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We develop a flexible framework for Bayesian estimation of impulse responses using Local Projections (LPs) with instrumental variables. It accommodates multiple shocks and instruments, accounts for autocorrelation in multi-step forecasts by jointly modeling all LPs as a seemingly unrelated system of equations, defines a flexible yet parsimonious joint prior for impulse responses based on a Gaussian Process, and allows for joint inference about the entire vector of impulse responses. We show via Monte Carlo simulations that our approach delivers more accurate point and uncertainty estimates than standard methods. To address misspecification, we propose an optional robustification step based on power posteriors.