
> To: [email protected]
> Subject: st: Difference in Difference vs. Fixed Effects
>
> Dear Stalist users,
>
> currently writing my Master thesis and working with
> Stata 12, I have the following problem.
>
> I have a dataset on two time periods (2010 and 2012) and two groups
> (treatment and control). There is no treatment in the baseline and the
> treatment group uptakes the treatment between 2010 and 2012. The uptake is
> non-random.
> Now, I want to estimate the impact in a difference in difference design.
> At first, I estimate the following model:
>  y b0+b1Time+b2Treatment+b3Time*Treatment+u
>
> using the -reg command:
>
> -reg y time treatment time*treatment, cluster (h1)
>
> while y is the outcome variable that is between 0 and 1 and h1 is the
> household identifier. I use the cluster option to account for the problem
> of serial correlation. In a second estimation I also include some other
> covariates.
>
> I always thought that this setting and a setting with fixed effects
> yield exactly the same result as long as one has only two points in time
> (in my case 2010 and 2012).
>
> However, estimating the same model with:
>
> - xtreg y Time Treatment Time*Treatment, fe vce(cluster h1)
>
> gives slightly different results. The difference increases when including
> more covariates, which are the same in both cases. As well, there is no
> variation in the households. Thus, the same households and the same
> variables are used in both estimations.
> Obviously, treatment is omitted in the xtreg case since it does not vary
> between time.
> However, I think that this should not change anything.
> My question is:
>  Is my model correctly specified or did I overlook something?
> And, if my estimation is correct: Why this difference? Is this "normal"? If
> so, what does it tell me then, i.e. what is the reason for it?
>
> Since I have already been stuck with this problem for quite a while, any
> help or literature suggestions  would be very much appreciated.  Hope
> this question is not too trivial for you.
>
> Best regards,
>
> Joerg
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```