A more powerful subvector Anderson Rubin test in linear instrumental variables regression

Abstract

We study subvector inference in the linear instrumental variables model assuming homoskedasticity but allowing for weak instruments. The subvector Anderson 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), controls size but is generally conservative. We propose a conditional subvector Anderson and Rubin test that uses datadependent critical values that adapt to the strength of identification of the parameters not under test. This test has correct size and strictly higher power than the subvector Anderson and Rubin test by Guggenberger et al. (2012). We provide tables with conditional critical values so that the new test is quick and easy to use. Application of our method to a model of risk preferences in development economics shows that it can strengthen empirical conclusions in practice.

On the Inconsistency of Nonparametric Bootstraps for the Subvector Anderson-Rubin Test

“…(2012) provides appropriate chi-squared critical value, and Guggenberger et al (2019) proposes a data-dependent critical value to further improve power. Kleibergen (2019) provides a subvector conditional likelihood ratio test.…”

Identification robust inference for moments based analysis of linear dynamic panel data models

“…The resulting confidence sets only have correct coverage when these remaining parameters are well identified, see Kleibergen (2005). Just in some isolated cases, such, as for example, when using the GMM-AR statistic in the homoskedastic linear instrumental variables regression model or in the linear factor model for determining risk premia in finance, can we prove that these confidence sets are valid without requiring the partialled out parameters to be well identified, see Guggenberger et al (2012Guggenberger et al ( , 2019, , and .…”

On the inconsistency of nonparametric bootstraps for the subvector Anderson–Rubin test

“…Now we study the asymptotic size of the two bootstrap tests. Following Guggenberger, Kleibergen, Mavroeidis and Chen (2012) and Guggenberger, Kleibergen and Mavroeidis (2019), we first define the parameter space under the null hypothesis in (2.3): Note: The results are based on 100,000 simulation replications.…”

“…However, according to Figure 1, the recentering bootstrap can be very conservative under weak identification. In sum, we could not recommend either bootstrap method as there exist methods that both have correct asymptotic size and are less conservative such as the conditional subvector AR test proposed by Guggenberger et al (2019).…”

“…Both methods can be very conservative under weak IVs and the pairs bootstrap can be very conservative even under strong IVs. We note that in the homoskedastic case,Guggenberger et al (2012) provides appropriate chi-squared critical value, andGuggenberger et al (2019) proposes Define the localization parameter space:H = h = (h ww , h wε ): ∃ {θ n = (γ n , Π n,x , Π n,w , F n ) ∈ Θ : n ≥ 1} such that → h ww ∈ [−∞, +∞] L and σ…”