# standard errors when bootstrap is not possible. delta method?

I run standard fixed effects regressions on a panel of aggregate firm level data (variables like average value added, average labor). I use the fixed effects that I estimate to simulate firm level data and apply the Simulated Method of Moments to estimate another parameter. How can I compute the standard errors of such parameter? Since I'm using estimated parameters (with an error term) to generate firm level data, the natural way should be bootstrap. However, I cannot "re-build" the starting panel because (with subsamples of firms). Is the delta method a possible way to compute the standard errors in my case? thank you!

## 1 Answer

You should be able to bootstrap data which has a panel structure.. Why exactly can you not "re-build" or, to stay in bootstrapping terms, "re-sample" the data and re-estimate the coefficients and generate a distribution for your coefficient of interest?

• Thank you for your reply. Basically I start from a panel of aggregate firm data and I compute several FE. Then I use these estimates to simulate firm level data and compute a parameter using Method of Simulated Moments. If I'm not wrong, in order to be able to bootrstrap I should re-create a panel of aggregate firm data and re-compute the FE and re-apply the MSM, but I cannot do that because I cannot build a new panel because i don't have the initial firm level data. – user2668703 Jul 31 '19 at 14:31
• Aha, well I suppose you should ask yourself where the source of uncertainty around your parameter estimate would come from. Is it from simulating firms based on your FE's or something else? If it is the first, then I don't see a problem in re-sampling your initial panel and re-calculating the MSM in a Monte Carlo style.. Alternatively, you could re-sample from your simulated firm data as well, which would not capture uncertainty in the FE, but more so in the second part of your approach. – Mark Verhagen Aug 2 '19 at 8:09