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Working Paper
Local Projections
A central question in applied research is to estimate the effect of an exogenous intervention or shock on an outcome. The intervention can affect the outcome and controls on impact and over time. Moreover, there can be subsequent feedback between outcomes, controls and the intervention. Many of these interactions can be untangled using local projections. This method’s simplicity makes it a convenient and versatile tool in the empiricist’s kit, one that is generalizable to complex settings. This article reviews the state-of-the art for the practitioner, discusses best practices and ...
Working Paper
Impulse Response Diagnostics for Priors on Parameters in Structural Vector Autoregressions
Structural impulse response functions may be estimated based on priors about the parameters of the structural VAR presentation. Even when such priors appear seemingly reasonable, they may imply an unintentionally informative prior for the structural impulse responses. Rather than pretending that the posterior of the impulse responses does not depend on this prior, the proposal in this paper is to verify that the prior distribution of the vector of impulse responses of interest is not unintentionally informative. Moreover, if the impulse response prior is intentionally informative, this point ...
Working Paper
The Conventional Impulse Response Prior in VAR Models with Sign Restrictions
Some studies have expressed concern that the Gaussian-inverse Wishart-Haar prior typically employed in estimating sign-identified VAR models may be unintentionally informative about the implied prior for the structural impulse responses. We discuss how this prior may be reported and make explicit what impulse response priors a number of recently published studies specified, allowing the readers to decide whether they are comfortable with this prior. We discuss what features to look for in this prior in the absence of specific prior information about the responses, building on the notion of ...
Working Paper
State-Dependent Local Projections
Do state-dependent local projections asymptotically recover the population responses of macroeconomic aggregates to structural shocks? The answer to this question depends on how the state of the economy is determined and on the magnitude of the shocks. When the state is exogenous, the local projection estimator recovers the population response regardless of the shock size. When the state depends on macroeconomic shocks, as is common in empirical work, local projections only recover the conditional response to an infinitesimal shock, but not the responses to larger shocks of interest in many ...
Working Paper
Nonparametric Local Projections
Nonlinearities play an increasingly important role in applied work when studying the responses of macroeconomic aggregates to policy shocks. Seemingly natural adaptations of the popular local linear projection estimator to nonlinear settings may fail to recover the population responses of interest. In this paper we study the properties of an alternative nonparametric local projection estimator of the conditional and unconditional responses of an outcome variable to an observed identified shock. We discuss alternative ways of implementing this estimator and how to allow for data-dependent ...
Working Paper
When Is the Use of Gaussian-inverse Wishart-Haar Priors Appropriate?
Several recent studies have expressed concern that the Haar prior typically employed in estimating sign-identified VAR models is driving the prior about the structural impulse responses and hence their posterior. In this paper, we provide evidence that the quantitative importance of the Haar prior for posterior inference has been overstated. How sensitive posterior inference is to the Haar prior depends on the width of the identified set of a given impulse response. We demonstrate that this width depends not only on how much the identified set is narrowed by the identifying restrictions ...