On relationships between numerical representations of interval orders and semiorders

The extent to which continuous numerical representations of interval orders are unique is considered. Apair of continuous, real-valued functions, <u, v>, represents an interval order, <X, >>, provided that for x, y ϵ X, x > y if and only if u(x) > v(y). Relationships which necessarily hold between any two such numerical representations are presented and a method by which one continuous representation can be derived from another is described. Similar considerations are made for special forms of continuous numerical representations of semiorders.     

Efficiency First or Equity First? Two Principles and Rationality of Social Choice

This paper formalizes two different principles to socially rank allocations under efficiency-equity trade off. The efficiency-first social preference relation ranks an allocation x higher than an allocation y if and only if (i) x is Pareto-superior to y or (ii) x and y are Pareto-noncomparable and x is equity-superior to y. The equity-first social preference relation reverses the order of application of the two criteria. We show that the efficiency-first relation may have a cycle, whereas the equity-first relation is transitive. We also characterize and compare the sets of maximal elements for these social preference relations in the Edgeworth box and examine the nonemptiness of the sets. Journal of Economic Literature Classification Numbers: D71, D63, D61.     

A strategy-proofness characterization of majority rule

Summary. A feasible alternative x is a strong Condorcet winner if for every other feasible alternative y there is some majority coalition that prefers x to y. Let (resp., denote the set of all profiles of linear (resp., merely asymmetric) individual preference relations for which a strong Condorcet winner exists. Majority rule is the only non-dictatorial and strategy-proof social choice rule with domain , and majority rule is the only strategy-proof rule with domain . Received: August 29, 2000; revised version: November 13, 2002 RID="*" ID="*"We are grateful to Wulf Gaertner and our two referees for insightful comments on a previous draft. Correspondence to: D. E. Campbell     

Choice and individual welfare

We propose an abstract method of systematically assigning a “rational” ranking to non-rationalizable choice data. Our main idea is that any method of ascribing welfare to an individual as a function of choice is subjective, and depends on the economist undertaking the analysis. We provide a simple example of the type of exercise we propose. Namely, we define an individual welfare functional as a mapping from stochastic choice functions into weak orders. A stochastic choice function (or choice distribution) gives the empirical frequency of choices for any possible opportunity set (framing factors may also be incorporated into the model). We require that for any two alternatives x and y, if our individual welfare functional recommends x over y given two distinct choice distributions, then it also recommends x over y for any mixture of the two choice distributions. Together with some mild technical requirements, such an individual welfare functional must weight every opportunity set and assign a utility to each alternative x which is the sum across all opportunity sets of the weighted probability of x being chosen from the set. It therefore requires us to have a “prior view” about how important or representative a choice of x at a given situation is.     

Numerical representation of intransitive preferences on a countable set

Let > be a preference relation on a countable set X. We prove that if > is acyclic (that is, has irreflexive transitive closure), then there exists a mapping u of X into $\text{R}$ such that x > y entails u(x)>u(y). We also give a simple proof of a representation theorem of Fishburn when > is an interval order.     

STATUS QUO IN THE WELFARE ANALYSIS OF TAX REFORMS

The welfare analysis of tax reforms most often consists of comparing the post‐reform distribution of individual welfare with the pre‐reform distribution or possibly that obtained from another reform as if they were completely independent. Such an “anonymous” approach does not take into account “changes” in individual situations, generally the main source of contention in any tax reform debate. This paper proposes a welfare criterion that allows comparison of reforms while taking into account individual status quo—i.e. pre‐reform—situations. This is done by extending standard utilitarian social welfare criteria to the case where individual utilities depend on initial income and income change.     

Algebra of Integrated Time Series: Evidence from Unit Root Analysis

It is argued if x_t ~ I(1) and y_t ~ I(1), then running a regression x_t on y_t would produce spurious results because e _t would generally be I(1). However, there may exist a ‘b’ such that e _t  = x _t - by _t is I(0), then running a regression x _t on y _t would not produce spurious results. This special case of two integrated time series is known in the literature as cointegration. In this particular case, x _t and y _t are said to be cointegrated. In our review of the development of the concept of cointegration, we identified that the underlying reason for this special case to arise is the proposition that if x _t  ~ I(d _x ), y _t  ~ I(d _y ), then z _t  = bx _t  + cy _t  ~ I(max(d _x ,d _y )). In this research, we offer evidence against this proposition.     

Some results on “an income fluctuation problem”

A consumer at each period, given the income available, y, has to decide how much to consume and save. If he consumes c ? 0 units he gets u(c) units of satisfaction or utility, and if x = y ? c ? 0 is the amount saved then the available income in the next period is rx + ω^k, where ω^k is a random variable, and r is an interest factor that is assumed to be known with certainty. Infinite time horizon problems are considered, and it is shown that if 0 < δr < 1, where 0 < δ < 1 is a discount factor, then the limiting policy is optimal. Questions about the behavior of the stock level, such as boundness, are considered, and an example is given that shows that the stock level might converge almost surely to infinity. Finally an economic explanation is given.     

Representing interval orders by a single real-valued function

Let > be an interval order on a topological space X, and let $\text{x > 1 y}$ if and only if there exists x′ with $\text{x?x′>y}$. Then >1 is a preference relation with transitive indifference, which, under suitable conditions, can be represented by a utility function v of the usual sort. In that case, maximisation of v (subject to contraints) leads to a most preferred point relative to >. Following both the Debreu-Rader and the Arrow-Hahn approaches, we discuss the existence and continuity of such a function v.     

会计法规与税法的差异与协调研究

经济体制改革的深入和市场经济的发展,促使税法制度与会计制度不断改革,并导致二者进一步分离。从中国税、会分离的现状出发,结合会计和税法相关理论,以中国现行的税法和会计制度、准则为依据,在探讨税法与会计差异的必然性和理论成因的基础上,从收入确认和费用扣除方面,全面、系统地分析了中国税法和会计的实务操作差异。关于如何处理会计与税法之间的差异,考虑到中国当前的实际情况,应当从宏观到微观自上而下建立一套行之有效的协调机制,逐步解决纳税实践中差异引发的问题。     

Preference for safety under the Choquet model: in search of a characterization

Victor prefers safety more than Ursula if whenever Ursula prefers a constant to an uncertain act, so does Victor. This paradigm, whose expected utility (EU) version is Arrow and Pratt’s more risk aversion concept, will be studied in the Choquet expected utility (CEU) model. Necessary condition Pointwise inequality between a function of the utility functions and another of the capacities is necessary and sufficient for the preference by Victor of safety over a dichotomous act whenever such is the preference of Ursula. However, increased preference for safety versus dichotomous acts does not imply preference by Victor of safety over a general act whenever such is the preference of Ursula. A counterexample will be provided, via the casino theory of Dubins and Savage. Sufficient condition Separation of the two functions by some convex function is sufficient for Victor to prefer safety more than Ursula, over general acts. Furthermore, a condition on the capacities will be presented for simplicity seeking, the preference by Victor over any act for some dichotomous act that leaves Ursula indifferent. This condition is met in particular if Victor’s capacity is a convex function of Ursula’s capacity. For these cases, the pointwise inequality (necessary) condition is a characterization of greater preference for safety, extending the Arrow–Pratt notion from EU to CEU and rank-dependent utility (RDU). These inequalities preserve the flavor of the “more pessimism than greediness” characterization of monotone risk aversion by Chateauneuf, Cohen and Meilijson in the RDU model and its extension by Grant and Quiggin to CEU. Preferences between safety and dichotomous acts are at the core of the biseparable preferences model of Ghirardato and Marinacci.     

Probabilistic dominance and status quo bias

Decision makers have a strong tendency to retain the current state of affairs. This well-documented phenomenon is termed status quo bias. We present the probabilistic dominance approach to status quo bias: an alternative is considered acceptable to replace the status quo only if the chances of a (subjectively) severe loss, relative to the status quo, are not too high. Probabilistic dominance is applied and behaviorally characterized in a choice model that allows for a range of status quo biases, general enough to accommodate unanimity, but also standard expected utility maximization. We present a comparative notion of “revealing more bias towards the status quo” and study its implications to the probabilistic dominance model of choice. Lastly, the model is applied to the endowment effect phenomenon and to a problem of international portfolio choice when investors are home biased.     

Tax Reform with Useful Public Expenditures

We examine the effects of tax reform in an endogenous growth with two types of useful public expenditures. The optimal fiscal policy shifts the tax base to private consumption and generally requires a change in the size of government. If a tax reform holds the size of government fixed to satisfy a revenue‐neutrality constraint, then the reform will be suboptimal; theory alone cannot tell us if welfare will be improved. For some model calibrations, we find that a revenue‐neutral consumption tax reform can result in large welfare gains. For other quite plausible calibrations, the exact same reform can result in tiny or even negative welfare gains as the revenue‐neutrality constraint becomes more severely binding. Overall, our results highlight the uncertainty surrounding the potential welfare benefits of fundamental tax reform.     

When is a tax neutral?

A proportional income tax is said to be neutral if variations in the tax rate do not affect the optimal composition of the consumption commodities of a utility maximizing consumer. It is shown that neutrality obtains if and only if the indirect utility function of the consumer is groupwise homothetic. If the income tax rates on labor and property incomes are allowed to differ, then neutrality obtains if and only if the indirect utility function of the consumer is homothetically separable. If, in addition, it is required that the proportional income tax be neutral with respect to not only consumption commodities but also to leisure, then 'the indirect utility function must have the form: $\text{V = V(f(w)+H}{}^1\text{(p))}$, where w and p are the normalized prices of leisure and consumption respectively, and H¹(p) is homogeneous of degree one in p.     

Resource egalitarianism with a dash of efficiency

We study the problem of defining inequality-averse social orderings over allocations of commodities when individuals have different preferences. We formulate a notion of egalitarianism based on the axiom that any dominance between consumption bundles should be reduced. This Dominance Aversion requirement is compatible with Consensus, a version of the Pareto principle saying that an allocation y is better than x whenever everybody finds that everyone?s bundle at y is better than at x. We characterize a family of multidimensional leximin orderings satisfying Dominance Aversion and Consensus.     

When is multidimensional screening a convex program?

A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis, quasi-linear utilities, and that agents can choose only pure strategies, we identify a structural condition on the value b(x,y) of product type y to agent type x — and on the principal?s costs c(y) — which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal?s problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal?s optimal strategy — and similarly of the strategy maximizing the expected welfare of the agents when the principal?s profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under reparametrization of agent and/or product types by diffeomorphisms, and (iii) a strengthening of Ma, Trudinger and Wang?s necessary and sufficient condition (A3w) for continuity of the correspondence between an exogenously prescribed distribution of agents and of products. We derive the persistence of economic effects such as the desirability for a monopoly to establish prices so high they effectively exclude a positive fraction of its potential customers, in nearly the full range of non-negatively cross-curved models.     

On enhanced cooperation

We analyze the issues relative to the formation of sub-unions in a federation, called enhanced cooperation agreements in the European Union. When centralization is not politically feasible, an agreement among a subset of countries may allow such countries to exploit benefits from coordination that would otherwise be lost. Other countries in the federation may object to the sub-union because it changes the status quo; if cooperation at the federal level becomes convenient in the future, the change in the status quo may adversely affect the countries which remained initially outside the sub-union. We show that as long as the countries can commit to coordinate on a policy which takes into account the utility of the excluded countries, sub-union formation may be optimal. The relative advantage of a sub-union towards immediate centralization increases when transfers are costly. On the other hand, if commitment is not possible then the excluded countries may be penalized. We use the results to discuss the newly introduced rules for enhanced cooperation agreements in the European Union.     

Should high-tax countries pursue revenue-neutral ecological tax reforms?

A politically intriguing question concerning the effects of a revenue-neutral ecological tax reform is whether such a political measure may succeed in providing a double dividend: to improve environmental quality and increase employment simultaneously. Theoretical studies reveal that for a competitive labor-market a green tax reform hardly yields a positive employment effect, whereas for a non-competitive market such an effect may well be obtained. However, little attention has focused on whether the ecological dividend remains attainable when an employment dividend accrues. We show for three different non-competitive labor-market scenarios that a positive employment effect can be expected, but that, for high-tax countries, environmental quality plausibly deteriorates when a revenue-neutral ecological tax reform is implemented.     

Viewpoint: Empirical evidence and tax policy design: lessons from the Mirrlees Review

Abstract This paper examines the role of evidence in drawing up the recommendations for tax reform in the Mirrlees Review. The arguments are organised loosely under five related headings: (i) Key margins of adjustment. (ii) Measurement of effective tax rates. (iii) The importance of information and complexity. (iv) Evidence on the size of responses. (v) Implications from theory for tax design. Although the Mirrlees Review focuses on all aspects of tax reform, the focus is this paper is on the taxation of earnings with some examples drawn from the taxation of consumption and savings.