clustered-standard-errors.domd

---
layout: post
title: xtreg fe - Clustered Standard Errors - Use Caution
---

I have been implementing a fixed-effects estimator in Python so I can
work with data that is too large to hold in memory.  To make sure I
was calculating my coefficients and standard errors correctly I have
been comparing the calculations of my Python code to results from
Stata.  This lead me to find a surprising inconsistency in Stata's
calculation of standard errors.  I illustrate the issue by comparing
standard errors computed by Stata's `xtreg fe` command to those
computed by the standard `regress` command.  To start, I use the first
hundred observations of the `nlswork` dataset:

    webuse nlswork, clear
    keep if _n <= 100

I then estimate a fixed-effects model using regress:

    regress ln_w age tenure i.idcode, vce(cluster idcode)

For comparison, I estimate the same model using `xtreg fe`:

    xtset idcode
    xtreg ln_w age tenure, fe vce(cluster idcode)

Notice that the coefficients on age and tenure match perfectly across
the two regressions, but the standard errors calculated by `xtreg fe`
are smaller.  This is due to a difference in the degrees of freedom
adjustment used.  `regress` counts the fixed effects as coefficients
estimated, while `xtreg fe` by default does not.  As Kevin Goulding
explains
[here](http://thetarzan.wordpress.com/2011/06/11/clustered-standard-errors-in-r/),
clustered standard errors are generally computed by multiplying the
estimated asymptotic variance by (M / (M - 1)) ((N - 1) / (N - K)).  M
is the number of individuals, N is the number of observations, and K
is the number of parameters estimated.  The standard `regress` command
correctly sets K = 12, `xtreg fe` sets K = 3.  Making the asymptotic
variance (99 - 12) / (99 - 3) = 0.90625 times the correct value.

To get the correct standard errors from `xtreg fe` use the `dfadj`
option:

    xtreg ln_w age tenure, fe vce(cluster idcode) dfadj

This seems like an option that could be missed easily.