We estimate a general equilibrium model with firm heterogeneity and a representative household with Epstein-Zin preferences. Firms face investment frictions and permanent shocks, which feature time-variation in common idiosyncratic skewness. Quantitatively, the model replicates well the cyclical dynamics of the cross-sectional output growth and investment rate distributions. Economically, the model generates business cycles through inefficiencies in the allocation of capital across firms. These cycles arise because (i) permanent Gaussian shocks give rise to a power law distribution in firm size and (ii) rare negative Poisson shocks cause time-variation in common idiosyncratic skewness. Despite the absence of firm-level granularity, a power law in the firm size distribution implies that idiosyncratic Poisson shocks have a large effect on the dynamics of aggregate consumption and wealth. In addition, shocks to aggregate wealth spill over to all firms in the economy because of Epstein-Zin preferences.