s p 500 cash stock price volatilities s p 500 stock return volatilities are compared to the volatilities of a matched set of stocks after controlling for cross sectional differences in firm attributes known to affect volatility no significant difference in volatility is observed between 1975 and 1983before the start of trade in index futures and index options since then s p 500 stocks have been relatively more volatile the difference is statistically but not economically significant the relative increase occurs primarily in daily returns and only to a lesser extent in longer interval returns other factors besides the start of derivative trade could be responsible for the small increase in volatility stock price volatility has received much attention in the popular press over the last few years especially since the october 19 1987 stock market crash the rise in volatility has alarmed investors regulators and the public in general some suggest that the start of trade in stock index futures and index options increased speculative activity that in turn destabilized cash markets causing higher volatility large trading activity in the derivative contracts makes the suggestion plausible volume in index futures and index options increased dramatically since their introductions in 1982 and 1983 by 1987 the average daily dollar volume in the s p 500 futures contracts alone exceeded the dollar volume of cash s p 500 trade by a factor of about two while the dollar value of the daily net change in total open interest is about 8 of s p 500 stock dollar volume speculative trade in futures and options frequently is accused of destabilizing underlying cash markets the charge has been made for more than a century in the agricultural precious metal and currency markets recent evidence by french and roll 1986 showing stock variance to be strongly related to trading session hours heightens these concerns unfortunately theoretical analyses of whether speculative trade destabilizes cash markets lead to conflicting conclusions depending on what assumptions are made 1 school of business administration university of southern california and office of economic analysis u s securities and exchange commission i wish to thank mary denny mcsweeny and steve hornstein for their valuable research assistance and the referee and editor for their many suggestions and insights the opinions expressed in this paper do not necessarily reflect those of the u s securities and exchange commission or those of the author s colleagues on its staff an increase in well informed speculative trade has two opposite effects on measured volatility it decreases volatility due to order flow imbalances caused by uninformed traders because informed traders provide liquidity in such events and it increases volatility due to new fundamental information since the information which is assumed to be generated at discrete time intervals is impounded into

a rank dependent utility model of uncertain lifetime abstract in a continuous time life cycle model of consumption with an uncertain lifetime we use a non parametric specification of rank dependent utility theory to characterize the preferences of the agent we prove that time consistency holds for a subclass of probability weighting function providing the foundation for a constant rate of time preference that interacts multiplicatively with the hazard rate instead of additively as in the yaari 1965 seminal model we calibrate both models to explain the hump in the life cycle consumption and show that the multiplicative model is more robust

female labour supply and marital status decisions a life cycle model this paper studies the interdependence between and the determinants of life cycle marital status and labour force participation decisions of women a dynamic utility maximization model is presented and estimated using longitudinal data on women from the panel study of income dynamics the mle method employed involves solving a dynamic programming problem further a minimum distance estimator is proposed which allows for the incorporation of wage data in a computationally simple way the estimates are used to predict changes in the life cycle patterns of employment marriage and divorce due to differences in education race the female s earnings and her potential husband s earnings the estimation results indicate that the utility gains to marriage are decreasing in the female s wage rate and increasing in her potential husband s earnings while the opposite is found for gains to working ignoring the endogeneity of marital status decisions is shown to lead to an underestimation of own and husband s wage effects on female labour supply

the impact of body weight on occupational mobility and career development this paper examines the relationship between individuals weight and their employment decisions over the life cycle i estimate a dynamic stochastic model of individuals annual joint decisions of occupation hours worked and schooling the model allows body weight to affect non monetary costs switching costs and distribution of wages for each occupation and also allows individuals employment decisions to affect body weight i use conditional density estimation to formulate the distributions of wages and body weight evolution i find that heavier individuals face higher switching costs when transitioning into white collar occupations earn lower returns to experience in white collar occupations and earn lower wages in socially intensive jobs simulating the model with estimated parameters decreased occupational mobility accounts for 10 percent of the obesity wage gap while contemporaneous wage penalties for body weight are small the cost over the life cycle is substantial an exogenous increase in initial body mass by 20 percent leads to a 10 percent decrease in wages over the life course

the effect of salaries and opportunity costs on duration in teaching evidence from michigan this paper demonstrates that salaries and opportunity costs have important influences on how long teachers stay in teaching the empirical work is based on a new longitudinal dataset providing information on the careers of 7800 michigan public school teachers the generalized least squares estimation technique accommodates censored observations time varying covariates and fixed effects one implication of the result is that predictions from the current generation of teacher supply and demand models are likely to be misleading copyright 1989 by mit press

how vouchers could change the market for education small probability that vouchers will in the foreseeable future be adopted on a large scale in any school district or state at the moment only three states have adopted publicly funded voucher programs and all of these programs are limited in scale nonetheless in recent years over 40 state legislatures have considered proposals to provide some type of voucher program or tuition tax credit for at least some families in a given state or school district and the children s scholarship fund see http www scholarshipfund org has helped create or expand privately funded voucher programs in numerous cities as vouchers become a more significant part of education policy debates the time is right to consider what we know and do not know about the likely effects of adopting various voucher schemes in the balance of this paper i describe both empirical and theoretical work on education that speaks to this topic i argue that we cannot confidently predict the outcomes that would result from various voucher schemes and i also stress that debates over vouchers per se are not informative details concerning funding targeting and discretion in the use of vouchers should greatly affect the outcomes associated with any particular voucher program still empirical evidence on the performance of public versus private schools as well as numerical results from existing simulation models suggest that policymakers should be able to design voucher programs that would be helpful to minority students in large cities public schools in large cities often perform poorly in minority neighborhoods and this is especially true in economically disadvantaged areas

job exit behavior of older men a dynamic programming model of job exit behavior and retirement is constructed and estimated using the method of simulated moments the model and estimation method allow for both unobserved individual effects and unobserved job specific match effects the model is estimated using two different assumptions about individual discount factors first a static model with the discount factor equal to zero is estimated then a dynamic model with the discount factor equal to 95 is estimated in both models it is found that bad health age and lack of education increase the probability of retirement the dynamic model performs better than the static model and has different implications for retirement behavior the job specific effects are an important source of unobserved heterogeneity copyright 1991 by the econometric society

a contribution to event study methodology with an application to the dutch stock market abstract this paper proposes an extended market model for event studies based on daily stock returns for actual data the assumptions of the simple market model are violated the return distribution is not normal and neither the variance of the error term nor the risk parameter beta are constant our model incorporates the generalized autoregressive conditional heteroskedasticity garch model with t distributed errors and a time dependent beta we test for anomalies by adding dummy variables in the regression equation our model is fairly general and could be used in a wide variety of event study situations we illustrate the model by an analysis of the weekend and the option expiration effect we use return data from the dutch stock market the weekend effect on stock returns is significant but no expiration effect could be detected

the quality and distribution of teachers under the no child left behind act the heart of accountability under the no child left behind nclb act is an attempt to change the existing incentives in schools with the ultimate objective that all students meet a proficiency standard existing research indicates that nothing is more important to high achieve ment as having effective teachers implying that the impact of new incentives on teachers will be central to any consideration of the accountability statutes tracing the impacts of nclb on the stock and distribution of teachers is none theless a difficult and uncertain task the belief that the quality of teachers matters a great deal to the quality of education received by students has actually proven hard to substantiate and the reasons for this difficulty are key to assessing the impacts of no child left behind a substantial body of research going back to the coleman et al 1966 report has attempted to link commonly used measures of teacher quality such as experience degree level and state teacher certification to student outcomes surprisingly except for perhaps the first few years of classroom experience no robust connection has appeared for example hanushek and rivkin 2006 review various studies attempting to identify characteristics of effective teachers one

conditional heteroscedasticity in time series of stock returns evidence and forecasts this article presents new evidence about the time series behavior of stock prices daily return series exhibit significant levels of second order dependence and they cannot be modeled as linear white noise processes a reasonable return generating process is empirically shown to be a first order autoregressive process with conditionally heteroskedastic innovations in particular generalized autoregressive conditional heteroskedastic garch 1 1 processes fit to data very satisfactorily various out of sample forecasts of monthly return variances are generated and compared statistically forecasts based on the garch model are found to be superior copyright 1989 by the university of chicago

uncertainty and hyperbolic discounting we propose an evolutionary explanation for the pattern of intertemporal preference reversals often ascribed to hyperbolic discounting we take the view that preferences manifested for example in urges cravings and inclinations are the outcome of evolutionary forces and so will induce animals or humans to make survival maximizing choices in typical decision problems we show that if the typical problem involves payoffs whose realization times are uncertain then optimal preferences give rise to relatively patient behavior when the time horizon is long but induce a switch to impatience when the horizon grows short such reversals do not entail dynamic inconsistency in typical decision problems behavior there is optimal however if a decision maker is confronted with a choice for which the realization time uncertainty falls outside the evolutionary norm her preferences may well prompt her to behave inconsistently we argue that if such a choice problem recurs her evolutionarily endowed aability to learn will lead her to make self commitments against these urges this abstract was borrowed from another version of this item

an empirical investigation of the possibility of stochastic systematic risk in the market model in most empirical work on the market model the parameters of that model are estimated by ordinary least squares effectively assuming that the systematic risk of an asset or portfolio is constant through time however a plausible alternative hypothesis would allow the systematic risk of the stock of a company to vary through time such variation may arise through the influence of either microeconomic factors such as operational changes in the company or changes in the business environment peculiar to the company or macroeconomic factors such as the rate of inflation general business conditions and expectations about relevant future events a detailed discussion of these points is provided by rosenberg and guy 1976a 1976b support for the hypothesis that systematic risk varies through time is provided in the studies by jacob 1971 blume 1975 and fabozzi and francis 1978 in this paper we allow the possibility that systematic risk of an asset is stochastic in principle an attempt to model this stochastic behavior could be made through allowing systematic risk to follow a member of the general arima class of models of box and jenkins 1970 ideally the available data would be employed to suggest a specific model from this general class however this approach has to face very serious we discuss the market model in which the possibility is allowed that beta is stochastic and obeys a first order autoregressive process following a brief discussion of methodological issues in the estimation and testing of such models results are reported on an empirical study of a large sample of monthly returns of common stock we find strong evidence indicating stochastic systematic risk but relatively little evidence against the random coefficient model

an examination of the robustness of the weekend effect this paper analyzes the robustness of the day of the week dow and weekend effects to alternative estimation and testing procedures the results show that sample size can distort the interpretation of classical test statistics unless the significance level is adjusted down ward specification tests reveal widespread departures from ols assumptions hypothe sis tests results are reported using robust econometric methods and a garch model the strength of the dow and weekend effect evidence appears to depend on the estimation and testing method both effects seem to have disappeared by 1975

the price effect of option introduction this paper examines the price effect of option introduction from 1974 to 1980 the introduction of individual options causes a permanent price increase in the underlying security beginning approximately three days before introduction the price effect appears to be associated with introduction and not announcement throughout the sample period excess returns volatility declines with option introduction systematic risk is unchanged there is a positive relation between the price increase and a measure of activity in the options market copyright 1989 by american finance association

volatility persistence and stock valuations some empirical evidence using garch summary in this paper issues of volatility persistence and the changing risk premium in the stock market are investigated using the garch estimation technique we get a point estimate of the index of relative risk aversion of 4 5 and confirm the existence of changing equity premiums in the us during 1962 1985 the persistence of shocks to the stock return volatility is so high that the data cannot reject a non stationary volatility process specification the results of this paper are consistent with malkiel and pindyck s hypothesis that it is the unforseen rise ini the investment uncertainty during 1974 that causes the market to plunge

testing the martingale hypothesis in deutsche mark futures with models specifying the form of heteroscedasticity summary we examine the form of heteroscedasticity in deutsche mark futures price data and compare different specifications of the particular way that the variance is changing over time the martingale hypothesis is tested with daily and weekly rates of change of futures prices for the deutsche mark and some evidence is found against this hypothesis in analyses of daily data from 1981 to 1985 this rejection of the martingale hypothesis may be attributed to trading day effects in foreign currency prices and the resulting day of the week patterns in futures prices when the martingale hypothesis is tested with weekly data the null hypothesis is retained

green expectations current effects of anticipated carbon pricing i report evidence that an anticipated strengthening of environmental policy increased emissions i find that the breakdown of the u s senate s 2010 climate effort generated positive excess returns

value functions for infinite period planning cost benefit and risk analysis studies that model tradeoffs between the present and the distant future by means of present value discounting have been criticized for according the future and thus future generations far too little importance this paper presents an alternative means of modeling tradeoffs between different periods that accords the future far more importance than present value discounting and that is no more difficult to apply the paper also presents a means of modeling the preference issue of concern for equity or stability between different periods

strotz meets allais diminishing impatience and the certainty effect abstract decision makers tend to exhibit a higher degree of impatience when considering a delay to an immediate reward than when contemplating an identical delay to an equal future reward this work argues that diminishing impatience originates from the distinction between the certain present and the risky future a simple functional representation of preferences exhibiting time inconsistency when the future is uncertain is derived experimental evidence which is inconsistent with other formulations that account for diminishing impatience supports the proposed approach the new theory uncovers a tight relation between diminishing impatience and well known behavioral regularities in choice under risk and uncertainty jel d12 d81

earnings announcements stock price adjustment and the existence of option markets this paper employs a new approach to study the effects of option trading on the behavior of underlying stock prices extant research compares distributional properties of the stock price at two points in time divided by an event in the option market that might affect price behavior as an alternative we examine the stock price adjustment to the release of quarterly earnings using samples of firms with and without listed options we find the two samples exhibit different adjustment processes with the nonoption firms requiring substantially more time to adjust since the advent of organized stock option trading the investment community

teacher quality in public and private schools under a voucher system the case of chile chile is unusual in having long term experience with nationwide school vouchers a key criticism of school voucher systems is that they make it easier for private schools to attract better teachers to the detriment of public schools this paper uses longitudinal data from chile to estimate a discrete choice dynamic programming dcdp model of teacher and nonteacher labor supply decisions and to explore how wage policies affect the composition of the teacher labor force in public and private schools in the model individuals first decide whether to get a teaching degree and then choose annually from among five work home sector alternatives empirical results show that private voucher schools attract better teachers than public schools however the existence of the private voucher sector also draws higher productivity individuals into the teaching profession

how does germany s green energy policy affect electricity market volatility an application of conditional autoregressive range models abstract based on a dynamic model for the high low range of electricity prices this article analyses the effects of germany s green energy policy on the volatility of the electricity market using european energy exchange data from 2000 to 2015 we find rather high volatility in the years 2000 2009 but also that the weekly price range has significantly declined in the period following the year 2009 this period is characterised by active regulation under the energy industry law enwg the eu emissions trading directive etd and the renewable energy law eeg in contrast to the preceding period price jumps are smaller and less frequent especially for day time hours implying that current policy measures are effective in promoting renewable energies while simultaneously upholding electricity market stability this is because the regulations strive towards a more and more flexible and market oriented structure which allows better integration of renewable energies and supports an efficient alignment of renewable electricity supply with demand

life cycle preferences revisited an axiomatic construction for life cycle preferences accounting for the finiteness and the randomness of life duration is provided we emphasize the role of intertemporal correlation aversion and explain why multiplicative preferences provide an interesting alternative to additive preferences allowing risk aversion and intertemporal elasticity of substitution to be separated implications regarding the shape of the optimal consumption profiles are discussed

incentives work getting teachers to come to school we use a randomized experiment and a structural model to test whether monitoring and financial incentives can reduce teacher absence and increase learning in india in treatment schools teachers attendance was monitored daily using cameras and their salaries were made a nonlinear function of attendance teacher absenteeism in the treatment group fell by 21 percentage points relative to the control group and the children s test scores increased by 0 17 standard deviations we estimate a structural dynamic labor supply model and find that teachers respond strongly to financial incentives our model is used to compute cost minimizing compensation policies jel i21 j31 j45 o15

comparative risk aversion a formal approach with applications to saving behavior we consider a formal approach to comparative risk aversion and applies it to intertemporal choice models this allows us to ask whether standard classes of utility functions such as those inspired by kihlstrom and mirman 1974 selden 1978 epstein and zin 1989 and quiggin 1982 are well ordered in terms of risk aversion moreover opting for this model free approach allows us to establish new general results on the impact of risk aversion on savings behaviors in particular we show that risk aversion enhances precautionary savings clarifying the link that exists between the notions of prudence and risk aversion

a theory of anticipated utility abstract a new theory of cardinal utility with an associated set of axioms is presented it is a generalization of the von neumann morgenstern expected utility theory which permits the analysis of phenomena associated with the distortion of subjective probability

the retirement consumption puzzle evidence from a regression discontinuity approach in this paper we investigate the size of the consumption drop at retirement in italy we use micro data on food and total non durable household spending covering the period 1993 2004 and evaluate the change in consumption that accompanies retirement by exploiting the exogenous variability in pension eligibility to correct for the endogenous nature of the retirement decision we take a regression discontinuity design approach and make the identifying assumption that consumption would be the same around the threshold for pension eligibility if individuals would not retire we check in our data that a non negligible fraction of individuals retire as soon as they become eligible and estimate at 9 8 the part of the non durable consumption drop that is associated with retirement induced by eligibility we show that such fall is not driven by liquidity problems for the less well off in the population and can be accounted for by drops in goods that are work related expenses or leisure substitutes however we also show that retirement induces a significant drop in the number of grown children living with their parents and this can account for most of the retirement consumption drop

dynamic labour force participation of married women and endogenous work experience this paper presents and estimates a dynamic model of married women s labour force participation and fertility in which the effect of work experience on wages is explicitly taken into account because current participation alters future potential earnings the investment return to work will be an important factor in the current work decision in any forward looking behavioural model the model is estimated using the national longitudinal surveys mature women s cohort we use the estimates of our model to predict changes in the lifecycle patterns of employment due to changes in schooling fertility husband s income and the magnitude of the experience effect on wages we find that although work experience increases the disutility of further work the effect is overwhelmed by the positive effect of experience on wages leading to persistence in the employment patterns of these women in addition we find that an increase in young children and in husband s income substantially reduces participation while increased schooling has a powerful positive impact on participation this paper presents an estimable structural dynamic model of married women s labour force participation and fertility in which wages are stochastic and work experience or cumulative participation is endogeneous the model is structural in the sense that the parameters which are estimated are contained in the fundamental relationships governing behaviour namely the utility function and the constraints the model is contained in the class of models which describe the life cycle capital accumulation process with endogeneous labour supply such as weiss 1972 and heckman 1976 it is closest in spirit to that of weiss and gronau 1981 1 the basic feature of their model and ours is that labour market participation affects future wages which then affects future participation the investment return to current work will necessarily be taken into account in any forward looking optimizing model as weiss and gronau note estimates of labour supply models have ignored the inherent behavioural dynamics associated with a positive wageexperience profile there is no adequate empirical treatment of the human capital investment dimension of the labour force participation decision in the literature heckman and willis 1977 have studied a sequential discrete choice model of the labour force participation of married women in a reduced form framework their work

a dynamic model of teacher labor supply the labor supply decisions of certified elementary and high school teachers are examined using data from a general longitudinal survey a significant decrease in the teaching participation rate tak

the influence of classroom characteristics on high school teacher turnover i introduction a number of authors have suggested that the u s will face a shortage of qualified teachers in the near future especially in the areas of math and science 1 school districts facing such a shortage could respond in a variety of ways for instance hiring standards could be lowered teachers could be asked to teach outside their areas of certification or funds permitting starting salaries could be increased in an effort to attract the most promising candidates still another option would be to raise teaching loads i e average class size or the number of classes taught thus making do with fewer teachers this option is particularly alluring in light of the fact that average class size has been falling rapidly in the u s over the last twenty years and yet no strong connection between smaller classes and increased student learning has been established 2 there is however a possible hidden cost that needs to be investigated before recommending such a course of action if teachers respond to larger or more frequent classes by quitting then a district that tries to solve its hiring problems in this fashion could simply be increasing its demand for new teachers this paper uses data from the new york state education department s personnel master file for the years 1979 to 1989 in order to investigate whether an increased teaching load affects the likelihood that a teacher will leave his or her district in order to obtain an unbiased sample of job lengths the sample is restricted to full time high school teachers who were newly hired in 1979 3 we estimate a discrete time hazard model in which teaching load is measured as the average class size taught by an individual the number of classes taught and the proportion of classes taught in the teacher s certified area in interpreting our results we pay special attention to whether the behavior of math and science teachers differs from that of other teachers this is an important issue because shortages of qualified teachers in these two areas are predicted to be especially acute ii background the market for teachers differs from a well functioning neoclassical labor market in that salaries are determined through a political process involving various levels of government the public and often teachers unions 4 if the demand for teachers increases as retirements and student enrollment increase then starting salaries cannot be counted on to quickly move to the market clearing level and thus a shortage of teachers becomes a possibility 5 few observers however believe that there will be an actual shortage of warm bodies the more likely scenario is that there will be a lack of teachers trained in specific areas and of high quality teachers in general see murnane et al 1991 1 2 given a limited budget what are the options available to a school district facing this type of shortage the district could settle for hiring lower quality teachers but this might be seen as an unnecessary measure with long term implications taken in response to what could be a temporary situation another option that has been suggested is to increase teacher workloads 6 whether this option is workable depends in part on the exit decisions of teachers a large number of empirical studies have investigated the determinants of teacher turnover however no work specifically directed toward capturing the effect of increased teaching responsibilities on turnover has been done 7 without knowing whether such an effect exists and what the magnitude of it might be informed policy decisions at the district level in response to a shortage of qualified teachers becomes impossible past studies have shown that the probability of a teacher leaving his or her job is high in the first few years after entering the profession falls after the third year 8 and again increases as the teacher nears retirement age murnane et al

the dynamics of teacher quality abstract an extensive literature finds that while teachers vary considerably in initial quality there are limited teacher quality dynamics except for the first few years of teaching teacher quality does not improve over the course of a teacher s career this study evaluates the importance of various modeling restrictions to the key findings of this literature using data covering all 5th grade public school teachers from the state of north carolina i replicate the findings of the previous literature using their restrictive experience assumptions however using an unrestricted experience model i find that for mathematics achievement there are high returns to later career teaching experience about twice as much dispersion in initial teacher quality as previously estimated and a pattern of negative selection where high quality teachers are more likely to exit

uncertain lifetime risk aversion and intertemporal substitution abstract this paper describes a simple utility function for dynamic choice problems under uncertain lifetime preferences are time consistent and similar to selden s ordinal certainty equivalent hypothesis for yaari s model of consumption savings decisions holding intertemporal substitution fixed the consumption growth rate is increasing decreasing in the mortality rate if risk aversion is lower higher than under expected utility preferences

recruiting and retaining teachers in the uk an analysis of graduate occupation choice from the 1960s to the 1990s this paper examines the market for teachers in the uk from 1960 to 2002 using six graduate cohort data sets we find that while there is no strong evidence that teachers are underpaid the relative wages in teaching compared with alternative professions have a significant impact on the likelihood of graduates choosing to teach this wage effect is strongest at times of low relative teachers wages or following a period of decline in those wages it is also strongest for those individuals who have more recently graduated and for men

compensation policies and teacher decisions a dynamic discrete choice framework with a flexible structure for unobserved heterogeneity is used to model the occupational decisions of individuals who are certified to teach in elementary and secondary schools the model is estimated using data from the national longitudinal study of the high school class of 1972 and is used to examine the effects of possible changes in the compensation policy for teachers

career paths and quit decisions evidence from teaching conventional models predict that workers consider employment opportunities and monetary rewards expected over their lifetimes when making current period decisions such as whether to quit a job this article tests the hypothesis that later career opportunities affect quit decisions by examining the relationship between teaching and school administration evidence on the extent to which administrative positions are available to teachers and the salary premia associated with them is presented discrete time logit hazard models of teacher quits estimated using data from new york state provide some support for the hypothesis though the magnitudes of the estimated effects are small

some further evidence on the stochastic properties of systematic risk although there is consensus in the finance literature that the beta risk of equity securities is stochastic there is considerable disagreement as to whether the var iation is purely random or exhibits autocorrelation through time to investigate this issue the authors employ a model that allows beta t o exhibit both random and autoregressive behavior simultaneously the y test this model against alternative specifications on a large sampl e of individual securities and randomly formed portfolios comprising 10 50 and 100 securities results are also presented for portfolios formed according to firm size copyright 1987 by the university of chicago

do public schools hire the best applicants despite a surplus of candidates for most teaching jobs a strong academic record does little for an applicants job prospects this does not appear to result from lukewarm interest on the part of such applicants or choosiness about the positions they accept administrators lack of interest in these candidates may reflect the weakness of competitive pressures in public education policies intended to improve teacher quality need to consider incentives on both the demand and supply sides of the market

uncertain lifetime and intertemporal choice risk aversion as a rationale for time discounting this article makes explicit the links between preferences over lotteries on length of life and intertemporal choice it shows that the approach used by traditional life cycle models to account for uncertain survival corresponds to a strong assumption of risk neutrality with respect to length of life relaxing such an assumption leads us to develop a more general formulation of lifetime utility in which time discounting is directly related to preferences over length of life exponential and hyperbolic discounting are found to result in a first approximation from constant and hyperbolic risk aversion with respect to length of life

leaving teaching in the uk a duration analysis in this paper the authors analyze the decision by teachers to leave the profession their results affirm the importance of relative earnings in the tenure and turnover decisions of teachers the econometric modeling approach used yields important insights into the appropriateness of adopting a flexible semiparametric specification of the duration dependence structure and of the unobserved heterogeneity distribution in duration models copyright 1995 by royal economic society

teacher mobility responses to wage changes evidence from a quasi natural experiment low mobility responses to wage changes imply rents associated with existing employment relationships for example continued employment after a wage cut all else equal reflects rents in the hand of the worker at the outset and symmetrically voluntary quits after a

the existence uniqueness and optimality of the terminal wealth depletion time in life cycle models of saving under uncertain lifetime and borrowing constraint abstract in life cycle models of saving under uncertain lifetime and borrowing constraint the consumer s wealth must be depleted before the maximum lifetime this paper investigates the existence uniqueness and optimality of the terminal wealth depletion time it is proved that the optimal terminal wealth depletion time if such exists must be unique if the equation that determines the optimal terminal wealth depletion has multiple solutions then the location of the optimal solution will depend on the configuration of the solutions an optimality test is developed to verify whether a candidate solution for the terminal wealth depletion time is indeed optimal the paper introduces a method new to economics the dubovitskii milyutin adjoint equation to analyze the properties of the optimal control problem