http://repub.eur.nl/res/aut/38/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/38841/ 2013-02-01T00:00:00Z http://repub.eur.nl/res/pub/37654/ 2012-09-19T00:00:00Z Financial institutions rely heavily on Value-at-Risk (VaR) as a risk measure, even though it is not globally subadditive. First, we theoretically show that the VaR portfolio measure is subadditive in the relevant tail region if asset returns are multivariate regularly varying, thus allowing for dependent returns. Second, we note that VaR estimated from historical simulations may lead to violations of subadditivity. This upset of the theoretical VaR subadditivity in the tail arises because the coarseness of the empirical distribution can affect the apparent fatness of the tails. Finally, we document a dramatic reduction in the frequency of subadditivity violations, by using semi-parametric extreme value techniques for VaR estimation instead of historical simulations. http://repub.eur.nl/res/pub/37658/ 2012-09-18T00:00:00Z Suppose the tails of the noise distribution in a regression exhibit power law behavior. Then the distribution of the OLS regression estimator inherits this tail behavior. This is relevant for regressions involving financial data. We derive explicit finite sample expressions for the tail probabilities of the distribution of the OLS estimator. These are useful for inference. Simulations for medium sized samples reveal considerable deviations of the coefficient estimates from their true values, in line with our theoretical formulas. The formulas provide a benchmark for judging the observed highly variable cross country estimates of the expectations coefficient in yield curve regressions. http://repub.eur.nl/res/pub/38974/ 2012-02-01T00:00:00Z It is widely agreed that when moving from fixed to floating exchange rates the increase in exchange rate volatility is not matched by an equivalent rise in the volatility of fundamentals. We argue and demonstrate that in inter-regime comparisons one has to account for 'missing variables' that compensate for the fundamental variables' volatility under fixed exchange rates. Previous studies have often used foreign exchange reserves, but without much success. We argue why reserves are not a reliable measure, while IMF credit support is. Our empirical analysis identifies IMF support as a crucial and significant compensating variable. http://repub.eur.nl/res/pub/32015/ 2012-01-01T00:00:00Z The Babylonian bridal auction, described by Herodotus, is regarded as one of the earliest uses of an auction in history. Yet, to our knowledge, the literature lacks a formal equilibrium analysis of this auction. We provide such an analysis for the two-player case with complete and incomplete information, and in so doing identify what we call the "Herodotus paradox". http://repub.eur.nl/res/pub/23653/ 2011-05-02T00:00:00Z Standard risk metrics tend to underestimate the true risks of hedge funds because of serial correlation in the reported returns. Getmansky et al. (2004) derive mean, variance, Sharpe ratio, and beta formulae adjusted for serial correlation. Following their lead, adjusted downside and global measures of individual and systemic risks are derived. We distinguish between normally and fat tailed distributed returns and show that adjustment is particularly relevant for downside risk measures in the case of fat tails. A hedge fund case study reveals that the unadjusted risk measures considerably underestimate the true extent of individual and systemic risks. http://repub.eur.nl/res/pub/20748/ 2010-09-01T00:00:00Z The dynamic properties of micro based stochastic macro models are often analyzed through a linearization around the associated deterministic steady state. Recent literature has investigated the error made by such a deterministic approximation. Complementary to this literature we investigate how the linearization affects the stochastic properties of the original model. We consider a simple real business cycle model with noisy learning by doing. The solution has a stationary distribution that exhibits moment failure and has an unbounded support. The linear approximation, however, yields a stationary distribution with possibly a bounded support and all moments finite. http://repub.eur.nl/res/pub/20754/ 2010-07-01T00:00:00Z The Babylonian bridal auction, described by Herodotus, is regarded as one of the earliest uses of an auction in history. Yet, to our knowledge, the literature lacks a formal equilibrium analysis of this auction. We provide such an analysis for the twoplayer case with complete and incompete information, and in so doing identify what we call the "Herodotus Paradox". http://repub.eur.nl/res/pub/20749/ 2010-06-01T00:00:00Z Actual portfolios contain fewer stocks than are implied by standard financial analysis that balances the costs of diversification against the benefits in terms of the standard deviation of the returns. Suppose a safety first investor cares about downside risk and recognizes the heavy tail feature of the asset return distributions. Then we show that optimal portfolio sizes are smaller than traditional correlation based diversification analysis suggests. http://repub.eur.nl/res/pub/18600/ 2010-05-01T00:00:00Z The dynamic properties of micro based stochastic macro models are often analyzed through a linearization around the associated deterministic steady state. Recent literature has investigated the errors made by such a deterministic approximation. Complementary to this literature we investigate how the linearization affects the stochastic properties of the original model. We consider a simple real business cycle model with noisy learning by doing. The solution has a stationary distribution that exhibits moment failure and has an unbounded support. The linear approximation, however, yields a stationary distribution with possibly a bounded support and all moments finite. http://repub.eur.nl/res/pub/19466/ 2010-03-01T00:00:00Z In affine models of foreign exchange rate returns, the nature of cross sectional interdependence in crisis periods hinges on the tail properties of the fundamentals' distribution. If the fundamentals exhibit thin tails like the normal distribution, the dependence vanishes asymptotically; while the dependence remains in the case of heavy tailed fundamentals as in case of the Student-t distribution. The linearity of the monetary model and heavy tail distributed fundamentals are sufficient conditions for fundamentals-based repeated joint currency crises. An estimator for the extreme exchange rate interdependencies is obtained and applied to Western, Asian and Latin American currency block data. http://repub.eur.nl/res/pub/17030/ 2009-08-31T00:00:00Z This paper presents a unified framework for characterizing symmetric equilibrium in simultaneous move, two-player, rank-order contests with complete information, in which each player's strategy generates direct or indirect affine "spillover" effects that depend on the rank-order of her decision variable. These effects arise in natural interpretations of a number of important economic environments, as well as in classic contests adapted to recent experimental and behavioral models where individuals exhibit inequality aversion or regret. We provide the closed-form solution for the symmetric Nash equilibria of this class of games, and show how it can be used to directly solve for equilibrium behavior in auctions, pricing games, tournaments, R&D races, models of litigation, and a host of other contests. http://repub.eur.nl/res/pub/16514/ 2009-04-01T00:00:00Z This paper presents a unified framework for characterizing symmetric equilibrium in simultaneous move, two-player, rank-order contests with complete information, in which each player's strategy generates direct or indirect affine "spillover" effects that depend on the rank-order of her decision variable. These effects arise in natural interpretations of a number of important economic environments, as well as in classic contests adapted to recent experimental and behavioral models where individuals exhibit inequality aversion or regret. We provide the closed-form solution for the symmetric Nash equilibria of this class of games, and show how it can be used to directly solve for equilibrium behavior in auctions, pricing games, tournaments, R&D races, models of ligitation, and a host of other contests. http://repub.eur.nl/res/pub/13676/ 2008-04-17T00:00:00Z Internet auctions attract numerous agents, but only a few become active bidders. A major difficulty in the structural analysis of internet auctions is that the number of potential bidders is unknown. Under the independent private value paradigm (IPVP)the valuations of the active bidders form a specific record sequence. This record sequence implies that if the number n of potential bidders is large, the number of active bidders is approximately 2 log n, explaining the relative inactivity. Empirical evidence for the 2 log n rule is provided. This evidence can also be interpreted as a weak test of the IPVP. http://repub.eur.nl/res/pub/14192/ 2008-01-01T00:00:00Z In an Internet auction, the expected payoff acts as a benchmark of the reasonableness of the price that is paid for the purchased item. Since the number of potential bidders is not observable, the expected payoff is difficult to estimate accurately. We approach this problem by considering the bids as a record and 2-record sequence of the potential bidder's valuation and using the Extreme Value Theory models to model the tail distribution of the bidder's valuation and study the expected payoff. Along the discussions for three different cases regarding the extreme value index γ, we show that the observed payoff does not act as an accurate estimation of the expected payoff in all the cases except a subclass of the case γ = 0. Within this subclass and under a second order condition, the observed payoff consistently converges to the expected payoff and the corresponding asymptotic normality holds. http://repub.eur.nl/res/pub/12362/ 2007-06-01T00:00:00Z Consider the portfolio problem of choosing the mix between stocks and bonds under a downside risk constraint. Typically stock returns exhibit fatter tails than bonds corresponding to their greater downside risk. Downside risk criteria like the safety first criterion therefore often select corner solutions in the sense of a bonds only portfolio. This is due to a focus on the asymptotically dominating first order Pareto term of the portfolio return distribution. We show that if second order terms are taken into account, a balanced solution emerges. The theory is applied to empirical examples from the literature. http://repub.eur.nl/res/pub/9513/ 2007-03-29T00:00:00Z The forward premium puzzle (FPP) is the negative correlation between the forward premium and the realized exchange rate return at maturities of a month and beyond. Some recent evidence shows that at maturities of multiple years and at the highest intra day frequency the correlation is positive and close to one. This paper contributes by using futures data instead of forwards to complete the maturity spectrum at the (multi-) day level. We find that the correlation only slowly turns negative as the number of days to maturity is increased to the monthly level. The typical shape of the premium correlation with regard to the forward maturity length appears to be V-shaped. http://repub.eur.nl/res/pub/8747/ 2007-02-14T00:00:00Z The stability of the financial system at higher loss levels is either characterized by asymptotic dependence or asymptotic independence. If asymptotically independent, the dependency, when present, eventually dies out completely at the more extreme quantiles, as in case of the multivariate normal distribution. Given that financial service firms' equity returns depend linearly on the risk drivers, we show that the marginals' distributions maximum domain of attraction determines the type of systemic (in-)stability. A scale for the amount of dependency at high loss lovels is designed. This permits a characterization of systemic risk inherent to different financial network structures. The theory also suggests the functional form of the economically relevant limit copulas. http://repub.eur.nl/res/pub/8072/ 2006-10-06T00:00:00Z Estimators of regression coefficients are known to be asymptotically normally distributed, provided certain regularity conditions are satisfied. In small samples and if the noise is not normally distributed, this can be a poor guide to the quality of the estimators. The paper addresses this problem for small and medium sized samples and heavy tailed noise. In particular, we assume that the noise is regularly varying, i.e., the tails of the noise distribution exhibit power law behavior. Then the distributions of the regression estimators are heavy tailed themselves. This is relavant for regressions involving financial data which are typically heavy tailed. In medium sized samples and with some dependency in the noise structure, the regression coefficient estimators can deviate considerably from their true values. The relevance of the theory is demonstrated for the highly variable cross country estimates of the expectations coefficient in yield curve regressions. http://repub.eur.nl/res/pub/8073/ 2006-10-01T00:00:00Z Exchange rate returns are fat-tailed distributed. We provide evidence that the apparent non-normality derives from the behavior of macroeconomic fundamentals. Economic and probabilistic arguments are offered for such a relationship. Empirical support is given by testing against normality and through investigating the tail shapes of the fundamentals' distributions. The currently available data sets on floating exchange rates permit a clearer picture than the relatively short spans with macroeconomic data available previously. http://repub.eur.nl/res/pub/12365/ 2006-08-01T00:00:00Z In this paper we study some prominent downside risk measures for heavy tailed distribution. Using the notion of regular variation to define heavy tailed distributions we provide approximations of the risk measures in the tail region. We show that the downside risk measures produce similar and consistent ranking of risk. However, Expected Shortfall may not always distinguish between the differing risk levels of assets. http://repub.eur.nl/res/pub/12364/ 2006-03-01T00:00:00Z The essence of the provocative statements in Mikosch (2005) is that copulas do not add much to our understanding of multivariate probabilistic questions. When first presented at the 4th International Conference on Extreme Value Analysis in Gothenburg, 15–19 August 2005, most discussants agreed with this conclusion. We do not necessarily disagree, but in the interest of the intellectual debate, we nevertheless want to advance a few arguments in defense of the copula concept. Copulas are a way to separate the dependence structure from the marginal probabilities. In our discussion, we first give two examples from economics as to how this separation can be useful. Subsequently, we argue that if one tries to model the dependence structure, the use of a specific copula should be motivated by the problem at hand. http://repub.eur.nl/res/pub/12368/ 2006-03-01T00:00:00Z The stock market collapse led to political tensions between generations due to the fuzzy definition of the property rights over the pension funds’ wealth. The problem is best resolved by the introduction of generational accounts. Modern consumption and portfolio theory shows that the younger generations should have the higher equity exposure due to their human capital. Stock market losses should be distributed smoothly over lifetime consumption by adjusting both current contributions and future entitlements. We present expressions for the substantial welfare losses involved in various practically relevant deviations from the optimal system. http://repub.eur.nl/res/pub/12370/ 2006-02-24T00:00:00Z Suppose $X_1, X_2, \\ldots$ are independent subexponential random variables with partial sums $S_n$. We show that if the pairwise sums of the $X_i$’s are subexponential, then $S_n$ is subexponential and $(S_n > x) ∼ \\sum_{i}^n P(X_i > x)(x \\rightarrow \\infty)$. The result is applied to give conditions under which $P(\\sum_{1}^\\infty c_iX_i > x)$ as $x \\rightarrow \\infty$, where $c_1, c_2, \\ldots$ are constants such that $\\sum_{1}^\\infty c_iX_i$ is a.s. convergent. Asymptotic tail probabilities for bivariate linear combinations of subexponential random variables are given. These results are applied to explain the joint movements of the stocks of reinsurers. Portfolio investment and retrocession practices in the reinsurance industry expose different reinsurers to the same subexponential risks on both sides of their balance sheets. This implies that reinsurer’s equity returns can be asymptotically dependent, exposing the industry to systemic risk. http://repub.eur.nl/res/pub/12367/ 2006-01-01T00:00:00Z Purpose – It is the purpose of this article to improve existing methods for risk management, in particular stress testing, for derivative portfolios. The method is explained and compared with other methods, using hypothetical portfolios. Design/methodology/approach – Closed form option pricing formulas are used for valuation. To assess the risk, future price movements are modeled by an empirical distribution in conjunction with a semi-parametrically estimated tail. This approach captures the non-linearity of the portfolio risk and it is possible to estimate the extreme risk adequately. Findings – It is found that this method gives excellent results and that it clearly outperforms the standard approach based on a quadratic approximation and the normal distribution. Especially for very high confidence levels, the improvement is dramatic. Practical implications – In applications of this type the present method is highly preferable to the classical Delta-Gamma cum normal distribution approach. Originality/value – This paper uses a “statistics of extremes” approach to stress testing. With this approach it is possible to estimate the far tail of a derivative portfolio adequately. http://repub.eur.nl/res/pub/12372/ 2006-01-01T00:00:00Z Paper prepared for the NBER project on “Risks of Financial Institutions”. We benefited from suggestions and criticism by many participants in the NBER project on “Risks of financial institutions”, in particular by the organizers Mark Carey (also involving Dean Amel and Allen Berger) and Rene Stulz, by our discussant Tony Saunders and by Patrick de Fontnouvelle, Gary Gorton, Andy Lo, Jim O’Brien and Eric Rosengren. Furthermore, we are grateful for comments we received at the 2004 European Finance Association Meetings in Maastricht, in particular by our discussant Marco da Rin and by Christian Upper, at the 2004 Ottobeuren seminar in economics, notably the thoughts of our discussant Ernst Baltensberger, of Friedrich Heinemann and of Gerhard Illing, as well as at seminars of the Max Planck Institute for Research on Collective Goods, the Federal Reserve Bank of St. Louis, the ECB and the University of Frankfurt. Gabe de Bondt and David Marques Ibanez supported us enormously in finding yield spread data, Lieven Baele and Richard Stehle kindly made us aware of pitfalls in Datastream equity data. Very helpful research assistance by Sandrine Corvoisier, Peter Galos and Marco Lo Duca as well as editorial support by Sabine Wiedemann are gratefully acknowledged. Any views expressed only reflect those of the authors and should not be interpreted as the ones of the ECB or the Eurosystem. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research. This paper derives indicators of the severity and structure of banking system risk from asymptotic interdependencies between banks’ equity prices. We use new tools available from multivariate extreme value theory to estimate individual banks’ exposure to each other (“contagion risk”) and to systematic risk. Moreover, by applying structural break tests to those measures we study whether capital markets indicate changes in the importance of systemic risk over time. Using data for the United States and the euro area, we can also compare banking system stability between the two largest economies in the world. Finally, for Europe we assess the relative importance of cross-border bank spillovers as compared to domestic bank spillovers. The results suggest, inter alia, that systemic risk in the US is higher than in the euro area, mainly as cross-border risks are still relatively mild in Europe. On both sides of the Atlantic systemic risk has increased during the 1990s. http://repub.eur.nl/res/pub/12443/ 2006-01-01T00:00:00Z http://repub.eur.nl/res/pub/7426/ 2005-12-07T00:00:00Z We study the dependence between the downside risk of European banks and insurers. Since the downside risk of banks and insurers differs, an interesting question from a supervisory point of view is the risk reduction that derives from diversification within large banks and financial conglomerates. We discuss the limited value of the normal distribution based correlation concept, and propose an alternative measure which better captures the downside dependence given the fat tail property of the risk distribution. This measure is estimated and indicates better diversification benefits for conglomerates versus large banks. http://repub.eur.nl/res/pub/12373/ 2005-12-01T00:00:00Z Risk managers use portfolios to diversify away the unpriced risk of individual securities. In this article we compare the benefits of portfolio diversification for downside risk in case returns are normally distributed with the case of fat-tailed distributed returns. The downside risk of a security is decomposed into a part which is attributable to the market risk, an idiosyncratic part, and a second independent factor. We show that the fat-tailed-based downside risk, measured as value-at-risk (VaR), should decline more rapidly than the normal-based VaR. This result is confirmed empirically. http://repub.eur.nl/res/pub/12375/ 2005-04-01T00:00:00Z Banks are linked through the interbank deposit market, participations like syndicated loans and deposit interest rate risk. The similarity in exposures carries the potential for systemic breakdowns. This potential is either strong or weak, depending on whether the linkages remain or vanish asymptotically. It is shown that the linearity of the bank portfolios in the exposures, in combination with a condition on the tails of the marginal distributions of these exposures, determines whether the potential for systemic risk is weak or strong. We show that if the exposures have marginal normal distributions the potential for systemic risk is weak, while if e.g. the Student distributions apply the potential is strong. http://repub.eur.nl/res/pub/6590/ 2005-03-01T00:00:00Z We study auctions in which the number of potential bidders is large, such as in Internet auctions. With numerous bidders, the expected revenue and the optimal bid function in a first price auction result in complicated expressions, except for a few simple distribution function for the bidders' valuations. We show that these expressions can be well approximated using extreme value theory without assuming a particular distribution function. The theory is applied to data from Internet auctions. http://repub.eur.nl/res/pub/12444/ 2005-01-01T00:00:00Z Het nieuwe financiële toetsingskader voor de pensioensector heeft een procyclische uitwerking. Om dit ongewenste effect te voorkomen, moet het toetsingskader beter aansluiten bij de moderne beleggingstheorie. http://repub.eur.nl/res/pub/12445/ 2004-11-26T00:00:00Z http://repub.eur.nl/res/pub/1800/ 2004-11-05T00:00:00Z Asymptotic tail probabilities for bivariate linear combinations of subexponential random variables are given. These results are applied to explain the joint movements of the stocks of reinsurers. Portfolio investment and retrocession practices in the reinsurance industry, for reasons of diversification, exposes different reinsurers to the same risks on both sides of their balance sheets. Assuming, in line with the industry practice that the risk drivers follow subexponential distributions, we derive (under mild conditions) when the reinsurer's equity returns are asymptotically dependent, exposing the industry to systemic risk. http://repub.eur.nl/res/pub/6602/ 2004-10-01T00:00:00Z Risk managers use portfolios to diversify away the un-priced risk of individual securities. In this paper we compare the benefits of portfolio diversification for downside risk in case returns are normally distributed with the case fat tailed distributed returns. The downside risk of a security is decomposed into a part which is attributable to the market risk, an idiosyncratic part and a second independent factor. We show that the fat-tailed based downside risk, measured as Value-at-Risk (VaR), should decline more rapidly than the normal based VaR. This result is confirmed empirically. http://repub.eur.nl/res/pub/6615/ 2004-09-12T00:00:00Z http://repub.eur.nl/res/pub/6618/ 2004-08-17T00:00:00Z The aim of the paper is to obtain confidence intervals for the tail index and high quantiles taking into account the optimal rate of convergence of the estimator. The common approach to obtaining confidence intervals presented in the literature is to use the normal distribution approximation at a non-optima1 rate. Instead, we propose to use the optimal rate, but then a bias term with unknown sign has to be estimated. We provide an estimator for this sign and the full programme to obtain the optimal confidence intervals. Moreover, we demonstrate the gain in coverage, and show the relevance of these confidence intervals by calculating the reduction in capital requirements in a financia1 Value at Risk exercise. Simulation results are also presented. It is weIl known that extreme value parameter estimators which balance the asymptotic bias squared and variance yield the lower asymptotic mean square error. Here we demonstrate the relevance of using the confidence bands for the quantiles using the optima1 number of order statistics on simulated and actua1 data. It appears that if one does not correct for the sign factor the confidence bands are considerably larger. In the financia1 application for the determination of appropriate capita1 buffers usage of the optima1 confidence band implies considerable reduction in capital provisioning. The band without the correction term sometimes requires about 10% more capital vis á vis the optimal band. Since investment banks nowadays have to provision against such losses by holding capital, .reduction in capital requirements in the order of 10% gives quite a significant reduction in operating costs. http://repub.eur.nl/res/pub/6601/ 2004-07-01T00:00:00Z Consider the portfolio problem of choosing the mix between stocks and bonds under a downside risk constraint. Typically stock returns exhibit fatter tails than bonds corresponding to their greater downside risk. Downside risk criteria like the safety first criterion therefore of ten select corner solutions in the sense of a bonds only portfolio. This is due to a focus on the asymptotically dominating first order Pareto term of the portfolio return distribution. We show that if second order terms are taken into account, a balanced solution emerges. The theory is applied to empirical examples from the literature. http://repub.eur.nl/res/pub/12459/ 2004-03-30T00:00:00Z It is by now well known that Þnancial returns exhibit heavy tails and are thus nonnormally distributed. This implies that extreme market conditions tend to happen more frequently than expected on the basis of the normal distribution, which is used so often in standard asset pricing approaches. From the point of view of international Þnan- cial stability and portfolio diversiÞcation, the strength of asset linkages during crisis periods matters even more, as the linkages determine the stability of the system as a whole. Several papers talk about increased correlation between Þnancial assets or markets during crisis periods. As has been argued before, the use of correlation analysis is not without problems though. Since the correlation concept is just an intermediary step in calculating probabilities, we prefer to deÞne market linkages in terms of conditional probabilities and the expected number of market crashes. http://repub.eur.nl/res/pub/6657/ 2004-03-12T00:00:00Z Banks provide risky loans to firms which have superior information regarding the quality of their projects. Due to asymmetric information the banks face the risk of adverse selection. Credit Value-at-Risk (CVaR) regulation counters the problem of low quality, i.e. high risk, loans and therefore reduces the risk of the bank loan portfolio. However, CVaR regulation distorts the operation of credit markets. We show that a binding CVaR constraint introduces credit rationing and lowers social welfare. CVaR regulation also affects the operation of monetary policy. http://repub.eur.nl/res/pub/12376/ 2004-01-01T00:00:00Z We characterize asset return linkages during periods of stress by an extremal dependence measure. Contrary to correlation analysis, this nonparametric measure is not predisposed toward the normal distribution and can allow for nonlinear relationships. Our estimates for the G-5 countries suggest that simultaneous crashes between stock markets are much more likely than between bond markets. However, for the assessment of financial system stability the widely disregarded cross-asset perspective is particularly important. For example, our data show that stock-bond contagion is approximately as frequent as flight to quality from stocks into bonds. Extreme cross-border linkages are surprisingly similar to national linkages, illustrating a potential downside to international financial integration. http://repub.eur.nl/res/pub/12458/ 2004-01-01T00:00:00Z Money and the Nation State: The Financial Revolution, Government and the World Monetary System. Foreword by Merton H. Miller. Edited by Dowd (Kevin) and Timberlake, Jr. (Richard H.). (New Brunswick, NJ and London: Transaction Publishers, 1998. Pp. viii+453. US $19.95 hardback. ISBN 1 56000 302 2, 1 56000 930 6.) http://repub.eur.nl/res/pub/6698/ 2003-11-17T00:00:00Z The creeping stock market collapse eroded the wealth of funded pension systems. This led to political tensions between generations due to the fuzzy definition of property rights on the pension funds wealth. We argue that this problem can best be resolved by the introduction of generational accounts. Using modern portfolio and consumption planning theory we show that the younger generations should have the higher equity exposure due to their human capital. Capital losses should be distributed smoothly over lifetime consumption. When stock markets are depressed equity should be bought, savings and consumption should be scaled down equiproportionally, and retirement should be postponed. Portfolio investment restrictions are quite costly. http://repub.eur.nl/res/pub/12446/ 2003-03-07T00:00:00Z In de discussie over het pensioenstelsel worden veel macro-economische misvattingen gedebiteerd. De gedachte dat de overheid moet opdraaien voor de onzekerheid in de pensioenen is macro-economisch gezien onjuist. De toezichthouder is redeloos, de volksvertegenwoordiging is radeloos, maar de pensioenfondsen zijn geenszins roekeloos. http://repub.eur.nl/res/pub/12380/ 2003-01-01T00:00:00Z This paper provides evidence that the choice of the foreign exchange regime is not of first order importance for achieving high output growth. It is argued that due to the forward looking nature of the foreign exchange market, exchange rate stability hinges on the current and anticipated coherency of monetary and fiscal policies. We demonstrate this empirically on a panel including potential EMU accession countries. By means of rank regression analysis we uncover the partial links across the regime specifics of the representative country versus the German regime during the 1990s. http://repub.eur.nl/res/pub/12381/ 2003-01-01T00:00:00Z A scientific way of looking beyond the worst-case return is to employ statistical extreme value methods. Extreme Value Theory (EVT) shows that the probability on very large losses is eventually governed by a simple function, regardless the specific distribution that underlies the return process. This limit result can be exploited to construct semi-parametric portfolio Value at Risk (VaR) estimates around and beyond the largest observed loss. Such extreme VaR estimates can be useful inputs for scenario analysis and stress testing. The aim of this chapter is to introduce the reader to extreme value theory and the statistics of extremes. http://repub.eur.nl/res/pub/12384/ 2002-08-29T00:00:00Z The state of the art of rendering fiat money valuable is either to impose a boundary condition or to make the boundary condition unimportant through an infinite sequence of markets so as to circumvent backward induction. We show fiat exchange may nevertheless arise in finite economies if agents have incomplete information about their relative position in the trade cycle or when the barter and autarky equilibria of the one-shot trading round support a monetary equilibrium with repeated trades. http://repub.eur.nl/res/pub/12383/ 2002-07-30T00:00:00Z Under the new Capital Accord, banks choose between two different types of risk management systems, the standard or the internal rating based approach. The paper considers how a bank's preference for a risk management system is affected by the presence of supervision by bank regulators. The model uses a principal–agent setting between a bank's owner and its risk management. The main conclusion is that previously unregulated institutions can be expected to switch to the lower quality standard approach subsequent to becoming regulated, i.e., the presence of regulation may induce a bank to decrease the quality of its risk management system. http://repub.eur.nl/res/pub/6824/ 2002-02-06T00:00:00Z This paper provides empirical evidence that, irrespective of the foreign exchange rate regime, countries with high monetary volatility have lower relative output growth rates. It is argued that due to the forward looking nature of the foreign exchange market, exchange rate stability hinges on the stability of the institutional structure within which monetary and fiscal policies are formulated. Subsequently, the likely endogenous response in the accession countries upon entry into EU and EMU is examined. This provides arguments for a rapid transition phase, possibly complemented by a one sided euroisation as a commitment device http://repub.eur.nl/res/pub/6840/ 2001-10-09T00:00:00Z Under the new Capital Accord banks can choose between different type of risk management systems. Using a stylized model of risk management systems which differ in quality and by modelling the relationship between the bank board and the risk manager, we consider the incentives for the adoption of a particular system. We show that in some cases banks may adversely adopt an unsophisticated risk management system in order to evade regulation. http://repub.eur.nl/res/pub/6858/ 2001-07-19T00:00:00Z We characterize asset return linkages during periods of stress by an extremal dependence measure. Contrary to correlation analysis, this non-parametric measure is not predisposed towards the normal distribution and can account for non-linear relationships. Our estimates for the G-5 countries suggest that simultaneous crashes in stock markets are about two times more likely than in bond markets. Moreover, stock-bond contagion is about as frequent as flight to quality from stocks into bonds. Extreme cross-border linkages are surprisingly similar to national linkages, illustrating a potential downside to international financial integration. http://repub.eur.nl/res/pub/6860/ 2001-06-30T00:00:00Z We derive, in a complete markets environment, an investor's optimal portfolio allocation subject to both a budget constraint and a probabilistic risk constraint. We demonstrate that the set of feasible portfolios need not be connected or convex, while the number of local optima increases exponentially with the number of securities implying that finding the optimal portfolio is computationally complex (NP hard). The resulting optimal portfolio allocation may not be monotonic in the state-price density. A novel type of financial innovation, which splits states of nature, is shown to weakly enhance welfare, restore monotonicity in the state-price density, and may reduce complexity. http://repub.eur.nl/res/pub/6859/ 2001-06-21T00:00:00Z Portfolio risk is in an important way driven by 'abnormal' returns emanating from heavy tailed distributed asset returns. The theory of regular variation and extreme values provides a model for this feature of financial data. We first review this theory and subsequently study the problem of portfolio diversification in particular. We show that if the portfolio asset return distributions are regulary varying at infinity, then Feller's convolution theorem implies that the portfolio diversification is more effective than if the underlying distribution would be normal. This is illustrated by a simulation study and an application to S&P stock returns. http://repub.eur.nl/res/pub/12449/ 2001-02-16T00:00:00Z We schrijven het begin van een nieuw millennium. Een Amsterdamse, Maastrichtse en Rotterdamse hoogleraar economie zitten in de skybox van het Tinbergen Instituut voor fundamenteel economisch onderzoek naar Feyenoord-Ajax te kijken en bespreken onderwijl het inburgeringsprogramma van de toekomstige prinses. Hen is door Kok gevraagd een salaris vast te stellen passend bij haar status en toekomstige werkzaamheden, maar tevens te letten op de bodem van de schatkist die al weer in zicht is door de komende ambtelijke loonronde. Dit doet de temperatuur in de skybox flink stijgen. http://repub.eur.nl/res/pub/12389/ 2001-02-01T00:00:00Z Tail index estimation depends for its accuracy on a precise choice of the sample fraction, i.e., the number of extreme order statistics on which the estimation is based. A complete solution to the sample fraction selection is given by means of a two-step subsample bootstrap method. This method adaptively determines the sample fraction that minimizes the asymptotic mean-squared error. Unlike previous methods, prior knowledge of the second-order parameter is not required. In addition, we are able to dispense with the need for a prior estimate of the tail index which already converges roughly at the optimal rate. The only arbitrary choice of parameters is the number of Monte Carlo replications. http://repub.eur.nl/res/pub/12387/ 2001-01-01T00:00:00Z Exciting information for risk and investment analysis is obtained from an exceptionally large and automatically filtered high frequency data set containing all the forex quote prices on Reuters during a ten-year period. It is shown how the high frequency data improve the efficiency of the tail risk cum loss estimates. We demonstrate theoretically and empirically that the heavy tail feature of foreign exchange rate returns implies that position limits for traders calculated under the industry standard normal model are either not prudent enough, or are overly conservative depending on the time horizon. http://repub.eur.nl/res/pub/6929/ 2000-11-21T00:00:00Z A simple auction-theoretic framework is used to examine symmetric litigation environments where the legal ownership of a disputed asset is unknown by the court. The court observes only the quality of the case presented by each party, and awards the asset to the party presenting the best case. Rational litigants influence the quality of their cases by hiring skillful attorneys. This framework permits us to compare the equilibrium legal expenditures that arise under a continuum of legal systems. The British rule, American rule, and some recently proposed legal reforms are special cases of our model. http://repub.eur.nl/res/pub/1652/ 2000-05-25T00:00:00Z Tail index estimation depends for its accuracy on a precise choice of the sample fraction, i.e. the number of extreme order statistics on which the estimation is based. A complete solution to the sample fraction selection is given by means of a two step subsample bootstrap method. This method adaptively determines the sample fraction that minimizes the asymptotic mean squared error. Unlike previous methods, prior knowledge of the second order parameter is not required. In addition, we are able to dispense with the need for a prior estimate of the tail index which already converges roughly at the optimal rate. The only arbitrary choice of parameters is the number of Monte Carlo replications. http://repub.eur.nl/res/pub/12390/ 2000-01-01T00:00:00Z http://repub.eur.nl/res/pub/12391/ 2000-01-01T00:00:00Z A safety-first investor maximizes expected return subject to a downside risk constraint. Arzac and Bawa [Arzac, E.R., Bawa, V.S., 1977. Portfolio choice and equilibrium in capital markets with safety-first investors. Journal of Financial Economics 4, 277–288.] use the Value at Risk as the downside risk measure. The paper by Gourieroux, Laurent and Scaillet estimates the optimal safety-first portfolio by a kernel-based method, we exploit the fact that returns are fat-tailed, and propose a semi-parametric method for modeling tail events. We also analyze a portfolio containing the two stocks used by Gourieroux et al. and discuss the merits of the safety-first approach. http://repub.eur.nl/res/pub/12394/ 2000-01-01T00:00:00Z We propose a semi-parametric method for unconditional Value-at-Risk (VaR) evaluation. The largest risks are modelled parametrically, while smaller risks are captured by the non-parametric empirical distribution function. A comparison of methods on a portfolio of stock and option returns reveals that at the 5 % level the RiskMetrics analysis is best, but for predictions of low probability worst outcomes, it strongly underpredicts the VaR while the semi-parametric method is the most accurate. http://repub.eur.nl/res/pub/12395/ 2000-01-01T00:00:00Z European wide monetary aggregates constructed from pre-unification data cannot be used as evidence that money demand in the euro area is stable. To overcome the Lucas critique, we apply the standard foreign exchange rate model. Since the uncoordinated country specific money supply system is abolished, the increased comovement between local monetary aggregates leaves little room for a free ride on the law of large numbers. Current monetary policy decisions must be based on untested relations, and given ‘the long and variable lags’, we conclude that the road towards monetary stability is a non-activist steady money supply policy. http://repub.eur.nl/res/pub/7711/ 1999-10-14T00:00:00Z The paper characterizes first and second order tail behavior of convolutions of i.i.d. heavy tailed random variables with support on the real line. The result is applied to the problem of risk diversification in portfolio analysis and to the estimation of the parameter in a MA(1) model. http://repub.eur.nl/res/pub/12451/ 1999-10-08T00:00:00Z De vrees dat verschillen in financiële structuur de transmissie van het Europese monetair beleid zullen bemoeilijken is overdreven. De financiële structuur in Europa zal door de komst van de euro harmoniseren. http://repub.eur.nl/res/pub/7727/ 1999-03-19T00:00:00Z There is a widely held view that existing differences in the capital and money market structures across EMU countries are an important matter of concern for the ECB, because they might hinder the uniform transmission of monetary policy actions. We argue that many aspects of financial structure are endogenous to the monetary policy regime in place. It is shown that capital market structures are heavily correlated with past inflation and inflation uncertainty. Since the EURO regime imposes a unified monetary policy, we suspect that the differences will wither. A single currency, a single money market rate and a uniform reserve requirement will rapidly harmonize the money markets. In sum, we predict that differential responses in the transmission of monetary policy actions through the money and capital markets are of minor concern for the ECB. http://repub.eur.nl/res/pub/12398/ 1999-01-01T00:00:00Z Tullock's analysis of rent seeking and overdissipation is reconsidered. We show that, while equilibrium strategies do not permit overdissipation in expectation, for particular realizations of players' mixed strategies the total amount spent competing for rents can exceed the value of the prize. We also show that the cross-sectional incidence of overdissipation in the perfectly discriminating contest ranges from 0.50 to 0.44 as the number of players increases from two to infinity. Thus, even though the original analysis of overdissipation is flawed, there are instances in which rent-seekers spend more than the prize is worth. http://repub.eur.nl/res/pub/7745/ 1998-10-09T00:00:00Z Large data sets in finance with millions of observations have become widely available. Such data sets enable the construction of reliable semi-parametric estimates of the risk associated with extreme price movements. Our approach is based on semi-parametric statistical extreme value analysis, and compares favourably with the conventional finance normal distribution based approach. It is shown that the efficiency of the estimator of the extreme returns may benefit from high frequency data. Empirical tail shapes are calculated for the German Mark-US Dollar foreign exchange rate, and we use the semi- parametric tail estimates in combination with the empirical distribution function to evaluate the returns on exotic options. http://repub.eur.nl/res/pub/7746/ 1998-09-08T00:00:00Z We advocate the use of absolute moment ratio statistics in conjunction with standard variance ratio statistics in order to disentangle linear dependence, non-linear dependence, and leptokurtosis in financial time series. Both statistics are computed for multiple return horizons simultaneously, and the results are presented in a comprehensive way using a graphical device. We construct a formal joint testing procedure based on bootstrapped and block-bootstrapped uniform confidence intervals. The methodology is hybrid because it combines a formal testing procedure with volatility curve pattern recognition based on expert opinions. An application to forex data illustrates the procedure. http://repub.eur.nl/res/pub/7751/ 1998-06-23T00:00:00Z A flurry of recent articles has argued on the basis of constructed European wide monetary aggregates that the demand for EURO's will be more stable than the current demand for national currencies. In policy circles this seemingly moderating effect of monetary integration figures as an additional argument pro union. On the basis of the standard foreign exchange rate model we argue that once the uncoordinated country specific money supply system is abolished, the coherence between local monetary aggregates increases dramatically, leaving little room for a free ride on the law of large numbers. The only road towards stability is prudent monetary policy. http://repub.eur.nl/res/pub/12399/ 1998-01-01T00:00:00Z The theoretical literature exploring various ramifications and applications of Tullock's (1980) rent-seeking model is extensive and rapidly growing. In contrast, there exist as yet only a few experimental evaluations of this model, with ambiguous results. Moreover, these studies focus on one particular case (proportional probabilities) and use a problematic experimental design. With an appropriate design we investigate the extreme cases of proportional probabilities and perfect discrimination, which offer the starkest contrast in theoretical predictions. We find substantial evidence for the predictive power of the rent-seeking model, particularly if one allows for the fact that people sometimes make mistakes or are confused about what to do. http://repub.eur.nl/res/pub/12400/ 1998-01-01T00:00:00Z Large data sets in finance with millions of observations have become widely available. Such data sets enable the construction of reliable semi-parametric estimates of the risk associated with extreme price movements. Our approach is based on semi-parametric statistical extreme value analysis, and compares favorably with the conventional finance normal distribution based approach. It is shown that the efficiency of the estimator of the extreme returns may benefit from high frequency data. Empirical tail shapes are calculated for the German Mark—US Dollar foreign exchange rate, and we use the semi-parametric tail estimates in combination with the empirical distribution function to evaluate the returns on exotic options. http://repub.eur.nl/res/pub/12403/ 1998-01-01T00:00:00Z The discrete time analogue of the continuous time Krugman target zone model is developed in order to capture the typical volatility clusters and fat-tailed distributed innovations of exchange rates. It is shown that under these more general stochastic conditions the S-shaped relation between exchange rate and fundamentals is preserved, but is less pronounced. The model is tested for its S-shape and stochastic properties. Two clearly distinct sets of EMS currencies are detected on the basis of the curvature features. One-step-ahead realignment probabilities are used as an alternative evaluation method. http://repub.eur.nl/res/pub/12460/ 1998-01-01T00:00:00Z http://repub.eur.nl/res/pub/12473/ 1998-01-01T00:00:00Z Keith Cuthbertson, Quantitative Financial Economics: Stocks, Bonds, and Foreign Exchange, Wiley, Chichester 1996. Pp. 470. http://repub.eur.nl/res/pub/12474/ 1998-01-01T00:00:00Z Discusses the issues in value-at-risk modeling and evaluation. Value of value at risk; Horizon problems and extreme events in financial risk management; Methods of evaluating value-at-risk estimates. http://repub.eur.nl/res/pub/7764/ 1997-12-28T00:00:00Z Economic problems such as large claims analysis in insurance and value-at-risk in finance, require assessment of the probability P of extreme realizations Q. This paper provided a semi-parametric method for estimation of extreme (P, Q) combinations for data with heavy tails. We solve the long standing problem of estimating the sample treshold of where the tail of the distribution starts. This is accomplished by the combination of a control variate type device and a subsample bootstrap technique. The subsample bootstrap attains convergence in probability, whereas the full sample bootstrap would only provide convergence in distribution. This permits a complete and comprehensive treatment of extreme (P, Q) estimation. http://repub.eur.nl/res/pub/12475/ 1997-12-16T00:00:00Z hlarket efficiency tests that rely on the martingale difference behavior of returns can be based on various volatility measures. This paper argues that, to be able to differentiate between dependence and fat-tailedness. one should look simultaneously at plots based on absolute returns and variances. If the distribution is heavy-tailed, this shows up in the absolute moment plots, but not in the variance related plots. Linear dependence. by contrast, is revealed in both plots. We provide and discuss an analytical and a simulation experime illustrating these points. http://repub.eur.nl/res/pub/7763/ 1997-11-26T00:00:00Z Accurate prediction of the frequency of extreme events is of primary importance in many financial applications such as Value-at-Risk (VaR) analysis. We propose a semi-parametric method for VaR evaluation. The largest risks are modelled parametrically, while smaller risks are captured by the non- parametric empirical distribution function. The semi-parametric method is compared with historical simulation and the J.P. Morgan RiskMetrics technique on a portfolio of stock returns. For predictions of low probability worst outcomes, RiskMetrics analysis underpredicts the VaR while historical simulation overpredicts the VaR. However, the estimates obtained from applying the semi-parametric method are more accurate in the VaR prediction. In addition, an option is used in the portfolio to lower downside risk. Finally, it is argued that current regulatory environment provides incentives to use the lowest quality VaR method available. http://repub.eur.nl/res/pub/12476/ 1997-08-16T00:00:00Z Univariate time series regressions of the forex return on the forward premium generate mostly negative slope coefficients. Simple and refined panel estimation techniques yield slope estimates that are much closer to unity. We explain the two apparently opposing results by allowing for both additive and multiplicative news. No arbitrage arguments imply that the multiplicative news component must be identical across all exchange rates at a given point in time. Cross section estimates reveal that the movements in the multiplicative news component are so large that a negative slope coefficient for the post Bretton Woods time series regressions is not inprobable. http://repub.eur.nl/res/pub/7804/ 1997-05-15T00:00:00Z This paper reconsiders Tullock's analysis of rent seeking and wasteful overdissipation. The purpose of this paper is to point out that even though his original analysis of overdissipation is technically flawed, the definition of overdissipation can be modified to explain instances in which rational rent-seekers spend more to win a prize than the prize is worth. We showed before that equilibrium mixed strategies in the Tullock game do not permit overdissipation in expectation: the expected total amount spent competing for rents cannot exceed the value of the prize. However, since the equilibrium involves mixed-strategies for particular realizations of the mixed strategies the total amount spent competing for rents can exceed the value of the prize! In fact, we show that the cross-sectional incidence of overdissipation may be quite high. For a symmetric perfectly discriminating contest (R = &inf;), the probability of overdissipation in a symmetric equilibrium ranges from exactly one-half in the two player case to approximately .44 as the number of players approaches infinity. http://repub.eur.nl/res/pub/7806/ 1997-01-29T00:00:00Z We use a subsample bootstrap method to get a consistent estimate of the asymptotically optimal choice of the sample fraction, in the sense of minimal mean squared error, which is needed for tail index estimation. Unlike previous methods our procedure is fully self contained. In particular, the method is not conditional on an initial consistent estimate of the tail index; and the ratio of the first and second order tail indices is left unrestricted, but we require the ratio to be strictly positive. Hence the current method yields a complete solution to tail index estimation as it is not predicated on a more or less arbitrary choice of the number of highest order statistics. http://repub.eur.nl/res/pub/12405/ 1997-01-01T00:00:00Z A precise estimation of the tail shape of forex returns is of critical importance for proper risk assessment. We improve upon the efficiency of conventional estimators that rely on a first order expansion of the tail shape, by using the second order expansion. Here we advocate a moments estimator for the second term. The paper uses both Monte Carlo simulations and the high frequency foreign exchange recordings collected by the Olsen corporation to illustrate the technique. http://repub.eur.nl/res/pub/12406/ 1996-01-01T00:00:00Z In a (first price) all-pay auction, bidders simultaneously submit bids for an item. All players forfeit their bids, and the high bidder receives the item. This auction is widely used in economics to model rent seeking, R&D races, political contests, and job promotion tournaments. We fully characterize equilibrium for this class of games, and show that the set of equilibria is much larger than has been recognized in the literature. When there are more than two players, for instance, we show that even when the auction is symmetric there exists a continuum of asymmetric equilibria. Moreover, for economically important configurations of valuations, there is no revenue equivalence across the equilibria; asymmetric equilibria imply higher expected revenues than the symmetric equilibrium. http://repub.eur.nl/res/pub/12407/ 1996-01-01T00:00:00Z The behaviour of the Hill estimator for the tail index of fat tailed distributions in the presence of local alternatives which have a thin tail is investigated. The converse problem is also briefly addressed. A local thin tail alternative can severely bias the Hill statistic. The relevance of this issue for the class of stable distributions is discussed. We conduct a small simulation study to support the analysis. In the conclusion it is argued that for moderate out of sample quantile analysis the problem of local alternatives may be less pressing. http://repub.eur.nl/res/pub/12409/ 1995-09-01T00:00:00Z This note provides some explanations and extensions for the interesting results in Ghose and Kroner (1995). Specifically, we address the following points: (1) It is shown that the stable distribution and the stationary ARCH distributions are partially nested with respect to their tail shapes; (2) A novel interpretation of the McCulloch estimator is developed from the vantage point of extreme value theory; (3) This interpretation not only explains the apparent bias in some of the reported estimates, but it also helps in remedying the problem. Taken together, all three points reinforce the main conclusion of Ghose and Kroner. http://repub.eur.nl/res/pub/12411/ 1995-01-01T00:00:00Z This paper compares foreign exchange market intervention in case there is no uncertainty about the extent of an imperfectly sustainable target zone and where there is uncertainty. A well-known example of the first case was the European Monetary System between 1979 and 1992. An example of the latter is the dirty floating of the dollar against the Dmark and yen after the so-called Louvre Accord in 1987. The analysis shows that the instantaneous effectiveness of intervention tends to be larger the more implicit the band policy is. Our empirical results which use Belgian and US intervention data support this claim. http://repub.eur.nl/res/pub/12412/ 1995-01-01T00:00:00Z Studies the effects of speed of international factor markets integration within a general equilibrium, two country model. Variant of Diamond's overlapping generations model; Effects of an international factor market liberalization; Determination of the amount of capital needed to integrate Eastern Europe with the European Community. http://repub.eur.nl/res/pub/12413/ 1994-12-01T00:00:00Z In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium exists when R>2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete, and show that full rent dissipation occurs when the strategy space is continuous. Our results are shown to be consistent with recent experimental evidence on the dissipation of rents. An earlier version of this paper circulated under the title, No, Virginia, There is No Overdissipation of Rents. We are grateful to Dave Furth and Frans van Winden for stimulating conversations, and for comments provided by workshop participants from the CORE-ULB-KUL IUAP project, Purdue University, Pennsylvania State University, Rijksuniversiteit Limburg, and Washington State University. We also thank Max van de Sande Bakhuyzen and Ben Heijdra for useful discussions, and Geert Gielens for computational assistance. An earlier version of the paper was presented at the ESEM 1992 in Brussels and the Mid-West Mathematical Economics Conference in Pittsburgh. All three authors would like to thank CentER for its hospitality during the formative stages of the paper. The second author has also benefited from the financial support of the Katholieke Universitieit Leuven and the Jay N. Ross Young Faculty Scholar Award at Purdue University. The third author benefitted from visiting IGIER where part of the paper was written. The third author also benefitted from grant IUAP 26 of the Belgian Government. http://repub.eur.nl/res/pub/12415/ 1994-02-01T00:00:00Z We analyze the existence of equilibrium in an asset market under asymmetric information. Price formation is modeled as a bilateral sealed bid auction where uninformed and informed traders submit limit orders to a computerized specialist. The computerized specialist is programmed to sell to the highest bidder and buy from the seller asking the lowest price. We show that this mechanism — which is designed to model the Globex and RAES trading institutions used in Chicago, London, New York, Paris, and Germany — yields an equilibrium in which the bid-ask spread is endogenously random and the passive specialist earns nonnegative profits. http://repub.eur.nl/res/pub/12417/ 1994-01-01T00:00:00Z http://repub.eur.nl/res/pub/12477/ 1994-01-01T00:00:00Z J. Hirschleifer and J.G.Riley, The Analytics of Uncerta&ty and Information, Cambridge University Press, Cambridge, etc., 1992. Pp. xi + 465. http://repub.eur.nl/res/pub/12478/ 1994-01-01T00:00:00Z http://repub.eur.nl/res/pub/12418/ 1993-12-01T00:00:00Z The paper demonstrates that in an environment of free banking where some agents have imperfect information regarding the circulation and debasement rates of alternative money suppliers, the equilibrium supply of money involves mixed strategies. It follows that the circulation and debasement rates are intrinsically stochastic, but that their averages are below the rates set by a monopoly bank. Empirical tests reveal that these predictions are consistent with the free banking era of the United States. The paper is also relevant for the discussion about the future monetary union in the EC. http://repub.eur.nl/res/pub/12419/ 1993-01-01T00:00:00Z In a world where a politician can explicitly auction off a prize to the high bidder, the standard auction literature can be used to analyse political behavior. The justice system, however, precludes politicians from explicitly selling the prize to the highest bidder. Thus politicians cannot let it become public knowledge that they are in the business of selling political favors. An institution has emerged in political markets to overcome this constraint which are termed as lobbying. Lobbyists make implicit payments to the politician through campaign contributions. If these up-front payments were rebated to those failing to receive the prize, it would be clear that the politician was selling favors. This article has examined an interesting principle arising in all-pay auctions. This principle states that a politician wishing to maximize political rents may find it in his best interest to exclude certain lobbyists from participating in the lobbying process, particularly lobbyists valuing most the political prize. http://repub.eur.nl/res/pub/12420/ 1993-01-01T00:00:00Z Non-parametric tolerance limits are employed to calculate soft margins such as advocated in Williamson's target zone proposal. In particular, the tradeoff between softness and zone width is quantified. This may be helpful in choosing appropriate margins. Furthermore, it offers policymakers a framework for reference in the case of changing exchange rate policy. The empirical applications include an evaluation of the EMS zone width. We also show that the procedures for calculating the soft margins are robust against alternative data-generating mechanisms. http://repub.eur.nl/res/pub/12453/ 1993-01-01T00:00:00Z M et behulp van recent ontwikkelde wisselkoersmodellen is het mogelijk hetgedrag van wisselkoersen in een wisselkoersstelsel als het EMS te bestuderen. Aan de hand van geschatte devaluatiekansen laten de auteurs zien dat het EMS tot 1987 voor veel munten ongeloofwaardig was. Na 1987 nam de geloofwaardigheid substantieel toe, totdat de recente valutacrises het stelsel omverwierpen. Er zijn tot nog toe weinig aanwijzingen dat de nieuwe opzet van het EMS met fluctuatiemarges van 15% niet houdbaar is. Ook het vasthouden van de gulden aan de 2,25% bandbreedte ten opzichte van de Duitse mark lijkt atteszins gerechtvaardigd. http://repub.eur.nl/res/pub/12424/ 1992-06-01T00:00:00Z We advance an explanation for the choice of the invoice currency of international trade contracts on the basis of strategic bargaining considerations. The choice of the invoice currency originates in a situation in which each trader takes into account the other party's bargaining power. The latter depends on the individual discount factor, whether one is the first or second proposer, and whether one is on the short or long side of the market. Along these lines we explain the Grassman bias for trade contracts to be invoiced in the exporter's currency. http://repub.eur.nl/res/pub/12422/ 1992-01-01T00:00:00Z We show that the Varian model of sales with more than two firms has two types of equilibria: a unique symmetric equilibrium, and a continuum of asymmetric equilibria. In contrast, the 2-firm game has a unique equilibrium that is symmetric. For the n-firm case the asymmetric equilibria imply mixed strategies that can be ranked by first-order stochastic dominance. This enables one to rule out asymmetric equilibria on economic grounds by constructing a metagame in which both firms and consumers are players. The unique subgame perfect equilibrium of this metagame is symmetric. http://repub.eur.nl/res/pub/12423/ 1992-01-01T00:00:00Z In the literature on the empirical unconditional distribution of foreign exchange rate returns there is indication that the type of distribution function is related to the form of exchange rate regime. The analysis has been hampered by the nonnestedness of alternative distribution models. The paper investigates the issue by means of extremal analysis which allows for a unified treatment. In particular, we try to sort out whether apparent distributional differences are due to differences in techniques or in regimes. http://repub.eur.nl/res/pub/12425/ 1992-01-01T00:00:00Z Considers the hybrid situation where some customers care only about the price while others have a brand preference or care about product characteristics. http://repub.eur.nl/res/pub/12426/ 1992-01-01T00:00:00Z For currencies with well developed forward markets several papers have investigated the conjectured negative relationship between trade and short term exchange rate volatility, without being very successful. A theoretical explanation for the empirical anomalies is provided by solving explicitly for the forward rate. Because importers and exporters are on opposite sides of the forward market, so is their exposure towards exchange rate volatility. Moreover, which trade flow benefits and which one loses from increased volatility is determined by the signs of the aggregate net foreign currency exposure and the aggregate measure of risk aversion. http://repub.eur.nl/res/pub/12427/ 1992-01-01T00:00:00Z Investigates three factors of economic growth. http://repub.eur.nl/res/pub/12479/ 1992-01-01T00:00:00Z http://repub.eur.nl/res/pub/12428/ 1991-01-01T00:00:00Z Several nonnested fat-tailed distributions have been advocated for modelling exchange rate returns. Instead of directly estimating these nonnested distributions we investigate the extremal distribution of the returns. The advantage is that the parameter which characterizes the amount of tail fatness can be estimated without maintaining a specific distribution, and hence enables one to test hypotheses. The parameter of the limit law is estimated by employing nonparametric procedures based on order statistics. The appropriateness of these procedures is assessed. Given this estimate one can derive bounds on the returns for very low probabilities on an excess. Such information is useful in evaluating the volatility of exchange rates. http://repub.eur.nl/res/pub/12429/ 1991-01-01T00:00:00Z Numerous articles have investigated the distribution of share prices, and find that the returns are fat tailed. Nevertheless, there is still controversy about the amount of probability mass in the tails, and hence about the most appropriate distribution to use in modeling returns. This controversy has proven hard to resolve, as the alternatives are non-nested. We employ extreme value theory, focusing exclusively on the larger observations in order to assess the tail shape within a unified framework. We find that at least the first two moments exist. This enables one to generate robust probabilities on large returns, which put the recent stock market swings into historical perspective. http://repub.eur.nl/res/pub/12430/ 1991-01-01T00:00:00Z Stable and GARCH processes have been advocated for modeling financial data. The aim of this note is to compare the two processes. It is shown that the unconditional distribution of variaties from a GARCH-like process, which explicity models the clustering of volatility and exhibits the fat-tail property as well, can be stable. Given suitable conditions the conditional distributions are stable as well. While it is generally realized that processes with variates that have unconditional nonnormal stable densities have a high frequency of ‘outliers’, it is less well known that they can exhibit the clustering phenomenon too. The clustering is obtained through stable subordination with conditional scaling. http://repub.eur.nl/res/pub/12432/ 1990-01-01T00:00:00Z If the real exchange rate follows approximately a random walk and in the presence of nontraded goods, a monetary union may generate a Pareto improvement. The argument is based on the analogy with the advantages that derive from the formation of a customs union. A novel unit roots test based on the arc sine law is advanced. http://repub.eur.nl/res/pub/12434/ 1990-01-01T00:00:00Z In the literature on the empirical distribution of foreign exchange rates there is now consensus that exchange rate yields are fat-tailed. Three problems, however, persist: (1) Which class of distribution functions is most appropriate? (2) Are the parameters of the distribution invariant over subperiods? (3) What are the effects of aggregation over time on the distribution? In this paper we employ extreme value theory to shed new light on these questions. We apply the theoretical results to EMS data. http://repub.eur.nl/res/pub/12480/ 1990-01-01T00:00:00Z http://repub.eur.nl/res/pub/12438/ 1989-01-01T00:00:00Z http://repub.eur.nl/res/pub/12439/ 1989-01-01T00:00:00Z The sign and size of estimates of the elasticity of currency substitution critically depend on the definition of the oppurtunity costs of holding money. We investigate possible biases by means of Monte Carlo experiments, as sufficient real data are not available. http://repub.eur.nl/res/pub/12440/ 1988-01-01T00:00:00Z Abstract--This paper develops the theory of currency substitution from a choice theoretic point of view. The main result offers a simple relationship between the relative amount of currencies held and their opportunity costs, i.e., interest and capital gains. Our hypothesis is tested by case studies for Canada and the Netherlands Antilles. In contradistinction with other studies, we conclude that the elasticity of currency substitution is very small and negative. It is shown how the omission of the interest term in other studies biases the elasticity of currency substitution considerably. http://repub.eur.nl/res/pub/12456/ 1985-01-01T00:00:00Z Vanwege de apartheidspolitiek in Zuid-Afrika overweegt de gemeente Rotterdam een handelsboycot van met name olie tegen dit land af te kondigen. Om tot een weloverwogen stellingname te komen heeft zij besloten een onderzoek te laten doen naar de effecten van een dergelijke boycot voor de economic van het Rijnmondgebied. De economische kosten zouden dan afgewogen kunnen worden tegen de, merendeels politieke, baten. Dit artikel, gebaseerd op het rapport Werkgelegenheidsaspecten van een olieboycot tegen Zuid-Afrika, inventariseert de gevolgen van een Rotterdamse boycot. Een dergelijke boycot kan verschillende vormen aannemen. Er kan sprake zijn van een eenzijdig embargo op de export van olie naar Zuid-Afrika, maar het is ook mogelijk dat Zuid-Afrika tegenmaatregelen neemt, zoals een boycot van Rotterdam. In dit artikel wordt een aantal verschillende scenario's besproken. http://repub.eur.nl/res/pub/12442/ 1983-01-01T00:00:00Z Comments on shortcomings in the analysis by Hori and Stein in 1977 on different stages of creditor-debtor relationship. Occurrence of two swithces in the relationship with economic growth towards steady state; Absence of relationship between flow of capital and output per capita in consumer goods; Features of the Hori and Stein model; Analysis of the stages of balance of payments.