on universal currency hedges this paper identifies five universal currency hedge ratio uhr definitions these are hedge positions in foreign bonds stated as a fraction of national or global equity portfolios that are the same for all investors regardless of nationality the first three involve the total demand for foreign bonds and depend on equities not being held for hedging purposes the last two are associated with variance minimizing regression hedges these hold in general but are designed exclusively for hedging other traded asset positions jensen s inequality makes the choice of measurement currency irrelevant and makes the hrs universal without affecting their values

commodity liquidity measurement and transaction costs we examine the performance of liquidity proxies in commodities the amihud measure has the largest correlation with liquidity benchmarks amivest and effective tick measures also perform well these proxies are useful for studies of commodity liquidity over a long time period and those that lack access to high frequency data we use various aspects of transaction costs such as spread depth immediacy and resiliency to give insight into the costs of different execution approaches transaction costs increase with volatility and exhibit mean reversion splitting trades over one hour can reduce trading costs by two thirds compared to an immediate execution the author 2011 published by oxford university press on behalf of the society for financial studies all rights reserved for permissions please e mail journals permissions oup com oxford university press

welfare estimation using aggregate and individual observation models a comparison using monte carlo techniques due to the weak behavioral foundations of aggregate demand models zonal travel cost models have been largely abandoned in favor of models based on individual observations however sample selection difficulties in individual observation models often require the use of distribution sensitive limited dependent variables estimators in this paper i use monte carlo simulations to investigate whether the bias from aggregation is worse than possible bias from these narrowly specified estimators somewhat surprisingly the results indicate that zonal models often outperform the individual observation models especially when using an aggregate model that incorporates intrazonal variance of the explanatory variables

conditional hedging and portfolio performance simple conditional currency hedging rules often increase risk adjusted portfolio returns and are thus of interest to investors several researchers have reported successful application of a forward hedge rule fhr in which one hedges whenever the foreign currency trades at a forward premium an alternative strategy a real interest rate hedge rule rir is based on hedging when the domestic real interest rate exceeds the foreign rate as an extension we propose a combination of these rules a real forward hedge rule rfhr we evaluate the performance of the rules for various currency stock and bond portfolios from the developed countries in tests of risk adjusted returns for 1976 1997 the rfhr significantly outperformed standard benchmarks and often beat the fhr and the rir moreover results of a simple dominance test for rolling 5 and 10 year periods suggest that the rfhr consistently improves portfolio performance for a u s investor

preference based strategic currency hedging this article considers the value to a given investor of volatility reduction through currency hedging relative to taking an unhedged position included is a decision framework to help international investors analyze how the potential risk reduction benefits of hedging interact with the investor s beliefs about the currency risk premium risk aversion and investment constraints to determine an optimal currency hedging strategy in our framework investors choose from nine hedging strategies each of which may be optimal under a specific set of assumptions the article concludes that a unitary hedge strategy is best for investors who do not forecast currency returns for those who make strategic currency return forecasts our aggregated results suggest an optimized hedge strategy using expected return inputs from an asset pricing model

a problem with observational equivalence disentangling the renter illusion hypothesis the renter illusion hypothesis argues that renters are more likely to support local public expenditures than homeowners because of a misperception about the actual costs and benefits they face numerous empirical studies have produced mixed results which are difficult to interpret because of the lack of micro foundations for the renter illusion hypothesis this paper helps fill that gap by introducing in a theoretical model the concept of renter illusion behaviour which can be seen as a rational behaviour in the presence of cognitive anomalies i e behavioural or bounded rationality and asymmetric information the resulting theoretical framework can be used to interpret and support a large share of micro and macro econometric findings in the previous empirical literature on renter illusion

cvar models with selective hedging for international asset allocation abstract we develop an integrated simulation and optimization framework for multicurrency asset allocation problems the simulation applies principal component analysis to generate scenarios depicting the discrete joint distributions of uncertain asset returns and exchange rates we then develop and implement models that optimize the conditional value at risk cvar metric the scenario based optimization models encompass alternative hedging strategies including selective hedging that incorporates currency hedging decisions within the portfolio selection problem thus the selective hedging model determines jointly the portfolio composition and the level of currency hedging for each market via forward exchanges we examine empirically the benefits of international diversification and the impact of hedging policies on risk return profiles of portfolios we assess the effectiveness of the scenario generation procedure and the stability of the model s results by means of out of sample simulations we also compare the performance of the cvar model against that of a model that employs the mean absolute deviation mad risk measure we investigate empirically the ex post performance of the models on international portfolios of stock and bond indices using historical market data selective hedging proves to be the superior hedging strategy that improves the risk return profile of portfolios regardless of the risk measurement metric although in static tests the mad and cvar models often select portfolios that trace practically indistinguishable ex ante risk return efficient frontiers in successive applications over several consecutive time periods the cvar model attains superior ex post results in terms of both higher returns and lower volatility

what floats your boat preference revelation from lotteries over complex goods abstract we examine a type of lottery used to distribute some publicly held resource access rights the lottery provides participants with the opportunity to choose among a set of simple gambles over multi attribute goods participant choices result in an endogenous distribution of success rates over gambles that reflects tradeoffs between the relative desirability of the available goods and the probability of winning when lottery winnings are multi attribute goods lottery outcomes provide sufficient information to estimate hedonic prices marginal utility and marginal rates of substitution among attributes we develop a model for characterizing preferences from this information set we apply our model to idaho s four rivers whitewater recreation lottery which allows applicants to apply for one permit among a large set of alternative river day combinations that provide varying river and weather characteristics this lottery structure shows promise as a foundation for economic experiments for preference revelation

were the returns from stocks and bonds of different countries really different in the 1980 s we analyzed the total equity returns of indexes from australia canada germany japan the uk and the us and total fixed income returns of indexes from all but australia excluded due to lack of data to see if the returns of stocks and bonds were statistically different across markets during the 1980s at the end of 1989 these countries represented over 87 of the market capitalization of the morgan stanley capital international msci world equity index and over 88 of the salomon brothers world bond index this study used monthly observations from january 1980 through december 1989 and examined returns based in local currency and hedged and unhedged us dollars we found that sample mean stock and bond returns during the 1980s were statistically indistinguishable across countries however because the sample variances were so large relative to the sample means it would have been difficult to detect differences in population means by any test we found evidence of variance heterogeneity which may be

the nested collective lottery that maximizes welfare under consumption interdependence we develop a generalized lottery mechanism in this article that allows people to choose to succeed separately while retaining both merits fairness and options to succeed jointly of the collective lottery developed by chen et al 2010 we use the rationing of hunting permits in the us and canada as examples to show the applicability of this generalized lottery mechanism

underpricing in public lotteries a critique of user pay and all pay tariffs i introduction a body of literature spanning from medical ethics to public economics has amassed regarding the nonmarket rationing of public resources a dominant focus has surrounded the merits and shortcomings of alternative rationing mechanisms as gauged by their effectiveness distributive justness and allocative efficiency these instruments include administrative criteria such as need merit or seniority based rules queues or waiting lines whereby access to the rationed good or service is determined by arrival times and lotteries whereby chance dictates the distribution of the good while nonmarket rationing in any case may lead to the misallocation of resources compared to rationing solely by price e g glaeser and luttmer 2003 empirical observation reveals that public agencies commonly distribute underpriced goods and services to individual consumers and firms the current study takes nonmarket rationing as given and investigates the properties of alternative lottery mechanisms the use of lot teries dates to biblical times boyce 1994 elster 1992 with modern examples including the military draft fienberg 1971 medical services cookson and dolan 2000 recreational privileges on public lands and waterways scrogin 2005 residential housing following hurricane katrina the white house office of the press secretary 2005 and public school admission and voucher programs berry cullen jacob and levitt 2006 from a design perspective lotteries are intriguing because they can take a variety of forms with each possessing unique incentive and revenue generating properties however given the purported inefficiencies of lottery rationing it is natural to question how they have sustained in allocative situations entailing public resources two explanations have emerged in the literature the first historic explanation is attributed to the fairness of the classic lottery mechanism in which the probability of being drawn is uniform and endogenous to the number of participants because entrants are equally likely to be drawn the mechanism is perceived as being nondiscriminatory empirical evidence presented in kemp and bolle 1999 supports this hypothesis in the rationing of some types of goods and services to individual consumers the fairness of lottery rationing is also consistent with the distributive objective of specific egalitarianism put forth by tobin 1970 and discussed later by elster 1992 whereby specific goods and services are allocated such that a greater degree of equality is attained relative to that of a competitive market while egalitarianism and efficiency would appear to be at odds che and gale 2007 demonstrated that lotteries can be more efficient than markets when individuals face binding wealth constraints in a similar vein wijkander 1988 demonstrated that social welfare can be increased by lottery rationing under certain conditions a second more objective explanation for the sustained use of lotteries is that public agencies may be legally constrained by price controls particularly when rationing to individuals and households taylor tsui and zhu 2003 acting as a self sustaining regulated monopolist the agency is confronted with selecting a rationing mechanism and a pricing policy that are both politically feasible and financially viable compared to need merit and seniority based allocation rules lotteries and queues are administratively simple and low cost to implement alternatively lotteries eschew the waiting time and coordination costs confronted by potential entrants under queuing however the initial distribution under lottery rationing may prove allocatively inefficient collectively the literature suggests that agency objectives may deviate from revenue maximization in distributing some types of scarce public resources with lotteries proving to be superior in some settings to alternative nonmarket rationing mechanisms

rational ignorance rational voter expectations and public policy a discrete informational foundation for fiscal illusion this paper demonstrates that rational ignorance properly defined allows the possibility that fiscal illusion affects policies in a democracy the implications of rational ignorance are examined in a setting where voters are assumed to completely understand the fiscal environment and make perfect use of any information that they possess in this setting it is demonstrated that ignorance may be rational manipulated and generate biased expectations over fiscal parameters

elections and aggregation interpreting econometric analyses of local governments this paper analyzes the provision of local government service under the assumption that fiscal policy is set by local officials in order to maximize the expected number of votes in the next election the model includes both the widely used median voter model and the average voter model as special cases further it is a convenient framework for empirical analyses numerical simulations indicate that the vote maximization model is capable of producing levels of government spending either greater or less than those predicted by the median voter model while exhibiting similar responses to changes in incomes grants prices etc thus the model captures the advantages of the median voter model without its objectionable features many avenues for further work remain i will mention briefly only a few of the most obvious the first is to make housing prices endogenously determined within the model in this way one could examine the role of both fiscal incentives capitalization and political incentives votes in the determination of optimal policies a second extension is to introduce explicitly the possibility of a mobile population and examine in the spirit of tiebout 1956 the effects of voting with your feet within the vote maximization framework the possibilities include both setting policies that de facto concede exit of some fraction of the current residents and or setting policies to attract new residents with particular characteristics another extension is to look at decisions over time despite widespread agreement upon the usefulness of the life cycle model of private consumption the median voter is essentially static it seems a minimal extension to include both government and private consumption in an intertemporal framework unfortunately the median voter may change over time making implementation of the median voter model problematic at best in practice intertemporal issues are important emphasizing the absence of an acceptable framework it is often suggested that elected officials will choose inappropriate intertemporal fiscal policies in response to the short run focus of the electoral process for example it appears plausible that officials will borrow in order to finance higher levels of spending and or lower taxes in the present because future residents are not present to vote against these policies the electoral process produces incorrect incentives in the same way this line of reasoning suggests that officials will undertake too little infrastructure investments because the benefits accrue to future residents one countervailing force is the effects of property capitalization to the extent that the local housing market correctly capitalizes future taxes and services into housing values current residents will be affected by inefficient policies and may use the electoral process to provide correct signals to officials there is another possibility as well to the extent that current officials recognize that inefficient current policies reduce the probability of future re election they have an incentive even in the absence of perfect capitalization to adopt intertemporally appropriate tax and spending policies intuitively the official must care about re election what if the particular individual chooses not to run for office again then to the extent that political parties or machines cause the individual to value the election of his successor i e to the extent that political legacies are important the adopted policies may satisfy the conditions for intertemporal efficiency the vote maximization approach provides a framework in which to analyze these issues lastly one could extend the model to situations in which officials care not only about election but also about the policies themselves this provides not only a different tradeoff between the tastes of the public and private sector but also a natural incentive for officials to seek re election

renter illusion fact or fiction the renter illusion hypothesis holds that renters underestimate their property tax burden and therefore support excessive levels of local expenditure a number of studies have reached results that are consistent with the hypothesis but so far empirical investigations have proceeded from the assumption that renter illusion is a fact and have investigated the implications of this fact no one has investigated renter illusion as such in other areas of fiscal illusion survey analyses of voter perceptions have yielded considerable insight into the validity of illusionary hypotheses this paper follows this method and investigates a representative sample of 1000 danish renters and home owners perception of the local property tax system the evidence raises doubts about the renter illusion hypothesis the survey findings are corroborated by an analysis of property taxation in danish municipalities

currency hedging for international portfolios this paper examines the benefits from currency hedging both for speculative and risk minimization motives in international bond and equity portfolios the riskreturn performances of globally diversified portfolios are compared with and without forward contracts over the period 1974 to 1990 inclusion of forward contracts results in statistically significant improvements in the performance of unconditional portfolios containing bonds conditional strategies are also implemented both in sample and out of sample and are shown to both significantly improve the risk return tradeoff of global portfolios and to outperform unconditional hedging strategies whether international portfolios should be hedged against currency risks is the subject of an active debate the theoretical side of the debate has been closely associated with two strands in the academic literature international asset pricing and optimal hedging in the futures markets in the international asset pricing model iapm of solnik 1974 optimal portfolios contain positions in forward contracts or equivalently foreign currency denominated bills these positions which can differ from the positions in foreign stocks have since been termed hedges black 1990 shows that under additional assumptions the hedge ratios should be identical for all investors regardless of their nationality universality and that investors should never fully hedge their foreign currency exposures similarly theoretical models from the futures literature produce demands for hedging instruments that contain both speculative and hedging components the empirical issue unanswered so far is whether adding forward contracts to international portfolios significantly improves the risk return profile of global investments empirical research has barely begun to respond to the challenges of theoretical models there exists little empirical evidence on either the relevance of black s universal hedge ratios or the optimality of hedge ratios less than one instead researchers have concentrated on the benefits of fully hedging exchange risk for example eun and resnick 1988 indicate that stock portfolios perform better when fully hedged but offer no statistical tests

exchange rate and foreign inflation risk premiums in global equity returns abstract we test for the pricing of exchange rate and foreign inflation risk in equities our tests are motivated by the empirical implications of the models of solnik 1974b solnik b 1974b the international pricing of risk an empirical investigation of the world capital market structure journal of finance 365 377 as revised by sercu 1980 sercu p 1980 a generalization of the international asset pricing model revue de l association francaise de finance 1 91 135 grauer et al 1976 grauer f litzenberger r stehle r 1976 sharing rules and equilibrium in an international capital market under uncertainty journal of financial economics 3 233 256 and adler and dumas 1983 adler m dumas b 1983 international portfolio choice and corporation finance a synthesis journal of finance 38 925 984 both exchange rate and foreign inflation risk factors can explain part of the within country cross sectional variation in returns our results have important implications for hedging exchange rate risk they also demonstrate that home bias at least in us equity portfolios cannot be the result of us investors efforts to hedge their domestic inflation

comparing welfare estimates of environmental quality changes from recreation demand models abstract this paper presents a procedure for examining the reliability of welfare estimates resulting from the estimation of multiple site recreation demand models a simulation approach is suggested where a utility function is combined with observations on individual and site characteristics to generate simulated data sets welfare measures associated with an improvement in site quality are calculated recreation demand models are estimated using the simulated data sets estimated welfare measures resulting from the recreation demand models are then compared to the true welfare measures calculated from the simulated data the procedure is demonstrated using two commonly employed recreation demand models

lottery rationed public access under alternative tariff arrangements changes in quality quantity and expected utility abstract a recent phenomenon is the emergence of quotas restricting individual access to public resources as regulators commonly ration access opportunities by lottery this paper extends the traditional open access destination choice framework for non market demand and welfare analysis conceptual results for one and two part tariff lotteries indicate that individuals may sustain welfare losses from improvements in quality or increases in the quota if aggregate demand is sufficiently responsive relative to individual utility nested random expected utility models reums are estimated with a panel dataset of individual choices of lottery rationed harvest rights for wild game empirical results indicate that the types and timing of tariff payments affect participation choices over rationed and open access alternatives and the benefits derived from changes in the quality and quantity of the lottery rationed access opportunities

allocation of goods by lottery i introduction many goods such as hunting permits oil drilling leases cellular telephone licenses and rights to fishing berths as well as some buds such as the military draft jury duty and who is to be thrown overboard on a sinking life raft are or have been allocated by lotteries in neo classical welfare economics the random distribution of property rights does not affect allocative efficiency as long as transferability is allowed and the transactions costs are non prohibitive lottery allocations however are generally not transferable thus lottery allocations are inefficient since the goods are not ultimately allocated to the users who value them the most a number of authors such as aubert 1959 fienberg 1971 eckhoff 1989 and elster 1989 36 122 have argued that lotteries are chosen as the allocative instrument because it represents a fair or just means of allocating the goods rawls 1971 374 and eckhoff 1989 have noted that where it is impractical to divide the goods equally among those who desire them a lottery serves to satisfy both the requirement that the process be fair and that the allocation problem be resolved relatively costlessly elster 1989 113 however notes that lotteries are not the only fair allocation mechanism for example he points out that in jewish ethics the problem of allocating an indivisible good such as life saving resources is resolved by denying it to everyone even economists would probably prefer a lottery to this resolution the fairness hypothesis has a rich history in the old testament lotteries are deemed a fair way of allocating goods such as the inheritance of land numbers 33 54 lotteries are also used to allocate bads in perhaps the most famous biblical example of use of lots jonah was chosen by lot to be sacrificed to appease god who had brought a storm that threatened to wreck the ship the story goes that the lot selected jonah because he was shirking his duties elsewhere and should not have even been on the vessel jonah 1 6 1 notice that fair here is taken to mean just given this theological foundation it is not surprising that the lottery has seen frequent use in legal history as well one of the most interesting cases occurred in swedish and finnish trials in the 17th and 18th centuries in cases where a man was murdered by a mob lotteries were used to allocate punishment since the law required an eye for an eye no more and no less eckhoff says that if it was impossible to ascertain which of them had dealt the mortal blow the courts determined that one of the responsible parties be sentenced to death and that the person be selected by lottery 1989 19 a similar use of lotteries occurs in military history to deal with cases of mass desertion in roman armies every tenth man was executed decimated and the remainder pardoned in more modern times the lottery has been used in u s law 2 first of course is the use of a lottery to decide who shall sit on a jury a connection between fairness and lotteries however has also appeared in the common law in an 1842 case u s v holmes which has been discussed by fienberg 1971 eckhoff 1989 and elster 1989 a ship sank in a heavy storm and the lone surviving life raft was in grave danger of sinking the crew threw overboard fourteen male passengers in an effort to save the rest when back in port after being rescued a crewman named holmes the only crew member who had not disappeared upon arrival to port was brought to trial for the deaths of the passengers the court ruled that the non essential members of the crew should have been thrown overboard before any passengers and if that was not sufficient then passengers should have been selected by lot which is the fairest mode elster 1989 65 the fact that a human life presumably a large cost was at stake ex post did not affect the decision 3 the environmental economics literature contains a number of references to the social preferences for and benefits of lottery allocations

property taxation and local public spending the renter effect the point of departure for this study is the pervasive finding that other things equal local jurisdictions tend to spend more on local services the larger the fraction of renters among their residents this paper seeks to determine the approximate magnitude of this renter effect by posing the question how much smaller would local public budgets be if all residents were home owners making use of two quite different approaches the paper finds a typical renter effect on local public expenditure on the order of ten percent this finding suggests that we might do well to reform the administration of the property tax so that changes in property tax liabilities on rental dwellings are directly and visibly transformed into changes of monthly rental payments

rationed access and welfare case of public resource lotteries pressures on public lands and waterways are resulting increasingly in the rationing of public access by lottery upon accounting for the uncertainties of random rationing discrete choice models lend themselves to analyzing participation in public resource lotteries and estimating welfare changes key to valuing lotteryrationed rights is accounting for changes in access probabilities that result from policy changes the empirical application models the discrete choices of more than 18 000 participants in a new mexico lottery system for elk harvest rights welfare estimates are obtained from simulated policy changes that affect individually and jointly the access probability and indirect utility

on optimal congestion abstract a number of classic papers conclude that if a congestible facility is the property of a profit maximizing entrepreneur he will impose a charge for use that induces the socially optimal level of use and congestion all these papers happen to deal with a special case in which that conclusion holds but it is not true in general in general the socially optimal level of use of a congestible facility is the level at which the marginal cost of providing the service is equal to the sum of the decreases in the users willingnesses to pay for a unit of service when the level of congestion is optimal and need not coincide with the level resulting from a profit maximizing charge this sum is derived from the integral under a fictitious demand curve constructed by imagining that the level of congestion is the same and optimal at all levels of the use charge

risk preferences over simple and compound public lotteries abstract lottery choice experiments with monetary payoffs have a long tradition for eliciting risk preferences this note demonstrates how risk preferences over multi attribute public lotteries may be estimated consistent with experimental findings results from simple and compound lottery choice models indicate significant differences in the degree of risk aversion between male and female applicants

applying regret theory to investment choices currency hedging decisions we apply regret theory an axiomatic behavioral theory to derive closed form solutions to optimal currency hedging choices investors experience regret of not having chosen the ex post optimal hedging decision hence investors anticipate their future experience of regret and incorporate it in their objective function we derive a model of financial decision making with two components of risk traditional risk volatility and regret risk we find results that are in sharp contrast with traditional expected utility loss aversion or disappointment aversion theories we discuss the empirical implications of our model and its ability to explain observed hedging behavior

equilibrium exchange rate hedging we assume a world like the one that gives the capital asset pricing model but with many goods and many countries we assume that investors in a given country have homothetic utility functions with the same weights and a currency that has a sure endof period value using a price index with those weights siegel s paradox derived from jensen s inequality makes investors want a positive amount of exchange risk when average risk tolerance is the same across countries every investor will hold the same mix of market risk through the world market portfolio of all assets and exchange risk in a diversified basket of foreign currencies in fact the ratio of exchange risk to market risk is equal to the average investor s risk tolerance we can write the ratio of exchange risk to market risk and the fraction of the market s exchange risk that investors hedge as depending on an average of world market risk premia an average of world market volatilities and an average of exchange rate volatilities the weights in these averages are the same as the weights of the different countries in the currency basket given these averages the ratio and the fraction hedged will not depend directly on exchange rate means or covariances in equilibrium we can use the ratio of exchange risk to market risk to measure average risk tolerance in this model risk tolerance is observable

property tax financing renting and the level of local expenditures the renter homeowner dichotomy has been systematically ignored in the local public goods literature the conventional justification for ignoring this dichotomy is that the only difference between the two groups of individuals is an innocuous accounting rule owners pay property taxes directly while renters pay property taxes indirectly via their rental payments to landlords 9 consequently when empirical studies after controlling for income and tastes find renter behavior that is discernably different from that of homeowners the explanation commonly offered is that renters are subject to fiscal illusion i e renters support higher levels of expenditures than homeowners because renters are unaware of the actual property tax burdens they bear 2 the fiscal illusion explanation despite its general acceptance is deficient on both empirical and theoretical grounds empirically the fiscal illusion hypothesis has not and probably cannot be directly tested 3 fiscal illusion is not so much a theory of renter behavior as it is a convenient ad hoc explanation for empirical results that are unexpected from the theory a revised theory of renter behavior cum illusion moreover would lack credibility to argue that even if time and again renters expectations are unfulfilled by experience i e they pay as much for increased services as owners when they expect not to yet renters consistently support higher levels of services would simply be untenable there are alternative possible explanations for renters behavior renters might have stronger preferences for public goods e g they may have a larger number of school age children renters

optimal pricing of public lotteries and comparison of competing mechanisms this article establishes optimal pricing rules for rationing indivisible units of rival and otherwise nonexcludable goods by lottery or a hybrid of a lottery and outright sale by posted price given the distributional objective of maximizing expected consumer surplus the solutions to unconstrained and constrained versions of the pricing problem may be expressed in classic inverse elasticity form with the lottery price appearing as an entry fee user fee or a combination of the two numerical analysis of a rich class of private value distributions indicates that sizable gains in expected consumer surplus can be realized over competitive pricing and zero pricing

lottery or waiting line auction abstract this paper studies the efficiencies of the two most widely used non price allocation mechanisms lotteries and waiting line auctions as our analysis suggests in addition to the fairness of the mechanism the use of lotteries in lieu of waiting line auctions can be also justified from an efficiency point of view in particular we show that the less dispersed consumers time valuations are the more efficient is a lottery relative to a waiting line auction in addition we identify four conditions under which a lottery dominates a waiting line auction in expected social surplus preserving furthermore the numerical simulations we conduct indicate that over a predominantly wide range of circumstances a lottery is more socially efficient than a waiting line auction as an allocative mechanism in the absence of a conventional price system