“The Granular Origins of Aggregate Fluctuations”: Supplementary Material

git = agIit + b ( lnSi,t−1 − lnSj,t−1;,j∈Ii ) gIit + c ( lnSi,t−1 − lnSj,t−1;,j∈Ii )2 gIit + εit (36) In this model, the loading of firm i can depend not only on the industry average gIit, but also on the size of the firm. To make coeffi cients easier to interpret, I recenter by lnSj,t−1, the average log size, so that the mean of the second term is 0. Table VI reports the first stage of a variety of specifications (with K = Q = 100). Size controls are only sometimes significant, but their incremental explanatory power is very small compared to the earlier specification that simply controls for gt and gIit. The second stage is reported in Table VII. The impact of the size control is very small. Hence, for practical purposes, one may recommend the two simplest versions of the granular residual, (33) and (34). Still, one lesson from Table VI is that large firms have if anything a smaller loading on the common shocks than small firms (column 5). Hence, constructing the granular residual by removing a constant mean slightly overcorrects large firms, and, prima facie, works against finding a high explanatory power of the granular residual. This bias against the granular residual is, however, small, as Table VII shows. Tables VIII and IX show some more regressions. In particular, I use K = 100 and Q = 1000. This is, it evaluates the “expected”behavior of the top 100 firms by examining the behavior of the top 1000 firms. Note that a diffi culty is that in the early part of the sample there are less than 1000 firms; then I take the maximum number of firms. The results are similar to Tables VI and VII, except that the R2 of the first stage (explaining firm-level growth rate) and the second stage (explain GDP growth) are a bit lower. That may be