Optimal Tax Deductions for Net Losses under Private Insurance with an Upper Limit

By Huang, Rachel J.; Tzeng, Larry Y. | Journal of Risk and Insurance, December 2007 | Go to article overview

Optimal Tax Deductions for Net Losses under Private Insurance with an Upper Limit


Huang, Rachel J., Tzeng, Larry Y., Journal of Risk and Insurance


ABSTRACT

Kaplow (1992b) shows that governments should not provide a tax deduction for net losses when a private insurance contract is available. However, his findings rest on the assumption that the private insurance is proportional coverage. We find that Kaplow's conclusions may not hold when the private insurance contract contains an upper limit. The findings of our article show that Kaplow's conclusions are sensitive to the assumption that the insurance contract is available in the private market.

INTRODUCTION

The federal government of the United States allows individuals to deduct some of their losses from their taxable income. (1) However, Kaplow (1991b, 1992b) proves that, when private insurance is available, tax deductions for net losses are inefficient. He shows that a tax deduction for net losses plays a similar role to a social insurance and reduces an individual's demand for private insurance. He also proves that a tax system without deductions for net losses Pareto dominates a tax system with deductions for net losses. In addition, he indicates that his finding is robust after taking moral hazard and administration costs into consideration. (2)

This article modifies Kaplow's (1992b) findings to explain why tax deductions for net losses might be socially optimal. In Kaplow (1992b), the private insurance is exogenously assumed to be proportional to coverage. However, in reality, the private market contains many other commonly used forms of insurance contract, such as a policy with an upper limit. Therefore, we reexamine whether Kaplow's (1992b) findings still hold when the form of the optimal private insurance is a contract with an upper limit. (3)

The literature has documented that the optimal private insurance contains an upper limit on coverage for the following reasons: price regulation (Raviv, 1979), the insured's option of bankruptcy (Huberman, Mayers, and Smith, 1983), the insured's option for converting or trading the damaged properties (Garratt and Marshall, 1996), or the manipulation of audit cost (Picard, 2000).

We first study whether a tax deduction for net losses is optimal, where the private insurance market is that characterized by Raviv (1979) in which the optimal private insurance is endogenously determined to be a policy limit contract due to price regulation. (4) We further show that the assumption of price regulation is not necessary for our main conclusion. We exogenously assume that the private insurance is a contract with an upper limit and reexamine whether the policy limit alone (without price regulation) makes tax deduction for net losses socially optimal.

The findings of our article show that Kaplow's (1992b) conclusions are sensitive to the assumptions regarding the form of the insurance contract in the private market. We show that, if the private insurance is a policy with an upper limit, then the government may have an incentive to provide a tax deduction for net losses to individuals.

In the section on "Optimal Tax Deductions for Net Losses," we examine the optimal tax deduction under private insurance with a policy limit. Our conclusions and applications are presented in the final section.

OPTIMAL TAX DEDUCTIONS FOR NET LOSSES

The optimal tax deduction is determined by a two-stage process. In the first stage, the government decides the tax deduction rate. In the second stage, given the tax deduction, the insured and the insurer choose the optimal form of the insurance contract in the private market. We solve the optimal tax deduction rate by means of a backward induction. Specifically, we evaluate whether the optimal tax deduction for net losses is zero.

Assume that a representative risk averse insured with initial wealth w faces a random loss x with a cumulative density function F (x) for 0 [less than or equal to] x [less than or equal to] L, where L is the maximum of the loss. …

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