# 1999 Working Papers

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#### 549 - When are Plurality Rule Voting Games Dominance-Solvable?

*Amrita Dhillon and Ben Lockwood*

This paper studies the dominance-solvability (by iterated deletion of weakly dominated strategies) of plurality rule voting games. For K > 3 alternatives and n > 3 voters, we find sufficient conditions for the game to be dominance-solvable (DS) and not to be DS. These conditions can be stated in terms of only one statistic of the game, the largest proportion of voters who agree on which alternative is worst in a sequence of subsets of the original set of alternatives. When n is large, “almost all” games can be classified as either DS or not DS. If the game is DS, a Condorcet Winner always exists when n > 4, and the outcome is always the Condorcet Winner when the electorate is sufficiently replicated

#### 546 - A Law of Scarcity for Games

*Alexander Kovalenkov and Myrna Holtz Wooders*

The "law of scarcity" is that scarceness is rewarded; recall, for example, the diamonds and water paradox. In this paper, furthering research initiated in Kelso and Crawford (1982, Econometrica 50, 1483-1504) for matching models, we demonstrate a law of scarcity for cores and approximate cores of games.

#### 545 - Elections and Strategic Positioning Games

*Frank H Page, Jr and Myrna Holtz Wooders*

We formalize the interplay between expected voting behavior and stragetic positioning behavior of candidates as a common agency problem in which the candidates (i.e. the principals) compete for voters (i.e. agents) via the issues they choose and the positions they take. A political situation is defined as a feasible combination of candidate positions and expected political payoffs to the candidates. Taking this approach, we are led naturally to a particular formalization of the candidates’ positioning game, called a political situation game. Within the context of this game, we define the notion of farsighted stability (introduced in an abstract setting by Chwe (1994)) and apply Chwe’s result to obtain existence of farsightedly stable outcomes. We compute the farsightedly stable sets for several examples of political situations games, with outcomes that conform to real-world observations.

#### 544 - Time-Inconsistent Candidates vs. Time-Inconsistent Voters: Imperfect Policy Commitment in Political Equilibrium

*Marco Pani and Carlo Perroni*

This paper examines whether policy commitment mechanisms, when available, will be used by the elected policymaker in a political-economy equilibrium. We describe a two-period repeated voting model where second-period outcomes depend on commitment choices made by an elected policymaker in the first period, and where elected candidates may choose to deviate from their preferred level of commitment, retaining discretionary control of policy variables, in order to secure a favourable second-period political outcome. The implications of different political tenure systems for the candidates who are elected, the policy targets that are selected, the degree of commitment to their implementation, and the policies that are actually implemented in the model are examined.

#### 542 - Adoption of an IMF Programme and Debt Rescheduling. An Empirical Analysis

*Silvia Marchesi*

The existence of an empirical relationship between the adoption of an IMF programme and the concession of a debt rescheduling by commercial and official creditors is tested using a bivariate probit model. If countries who have arrangements with the IMF are more likely than others to obtain a rescheduling of their external debt we could conclude that the adoption of an IMF programme could work as a sort of signal of a country’s “good willingness”, which is thus rewarded with the debt relief. The results confirm the existence of a significant effect of the adoption of an IMF programme on the subsequent concession of a debt rescheduling by creditors.

#### 540 - The Allocation of Carbon Permits within One Country: A General Equilibrium Analysis of the United Kingdom

*T. Huw Edwards and John P. Hutton*

As part of the Kyoto agreement on limiting carbon emissions, from 2008 onwards an international market in auctionable carbon permits will be established. This raises the issue of whether trading should be simply between governments or between companies, or in the latter case how such permits should be allocated. Our paper uses the British section of a CGE model of the European energy sectors to evaluate the economics of various methods of allocating permits within a country, as discussed in Lord Marshall’s recent report to the British government. The option of allocation entirely by auction is similar to the setting of a carbon tax, and the recycling of revenues to reduce or offset other economic distortions could produce a potential net benefit to incomes and employment. 'Grandfathering' some of the permits free to large firms, according to their base year carbon emissions, would mean loss of the benefits of recycling auction revenues. This might be exacerbated if it created windfall profits repatriated by foreign shareholders. The third major alternative is to review the allocation regularly, awarding permits to all firms according to a ‘benchmark’ allocation, based on 'best practice' as estimated by outside experts. This would be similar in practice to recycling the revenue as an output subsidy to the industry, though it could be complicated to implement. Such a system could allow much of the potential ‘double dividend’ to be realised, though it might still be preferable to auction permits, with the revenues used to offset taxes across a wider spread of industry.

#### 539 - Child Support Reform: Some Analysis of the 1999 White Paper

*Gillian Paul and Ian Walker*

This paper uses a sample of lone mothers (and former lone mothers who are now repartnered) drawn from the 1997 Family Resources Survey to analyse the potential effects of reforming the UK system of Child Support. The main deficiency of the data is that non-resident fathers cannot be matched to the mothers in the data and this is overcome by exploiting information from another dataset which gives the joint distribution of the characteristics of separated parents. The effects of reforming the Child Support system is simulated for the amount of maintenance liabilities, the amount paid and the net incomes of households containing mothers with care and households containing non-resident fathers. The likely effects of the reform are simulated at various levels of compliance. The analysis highlights the need for further research into the incentive effects of Child Support on individual behaviour.

#### 538 - A Further Extension of the KKMS Theorem

*Yakar Kannai and Myrna Holtz Wooders*

Recently Reny and Wooders ([23]) showed that there is some point in the intersection of sets in Shapley's ([24]) generalization of the Knaster-Kuratowski-Mazurkiwicz Theorem with the property that the collection of all sets containing that point is partnered as well as balanced. In this paper we provide a further extension by showing that the collection of all such sets can be chosen to be strictly balanced, implying the Reny-Wooders result. Our proof is topological, based on the Eilenberg-Montgomery fixed point Theorem. Reny and Wooders ([23]) also show that if the collection of partnered points in the intersection is countable, then at least one of them is minimally partnered. Applying degree theory for correspondences, we show that if this collection is only assumed to be zero dimensional (or if the set of partnered and strictly balanced points is of dimension zero), then there is at least one strictly balanced and minimally partnered point in the intersection. The approach presented in this paper sheds a new geometric-topological light on the Reny-Wooders results.

#### 537 - An Explicit Bound on E For Nonemptimess of E-Cores of Games

*Alexander Kovalenkov and Myrna Holtz Wooders*

We consider parameterized collections of games without side payments and determine a bound on E so that all suffciently large games in the collection have non-empty E-cores. Our result makes explicit the relationship between the required size of E for non-emptiness of the E-core, the parameters describing the collection of games, and the size of the total player set. Given the parameters describing the collection, the larger the game, the smaller the E that can be chosen

#### 536 - Epsilon Cores of Games and Economies with Limited Side Payments

*Alexander Kovalenkov and Myrna Holtz Wooders*

We introduce the concept of a parameterized collection of games with limited side payments, ruling out large transfers of utility. Under the assumption that the payoff set of the grand coalition is convex, we show that a game with limited side payments has a nonempty E-core. Our main result is that, when some degree of side-paymentness within nearly-effective small groups is assumed, then all payoffs in the E-core treat similar players similarly. A bound on the distance between E-core payoffs of any two similar players is given in terms of the parameters describing the game. These results add to the literature showing that games with many players and small effective groups have the properties of competitive markets.

#### 535 - Approximate Cores of Games and Economies with Clubs

*Alexander Kovalenkov and Myrna Holtz Wooders*

We introduce the framework of parameterized collections of games and provide three nonemptiness of approximate core theorems for arbitrary games with and without sidepayments. The parameters bound (a) the number of approximate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact effectiveness. The theorems are based on a new notion of partition-balanced profiles and approximately partition-balanced profiles. The results are then applied to a new model of an economy with clubs. In contrast to the extant literature, our approach allows both widespread externalities and uniform results.

#### 534 - Economic Integration and Human Capital Investment

*Norman Ireland and Guido Merzoni*

In this paper we seek to characterise a market for heterogeneous managers created by heterogeneous firms and the decisions on investment in both sector-specific and firm-specific human capital when those decisions are made prior to the realisation of firms' profitability and the degree of markets’ integration may vary. We consider the (Nash) equilibrium and relate this to a first-best allocation. The rent-seeking motives of managers and firms will generally make sector- and firm-specific investment decisions not socially optimum, both with respect to the number of investors and the level of each investment. The effect on welfare of markets’ integration varies with the nature of the skills considered. With more general, sector-specific, skills more integration, by increasing the matching ability of the market, reduces the distortion caused by rent-seeking, and increases social welfare. However, with more specific skills the increased matching ability of a more integrated market, by making managers more mobile, destroys some firm-specific human capital and so reduces welfare.

#### 533 - Investment Subsidies and Time Consistent Environmental Policy

*Lisandro Abrego and Carlo Perroni*

'We describe a model of dynamic poluution abatement choices with heterogeneous agents, where, due to the presence of a distributional objective and to the absence of incentive-compatible compensation mechanisms, the choice of a second-best level of emission taxation is time-inconsistent. In this model, we investigate whether investment subsidies can act as a substitute for policy commitment.'

#### 532 - Low-Pay Transitions and Attrition Bias in Italy: An Analysis Using Simulation Based Estimation

*Lorenzo Cappellari*

'This paper analyses the extent to which existing econometric models of low-pay transition probabilities in Italy are biased by the presence of endogenous panel attrition. Non-random exits from the sample of wage earners may result from both demand and supply side factors and this could lead to under- or overestimation (respectively) of the extent of low-wage persistence. The analysis is carried out by extending the bivariate probit model used in Cappellari [1999] (where starting state and transition probabilities are jointly modelled thus tackling the endogeneity of the conditioning starting wage state) with a third equation which controls for the non-randomness of panel attrition. The resulting trivariate probit model with endogenous switching, whose evaluation is not feasible within the routines customarily available in microeconometric packages, is implemented by applying simulation estimation techniques. Results show the ignorability of attrition in SHIW data, thus pointing towards the robustness of the results previously obtained without controlling for attrition.'

#### 531 - Low-Wage Mobility in the Italian Market

*Lorenzo Cappellari*

'This paper uses SHIW panel data for 1993 and 1995 to model individual transition probabilities at the bottom of the Italian wage distribution. The analysis is based on a bivariate probit model with endogenous switching which allows tackling the initial conditions problem, i.e. the potential endogeneity of the conditioning starting state. Results show the appropriateness of such a choice: the correlation between state and transition probabilities is significantly different from zero, while overlooking endogeneity leads to overstatement of both size and significance of coefficients in the transition equation. The paper shows that while some factors such as education, sex and geographical location have an effect on low-pay persistence, job related variables are more effective in avoiding falls into low-pay from higher pay. It is also shown how raw persistence involves a considerable share of true state dependence, pointing towards the existence of low-pay stigma.'

#### 530 - Heterogeneity and the Distribution of Wages

*V.Bhaskar and Ted To*

A number of theories (search and efficiency wages) have been developed, in part, to explain why identically able workers are often paid different wages. However, when there is a minimum wage, they do not explain the resulting "spike" in the wage distribution. Our model's predictions are consistent with this evidence. We assume that workers are equally able but have heterogeneous preferences for non-wage characteristics, while employers have heterogeneous productivity characteristics. This results in a model of labor market oligopsony where "inside" and "outside" forces interact, producing wage dispersion as well as a spike at the minimum wage.

#### 529 - Minority Control: An Analysis of British Companies Using Voting Power Indices

*Dennis Leech*

'An exercise in the empirical use of voting power indices from cooperative game theory to applied ownership data for large companies, this paper contributes in two areas: (1) the analysis of company control based on shareholding voting power, and (2) the empirical use of power indices and understanding of the comparative properties of different indices. New algorithms for calculating power indices, which quantify voting power in weighted voting bodies like company meetings, are applied to detailed data on beneficial ownership of 444 large UK companies without majority control. The results show that the Banzhaf index is, and the Shapley-Shubik index is not, useful for this analysis and a control classification of the firms is obtained.'

#### 528 - Identification and Estimation of a Labour Market Model for the Tradeables Sector: The Greek Case

*Costas Milas and Jesus G. Otero*

'This paper derives a theoretical labour market model for the tradeables sector of a small open economy. Using Greek manufacturing data and applying multivariate cointegrating techniques, two cointegrating vectors are estimated based on the a priori restrictions provided by the theoretical model; a labour demand and a real exchange rate equation, respectively. The short-run estimates of the model suggest that labour decisions not only depend upon past disequilibria in the labour market, but also on the discrepancy between the real exchange rate and its implied long-run equilibrium relationship, that is, the magnitude of the real exchange rate misalignment.'

#### 527 - Production Externalities and Two-Way Distortion in Principal-Multi-Agent Problems

*Ben Lockwood*

'This paper studies an otherwise standard principal-agent problem with hidden information, but whether there are positive production externalities between agents: the output of any agent depends positively on the effort expended by the other agents. It is shown that the optimal contract for the principal exhibits two-way distortion: the effort of any agent is oversupplied (relative to the first-best) when his marginal cost effort is low, and undersupplied his marginal cost of effort is high. This pattern of distortion cannot otherwise arise in optimal single- or multi-agent incentive contracts, unless there are countervailing incentives. However, unlike the countervailing incentives case, the pattern of distortion is robust to the precise form of the externality. '

#### 526 - Time, Self-Selection and User Charges for Public Goods

*Dan Anderberg, Fredrik Andersson and Alessandro Balestrino*

Many public goods generate utility only when combined with a time-input. Important examples include road networks and publicly provided leisure facilities. If it is possible to charge for the time spent using the public good it is generally a second-best Pareto optimal policy to do so even in the absence of congestion. An optimal linear user charge is analysed within a standard optimum income-tax framework. Second-best public good provision in the presence of a user charge is also characterized and factors that influence the direction of optimal distortion of the public good supply are identified.

#### 525 - Gradualism and Irreversibility

*Ben Lockwood and Jonathan P. Thomas*

This paper considers a class of two-player dynamic games in which each player controls a one-dimensional variable which we interpret as a level of cooperation. In the base model, there is an irreversibility constraint stating that this variable can never be reduced, only increased. It otherwise satisfies the usual discounted repeated game assumptions. Under certain restrictions on the payoff function, which make the stage game resemble a continuous version of the Prisoners' Dilemma, we characterize efficient symmetric equilibria, and show that cooperation levels exhibit gradualism and converge to a level strictly below the one-shot efficient level: the irreversibility induces a steady-state as well as a dynamic inefficiency. As players become very patient, however, payoffs converge to (though never attain) the efficient level. We also show that a related model in which an irreversibility arises through players choosing an incremental variable, such as investment, can be transformed into the base model with similar results. Applications to a public goods sequential contribution model and a model of capacity reduction in a declining industry are discussed. The analysis is extended to incorporate partial reversibility, asymmetric equilibria, and sequential moves.