Optimal Capital Income Taxation with Incomplete Markets, Borrowing Constraints, and Constant Discounting

Chamley (1986) showed, for a wide class of representative-agent dynamic models, that the optimal capital income tax rate is zero in the long run, and Lucas (1990) used this result to argue the U.S. economy could gain the equivalent of several percent of consumption by cutting its capital income tax to zero. This paper shows the opposite conclusion holds once markets are incomplete in the specific sense studied by Bewley (1986): a continuum of infinitely lived agents facing uninsured, idiosyncratic shocks to their productivity, unable to borrow against future income, who can divide their time between taxable market work and untaxable home production. Because these agents cannot insure against bad luck, they hold assets partly as a precautionary buffer, and their collective asset demand rises without bound as the after-tax return on assets approaches the rate of time preference – a force strong enough that, absent any tax on capital, the economy’s capital stock permanently exceeds the modified-golden-rule level implied by efficient allocation. The paper proves that the solution to the government’s dynamic Ramsey optimal-tax problem requires the economy’s pre-tax return to converge to the rate of time preference (as in the standard modified golden rule) while its after-tax return converges to something strictly lower – which is only possible with a permanently positive capital income tax rate – and shows this result nests Chamley’s zero-tax conclusion exactly as the special case with no idiosyncratic risk. A calibrated quantitative version of the model, varying risk aversion, the persistence and variability of earnings shocks, and the labor supply elasticity, finds that plausible parameterizations can generate long-run optimal capital income tax rates ranging from near zero up to and above the roughly 35-40% rates estimated for the U.S. economy, so that, in the authors’ words, “one cannot easily dismiss the possibility that the observed tax rates on capital and labor income for the U.S. economy are fairly close to being (long run) optimal.”

Uninsured Idiosyncratic Risk and Aggregate Saving

This paper builds a version of the Brock-Mirman [1972] neoclassical growth model modified so that a continuum of infinitely-lived agents face uninsured idiosyncratic labor-endowment shocks and a borrowing constraint, rather than complete insurance markets, and analyzes the resulting stochastic general equilibrium. With incomplete markets, each agent optimally accumulates or decumulates assets to smooth consumption against uninsurable earnings risk while avoiding the borrowing limit; aggregating optimal individual behavior across the population’s endogenous cross-section distribution of asset holdings determines a stationary equilibrium in which per capita capital demanded by firms equals per capita assets supplied by households. Because a positive probability of a long run of bad earnings draws makes consumers unwilling to let their asset holdings approach the borrowing limit indefinitely, the equilibrium interest rate is necessarily below the rate of time preference, and the aggregate capital stock and saving rate are necessarily higher than in the corresponding full-insurance (representative-agent) economy – a conclusion that, in this infinite-horizon, general-equilibrium setting, holds regardless of whether marginal utility is convex. Calibrating the model to postwar U.S. growth and business-cycle parameters and to empirically estimated earnings-risk processes, Aiyagari finds that the quantitative contribution of uninsured idiosyncratic risk to the aggregate saving rate is modest – no more than about three percentage points – for moderate, empirically plausible values of risk aversion, earnings variability, and earnings persistence, though the saving rate can rise by seven to fourteen percentage points under substantially higher variability and persistence than the data suggest. The model also implies that individuals achieve significant consumption smoothing and welfare gains (on the order of 14 percent of per capita consumption in one example) by trading in asset markets rather than simply consuming their income each period, and it qualitatively reproduces several features of observed income and wealth distributions – positive skewness, and much greater dispersion in wealth than in income – although it falls well short of the degree of wealth inequality found in U.S. data.

S. Rao Aiyagari | Macro Paper Warehouse

Optimal Capital Income Taxation with Incomplete Markets, Borrowing Constraints, and Constant Discounting

Uninsured Idiosyncratic Risk and Aggregate Saving