Dynamics of Entrepreneurship Under Incomplete Markets
45 Pages Posted: 24 Feb 2011 Last revised: 9 Nov 2011
Date Written: November 3, 2011
An entrepreneur faces non-diversifiable business risk and liquidity constraints. We provide a unified framework that embeds these frictions to study interdependent business start-up/entry, capital accumulation/asset sales, portfolio allocation, consumption/saving, and business exit decisions. Liquid wealth mitigates financial constraints and critically influences the entrepreneur's decision making. An entrepreneur invests less in business, consumes less, and allocates less to the market portfolio in order to preserve liquidity for precautionary purposes. We develop the counterpart of the q theory of investment for firms run by non-diversified entrepreneurs, and propose corresponding measures for average q and marginal q. Corporate investment depends on both marginal q and the marginal value of wealth. The wedge between average q and marginal q is non-monotonic in liquidity. With illiquid capital stock, the endogenous liquidation option provides significant flexibility for the entrepreneur to manage downside risk, causes firm value to be convex in liquidity and investment to decrease in liquidity near the endogenous exit boundary. The flexibility to accumulate wealth before entering entrepreneurship is highly valuable, and the wealth effect is significant for entrepreneurship. The optimal entry decision critically depends on the outside option, the start-up cost, risk aversion, and wealth. Heterogeneity among entrepreneurs is thus important. Our model yields an operational framework to calculate the private equity idiosyncratic risk premium. Quantitatively, the interactive effects of incomplete-markets frictions and capital illiquidity on investment and value are significant.
Keywords: idiosyncratic risk premium, hedging, liquidity constraints, precautionary saving, portfolio choice, investment, entry, exit, the q theory of investment, real options
JEL Classification: G11, G31, E2
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