Hi,

I would be really very grateful for any suggestion on the following topic. I already searched quite a bit in the stata forum and could not find a threat answering this concrete question (sorry in advance if I oversaw any threat!).

I am modelling a (two-way) fixed effects regression with clustered standard errors (i.e. xtreg, fe vce(cluster id)).
My data is unbalanced. It consists of 862 groups/individuals (3326 obs) and a range of 2 to 9 obs (=waves/years) per group/individual. The average number of observations per group is 3.9.

The treatment variable is coded as 0-1-dummy.
There is one pre-treatment observation per individual (i.e. group). But individuals are not treated at the same point in time (i.e. no classic DiD model possible).
For all treated individuals, there are 1 to 8 treated observations. They do not return to a non-treated state.

Substantially, I estimate if the fathers take-up of parental leave changes the cross-sex couples gender division of labour in the mid-term (i.e. one year after the child was born). My dependent variable is the subjective perception of the fathers share in the couple division of f.ex. child care (in percent).

I am wondering, how to determine the number of observations after treatment.
Is it reasonable to include all observations after treatment per individual that exist in my data set?
1. Or would that be problematic, because due to serial correlation and correction for clustered standard errors I somehow underpower my model when I include more observations after treatment?
2. Or would that be problematic, because I do not assume that the treatment has a constant effect over time (at least not over 7 years)?
3. OR is it problematic to cut the observations after treatment (f.ex. to 1 observation after treatment) because my time-variant controls are somehow put at a disadvantage (i.e. less observations and less precise estimates)?

Power is a real issue in my models due to the small sample (which is why in a second step I estimate power analyses).
The number of groups/individuals for my main treatments are:
Model 1/Treatment 1 (parental leave uptake in general by fathers): treated individuals = 190.
Model 2/Treatment 2 (parental leave uptake by length of leave by fathers): treated individuals long leave = 40, short leave = 150.

Here is one example of Treatment 2 (if I limit the number of observations after treatment to 3 observations, the effect of fathers taking long leave is significantly different from zero at 1 % significance level).

Code:
Fixed-effects (within) regression               Number of obs     =      2,888
Group variable: id                              Number of groups  =        862

R-sq:                                           Obs per group:
within  = 0.0155                                         min =          1
between = 0.0282                                         avg =        3.4
overall = 0.0241                                         max =          4

F(13,861)         =       2.40
corr(u_i, Xb)  = 0.0392                         Prob > F          =     0.0035

(Std. Err. adjusted for 862 clusters in id)

Robust
i~t_m_percent       Coef.   Std. Err.      t    P>t     [95% Conf. Interval]

egbezugR_lang
1-2 M      .780363    1.38431     0.56   0.573    -1.936654     3.49738
3+ M      6.72861   2.600056     2.59   0.010     1.625419     11.8318

wave
2 2009/10    -.0364923    1.30846    -0.03   0.978    -2.604636    2.531651
3 2010/11    -3.351699   1.292057    -2.59   0.010    -5.887649   -.8157494
4 2011/12    -2.581918   1.299806    -1.99   0.047    -5.133078   -.0307577
5 2012/13    -2.673929     1.3737    -1.95   0.052    -5.370122    .0222635
6 2013/14    -3.061289   1.592486    -1.92   0.055    -6.186897    .0643195
7 2014/15    -5.009589   1.738678    -2.88   0.004    -8.422133   -1.597045
8 2015/16    -4.071387   2.015904    -2.02   0.044    -8.028048   -.1147249
9 2016/17    -4.691198   2.123619    -2.21   0.027    -8.859273   -.5231232

1.ehe   -.5543271   1.382612    -0.40   0.689    -3.268012    2.159358

nkinderhh
2    -2.116772   1.087172    -1.95   0.052     -4.25059    .0170457
3+    -3.839472   2.415717    -1.59   0.112    -8.580856    .9019127

_cons    33.55253   1.495337    22.44   0.000      30.6176    36.48746

sigma_u   14.216154
sigma_e   12.339163
rho   .57033092   (fraction of variance due to u_i)


Here is one example of Treatment 1 (if I do not limit the number of observations after treatment, the effect of fathers taking long leave is significantly different from zero at 5 % significance level).

Code:
Fixed-effects (within) regression               Number of obs     =      3,975
Group variable: id                              Number of groups  =        862

R-sq:                                           Obs per group:
within  = 0.0110                                         min =          2
between = 0.0586                                         avg =        4.6
overall = 0.0391                                         max =          9

F(13,861)         =       2.57
corr(u_i, Xb)  = 0.1107                         Prob > F          =     0.0017

(Std. Err. adjusted for 862 clusters in id)

Robust
i~t_m_percent       Coef.   Std. Err.      t    P>t     [95% Conf. Interval]

egbezugR_lang
1-2 M    -.3975052   1.306613    -0.30   0.761    -2.962024    2.167014
3+ M     5.789916   2.609071     2.22   0.027     .6690317     10.9108

wave
2 2009/10     .3451049   1.285809     0.27   0.788    -2.178583    2.868793
3 2010/11    -2.601317   1.291027    -2.01   0.044    -5.135244   -.0673888
4 2011/12    -1.660287   1.285891    -1.29   0.197    -4.184136    .8635614
5 2012/13    -.9978387   1.281961    -0.78   0.437    -3.513973    1.518295
6 2013/14      -.29582   1.352524    -0.22   0.827    -2.950449    2.358809
7 2014/15    -2.138801   1.373577    -1.56   0.120    -4.834752    .5571496
8 2015/16    -1.367841   1.408617    -0.97   0.332    -4.132567    1.396884
9 2016/17    -.8932695   1.434341    -0.62   0.534    -3.708484    1.921945

1.ehe   -.1544514   1.162809    -0.13   0.894    -2.436724    2.127821

nkinderhh
2    -2.342018   .8708863    -2.69   0.007    -4.051327   -.6327097
3+    -4.092713   1.512708    -2.71   0.007     -7.06174   -1.123686

_cons    31.92636   1.401207    22.78   0.000     29.17618    34.67654

sigma_u   14.048032
sigma_e   11.974386
rho   .57918407   (fraction of variance due to u_i)
Thank you very much in advance!

All the best,
Julia