Introducing the granular hypothesis, Gabaix (2011) shows that the idiosyncratic shocks of a few "granular" firms account for a significant fraction of aggregate fluctuations of the US business cycle. In the literature, however, the question of how many are the granular firms in an economy is left unanswered. Using Spanish data, we propose a novel methodology to calibrate the granular size of the economy, i.e. the number of granular firms.
We analyse the time evolution of the empirical cross-sectional distribution of firms’ profit and growth rates. In particular, we analyse the conditional properties of the empirical distributions depending on the size of the firms and the business cycle phase. In order to do so, we employ the Laplace distribution as a benchmark, further considering the Subbotin and Asymmetric Exponential Power (AEP hereafter) distributions, to capture the potential asymmetry and leptokurtosis of the empirical distribution. Our results show that the profit rates of large firms are characterised by an asymmetric Laplace distribution with parameters largely independent of the business cycle phase. Small firms, instead, are characterised by the AEP distribution, which accounts for the conditional dependence of distribution on the phase of the business cycle. We observe that the largest firms are more robust to downturns compared to the small firms, given their invariant distributional characteristics during crisis periods.
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