Jorda's LP: compute standard deviations of IRFs

[RomainR]

Dear all,
I estimate Jorda’s local projections. The LHS variable (called it Y) is in first difference in the local regressions. My interest is in getting the IRFs of the LHS variable in level. Accordingly, if the vector of coefficients of interest (the one associated with the shock variable in the local projections) is called beta, I estimate the IRF of Y (in level) by using the accumulate function:
accumulate beta / betaacc
First, do you think it’s the correct way to recover the IRFs of Y in level from local regressions in which the RHS variable is Y(t)-Y(t-1)?
And second, how can I compute the standard deviation of the IRF of Y in level? Maybe I’m wrong, but I think I can’t accumulate standard deviations (of beta) in the same way I did for coefficients beta. I guess I have to consider for the covariance between beta(h) and beta(h-1), but concretly how to fix it?
I hope you got my point.
Thanks in advance,
Best,
Romain

[TomDoan]

1. You definitely cannot add the standard deviations. The variance of a linear combination is a quadratic form in the joint covariance matrix of the coefficients---which doesn't exist in this case because the h-step responses are estimated separately.
2. I don't think that idea even works. The relationship between the lagged regression in differences and the lagged regressions in levels isn't as simple as it is without the gaps. If you want to apply Jorda to levels, you have to estimate in levels.

[RomainR]

Many thanks Tom. Your replies are versy useful.
Romain