Correct all observations for yearly trend

[Pierre Elias]

Dear Stata-users,

I analyze the effect of a policy on a panel data of 30.000 firms. My data runs from 2004 to 2012.
My summary statistics suggest that the policy targeted firms with specific characteristics.

To go further in my analysis, i would like to estimate, with a probit model, the probability for a firm i, from a sector s to become a treated firm. The treatment have begun in 2007.

Nevertheless if the firms' characteristics are affected by annual common shocks, my computation for the pre-treatment average characteristics could be noisy.

I would like to correct all observations for yearly trend of every sector (I have a specific variable for the code of the sector). How can i correct for yearly trend of every sector?

Thanks in advance,

Pierre

[Jeff Wooldridge]

Pierre: How many sectors do you have? If not too many you can simply regress each variable that you want detrended on interactions between the time trend and a full set of sector dummies. The residuals from these regressions are the detrended variables. However, any subsequent analysis will not take account of the estimated trend parameters, so the inference won't be quite correct.

Would it suit your purpose to estimate the probit model and include the trend/sector interactions directly? You might even be able to include sector/year interactions for a completely flexible specification (which only makes sense starting in 2007, as you know the probability of treatment is zero before that).

It sounds like this is leading to some sort of propensity score matching or weighting. I suggest not dismissing a standard fixed effects analysis where you control for sector-by-year effects and allow for firm fixed effects, and maybe firm-specific linear trends.

If you have many sectors, you can write a small loop to do the detrending by sector, but I'm not sure you need that. JW

[Xueting Dou]

Pierre: How many sectors do you have? If not too many you can simply regress each variable that you want detrended on interactions between the time trend and a full set of sector dummies. The residuals from these regressions are the detrended variables. However, any subsequent analysis will not take account of the estimated trend parameters, so the inference won't be quite correct.

Would it suit your purpose to estimate the probit model and include the trend/sector interactions directly? You might even be able to include sector/year interactions for a completely flexible specification (which only makes sense starting in 2007, as you know the probability of treatment is zero before that).

It sounds like this is leading to some sort of propensity score matching or weighting. I suggest not dismissing a standard fixed effects analysis where you control for sector-by-year effects and allow for firm fixed effects, and maybe firm-specific linear trends.

If you have many sectors, you can write a small loop to do the detrending by sector, but I'm not sure you need that. JW

Dear Jeff,

Your suggestion on specifications here is very inspiring. I usually try my best to write down all specifications I would like to look into after checking the data but before running any regressions.

My question is, is there a good way to systematically identify which specifications are feasible without actually testing them? For example, in this case, we have firms, sectors, and years, I would also like to try firm-by-year fixed effects, maybe together with other structures. But how can I tell whether or not the variation in the data is sufficient for my specifications?

I think this has something to do with degrees of freedom. I have some sense of that but not fully clear as I would love to be. Would you please briefly mention it, or suggest some readings for me?

Thank you very much! Katherine