Experimental evidence on inflation expectation formation

Using laboratory experiments within a New Keynesian sticky price framework, we study the process of inflation expectation formation. We focus on adaptive learning and rational expectations contrary to the previous literature that mostly studied simple heuristics. Using a test for rational expectations that allows heterogeneity of expectations we find that we cannot reject rationality for about 40% of subjects. More than 20% of subjects are also best described by adaptive learning models, where they behave like econometricians and update their model estimates every period. However, rather than using a single forecasting model, switching between models describes their behavior better. Switching is more likely to occur when experimental economy is in a recession.     

Good luck or good policy? An expectational theory of macro volatility switches

In an otherwise unique-equilibrium model, agents are segmented into a few informational islands according to the signal they receive about others' expectations. Even if agents perfectly observe fundamentals, rational-exuberance equilibria (REX) can arise as they put weight on expectational signals to refine their forecasts. Constant-gain adaptive learning can trigger jumps between the equilibrium where only fundamentals are weighted and a REX. This determines regime switching in macro volatility despite unchanged monetary policy and time-invariant distribution of exogenous shocks. In this context, a tight inflation-targeting policy can lower expectational complementarity preventing rational exuberance, although its effect is non-monotone.     

The forward method as a solution refinement in rational expectations models

This paper generalizes the standard forward method of recursive substitution to a general class of linear rational expectations models with potentially multiple fundamental solutions. It is shown that the existence and uniqueness of the well-known forward solution are preserved in a general context. We also propose a key property embedded in the forward solution - the no-bubble condition - as an economically sensible solution refinement in the class of fundamental solutions. In the literature, the no-bubble condition has been assumed to rule out non-fundamental bubble solutions. We show that the forward solution is the only rational expectations equilibrium satisfying the no-bubble condition and consequently, it is the most relevant fundamental solution within the class of fundamental equilibria. Several economic examples are provided where the fundamental solutions obtained by other solution methods and refined by other solution selection criteria violate the no-bubble condition.     

ORDINARY LEAST SQUARES LEARNING AND NONLINEARITIES IN MACROECONOMICS

Abstract.  The paper reviews the literature on adaptive learning in macroeconomic settings where the formation of expectations is particularly relevant. Special attention will be given to simple two-period overlapping generations models with a unique fixed point perfect foresight equilibrium; in this kind of scenario, eventual long-term periodic and a-periodic cycles are exclusively the result of the process of learning. The outcome that high rates of money growth have a potentially destabilizing effect generating periodic fluctuations and chaos is emphasized. The persistence of systematic forecast errors in a scenario where agents are supposed to act rationally is relevant in this context and it will be thoroughly discussed resorting to the notions of self-fulfilling mistakes, consistent expectations equilibria and beliefs equilibria.     

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.     

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.     

E-stability and stability of adaptive learning in models with private information

The paper demonstrates how the E-stability principle introduced by Evans and Honkapohja [2001. Learning and Expectations in Macroeconomics. Princeton University Press, Princeton, NJ] can be applied to models with heterogeneous and private information in order to assess the stability of rational expectations equilibria under learning. The paper extends already known stability results for the Grossman and Stiglitz [1980. On the impossibility of informationally efficient markets. American Economic Review 70, 393–408] model to a more general case with many differentially informed agents and to the case where information is endogenously acquired by optimizing agents. In both cases it turns out that the rational expectations equilibrium of the model is inherently E-stable and thus locally stable under recursive least squares learning.     

AGRICULTURAL PRICE INSTABILITY: A SURVEY OF COMPETING EXPLANATIONS AND REMEDIES

Abstract There are two explanations for agricultural price dynamics. One follows cobweb logic and models fluctuations driven by expectation errors but emphasises that these expectations create complex dynamics and possibly chaos. The other stems from the rational expectations tradition of dynamics driven by real shocks. The empirical evidence tends to support the latter, but is not conclusive. The rational expectations model generates an optimal dynamic path from which no improvement can be expected from public intervention. However, if we take account of all the potential market failures in agricultural markets, and especially in developing countries, this conclusion might require some qualifications, although an appropriate policy design for stability has still to be achieved. This paper surveys the positive and normative literature on agricultural prices, highlighting empirical evidence and identifying remaining unresolved issues.     

STABILISATION POLICY,RATIONAL EXPECTATIONS AND PRICE‐LEVEL VERSUS INFLATION TARGETING: A SURVEY

We survey literature comparing inflation targeting (IT) and price‐level targeting (PT) as macroeconomic stabilisation policies. Our focus is on New Keynesian models and areas that have seen significant developments since Ambler's (2009, Price‐level targeting and stabilisation policy: a survey. Journal of Economic Surveys 23(5): 974–997) survey: optimal monetary policy; the zero lower bound; financial frictions and transition costs of adopting a PT regime. Ambler's conclusion that PT improves social welfare in New Keynesian models is fairly robust, but we note an interesting split in the literature: PT consistently outperforms IT in models where policymakers commit to simple Taylor‐type rules, but results in favour of PT when policymakers minimise loss functions are overturned with small deviations from the baseline model. Since the beneficial effects of PT appear to hang on the joint assumption that agents are rational and the economy New Keynesian, we discuss survey and experimental evidence on rational expectations and the applied macro literature on the empirical performance of New Keynesian models. Overall, the evidence is not clear‐cut, but we note that New Keynesian models can pass formal statistical tests against macro data and that models with rational expectations outperform those with behavioural expectations (i.e. heuristics) in direct statistical tests. We therefore argue that policymakers should continue to pay attention to PT.     

Learning in linear models with expectational leads

Models with expectational leads typically admit multiple rational expectations solutions. Based on the ordinary least-squares algorithm, this paper provides an adaptive learning scheme which allows a forecasting agent to select a particular solution on economic grounds. Conditions are given under which this scheme converges to rational expectations solutions globally for all initial conditions. We strengthen convergence results in relaxing standard assumptions and in providing conditions ensuring algorithm convergence which are easier to verify and to interpret than those previously known.     

Fundamentalists vs. chartists: Learning and predictor choice dynamics

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.     

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.     

House price dynamics: Fundamentals and expectations

We investigate whether expectations that are not fully rational have the potential to explain the evolution of house prices and the price-to-rent ratio in the United States. First, a stylized asset-pricing model solved under rational expectations is used to derive a fundamental value for house prices and the price–rent ratio. Although the model can explain the sample average of the price–rent ratio, it does not generate the large and persistent fluctuations observed in the data. Then, we consider a rational bubble solution, an extrapolative expectations solution and a near rational bubble solution. In this last solution agents extrapolate the future from the latest realizations and the degree of extrapolation is stronger in good times than in bad times, generating waves of over-optimism. We show that under this solution the model not only is able to match key moments of the data but can also replicate the run up in the U.S. house prices observed over the 2000–2006 period and the subsequent sharp downturn.     

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.     

On the initialization of adaptive learning in macroeconomic models

We review and evaluate methods previously adopted in the applied literature of adaptive learning in order to initialize agents’ beliefs. Previous methods are classified into three broad classes: equilibrium-related, training sample-based, and estimation-based. We conduct several simulations comparing the accuracy of the initial estimates provided by these methods and how they affect the accuracy of other estimated model parameters. We find evidence against their joint estimation with standard moment conditions: as the accuracy of estimated initials tends to deteriorate with the sample size, spillover effects also deteriorate the accuracy of the estimates of the model’s structural parameters. We show how this problem can be attenuated by penalizing the variance of estimation errors. Even so, the joint estimation of learning initials with other model parameters is still subject to severe distortions in small samples. We find that equilibrium-related and training sample-based initials are less prone to these issues. We also demonstrate the empirical relevance of our results by estimating a New Keynesian Phillips curve with learning, where we find that our estimation approach provides robustness to the initialization of learning. That allows us to conclude that under adaptive learning the degree of price stickiness is lower compared to inferences under rational expectations.     

Asset pricing with expectation shocks

This paper adds persistent shocks into the adaptive learning expectation formation process in stochastic growth asset pricing production and endowment economies. These expectation shocks, designed to capture psychological elements which can arise from news, changes in sentiment, herding and bandwagon effects, generate waves of optimism and pessimism in equity price forecasts. The paper estimates parameters of the expectation shock and adaptive learning process with the method of simulated moments, and compares simulation results to U.S. economic and financial market stylized facts. Numerical results for both the estimated production and endowment economies show that the expectation shock model matches several of the stylized facts better than does a model that assumes rational expectations or adaptive learning alone.     

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.     

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.     

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.     

The existence of rational expectations equilibria in a large economy with noisy price observations

Non-revealing rational expectations equilibria exist in microeconomic pure exchange economies in which a continuum of uninformed agents have suitably distributed noisy price observations. Slight dispersion in the prices observed by the subset of uninformed consumers is the key condition for continuity (and smoothness) of aggregate excess demand, although individual demands are discontinuous. It leads to equilibria in which markets approximately clear in a strong sense. The equilibria are obtained by applying a fixed point argument to state-dependent excess demand functions.