Pareto-improving tax policies under hyperbolic discounting

See Frederick et al. (2002) and Loewenstein and Prelec (1992) for broad discussion on present-biased preferences.

The hyperbolic discounting model is applied in various economic models such as a repeated-games model by Chade et al. (2008), a contract design model by DellaVigna and Malmendier (2004), entrepreneurs’ investment decisions by Grenadier and Wang (2007), unfunded social security system programs by Kumru and Thanopoulos (2008), mechanism design problems by Gilpatric (2008), a general equilibrium asset pricing model by Krusell et al. (2002b), and principal–agent problems with moral hazard by Yılmaz (2013).

Different from Laibson (1997), in Pavoni and Yazici (2017)’s model, the hyperbolic discounting factor is not constant over time but instead depends on time, and the proportional capital tax rate is also allowed to be distinct in different time periods. They showed that especially with log-linear utility functions, if the hyperbolic discounting factor is not constant, the optimal tax rate is not constant, either. They also use the CES utility function and find the optimal life-cycle capital taxation to maximize the time-zero preferences.

See also O’Donoghue and Rabin (2001, 2003) and Krusell et al. (2002a).

The government intervention might improve the current period’s intertemporal utility if the consumer is naive. Naivete causes the consumer to have the wrong objective maximization problem, which provides a justification for the government intervention. However, even with naive consumers, the government cannot get a consensus from consumers because naive consumers believe that any government action cannot improve that period’s intertemporal utility.

In this paper, we assume that the consumer is sophisticated about herself and also sophisticated about government policies. In Guo and Caliendo (2014), under the fully funded social security scheme that is equivalent to a balanced lump-sum tax-transfer plan, if the consumer is sophisticated about the government policy and the market is complete, the policy would not be effective. This is because in a complete market, the consumer can make the government forced savings ineffective by decreasing private savings. However, in our paper the reason the tax policy is effective even though the consumer is sophisticated is that the proposed tax policies affect the marginal cost of savings, which cannot be altered by the consumer.

In the steady-state model, we focus on capital taxation, but not income nor consumption taxation. Imposing proportional capital subsidy is mathematically equivalent to proportionally lowering the real gross interest rate, which makes the mathematical approach simpler.

Laibson (1997) used 0.6 for the benchmark value for \(\beta \)

The similar type of numerical methodology has been introduced in Laibson (1997, p. 466).

The numerical analyses in this subsection were performed with MATLAB 9. All MATLAB codes can be downloaded from minwook.host22.com/code/PAT.zip.

If the production function is linear, we can show that \(\widehat{k} _{2}^{\prime \prime }(k_{1})=0\) from equation (60). Then, the second-order condition is globally strictly negative, which guarantees uniqueness of equilibria like in Laibson (1996).