discounting in a world of limited growth this paper explores the consequences fordiscounting of assuming limits to growth one of the main determinants of the discount rate is the rate of economic growth if growth rates decline in the future then the discount rate should not be constant but also decline over time in fact we would then need not a single discount rate but rather a variable discount schedule this would imply higher present values for the distant future the paper analyses how discount rates would vary with different assumptions about the patterns of growth and the pure rate of time preference

how should we incentivize private landowners to produce more biodiversity globally much biodiversity is found on private land acting to conserve such biodiversity thus requires the design of policies which influence the decision making of farmers and foresters in this paper we outline the economic characteristics of this problem before reviewing a number of policy options such as conservation auctions and conservation easements we then discuss a number of policy design problems such as the need for spatial coordination and the choice between paying for outcomes rather than actions before summarizing what the evidence and theory developed to date tell us about those aspects of biodiversity policy design which need careful attention from policy makers and environmental regulators

heterogeneous expectations adaptive learning and evolutionary dynamics this paper presents a linear self referential macroeconomic model with the possibility of multiple equilibria where agents have the choice of using one of two forecasting models one of minimum state variable form and the other of sunspot form to form expectations of current and future prices endogenous predictor selection is modeled as an evolutionary game where individuals choose among the forecasting models based on relative performance some nash solutions are not relevant as they are not stable under evolutionary or adaptive learning finally it is shown that the sunspot equilibrium is fragile against temporary shocks to information costs

stability properties for learning with heterogeneous expectations and multiple equilibria the bounded rationality literature has studied heterogeneous learning rules under models with a single equilibrium this paper examines learning with heterogeneous expectations in a simple macroeconomic model with multiple equilibria stability properties of this model are determined by the distribution of heterogeneity these results differ greatly from those which impose homogenous expectations a priori when the level of heterogeneity is allowed to vary stability conditions become more restrictive due to the stationarity requirements of the simpler more parsimonious updating rule finally i find that the two equilibria exchange stability when the mse of using this simpler updating rule is minimized

an examination of the fisher hypothesis the case of turkey this study examines the famous fisher hypothesis fh for turkey fh asserts that nominal interest rates adjust on a one to one basis to expected changes in inflation rates using the johansen cointegration method for the turkish monthly interest rate and inflation rate data we find that it is possible to determine the long run relationship but not the one to one basis between nominal interest rates and inflation our findings suggest that full fh does not hold but there is a very powerfull fisher effect in the case of turkey from 1990 to 2003

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

measures of fit for rational expectations models this survey provides a detailed description of some of the recent theoretical and empirical literature on rational expectations econometrics the survey pays special attention to non stationarity of the data and to the various methods for evaluating rational expectations models that have been developed as alternatives to the classical statistical approach of testing overidentifying restrictions these methods have become very popular and widely used in empirical research we provide an illustration using danish stock market data and we summarize the many results obtained recently using these measures in areas as diverse as stock prices the term structure of interest rates exchange rates consumption and saving the balance of payments tax smoothing hyperinflation and linear quadratic adjustment cost models for inventories labour demand and money demand

spatial heterogeneity contract design and the efficiency of carbon sequestration policies for agriculture abstract in this paper we develop methods to investigate the efficiency of alternative contracts for carbon c sequestration in cropland soils taking into account the spatial heterogeneity of agricultural production systems and the costs of implementing more efficient contracts we describe contracts being proposed for implementation in the united states and other countries that would pay farmers for adoption of specified practices per hectare contracts we also describe more efficient contracts that would pay farmers per tonne of soil c sequestered and we show how to estimate the costs of implementing these more efficient contracts in a case study of a major agricultural region in the united states we confirm that the relative inefficiency of per hectare contracts varies spatially and increases with the degree of spatial heterogeneity the results also show that per hectare contracts are as much as five times more costly than per tonne contracts a degree of inefficiency similar to that found in assessments of command and control industrial emissions regulations measurement costs to implement the per tonne contracts are found to be positively related to spatial heterogeneity but are estimated to be at least an order of magnitude smaller than the efficiency losses of the per hectare contract for reasonable error levels this finding implies that contracting parties could afford to bear a significant cost to implement per tonne contracts and achieve a lower total cost than would be possible with the less efficient per hectare contracts

the fragility of sunspots and bubbles abstract expectational stability e stability is used to examine the multiplicity of solutions in a range of rational expectations models of interest including muth s inventory model and an overlapping generations model in these model it is found that sunspot and other rational bubble solutions are either e unstable or weakly but not strongly e stable

experimental evidence on the persistence of output and inflation this article presents experimental evidence from a monetary sticky price economy in which output and inflation depend on expected future inflation rational inflation expectations do not allow for persistent deviations of output and inflation following a monetary shock in the experimental sessions however output and inflation display considerable persistence and regular cyclical patterns

popularity of reinforcement based and belief based learning models an evolutionary approach in an evolutionary model players from a given population meet randomly in pairs each instant to play a coordination game at each instant the learning model used is determined via some replicator dynamics that respects payoff fitness we allow for two such models a belief based best response model that uses a costly predictor and a costless reinforcement based one this generates dynamics over the choice of learning models and the consequent choices of endogenous variables we report conditions under which the long run outcomes are efficient or inefficient and they support the exclusive use of either of the models or their co existence

monetary policy and learning from the central bank s forecast abstract we examine the expectational stability e stability of rational expectations equilibrium ree in a standard new keynesian model in which private agents refer to the central bank s forecast in the process of adaptive learning to satisfy the e stability condition in this environment the central bank must respond more strongly to the expected inflation rate than the extent to which the taylor principle suggests however the central bank s strong reaction to the expected inflation rate raises the possibility of indeterminacy of the ree in considering these problems a robust policy requires responding to the current inflation rate to a certain degree

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

on the robustness of bubbles in linear re models the authors analyze the expectational stability e stability of the different solutions of a linear rational expectations model in which the endogenous variable depends on expectations of its current and future values formed in the past and also on its own lagged value it is shown that continuum of bubble solutions cannot be strongly e stable in contrast for certain parameter values a particular solution that would normally be identified as a bubble solution can be strongly e stable the results are applied to a macroeconomic model with real balance effects copyright 1992 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

a new keynesian model with heterogeneous expectations abstract within a new keynesian model we incorporate bounded rationality at the individual agent level and we determine restrictions on expectations operators sufficient to imply aggregate is and as relations of the same functional form as those under rationality this result provides dual implications the strong nature of the restrictions required to achieve aggregation serve as a caution to researchers imposing heterogeneous expectations at an aggregate level may be ill advised on the other hand accepting the necessary restrictions provides for tractable analysis of expectations heterogeneity as an example we consider a case where a fraction of agents are rational and the remainder are adaptive and find specifications that are determinate under rationality may possess multiple equilibria in case of expectations heterogeneity

monetary policy with heterogeneous and misspecified expectations in the recent literature on monetary policy and learning it has been suggested that private sector s expectations should play a role in the policy rule implemented by the central bank as they could improve the ability of the policymaker to stabilize the economy private sector s expectations in these studies are often taken to be homogeneous and rational at least in the limit of a learning process in this paper instead we consider the case in which private agents are heterogeneous in their expectations formation mechanisms and hold heterogeneous expectations in equilibrium we investigate the impact of this heterogeneity in expectations on central bank s policy implementation and on the ensuing economic outcomes and the general result that emerges is that the central bank should disregard inaccurate private sector expectations and solely base its policy on the accurate ones

fundamentalists vs chartists learning and predictor choice dynamics abstract in a simple forward looking univariate model of price determination we investigate the evolution of expectations dynamics in the presence of two types of agents fundamentalists and chartists in particular we combine evolutionary selection among heterogeneous classes of models through predictor choice dynamics based on a logit model with adaptive learning in the form of parameters updating within each class of rules we find that for different parameterizations it can happen that fundamentalists drive chartists completely out of the market or vice versa and also that heterogeneous equilibria in which fundamentalists and chartists coexist are possible interestingly though only equilibria in which fundamentalists outperform chartists turn out to be adaptively learnable by agents

adaptive learning endogenous uncertainty and asymmetric dynamics abstract i present a simple model where forecasting confidence affects aggregate demand it is shown that this model has similar stability properties under statistical and evolutionary learning as a model without a confidence affect from this setup i introduce expectational business cycles where output fluctuates due to learning heterogeneous forecasting models and random changes in the efficient forecasting model agents use one of two forecasting models to forecast future variables while heterogeneity is dictated via an evolutionary process increased uncertainty due to a shock to the structure of the economy may result in a sudden decrease in output as agents learn the equilibrium output slowly increases to its equilibrium value expectational business cycles tend to arrive faster last longer and are more severe as agents possess less information

short term interest rates as predictors of inflation comment in this note i raise two questions regarding fama s results the first is whether similar tests based on an information set somewhat broader than the past history of consumer price inflation will support fama s findings the second is whether given fama s data and model his results fully support his hypotheses the answer to both questions is no if one accepts the accuracy of the data during fama s sample period the current monthly rate of change of consumer prices ct is significantly related to the three previous monthly rates of change of

disadvantageous oil tariffs and dynamic consistency a large importer who places relatively greater weight on future than current oil consumption will import less oil in the future than if it were able to commit itself in advance to future tariffs and may find itself worse off than if it were unable to impose tariffs at all futures markets and storage modify these adverse effects and may avoid the problem of dynamic inconsistency copyright 1990 by american economic association

estimation of the specification error in the fisher equation this paper asks how false is the fisher hypotheis previous work has asked is the fisher hypothesis true the framework here characterizes the specification error in the the fisher equation as model noise following durlauf and hall 1988 1989a 1989b the noise provides a metric for the specification error for the post war period to october 1979 the variance of the noise is small while after that date it is apparently large that is using a method that contains many previous tests of the fisher effect in explaining nominal in explaining nominal interest rate movements mishkin 1991 has criticized this consensus as reflection a common stochastic trend in inflation and nominal interest rates prior to october 1979 the test here is immune to this criticism as i use the ex post real interest rate as the regressand and show that at least prior to october 1979 it obeys a sationary process

time inconsistent resource conservation contracts abstract are certain types of commonly observed resource conservation contracts inefficient in this paper we construct a model embodying realistic characteristics of resource contracts we find that resource contracts that share these characteristics are economically inefficient this inefficiency stems from a time inconsistency inherent in the contracts there are two possible ways to overcome this time inconsistency the first is to employ a sufficiently large penalty for early termination of the contract the second and possibly easier method is to offer an upward sloping conservation payment schedule so far overlooked by policy makers under this payment schedule the agent s ex ante and ex post contract choices coincide social externalities are fully internalized and the contractual outcome is economically efficient even in the absence of a penalty for early termination

the cost effectiveness of conservation payments international donors invest billions of dollars to conserve ecosystems in low income nations the most common investments aim to encourage commercial activities such as ecotourism that indirectly generate ecosystem protection as a joint product we demonstrate that paying for ecosystem protection directly can be far more cost effective although direct payment initiatives have imposing institutional requirements we argue that all conservation initiatives face similar challenges thus conservation practitioners would be well advised to implement the first best direct payment approach rather than a secondbest policy option an empirical example illustrates the spectacular cost savings that can be realized by direct payment initiatives

environmental policy under a non market discount rate abstract this paper looks at pollution emissions when a non market discount rate is used to evaluate environmental policy and policy is subject to continuous review through time it is shown that a non market rate leads to time inconsistent policy future regulators will want not to follow the current regulator s optimal plans even when the current regulator has perfect foresight and there is no uncertainty therefore the discount rate has different effects depending on whether government can commit to future environmental regulation we then show in a simple linear model that when the environmental discount rate is below the market rate pollution is higher under no commitment than under commitment even under no commitment however a lower discount rate leads to lower emissions we argue that the debate might be better framed over prices i e the value of the environment in the future rather than the discount rate this treatment removes the inconsistency problem yet ensures that future generations interests are represented in policy decisions

what does the term structure tell us about future inflation abstract this empirical analysis indicates that for maturities of six months or less the term structure of nominal interest rates provides almost no information about the future path of inflation but does provide information about the term structure of real interest rates however as maturities lengthen to nine and twelve months the nominal term structure begins to contain information about future inflation but ceases to provide information about the real term structure these results are explained by differences in the relative variability of expected future inflation changes and real term structure slopes at different points in the term structure

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

short term interest rates as predictors of inflation on testing the hypothesis that the real rate of interest is constant in an innovative and provocative paper in this review eugene fama presents evidence which appears to be consistent with the joint hypothesis that the real rate of interest ignoring taxes is a constant and that the market for u s treasury bills is efficient in the sense of embodying rational expectations those findings are strikingly at variance with a long list of previous studies which seemed to support the view that the real rate of interest varies over time and can be related to economic variables such as real output monetary policy and so forth 2 the methodologies which lead to these contradictory conclusions are quite different previous studies had followed the lead of irving fisher by relating nominal interest rates to distributed lags on past rates of inflation 3 these distributed lags are generally interpreted as approximations to the market s expected rate of inflation and thus any remaining variation is attributed to variation in the real rate 4 fama s methodology on the other hand draws on the fact that the difference between the market interest rate and the subsequently observed rate of inflation the ex post real interest rate consists by definition of the ex ante real interest rate plus a pure forecasting error 5 the hypothesis of market efficiency implies that these forecasting errors must be serially random thus observing ex post real rates is equivalent to observing ex ante real rates with random measurement error these errors of course confound the problem of identifying variation in the ex ante real rate in this paper we will argue that the relative magnitude of these measurement errors is such that the tests carried out by fama were not powerful enough to reject the joint hypothesis that the ex ante real rate is a constant and expectations are rational more powerful tests which are presented in this paper using the same data do lead to rejection of that hypothesis of course rejection