Small sample adjustment changes for `vcov="hetero"` with `fixest` 0.13?

[s3alfisc]

Hi fixest team,

I am currently aligning pyfixest with the new fixest defaults shipped with 0.13 and I struggle to replicate small sample adjustments for heteroskedastic error. My tests fail! 😅

It appears to me that with the new version, some default ssc adjustment have changed?

I do not find any reference in the changelog.

Changes I spot:

• The G.adj arg seems no longer applied for heteroskedastic errors. This makes a lot of sense to me and is in line with the ssc / standard error vignette ✅
• The K.adjlogic for hetero errors is switched from (N-1) / (N - df.k) to n/(n - df.k)).

Can you confirm? I suppose this is intentional but thought I'd better flag it, as I did not see a reference in the changelog.

Should I open a PR to clarify the ladder point in the docs and changelog?

Thanks!

Under 0.13.2, I find:

> fixest:::vcov_hetero_internal
function (bread, scores, sandwich, nthreads, ssc, n, K, ...) 
{
    if (!sandwich) {
        vcov_mat = cpp_crossprod(scores, 1, nthreads)
    }
    else {
        vcov_mat = cpp_crossprod(cpp_matprod(scores, bread, nthreads), 
            1, nthreads)
    }
    if (ssc$K.adj) {
        adj = n/(n - K)
        vcov_mat = vcov_mat * adj
    }
    vcov_mat
}
<bytecode: 0x11b2e4048>
<environment: namespace:fixest>
> fixest:::vcov_iid_internal
function (bread, ssc, object, n, K, ...) 
{
    if (ssc$K.adj) {
        adj = (n - 1)/(n - K)
        bread = bread * adj
    }
    bread
}
<bytecode: 0x139ea59a8>
<environment: namespace:fixest>

Under fixest 0.12, I found

> fixest:::vcov_hetero_internal
function (bread, scores, sandwich, ssc, nthreads, ...) 
{
    if (!sandwich) {
        vcov_noAdj = cpp_crossprod(scores, 1, nthreads)
    }
    else {
        n = nrow(scores)
        adj = ifelse(ssc$cluster.adj, n/(n - 1), 1)
        vcov_noAdj = cpp_crossprod(cpp_matprod(scores, bread, 
            nthreads), 1, nthreads) * adj
    }
    vcov_noAdj
}
<bytecode: 0x13b31a6a0>
<environment: namespace:fixest>
> fixest:::vcov_iid_internal
function (bread, ...) 
{
    bread
}
``

[kylebutts]

I think N / (N - K) is the correct adjustment to make:

• http://qed.econ.queensu.ca/dm-book/EIE-davidson-mackinnon-2021.pdf

• https://www.econstor.eu/bitstream/10419/189084/1/qed_wp_0537.pdf

If I remember correctly, what was happening was for HC1, ssc had cluster.adj = TRUE by default. So, K.adj applied (N - 1) / (N - K) and G.adj applied N / (N - 1). The product then was N / (N - K).
So since we do not apply G.adj anymore, we just use N / (N - K)

Maybe when you made those changes you did not make both changes at the same time?

[s3alfisc]

Yes, the new default makes sense to me. Thanks for confirming@kylebutts!

Should I open a Pr to update the change log to state that the G.adj arg is no longer applied to hetero errors and that the K.adj arg sets N/(N-k) ans not (N-1)/(N-k) as stated in the docs?

[kylebutts]

Sure! Maybe as a sub-bullet point to "the arguments of the function ssc are renamed:"

• The argument G.adj now only applies for clustered standard errors. The HC1 standard errors do not change in this version.
• The argument K.adj applies for all standard errors

[s3alfisc]

Quick follow up here: for time series HAC, G.adj does still impact the standard errors, and K.adj applies the old (N-1) / (N-k_df).

To align with the new hetero defaults, it might make sense to align these as well?

library(fixest)
packageVersion("fixest")
data(mtcars)
head(mtcars)
mtcars$time = 1:nrow(mtcars)


fit = feols(mpg  ~ cyl, data = mtcars, vcov = vcov_NW(time = ~time, lag = 4))

a = vcov_NW(fit, ssc = ssc(K.adj = TRUE), time = ~time, lag = 4)
b = vcov_NW(fit, ssc = ssc(K.adj = FALSE), time = ~time, lag = 4)
a / b
#            (Intercept)      cyl
# (Intercept)    1.033333 1.033333
# cyl            1.033333 1.033333
N = nrow(mtcars)
k_df = 2
(N-1) / (N-k_df)
#[1] 1.033333

a = vcov_NW(fit, ssc = ssc(K.adj = FALSE, G.adj = TRUE), time = ~time, lag = 4)
b = vcov_NW(fit, ssc = ssc(K.adj = FALSE, G.adj = FALSE), time = ~time, lag = 4)
a / b
#> a / b
#            (Intercept)      cyl
#(Intercept)    1.032258 1.032258
#cyl            1.032258 1.032258

I can try to open a PR for this in the next days if you're up for it!