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

According to recent macroeconomic studies, microeconomic shocks can generate aggregate fluctuations (the granular hypothesis). I test this idea by studying the variance and tail probability of aggregate output induced by microeconomic shocks. I show that both of these are determined by the size of the largest firm: The slow decay of the aggregate variance found by Gabaix (2011) is caused by the asymptotic behavior of the size of the largest firm. The tail probability of aggregate output is essentially equivalent to the probability of a large shock hitting the largest firm. I then apply these results to firm-level data in Japan. I find that microeconomic shocks would generate only small fluctuations, and not a large deviation, in aggregate output. Thus, the empirical granularity in Japan (i.e., the size of the largest firm) is not large enough to cause substantial aggregate fluctuations.