Delta-method inference for a class of set-identified SVARs

Abstract

We study vector autoregressions that impose equality and/or inequality restrictions to set-identify the dynamic responses to a single structural shock. We make three contributions. First, we present an algorithm to compute the largest and smallest value that an impulse-response coefficient can attain over its identified set. Second, we provide conditions under which these largest and smallest values are directionally differentiable functions of the model’s reduced-form parameters. Third, we propose a delta-method approach to conduct inference about the structural impulse-response coefficients. We use our results to assess the effects of the announcement of the Quantitative Easing program in August 2010.