The Role of Granularity in the Variance and Tail Probability of Aggregate Output

Recent macroeconomic studies show that microeconomic shocks can be another source of aggregate fluctuations (the granular hypothesis). To test this idea, I study the micro-originated variance and tail probability of aggregate output implied by models in the literature (Acemoglu et al. (2012); Baqaee and Farhi (2019)). By giving the asymptotic behavior of the variance and the upper bound of the tail probability, I show that the micro-originated aggregate fluctuations are determined by the size of the largest firm. By using this result and firm-level data in Japan, I quantify the micro-originated variance and tail probability of aggregate output. I find that given the empirical heterogeneity of firm size in Japan, microeconomic shocks generate only small fluctuations of aggregate output (measured by the variance) but not a large deviation of aggregate output (measured by the tail probability).