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# Thomas Philippon

This discussion focuses on one of the theoretical questions raised by the paper: are credit-constrained firms more sensitive to taxes on retained earnings than unconstrained firms? To assess this issue, I consider a two-period model. Capital, k, is invested in the first period and delivers profits, f( k), in the second period. The firm receives an income of yin the first period. The manager of the firm decides how much to invest, k, how much to borrow, b, and how much income to distribute to current investors, d. To capture credit constraints, I assume that the cost of borrowing is increasing in the amount borrowed, according to a function c( b). Finally, retained earnings are taxed at rate τ. The firm’s program is therefore

subject to the resource constraint, k= b+ (1 + τ) ( yd), and the constraint on distributions to current investors, 0 ≤ dy. I consider several cases.

The case of no credit constraint is defined as c( b) = b. The solution is d= y, b= k, and f′ ( k) = 1 + r. The firm obtains a perfect tax arbitrage with a leverage of 100 percent. Investment is unaffected by taxes on retained earnings.

For the case of no borrowing, suppose that bis forced to be zero. This prevents the tax arbitrage. Provided that the marginal product is high enough relative to current income, the firm will choose d= 0 and k= (1 − τ) y. In this case, taxes on retained earnings decrease investment. Comparing this result with the previous benchmark suggests that constrained firms should indeed be more tax-sensitive than unconstrained firms. This, however, need not be true.

The case of fake borrowing, in which b= 0, hides two separate issues: the presence of credit constraints and the absence of the tax arbitrage. However, it is possible to obtain the tax arbitrage even with no real borrowing. Suppose that a bank is a current investor in the firm. The firm pays d= yto the bank, [End Page 41]and the bank makes a loan b= yto the firm. This allows the firm to pay no taxes, while the bank has no real exposure to the firm. In this equilibrium, k= y. Credit constraints are completely binding, but investment does not respond to taxes on retained earnings.

Based on the above discussion, it seems to me that the correct benchmark is a model in which all firms are somewhat constrained, but some are more constrained than others. This model has two types of solutions: the interior solution and the corner solution. In the interior solution, where d> 0, the first-order conditions are

and

provided that d> 0. These conditions imply that

Investment does not depend on the function c(.), despite the fact that the credit constraint is binding. This is because the firm can adjust its current distributions, and the distribution margin insulates investment at the margin.

In the corner solution, with d= 0,

For firms that do not pay dividends, investment is sensitive to credit constraints at the margin.

The typical classification of firms into groups that are likely to be constrained and groups that are unlikely to be constrained is usually based on current income or on distributions. Suppose then that there are firms with high income, y H, and firms with low income, y L. High-income firms are in the interior solution, with positive dividends, while low-income firms are in the corner solution. Based on equations 1and 2, it is not obvious that the elasticity of investment to taxes is higher for the more constrained groups. It depends on the function, c(.). The answer to the initial question, therefore, is that while it is plausible [End Page 42]that more constrained firms react more to changes in taxes on retained earnings than less constrained ones, this is not necessarily the case.

In 1982 Chile experienced its largest recession since the Great Depression. Real GDP declined by about 15 percent between 1981 and 1983, while unemployment increased from 10 to around 20 percent, and investment plummeted from 23 to 10 percent of GDP. Despite the magnitude... 