The U-shaped Investment Curve: Theory and Evidence

This paper examines how the investment of financially constrained firms varies with their level of internal funds. We develop a theoretical model of optimal investment under financial constraints. Our model endogenizes the costs of external funds and allows for negative levels of internal funds. We show that the resulting relationship between internal funds and investment is U-shaped. In particular, when a firm's internal funds are negative and sufficiently low, a further decrease leads to an increase in investment. This effect is driven by the investor's participation constraint: when part of any loan must be used to close a financing gap, the investor will provide funds only if the firm invests at a scale large enough to generate the revenue that enables the firm to repay. We test our theory using a data set with close to 100,000 firm-year observations. The data strongly support our predictions. Among other results, we find a negative relationship between measures of internal funds and investment for a substantial share of financially constrained firms. Our results also help to explain some contrasting findings in the empirical investment literature.