answering the skeptics yes standard volatility models do provide accurate forecasts a voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using arch and stochastic volatility models while most of these studies have documented highly significant in sample parameter estimates and pronounced intertemporal volatility persistence traditional ex post forecast evaluation criteria suggest that the models provide seemingly poor volatility forecasts contrary to this contention we show that volatility models produce strikingly accurate interdaily forecasts for the latent volatility factor that would be of interest in most financial applications new methods for improved ex post interdaily volatility measurements based on high frequency intradaily data are also discussed

the pricing of options on assets with stochastic volatilities one option pricing problem that has hitherto been unsolved is the pricing of a european call on an asset that has a stochastic volatility this paper examines this problem the option price is determined in series form for the case in which the stochastic volatility is independent of the stock price numerical solutions are also produced for the case in which the volatility is correlated with the stock price it is found that the black scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity one option pricing problem that has hitherto remained unsolved is the pricing of a european call on a stock that has a stochastic volatility from the work of merton 12 garman 6 and cox ingersoll and ross 3 the differential equation that the option must satisfy is known the solution of this differential equation is independent of risk preferences if a the volatility is a traded asset or b the volatility is uncorrelated with aggregate consumption if either of these conditions holds the risk neutral valuation arguments of cox and ross 4 can be used in a straightfoward way this paper produces a solution in series form for the situation in which the stock price is instantaneously uncorrelated with the volatility we do not assume that the volatility is a traded asset also a constant correlation between the instantaneous rate of change of the volatility and the rate of change of aggregate consumption can be accommodated the option price is lower than the blackscholes b s 1 price when the option is close to being at the money and higher when it is deep in or deep out of the money the exercise prices for which overpricing by b s takes place are within about ten percent of the security price this is the range of exercise prices over which most option trading takes place so we may in general expect the b s price to overprice options this effect is exaggerated as the time to maturity increases one of the most surprising implications of this is that if the b s equation is used to determine the implied volatility of a near the money option the longer the time to maturity the lower the implied volatility numerical solutions for the case in which the volatility is correlated with the stock price are also examined the stochastic volatility problem has been examined by merton 13 geske 7 johnson 10 johnson and shanno 11 eisenberg 5 wiggins 16 and

why has u s inflation become harder to forecast we examine whether the u s rate of price inflation has become harder to forecast and to the extent that it has what changes in the inflation process have made it so the main finding is that the univariate inflation process is well described by an unobserved component trend cycle model with stochastic volatility or equivalently an integrated moving average process with time varying parameters this model explains a variety of recent univariate inflation forecasting puzzles and begins to explain some multivariate inflation forecasting puzzles as well

factor input in nhs hospitals there has been little empirical work on the amount of substitution through time amongst the various resources used by the hospital sector this neglect arises largely from the lack of adequate time series data on resource levels this study uses data previously collected by one of the authors to examine trends in the use and cost of labour and capital resources by the nhs hospital sector over the period 1951 to 1981 a small econometric model is used to quantify the degree of substitution that occurred over that period ref

evaluating interval forecasts a complete theory for evaluating interval forecasts has not been worked out to date most of the literature implicitly assumes homoskedastic errors even when this is clearly violated and proceed by merely testing for correct unconditional coverage consequently i set out to build a consistent framework for conditional interval forecast evaluation which is crucial when higher order moment dynamics are present the new methodology is demonstrated in an application to the exchange rate forecasting procedures advocated in risk management

real time density forecasts from bayesian vector autoregressions with stochastic volatility central banks and other forecasters are increasingly interested in various aspects of density forecasts however recent sharp changes in macroeconomic volatility including the great moderation and the more recent sharp rise in volatility associated with increased variation in energy prices and the deep global recession pose significant challenges to density forecasting accordingly this paper examines with real time data density forecasts of u s gdp growth unemployment inflation and the federal funds rate from bayesian vector autoregression bvar models with stochastic volatility the results indicate that adding stochastic volatility to bvars materially improves the real time accuracy of density forecasts this article has supplementary material online

econometric studies in health economics a survey of the british literature this paper provides a survey of british applied econometric work in the field of health economics as well as reviewing the literature it suggests some avenues for future research it covers six main areas the supply of health care the demand for health care non medical influences on health market and non price rationing evaluation of health care systems and planning budgeting and monitoring mechanisms

value at risk estimation with the optimal dynamic biofuel portfolio abstract in the past petroleum companies only paid attention to hedging the variation in the crude oil price and volatility however they have now expanded their analysis to encompass renewable sources such as corn and soybeans under the current low carbon biofuel obligations this paper employs garch 1 1 and arji models to estimate the one day ahead value at risk var of the optimal dynamic biofuel portfolio which consists of crude oil corn and soybeans the optimal blended standard is subject to the dual limitations of minimum production costs and the lowest biofuel using requirements our empirical findings confirm that the arji model is more suitable than the garch 1 1 model and further captures the discontinuous jump behavior from the in the sample data the results of out of sample forecasts also are represented that our models play important roles in var estimation and risk management for biofuel portfolio we therefore suggest that the petroleum companies should simultaneously pay attention to jump risk in hedging material costs in the prices of energy related crops

forecasting portfolio value at risk with nonparametric lower tail dependence estimates abstract we propose to forecast the value at risk of bivariate portfolios using copulas which are calibrated on the basis of nonparametric sample estimates of the coefficient of lower tail dependence we compare our proposed method to a conventional copula garch model where the parameter of a clayton copula is estimated via canonical maximum likelihood the superiority of our proposed model is exemplified by analyzing a data sample of nine different bivariate and one nine dimensional financial portfolio a comparison of the out of sample forecasting accuracy of both models confirms that our model yields economically significantly better value at risk forecasts than the competing parametric calibration strategy

do banks overstate their value at risk abstract this paper is the first empirical study of banks risk management systems based on non anonymous daily value at risk var and profit and loss data using actual data from the six largest canadian commercial banks we uncover evidence that banks exhibit a systematic excess of conservatism in their var estimates the data used in this paper have been extracted from the banks annual reports using an innovative matlab based data extraction method out of the 7354 trading days analyzed in this study there are only two exceptions i e days when the actual loss exceeds the disclosed var whereas the expected number of exceptions with a 99 var is 74 for each sample bank we extract from historical vars a risk overstatement coefficient ranging between 19 and 79 we attribute var overstatement to several factors including extreme cautiousness and underestimation of diversification effects when aggregating vars across business lines and or risk categories we also discuss the economic and social cost of reporting inflated vars

taxes and pensions pension benefit rules depend on individual history far more than taxes do and age plays a much larger role in pension determination than in tax determination apart from some simulation studies theoretical studies of optimal tax design typically contain neither a mandatory pension system nor the behavioral dimensions that lie behind justifications commonly offered for mandatory pensions conversely optimizing models of pension design typically do not include annual taxation of labor and capital incomes after spelling out this contrast and reviewing and rejecting zero taxation of capital income based on the atkinsonstiglitz and chamley judd results this article raises the issue of tax favored retirement savings a topic where the two subjects come together when i was a young economist i thought methodology was uninteresting and unnecessary just something old guys did when they didn t have anything better to do i taught theory and public finance and the applied theory i did was with an eye on relevance for policy questions although i had had almost no experience with thinking about policy just a summer job with the council of economic advisors under president kennedy now that i am at a stage where methodology is age appropriate i think it is important some of this comes from the natural aging process and some comes from my extended involvement in various policy processes primarily about pensions not taxes in particular i am concerned that too many economists take the findings of individual studies literally as a basis for policy thinking rather than seeking inferences from an individual study to be combined with inferences from other studies that consider other aspects of a policy question as well as with intuitions about aspects of policy that are not in the models to me taking a model literally is not taking the model seriously it is worth remembering that models are incomplete indeed that is what it means to be a model we construct multiple models to highlight different aspects of an issue so thinking thoroughly about policy calls for thinking through multiple models and requires recognizing issues that have not made it into any of the

a new pearson type qmle for conditionally heteroscedastic models this article proposes a novel pearson type quasi maximum likelihood estimator qmle of garch p q models unlike the existing gaussian qmle laplacian qmle generalized non gaussian qmle or lad estimator our pearsonian qmle pqmle captures not just the heavy tailed but also the skewed innovations under strict stationarity and some weak moment conditions the strong consistency and asymptotic normality of the pqmle are obtained with no further efforts the pqmle can be applied to other conditionally heteroscedastic models a simulation study is carried out to assess the performance of the pqmle two applications to four major stock indexes and two exchange rates further highlight the importance of our new method heavy tailed and skewed innovations are often observed together in practice and the pqmle now gives us a systematic way to capture these two coexisting features

roughing it up including jump components in the measurement modeling and forecasting of return volatility a rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from high frequency returns coupled with simple modeling procedures building on recent theoretical results in barndorff nielsen and shephard 2004a 2005 for related bi power variation measures the present paper provides a practical and robust framework for non parametrically measuring the jump component in asset return volatility in an application to the dm exchange rate the s p500 market index and the 30 year u s treasury bond yield we find that jumps are both highly prevalent and distinctly less persistent than the continuous sample path variation process moreover many jumps appear directly associated with specific macroeconomic news announcements separating jump from non jump movements in a simple but sophisticated volatility forecasting model we find that almost all of the predictability in daily weekly and monthly return volatilities comes from the non jump component our results thus set the stage for a number of interesting future econometric developments and important financial applications by separately modeling forecasting and pricing the continuous and jump components of the total return variation process

time series copulas for heteroskedastic data we propose parametric copulas that capture serial dependence in stationary heteroskedastic time series we suggest copulas for first order markov series and then extend them to higher orders and multivariate series we derive the copula of a volatility proxy based on which we propose new measures of volatility dependence including co movement and spillover in multivariate series in general these depend upon the marginal distributions of the series using exchange rate returns we show that the resulting copula models can capture their marginal distributions more accurately than univariate and multivariate generalized autoregressive conditional heteroskedasticity models and produce more accurate value at risk forecasts

modeling and forecasting extreme commodity prices a markov switching based extreme value model abstract we propose a markov switching multifractal peaks over threshold msm pot model to capture the dynamic behavior of the random occurrences of extreme events exceeding a high threshold in time series of returns this approach allows introducing changes of regimes in the conditional mean function of the inter exceedance times i e the time between two consecutive extreme events in order to admit the presence of short and long term memory patterns further through its multifractal structure the msm pot approach is able to capture the typical stylized facts of extreme events observed in financial time series such as temporal clustering of the size of exceedances and temporal behavior of tail thickness we compare the performance of the msm pot model with competing self exciting models and a garch evt approach in an in and out of sample var forecasting exercise based on the extreme returns of six daily commodity futures prices i e brent and wti crude oil cocoa cotton copper and gold empirical results suggest that the var estimates generated by the msm pot model for the returns analyzed produce the most accurate forecasts

multivariate density forecast evaluation and calibration in financial risk management high frequency returns on foreign exchange we provide a framework for evaluating and improving multivariate density forecasts among other things the multivariate framework lets us evaluate the adequacy of density forecasts involving cross variable interactions such as time varying conditional correlations we also provide conditions under which a technique of density forecast calibration can be used to improve deficient density forecasts and we show how the calibration method can be used to generate good density forecasts from econometric models even when the conditional density is unknown finally motivated by recent advances in financial risk management we provide a detailed application to multivariate high frequency exchange rate density forecasts

continuous cascade models for asset returns abstract in this paper we make a short overview of continuous cascade models recently introduced to model asset return fluctuations we show that these models account in a very parcimonious manner for most of stylized facts of financial time series we review in more details the simplest continuous cascade namely the log normal multifractal random walk mrw it can simply be considered as a stochastic volatility model where the log volatility memory has a peculiar logarithmic shape this model possesses some appealing stability properties with respect to time aggregation we describe how one can estimate it using a gmm method and we present some applications to volatility and var value at risk forecasting

forecasting daily supermarket sales using exponentially weighted quantile regression inventory control systems typically require the frequent updating of forecasts for many different products in addition to point predictions interval forecasts are needed to set appropriate levels of safety stock the series considered in this paper are characterised by high volatility and skewness which are both time varying these features motivate the consideration of forecasting methods that are robust with regard to distributional assumptions the widespread use of exponential smoothing for point forecasting in inventory control motivates the development of the approach for interval forecasting in this paper we construct interval forecasts from quantile predictions generated using exponentially weighted quantile regression the approach amounts to exponential smoothing of the cumulative distribution function and can be viewed as an extension of generalised exponential smoothing to quantile forecasting empirical results are encouraging with improvements over traditional methods being particularly apparent when the approach is used as the basis for robust point forecasting

value at risk estimation by threshold stochastic volatility model this article proposes a threshold stochastic volatility model that generates volatility forecasts specifically designed for value at risk var estimation the method incorporates extreme downside shocks by modelling left tail returns separately from other returns left tail returns are generated with a t distributional process based on the historically observed conditional excess kurtosis this specification allows var estimates to be generated with extreme downside impacts yet remains empirically widely applicable this article applies the model to daily returns of seven major stock indices over a 22 year period and compares its forecasts to those of several other forecasting methods based on back testing outcomes and likelihood ratio tests the new model provides reliable estimates and outperforms others

risk assessment of oil price from static and dynamic modelling approaches the price gap between west texas intermediate wti and brent crude oil markets has been completely changed in the past several years the price of wti was always a little larger than that of brent for a long time however the price of wti has been surpassed by that of brent since 2011 the new market circumstances and volatility of oil price require a comprehensive re estimation of risk therefore this study aims to explore an integrated approach to assess the price risk in the two crude oil markets through the value at risk var model the var is estimated by the extreme value theory evt and garch model on the basis of generalized error distribution ged the results show that evt is a powerful approach to capture the risk in the oil markets on the contrary the traditional variance covariance vc and monte carlo mc approaches tend to overestimate risk when the confidence level is 95 but underestimate risk at the confidence level of 99 the var of wti returns is larger than that of brent returns at identical confidence levels moreover the ged garch model can estimate the downside dynamic var accurately for wti and brent oil returns

income taxation with intergenerational mobility can higher inequality lead to less progression abstract we introduce the notion of social mobility into an optimal income tax model this is done by allowing earning abilities to be partly innate and partly acquired through investments in human capital education the implications for the optimal re distributive policy are studied

capturing deep tail risk via sequential learning of quantile dynamics abstract this paper develops a conditional quantile model that can learn long term and short term memories of sequential data it builds on sequential neural networks and yet outputs interpretable dynamics we apply the model to asset return time series across eleven asset classes using historical data from the 1960s to 2018 our results reveal that it extracts not only the serial dependence structure in conditional volatility but also the memories buried deep in the tails of historical prices we further evaluate its value at risk forecasts against a wide range of prevailing models our model outperforms the garch family as well as models using filtered historical simulation conditional extreme value theory and dynamic quantile regression these studies indicate that conditional quantiles of asset return have persistent sources of risk that are not coming from those responsible for volatility clustering these findings could have important implications for risk management in general and tail risk forecasts in particular

health and wage a simultaneous equation model with multiple discrete indicators in this article we propose all econometric approach for estimating the simultaneouls effects of health and wages in a structural equations framework in the theoretical works of grossmana 1972a 1972b health is viewed as anl elldogen1oulsly determined capital stock the demand for health should rise with the wage rate as the rate of return to health investment increases with wage onl the other hand better health should raise market productivity and hence wages since health capital is an abstract theoretical concept it can hardly be measured quantitatively however most population surveys include various health indicators these indicators are usually discrete variables in the empirical work of grossman and benham 1974 these qualitative indicators are treated as continuous variables and two stage least squares estimation techniques are used this specification raises various econometric problems see e g goldberger 1964 pp 248 255 domencich and mcfadden 1975 and nerlove and press 1973 a satisfactory specification should take into account the discrete nature of the indicators our specification generalizes the dummy variables simultaneous equations system of heckman 1978 the measurement models of joreskog and goldberger 1975 and is closely related to the models of muthe n 1976 1979 muthen studies full information maximum likelihood procedures for estimation except for very simple cases this does not generally yield feasible or tractable procedures in this article we introduce a tractable procedure for statistical estimation and testing this specification and the estimation procedure is then applied to study the joint dependence of health and wages another departure of our approach from others is that we will test and correct the possible incompatibility of the various health capital indicators in the population surveys one may have subjective health indicators such as self evaluation of health which may reflect different populations perception of health we propose a statistical procedure for testing measurement compatibility and if required for correcting this problem this article is divided into two parts initially we describe the model specification estimation and statistical tests in a general simultaneous equation model with multiple discrete indicators in the second part of the paper we consider specification of a simultaneous equation model for health and wages the model

optimal taxation of bequests in a model with initial wealth we formulate an optimal taxation model where parents leave bequests to their descendants for altruistic reasons in contrast to the standard model individuals differ not only in earning abilities but also in initial inherited wealth in this model a redistributive motive for an inheritance tax which is equivalent to a uniform tax on all expenditures arises given that initial wealth increases with earning abilities the introduction of the inheritance tax either increases intertemporal social welfare or has an ambiguous effect depending on whether the external effect related to altruism is accounted for in the social objective

national health service waiting lists a discussion of competing explanations and a policy proposal abstract a discussion of the main arguments advanced to explain waiting lists in britain s national health service nhs is presented in a framework which focuses upon demand and supplier induced demand considerations the difficulties associated with determining an optimum waiting list are explicitly emphasised hence it is in the context of an alleged requirement to reduce numbers waiting that the proposal to offer a price subsidy for private medical care is appraised such a policy is compared with that of direct expansion of expenditure on the nhs attention is drawn to the second round effects of supplier induced demand which may be associated with these policies

semi parametric estimation of hurdle regression models with an application to medicaid utilization this paper develops a semi parametric estimation method for hurdle two part count regression models the approach in each stage is based on laguerre series expansion for the unknown density of the unobserved heterogeneity the semi parametric hurdle model nests poisson and negative binomial hurdle models which have been used in recent applied literature the empirical part of the paper evaluates the impact of managed care programmes for medicaid eligibles on utilization of health care services using a key utilization variable the number of doctor and health centre visits health status measures and age seem to be more important in determining health care utilization than other socio economic and enrollment variables the semi parametric approach is particularly useful for the analysis of overdispersed individual level data characterized by a large proportion of non users and highly skewed distribution of counts for users 1997 john wiley sons ltd

health as an unobservable a mimic model of demand for health care abstract this paper develops a model to analyze the demand for health care it differs from current practice in that 1 it deals explicitly with the complex relation between income health health insurance and the demand for health care and 2 health is treated as an unobservable variable we present the maximum likelihood estimates of an eleven equation simultaneous multiple indicator multiple causes mimic model containing two simultaneously determined unobservables and in total nine indicators data used stem from a health care survey among 8000 households in the netherlands the results show among other things that health and permanent income have mutual positive impacts both age and education have important direct and indirect via permanent income effects on health the estimated impact of the availability of health care on individual demand confirms similar results based on aggregated data

capital income taxation and the atkinson stiglitz theorem abstract accounting for the role of financial system and money holdings in an optimal nonlinear income tax model we argue that capital income taxation is a non redundant policy tool even if individual preferences are separable between leisure and other goods

the demand for health some new empirical evidence this paper presents some new estimates of the pure investment and pure consumption models of the demand for health in contrast to previous studies the paper presents parameter estimates of both reduced form and structural demand for health care equations the latter which are obtained by treating health capital as a latent variable in a recursive equation system provide a safer way of checking the consistency of the model s predictions with the data the present analysis of the pure consumption model differs from previous analyses in its recognition of the dependency of the shadow price of initial assets on the entire lifetime profiles of the model s exogenous variables the paper also explores the implications in terms of reliability of parameter estimates of the failure on the part of previous studies to recognize this

redistribution with unobservable bequests a case for taxing capital income this paper addresses the question of the optimal taxation of labour and interest income in an overlapping generations model with two unobservable characteristics ability and inheritance we assume realistically that saving can only be taxed anonymously whereas the tax on labour earnings can be individualized and made non linear in such a setting we show that a withholding tax on interest income along with a non linear tax on labour income is desirable the role of interest income taxation is to indirectly tax inherited wealth

capital income taxation when inherited wealth is not observable this paper extends the atkinson stiglitz model of direct and indirect taxation to a dynamic setting with two unobservable characteristics productive ability and inherited wealth bequests are motivated by the joy of giving a child s inheritance is a random variable with a probability distribution that depends on his parent s investment in a bequest technology public borrowing is assumed and implies the modified golden rule we study the optimal tax policy when two instruments are available a non linear wage income tax and a proportional tax on capital income we show that the second instrument ought in general to be used but that the tax rate is not necessarily positive however a positive tax rate is more likely when there is a positive correlation between inherited wealth and innate ability

a model of declining health and retirement the declining u s average retirement age has been difficult to reconcile with cross section evidence that poor health is a primary cause of early retirement this paper reconciles those observations by building a grossman type model of investment in health distinguished from its predecessor by a more formal treatment of initial conditions a discontinuous mid life increase in health investment retirement is shown in general to be part of the optimal investment strategy time series productivity increases are shown to lower the optimal retirement age while varying health endowments and depreciation rates are shown to be able to account for cross section retirement age variations

frontier estimation how useful a tool for health economics the journal is pleased to publish in this issue three papers that apply frontier estimation techniques to hospitals and nursing homes together with an exchange over the usefulness of those techniques in the health care context the papers represent the current state of the art with respect to applications of frontier estimation in health care because of the growing popularity of the technique no doubt in part from its availability in standard software packages it seems useful to take this opportunity to appraise its usefulness one might begin by asking usefulness for what assuming one could define a frontier with certainty how would one use such knowledge a straightforward application in health care appears to be to reimbursement because both data envelopment analysis dea and stochastic frontier estimation specify the least cost mix of inputs for a given output both methods can in principle be used to determine whether a given firm hospital or nursing home is efficient and if the answer to that question is no the magnitude of any inefficiency it is not a large step from that information to the notion that a regulator should reduce the firm s budget by the amount of the measured inefficiency indeed vitaliano and toren mention the boren amendment s requirement that the medicaid program reimburse hospitals and nursing homes at the cost incurred by an efficiently operated

how relevant is volatility forecasting for financial risk management it depends if volatility fluctuates in a forecastable way volatility forecasts are useful for risk management hence the interest in volatility forecastability in the risk management literature volatility forecastability however varies with horizon and different horizons are relevant in different applications moreover existing assessments of volatility forecastability are plagued by the fact that they are joint assessments of volatility forecastability and an assumed model and the results can vary not only with the horizon but also with the assumed model to address this problem we develop a model free procedure for assessing volatility forecastability across horizons perhaps surprisingly we find that volatility forecastability decays quickly with horizon volatility forecastability although clearly of relevance for risk management at the short horizons relevant for say trading desk management may be much less important at longer horizons

unemployment and mortality in post war scotland abstract one of the more controversial topics in the literature examining the influence of unemployment on health is the hypothesised relation between unemployment and mortality this paper presents a time series analysis of unemployment and mortality in post war scotland using a variety of model specifications and several measures of the age and duration structure of male unemployment we find little evidence of a consistent association between unemployment and male mortality from all causes in different age cohorts unemployment however appeared to be more closely associated with variations in mortality rates from ischaemic heart disease but the direction of effect was sensitive to the choice of maximum lag length between unemployment and mortality there was also little evidence that per capita real incomes or health expenditure exerted a significant influence on mortality our general findings and the methodological limitations of macro studies of the relationship between unemployment and mortality highlight the importance of investigating the health consequences of unemployment using well controlled longitudinal studies of individuals

value at risk for long and short trading positions in this paper we model value at risk var for daily stock index returns using a collection of parametric models of the arch family based on the skewed student distribution we show that models that rely on a symmetric density distribution for the error term underperform with respect to skewed density models when the left and right tails of the distribution of returns must be modelled thus var for traders having both long and short positions is not adequately modelled using usual normal or student distributions we suggest using an aparch model based on the skewed student distribution to fully take into account the fat left and right tails of the returns distribution this allows for an adequate modelling of large returns defined on long and short trading positions the performances of all models are assessed on daily data for the cac40 dax nasdaq nikkei and smi stock indexes we also compute the expected short fall and the average multiple of tail event to risk measure for the new model

caviar conditional autoregressive value at risk by regression quantiles value at risk var has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes var is defined as the value that a portfolio will lose with a given probability over a certain time horizon usually one or ten days despite its conceptual simplicity its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions interpreting the var as the quantile of future portfolio values conditional on current information we propose a new approach to quantile estimation which does not require any of the extreme assumptions invoked by existing methodologies such as normality or i i d returns the conditional autoregressive value at risk or caviar model moves the focus of attention from the distribution of returns directly to the behavior of the quantile we specify the evolution of the quantile over time using a special type of autoregressive process and use the regression quantile framework introduced by koenker and bassett to determine the unknown parameters since the objective function is not differentiable we use a differential evolutionary genetic algorithm for the numerical optimization utilizing the criterion that each period the probability of exceeding the var must be independent of all the past information we introduce a new test of model adequacy the dynamic quantile test applications to simulated and real data provide empirical support to this methodology and illustrate the ability of these algorithms to adapt to new risk environments

demand for health a generalised grossman model the demand for health and medical care is analysed within a generalised grossman type health investment model its underlying assumptions are shown to differ from those employed earlier in a manner which avoids some of the criticisms levelled at grossman s model the comparative static predictions of the generalised model are examined and it is demonstrated that most previous health investment models are derivable from it also the present model is applicable to a new wider range of problems thus increasing the scope of economic explanations of health behaviour