learning to believe in sunspots a number of authors have shown that competitive economies may possess sunspot equilibria that is rational expectations equilibria in which purely extrinsic uncertainty affects equilibrium prices and allocations 2 such results demonstrate that it does not require a lack of faith in the rationality of market participants to believe that competitive markets may be subject to purely speculative fluctuations driven solely by expectations 3 the mere existence of sunspot equilibria as solutions to a system of marketclearing conditions however might not be judged sufficient to indicate that competitive markets with rational participants could ever be subject to speculative instability the sunspot equilibria represent states of affairs in which agents act differently in the case of different realizations of the sunspot variable and it is rational for each agent to do so but it might be thought unlikely that the beliefs of all the participants in the market could ever come to be coordinated so as to bring about an equilibrium of that kind it is rational to believe that sunspots convey information about future states of affairs once the economy is in a sunspot equilibrium but why would rational agents ever begin to believe in such a thing so as to create the conditions under which the belief is rational in order to address such a question one must go beyond the mere statement of the conditions for equilibrium and discussion of what states of affairs satisfy them one must specify an explicit dynamic process according to which the beliefs of agents adjust when out of equilibrium any exercise of this kind is necessarily unsatisfactory as there is no univocal meaning for the postulate of rational behavior outside of an equilibrium it may well be the case that

hedge fund seeding via fees for seed swaps under idiosyncratic risk we develop a dynamic valuation model of the hedge fund seeding business by solving the consumption and portfolio choice problem for a risk averse manager who launches a hedge fund through a seeding vehicle this vehicle i e fees for seed swap specifies that a strategic partner seeder provides a critical amount of capital in exchange for participation in the funds revenue our results indicate that the new swap not only solves the serious problem of widespread financing constraints for new and early stage funds esfs managers but can be highly beneficial to both the manager and the seeder if structured properly

valuing thinly traded assets we model illiquidity as a restriction on the stopping rules investors can follow in selling assets and apply this framework to the valuation of thinly traded investments we find that discounts for illiquidity can be surprisingly large approaching 30 50 in some cases immediacy plays a unique role and is valued much more than ongoing liquidity we show that investors in illiquid enterprises have strong incentives to increase dividends and other cash payouts thereby introducing potential agency conflicts we also find that illiquidity and volatility are fundamentally entangled in their effects on asset prices this aspect may help explain why some assets are viewed as inherently more liquid than others and why liquidity concerns are heightened during financial crises this paper was accepted by gustavo manso finance

incomplete markets and the suboptimality of rational expectations abstract we study in this article a model of incomplete markets which can function under both rational and non rational expectations it is shown that because of the incompleteness of markets rational expectations equilibria can be pareto dominated by equilibria with non rational expectations

learning convergence and stability with multiple rational expectations equilibria abstract for a linear model with multiple rational expectations equilibria ree we discuss the set of possible ree solutions include i locally unique minimal state variable solutions taking an ar 1 form and ii continua of solutions which may depend on sunspots we analyze the convergence of econometric learning to the different ree there exist cases with more than one stable ar 1 solution it is also possible for a continuum of solutions to be stable but this property is not robust to overparametrization an application is developed and it is suggested that the exhibited phenomena may arise in applied macroeconomic models

stability of cycles and expectations the actual dynamics of an economy depends on how agents forecast the future at every date as a function of their information on the past while possibly learning the structure of their environment we show in the case of a one dimensional state variable that under mild conditions on expectations functions a given cycle with perfect foresight that is stable in the actual dynamics is stable in a fictitious backward perfect foresight dynamics we exhibit a restricted class of expectations functions for which the converse is true

a general framework for evaluating executive stock options abstract motivated by recent recommendations by both european and american accounting standards boards that executive stock options be expensed in firms statements we provide an analytical and flexible framework for their evaluation our approach takes into account the vesting period american style resetting and reloading provisions that are features of many option programs and also considers the trading restriction on executives we identify a recursive structure in the stream of options that are granted to the executive over the course of her employment by exploiting this we are able to obtain a near explicit formula for the option value this enables us to discuss the joint effects of the different features on the exercising strategies and firms granting cost especially we highlight some significant interactions among these features

real options with constant relative risk aversion real options problems have recently attracted much attention worldwide one such problem is how to deal with claims on non traded assets often there is another traded asset which is correlated to the non traded asset and this traded asset is used as a proxy for hedging purposes we introduce a second non traded log brownian asset into the well known merton investment model with power law utility the investor has a claim on units of the non traded asset and the question is how to price and hedge this random payoff the presence of the second brownian motion means that we are in the situation of incomplete markets we propose an approximation to the solution for the optimal reservation price and hedge which is accurate when the position is small in comparison to wealth the resulting loss when a suboptimal proxy strategy is followed is shown to be approximately quadratic in 1

paper millionaires how valuable is stock to a stockholder who is restricted from selling it abstract many firms have stockholders who face severe restrictions on their ability to sell their shares and diversify the risk of their personal wealth we study the costs of these liquidity restrictions on stockholders using a continuous time portfolio choice framework these restrictions have major effects on the optimal investment and consumption strategies because of the need to hedge the illiquid stock position and smooth consumption in anticipation of the eventual lapse of the restrictions these results provide a number of important insights about the effects of illiquidity in financial markets

portfolio claustrophobia asset pricing in markets with illiquid assets many classes of assets are illiquid or nonmarketable in that they cannot always be traded immediately thus a portfolio position in these becomes at least tem porarily irreversible we study the asset pricing implications of this type of illiquidity in an exchange economy with heterogeneous agents in this market one asset is always liquid the other asset can be traded initially but then not again until after a blackout period illiquidity has a dramatic effect agents abandon diversification and choose polarized portfolios instead the value of liquidity can represent a large portion of the equilibrium price of an asset jel g11 g12

returns to education and wage equations the paper shows why considering a number of education dependent covariates in a wage equation decreases the coefficient of education in that equation this result is illustrated empirically with a meta analysis for portugal the education coefficient decreases when covariates are used that can be considered post education decisions on the other hand it is independent of sample size tenure and whether hourly or monthly wages are used these results support the use of a simple specification of the mincer equation for the study of the total returns to education

sufficient conditions for the existence of sunspot equilibria abstract this paper reports on conditions on agents preferences and endowments sufficient to guarantee the existence of sunspot equilibria in a simple overlapping generations model of pure exchange sunspot equilibria are those in which uncertainty extrinsic to the economy operates through expectations to yield a fulfilled expectations competitive equilibrium in which the extrinsic randomness has real effects on prices and allocations the paper also provides necessary and sufficient conditions for these equilibria to have agents trading in a fixed stock of valued fiat money the condition derived can be interpreted as requiring that intertemporal income effects appropriately dominate substitution effects

liquidity maturity and the yields on u s treasury securities the efrect8 of aaaet liquidity on expected retuma for ts with infinite maturities toc ka are eumined for bonda treuury notes and bills with matched maturities of lellll than 6 months the yield to maturity ill higher on notes which have lower liquidity the yield di1ferential between notes and billa is a decreuing and convex function of the time to maturity the results provide a robult confirmation of the liquidity effect in auet pricing this paper studies empirically the effects of the liquidity of capital assets on their prices amihud and mendelson 1986 1989 proposed that liquidity affects asset prices because investors require a compensation for bearing transaction costs transaction costs paid whenever the asset is traded form a sequence of cash outflows the discounted value of this cost stream proxies for the value 1088 due to illiquidity which lowers the asset s value for any given cash flow that the asset generates 1 as a result the return on assets should be an increasing function of their illiquidity other things equal for stocks the illiquidity effect is expected to be strong because their transaction cost sequence is infinite amihud and mendelson 1986 1989 demonstrated that common stocks with lower liquidity yielded significantly higher average returns after controlling for risk and for other factors these results on the importance of liquidity in the pricing of stocks raise additional questions i does the liquidity effect depend on the specific controls used by amihud and mendelson 1986 1989 1 ii does illiquidity have a similarly strong effect on the pricing of bonds whose maturities are finite and iii if liquidity affects bond yields how is this effect related to the bond s time to maturity

information expected utility and portfolio choice we study the consumption investment problem of an agent with a constant relative risk aversion preference function who possesses noisy information about the future prospects of a stock we also solve for the value of information to the agent in closed form we find that information can significantly alter consumption and asset allocation decisions for reasonable parameter ranges information increases consumption in the vicinity of 25 information can shift the portfolio weight on a stock from 0 to around 70 thus de pending on the stock beta the weight on the market portfolio can be considerably reduced with information causing the appearance of underdiversification the model indicates that stock holdings of informed agents are positively related to wealth unrelated to systematic risk and negatively related to idiosyncratic uncertainty we also show that the dollar value of information to the agent depends linearly on his wealth and decreases with both the propensity to intermediate consumption and risk aversion

returns to education a further international update and implications this paper updates evidence on the returns to investment in education by adding estimates for new countries and refining existing estimates to bring the total number of country cases to over 60 the new cross country evidence confirms and reinforces earlier patterns namely that returns are highest for primary education the general curricula the education of women and countries with the lowest per capita income the findings have important implications for directing future investment in education which for efficiency and equity purposes should concentrate on these priority areas

are negative option prices possible the callable u s treasury bond puzzle market prices for callable treasury bonds often imply negative values for the implicit call option the author considers a variety of possible explanations for these negative values including the treasury s track record in calling bonds optimally tax related effects tax timing options and bond liquidity none of these factors accounts for the negative values although the costs of short selling may explain why these apparent arbitrage opportunities persist over time why these implicit call values become negative in the first place remains a puzzle copyright 1992 by university of chicago press

education and entrepreneurial success this paper estimates the effect of education on the success of entrepreneurial activity using survey data from malawi an instrument variable approach is used to address the endogeneity of education we find a significant and substantial effect of an added year of primary education on entrepreneurial profitability this is consistent with theoretical arguments that primary schooling provides a generalised form of competence that underpins the variety of skills an entrepreneur needs to succeed in business results are robust to non random selection into entrepreneurship

rule 144 volume limitations and the sale of restricted stock in the over the counter market this research analyses the impact of actual sales of unregistered securities in the over the counter market under rule 144 as promulgated by the securities and exchange commission sec our intent is to examine the volume limitation provision of the rule and to determine the degree to which sales under the rule adversely impact on secondary trading markets after describing rule 144 we develop data on actual transactions under the rule and the size of those sales relative to the legal ceilings and the trading volume typically observed for the securities in our sample our approach relies on the market model and the estimation of residuals on or about the actual sale date to determine if there are systematic effects across all firms and by specific subcategories of sellers which might reduce investor wealth in ways inconsistent with an efficient capital market and contrary to the interests of investors the results support the general view that there is no adverse impact on investor returns from actual sales of unregistered stock under rule 144 the enlightened self interest of selling shareholders with substantial holdings acts to curb any tendency for them to create any price pressure which could adversely impact trading markets it would appear that the sec was justified in relaxing the proposed rate of sale and volume limitation of rule 144 on average and net of transaction costs no potential investors have been made worse off and some sellers are made better off nonetheless the market disruption hypothesis implicit in the regulation of these sales cannot be completely dismissed for all vendor or issuer categories until the role of new information in these transactions is fully resolved preliminary findings suggest that sales in high technology issuers and sales by those who acquired their stock in private placements deserve more careful attention than this focused analysis of the disruptive impact of these sales has provided

stabilizing competitive business cycles abstract we study how stylized monetary proportional money transfers fiscal lump sum money transfers and public expenditure policies may eliminate endogenous deterministic cycles and stationary markov sunspot equilibria in a simple version of the overlapping generations model we also present new constructive methods for analyzing stationary markov sunspot equilibria in such a framework

adaptive learning and monetary exchange abstract this paper investigates three classic questions in monetary theory how can an intrinsically worthless asset such as fiat money maintain value as a medium of exchange what are the short run and long run effects of a change in the money supply what is the social cost of inflation i answer these questions using a microfounded model of monetary exchange that replaces the rational expectations assumption with an adaptive learning rule first i show that monetary exchange is a robust arrangement in the sense that agents are able to learn the stationary monetary equilibrium while the non monetary equilibrium is unstable under learning second an unanticipated monetary injection has real effects in the short run because learning the value of money takes time in the long run agents successfully learn the value of money hence money is neutral third under a constant money growth policy an increase in the growth rate of money increases output in the short run producing a short run phillips curve a ten percent increase in the money growth rate has a social cost of 0 41 percent of output per year alternatively a ten percent decrease in the money growth rate has a social benefit of 0 37 percent of output per year

risk aversion indivisible timing options and gambling in this paper we model the behavior of a risk averse agent who seeks to maximize expected utility and who has an indivisible asset and a timing option over when to sell this asset our main contribution is to show that contrary to intuition optimal behavior for such a risk averse agent can include risk increasing gambles for example a manager with a choice over when to disinvest from a project a private homeowner with a property to sell or an employee with a grant of american style stock options may be better off taking positions in other assets with zero sharpe ratio that are uncorrelated with the underlying project house or stock price risk the results have wider implications for the modeling and interpretation of portfolio optimization problems involving american style timing decisions

how does illiquidity affect delegated portfolio choice in response to how they are compensated mutual fund managers who are underperforming by mid year are likely to increase the risk of their portfolios toward the year end we argue that an increase in the liquidity of the stocks that managers use to shift risk can lead to an increase in the size of their risky bets this in turn hurts fund investors by increasing the costs of misaligned incentives associated with delegated portfolio management we provide both theoretical and empirical results that are consistent with this argument we use decimalization as an exogenous shock to liquidity to identify causal effects

rationalizable strategic behavior the notion of equilibrium proposed by nash 19 has come to play a dominant role in economic applications of noncooperative games while analyses of nash equilibria have unquestionably contributed to our understanding of economic behavior it would be unreasonably optimistic to maintain that nash solved the problem of noncooperative strategic choice there is a small literature beginning with ellsberg 6 and a much larger oral tradition which argues that nash behavior is neither a necessary consequence of rationality nor a reasonable empirical proposition in this paper i take the view that although there may be various reasons why an agent might select a nash strategy the notion of an equilibrium has little intrinsic appeal within a strategic context when an agent reaches a decision in ignorance of the strategies adopted by other players rationality consists of making a choice which is justifiable by an internally consistent system of beliefs rather than one which is optimal post hoc this point of view is not original indeed most serious justifications of the nash hypothesis embrace such an approach arguing that agents will expect the game to yield a nash outcome and consequently will choose their equilibrium strategies nevertheless when we think in terms of maximizing utility subject to expectations rather than realizations it becomes clear that the nash hypothesis far from being a consequence of rationality arises from certain restrictions on agents expectations which may or may not be plausible depending upon the game being played we are then quite naturally led to ask are there any restrictions of individuals expectations and hence choices which are required by rationality alone rather than by subjective plausibility this paper is concerned with defining justifying characterizing and refining a criterion for rational strategic choice which i label rationalizability

on the complexities of complex economic dynamics complex economic nonlinear dynamics endogenously do not converge to a point a limit cycle or an explosion their study developed out of earlier studies of cybernetic catastrophic and chaotic systems complexity analysis stresses interactions among dispersed agents without a global controller tangled hierarchies adaptive learning evolution and novelty and out of equilibrium dynamics complexity methods include interacting particle systems self organized criticality and evolutionary game theory to simulate artificial stock markets and other phenomena theoretically bounded rationality replaces rational expectations complexity theory influences empirical methods and restructures policy debates

an exploration of the eductive justifications of the rational expectations hypothesis this paper examines justifications of the rational expectations hypothesis that rely on the analysis of the agents mental forecasting educing activity which involves forecasting the forecasts of others etc the corresponding concept of eductive learning stability based on the game theoretical concept of rationalizability is primarily used within the classical muth model conditions for coordination of beliefs are interpreted and discussed they are robust to the introduction of noise more generally eductive stability fits economic intuition on coordination stability increases when the industry product differentiation increases and when decisions are sequential and observable copyright 1992 by american economic association

rationalizable strategic behavior and the problem of perfection this paper explores the fundamental problem of what can be inferred about the outcome of a noncooperative game from the rationality of the players and from the information they possess the answer is summarized in a solution concept called rationalizability strategy profiles that are rationalizable are not always nash equilibria conversely the information in an extensive form game often allows certain unreasonable nash equilibria to be excluded from the set of rationalizable profiles a stronger form of rationalizability is appropriate if players are known to be not merely rational but also cautious what constitutes rational behavior in a noncooperative strategic situation this paper explores the issue in the context of a wide class of finite noncooperative games in extensive form the traditional answer relies heavily upon the idea of nash equilibrium nash 17 the position developed here however is that as a criterion for judging a profile of strategies to be reasonable choices for players in a game the nash equilibrium property is neither necessary nor sufficient some nash equilibria are intuitively unreasonable and not all reasonable strategy profiles are nash equilibria the fact that a nash equilibrium can be intuitively unattractive is well known the equilibrium may be imperfect introduced into the literature by selten 20 the idea of imperfect equilibria has prompted game theorists to search for a narrower definition of equilibrium while this research some of which will be discussed here has been extremely instructive it remains inconclusive theorists often agree about what should happen in particular games but to capture this intuition in a general solution concept has proved to be very difficult if this paper is successful it should make some progress in that direction the other side of the coin has received less scrutiny can all non nash profiles really be excluded on logical grounds i believe not the standard justifications for considering only nash profiles are circular in nature or make gratuitous assumptions about players decision criteria or beliefs the following discussion of these points is extremely brief due to space constraints more detailed arguments may be found in pearce 18

convergence of least squares learning in environments with hidden state variables and private information we study the convergence of recursive least squares learning schemes in economic environments in which there is private information the presence of private information leads to the presence of hidden state variables from the viewpoint of particular agents by applying theorems of ljung we extend some of our earlier results to characterize conditions under which a system governed by leastsquares learning will eventually converge to a rational expectations equilibrium we apply insights from the learning results to formulate and compute the equilibrium of a version of townsend s model

on endogenous competitive business cycles the belief that the long run equilibrium of a competitive monetary economy that does not experience any exogeneous shocks whether originating from the external environment or from policy should be modelled as a state that is stationary or perhaps growing at a constant rate seems to be deeply rooted in the mind of some economists

market valuation of employee stock options this study investigates whether investors incorporate the value of a firm s outstanding employee stock options into its stock price i estimate the outstanding options value for a sample of firms for which outstanding fixed options exceed 5 of outstanding common shares in 1988 i find a negative correlation between the value of outstanding options and a firm s share price the correlation is stronger i for the option s intrinsic value than for the option s time value ii for options that are later in their vesting stage than earlier in their vesting stage and iii for large firms than for small firms in addition the fasb s method for calculating compensation expense has no explanatory power in the presence of this paper s calculation of the options value

how much can marketability affect security values how marketability affects security prices is one of the most important issues in finance we derive a simple analytical upper bound on the value of marketability using option pricing theory we show that discounts for lack of marketability can potentially be large even when the illiquidity period is very short this analysis also provides a benchmark for assessing the potential costs of exchange rules and regulatory requirements restricting the ability of investors to trade when desired furthermore these results provide new insights into the relation between discounts for lack of marketability and the length of the marketability restriction

the challenge of monetary theory departing from custom i want to address a problem that needs to be solved rather than one that has been solved i do not have much to contribute to its solution but i believe that the problem is important and want to focus attention on it in general terms the problem is to find appropriate conceptual foundations for monetary economics i believe that we do not as yet have a suitable theoretical framework for studying the functioning of a monetary system the main obstacle to the development of such a framework is our habit of thinking in terms of frictionless organized i e walrasian markets the problem is partly a problem of language the central concepts of economics demand supply and price are concepts that presuppose a system of centralized walrasian markets we are used to thinking in terms of these concepts and we tend to apply them rather automatically to the market for money frequently without realizing that the market for money must be a rather non walrasian market if indeed it can be called a market at all more or less all the models of monetary economics that are being used in practice proceed in this way using artifical adaptations of the walrasian centralized markets model to accommodate money without actually giving an account of what the role of money in the economy is the problem is one of pure economic theory however it bears on many important questions of applied economics and economic policy to study the relation between money income and prices we need a framework which gives a satisfactory account of the relation between the monetary system and the price mechanism to study the effects of central bank open market

the exercise and valuation of executive stock options abstract in theory hedging restrictions faced by managers make executive stock options more difficult to value than ordinary options because they imply that exercise policies of managers depend on their preferences and endowments using data on option exercises from 40 firms this paper shows that a simple extension of the ordinary american option model which introduces random exogenous exercise and forfeiture predicts actual exercise times and payoffs just as well as an elaborate utility maximizing model that explicitly accounts for the nontransferability of options the simpler model could therefore be more useful than the preference based model for valuing executive options in practice

lifetime investment and consumption using a defined contribution pension scheme during the accumulation phase of a defined contribution pension scheme a scheme member invests part of their stochastic income in a portfolio of a stock and a bond in order to build up sufficient funds for retirement it is assumed that the remainder of their salary pre retirement is consumed an annuity is purchased at retirement and the stock allocation and consumption pre retirement maximise the total expected lifetime consumption using a cara utility function perfect correlation between the scheme member s income and the stock price leads to analytical expressions for the controls for a general income model if the correlation is imperfect then analytical controls are found for two particular stochastic income models

why are the returns to schooling higher for women than for men many studies have found that the impact of schooling on earnings is greater for females than for males despite the fact that females tend to earn less both absolutely and controlling for personal characteristics this study investigates possible reasons for this effect using data from the national longitudinal survey of youth 1979 one explanation is that education appears to have a double effect on the earnings of women it increases their skills and productivity as it does with men and in addition it appears to reduce the gap in male and female earnings attributable to factors such as discrimination tastes and circumstances the latter appear to account for about half of the differential in the returns to schooling

asset markets with insider trading disclosure rule and reselling constraint an experimental analysis abstract we investigate the impact of compulsory insider trading disclosure and its combination with a mandatory holding rule on price predictability and asset mispricing we modify the dynamic price adjustment model to account for insiders private information our results show that insiders produce weakly characterized price signals that induce a less than proportional price adjustment to the changes in the dividend value in both markets with disclosure rule and holding requirement in comparison with unregulated markets a shift in insiders strategies from information motivated to liquidity motivated trading appears to fuel the impairment of price predictability in regulated markets the exacerbation of asset mispricing in markets with holding restriction is characterized by a growth in the speculative transactions and loss making trading proposals

optimal asset allocation with fixed term securities we investigate the optimal asset allocation of an investor who can invest in a fixed term security that is only traded at time 0 using a generalized martingale approach we solve the investor s optimal portfolio problem determine the optimal allocation to fixed term securities and provide a representation of trading strategies in terms of a liquidity related derivative we apply our approach to two benchmark scenarios fixed term fixed rate bank deposits and unspanned closed end securities that can only be traded at time 0 we show that both can be key parts of the investor s optimal asset mix and we investigate the dependence of optimal allocations to fixed term investments implied liquidity premia and other characteristics on the underlying model parameters

optimal exercise prices for executive stock options although exercise prices for executive stock options can be set either below or above the grant date market price in practice virtually all options are granted at the money we offer an economic rationale for this apparent puzzle by showing that pay to performance incentives for risk averse undiversified executives are typically maximized by setting exercise prices at or near the grant date market price we provide an operationally useful alternative to black scholes 1973 for the purpose of both valuing executive stock options and measuring the incentives created by options our framework has implications not only for exercise price policies but also for indexed options option repricings exchanges of cash for stock based compensation and the design of bonus plans

pricing executive stock options under employment shocks abstract we obtain explicit expressions for the subjective objective and market value of perpetual executive stock options esos under exogenous employment shocks driven by an independent poisson process previously we obtain the executive s optimal exercise policy from the subjective valuation that is necessary for the objective one or fair value the perpetual eso is compared with the true finite maturity eso finding that the approximation is reasonably good to illustrate the usefulness of the objective valuation for accounting purposes we analyze the statistical distribution of the fair value when there is uncertainty about the employment shock intensity finally the role of esos in the design of executives incentives is also discussed

imperfect competition and the suboptimality of rational expectations abstract this paper investigates whether nonrational expectations can lead to outcomes which other things being equal pareto dominate rational expectations outcomes in order to carry out this investigation we construct an intertemporal micro based macroeconomic model with the two following strong points a it accommodates both rational and non rational expectations b both prices and quantities are determined by optimizing agents in particular prices are determined by explicit price setters using objective demand curves in this model the first theorem of welfare holds so that the walrasian equilibrium with rational expectations cannot be pareto dominated this conclusion is extremely fragile however and we show that as soon as some degree of imperfect competition is present rational expectations are suboptimal in the sense that they are dominated by irrational expectations

money and interest in a cash in advance economy the authors analyze an aggregative general equilibrium model in which the use of money is motivated by a cash in advance constraint applied to purchases of a subset of consumption goods the system is subject to both real and monetary shocks which are economy wide and observed by all they develop methods for verifying the existence of characterizing and explicitly calculating equilibria copyright 1987 by the econometric society

dynamic trading policies with price impact abstract in this paper we analyze the optimal policy for a risk averse agent who wants to sell a large block of shares of a risky security in the presence of price impact and transactions costs our framework reduces to the standard merton portfolio problem in the absence of any market frictions optimal liquidation results in revenue distributions which are substantially different from those generated by a naive strategy the main tradeoff involves choosing between revenue distributions which have high means versus those which have low variances furthermore our results suggest that the effective liquidity of a security depends on its return distribution and on the characteristics of the agent carrying out the trade as well as on the price impact function

liquidity taxes and short term treasury yields this article investigates differences in yields on identical treasury notes and bills and shows that they reflect differences in liquidity immediacy risk and taxes it proposes an empirical measure for differences in the liquidity risk of notes and bills the volatility ofthe underlying rate times the ratio of bills turnover to notes turnover because differential taxes affect sellers but not buyers of bills and notes the results reject free of informational problems the hypothesis that the notes demand curve is horizontal note bill yield differences also decrease with inventories of notes the less liquid asset

iterated elimination of dominated strategies in a bertrand edgeworth model we consider a bertrand edgeworth model of price competition firms have identical and constant marginal costs and finite exogeneous capacities firms choose prices our interest is in the set of those prices which are left over after the iterated elimination of dominated strategies we show that in two circumstances this set will be close to the set containing only the marketclearing walrasian price i if any n 1 out of n firms assumed to be in the market have sufficient capacity to cover demand at marginal costs ii if any given total capacity is owned by a very large number of very small firms

why governments should invest more to educate girls abstract women and men often receive the same percentage increase in their wage rates with advances in schooling because these returns decline with more schooling the marginal returns for women will tend to exceed those for men especially in countries where women are much less educated the health and schooling of children are more closely related to their mother s education than father s more educated women work more hours in the market labor force broadening the tax base and thereby potentially reducing tax distortions these three conditions it is argued justify the disproportionate allocation of public expenditures toward women s education

explicit solutions to an optimal portfolio choice problem with stochastic income abstract this paper solves in closed form the optimal portfolio choice problem for an investor with negative exponential utility over terminal wealth facing imperfectly hedgeable stochastic income the returns on income and the stock are imperfectly correlated so the market is incomplete we identify how an investor adjusts their merton rev econ statist 51 1969 247 portfolio of the stock and riskless asset via an intertemporal hedging demand in reaction to the stochastic income under general assumptions on the process governing the income the sign of the hedging demand is the opposite of the sign of the correlation between the income and stock the optimal portfolio in the stock is long stock if the risk premium is positive and correlation negative and short if these signs are reversed specializing in turn to normally distributed income and lognormally distributed income with or without mean reversion the effect of a number of parameters on the optimal portfolio in the stock can be studied when the risk premium on the stock and correlation have opposite signs the optimal portfolio decreases in magnitude with risk aversion unhedgeable variance of income and time and increases in magnitude with the magnitude of correlation under both the lognormal without mean reversion and normal models for income these relationships do not necessarily hold if the signs on the risk premium and correlation are the same in particular the optimal portfolio is not necessarily monotone in risk aversion violating well known static results in models without income when income follows a lognormal model with mean reversion more complicated behavior can occur for instance the optimal portfolio does not have to be monotonic in time regardless of the signs of correlation and the risk premium

the returns to education in africa some new estimates abstractwe estimate the rate of return to education for 12 african countries using recent data and a range of methodologies which we apply consistently across all countries our findings confirm that the return to basic education is the lowest 7 10 the returns to upper secondary and tertiary education are similar to one another 25 30 accounting for the risk of joblessness increases these rates of return particularly for basic education and for women at tertiary level our results at the country level suggest that great care should be taken in choosing the appropriate methodology to estimate rates of return

adaptive expectations coordination in an economy with heterogeneous agents abstract in this paper we study the problem of expectations coordination on the stationary state in a one dimensional economy with heterogeneous agents we consider a constant gain adaptive learning rule we allow for heterogeneity of the fundamentals and of the constant gain parameters we show that these two sources of heterogeneity may create difficulties to the process of coordination

transaction costs and asset prices a dynamic equilibrium model in this article we study the effects of transaction costs on asset prices we assume an overlapping generations economy with a riskless liquid bond and many risky stocks carrying proportional transaction costs we obtain stock prices and turnover in closed form surprisingly a stock s price may increase in transaction costs and a more frequently traded stock may be less adversely affected by an increase in transaction costs calculations based on the marginal investor overestimate the effects of transaction costs for realistic parameter values transaction costs have very small effects on stock prices but large effects on turnover

the price of options illiquidity the purpose of this paper is to examine the effect of illiquidity on the value of currency options we use a unique dataset that allows us to explore this issue in special circumstances where options are issued by a central bank and are not traded prior to maturity the value of these options is compared to similar options traded on the exchange we find that the nontradable options are priced about 21 percent less than the exchange traded options this gap cannot be arbitraged away due to transactions costs and the risk that the exchange rate will change during the bidding process

rationalizability learning and equilibrium in games with strategic complementarities we study a rich class of noncooperative games that includes models of oligopoly competition macroeconomic coordination failures arms races bank runs technology adoption and diffusion r d competition pretrial bargaining coordination in teams and many others for all these games the sets of pure strategy nash equilibria correlated equilibria and rationalizable strategies have identical bounds also for a class of models of dynamic adaptive choice behavior that encompasses both best response dynamics and bayesian learning the players choices lie eventually within the same bounds these bounds are shown to vary monotonically with certain exogenous parameters we study the class of noncooperative supermodular games introduced by topkis 1979 and further analyzed by vives 1985 1989 who also pointed out the importance of these games in industrial economics supermodular games are games in which each player s strategy set is partially ordered the marginal returns to increasing one s strategy rise with increases in the competitors strategies so that the game exhibits strategic complementarity 2 and if a player s strategies are multidimensional marginal returns to any one com ponent of the player s strategy rise with increases in the other components this class turns out to encompass many of the most important economic applications of noncooperative game theory in macroeconomics diamond s 1982 search model and bryant s 1983 1984 rational expectations models can be represented as supermodular games in each of these models more activity by some members of the economy raises the returns to increased levels of activity by others in oligopoly theory some models of bertrand oligopoly with differentiated products qualify as supermodu lar games in these games when a firm s competitors raise their prices the marginal profitability of the firm s own price increase rises a similar structure is present in games of new technology adoption such as those of dybvig and spatt 1983 farrell and saloner 1986 and katz and shapiro 1986 when more users hook into a communication system or more manufacturers adopt an interface standard the marginal return to others of doing the same often rises similarly in some specifications of the bank runs model introduced by diamond and dybvig 1983 when more depositors withdraw their funds from a bank it is more worthwhile for other depositors to do the same in the warrant exercise

diversification and its discontents idiosyncratic and entrepreneurial risk in the quest for social status social status concerns influence investors decisions by driving a wedge in attitudes toward aggregate and idiosyncratic risks i model such concerns by emphasizing the desire to get ahead of the joneses which implies that aversion to idiosyncratic risk is lower than aversion to aggregate risk the model predicts that investors hold concentrated portfolios in equilibrium which helps rationalize the small premium for undiversified entrepreneurial risk in the model status concerns are more important for wealthier households consequently these households own a disproportionate share of risky assets particularly private equity and experience greater volatility of consumption consistent with empirical evidence diversification and risk sharing are fundamental principles of modern finance and macroeconomics however empirical evidence suggests that household portfolios are poorly diversified with many people reporting substantial holdings of a single stock for the wealthiest households large shares in closely held businesses constitute a particularly important source of risk e g heaton and lucas 2000a it is not surprising that entrepreneurs bear substantial undiversified risk since it is important for mitigating moral hazard and or adverse selection problems yet from a standpoint of portfolio theory entrepreneurship does not appear to be well compensated implying that many investors are willing to take poorly rewarded risks despite the availability of superior investment opportunities such as public equity that earns a large risk premium e g moskowitz and vissing j0rgensen 2002 hall and woodward 2007

expectational stability and the multiple equilibria problem in linear rational expectations models linear models involving expectations of future endogenous variables generally have multiple rational expectations equilibria this paper investigates the stability of solutions in the disequilibrium sense of whether given a small deviation of expectations functions from some rational expectations equilibrium the system returns to that solution under a natural revision rule weak and strong local stability are distinguished stability conditions are calculated for a simple general linear model and applied to two macroeconomic examples in some cases there is a unique stable equilibrium in other cases a continuum of equilibria forms a weakly but not strongly stable class

does option compensation increase managerial risk appetite this paper solves the dynamic investment problem of a risk averse manager compensated with a call option on the assets he controls under the manager s optimal policy the option ends up either deep in or deep out of the money as the asset value goes to zero volatility goes to infinity however the option compensation does not strictly lead to greater risk seeking sometimes the manager s optimal volatility is less with the option than it would be if he were trading his own account furthermore giving the manager more options causes him to reduce volatility managers with convex compensation schemes play an important role in financial markets this paper solves for the optimal dynamic investment policy for a risk averse manager paid with a call option on the assets he controls the paper focuses on how the option compensation impacts the manager s appetite for risk when he cannot hedge the option position on one hand the convexity of the option makes the manager shun payoffs that are likely to be near the money under the optimal policy the manager either significantly outperforms his benchmark or else incurs severe losses furthermore in examples of optimal trading strategies asset volatility goes to infinity as asset value goes to zero yet option compensation does not strictly lead to greater risk seeking as asset value grows large or if the evaluation date is far away the manager moderates asset risk for example if the manager has constant relative risk aversion crra asset volatility converges to the merton constant as asset value goes to infinity in some situations the manager actually chooses a lower asset volatility than he would if he were investing on his own because the leverage inherent in his option magnifies his exposure to the asset volatility in addition with all constant or decreasing absolute risk averse utility functions from the hyperbolic absolute risk averse hara class giving the manager more options causes him to reduce asset volatility in the crra case for example the manager targets a fixed volatility for his personal

returns to investment in education a global update the author updates compilations of rate of return estimates to investment in education published since 1985 and discusses methodological issues surrounding those estimates some key patterns among the three main levels of education primary education continues to exhibit the highest social profitability in all world regions private returns are considerably higher than social returns because of the public subsidization of education the degree of public subsidy increases with the level of education which is regressive social and private returns at all levels generally decline by the level of a country s per capita income overall the returns to female education are higher than those to male education but at individual levels of education the pattern is more mixed the returns to the academic secondary school track are higher than the vocational track since unit cost of vocational education is much higher and the returns for those who work in the private competitive sector of the economy are higher than in the public noncompetitive sector and the returns in the self employment unregulated sector of the economy are higher than in the dependent employment sector controversies in the literature are discussed in the light of the new evidence the undisputable and universal positive correlation between education and earnings can be interpreted in many ways the causation issue on whether education really affects earnings can be answered only with experimental data generated by randomly exposing different people to various amounts of education given the fact that moral and pragmatic considerations prevent the generation of such pure data researchers have to make do with indirect inferences or natural experiments some have been attempted the author looks at the research on overeducation or surplus schooling the conclusions reinforce earlier patterns they confirm that primary education continues to be the number one investment priority in developing countries they also show that educating females is marginally more profitable than educating males that the academic secondary school curriculum is a better investment than the technical vocational tract and that the returns to education obey the same rules as investment in conventional capital that is they decline as investment is expanded