Manipulation and the Pareto rule

This paper examines rules that map preference profiles into choice sets. There are no agendas other than the entire set of alternatives. A rule is said to be “manipulable” if there is a person i, and a preference profile, such that i prefers the choice set obtained when he is dishonest to the one obtained when he is honest. It is “nonmanipulable” if this can never happen. The paper indicates how preferences over choice sets might be sensibly derived from preferences over alternatives, and discusses seven different notions of manipulability associated with seven different assumptions about preferences over sets of alternatives. The paper has two sections of results. In the first I show that the Pareto rule, that is, the rule that maps preference profiles into corresponding sets of Pareto optima, is nonmanipulable in four of the seven senses of manipulability, and manipulable in three of them. In the second section, I examine this conjecture: If an arbitrary rule is nonmanipulable and nonimposed, and if indifference is disallowed, then every choice set must be contained in the set of Pareto optima. The conjecture is true under the strongest definition of nonmanipulability.     

A characterization of consistent collective choice rules

We characterize a class of collective choice rules such that collective preference relations are consistent. Consistency is a weakening of transitivity and a strengthening of acyclicity requiring that there be no cycles with at least one strict preference, which excludes the possibility of a “money pump.” The properties of collective choice rules used in our characterization are unrestricted domain, strong Pareto, anonymity and neutrality. If there are at most as many individuals as there are alternatives, the axioms provide an alternative characterization of the Pareto rule. If there are more individuals than alternatives, however, further rules become available.     

IRRATIONALITY‐PROOFNESS: MARKETS VERSUS GAMES

How robust are economic models to the introduction of irrational agents? The Pareto efficiency of competitive equilibria is not robust since one irrational agent leads to inefficiency. But the property that rational agents cannot use their own resources to Pareto improve on their competitive allocation holds regardless of the number of irrational agents. Full production efficiency can be robust as well, but irrational firms introduce a trade‐off between efficiency and the attainment of Pareto improvements. Regarding games, I show that while existing implementation mechanisms are sensitive to the presence of irrational agents, there are robust alternatives with attractive welfare properties.     

Weak Independence and Social Semi‐Orders

This paper provides variants of Arrow's impossibility theorem, which states that there exists no non‐dictatorial aggregation rule satisfying weak Pareto, independence of irrelevant alternatives and collective rationality. In this paper, independence of irrelevant alternatives and collective rationality are simultaneously relaxed. Weak independence is imposed instead of independence of irrelevant alternatives. Social preferences are assumed to satisfy the semi‐order properties of semi‐transitivity and the interval‐order property. We prove that there exists a vetoer when the number of alternatives is greater than or equal to six.     

Pareto violations of parliamentary voting systems

It has been known for a long time that many binary voting rules can select a Pareto dominated outcome, that is an outcome such that there exists some other alternative which is preferred by every voter. In this paper, we show that some of these rules can select an outcome Pareto dominated in a much stronger sense. Furthermore, our main results are concerned with the evaluation of the likelihood of Pareto dominated outcomes under four social choice rules commonly used in Parliaments or in committees. Given a set of four alternatives and a set of n individuals, we assume anonymous profiles and using analytical methods we compute the proportion of profiles at which the Pareto criterion is violated. Our results show that one should not be especially worried about the existence of the possibility as such. We are grateful to two anonymous referees for very helpful remarks and suggestions.     

A GENERALIZED GIBRAT'S LAW*

Many economic and non‐economic variables such as income, wealth, firm size, or city size often distribute Pareto in the upper tail. It is well established that Gibrat's law can explain this phenomenon, but Gibrat's law often does not hold. This note characterizes a class of processes, one that includes Gibrat's law as a special case, that can explain Pareto distributions. Of particular importance is a parsimonious generalization of Gibrat's law that allows size to affect the variance of the growth process but not its mean. This note also shows that under plausible conditions Zipf's law is equivalent to Gibrat's law.     

Coalitional manipulation and the Pareto rule

This paper examines aggregation procedures that map profiles of individual preferences into choice sets. An aggregation procedure is said to be “manipulable by a coalition” if there is a group of individuals, and a preference profile, such that every member of the group prefers the choice set obtained when they are misrepresenting their preferences, to the one obtained when they are honest. We show that the Pareto rule, which is an aggregation procedure that maps profiles of individual preferences into corresponding sets of Pareto optima, is not manipulable by any coalition of individuals under various behavioural assumptions which relate preferences over choice sets to preferences over alternatives. The non-manipulability of the Pareto rule by a single individual follows as a special case under these behavioural assumptions.     

A Nonparametric Test for I(0)

There is frequently interest in testing that a scalar or vector time series is I(0), possibly after first-differencing or other detrending, while the I(0) assumption is also taken for granted in autocorrelation-consistent variance estimation. We propose a test for I(0) against fractional alternatives. The test is nonparametric, and indeed makes no assumptions on spectral behaviour away from zero frequency. It seems likely to have good efficiency against fractional alternatives, relative to other nonparametric tests. The test is given large sample justification, subjected to a Monte Carlo analysis of finite sample behaviour, and applied to various empirical data series.     

Stability and Turbulence in the Size Distribution of Firms: Evidence from Dutch Manufacturing

This paper examines the shape of the firm size distribution over time and across sectors, using a longitudinal data set of manufacturing firms in the Netherlands in 1978–1998. Although the size distribution is highly skewed and resembles the Pareto law, a variety of patterns emerge across sectors, with the lognormal providing a better fit in some sectors. The size distribution and the underlying firm dynamics evolve over time. In the long term, the distribution has become less skewed and thinner at the tails, the slope of the Pareto law has declined, and mobility of firms at the lower tail has increased. In addition, the slope of the Pareto law tends to become steeper in correspondence with an economic recession, with peaks of mobility of firms at different size classes.     

On the possibility of reasonable consistent majoritarian choice: Some positive results

Strictly Majoritarian Social Choice Functions (SMSCFs) are such that the choice on an agenda can be defined with the knowledge of the simple majority relation on the agenda as the sole information. The possibility for SMSCFs to satisfy both the General Pareto condition and choice consistency conditions strong enough to be meaningful has been doubted. Here we exhibit three reasonable SMSCFs that do both. One of them can be interpreted as eliminating from the agenda all alternatives one can suspect of being Pareto dominated by some other. We compare some of their properties with those of the SMSCFs already known in the literature.     

A NONPARAMETRIC TEST FOR COMPARING VALUATION DISTRIBUTIONS IN FIRST‐PRICE AUCTIONS

This article proposes a nonparametric test for comparing valuation distributions in first‐price auctions. Our test is motivated by the fact that two valuation distributions are the same if and only if their integrated quantile functions are the same. Our method avoids estimating unobserved valuations and does not require smooth estimation of bid density. We show that our test is consistent against all fixed alternatives and has nontrivial power against root‐N local alternatives. Monte Carlo experiments show that our test performs well in finite samples. We implement our method on data from U.S. Forest Service timber auctions.     

The Pareto-Scorza Polemic on Collective Economic Welfare

This paper reviews the 1902–03 polemic between Vilfredo Pareto and Gaetano Scorza, an Italian mathematician, on the validity of what is now referred to as the first law of welfare economics – i.e. the proposition that a point of equilibrium determined under conditions of free competition is Pareto optimal. It establishes that, contrary to the received view, Pareto did not write at cross-purposes to Scorza and his work published after the polemic does not suggest that Pareto eventually sided with Scorza on the issue of collective economic welfare.     

Arrovian aggregation in economic environments: how much should we know about indifference surfaces?

Arrow's celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and non-dictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about indifference surfaces is needed to construct social ordering functions satisfying the weak Pareto principle and anonymity. We show that local information such as marginal rates of substitution or the shapes “within the Edgeworth box” is not enough, and knowledge of substantially non-local information is necessary.     

On testing the logistic assumption in binary dependent variable models

This paper shows that the LM test for the validity of the logistic distribution commonly assumed in Binary Dependent Variable Models (i.e., the logit model) developed by Poirier (1980) can be obtained from a simple artificial regression. Monte Carlo simulations examine the small sample behaviour of the test statistic in comparison to the Information Matrix test for the logit model developed by Orme (1988) and Davidson and MacKinnon (1989), and two versions of the Reset test for limited dependent variable models suggested by Pagan and Vella (1989). Our results suggest that the LM test compares favourably under the null. The tests also appear to have varying power properties against different alternatives which suggests that they should all be used in investigating the validity of the logit model.     

Wald,likelihood ratio,and infinite induced test statistics for joint one-sided hypothesis

The relationship between certain infinite induced test statistics and the Wald and likelihood ratio statistics for testing hypothesis with one-sided alternatives is considered. In addition, it is shown that one of these infinite induced statistics reduces to a simple finite induced test statistic when the Wald statistic is equal to zero.     

Identifying Laffer Bounds: A Sufficient‐Statistics Approach with an Application to Germany

We derive a simple sufficient‐statistics test for whether a nonlinear tax‐transfer system is second‐best Pareto efficient. If it is not, then it is beyond the top of the Laffer curve and there exists a tax cut that is self‐financing. The test depends on the income distribution, extensive and intensive labor supply elasticities, and income effect parameters. A tax‐transfer system is likely to be inefficient if marginal tax rates are quickly falling in income. We apply this test to the German tax‐transfer system, and we find that the structure of effective marginal tax rates is likely to be inefficient in the region where transfers are phased out.     

The Supporting Line Property and the Additive Choice Function for Two-Dimensional Choice Problems

The paper provides an axiomatic characterization of the additive choice function using the additivity property. It is seen that, along with Pareto optimality, symmetry, and a supporting line property, the additivity axiom uniquely characterizes the additive choice function. The additive choice function as defined in this paper does not satisfy Nash's assumption of the independence of irrelevant alternatives. This raises the question of when a choice function is representable, an issue addressed in an appendix.     

What do we know about real exchange rate nonlinearities?

Nonlinear modeling of adjustments to purchasing power parity has recently gained much attention. However, a huge body of the empirical literature applies ESTAR models and neglects the existence of other competing nonlinear models. Among these, the Markov Switching AR model has a strong substantiation in international finance. Our contribution to the literature is fivefold: First, ESTAR and MSAR models from a unit root perspective are compared. To this end, a new unit root test against MSAR is proposed as the second contribution. Thirdly, the case of misspecified alternatives in a Monte Carlo setup with real world parameter constellations is studied. The ESTAR unit root test is not indicative, while the MSAR unit test is robust. Fourthly, the case of correctly specified alternatives is considered and low power of the ESTAR but not for the MSAR unit root test is observed. Fifthly, an empirical application to real exchange rates suggests that they may indeed be explained by Markov Switching dynamics rather than ESTAR.     

Neutrality in arrow and other impossibility theorems

Summary. Although not assumed explicitly, we show that neutrality plays an important role in Arrow and other impossibility theorems. Applying it to pivotal voters we produce direct proofs of classical impossibility theorems, including Arrow's, as well as extend some of these theorems. We further explore the role of neutrality showing that it is equivalent to Pareto or reverse Pareto, and to effective dictatorship for non-null social welfare functions satisfying the principle of independence of irrelevant alternatives. It is also equivalent to Wilson's Citizens' Sovereignty--which is related to the intuition that symmetry over alternatives makes social preference depend only on citizens' preferences. We show that some of these results are more fundamental than others in that they extend both to infinite societies and to considerably smaller domains of preferences. Finally, as an application of Arrow's theorem, we provide a simple proof of the Gibbard-Satterthwaite theorem.Received: 13 April 2000, Revised: 6 December 2002, JEL Classification Numbers: D71, C70.I thank Salvador Barberá, Luis Corchón, Cesar Martinelli, Eric Maskin, Tomas Sjöström, Ricard Torres, José Pedro Ubeda, and an anonymous referee for feedback. The proofs of Arrow's theorem and two Wilson's theorems come from a note I wrote in 1987 at Universitat Autónoma de Barcelona (Ubeda [16]). In 1996 Geanakoplos [7] wrote a proof of Arrow's theorem similar but not identical to mine. All work in this paper is independent of his.     

Unit root testing against an ST–MTAR alternative: finite-sample properties and an application to the UK housing market

A class of smooth transition momentum-threshold autoregressive (ST–MTAR) tests is proposed to allow testing of the unit root hypothesis against an alternative of asymmetric adjustment about a smooth nonlinear trend. Monte-Carlo simulation is employed to derive finite-sample critical values for the proposed test and illustrate its attractive power properties against a range of stationary alternatives. The empirical relevance of the ST–MTAR test is highlighted via an application to aggregate house price data for the UK. Interestingly, house prices are found to exhibit structural change characterized a fitted logistic smooth transition process, with the newly proposed ST–MTAR test providing the most significant results of the alternative smooth transition unit root tests available.