Imperfect information and the house price in a general-equilibrium model

House prices have inertia, which may be because housing-market participants need time to recognize long booms and recessions. Within a dynamic stochastic general-equilibrium model with an endogenous market for housing, I consider the case of rational expectations subject to imperfect information about the persistence of exogenous shocks. I evaluate the performance of the model against the last 40 years of key U.S. macroeconomic data. Bayesian comparison strongly favors the model over the baseline case with perfect information. Under imperfect information, agents rely on learning to form expectations, which improves the ability of the model to generate realistic low-frequency house-price dynamics. However, as long as the agents form expectations rationally, the improvement is limited. Furthermore, to confine price inertia within the housing market is a challenge for the general-equilibrium approach.     

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.     

Learning, monetary policy rules, and macroeconomic stability

Several papers have documented a regime switch in US monetary policy from ‘passive’ and destabilizing in the pre-1979 period to ‘active’ and stabilizing afterwards. These studies typically work with DSGE models with rational expectations.This paper relaxes the assumption of rational expectations and allows for learning instead. Economic agents form expectations from simple models and update the parameters through constant-gain learning. In this setting, the paper aims to test whether monetary policy may have been a source of macroeconomic instability in the 1970s by inducing unstable learning dynamics.The model is estimated by Bayesian methods. The constant-gain coefficient is jointly estimated with the structural and policy parameters in the system.The results show that monetary policy was respecting the Taylor principle also in the pre-1979 period and, therefore, did not trigger macroeconomic instability.     

An Econometric Analysis of Polish Inflation Dynamics with Learning about Rational Expectations

Rational expectations modelling has been criticized for assuming that economic agents can learn quickly about and compute rational price expectations. In response, various authors have studied theoretical models in which economic agents use adaptive statistical rules to develop price expectations. A goal of this literature has been to compare resulting learning equilibria with rational expectations equilibria. The lack of empirical analysis in this literature suggests that adaptive learning makes otherwise linear dynamic models nonlinearly intractable for current econometric technology. In response to the lack of empirical work in this literature, this paper applies to post-1989 monthly data for Poland a new method for modelling learning about price expectations. The key idea of the method is to modify Cagan’s backward-looking adaptive-expectations hypothesis about the way expectations are actually updated to a forward-looking characterization which instead specifies the result of learning. It says that, whatever the details of how learning actually takes places, price expectations are expected to converge geometrically to rationality. The method is tractable because it involves linear dynamics. The paper contributes substantively by analyzing the recent Polish inflation, theoretically by characterizing learning, and econometrically by using learning as a restriction for identifying (i.e., estimating wth finite variance) unobserved price expectations with the Kalman filter. This revised version was published online in July 2006 with corrections to the Cover Date.     

Optimal fiscal policy under learning

This paper characterizes optimal fiscal policy when agents learn about future taxation. A benevolent and fully rational government chooses taxes on labor income and state-contingent bonds to finance public spending, considering that private agents form their expectations through a learning algorithm. Facing a trade-off between distortionary taxes and distorted expectations, the Ramsey planner chooses the policy that minimizes the total cost of distortions. The analysis produces two main results. First, the government will use fiscal variables to manipulate expectations, reducing taxes and issuing debt at times of pessimism and doing the opposite at times of optimism. This speeds up learning. Second, the expectation-dependent fiscal plan is also history-dependent, and it prescribes taxes that are not as smooth and more persistent than under rational expectations. These findings are robust to alternative learning algorithms.     

Switching from complete to incomplete information

We construct an elementary mechanism [Dutta, B., Sen, A., Vohra, R., 1995. Nash implementation through elementary mechanisms in economic environments. Review of Economic Design 1, 173–203] that Nash implements the constrained Walrasian correspondence. We extend it to incomplete and non-exclusive information economies by enlarging the message space of agents. In addition, measurability restrictions on allocations with respect to prices proper to constrained rational expectations equilibria are imposed in the outcome function. We show that by imposing such restrictions, the mechanism Bayesian implements the constrained rational expectations equilibrium correspondence. This result shows game-theoretic connections between these two market equilibrium concepts. However, these connections are obtained at the price of strong restrictions on the behavior of agents.     

A New Keynesian model with staggered price and wage setting under learning

This paper provides a study of the implications for economic dynamics when the central bank sets its nominal interest rate target in response to variations in wage inflation. I provide results on the existence, uniqueness, and stability under learning of rational expectations equilibrium for alternative specifications of the manner in which monetary policy responds to economic shocks when nominal rigidities are present. Monopolistically competitive producers set prices via staggered price contracts, and households set nominal wages in the same fashion. In this setting, the conditions for determinacy and learnability of rational expectations equilibrium differ from a model where only prices are sticky. I find that when the central bank responds to wage and price inflation and to the output gap, a Taylor principle for wage and price inflation arises that is related to stability under learning dynamics. In other words, a moderate reaction of the interest rate to wage inflation helps to avoid instability under learning and indeterminacy.     

Dangers of commitment under rational expectations

Within a New Keynesian framework, interest rate rules that respond to public expectations lead to determinate and expectationally stable solutions for any level of commitment, as shown by Waters (Macroecon Dyn 13(4):421–449, 2009). That paper also demonstrates gains to commitment, under least square learning, though over-commitment can lead to some very poor outcomes for some parameter values. This paper shows an identical outcome under rational expectations. The optimal level of commitment is unchanged if there are observation errors in the policymaker’s knowledge of public expectations, which is not the case under learning. However, if there is sufficient policymaker uncertainty about the parameter values, partial commitment is best.     

The stability of macroeconomic systems with Bayesian learners

We study abstract macroeconomic systems in which expectations play an important role. Consistent with the recent literature on recursive learning and expectations, we replace the agents in the economy with econometricians. Unlike the recursive learning literature, however, the econometricians in the analysis here are Bayesian learners. We are interested in the extent to which expectational stability remains the key concept in the Bayesian environment. We isolate conditions under which versions of expectational stability conditions govern the stability of these systems just as in the standard case of recursive learning. We conclude that Bayesian learning schemes, while they are more sophisticated, do not alter the essential expectational stability findings in the literature.     

The implications of financial frictions and imperfect knowledge in the estimated DSGE model of the U.S. economy

In this paper, I study how alternative assumptions about expectation formation can modify the implications of financial frictions for the real economy. I incorporate a financial accelerator mechanism into a version of the Smets and Wouters (2007) DSGE framework and explore the properties of the model assuming, on the one hand, complete rationality of expectations and, alternatively, several learning algorithms that differ in terms of the information set used by agents to produce the forecasts. I show that the implications of the financial accelerator for the business cycle may vary depending on the approach to modeling the expectations. The results suggest that the learning scheme based on small forecasting functions is able to amplify the effects of financial frictions relative to the model with Rational Expectations. Specifically, I show that the dynamics of real variables under learning is driven to a significant extent by the time variation of agents’ beliefs about financial sector variables. During periods when agents perceive asset prices as being relatively more persistent, financial shocks lead to more pronounced macroeconomic outcomes. The amplification effect rises as financial frictions become more severe. At the same time, a learning specification in which agents use more information to generate predictions produces very different asset price and investment dynamics. In such a framework, learning cannot significantly alter the real effects of financial frictions implied by the Rational Expectations model.     

Learning about monetary policy rules when the cost-channel matters

We study how monetary policy may affect determinacy and expectational stability (E-stability) of rational expectations equilibrium when the cost channel of monetary policy matters. Focusing on instrumental Taylor-type rules and optimal target rules, we show that standard policies can induce indeterminacy and expectational instability when the cost channel is present. A naïve application of the traditional Taylor principle could be misleading, and expectations-based reaction function under discretion does not always induce determinate and E-stable equilibrium. This result contrasts with the findings of Bullard and Mitra [2002. Learning about monetary policy rules. Journal of Monetary Economics 49, 1105–1129] and Evans and Honkapohja [2003. Expectations and stability problem for optimal monetary policies. Review of Economic Studies 70, 807–824] for the standard new Keynesian model. The ability of the central bank to commit to an optimal policy is an antidote to these problems.     

Sentiment and the U.S. business cycle

Psychological factors are commonly believed to play a role on cyclical economic fluctuations, but they are typically omitted from state-of-the-art macroeconomic models.This paper introduces “sentiment” in a medium-scale DSGE model of the U.S. economy and tests the empirical contribution of sentiment shocks to business cycle fluctuations.The assumption of rational expectations is relaxed. The paper exploits, instead, observed data on expectations in the estimation. The observed expectations are assumed to be formed from a near-rational learning model. Agents are endowed with a perceived law of motion that resembles the model solution under rational expectations, but they lack knowledge about the solution’s reduced-form coefficients. They attempt to learn those coefficients over time using available time series at each point in the sample and updating their beliefs through constant-gain learning. In each period, however, they may form expectations that fall above or below those implied by the learning model. These deviations capture excesses of optimism and pessimism, which can be quite persistent and which are defined as sentiment in the model. Different sentiment shocks are identified in the empirical analysis: waves of undue optimism and pessimism may refer to expected future consumption, future investment, or future inflationary pressures.The results show that exogenous variations in sentiment are responsible for a sizable (above forty percent) portion of historical U.S. business cycle fluctuations. Sentiment shocks related to investment decisions, which evoke Keynes’ animal spirits, play the largest role. When the model is estimated imposing the rational expectations hypothesis, instead, the role of structural investment-specific and neutral technology shocks significantly expands to capture the omitted contribution of sentiment.     

Rational expectations equilibrium and the strategic choice of costly information

This paper studies costly information acquisition in one-good production economies when agents acquire private information and prices transmit information. Before asset markets open, agents choose the quality of their private information. After this information stage, agents trade assets in sequentially complete markets taking into account their private information and the information revealed by equilibrium prices (rational expectations equilibrium, (Radner, R., 1979. Rational expectations equilibrium: generic existence and the information revealed by prices, Econometrica 47, 655–678.)). An overall equilibrium in asset and information market is defined as a Nash equilibrium of the information game in which agents’ actions are information choices and their utility payoffs are the ex-ante expected utilities of the corresponding rationale expectations equilibrium. This paper shows that for a generic set of economies parameterized by endowments and productivity shocks, an overall equilibrium in information and asset market (a Nash equilibrium of the induced information game) with costly information acquisition and fully-revealing prices exists. In other words, informational efficiency is in general consistent with costly information acquisition.     

Learning in an estimated medium-scale DSGE model

We evaluate the empirical relevance of learning by private agents in an estimated medium-scale DSGE model. We replace the standard rational expectations 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 produce very similar results, and only the transition dynamics that are generated by specific initial beliefs seem to improve the fit. If, instead, agents use only a reduced information set in forming the perceived law of motion, the implied model dynamics change and, depending on the specification of the initial beliefs, the marginal likelihood of the model can improve significantly. These best-fitting models add additional persistence to the dynamics and this reduces the gap between the IRFs of the DSGE model and the more data-driven DSGE-VAR model. However, the learning dynamics do not systematically alter the estimated structural parameters related to the nominal and real frictions in the DSGE model.     

Solving generalized multivariate linear rational expectations models

We generalize the linear rational expectations solution method of Whiteman (1983) to the multivariate case. This facilitates the use of a generic exogenous driving process that must only satisfy covariance stationarity. Multivariate cross-equation restrictions linking the Wold representation of the exogenous process to the endogenous variables of the rational expectations model are obtained. We argue that this approach offers important insights into rational expectations models. We give two examples in the paper—an asset pricing model with incomplete information and a monetary model with observationally equivalent monetary-fiscal policy interactions. We relate our solution methodology to other popular approaches to solving multivariate linear rational expectations models, and provide user-friendly code that executes our approach.     

Tests for bounded rationality with a linear dynamic model distorted by heterogeneous expectations

The purpose of this paper is to develop a methodology which will use economic data to detect the existence of boundedly rational economic agents. The bounded rationality model presented in this paper generalizes a linear dynamic rational expectations model by nesting two types of expectations. In this paper, it is claimed that the bounded rationality model as presented can be transformed into an optimal regulator problem with distortions. As a result, the methodologies developed by the optimal control theory can be used to solve the model. The likelihood function for the model is constructed by the Kalman filtering using the solution of the model. Maximum Likelihood Estimation (MLE) is performed to test for bounded rationality in the U.S. cattle market for the period from 1900 to 1990. The empirical results indicate that some fraction of economic agents in the market are boundedly rational.     

Online doctor-patient dynamic stable matching model based on regret theory under incomplete information

With the development of the Internet era, online medical community is increasingly favored by patients and health care workers. How to make a reasonable doctor-patient matching and meet patients' relevant needs through online medical platform is the key to realizing effective allocation of medical resources. This paper proposes an online doctor-patient dynamic stable matching model to deeply investigate the online doctor-patient matching problem under incomplete information. Firstly, we assign the score to each doctor based on the patient's attribute expectations and the doctor's evaluation information. Considering the difficulty of obtaining complete information in real life and different attribute representations, we propose incomplete information filling methods based on collaborative filtering algorithm. To make the filling result more reasonable, we introduce probabilistic linguistic information entropy to process the incomplete information. Secondly, considering psychological behavior, we use regret theory to calculate patients' satisfaction with doctors. Finally, with the definitions of rational matching and stable matching, we propose a doctor-patient dynamic stable matching model. This model can solve the problems like a temporary appointment and private matching and ensure the stability of matching. In addition, the model proposed in this paper considers not only patients' but also the doctors' needs. The case of online doctor-patient matching is based on “haodf.com”, and through comparative analysis can prove the effectiveness and superiority of this method.     

Competitive market equilibrium under asymmetric information

This paper studies the existence of a competitive market equilibrium under asymmetric information. There are two agents involved in the trading of the risky assets: an “informed” trader and an “ordinary” trader. The market is competitive and the ordinary agent can infer the insider information from the price dynamics of the risky assets. The insider information is considered to be the total supply of the risky assets. The definition of market equilibrium is based on the law of supply-demand as described by a rational expectations equilibrium of the Grossman and Stiglitz (Am Econ Rev 70:393–408, 1980) model. We show that equilibrium can be attained by linear dynamics of an admissible price process of the risky assets for a given linear supply dynamics.      

Solving DSGE portfolio choice models with dispersed private information

Noisy rational expectations models, in which agents have dispersed private information and extract information from an endogenous asset price, are widely used in finance. However, these linear partial equilibrium models do not fit well in modern macroeconomics that is based on non-linear dynamic general equilibrium models. We develop a method for solving a DSGE model with portfolio choice and dispersed private information. We combine and extend existing local approximation methods applied to public information DSGE settings with methods for solving noisy rational expectations models in finance with dispersed private information.     

Precautionary behavior and consumer information: A Markov process approach

This paper explores the role of consumer confidence in the equilibrium of a dynamic macroeconomic growth model with rational expectations. Consumers face an uncertain future income stream due to a Markov stochastic process that affects production. Changes in the properties of this process change consumer information sets and optimal policies in the rational expectations format. Increases in “persistence” in the shock process are considered; this is identified with the consumer's subjective assessment of future economic conditions. Two cases are considered: where either good or bad states of the process are more likely to persist into the future, and where bad states persist unconditionally at the expense of good. Consistent with earlier treatments of savings under uncertainty (Barsky, Mankiw and Zeldes 1986, and Skinner 1988), the consumer's response to increased income uncertainty is to exhibit precautionary saving behavior. The infinite-horizon growth model format used offers significant improvement over other finite-horizon life cycle models. Specifically, the model is a full general equilibrium model and the solutions are rational expectations solutions. The technique also is easily adapted to other recursive decision problems under uncertainty.