further results on asset pricing with incomplete information abstract this paper extends the analysis of asset pricing when information is incomplete by relaxing some of the restrictive assumptions of the gaussian model studied earlier in the literature for the information structure considered the posterior beliefs of the investor the conditional distribution of the current state given the past observations are characterized by two sets of sufficient statistics implementable in the form of a filter i the vector of conditional means and ii a set of sufficient statistics for the conditional variance covariance matrix a separation theorem is demonstrated and used to produce a closed form solution for the interest rate process when the investor s utility function is logarithmic in this context we examine the informational efficiency properties of the interest rate and analyze the stochastic shifts in the volatility of the interest rate process

jump diffusion processes and the term structure of interest rates the authors investigate the term structure of interest rates when the underlying state variables and production technologies follow the jump diffusion processes even in some cases where the traditional expectations theory about the term structure is consistent with general equilibrium under diffusion processes the traditional theory is not consistent under jump diffusion processes it is shown that bond prices are strictly higher under jump risks than otherwise and that consumers with logarithmic utility functions will develop hedge portfolios in the presence of jump diffusion a number of continuous time asset pricing models have been derived under stochastic diffusion processes with continuous sample paths see e g black and scholes 2 merton 21 breeden 3 and cox ingersoll and ross 8 however recent empirical studies see e g brown and dybvig 4 feinstone 10 and jarrow and rosenfeld 17 suggest that the underlying processes may follow

consumption and equilibrium interest rates in stochastic production economies in this paper we analyze the behavior of equilibrium real interest rates in an identical consumer economy in which the preferences are represented by time additive logarithmic utility functions and production technologies are cobb douglas with stochastic constant returns to scale the following main results are established i when there is no relative price uncertainty it is shown that the equilibrium interest rate exhibits a mean reverting tendency a nontrivial steady state distribution is found to exist for the equilibrium interest rate the properties of the equilibrium interest rate are also derived and discussed ii in a multigood economy even with additive preferences across goods the equilibrium interest rates depend explicitly on relative prices the substitution possibilities in production technologies induce this result this is in contrast to the findings of richard and sundaresan 11 who show that the analytical general equilibrium term structure of interest rates formula of cox ingersoll and ross 5 is unaffected by the introduction of relative price uncertainty when the technologies are linear and hence involve no substitution furthermore we relate our results to those of cox ingersoll and ross 5 breeden 3 and richard and sundaresan 11 with special emphasis on stochastic production and realtive price uncertainty

stochastic equilibria existence spanning number and the no expected financial gain from trade hypothesis stochastic equilibria under uncertainty with continuous time security trading and consumption are demonstrated in a general setting a common question is whether the current price of a security is an unbiased predictor of the future price of the security plus intermediate dividends this is the hypothesis of no expected financial gains from trade the relevance of this hypothesis in multi good economies is called into question by the following demonstrated fact for each set of probability assessments there exists a corresponding equilibrium one with the original agents original equilibrium allocations and no expected financial gains from trade under the given probability assessments the spanning number of the economy is defined as the fewest number of security markets required to sustain a complete markets equilibrium in a dynamic sense made precise in the paper the spanning number is linked directly to agent primitives in particular the manner in which new information resolves uncertainty over time the spanning number is shown to be invariant under bounded changes in expectations several examples are given in which the spanning number is finite even though the number of potential states of the world is infinite

the term structure of interest rates in a partially observable economy this paper investigates the term structure of interest rates in a multiperiod production and exchange economy with incomplete information unable to observe their stochastic investment opportunities investors engage in dynamic bayesian inference this results in the endogenous identification of a more complex production function which generates a richer term structure resembling the one that actual market prices imply in addition this paper introduces a characteristic function of the term structure and demonstrates that in contrast with a fully observable economy the widely investigated expectations hypothesis holds true only if interest rates are nonstochastic this paper investigates the term structure of interest rates in a dynamic production and exchange economy with an unobservable productivity factor in order to estimate the unobservable stochastic investment opportunities rational investors engage in dynamic bayesian inference anticipated changes in investors quality of information about the fluctuations of the economic state variable affect equilibrium demands and prices this results in the endogenous identification of a more complex production function which induces a richer term structure term structures of interest rates in a partially observable economy resemble term structure curves that actual market prices imply this paper also introduces a characteristic function of the term structure and demonstrates that in contrast with a fully observable economy the widely investigated expectations

logarithmic preferences myopic decisions and incomplete information this paper examines a dynamic production economy with incomplete information and shows that the set of myopic preferenees those that induee myopic decisions depends on the representation of the information flow for example logarithmic preferenees are nonmyopic when some of the economic state variables are unobservable the analysis offers a broader definition of myopic behavior termed generalized myopia which is independent of the representation of the information flow allowing for any smooth concave utility function logarithmic preferenees endogenously emerge as necessary for generalized myopia in incomplete information economies and when combined with restrictions on the information structure they become sufficient i introduction this paper investigates myopic decisions and myopic preferenees in an in complete information production economy with continuous consumption and in vestment the paper interprets myopic decisions as those that do not use informa tion regarding future investment opportunities and identifies specific conditions for myopia within the model although previous research in financial economics has associated logarithmic preferenees with myopic behavior this analysis demonstrates that logarithmic preferenees necessarily induee myopic behavior only when all the economic state variables are observable based on this analysis the paper proposes a broader definition of myopia termed generalized myopia that is independent of the information flow representation the paper also provides nec essary and sufficient conditions for the existence of generalized myopia within both complete and incomplete information economies while the analysis allows for any smooth concave utility function logarithmic preferenees endogenously arise as necessary for generalized myopia in incomplete information economies and when combined with restrictions on the information structure they become sufficient

term premiums in bond returns abstract this paper examines expected returns on u s treasury bills and on u s government bond portfolios expected bill returns are estimated from forward rates and from sample average returns both estimation methods indicate that expected returns on bills tend to peak at eight or nine months and never increase monotonically out to twelve months reliable inferences are limited to treasury bills and thus to maturities up to a year the variability of longer term bond returns preempts precise conclusions about their expected returns

an intertemporal general equilibrium model of asset prices this paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices in this model asset prices and their stochastic properties are determined endogenously one principal result is a partial differential equation which asset prices must satisfy the solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy in this paper we develop a general equilibrium asset pricing model for use in applied research an important feature of the model is its integration of real and financial markets among other things the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables the model is fully consistent with rational expectations and maximizing behavior on the part of all agents our framework is general enough to include many of the fundamental forces affecting asset markets yet it is tractable enough to be specialized easily to produce specific testable results furthermore the model can be extended in a number of straightforward ways consequently it is well suited to a wide variety of applications for example in a companion paper cox ingersoll and ross 7 we use the model to develop a theory of the term structure of interest rates many studies have been concerned with various aspects of asset pricing under uncertainty the most relevant to our work are the important papers on intertemporal asset pricing by merton 19 and lucas 16 working in a continuous time framework merton derives a relationship among the equilibrium expected rates of return on assets he shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes the random output of these processes is exogenously determined and perishable assets are defined as claims to all or a part of the output of a process and the equilibrium determines the asset prices our theory draws on some elements of both of these papers like merton we formulate our model in continuous time and make full use of the analytical tractability that this affords the economic structure of our model is somewhat similar to that of lucas however we include both endogenous production and

state price densities under heterogeneous beliefs the smile effect and implied risk aversion abstract it has been widely noted in the empirical literature that state price densities implicit in financial asset prices are not log normal this paper shows that this phenomenon can be caused by heterogeneity in investors beliefs it derives the state price density under heterogeneous beliefs in closed form and demonstrates that heterogeneous beliefs can give rise to multimodal state price densities consequences for the smile effect in implied option volatility and for measures of risk aversion inferred from empirical state price densities are discussed

empirical estimates of the direct rebound effect a review beginning with william stanley jevons in 1865 a number of authors have claimed that economically justified energy efficiency improvements will increase rather than reduce energy consumption jevons paradox is extremely difficult to test empirically but could have profound implications for energy and climate policy this paper summarises and critiques the arguments and evidence that have been cited in support of jevons paradox focusing in particular on the work of len brookes and harry saunders it identifies some empirical and theoretical weaknesses in these arguments highlights the questions they raise for economic orthodoxy and points to some interesting parallels between these arguments and those used by the biophysical school of ecological economics while the evidence in favour of jevons paradox is far from conclusive it does suggest that economy wide rebound effects are larger than is conventionally assumed and that energy plays a more important role in driving productivity improvements and economic growth than is conventionally assumed 2008 elsevier ltd all rights reserved

equilibrium interest rates and multiperiod bonds in a partially observable economy this paper analyzes the market for financial assets in a production and exchange economy with several realized outputs and a single unobservable source of nondiversifiable risk the paper demonstrates that for a large class of diffusion outputs and preferences optimizing consumers first estimate the realizations of the unobservable factor and then use these estimates to determine portfolio and consumption rules moreover the explicit consideration of this unobservable productivity factor affects equilibrium demands and prices the equilibrium spot rate of interest emerges as the best estimate of the unobservable factor and multiperiod default free bonds arise as the optimal hedge for the unobservable changes of the stochastic investment opportunity set this paper analyzes the market for financial assets in a production and exchange economy with several realized outputs and a single unobservable source of nondiversifiable risk the paper poses and answers three questions 1 how do consumers determine equilibrium demands and prices when their investment opportunities are unobservable 2 in equilibrium what financial assets provide an optimal hedge for the

demographic change intergenerational linkages and public education in this brief paper i explore several issues related to u s demographic change and the political economy of public education i describe the existing empirical evidence that suggests that older and childless voters are less likely to support public school spending than younger voters with children i then note several unresolved issues about the degree to which rational self interest should lead older voters to vote for low levels of public school spending excerpt

balanced budget redistribution as the outcome of political competition this paper models balanced budget redistribution between socio economic groups as the outcome of electoral competition between two political parties equilibrium is unique in the present model and a sufficient condition for existence is given requiring that there be enough stochastic heterogeneity with respect to party preferences in the electorate the validity of hotelling s principle of minimum differentiation and of director s law are examined under alternative hypotheses concerning administrative costs of redistributions and voter s possibilities both of abstaining from voting and of becoming campaign activists for one of the parties the policy strategy of expected plurality maximization is contrasted with the strategy of maximizing the probability of gaining a plurality incomes are fixed and known so lump sum taxation is feasible however constraints on tax transfer differentiation between individuals are permitted in the analysis

the empirical implications of the cox ingersoll ross theory of the term structure of interest rates the one factor version of the cox ingersoll and ross model of the term structure is estimated using monthly quotes on u s treasury issues trading from 1952 through 1983 using data from a single yield curve it is possible to estimate implied short and long term zero coupon rates and the implied variance of changes in short rates analysis of residuals points to a probable neglected tax effect the term structure of interest rates is important to economists because the relationship among the yields on default free securities that differ in their term to maturity reflects the information available to the market about the future course of events the expectations hypothesis the liquidity preference hypothesis hicks 10 and the market segmentation hypothesis culbertson 6 are theories of the term structure that predict little more than that the implied forward rate is either equal to or not equal to the expectation of future spot rates cox ingersoll and ross 5 cir model the term structure of interest rates in a competitive equilibrium context their model has elements in common with the earlier hypotheses of the term structure however the cir model has a rich class of empirical implications not only for the pricing of default free securities but also for the pricing of bond options callable bonds and other types of financial claims this paper examines the extent to which the model in its simplest one factor form is descriptive of the prices of u s treasury bills bonds and notes traded from 1952 to 1983 section i describes the model and the parsimonious representation of bond prices which it implies section ii describes the data and section iii outlines the preliminary results obtained by fitting the model to observed data the final section outlines directions for future research

education spending in an aging america abstract in this paper we use a national panel of public school districts to study the impact of an aging population on public education spending in contrast to previous analyses that use state level data we find that the elderly have only a modest overall negative effect on education spending at the district level our results confirm however that a growing share of elderly at the state level tends to depress state spending on education these results are consistent with the hypothesis that the elderly believe only higher local spending is capitalized into house values

self interest and public funding of education abstract the objective of this paper is to study whether publicly funded education can emerge as a political and economic equilibrium in an overlapping generations economy in which selfish agents vote for public funding of education the presence of complementarities between capital and labor in the production function implies that by improving the skills of next period s workers public funding of education increases the return on capital as a result savers will support a publicly financed education system in order to enhance their future income a version of the model calibrated using u s data generates large shares of gnp allocated to education hence the non altruistic incentive to support public education is quantitatively important

existence of arrow radner equilibrium with endogenously complete markets under incomplete information abstract a stochastic pure exchange economy with incomplete information is studied where one risky asset and a locally riskless bond are traded the underlying risks are described by a k dimensional brownian motion with k 2 the brownian motion is not directly observable agents observe only asset prices and dividends existence of an arrow radner equilibrium is established in such an equilibrium asset prices result such that every informationally feasible consumption plan can be financed by trading in the risky asset and the bond in this sense the resulting asset market is complete journal of economic literature classification numbers g12 g14 d51

questioning demand a study of regretted purchases in great britain abstract this paper presents findings from a nationally representative household survey on the tendency to regret purchases across 20 product groups the survey reveals that the vast majority of adults in great britain 82 have regretted a purchase in the past post purchase regret is shown to be particularly prevalent for clothing footwear and takeaway food the tendency to regret purchases appears to reduce with age and to be more common amongst white collar rather than blue collar workers combining survey results with average price estimates gives an estimated aggregate annual expenditure on regretted purchases of 5 25bn equivalent to 2 10 of annual consumer spending on goods in great britain these findings are interesting because they suggest that there is a degree of self assessed over consumption that if reduced could help to reduce pressures on the environment

optimal portfolio choice under incomplete information models of asset pricing generally assume that the variables which characterize the state of the economy are observable however the distributional properties of asset prices that are relevant for portfolio decisions are in general not observable and therefore must be estimated the estimation of expected returns is a particularly difficult problem and estimation errors are likely to be substantial in this light it is reasonable to examine whether the assumption of observability of expected returns and other relevant state variables causes significant mis specification in equilibrium models of asset prices this paper has three main objectives first to derive optimal estimators for the unobservable expected instantaneous returns using observations of past realized returns second to establish that estimation and portfolio choice can be solved in two separate steps third to analyze the impact of estimation error on investment choices the estimators of expected returns are in general not consistent i e the estimation error does not tend to disappear asymptotically the effects of the estimation error therefore cannot be ignored even if realized returns are observed continuously over an infinite time period

single factor heath jarrow morton term structure models based on markov spot interest rate dynamics this paper considers the class of heath jarrow morton term structure models where the spot interest rate is markov and the term structure at time t is a function of time maturity and the spot interest rate at time t a representation for this class of models is derived and i show that the functional forms of the forward rate volatility structure and the initial forward rate curve cannot be arbitrarily chosen i provide necessary and sufficient conditions indicating which combinations of these functional forms are allowable i also derive a partial differential equation representation of the term structure dynamics that does not require explicit modeling of both the market price of risk and the drift term for the spot interest rate process using the analysis presented in this paper a class of intertemporal term structure models is derived

general equilibrium properties of the term structure of interest rates abstract the paper examines the allocation of consumption and investment in a three date binomial model in order to determine the sign of the real term structure premium in general equilibrium when production functions are concave markets are complete and future production possibilities are the same irrespective of which state of the world occurs the term structure premium will be positive in incomplete markets constant or increasing absolute risk aversion is sufficient to guarantee a positive term structure premium although in the more likely case of decreasing absolute risk aversion a negative premium cannot be ruled out

expected life time utility and hedging demands in a partially observable economy this paper analyzes the expected life time utility and the hedging demands in an exchange only representative agent general equilibrium under incomplete information we derive an expression for the investor s expected life time utility and analyze his hedging demands for intertemporal changes in the stochastic unobservable growth of the endowment process and the changing quality of information regarding these changes the hedging demands consist of two components which could work in opposite directions so that a conservative consumer may end up having positive hedging demands our results are qualitatively different from those prevailing under constant growth cf brennan m j 1998 the role of learning in dynamic portfolio decisions european finance review 1 295 306 ziegler a 2003 incomplete information and heterogeneous beliefs in continuous time finance springer berlin chapter 2

are we consuming too much this paper articulates and applies frameworks for examining whether consumption is excessive we consider two criteria for the possible excessiveness or insufficiency of current consumption one is an intertemporal utility maximization criterion actual current consumption is deemed excessive if it is higher than the level of current consumption on the consumption path that maximizes the present discounted value of utility the other is a sustainability criterion which requires that current consumption be consistent with non declining living standards over time we extend previous theoretical approaches by offering a formula for the sustainability criterion that accounts for population growth and technological change in applying this formula we find that some poor regions of the world are failing to meet the sustainability criterion in these regions genuine wealth per capita is falling as investments in human and manufactured capital are not sufficient to offset the depletion of natural capital

interest rates and monetary policy uncertainty abstract this paper analyzes a model in which optimizing households are uncertain about monetary policy and learn about it over time in this model the variance of changes in nominal and ex post real interest rates increases with the variance of the household s predictive distribution over money growth a positive relation between unexpected changes in nominal interest rates and the money stock results from monetary policy uncertainty finally if money growth covaries negatively with real wealth an increase in monetary policy uncertainty increases the expected real rate of interest and decreases the nominal rate of interest

volatility momentum and time varying skewness in foreign exchange returns this article tests a stochastic volatility model of exchange rates that links both the level of volatility and its instantaneous covariance with returns to pathwise properties of the currency in particular the model implies that the return volatility covariance behaves like a weighted average of recent returns and hence switches signs according to the direction of trends in the data this implies that the skewness of the finite horizon return distribution likewise switches sign leading to time varying implied volatility smiles in options prices the model is fit and assessed using bayesian techniques some previously reported volatility results are accounted for by the fitted models the predicted pattern of skewness dynamics accords well with that found in historical options prices

aging population and education finance abstract conventional wisdom suggests that aging of population will increase political pressure to tilt the composition of social spending in favor of the elderly while potentially sacrificing other publicly provided goods such as education this view seems to be supported by recent empirical findings that per child public education spending tends to be lower in us jurisdictions with higher fraction of elderly residents do these cross sectional findings also carry the dynamic implication that longevity will lead over time to waning political support for funding of public education this paper challenges such implication we present a model that is consistent with the aforementioned cross sectional regressions yet predicts an overall positive impact of increasing longevity on public education funding and economic growth

asset pricing in a production economy with incomplete information this paper analyzes an economy in which investors operate under partial information about technology relevant state variables it is shown that for gaussian information structures under incomplete observations the consumer s problem can be transformed into an equivalent program with a completely observed state the conditional expectation of the underlying unobservable state variables a consequence of this transformation is that classic results in finance remain valid under an appropriate reinterpretation of the state variables the static capital asset pricing model capm of sharpe 24 lintner 16 and mossin 20 states that the expected premium on any risky asset is proportional to the premium on the market as a whole this theoretical linear relationship however is subject to criticisms on two grounds first it does not seem to be supported by the empirical evidence second it is based on the premises of a constant opportunity set merton 19 subsequently relaxes this assumption and shows that when the opportunity set fluctuates over time due to changes in the state of the economy individual securities are also priced with respect to selected portfolios funds providing a hedge against unanticipated fluctuations 2 more recently breeden 3 has extended merton s results by emphasizing the role of aggregate consumption in pricing relationships in this paper we seek to further our understanding of asset pricing by relaxing the assumption that investors observe the state of the economy in the mertonbreeden framework observed state variables affect the means and variances of asset returns implying deformations of the opportunity set over time from a practical point of view it seems that this complete information assumption is violated investors in financial markets operate under partial knowledge of the microvariables which influence production and the returns on assets their decisions rely mostly on information through noisy channels such as newspapers technical reviews or weather reports in this paper we attempt to model such

the volatility of short term interest rates an empirical comparison of alternative models of the term structure of interest rates we estimate and compare a variety of continuous time models of the short term riskless rate using the generalised method of moments we find that the most successful models in capturing the dynamics of the short term interest rate are those that allow the volatility of interest rate changes to be highly sensitive to the level of the riskless rate a number of well known models perform poorly in the comparisons because of their implicit restrictions on term structure volatility we show that these results have important implications for the use of different term structure models in valuing interest rate contingent claims and in hedging interest rate risk