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Working Paper
The Role of the Prior in Estimating VAR Models with Sign Restrictions
Several recent studies have expressed concern that the Haar prior typically imposed in estimating sign-identified VAR models may be unintentionally informative about the implied prior for the structural impulse responses. This question is indeed important, but we show that the tools that have been used in the literature to illustrate this potential problem are invalid. Specifically, we show that it does not make sense from a Bayesian point of view to characterize the impulse response prior based on the distribution of the impulse responses conditional on the maximum likelihood estimator of ...
Working Paper
The Anatomy of Out-of-Sample Forecasting Accuracy
We introduce the performance-based Shapley value (PBSV) to measure the contributions of individual predictors to the out-of-sample loss for time-series forecasting models. Our new metric allows a researcher to anatomize out-of-sample forecasting accuracy, thereby providing valuable information for interpreting time-series forecasting models. The PBSV is model agnostic—so it can be applied to any forecasting model, including "black box" models in machine learning, and it can be used for any loss function. We also develop the TS-Shapley-VI, a version of the conventional Shapley value that ...
Working Paper
Asymmetry, Complementarities, and State Dependence in Federal Reserve Forecasts
Forecasts are a central component of policy making; the Federal Reserve''s forecasts are published in a document called the Greenbook. Previous studies of the Greenbook''s inflation forecasts have found them to be rationalizable but asymmetric if considering particular sub-periods, e.g., before and after the Volcker appointment. In these papers, forecasts are analyzed in isolation, assuming policymakers value them independently. We analyze the Greenbook fore- casts in a framework in which the forecast errors are allowed to interact. We find that allowing the losses to interact makes the ...
Working Paper
The Anatomy of Out-of-Sample Forecasting Accuracy
We develop metrics based on Shapley values for interpreting time-series forecasting models, including“black-box” models from machine learning. Our metrics are model agnostic, so that they are applicable to any model (linear or nonlinear, parametric or nonparametric). Two of the metrics, iShapley-VI and oShapley-VI, measure the importance of individual predictors in fitted models for explaining the in-sample and out-of-sample predicted target values, respectively. The third metric is the performance-based Shapley value (PBSV), our main methodological contribution. PBSV measures the ...
Working Paper
Joint Bayesian Inference about Impulse Responses in VAR Models
Structural VAR models are routinely estimated by Bayesian methods. Several recent studies have voiced concerns about the common use of posterior median (or mean) response functions in applied VAR analysis. In this paper, we show that these response functions can be misleading because in empirically relevant settings there need not exist a posterior draw for the impulse response function that matches the posterior median or mean response function, even as the number of posterior draws approaches infinity. As a result, the use of these summary statistics may distort the shape of the impulse ...