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We thank the many people who have given us advice, including David Bates, Michael Brandt, Rodrigo Guimaraes, Sydney Ludvigson, Monika Piazzesi, Thomas Sargent, Romeo Tedongap, Michael Woodford, and Liuren Wu, as well as participants in seminars at, and conferences sponsored by, the AEA, the Bank of England, Bocconi, CEPR (Gerzensee meetings), the Federal Reserve, Glasgow, Harvard, IDEI/SCOR (conference on extremal events), LBS, Leicester, LSE, Minnesota, MIT, Moscow HSE, NBER (summer institute), NYU, Penn, Princeton, RCEA Rimini (workshop on money and finance), SoFiE (conference on extreme events), SIFR, Toulouse (conference on financial econometrics), and UC Davis. 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