Identification Through Heterogeneity

Abstract

We analyze set identification in Bayesian vector autoregressions (VARs). Because set identification can be challenging, we propose to include micro data on heterogeneous entities to sharpen inference. First, we provide conditions when imposing a simple ranking of impulse-responses sharpens inference in bivariate and trivariate VARs. Importantly, we show that this set reduction also applies to variables not subject to ranking restrictions. Second, we develop two types of inference to address recent criticism: (1) an efficient fully Bayesian algorithm based on an agnostic prior that directly samples from the admissible set and (2) a prior-robust Bayesian algorithm to sample the posterior bounds of the identified set. Third, we apply our methodology to U.S. data to identify productivity news and defense spending shocks. We find that under both algorithms, the bounds of the identified sets shrink substantially under heterogeneity restrictions relative to standard sign restrictions.

A narrative approach to a fiscal DSGE model

“…The DSGE‐SVAR estimate is consistent with other estimates of multipliers that use variation in defense spending: Ramey (, p. 31) estimates a 5‐year cumulative multiplier of 1.2. Amir‐Ahmadi and Drautzburg (, Figure 4.13) identified an interval of 1.0 to 3.0 consistent with macro sign restrictions and industry‐level heterogeneity restrictions at the 5‐year horizon.…”

A Framework for Eliciting, Incorporating, and Disciplining Identification Beliefs in Linear Models

“…This paper contributes to a small but growing literature on the Bayesian analysis of partially-identified models, including Poirier (1998), Gustafson (2005), Richardson et al (2011), Moon and Schorfheide (2012), Kitagawa (2012), Hahn et al (2016), Kline and Tamer (2016), and Gustafson (2015). Some recent contributions to the literature on structural vector autoregression models (Amir-Ahmadi and Drautzburg, 2016;Arias et al, 2016;Baumeister and Hamilton, 2015) also explore related ideas. Our results also relate to a large literature on estimating the effect of mis-measured binary regressors.…”

SVARs Identification Through Bounds on the Forecast Error Variance

“…The previous section showed that bounds on the FEVD reduce the identified set for small-scale models. However, there is a well-known trade-off between sharp identification and computation (Uhlig, 2017;Amir-Ahmadi and Drautzburg, 2018;Giacomini and Kitagawa, 2018;Gafarov, Meier, and Olea, 2018). In fact, tight restrictions can potentially lead to sets with zero measure, or empty sets; thus, it is crucial to distinguish when the identification is sharp because the identified set has a reduced but positive measure, and when constraints are too tight and lead to empty sets.…”

“…Remarkably, nondogmatic bounds on the FEVD identify structural parameters more successfully than sign restrictions and deliver very informative results. The paper shows the approach here is also more effective than alternative strategies of set-reduction, including standard equality restrictions on the FEVD, narrative sign restrictions (Antolín-Díaz and Rubio-Ramírez, 2018;Ludvigson, Ma, andNg, 2018, 2019), constraints on the monetary policy equation (Arias, Caldara, and Rubio-Ramirez, 2019) and the ranking of IRFs (Amir-Ahmadi and Drautzburg, 2018).…”

“…Sign restrictions usually deliver a set of structural parameters with very different implications for IRFs, elasticities, historical decomposition (HD) and forecast error variance decomposition (FEVD). On the one hand, this makes obtaining precise estimation, informative inference and meaningful economic results challenging (Uhlig, 2005;Paustian, 2007;Mountford, 2005;Rafiq and Mallick, 2008;Arias, Caldara, and Rubio-Ramirez, 2019;Antolín-Díaz and Rubio-Ramírez, 2018;Amir-Ahmadi and Drautzburg, 2018). On the other hand, some of the admissible structural models can contain implausible implications, which is even worse.…”