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Third Quarter 2021, 
Vol. 103, No. 3
Posted 2021-07-01

Optimal Capital Taxation and Precautionary Savings

by Yunmin Chen, YiLi Chien, and C.C. Yang


There are multiple reasons to motivate the role of capital taxation in the heterogenous-agent incomplete-markets (HAIM) model. One is the production inefficiency caused by precautionary savings. The other is the wealth redistribution role played by capital taxation. To distinguish between these two reasons, this article uses an analytical tractable HAIM model with a degenerated distribution of wealth while preserving the role of precautionary savings. The degenerated wealth distribution shuts down the distributional role played by capital taxation. Our results show that, with no role to play for redistribution, the government bond is more suitable than capital tax for addressing the production inefficiency caused by households' precautionary savings in the HAIM model.

Yunmin Chen is an assistant professor at Shandong University. YiLi Chien is a research officer and economist at the Federal Reserve Bank of St. Louis. C.C. Yang is a distinguished research fellow at the Institute of Economics, Academia Sinica.


In the Ramsey taxation literature, pivotal work by Chamley (1986) shows that the best way for the government to finance its expenditures in the long run is to tax labor but not capital in a representative-agent model. The recent work by Chari, Nicolini, and Teles (2020) clarifies the conditions and assumptions required to support the zero capital tax result. How­ever, the optimal outcome of this important taxation problem is relatively less understood in the heterogeneous-agent incomplete-markets (HAIM) framework. The HAIM model considers an environment in which households are subject to uninsurable idiosyncratic shocks and ad hoc borrowing restrictions; in response, households buffer their consumption against adverse shocks via precautionary savings. During the past two decades, the HAIM model has become a standard workhorse for policy evaluations in the current state-of-the-art macroeconomics that jointly addresses aggregate and inequality issues.

Given the importance and popularity of the HAIM model, paralleling the work of Chamley (1986), it is natural to ask, "What is the prescription of Ramsey capital taxation in the long run for the HAIM economy?" There are several important attempts to investigate this question, such as in Aiyagari (1995); Conesa, Kitao, and Krueger (2009); and Dávila et al. (2012). However, some issues still remain unsettled. For example, a possible reason for the positive capital taxation resides in the production efficiency argument. In the equilibrium of the HAIM model, production could be inefficient in the sense that the marginal product of capital is lower than that implied by the so-called "modified golden rule" (MGR hereafter), which is due to the overaccumulation of capital resulting from the precautionary savings of households. However, there are some other reasons to motivate the role of capital taxation in the HAIM economy. For example, in HAIM environments without public debt, the works by Dávila et al. (2012); Krueger and Ludwig (2018); and Conesa, Kitao, and Krueger (2009) suggest that capital taxation or subsidization could also serve to redistribute wealth and thereby improve welfare. This then raises the following question: How do optimal capital taxation and optimal public debt relate to the issue of capital overaccumulation caused by precautionary savings in the HAIM environment?

To answer these questions, we simplify the HAIM model in a particular way so that wealth distribution is degenerated each period. Our article adopts the model of Chen et al. (2021), which follows the work of Lucas (1990) and Heathcote and Perri (2018). More specifically, a special risk-sharing technology is introduced such that individual members within a family are able to pull their wealth by the end of each period. As a result, wealth distribution is totally degenerated each period and hence capital tax can no longer play a role for wealth redistribution. Despite wealth-redistributing technology, our model still preserves income/consumption inequality as well as households' precautionary-saving motives.

By isolating the redistributive role of capital tax, our model is therefore suitable for answering the following specific question: Should the government tax capital to achieve the MGR purely because of the production inefficiency caused by precautionary savings? Our results demonstrate that the Ramsey planner intends to increase the supply of government bonds until no individuals are borrowing-constrained in the long run. That is to say, the needs of precautionary savings are fully met by the supply of public debt, and hence capital is no longer overaccumulated. As a result, the long-run optimal capital tax rate becomes zero. In short, with no role to play in redistribution, the government bond is more suitable than capital tax for addressing the production inefficiency caused by precautionary savings in the HAIM model. These results are totally consistent with the recent studies by Chen et al. (2021) and Chien and Wen (2020). However, the later article relies critically on quasi-linear preferences to derive their results.

Our article is related to the earlier work of Aiyagari (1995), which shows that a positive capital tax should be imposed to implement the MGR in an assumed Ramsey steady state. Our zero-capital-taxation result should not be seen as a contradiction to his result, since there is no wealth distribution in our model. Instead, our result helps to clarify that the positive capital tax result in the Aiyagari model is not driven purely by the MGR but is more likely due to the wealth-redistribution role of capital tax.

The remainder of the article is organized as follows: Section 2 describes the model, derives the competitive equilibrium, and provides sufficient conditions for the Ramsey planner to support a competitive equilibrium. Section 3 shows how to solve for the Ramsey allocation analytically and how to derive the optimal capital tax in a Ramsey steady state. Section 4 concludes the study.

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