NBER WORKING PAPER SERIES CAPITAL SHARE DYNAMICS WHEN FIRMS INSURE WORKERS

Although the aggregate capital share for U.S. firms has increased, the firm-level capital share has decreased on average. The divergence is due to the largest firms. While these mega-firms now produce a larger output share, their labor compensation has not increased proportionately. We develop a model in which firms insure workers against firm-specific shocks. More productive firms allocate more rents to shareholders, while less productive firms endogenously exit. Increasing firm-level risk delays the exit of less productive firms and increases the measure of mega-firms, raising the aggregate capital share and lowering it on average. We present evidence supporting this mechanism. Barney Hartman-Glaser University of California at Los Angeles 110 Westwood Plaza Suite C421 Los Angeles, CA 90095 barney.hartman-glaser@anderson.ucla. edu Hanno Lustig Stanford Graduate School of Business 655 Knight Way Stanford, CA 94305 and NBER hlustig@stanford.edu Mindy X. Zhang University of Texas at Austin 2110 Speedway B6600 Austin, TX 78703 xiaolan.zhang@mccombs.utexas. edu Over the last decades, publicly traded U.S. firms have experienced a large increase in firm-specific volatility of both firm-level cash flow as well as returns (see, e.g., Campbell, Lettau, Malkiel, and Xu, 2001; Comin and Philippon, 2005; Zhang, 2015; Bloom, 2014; Herskovic, Kelly, Lustig, and Van Nieuwerburgh, 2015). At the same time, the share of total value added that accrues to the owners of these firms (i.e., the aggregate capital share) has also increased (see Karabarbounis and Neiman, 2014; Piketty and Zucman, 2014). We find that the aggregate factor shares are largely determined by the firm-level factor shares of the largest U.S. firms in the right tail of the size distribution. These mega-firms have experienced substantial increases in their capital share, even though the capital share at the average U.S. firm has decreased. The aggregate factor share dynamics in the U.S. economy are well understood, but the firm-level factor share dynamics are not. Between 1960 and 2010, the U.S. labor share of total output in the non-farm business sector of the U.S. economy has shrunk by 15%. This phenomenon does not appear to be limited to the U.S. (see, e.g., Piketty and Zucman, 2014). In the universe of U.S. publicly traded firms, we find that the capital share, measured as total operating income divided by total value added (plotted in Figure I), has increased from 40% to 60% since 1980, while the labor share has experienced a similar decline. Our key empirical contribution is to show that the increase in the capital share is concentrated among the largest, publicly traded firms in the U.S. Figure II shows the relationship between firm size and the ratio of capital income to sales (which is a measure of the capital share of profits). In 1970, there was essentially no relation between firm size and capital income to sales ratio. By 2010, this ratio was strongly increasing in size. This shift caused the average and aggregate capital share to diverge: The equal-weighted average capital share of publicly traded companies has declined since the 1980s. We develop an equilibrium model that links these observations regarding volatility and factor share provides novel implications for national income accounting. Our model demonstrates that when shareholders insure workers against idiosyncratic risk, capital shares vary substantially over the size distribution of firms, with the largest and most productive firms having the highest capital share. We show that these compositional changes in firm-level capital shares have first-order implications for the aggregate capital share. Shareholders of publicly traded firms can diversify away idiosyncratic firm-specific risk, while risk-averse workers cannot; therefore, it is efficient to provide workers with insurance against firm-specific risk. We analyze a simple compensation contract in an equilibrium model of industry dynamics (see, e.g., Hopenhayn, 1992). This contract pays workers a fixed wage while allocating the remainder of the profits to shareholders. The level of compensation is set in equilibrium to capture the value of ex ante identical firms, as in Atkeson and Kehoe