Optimal state-contingent capital taxation: when is there an indeterminacy?
Several recent papers on dynamically optimal taxation have derived an indeterminacy result regarding state-contingent capital taxation in stochastic models with state-contingent government liabilities. The indeterminacy arises because the government has N degrees of freedom to set tax rates on capital income in N states of nature, only subject to a single constraint that assures an optimal level of capital investment. The paper shows that this indeterminacy result is a consequence of the assumption that the economy has only a single production technology. If there are many technologies, there will be additional constraints, because differences in capital income tax rates in different states of nature will create incentives to invest in those technologies that have high payoffs in states with relatively low tax rates. If there are a large number of technologies, both the structure of capital tax rates and the structure of government debt are tied down in many dimensions.
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