Optimal allocation of relief funds: the case of the paycheck protection program

The Paycheck Protection Program (PPP) was a large and unprecedented small-business support program that allocated $800 billion in loans and grants to small businesses following the onset of the COVID-19 crisis. This paper explores the optimal allocation of funds across firms and the distortions caused by allocating these funds through banks. We show that it can be optimal to allocate funds to the least or most affected firms depending on the underlying distribution of the shock that firms face, the firms' financial position, and the total budget available for the program. In the model, as in the data, banks distort the allocation toward firms with more pre-pandemic debt and those less affected by the COVID-19 crisis. We characterize how this misallocation depends on the degree of asymmetric information between banks and the government. In an empirical application of our model, we estimate the PPP's effectiveness and compare it with alternative policies. A policy targeted at the smallest firms could have increased the program's effectiveness significantly.