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Abstracts of 2000 Working Papers

WORKING PAPER NO 583

Members' Voting Power in the Governance of the International Monetary Fund
Dennis Leech

In general in an organisation whose system of governance involves weighted voting, a member's weight in terms of the number of votes and the formal power it represents differ. Power indices provide a means of analysing this difference. The paper uses new algorithms for computing power indices for large games. Three analyses are carried out: (1) the distribution of Banzhaf voting power among members in 1999; the results show that the United States has considerably more power over ordinary decisions than its weight of 17% but that the use of special supermajorities limits its power; (2) the effect of varying the majority requirement on the power of the IMF to act and the powers of members to prevent and initiate action (Coleman indices); the results show the effect of supermajorities severely limits the power to act and therefore renders the voting system ineffective in democratic terms, also the sovereignty of the United States within the IMF is effectively limited to just the power of veto; (3) the paper proposes the determination of the weights instrumentally by means of an iterative algorithm to give the required power distribution; this would be a useful procedure for determining appropriate changes in weights consequent on changes to individual countries' quotas; this is applied to the 1999 data. Policy recommendations are, first, that the IMF use only simple majority voting, and discontinue using special supermajorities, and, second, allocate voting weight instrumentally using power indices.
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WORKING PAPER NO 582

Candidate Entry, Screening, and the Political Budget Cycle
Eric Le Borgne and Ben Lockwood

We investigate whether relevant private information about citizens’ competence in political ffice can be credibly revealed by their entry and campaign expenditure decisions, as opposed to choice of policy once in office. We find that this depends on whether voters and candidates have common or conflicting interests; only in the former case can entry be revealing in equilibrium. We apply these results to Rogoff’s (1990) model of the political budget cycle, allowing for candidate entry, as well as elections: as interests are common, low-ability candidates are screened out at the entry stage, and so there is no signaling via fiscal policy (i.e. no “political budget cycle”). In a variant of the Rogoff. model where citizens differ in honesty, rather than ability, interests are conflicting, and so the political budget cycle can persist in equilibrium.
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WORKING PAPER NO 581

Is Comprehensive Education Really Free? A Case Study of the Effects of Secondary School Admissions Policies on House Prices in One Local Area.
Dennis Leech and Erick Campos

This paper reports on a study that tests the anecdotal hypothesis that parents are willing to pay a premium to secure places for their children in popular and oversubscribed comprehensive schools. Since many local education authorities use admissions policies based on catchment areas and places in popular schools are very hard to obtain from outside these areas - but very easy from within them - parents have an incentive to move house for the sake of their children's education. This would be expected to be reflected in house prices. The study uses a cross sectional sample based on two popular schools in one local education authority area, Coventry. Differences in housing quality are dealt with by using the technique of hedonic regression and differences in location by sample selection within a block sample design. The sample was chosen from a limited number of locations spanning different catchment areas in order to reduce both observable and unobservable variability in nuisance effects while maximising the variation in catchment areas. The results suggest that there are strong school catchment area effects. For one of the two popular schools we find a 20 percent premium and for the other a 16 percent premium on house prices ceteris paribus.
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WORKING PAPER NO 580

Do Elections Always Motivate Incumbents?
Eric Le Borgne and Ben Lockwood

This paper studies a principal-agent model of the relationship between office-holders and the electorate, where the office-holder is initially uninformed about herability (following Holmström, 1999). If office-holder effort and ability interact in the “production function” that determines performance in office, then an office-holder has an incentive to experiment, i.e. raise effort so that performance becomes a more accurate signal of her ability. Elections reduce the experimentation effect, and the reduction in this effect may more than o¤set the positive “career concerns” effect of elections on effort. Moreover, when this occurs, appointment of officials (random
selection from the citizenry and tenure) may Pareto-dominate elections.
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WORKING PAPER NO 579

Computing Classical Power Indices For Large Finite Voting Games
Dennis Leech

Voting Power Indices enable the analysis of the distribution of power in a legislature or voting body in which different members have different numbers of votes. Although this approach to the measurement of power, based on co-operative game theory, has been known for a long time its empirical application has been to some extent limited, in part by the difficulty of computing the indices when there are many players. This paper presents new algorithms for computing the classical power indices, those of
Shapley and Shubik (1954) and of Banzhaf (1963), which are essentially modifications of approximation methods due to Owen, and have been shown to work well in real applications. They are of most utility in situations where both the number of players is large and their voting weights are very non-uniform, some members having considerably larger numbers of votes than others, where Owen's approximation methods are least accurate. The suggestion is made that the availability of such improved algorithms might stimulate further applied research in this field.
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WORKING PAPER NO 578

'Reverse Hysteresis': R&D Investment with Stochastic Innovation
Helen Weeds

We consider optimal investment behavior for a firm facing both technological and economic uncertainty, in the context of a research project with unpredictable outcomes. The optimal investment strategy, in the form of a pair of trigger points for investment and abandonment, is derived. As in Dixit (1989), the investment trigger exceeds the Marshallian investment point. However the abandonment trigger may exceed the Marshallian exit point, in contrast to the Dixit result, giving rise to ‘reverse hysteresis.’ Thus the firm tends to abandon research rapidly as profitability declines, at times despite the existence of positive expected profits. The model also provides a unified framework encompassing two existing models as limiting cases.
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WORKING PAPER NO 577

Sleeping Patents and Computsory Licensing: An Options Analysis
Helen Weeds

Why should a firm wish to create a new technology that it will leave unexploited for some time? Sleeping patents have long been perceived as anticompetitive devices, used by dominant firms to block entry into their market. In a real options framework with both economic and technological uncertainty, we show that a sleeping patent may arise as the result of optimal forward-looking behavior, in the absence of any anticompetitive motive. We also consider the effect of possible measures to enforce the development of sleeping patents and find that these are likely to harm incentives for firms to engage in research.
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WORKING PAPER NO 576

Strategic Delay in a Real Optimna Model of R&D Competition
Helen Weeds

This paper considers irreversible investment in competing research projects with uncertain returns under a winner-takes-all patent system. Uncertainty takes two distinct forms: the technological success of the project is probabilistic, while the economic value of the patent to be won evolves stochastically over time. According to the theory of real options uncertainty generates an option value of delay, but with two competing firms the fear of preemption would appear to undermine this approach. In non-cooperative equilibrium two patterns of investment emerge depending on parameter values. In a preemptive leader-follower equilibrium firms invest sequentially and option values are reduced by competition. A symmetric outcome may also occur, however, in which investment is more delayed than the
single-firm counterpart. Comparing this with the optimal cooperative investment pattern, investment is found to be more delayed when firms act non-cooperatively, as each holds back from investing in the fear of starting a patent race. Implications of the analysis for empirical and policy issues in R&D are considered.
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WORKING PAPER NO 575

Networks, Options and Preemption
Robin Mason and Helen Weeds

This paper examines the irreversible adoption of a technology whose returns are uncertain, when there is an advantage to being the first adopter, but a network advantage to adopting when others also do so. Two patterns of adoption emerge: sequential, in which the leader aggressively preempts its rival; and a more accommodating outcome in which the firms adopt simultaneously. There are two main results. First, conditional on adoption being sequential, the follower adopts at the incorrect point, compared to the co-operative solution. The leader adopts at the co-operative point when there is no preemption, and too early if there is preemption. Secondly, there is insufficient simultaneous adoption in equilibrium. The paper examines the effect of uncertainty, network effects and preemption on these ineffciencies. Standard results do not always hold. For example, the analysis raises
the unusual possibility that an increase in uncertainty may cause the first mover to adopt the technology earlier.
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WORKING PAPER NO 574

A Nonscale Growth Model with R&D and Human Capital Accumulation
Maria-Joao Ribeiro

This paper aims to contribute to the new growth theory with a model in which the engine of growth is human capital growth. Building on Romer's [1990] model, two new functions are introduced: (1) a specification for the production of new designs that assumes no externalities and no inventions before time zero; and (2) A specification for the accumulation of human capital technically similar to that in Lucas [1988]. As opposed to Romer's model, the scale-effects prediction is eliminated because technological growth does not depend on the number of researchers, but instead on the rate of growth of human capital. Moreover, the model introduced carries a new prediction: Growth depends positively on the ratio of final-good workers to researchers.
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WORKING PAPER NO 573

Buybacks of Domestic Debt in Public Debt Management
Silvia Marchesi

In the model a fiscal stabilisation is announced under asymmetry of information between the government and the private investors. The government could be of two types: a dry type and a wet type, according to the amount of spending cuts it decides to make. Private investors may thus lack confidence in the stabilisation program and interest rates would be too high, reflecting this lack of credibility. A dry type which has to finance new spending may want to signal its resolution (type) in order to lower its interest costs and one way to do that would be to repurchase a fraction of the outstanding debt. The wet type could also decide to buyback some of its debt in order to pretend to be a dry type and to (possibly) lower its interest payments. It is showed that a critical amount of buyback exists such that the two types could be separated.
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WORKING PAPER NO 572

The Dummies Guide' to Lottery Design
Ian Walker and Juliet Young

This paper outlines the issues relevant to the operation of lottery games. We consider how such games should be designed, what a portfolio of games might look like, how the operator should be regulated, how spending on lottery games should be taxed, and what considerations are relevant to the use of the revenue from such games.

Our research suggests that the lottery tickets sales depend positively on the proportion of revenue returned as prizes (i.e the mean of the prize distribution), the skewness in the prize distribution (e.g how much of the prize money goes to the jackpot), and negatively on the variance in the prize distribution. Thus good causes revenue might be higher if the game were meaner (less of the stakes used as prize money), or if more of the prize money was used for the jackpot, or if the variance in the expected
prizes were reduced. In practice, it is difficult to change one aspect of the design of the prize distribution without having a counterveiling effect on another aspect. Thus, it is difficult to make judgements about the merits of alternative game designs without looking at all of the parameters being proposed.

We find no empirical evidence to suggest that there is any merit in having much of the take-out (the revenue that is not returned as prizes) dedicated to good-causes, and no evidence that the nature of the operator might make any difference.

The current “beauty contest” process of choosing an operator is fraught with risk and we suggest that, subject to a probity
check, the license should be auctioned.
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WORKING PAPER NO 571

Trade Bloc Formation Under Imperfect Competition
Paola Conconi

We examine the endogenous formation of trade blocs when markets are characterized by imperfect competition and governments use import tariffs and export subsidies to alter the strategic interactions between oligopolistic firms. Using a simple model of intra-industry trade between three ex-ante symmetric countries, we find that, while 'pure' customs unions - entailing tariff cooperation only - are stepping stones towards global free trade, 'impure' customs unions - involving the coordinated use of both tariffs and subsidies - are stumbling blocs against it. Our analysis suggests that an international ban on export subsidies could held to sustain global free trade.
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WORKING PAPER NO 570
Green and Producer Lobbies: Enemies or Allies?
Paola Conconi

In this paper we employ a common agency model to study the role of green and producer lobbies in the determination of trade and environmental policies. We focus on two large countries that are linked by trade flows and transboundary pollution externalities. We show that the nature of the relationship between lobbies and the relative efficiency of unilateral and cooperative policy outcomes depend crucially on three factors: the type of policy regime, whether governments act unilaterally or cooperatively, and the extend of the 'pollution leakages'.

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WORKING PAPER NO 569
The Assignment of Powers in Federal and Unitary States
Ben Lockwood

This paper studies a model where the power to set policy (a choice of project) may be assigned to central or regional government via either a federal or unitary referendum (constitutional rule, CR). The benefit of central provision is an economy of scale, while the cost is political inefficiency. The relationship between federal and unitary CRs is characterized in the asymptotic case as the number of regions becomes large, under the assumption that the median project benefit in any region is a random draw from a fixed distribution, G. Under some symmetry assumptions, the relationship depends only on the shape of G, not on how willingnesses to pay are distributed within regions. The relationship to Cremer and Palfrey's (1996) "principle of aggregation" is established. Asymptotic results on the efficiency of the two CRs are also provided.

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WORKING PAPER NO 568
"Are People Willing to Pay to Reduce Others' Incomes?
Daniel Zizzo and Andrew Oswald

This paper studies utility interdependence in the laboratory. We design an experiment where subjects can reduce (“burn”) other subjects’ money. Those who burn the money of others have to give up some of their own cash. Despite this cost, and contrary to the assumptions of economics textbooks, the majority of our subjects choose to destroy at least part of others’ money holdings. We vary experimentally the amount that subjects have to pay to reduce other people’s cash. The implied price elasticity of burning is calculated; it is mostly less than unity. There is a strong correlation between wealth, or rank, and the amounts by which subjects are burnt. In making their decisions, many burners, especially disadvantaged ones, seem to care about whether another person ‘deserves’ the money he has. Deservingness is not simply a matter of relative payoff.

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WORKING PAPER NO 567
"Tax Competition and Tax Co-Ordination Under Destination and Origin Principles: A Synthesis
Ben Lockwood

This paper proposes a general framework for analysing commodity tax competition under destination and origin principles, based on three possible tax spillovers, the consumer price spillover, the producer price/terms of trade spillover, and rent spillovers. A model is presented which can be extended to accomodate all three spillovers. Using this model, many of the results in the existing literature can be derived, compared, and extended.

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WORKING PAPER NO 566
"Renegotiation of Social Contracts by Majority Rule"
Dan Anderberg and Carlo Perroni

We consider renegotiation of social earnings insurance arrangements by majority voting in an economy where ex-ante identical individuals make unobservable private investments in education. We show that voting-based renegotiation can result in a higher expected level of investment in comparison to the case where social insurance is determined by an appointed social planner. We also find that, with voting-based renegotioation, the availability of costly ex-post information about private investment can help overcome commitment problems. These findings call into question the practice of using a representative-consumer approach when modelling dynamic policy problems in large economies.

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WORKING PAPER NO 565
"P-Star-Model Based Analysis of Inflation Dynamic in the Czech Republic"
Jan Frait, Lobos Komarek and Lumir Kulhanek

The paper presents a version of the P* model of inflation dynamics for a small open economy and applies it to the Czech economy time series from the period of 1991-1999. The paper is organised as follows. Section 2 presents a brief discussion of the monetary policy indicators issue. Section 3 describes the logics of the P* model. Section 4 explains the extension of the basic model to the case of a small open economy. Section 5 applies the model to the Czech economy data and presents the estimates of the Czech inflation dynamics determination.
The results of the estimates suggest that the dynamics of the Czech inflation evolves in line with a P* model logic: the inflation in the current period changes to close the price gap, i.e. the gap between actual and equilibrium price level. The foreign component of the price gap seems to be more important than domestic component which supports the hypothesis that the equilibrium price level in the Czech Republic is to a large extent determined by the monetary policy in the EU via the explicit or implicit peg of the Czech currency exchange rate to EUR. The overall results show that the inflation in the Czech Republic is primarily a monetary phenomenon.

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WORKING PAPER NO 564
"Shareholder Power and Corprate Governace"
Dennis Leech
The pattern of ownership and control of British industry is unusual compared with most other countries in that ownership is relatively dispersed. Typically the largest shareholder in any large listed company is likely to own a voting minority of the shares. Majority ownership by a single shareholder is unusual. It is not uncommon for the largest shareholding to be under 20 percent and in many cases it is much less than that. A broadly similar pattern is observed in the USA.
Two inferences about corporate governance are conventionally drawn from this, following the early work of Berle and Means: (1) All but the very largest shareholders are typically too small to have any real incentive to participate in decision making; (2) All but the very largest shareholdings are too small to have any real voting power. The question of voting power is the focus of this paper. Conventional analyses use a rule of thumb of 20%, assuming shareholders to be fundamentally passive in relation to the running of the company, whatever their style of investment management, unless one of them is above this figure. The London Stock Exchange defines a controlling holding to be one greater than 30 percent. Much empirical work uses declarable stakes, which in the UK are those of 3 percent or more, and disregards anything smaller assuming it to be powerless. In fact, however, a 1% stake in the 100th largest company (Smiths Industries) is worth about £29million, which suggests its owner has strong incentives to be active, and might wish to use his voting power.
Theoretical voting power of minority shareholding blocks is studied using the game-theoretic idea of voting power indices. This is applied to a model of ownership control based on the definition of control used by Berle and Means in their classic study. The results give support for use of a 20 percent rule in many cases but not all. Also they support the idea that many companies are potentially controlled by a block of a few large shareholders working in concert.

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WORKING PAPER NO 563
"An Empirical comparison of the performance of Classical Power Indicies"
Dennis Leech
Power indices are general measures of the relative voting power of individual members of a voting body. They are useful in helping understand and design voting bodies particularly those which employ weighted voting, in which different members having different numbers of votes. It is well known that in such bodies a member's voting power, in the sense of their capacity to affect the outcomes of votes called, rarely corresponds to the actual number of votes allocated to him. Many voting bodies for which this is an important consideration exist: examples include international organisations (notably the World Bank, the IMF, the European Union), the US presidential Electoral College and corporations in which votes are proportionate to stockholdings.
Two classical power indices dominate the literature: the Shapley-Shubik index and the Banzhaf index (also known by other names). Both are based on the idea that a member's power depends on the relative number of times they can change a coalition from losing to winning by joining it and adding their vote. They may be defined in probabilistic terms as the probability of being able to swing the result of a vote, where all possible outcomes are taken as equiprobable. The indices differ however in the way they count voting coalitions. In probabilistic terms they use different coalition models and therefore differ in precisely what is meant by equiprobable outcomes.
The indices have been used in a number of empirical applications but their relative performance has remained an open question for many years, a factor, which has hindered the wider acceptance of the approach.
Where both the indices have been used for the same case, they have often given different results, sometimes substantially so, and theoretical studies of their properties have not been conclusive. There is therefore a need for comparative testing of their relative performance in practical contexts. Very little work of this type has been done however for a number of reasons: lack of independent indicators of power in actual voting bodies with which to compare them, difficulties in obtaining consistent data on a voting body over time with sufficient variation in the disposition of votes among members of actual legislatures and the lack of independent criteria against which the results of the indices may be judged. It has also been hampered to some extent by lack of easily available algorithms for computing the indices in large games.
This paper assesses the indices against a set of reasonable criteria in terms of shareholder voting power and the control of the corporation in a large cross section of British companies. Each company is a separate voting body and there is much variation in the distribution of voting shares among them. Moreover reasonable criteria exist against which to judge the indices. New algorithms for the Shapley-Shubik and Banzhaf indices are applied to detailed data on beneficial ownership of 444 large UK companies without majority control. Because some of the data is missing, both finite and oceanic games of shareholder voting are studied to overcome this problem.
The results, judged against these criteria, are unfavorable to the Shapley-Shubik index and suggest that the Banzhaf index much better reflects the variations in the power of shareholders between companies as the weights of shareholder blocks vary.

Keywords: Power indices; Shapley-Shubik index; Banzhaf index; oceanic games; co-operative game theory.

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WORKING PAPER NO 562
"Asset Ownership and Investment Incentives Revisited"
David de Meza and Ben Lockwood

Previous work on the property rights theory of the firm suggests that in the presence of outside options, asset ownership may demotivate managers. This paper shows that this conclusion relies on the assumption that a manager’s outside option only depends on her own investment. In many cases, an asset owner has the opportunity to continue with a project even if the team breaks up. The investments of non-owners may then be devalued, but are typically not wholly lost to the owner. This weakens the bargaining power of the non-owner. So, in the presence of cross effects, outside options do not necessarily overturn the property of the original Grossman-Hart-Moore model that an asset transfer may motivate the gainer and demotivate the loser.

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WORKING PAPER NO 561
"Inconsequential Arbitrage"
Frank H Page Jr, Myrna H. Wooders and Paulo K.Monteiro

We introduce the concept of inconsequential arbitrage and, in the context of a model allowing short-sales and half-lines in indifference surfaces, we prove that inconsequential arbitrage is sufficient for existence of equilibrium. With a slightly stronger condition of local nonsatiation than required for existence of equilibrium and with a mild uniformity condition on arbitrage opportunities, we show that the existence of a pareto-optimal allocation implies inconsequential arbitrage, implying that inconsequential arbitrage is necessary and sufficient for existence of an equilibrium. By further strengthening our nonsatiation condition, we obtain a second welfare theorem for exchange economies allowing short sales. To further understand inconsequential arbitrage, we introduce the notion of exhaustible arbitrage and we show that any inconsequential arbitrage is exhaustible. We also compare inconsequential arbitrage to the conditions limiting arbitrage of hart (1974) and Werner (1987), as well as to the conditions recently introduced by Dan, Le Van, and Magnien (1999) and Allouch (1999). For example, we show that the condition of Hart (translated to a general equilibrium setting) and the condition of Werner are equivalent. We then show that the Hart/Werner conditions imply inconsequential arbitrage. To highlight the extent to which we extend Hart and Werner, we construct an example of an exchange economy in which inconsequential arbitrage holds (and is necessary and sufficient for existence), while the Hart/Werner conditions do not hold. Finally, under additional conditions on the model, we show that if agents' indifference surfaces contain no half lines, then inconsequential arbitrage, the Hart/Werner conditions, the Dana, Le Van, and Magnien condition, and Allouch's conditions are all equivalent - and in turn, equivalent to the existence of equilibrium.

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WORKING PAPER NO 560
"Commuting in Great Britain in the 1990s"
Andrew Benito and Andrew J. Oswald

The paper studies commuting in Great Britain in the 1990s. The average one-way commute to work is now 38 minutes in London, 33 minutes in the south-east, and 21 minutes in the rest of the country. There are three other findings. First, commuting times are especially long among the highly educated, among home-owners, and among those who work in large plants and offices. In Britain, people with university degrees spend 50% more time travelling to work than those with low qualifications. Private renters do much less commuting than owner-occupiers. Second, there has recently been a rise in commuting times in the south-east and the capital. In our sample, full-time workers in London have lost 70 minutes per week of leisure time to commuting during the course of the 1990s. By contrast, outside the south-east of Britain, there has been no increase in commuting over this decade. In the south-east, 30% of workers now take at least 45 minutes to get to work. In the rest of the country, only 10% do. Third, after controlling for other factors and allowing for the endogeneity of the wage rate, there is a ceteris paribus inverse relationship between commuting hours and hourly pay.

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WORKING PAPER NO 559
"Housing Subisidies and Work Incentives in Great Britain"
Paul Bingley and Ian Walker

In Great Britain the move away from rented accommodation to owner occupation is leaving behind a large group of households with low incomes, wages and hours of work, and high housing costs, who are increasingly in receipt of welfare transfers. The disparity along all of these dimensions between renters and owner occupiers has continued to grow since the 1970’s.

The relationship between housing costs, wages and transfer programmes is complex and yet plays an important part in determining the incentive to work for individuals in low income or high housing cost households. While it is true that many individuals who are in these categories are out of the labour force (retired, sick and disabled), there are many who are not and whose incentive to seek work, or to work harder if already in work, could be modified by directly changing the rent levels they face or indirectly via changes to the structure of programmes designed to subsidise housing for the poor.

Here we estimate a static discrete choice labour supply model which allows for housing benefit programme participation. We use samples of 42491 married women and 13340 unmarried women drawn from Great Britain Family Resources Surveys 1994/5-97/8. We find that women are quite responsive to labour supply incentives, housing benefit income has similar incentive effects to earned income which suggests any "stigma" is small. Our analysis is complemented by simulating housing benefit and direct rent subsidy reforms.

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WORKING PAPER NO 558
"Issue Linkage and Issue Tie-in in Multilateral Negotiations"
Paola Conconi and Carlo Perroni

We describe a model of international, multidimensional policy coordination where countries can enter into selective and separate agreements with different partners along different policy dimensions. The model is used to examine the implications of negotiation tie-in - the requirement that agreements must span multiple dimensions of interaction - for the viability of multilateral cooperation when countries are linked by international trade flows and transboundary pollution. We show that, while in some cases negotiation tie-in has either no effect or can make multilateral cooperation more viable, in others a formal tie-in constraint
can make an otherwise viable joint multilateral agreement unstable.

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WORKING PAPER NO 557
"Staggered Wages and Output Dynamics under Disinflation"
Guido Ascari and Neil Rankin

We study the output costs of a reduction in monetary growth in a dynamic general equilibrium model with staggered wages. The money wage is fixed for two periods, and is chosen according to intertemporal optimisation. Agents have labour market monopoly power. We show that the introduction of microfoundations helps to resolve the puzzle raised by directly postulated models, namely that disinflation in staggered pricing models causes a boom. In our model disinflation, whether unanticipated or anticipated, unambiguously causes a slump.

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WORKING PAPER NO 556
"Cartel Stability and Product Differentiaiton: How Much Do the Size of the Cartel and the Size of the Industry Matter?"
Pedro Posada

This article analyses how the degree of product differentiation, the size of the cartel and the size of the industry affect the stability of a cartel formed by any number of firms in an industry of any size. The paper considers a supergame-theoretic model to define stability. After a non-loyal member leaves the cartel, two possible reactions by the remaining members of the cartel are assumed. The first one is a trigger strategy where the cartel dissolves after one member has left and the second is one where the cartel keeps acting as a cartel with one member less. The work also extends the analysis to investigate the stability of the remaining cartel. The results indicate that the relation between the cartel stability and the degree of differentiation of the products depends considerably on the size of the cartel, the size of the industry and the reaction of the loyal members of the cartel.

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WORKING PAPER NO 555
"Micro Evidence on Human Capital as the Engine of Growth"
Philip Trostel

This study examines a crucial assumption in much of the recent work on endogenous growth, namely, constant returns to scale in the production of human capital. A simple model is constructed to show that the returns to scale in human capital production can be inferred from the relationship between the wage rate and years of schooling. A large international micro dataset is used to estimate this relationship. The empirical evidence is decisive. There are decreasing returns to scale in human capital production; that is, the micro-level evidence is not supportive of endogenous growth driven by human capital accumulation.

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WORKING PAPER NO 554
"Education and Work"
Philip Trostel and Ian Walker

This paper examines the linkage between the incentives to work and to invest in human capital through education. These incentives are shown to be mutally reinforcing in a simple stylized model. This theoretical predicton is investigated empirically using three large micro datasets covering a broad set of countries. As one might expect, education and work are strongly (positively) correlated. This correlation has important implications for models of fiscal policy and economic growth. It also has important implications for the estimation of labor supply and the rate of return to education.

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WORKING PAPER NO 553
"Measuring Social Capital: Culture as an Explanation of Italy's Economic Dualism"
Francesco Galassi and Stephen Pudney

The paper presents a quantitative test of the oft-repeated view that Italy’s backward and poor South suffered from low “social capital”, a tendency to defect from co-operative engagements. The problem with such assertions is that they run the risk of taking as evidence in favour of the hypothesis the very observations that need to be explained. The analysis carried out in this work tries to break out of this impasse by analysing the conditions under which it was ex ante welfare-improving for farmers in early 20th century Italy to join an unlimited liability rural co-operative bank which would give them access to cheaper credit but also exposed them to the risk of their neighbours’ defection. These co-ops are a prime testing ground for the cultural explanation in that they spread rapidly throughout Northern Italy in the late 19th century, but never gained a similar popularity in the South. I estimate the switching function for these co-ops in different parts of the country to test whether Northern and Southern farmers faced significantly different choice sets when making the decision to join. Identical choice sets but differential responses would of course favour the cultural explanation of the South’s backwardness. The results suggest that for the same parameter values, the choice sets for North and South were different, though whether this difference was large enough to explain the full difference in responses is not completely clear.

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WORKING PAPER NO 552
"Output Risk in Tuscan Agriculture in the Late 19th and Early 20th Centuries"
Francesco Galassi and Stephen Pudney

We analyse output risk in Italian agriculture over the period 1870-1914. We use data on a set of 16 tenanted plots grouped into three farms comprising a single large estate. We estimate the degree of risk associated with each separate crop, with the portfolio of crops at the level of the plot, the farm and the estate. We highlight two particular features: the relatively high risk associated with tree crops (wine, oil and nuts); and the substantial scope for the landlord to reduce risk through crop diversification across plots. We discuss the implications of these for tenure contract theory.

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WORKING PAPER NO 551
"A Penny for your Thoughts: e-mail and the under-valuation of expert time"
Chris Willmore

The cost incurred by the sender of an e-mail does not reflect the costs to the recipient, leading to a larger number of messages being sent than is optimal for the general welfare. As a solution, we suggest a per-message e-mail tax on the sender similar to that proposed by Shiman (1996), with the addition of a recipient-determined 'contact list'. The recipient derives utility from messages sent by those on this list, and they are not to be taxed when sending messages to the recipient. We recommend that the tax revenue be divided between a regulating body and the e-mail recipient's Internet service provider.

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WORKING PAPER NO 550
"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, when payoffs are smooth, 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.

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