Modern tools for macroeconomic policy evaluation and causal inference often use sufficient statistics which are nonlinear functions of impulse responses. When impulse responses are only set-identified, these statistics are themselves ambiguous. I highlight the trade-off between desirable priors for impulse responses and the implied priors for these sufficient statistics. By expressing each statistic as a function of the VAR’s orthogonal reduced-form parameters, I (i) can correct the implied prior within standard algorithms (ii) show that a Robust Bayes procedure can be applied, which correctly reports the ambiguity, and (iii) impose economically motivated restrictions on the statistic via restrictions on those parameters. This combination tightens identified sets and sharpens conclusions about dynamic causal effects.

Presented at:  Econometric Society European Winter Meeting  (December 2025), Macro Lunch Università Cattolica (September 2025), Sailing the Macro (Sicily, September 2025, regular session), Junior Milan Time Series Workshop (March 2025, poster), PRIN Workshop (June 2025, Poster) , Örebro Workshop on Macro- and Financial Econometrics  (November 2025)

Researchers often confront regressions where key covariates are missing or only interval-observed. Common fixes, e.g imputation or auxiliary modeling assumptions, resolve ambiguity at the expense of credibility. Instead, we derive the sharp identified set, the smallest parameter set consistent with both the data and the maintained regression model. A computationally tractable (Hausdorff consistent) estimator for this set is provided with associated asymptotic (uniformly) valid confidence regions for the true parameter. Technically, this is achieved by extending a previous random set framework for finitely many moments to infinite-dimensional Polish (separable and complete) spaces.

Power priors modify the historical likelihood by raising it to the power of a discount factor, allowing researchers to downweight past or external data. This generalizes the standard Bayesian updating formula and provides a flexible framework for incorporating external information into macroeconomic models. We extend the theoretical foundations of power priors to vector autoregressions (VARs) and show that they are equivalent to simple hierarchical structures—while preserving conjugacy and compatibility with modern structural identification methods. Applications include cross-country borrowing to improve forecast accuracy, sharper estimation of long-run Phillips curves, and a novel sensitivity analysis tool based on observation-specific discounting.

Presented at: IAAE 2025 Turin (June 2025)

This paper shows the merit of one-sided conformal prediction methods for quantile forecasting. Our approach converts point forecasts of any kind of model into quantile predictions. Through simulations and an application in nowcasting US GDP tail risk using numerous high-frequency regressors, we demonstrate that conformal quantile forecasts are accurately calibrated for high dimensional problems, unlike bootstrap quantiles. Additionally, our algorithm produces comparable results to a leading nowcasting approach in a fraction of its computing time. In a second application we use our proposal to forecast percentiles of a distribution as quantile crossing is ruled out by construction.

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Presented at: 3rd International Econometrics PhD Conference (November 2023), VTSS Virtual Workshop for Junior Researchers in Time Series (March 2024)