We provide new evidence that large firms or establishments are more sensitive than small ones to business cycle conditions. Larger employers shed proportionally more jobs in recessions and create more of their new jobs late in expansions, both in gross and net terms. The differential growth rate of employment between large and small firms varies by about 5% over the business cycle. Omitting cyclical indicators may lead to conclude that, on average, these cyclical effects wash out and size does not predict subsequent growth (Gibrat's law). We employ a variety of measures of relative employment growth, employer size and classification by size. We revisit two statistical fallacies, the Regression and Reclassification biases, that can affect our results, and we show empirically that they are quantitatively modest given our focus on relative cyclical behavior. We exploit a variety of (mostly novel) U.S. datasets, both repeated cross-sections and job flows with employer longitudinal information, starting in the mid 1970's and now spanning four business cycles. The pattern that we uncover is robust to different treatments of entry and exit of firms and establishments, and occurs within, not across broad industries, regions and states. Evidence on worker flows suggests that the pattern is driven at least in part by excess layoffs by large employers in and just after recessions, and by excess poaching by large employers late in expansions. We find the same pattern in similar datasets in four other countries, including full longitudinal censuses of employers from Denmark and Brazil. Finally, we sketch a simple firm-ladder model of turnover that can shed light on these facts, and that we analyze in detail in companion papers.