Optimal Capital - Labor Taxes under Uncertainty and Default Constraints of the Government

This paper describes the behavior of tax policies under incomplete financial markets. The government finances a stochastic stream of expenditures by collecting the capital income and the labor income taxes, and issuing a one-period bond which pays state-contingent returns. We show that putting limits on the amount of the bond that can be chosen each period helps improve the predictions for volatility and autocorrelations of both capital income and labor income taxes. The welfare loss due to market incompleteness is small and comes only because of reducing the initial high taxation of capital income. Even for the utility specifications for which the Chamley-Judd result of zero long-run capital income taxation holds, the model generates a path of ex ante expected capital income taxes that may have zero, positive, or negative mean. The reason is that any binding limit on the amount of debt or savings the Ramsey planner wants to accumulate has a permanent effect on the whole future sequence of tax rates. Chari, Christiano and Kehoe (1994) were the first in describing how capital and labor income taxes should behave over the business cycle. However, their results rely heavily on a huge initial capital levy which allows the government to accumulate rapidly enough savings to insure against future shocks to the budget. As a consequence, in the long-run the capital income taxation is abolished and each period the consumers get indebted by the amount close to the periodÌs GDP. Along with recent evidence in favor of incomplete rather than complete credit markets facing the government (Marcet and Scott, 2001), consumerÌs willingness to default on debt serves as a motivation to put some restriction on plannerÌs savings. An upper limit on government debt, unless it is very tight, is there mainly for smoothing the transition behavior of the economy, since we know that in the complete markets case, the planner issues debt only in the initial period and switches to savings from the next one onwards. It turns out that putting debt limits as a simple way of introducing incomplete markets has little effect on the long run allocations, while the influence for the tax policies of either transitionally or permanently binding limits on borrowing and saving is very sound. Even loose and only occasionally binding limits on debt are enough to alleviate the initial capital levy and decrease the long-run savings of the planner. Transitionally binding limits lead to the expected capital income taxes that may differ from zero even in the long-run and even for the periods when the limits do not bind. Tight limits on both debt and savings of the planner completely eliminate the initial capital levy and change the transitional behavior of labor taxes. We derive an analytical expression for labor tax rates for a class of utilities separable in consumption and leisure and show that they should have a higher variance compared to the complete markets case. The lower limit binding should lead to a cut in labor income taxes, while the trying to issue more debt than its upper limit should imply an increase in the labor income taxes. As for the expected capital income taxes, simulation results show that whenever the lower limit binds, the consumer should expect a capital income subsidy while binding lower limit leads to a positive expected capital income tax for the next period. The main reason lies in the incomplete insurance against the future uncertainty. In the economy what matters is the sum of both available assets, bonds and capital. Therefore, subsidizing capital stimulates more capital accumulation as a substitute for buying bonds. The basic intuition for such an important role of debt limits for tax policies is that the state-contingent debt which served as a shock absorber is now limited. So, the planned sequence of current and future taxes has to be adjusted each period. Thus, if ever in the past the planner has been short of debt or savings, todayÌs taxes should partly compensate for that. We solve this model numerically using short-run simulations inside the Parameterized Expectations Algorithm by Marcet and then describe the modelÌs simulation properties. There are several computational issues: the initial Ramsey problem is not recursive, so we have to enlarge the state space using the recursive contracts approach by Marcet and Marimon. Also the transitional behavior of allocations and taxes is very different from their long-run characteristics. Thus, to approximate well the policy function during the transition, we choose to run many short Monte Carlo simulations. Finally, to solve this model, we have to iterate on a key Lagrange multiplier representing the cost of distortionary taxation.