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)
All the best,
Julia
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