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I was reading the following paper by Henrik Kleven et al.

https://www.henrikkleven.com/uploads/3/7/3/1/37310663/kleven-landais-sogaard_nber-w24219_jan2018.pdf

The estimate the child penalty on wage through an event study as follows (See equation (1) in page 9):

$$ln(w_{ist})=\sum_{j\neq -1}\alpha_{j}I[j=t]+\sum_{k}\beta_{k}I[k=age_{is}]+\sum_{y}\gamma_{y}I[y=s]+\varepsilon_{ist}$$

$i$, $s$, and $t$ denote individual, year, and event time. $j=0$ is the first year an individual has a baby. $\beta$ and $\gamma$ indicate age dummies and year dummies. Event time dummies $\alpha_{j}$ captures the causal effect of having a baby on wage.

This is a silly question. Is it possible to control for individual fixed effect $\sum_{x}\delta_{x}I[x=i]$ after controlling for event time dummy, age dummy, and year dummy? Technically it will be possible, but does it make sense? My instinct is that it should not be included. There must be a reason why it is not controlled. But I can't understand why.

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    $\begingroup$ If they had individual fixed effects could they then do the decomposition they do later and say something about gender pay gap? $\endgroup$ – Jesper Hybel Jun 12 at 9:03
  • $\begingroup$ @JesperHybel That makes sense. But I just ran regressions with female sample from a different country. Event time dummy did not make any sense. There was insane pretrend. $\endgroup$ – hbkn Jun 13 at 2:31
  • $\begingroup$ yeah ok, I have the data for the article you cited, but would have to merge datasets first. But could try to run it at some point if I get the time. $\endgroup$ – Jesper Hybel Jun 13 at 8:25
  • $\begingroup$ @JesperHybel Thanks! You have absolutely no obligation to do the analysis. I just felt that there must be an ex-ante reason why it should not be included. Thanks so much anyway. $\endgroup$ – hbkn Jun 13 at 14:36

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