On the Asymptotic Sizes of Subset Anderson-Rubin and Lagrange Multiplier Tests in Linear Instrumental Variables Regression

Abstract

We consider tests of a simple null hypothesis on a subset of the coefficients of the exogenous and endogenous regressors in a single-equation linear instrumental variables regression model with potentially weak identification. Existing methods of subset inference (i) rely on the assumption that the parameters not under test are strongly identified, or (ii) are based on projection-type arguments. We show that, under homoskedasticity, the subset Anderson and Rubin (1949) test that replaces unknown parameters by limited information maximum likelihood estimates has correct asymptotic size without imposing additional identification assumptions, but that the corresponding subset Lagrange multiplier test is size distorted asymptotically.

Predictability of the Brazilian consumption growth: the relevance of anticipated growth rates in income and credit

“…Based on effective and simulated data for the US economy, Ludvigson (1999) concludes that anticipated income and credit growth rates have predictive content for the consumption growth rate. Brady (2008) re-estimates the Ludvigson (1999) model using US aggregate data, and the findings are 9 As mentioned by Ludvigson (1999), the model proposed by Deaton (1991) corresponds to the case in which ω approaches infinity, and consumers cannot borrow. 10 Specifically, Ludvigson's (1999) model has a constant interest rate, R.…”

“…Essentially, the test uses the LIML estimates for the strongly identified parameters, allowing us to construct a robust confidence interval for a subset of endogenous variables. Guggenberger et al (2012) show that this subset AR test has the correct asymptotic size, while subset tests based on the Lagrange Multiplier are distorted asymptotically. In addition, because the Lagrange Multiplier appears in the conditional likelihood ratio (CLR) subset test, Guggenberger et al (2012) conjecture that the CLR is also distorted.…”

“…where D t and Y t are the consumers' respective debt and income in period t. The parameter ω is fixed and known, and ξ t is an aggregate shock to the credit ceiling in period t, being independent of individual income. 9 The constraint (5) leads to the following Euler equation: 10…”

“…These confidence intervals are based on tests similar to the Anderson-Rubin (AR) one (Anderson et al, 1949). Guggenberger et al (2012) develop a test based on the AR statistic, which is suitable for when there are many endogenous variables. Essentially, the test uses the LIML estimates for the strongly identified parameters, allowing us to construct a robust confidence interval for a subset of endogenous variables.…”

A Powerful Subvector Anderson–rubin Test in Linear Instrumental Variables Regression With Conditional Heteroskedasticity

“…By robust, we mean a testing procedure for a hypothesis of (or a confidence region for) a subset of the structural parameter vector such that the asymptotic size is bounded by the nominal size for a parameter space that allows for weak or partial identification. Recent contributions to robust subvector inference have been made in the context of the linear instrumental variables (IVs) model (see, for example, Dufour and Taamouti, 2005;Guggenberger et al, 2012;hereafter Guggenberger, Kleibergen, and Mavroeidis, 2019;hereafter GKM19;Kleibergen, 2021), GMM models (see, for example, Chaudhuri and Zivot, 2011;Andrews and Cheng, 2014;Andrews and Mikusheva, 2016;Andrews, 2017;Han and McCloskey, 2019), and also models defined by moment (in)equalities (see, for example, Bugni, Canay, and Shi, 2017;Gafarov, 2019;Kaido, Molinari, and Stoye, 2019). GKM19 introduce a new subvector test that compares the AR subvector statistic to conditional critical values that adapt to the strength or weakness of identification and verify that the resulting test has correct asymptotic size for a parameter space that imposes conditional homoskedasticity (CHOM) and uniformly improves on the power of the projected AR test studied in Dufour and Taamouti (2005).…”