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Heterogeneous firm models are ubiquitous in modern macroeconomics. We revisit a central feature of these models: the idiosyncratic shock process faced by firms. Using a large representative firm-level dataset, we document nonparametrically that the common assumption, a Gaussian AR(1) shock process, is at odds in important ways with observed fat-tailed firm dynamics. We embed these findings within a standard quantitative general equilibrium heterogeneous firm dynamics model and show that the nature of firm-level shocks has a sizable quantitative effect on the economy's responsiveness to aggregate shifts