Liqun Liu

Substituting one risk increase for another: A method for measuring risk aversion

This paper defines the rate of substitution of one stochastic change to a random variable for another. It then focuses on the case where one of these changes is an nth degree risk increase, and the other is an mth degree risk increase, where n>m⩾1. The paper shows that the rate of substitution for these two risk increases can be used to provide a broader definition and two additional characterizations of the nth degree Ross more risk averse partial order. The implications for local intensity measures of nth degree risk aversion are also examined. The analysis organizes the existing results as well as generates new ones.

Relative Efficiency of AD Valorem and Unit Taxes: The Case of Endogenous Quality

This article studies the relative efficiency of unit and ad valorem taxes in a competitive market in which the quality of product is endogenous. The author finds that the relative efficiency of these two taxes depends on exactly how individuals value the quality of a product. Specifically, the unit tax welfare dominates the ad valorem tax in the “casket” case and the “full-price” case, whereas the ad valorem tax welfare dominates the unit tax in the “lightbulb” case.

A Generalized Approach to Multigeneration Project Evaluation

In this article, we generalize the existing descriptive approach to multigeneration public project evaluation, taking into account distortionary taxes on capital income. In contrast to conventional wisdom, we show that such generalization does not require a project-specific social discount rate (SDR) expressed as a weighted average of gross and net rates of return. What emerges is the concept of the marginal cost of public funds (MCF) that has the convenient property of project independence. In addition, the MCF-based criterion identifies projects that, along with appropriate intergenerational transfers through time-varying head taxes, are Pareto improving, and is, therefore, independent of any utilitarian social welfare function being used.

THE INCREASING CONVEX ORDER AND THE TRADE‐OFF OF SIZE FOR RISK

One random variable is larger than another in the increasing convex order if that random variable is preferred or indifferent to the other by all decision makers with increasing and convex utility functions. Decision makers in this set prefer larger random variables and are risk loving. When a decision maker whose utility function is increasing and concave is indifferent between such a pair of random variables, a trade-off of size for risk is revealed, and this information can be used to make comparative static predictions concerning the choices of other decision makers. Specifically, the choices of all those who are strongly more (or less) risk averse than the reference decision maker can be predicted. Thus, the increasing convex order, together with Rosss (1981) definition of strongly more risk averse, can provide additional comparative static findings in a variety of decision problems. The analysis here discusses the decisions to self-protect and to purchase insurance.

Discounting according to Output Type

Federal discount rate policies advocate both a high rate representing the marginal productivity of capital and a low rate representing the government borrowing rate. These differential discount rate policies could be inconsistent and biased in favor of projects on which the lower discount rate is applied. This paper shows that the coexistence of different discount rates may be appropriate, depending on the type of project output. When a projects outputs are perfect substitutes for private consumption, both its costs and benefits should be discounted using the marginal productivity of capital. However, if the projects outputs are separable in the utility function, the benefits should be discounted using the net (of tax) rate of return.

Market Substitution and the Pareto Dominance of Ad Valorem Taxation

Based on product homogeneity and Cournot competition, past literature has uniformly shown that ad valorem taxation welfare dominates unit taxation in noncompetitive markets. This paper allows goods in a market to be heterogeneous and firms to be Bertrand competing. We confirm the short-run findings of others that consumer welfare and overall welfare are always higher under ad valorem taxation. However, ad valorem taxation generates larger profits (hence Pareto dominates) only when market demand is elastic, perhaps explaining the persistence of unit taxation in markets with inelastic demand. The effects on ad valorem Pareto dominance of within- and between-market substitutability, number of firms in the taxed market, and the level of taxation are also investigated. In the long run, an equal-revenue substitution of ad valorem taxation for unit taxation reduces consumer price, which is welfare improving, but also reduces variety when market demand is elastic, which is welfare decreasing. Nonetheless, ad valorem welfare dominance still holds in the long run.

Endogenous Patient Responses and the Consistency Principle in Cost-Effectiveness Analysis

In addition to incurring direct treatment costs and generating direct health benefits that improve longevity and/or health-related quality of life, medical interventions often have further or “unrelated” financial and health impacts, raising the issue of what costs and effects should be included in calculating the cost-effectiveness ratio of an intervention. The “consistency principle” in medical cost-effectiveness analysis (CEA) requires that one include both the cost and the utility benefit of a change (in medical expenditures, consumption, or leisure) caused by an intervention or neither of them. By distinguishing between exogenous changes directly brought about by an intervention and endogenous patient responses to the exogenous changes, and within a lifetime utility maximization framework, this article addresses 2 questions related to the consistency principle: 1) how to choose among alternative internally consistent exclusion/inclusion rules, and 2) what to do with survival consumption costs and earnings. It finds that, for an endogenous change, excluding or including both the cost and the utility benefit of the change does not alter cost-effectiveness results. Further, in agreement with the consistency principle, welfare maximization implies that consumption costs and earnings during the extended life directly caused by an intervention should be included in CEA.

The Excess Burden of the Social Security Payroll Tax

The conventional measure of the excess burden of a discrete increase in the rate of either a labor income tax or an excise tax is typically represented by a trapezoid in the supply/demand framework. This article adopts an alternative view of the incremental excess burden due to Mayshar and finds that the excess burden of a discrete increase in the rate of either a labor tax or an excise tax is represented by a triangle plus a rectangle, which is smaller than the conventional trapezoid for labor income taxes but larger than it for excise taxes. The new measure indicates an excess burden for U.S. social security tax (in the labor market alone) that is 10 to 50 percent of what is captured by the traditional trapezoid.

Social Security’s Individual Value and Aggregate Burden

Using a simple expected utility function, we derive discount-rate adjustments for uncertain future expenditures (costs) and revenues (benefits). We apply these results to the individual’s valuation of the Social Security contract, to aggregate measures of Social Security’s obligations, and then to the possibility of a Pareto-improving transition to self-funded retirement savings. Individually, the existing Social Security contract has a negative value for all new entrants to the program. When the value of the program is adjusted for risk, it is possible for a “big bang” transition to self-funded retirement savings to be Pareto improving.

The welfare gain from replacing the health insurance tax exclusion with lump-sum tax credits

This paper analyzes the welfare gain from replacing the tax exclusion of employer-provided health insurance with a lump-sum tax credit. It differs from earlier studies in that we look at the welfare cost of health insurance tax exclusion as coming directly from excessive health insurance rather than from overconsumption of medical care and that we account for the labor market effect of the tax exclusion on welfare. Both differences work to produce a smaller tax reform welfare gain. For a set of mid-range parameter values, the welfare gain is about 21% of current health insurance tax expenditures. In addition, government tax expenditures would fall by 38%, and health insurance spending would fall by 77% after the reform.