Weighting in a fixed effect model with reghdfe

[Mariela Dal Borgo]

Hello,

I am running a fixed effects model using the command reghdfe. The fixed effects are at the firm and bank level (and their interactions).

My dependent variables are loan characteristics, for instance, interest rate or maturity. The treatment is at the bank level. I would like to keep the analysis at the loan-level and weight the regressions by loan volume to capture the fact that banks care more about the pricing of bigger than of smaller loans.

I was thinking to use analytic weights [aw=volume], but I am not sure whether this is correct. I read that analytic weights are used when the observations are an average and you want to weight more the ones that are more precisely computed. Even though each observation is a loan characteristic, computed as the (volume-weighted) average of several credit lines that a firm has with a given bank, I do not want to weight the regression by the number of credit lines but by the total loan volume that a firm has with a given bank. I think that probability or frequency weights would not help either and “importance weights” are not available. So, I wonder if I should stick to the unweighted regressions instead?

Thanks a lot for any advice!

Best,

Mariela

[Sergio Correia]

> The fixed effects are at the firm and bank level (and their interactions).

Do you mean you are doing something like reghdfe .. , absorb(firm#bank) ?

> I was thinking to use analytic weights [aw=volume], but I am not sure whether this is correct

According to this Stata FAQ, aweights also solve general heteroskedasticity problems.

You might also do pweights (after all, AFAIK pweights are literally the same as running aweights + robust or clustered standard errors). See the end of page 6 here

[Mariela Dal Borgo]

Hello Sergio,

Thanks for the references! Yes, in some specifications I use: reghdfe .. , absorb(firm#bank). My setup is similar to the example of the villages in page 4 of the second note you mentioned. I also do clustering by bank.

Actually, the purpose of using weights in my case is not to solve the heteroskedasticity, but rather to increase the importance of some observations in the regression (I don’t know how to put it more technically).

I am now thinking, using analytic weights where the weights are the loan volume will be equivalent to assume that a loan of $1,000 at a 5% interest rate is the average of 1,000 loans with an average rate of 5%, and with potentially different firm characteristics that are also averaged out (the X’s).

Using frequency weights instead will be equivalent to assume that there are 1,000 loans at a 5% interest rate, where all the firm characteristics are the same for each loan (i.e. duplicate observations). Perhaps this is more appropriate because in the analytic weights the X’s do not need to be the same.

In my data using frequency weights results in a numeric overflow when running reghdfe (perhaps due to some very large loan volumes?). But anyway, they should give the same point estimates as the analytic weights, I’ll see if I can recover the s.e. using the formula in the footnote #2 of the note you sent me.

Thanks again!

Best,

Mariela

[Sergio Correia]

> Actually, the purpose of using weights in my case is not to solve the heteroskedasticity, but rather to increase the importance of some observations in the regression (I don’t know how to put it more technically).


There are some cases where weights fix biases in regression specifications (I recall something like that in models with bank fixed effects where you need to weight by the growth of each bank's lending; but I forgot the name of the paper that does it). But all in all, those cases are backed by strong theory.

Also, the idea of weights is exactly to increase the importance of some obs. with respect to other observations (except freq weights which increases the importance of all obs).

BTW, I would strongly advise against doing freq. weights as that would make the results look too nice in terms of standard errors.

Good luck,
S

[Mariela Dal Borgo]

Yes, I guess there are several reasons to use weights... I wanted to use them because it is pretty standard to present summary statistic of loan characteristics that are volume weighted - I think it is intuitive. It’s just that I have not seen papers in the related literature that use the weights in the regressions in the way I want,.
I can’t use the freq weights directly anyway because of the numeric overflow problem (they seem to me the ones that get closer to what I want to do but thanks for the advice on the s.e) and not sure if conceptually it would be correct to use the analytic weights.
Thanks again for your comments!
Best,

Mariela