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Are optimism shocks an important source of business cycle fluctuations? Are deficit-financed tax cuts better than deficit-financed spending to increase output? These questions have been previously studied using structural vector autoregressions (SVAR) identified with sign and zero restrictions and the answers have been positive and definite in both cases. Although the identification of SVARs with sign and zero restrictions is theoretically attractive because it allows the researcher to remain agnostic with respect to the responses of the key variables of interest, we show that current implementation of these techniques does not respect the agnosticism of the theory. These algorithms impose additional sign restrictions on variables that are seemingly unrestricted that bias the results and produce misleading confidence intervals. We provide an alternative and efficient algorithm that does not introduce any additional sign restriction, hence preserving the agnosticism of the theory. Without the additional restrictions, it is hard to support the claim that either optimism shocks are an important source of business cycle fluctuations or deficit-financed tax cuts work best at improving output. Our algorithm is not only correct but also faster than current ones.

We present a general framework for Bayesian estimation and causality assessment in epidemiological models. The key to our approach is the use of sequential Monte Carlo methods to evaluate the likelihood of a generic epidemiological model. Once we have the likelihood, we specify priors and rely on a Markov chain Monte Carlo to sample from the posterior distribution. We show how to use the posterior simulation outputs as inputs for exercises in causality assessment. We apply our approach to Belgian data for the COVID-19 epidemic during 2020. Our estimated time-varying-parameters SIRD model captures the data dynamics very well, including the three waves of infections. We use the estimated (true) number of new cases and the time-varying effective reproduction number from the epidemiological model as information for structural vector autoregressions and local projections. We document how additional government-mandated mobility curtailments would have reduced deaths at zero cost or a very small cost in terms of output.