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The Chamley-Judd result of zero optimal capital taxation says that 0 capital taxation are required in order to maximize welfare at the steady state.

The result is 30 years old. Still assuming that we only care about the steady state, what's the literature's take on that? How esoteric is it? Or in other words, are there simple extensions of the model that completely overcome the result?

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There is quite a bit of work being done in that area. One very recent example is Straub and Werning's working paper "Positive Long Run Capital Taxation: Chamley-Juff Revisited." The point seems to be that we need to consider the rate of convergence to the steady state.

Also, there is other literature that gives some competing results (e.g., "the new dynamic public finance" literature). For a more complete summary of mainstream objections, see Diamond and Saez, "The Case for a Progressive Tax: From Basic Research to Policy Recommendations," (JEP, 2011). They devote a whole section to why they think the Chamley-Judd result is not policy relevant.

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You had me at "JEP" –  Steve S Nov 19 at 0:37

Ljungqvist and Sargent (2004). Recursive macroeconomic theory 2n ed. (ch. 15) present and review the issue. In the Concluding Remarks section, they mention two environments, where the "zero-optimal-capital tax rate" does not hold:

Aiyagari(1995) presents a model with heterogeneous agents, incomplete insurance markets and borrowing constraints (i.e. a "Bewley" model): the optimal capital tax rate is positive, even in the long run. Insight: incomplete markets lead to excessive precautionary saving, leading to over-accumulation of capital. The positive capital tax rate offsets that.

Golosov, Kocherlakota and Tsyvinski (2003) introduce private information (the government cannot observe the hidden skill levels of different households). The tax system becomes an optimal dynamic incentive mechanism, leading to positive optimal capital tax rate.

Note that the result depends also on the feasibility of government commitment. If a commitment mechanism is not in place, it will be optimal for the government to "renege on its promise and levy a confiscatory tax on capital", as L & S write.

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