An Automatic Test of Super Exogeneity*

Abstract

We develop a new automatically-computable test for super exogeneity, using a variant of generalto-specific modeling. Based on the recent developments of impulse saturation applied to marginal models under the null that no impulses matter, we select the significant impulses for testing in the conditional. Since zero-mean changes are relatively undetectable in both VARs and conditional equations, we focus on location shifts, although we also discuss variance changes. The approximate analytical non-centrality of the test is derived for a failure of weak exogeneity when there is a shift in the marginal process. Monte Carlo simulations confirm the empirical accuracy of the nominal significance levels under the null, and show rejections for this failure of super exogeneity. An empirical application to UK M1 delivers new results for this much-studied data set.

Evaluating Forecasts, Narratives and Policy Using a Test of Invariance

“…The test was able to detect failures of invariance when weak exogeneity failed and the marginal processes changed from a location shift. Compared to the nearest corresponding experiment in Hendry and Santos (2010), the potency of F Inv is considerably higher for SIS at α 2 = 0.01 than IIS at α 2 = 0.025 (both at α 1 = 0.025) as shown in Figure 5. A test rejection outcome by F Inv indicates a dependence between the conditional model parameters and those of the marginals, warning about potential mistakes from using the conditional model to predict the outcomes of policy changes that alter the marginal processes by location shifts, which is a common policy scenario.…”

“…Many tests for super exogeneity have been proposed since Engle et al (1983): see e.g., (Hendry 1988;Favero and Hendry 1992;Engle and Hendry 1993;Psaradakis and Sola 1996;Jansen and Teräsvirta 1996;Hendry and Santos 2010), including tests based on co-breaking as in Krolzig and Toro (2002), and Hendry and Massmann (2007). Here we propose a test of invariance based on step-indicator saturation (denoted SIS), following Castle et al (2015).…”

“…Ericsson and Reisman (2012) propose combining IIS and SIS in 'super saturation ' and Ericsson (2016) uses IIS to adjust an ex post mis-match between the truncated FMI Greenbook 'post-casts' and GDP outcomes. 5 The invariance test proposed here is the extension to SIS of the IIS-based test of super exogeneity in Hendry and Santos (2010). SIS is applied to detect location shifts in models of policy instruments, then any resulting significant step indicators are tested in the model for the target variables of interest.…”

“…Super exogeneity, which is required for policy validity, can be tested by checking whether any significant location shifts in models of the policy instruments are significant in the model of the target variables. The proposed test is an extension of the test for super exogeneity using impulse indicator saturation proposed in Hendry and Santos (2010).…”

Unpredictability in economic analysis, econometric modeling and forecasting

“…In other arenas, location shifts can play a positive role in clarifying both causality, as demonstrated in White and Kennedy (2009), and super exogeneity (see Hendry and Santos, 2010). Also White (2006) considers estimating the effects of natural experiments, many of which involve large location shifts.…”