learning to believe in sunspots a number of authors have shown that competitive economies may possess sunspot equilibria that is rational expectations equilibria in which purely extrinsic uncertainty affects equilibrium prices and allocations 2 such results demonstrate that it does not require a lack of faith in the rationality of market participants to believe that competitive markets may be subject to purely speculative fluctuations driven solely by expectations 3 the mere existence of sunspot equilibria as solutions to a system of marketclearing conditions however might not be judged sufficient to indicate that competitive markets with rational participants could ever be subject to speculative instability the sunspot equilibria represent states of affairs in which agents act differently in the case of different realizations of the sunspot variable and it is rational for each agent to do so but it might be thought unlikely that the beliefs of all the participants in the market could ever come to be coordinated so as to bring about an equilibrium of that kind it is rational to believe that sunspots convey information about future states of affairs once the economy is in a sunspot equilibrium but why would rational agents ever begin to believe in such a thing so as to create the conditions under which the belief is rational in order to address such a question one must go beyond the mere statement of the conditions for equilibrium and discussion of what states of affairs satisfy them one must specify an explicit dynamic process according to which the beliefs of agents adjust when out of equilibrium any exercise of this kind is necessarily unsatisfactory as there is no univocal meaning for the postulate of rational behavior outside of an equilibrium it may well be the case that

an approximation of the distribution of learning estimates in macroeconomic models abstract adaptive learning under constant gain allows persistent deviations of beliefs from equilibrium so as to more realistically reflect agents attempt of tracking the continuous evolution of the economy a characterization of these beliefs is therefore paramount to a proper understanding of the role of expectations in the determination of macroeconomic outcomes in this paper we propose a simple approximation of the first two moments mean and variance of the asymptotic distribution of learning estimates for a general class of dynamic macroeconomic models under constant gain learning our approximation provides renewed convergence conditions that depend on the learning gain and the model s structural parameters we validate the accuracy of our approximation with numerical simulations of a cobweb model a standard new keynesian model and a model including a lagged endogenous variable the relevance of our results is further evidenced by an analysis of learning stability and the effects of alternative specifications of interest rate policy rules on the distribution of agents beliefs

policy change and learning in the rbc model what is the impact of surprise and anticipated policy changes when agents form expectations using adaptive learning rather than rational expectations we examine this issue using the standard stochastic real business cycle model with lump sum taxes agents combine knowledge about future policy with econometric forecasts of future wages and interest rates dynamics under learning can have large impact effects and a gradual hump shaped response and tend to be prominently characterized by oscillations not present under rational expectations these fluctuations reflect periods of excessive optimism or pessimism followed by subsequent corrections

performance of monetary policy with internal central bank forecasting abstract recent models of monetary policy have analyzed the desirability of different optimal and ad hoc interest rules under the restrictive assumption that forecasts of the private sector and the central bank are homogeneous this paper studies the implications of heterogeneity in forecasting by the central bank and private agents for the performance of interest rules in a framework of econometric learning

escape dynamics in learning models this article illustrates and characterizes how adaptive learning can lead to recurrent large fluctuations learning models have typically focused on the convergence of beliefs towards an equilibrium however in stochastic environments there may be rare but recurrent episodes where shocks cause beliefs to escape from the equilibrium generating large movements in observed outcomes i characterize the escape dynamics by drawing on the theory of large deviations developing new results which make this theory directly applicable in a class of learning models the likelihood frequency and most likely direction of escapes are all characterized by a deterministic control problem i illustrate my results with two simple examples

first impressions matter signalling as a source of policy dynamics we provide the first direct empirical support for the importance of signalling in monetary policy by testing two key predictions from a novel structural model first all policymaker types should become less tough on inflation over time and secondly types that weigh output more should have a more pronounced shift voting data from the bank of england s monetary policy committee strongly support both predictions counterfactual results indicate signalling has a substantial impact on interest rates over the business cycle and improves the committee designer s welfare implications for committee design include allowing regular member turnover and transparency regarding publishing individual votes

unionised labour market and strategic production decision of a multinational i show that a foreign firm may sell the same product through both foreign direct investment fdi and export and this decision depends on the size of the product market it happens irrespective of whether the labour market in the domestic country or in the foreign country is unionised unlike the existing works focusing on risk diversification in presence of demand or cost uncertainty i explain the co existence of fdi and export in a world with certainty the endogenous determination of the wage rate plays an important role for my results my analysis shows the effects of the fixed cost of fdi and competition in the product market on the production strategy of the foreign firm

learning under fear of floating in recent years a large fraction of economies overcame the fear of floating we study a model that describes the policy of a central bank uncertain about whether currency depreciations cause output to expand textbook model or contract balance sheet model we conclude that the movement away from fear of floating may not be explained by bayesian or robust policies when the private sector anticipates the central bank s policy and endogenously determines the model central banks may fall in a learning trap an increase in financial volatility provides an escape to such trap that replicates patterns in the data

high frequency trading and extreme price movements abstract are endogenous liquidity providers elps reliable in times of market stress we examine the activity of a common elp type high frequency traders hfts around extreme price movements epms we find that on average hfts provide liquidity during epms by absorbing imbalances created by non high frequency traders nhfts yet hft liquidity provision is limited to epms in single stocks when several stocks experience simultaneous epms hft liquidity demand dominates their supply there is little evidence of hfts causing epms

paying for market quality many financial markets including electronic limit order markets assign designated liquidity providers lps we study the experience of the stockholm stock exchange where listed firms contract directly with lps our analysis offers insights regarding situations where designated liquidity provision may be beneficial in addition we consider the form of liquidity provision contracts including affirmative obligations required of the lp and compensation for lp services we find that low current trading activity wide spreads and higher information asymmetry increase the attractiveness of contracted liquidity provision the evidence indicates that lps trade against market movements and in times of wide spreads on balance firms contracting with lps experience a decreased cost of capital and significant improvements in market quality and price discovery

agents as empirical macroeconomists thomas j sargent s contribution to economics thomas j sargent has fundamentally changed and in the words of art rolnick who interviewed him in 2010 irrevocably transformed the field of macroeconomics whether as sole author as co author with collaborators as an author influenced by others or as a teacher of the profession influencing others this paper is about his contribution to our field the nobel memorial prize to thomas j sargent and christopher a sims has been awarded for the empirical research on cause and effect in the macroeconomy or more broadly for macroeconometrics one often likes to distinguish between theorists on the one hand and empiricists and econometricians on the other thomas j sargent holds a unique position in between a key theme in a large part of his work has been to put the agents in his model on equal footing with the econometrician who is observing data from the model i e to assume that agents are themselves empirical macroeconomists or macroeconometricians in this paper i use this theme to examine his work and his contributions to the study of economics

learning the ramsey outcome in a kydland prescott economy abstract we study if adaptive learning by a central bank cb in the kydland and prescott environment can steer the economy to the pareto optimal outcome our cb evaluates its potential strategies regarding the announced and the actual inflation rate through expectations of the performance of these strategies formed thanks to its mental model of the economy this model is forward looking and adaptive at the same time as a starting point we follow arifovic et al 2010 and initially assume that there are two types of agents believers who set their inflation forecast equal to the announced inflation and non believers who form static optimal forecast coupled with a forecast error correction mechanism our results show that the economy can reach near ramsey outcomes most of the time in the absence of believers the economies almost always converge to the ramsey outcome in their experiments with human subjects arifovic and sargent 2003 showed that experimental economies reach and stay close to the ramsey outcome most of the time giving support to the just do it policy recommendation in light of the experimental findings our model is of particular interest as it is the only agent based or adaptive learning model that consistently selects the ramsey outcome in this context

high frequency trading and comovement in financial markets abstract using the staggered entry of chi x in 12 european equity markets as a source of exogenous variation in high frequency trading hft we find that hft causes significant increases in comovement in returns and in liquidity about one third of the increase in return comovement is due to faster diffusion of market wide information we attribute the remaining two thirds to correlated trading strategies of hfts the increase in liquidity comovement is consistent with hft liquidity providers being better able to monitor other stocks and adjust their liquidity provision accordingly our findings suggest a channel by which hft impacts the cost of capital

reputation and time consistency recent work has shown that reputational arguments based on trigger strategies can sometimes be used to deal with the problem of time inconsistency in government policy this idea was exploited by robert barro and david gordon 1983 in a model of inflation and by v v chari and patrick kehoe 1988 in a model of capital taxation here it is shown that reputational arguments of this sort are widely applicable 2 a general policy model is developed based on an economy that is stationary over time contains identical households and has no endogenous state variables it is shown in general that the infinite horizon version of this model has equilibria in trigger strategies that yield outcomes strictly better than those attainable as equilibria in the one period model

escaping nash inflation an ordinary differential equation ode gives the mean dynamics that govern the convergence to self confirming equilibria of self referential systems under discounted least squares learning another ode governs escape dynamics that recurrently propel away from a self confirming equilibrium in a model with a unique self confirming equilibrium the escape dynamics make the government discover too strong a version of the natural rate hypothesis the escape route dynamics cause recurrent outcomes close to the ramsey commitment inflation rate in a model with an adaptive government

learning and price volatility in duopoly models of resource depletion the aim of this paper is to provide a theoretical model that can account for price fluctuations in depletable resource markets we do so by introducing learning into a hotelling style duopoly model of optimal resource depletion before the depletable resource becomes scarce the self confirming equilibrium of the model mirrors noncooperative rational expectations equilibrium in that supply is high and price is low although learning does induce occasional upward price spikes that are followed by a long period of falling price once the depletable resource becomes scarce the dynamics of the market change significantly with the self confirming equilibrium mirroring the cooperative rather than noncooperative rational expectations equilibrium supply is low and price is high price spikes still occur but against a background of increasing prices when scarcity is sufficient then the market is permanently in a self confirming equilibrium that is equivalent to cooperative rational expectations equilibrium

learning large deviations and recurrent currency crises this article studies a version of obstfeld s journal of international economics 43 1997 61 77 escape clause model the model is calibrated to produce three rational expectations equilibria two of these equilibria are e stable and one is unstable dynamics are introduced by assuming that agents must learn about the government s decision rule it is assumed they do this using a stochastic approximation algorithm it turns out that as a certain parameter describing the sensitivity of beliefs to new information gets small the algorithm converges to a small noise diffusion process the dynamics of exchange rate changes are then characterized using large deviation techniques from freidlin and wentzell random perturbations of dynamical systems second edition berlin springer verlag 1998 these methods describe the sense in which the limiting distribution of exchange rate changes is approximated by a two state markov switching process where the two states correspond to the two e stable equilibria the model is calibrated to the exchange rate histories of argentina brazil and mexico currency crises in these countries resemble the predicted escape routes of the model a key feature of these escape routes is that expectations of a devaluation erupt suddenly without large contemporaneous shocks this is consistent with evidence showing that crises are often poorly anticipated by financial markets

convergence of least squares learning in environments with hidden state variables and private information we study the convergence of recursive least squares learning schemes in economic environments in which there is private information the presence of private information leads to the presence of hidden state variables from the viewpoint of particular agents by applying theorems of ljung we extend some of our earlier results to characterize conditions under which a system governed by leastsquares learning will eventually converge to a rational expectations equilibrium we apply insights from the learning results to formulate and compute the equilibrium of a version of townsend s model

self confirming equilibrium and the lucas critique we examine the role of off path superstitions in macro economics and show how a false belief about off path play is the key element underlying both the lucas critique and the game theoretic concept of self confirming equilibrium however the impact of false beliefs in these two cases is different in the lucas case a policy maker s incorrect beliefs about off path play can lead to the adoption of mistaken policy innovation however the consequences of such an innovation provide evidence that the belief that motivated them was wrong in contrast play may never escape an undesirable self confirming equilibrium as the action implied by the mistaken belief does not generate data that contradicts it escape from the self confirming equilibrium requires that players do a sufficient amount of experimentation with off path actions

heterogeneous expectations optimal monetary policy and the merit of policy inertia the design and analysis of optimal monetary policy is usually guided by the paradigm of homogeneous rational expectations instead we examine the dynamic consequences of design and implementation strategies when the actual economy features expectational heterogeneity agents have either rational or adaptive expectations consequently the central bank s ability to achieve price stability under heterogeneous expectations depends on its objective and implementation strategy an expectations based reaction function which appropriately conditions on private sector expectations performs exceptionally well however once the objective introduces policy inertia popular strategies have similar determinacy properties but they are less operational this finding calls for new implementation strategies under interest rate stabilization

program duplication in higher education is not necessarily bad abstract public systems of higher education have recently attempted to cut costs by providing financial incentives to cut duplicated programs i e programs that are offered at different institutions we study the profit and welfare effects of reducing program duplication against the background of a funding system reform in flanders belgium we find that dropping duplicated programs at individual institutions tends to be socially undesirable due to the students low willingness to travel to other institutions and to the limited fixed cost and variable cost savings furthermore we find that the financial incentives offered to drop programs may be very ineffective leading to both undesirable reform and undesirable status quo these findings emphasize the complexities in regulating product diversity in higher education and serve as a word of caution towards the various decentralized financial incentive schemes that have recently been introduced

escaping volatile inflation why has inflation been so stable in developed economies since the early 1990s in this paper we answer that the united states and other countries may have escaped from a volatile inflation equilibrium our argument builds on the story proposed by tom sargent in the conquest of american inflation where the fall in inflation in the 1980s was attributed to changing government beliefs to explain the escape in inflation volatility we unwind one of sargent s simplifications and allow the government to react to some of the shocks in the economy in this case when government beliefs turned against the phillips curve in the 1980s they not only led to an escape from high inflation but also stopped government using changes in inflation to offset shocks inflation and inflation volatility therefore escaped in tandem our analysis also sheds some light on why the escape in inflation occurred at the time it did

learning hypothesis testing and rational expectations equilibrium abstract foster and young 2003 provide a model of learning by hypothesis testing that spends almost all of the time approximating nash equilibria of a repeated game here i extend this learning model to a macroeconomic setting where agents decisions are informed by hypotheses they hold regarding the economy they periodically test these hypotheses against observed data and replace them if they fail under certain conditions agents who learn in this way spend a large fraction of the time approximating rational expectations equilibria

liquidity provision contracts and market quality evidence from the new york stock exchange we exploit a discontinuity in the new york stock exchange designated market maker dmm contract to identify causal effects of dmm participation on equilibrium market outcomes we document that contractual features that enhance dmm participation are associated with increased depth narrower bid ask spreads and higher rates of price improvement with most of the improvements attributable to increases in liquidity provision on markets other than the nyse these results cannot be attributed to the mechanical effects of the contractual changes and support the interpretation that market making is characterized by strategic complementarity received october 7 2017 editorial decision december 10 2018 by editor itay goldstein

anticipated fiscal policy and adaptive learning abstract the impact of anticipated policy changes when agents form expectations using adaptive learning rather than rational expectations is considered agents are assumed to combine limited structural knowledge with a standard adaptive learning rule these issues are analyzed using two well known set ups an endowment economy and the ramsey model in our scenario there are important deviations from both rational expectations and purely adaptive learning the approach could be applied to other frameworks

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

learning adaptive expectations and technology shocks this study explores the macroeconomic implications of adaptive expectations in a standard growth model we show that the self confirming equilibrium under adaptive expectations is the same as the steady state rational expectations equilibrium for all admissible parameter values but that dynamics around the steady state are substantially different between the two equilibria the differences are driven mainly by the dampened wealth effect and the strengthened intertemporal substitution effect not by escapes emphasised by williams 2003 consequently adaptive expectations can be an important source of frictions that amplify and propagate technology shocks and seem promising for generating plausible labour market dynamics

learning in an estimated medium scale dsge model in this paper we evaluate the empirical relevance of learning by private agents in an estimated medium scale dsge model we replace the standard rational expectation assumption in the smets and wouters 2007 model by a constant gain learning mechanism if agents know the correct structure of the model and only learn about the parameters both expectation mechanisms resultin asimilarfit and onlythetransition dynamicsthatare generated byspecific initial beliefs can distinguish the two approaches if in addition agents use only a reduced information set in forming the perceived law of motion the implied model dynamics change and for some initial beliefs the marginal likelihood of the model is further improved however the estimated gain parameter is estimated to be small which suggests a crucial role for the initial beliefs to explain the improved fit the learning models with the highest posterior probabilities add some additional persistence to the dsge model that reduce the gap between the irfs of the dsge model and the more data driven dsge var model however the additional dynamics that are introduced by the learning process do not systematically alter the estimated structural parameters related to the nominal and real frictions in the dsge model jel codes c11 d84 e30 e52

practical policy evaluation abstract in the wake of the lucas 1976 the study of appropriate macroeconomic policy has largely focused on the comparison of different regimes rules in practice few policymakers are faced with making those kinds of choices i examine the problem of a policymaker making but one in a sequence of similar decisions my main result is that the policymaker s optimal response to the current state can be found by applying regression methods to past macroeconomic data i argue that macroeconomic policy evaluation intended to be of practical value should rely less on putatively structural macroeconomic models and more on regression based approaches

make take structure and market quality evidence from the u s options markets we examine the make take structure which compensates liquidity suppliers and charges liquidity demanders in the options markets where it competes with a traditional structure that uses payments for order flow using the introduction of the make take structure as an event we find that execution costs including fees for liquidity demanders decline after the event for the affected options that the make take structure encourages market makers to improve quoted prices and that brokers change their routing behavior to include fees in the routing decision the decline in execution costs is consistent with the benefits of the increased quote competition from the make take structure prevailing over the fees the structure charges to liquidity demanders this paper was accepted by wei jiang finance

learning and model validation this paper studies adaptive learning with multiple models an agent operating in a self referential environment is aware of potential model misspecification and tries to detect it in real time using an econometric specification test if the current model passes the test it is used to construct an optimal policy if it fails the test a new model is selected as the rate of coefficient updating decreases one model becomes dominant and is used almost always dominant models can be characterized using the tools of large deviations theory the analysis is used to address two questions posed by sargent s phillips curve model

the great inflation was not asymmetric international evidence the rise and fall of inflation during the great inflation were events of approximately equal duration in developed economies relying on data driven methods this paper shows the american experience in which inflation fell more quickly than it rose was anomalous this suggests that theories explaining the asymmetry in the american data may not be so applicable to a broader sample of countries

a simple recursive forecasting model abstract we compare the performance of alternative recursive forecasting models a simple constant gain algorithm used widely in the learning literature both forecasts well out of sample and also provides the best fit to the survey of professional forecasters

high frequency trading and end of day price dislocation abstract we show that the presence of high frequency trading hft has significantly mitigated the frequency and severity of end of day price dislocation the effect of hft is more pronounced on days when end of day price dislocation is more likely to be the result of market manipulation moreover the effect of hft is more pronounced than the role of trading rules surveillance enforcement and legal conditions in curtailing the frequency and severity of end of day price dislocation we show our findings are robust to different proxies of the start of hft by trade size cancellation of orders and co location

why inflation rose and fell policy makers beliefs and u s postwar stabilization policy this paper provides an explanation for the run up of u s inflation in the 1960s and 1970s and the sharp disinflation in the early 1980s which standard macroeconomic models have difficulties in addressing i present a model in which rational policymakers learn about the behavior of the economy in real time and set stabilization policy optimally conditional on their current beliefs the steady state associated with the self confirming equilibrium of the model is characterized by low inflation however prolonged episodes of high inflation ending with rapid disinflations can occur when policymakers underestimate both the natural rate of unemployment and the persistence of inflation in the phillips curve i estimate the model using likelihood methods the estimation results show that the model accounts remarkably well for the evolution of policymakers beliefs stabilization policy and the postwar behavior of inflation and unemployment in the united states

market conditions fragility and the economics of market making abstract using audit trail data from the toronto stock exchange we find that market makers scale back in unison when market conditions are unfavorable which contributes to covariation in liquidity supply both within and across stocks market conditions lower aggregate participation via their impact on trading profits and risk contrary to regulatory view higher stock volatility is associated with more participation and higher profits even after controlling for other market conditions including stock volume fragility concerns extend to larger stocks and to active participants the designated market maker mitigates periodic illiquidity created by synchronous withdrawal of market makers in large and small stocks

bubbles and crashes gradient dynamics in financial markets abstract fund managers respond to the payoff gradient by continuously adjusting leverage in our analytic and simulation models the base model has a stable equilibrium with classic properties however bubbles and crashes occur in extended models incorporating an endogenous market risk premium based on investors historical losses and constant gain learning when losses have been small for a long time asset prices inflate as fund managers increase leverage then slight losses can trigger a crash as a widening risk premium accelerates deleveraging and asset price declines

shocks and government beliefs the rise and fall of american inflation working paper 2004 22 september 2004 abstract the authors use a bayesian markov chain monte carlo algorithm to estimate a model that allows temporary gaps between a true expectational phillips curve and the monetary authority s approximating nonexpectational phillips curve a dynamic programming problem implies that the monetary authority s inflation target evolves as its estimated phillips curve moves the authors estimates attribute the rise and fall of post world war ii inflation in the united states to an intricate interaction between the monetary authority s beliefs and economic shocks shocks in the 1970s altered the monetary authority s estimates and made it misperceive the tradeoff between inflation and unemployment that misperception caused sharp rise in inflation in the 1970s the authors estimates indicate that policy makers updated their beliefs continuously by the 1980s policy makers beliefs about the phillips curve had changed enough to account for fed chairman paul volcker s conquest of u s inflation in the early 1980s jel classification e3 e5 key words updating beliefs policy evaluation self confirming equilibrium nash inflation ramsey outcomes i introduction today many statesmen and macroeconomists believe that inflation can largely be determined by a government monetary authority then why did the federal reserve board preside over high us inflation during the late 1960s and the 1970s and why under paul volcker did it rapidly bring inflation down during the early 1980s this paper answers these questions by estimating a model that features a particular process that makes a procession of economic shocks induce the monetary authority to alter its model of inflation unemployment dynamics the phillips curve at each date t the monetary authority updates its beliefs about the phillips curve and then recomputes a first period action recommended by a phelps problem a discounted dynamic programming problem that minimizes the expected value of a discounted quadratic loss function of inflation and unemployment 1 the monetary authority pursues the same objectives at each date using the same structural model with only its estimates of that model changing over time 2 this model of the systematic part of inflation puts the monetary authority s beliefs about the phillips curve front and center 3 we assume that the monetary authority s model of the phillips curve deviates in two subtle but important ways from what it would be in a rational expectations model e g kydland and prescott 1977 the first deviation is that while the true phillips curve is like kydland and prescott s we assume that the monetary authority omits the public s expected rate of inflation from its phillips curve by itself this omission need not prevent the outcomes of our model from coinciding with those of kydland and prescott s nor need it imply that the government s model is wrong in a way that could be detected from even an infinite sample whether the monetary authority s model is wrong in a statistically detectable way depends on how we allow the monetary authority to reestimate the parameters of its model in particular if the monetary authority were to believe that the coefficients of its phillips curve are constant over time then its estimates would converge to ones that support a self confirming equilibrium sce after convergence its estimated phillips curve would correctly describe occurrences along the sce path for inflation and unemployment such an after convergence version of our model has little hope of explaining the rise and fall of us inflation that model would have inflation fluctuating randomly around a constant sce level that coincides with kydland and prescott s time consistent suboptimal i e excessive level 4 this outcome motivates our second subtle deviation from a rational expectations equilibrium

optimized taylor rules for disinflation when agents are learning abstract when private agents learn a new policy rule an optimal simple taylor rule for disinflation differs substantially from that under full information the central bank can reduce target inflation without much difficulty but adjusting reaction coefficients on lagged inflation and output is more costly temporarily explosive dynamics emerge when there is substantial disagreement between perceived and actual feedback parameters making the transition highly volatile the bank copes by choosing reaction coefficients close to the private sector s prior mode thereby sacrificing long term performance in exchange for achieving lower transitional volatility