Stata中ivregress 2SLS与reg的默认方差估计量为何差异显著？

Great question—this boils down to how Stata handles finite-sample corrections and test statistics differently between the two commands by default. Let's break it down by scenario:

• Classic (homoskedastic) standard errors
  By default, ivregress 2SLS skips the finite-sample correction factor (N/(N-k)) and uses a Z-test. In contrast, reg automatically applies this correction and uses a t-test out of the box. To make ivregress 2SLS match reg's default behavior here, just add the small option—it will apply the finite-sample correction and switch to a t-test.

• Robust standard errors
  When using robust SEs (via the robust option), ivregress 2SLS defaults to HC0 standard errors paired with a Z-test. But reg uses HC1 SEs (which include the finite-sample correction) and a t-test by default. Again, specifying the small option will make ivregress 2SLS switch to HC1 SEs and t-tests, aligning it with reg's default setup.

• Clustered standard errors
  The same logic applies to clustered SEs (with cluster(varname)). ivregress 2SLS doesn't apply finite-sample corrections and uses Z-tests by default. Add the small option to enable the relevant corrections and switch to t-tests, matching how reg behaves with clustered SEs out of the box.

内容的提问来源于stack exchange，提问作者luke.sonnet