Abstract
We study subvector inference in the linear instrumental variables model allowing for arbitrary forms of conditional
heteroskedasticity and weak instruments. The subvectorAnderson and Rubin (1949) test that uses chi square critical
values with degrees of freedom reduced by the number of parameters not under test, proposed by Guggenberger,
Kleibergen, Mavroeidis, and Chen (2012), has correct asymptotic size under conditional homoskedasticity but is generally
conservative.
Guggenberger, Kleibergen, Mavroeidis (2019) propose a conditional subvector Anderson and Rubin test that uses data
dependent critical values that adapt to the strength of identification of the parameters not under test. This test also has
correct asymptotic size under conditional homoskedasticity and strictly higher power than the
subvector Anderson and Rubin test by Guggenberger et al. (2012).
Here we first generalize the test in Guggenberger at al (2019) to a setting that allows for a general Kronecker product
structure which covers conditional homoskedasticity and some forms of conditional heteroskedasticity. To allow for
arbitrary forms of conditional heteroskedasticity, we propose a two step testing procedure. The first step, akin to a
technique suggested in Andrews and Soares (2010) in a different context, selects a model, namely general Kronecker
product structure or not. If the former is selected, then in the second step the generalized version of Guggenberger et al.
(2019) is used, otherwise a particular version of a test robust to arbitrary forms of conditional heteroskedasticity suggested
in Andrews (2017) is used. We show that the new two step test has correct asymptotic size and is more powerful and
quicker to run than several alternative procedures suggested in the recent literature.
Organizzatori
Alessandra Luati e Giuseppe Cavaliere