3
$\begingroup$

I am fitting a linear model on some panel data

$$y_{it} = \sigma_{cr} + x_{it}^\top\beta + \mu_i + \delta_t+ \epsilon_{it}$$

where $\mu_i$ is individual fixed effect (in the sense used in econometrics) $\delta_t$ are time dummies and $\sigma_{cr}$ is a dummy for area of work and area of residence of individual $i$ at time $t$.

So $c = c(i,t)$ where $c(i,t)$ is the area of individual i in time t. So $r = r(i,t)$ where $r(i,t)$ is the area of individual i in time t.

The places of work and the places of residence are defined as political municipalities. Assume that the median number in each $(c,r)$-group at a given time $t_0$ is is around 5000 measuring group size as $\#\{i\lvert c(i,t_0)=c,r(i,t_0)=r \}$.

The dummies $\sigma_{cr}$ are only identified by individuals who change either area of residence or area of work. Still I am a bit concerned about the empirical identification. Are there any checks I should/could do to investigate this?

$\endgroup$
  • $\begingroup$ So $\sigma_{cr}$ could have index $_{it}$ for completeness? $\endgroup$ – Richard Hardy Nov 5 '19 at 11:56
  • $\begingroup$ yes that is correct $\endgroup$ – Stop Closing Questions Fast Nov 5 '19 at 12:57
  • $\begingroup$ Just so that your setting is clear: is it possible (or not) that several people have the same area of work and home at a given time? $\endgroup$ – Alex. C-L - Reinstate Monica Nov 6 '19 at 9:16
  • $\begingroup$ yes that is correct $\endgroup$ – Stop Closing Questions Fast Nov 6 '19 at 9:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.