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.     

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.     

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.     

The role of beliefs in inference for rational expectations models

This paper discusses inference for rational expectations models estimated via minimum distance methods by characterizing the probability beliefs regarding the data generating process (DGP) that are compatible with given moment conditions. The null hypothesis is taken to be rational expectations and the alternative hypothesis to be distorted beliefs. This distorted beliefs alternative is analyzed from the perspective of a hypothetical semiparametric Bayesian who believes the model and uses it to learn about the DGP. This interpretation provides a different perspective on estimates, test statistics, and confidence regions in large samples, particularly regarding the economic significance of rejections in rational expectations models. A suggestive application to the equity premium puzzle is examined.     

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.     

Alternative procedures for converting qualitative response data to quantitative expectations: An application to Australian manufacturing

This paper analyses and extends alternative procedures for converting qualitative expectations responses to quantitative expectations. A number of conversion procedures is investigated, including the probability model, the time-varying parameter probability model, and the regression approach. The informational content of the survey expectations is compared with simple time series models. It is found that the expectations models are superior for many series, both in terms of producing lower forecast root mean square error (RMSE) values and in detecting turning points in the actual data. Survey expectations are also tested for rational expectations in aggregate using the orthogonality test.     

Rationality,specification tests,and macroeconomic models

Rational expectation models embody cross-equation restrictions that are implied by the theory of rational expectations. In this paper we illustrate how tests of these restrictions may be implemented in terms of general macroeconomic models by employing the models of Taylor and Sargent as examples. In addition, the more important issue of the proper interpretation of the results of these tests is addressed. We contend that tests for rationality should become part of the model-building process as they are akin to specification tests for models in which rational expectations is treated as the maintained hypothesis. A procedure is suggested when the restriction are inconsistent with data. Special emphasis is placed upon examining how changes in specifications of the model's exogenous variables can influence test results.     

Binary choice under social interactions: an empirical study with and without subjective data on expectations

This paper examines two methods of modeling binary choice with social interactions: models assuming homogeneous rational expectations and models using subjective data on expectations. Exploiting a unique survey conducted during the 1996 US presidential election that was designed to study voting behavior under social context, we find that in various model specifications using subjective expectations consistently improves models' goodness‐of‐fit; and that subjective expectations are not rational as formulated by Brock and Durlauf. Specifically, members' characteristics are individually important in forming expectations. We also include correlated effect in the rational expectation model. This extension provides a remedy to the selection issues that often arise in social interaction models. Copyright © 2008 John Wiley & Sons, Ltd.     

Are employment decisions based on rational expectations?

Conventional employment functions with partial adjustment to output fitted to quarterly data tend to have positively autocorrelated residuals, to imply implausibly high returns to scale and almost always fail tests for parameter stability. The hypothesis of this paper is that mis-specified expectations are the main cause of these findings and rational and adaptive expectations models are compared. Further, employment is conditioned not on output but on variables which firms can more reasonably take as exogenous. ‘Disequilibrium’ features of labour markets are introduced by making adjustment costs depend upon current and expected labour market tightness.One of the implications of rational expectations is that the revision between points in time t and $\text{t ? 1}$ in the expected value of any variable should be independent of any information available before t and serially uncorrelated. Given a model of a forward looking firm whose hiring decisions are subject to quadratic adjustment costs, an appropriately transformed employment equation can be derived which has a very similar structure to the Koyck transformed employment equation which corresponds to adaptive expectations. Maximum likelihood estimation of the adaptive expectations form gives parameter estimates for quarterly British data for the manufacturing sector which are so unreasonable that this hypothesis can be rejected. Maximum likelihood estimation of the rational expectations form would involve modelling the stochastic processes of all the driving variables. However, conditional upon one parameter, consistent estimates of the remaining parameters can be obtained by OLS and these accord well with economic theory. This is the direct evidence in favour of the rational expectations hypothesis. However, it can also explain why the adaptive expectations form gives such poor results and why conventional employment functions give the unsatisfactory results referred to above. Further, rational expectations provides an explanation for the common finding, particularly in the context of employment and the demand for durable goods, of implausibly low or wrong signed levels effects in more general quarterly time series models with lagged dependent variables.     

Testing Steady‐State Restrictions of Linear Rational Expectations Models when Data are Highly Persistent*

Steady‐state restrictions are commonly imposed on highly persistent variables to achieve stationarity prior to confronting rational expectations models with data. However, the resulting steady‐state deviations are often surprisingly persistent indicating that some aspects of the underlying theory may be empirically problematic. This paper discusses how to formulate steady‐state restrictions in rational expectations models with latent forcing variables and test their validity using cointegration techniques. The approach is illustrated by testing steady‐state restrictions for alternative specifications of the New Keynesian model and shown to be able to discriminate between different assumptions on the sources of the permanent shocks.     

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.     

Estimation and solution of linear rational expectations models using a polynomial matrix factorization

A method to solve and estimate multivariate linear rational expectations models is described. The method is based on an iterative factorization of the polynomial matrix that describes the lags and expected leads in the model. Our experience is that the method works well in a variety of applications where other methods are either difficult or expensive to use.     

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.     

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.     

Survey evidence on the rationality of expectations

Data on expectations collected by business surveys offer the opportunity to test the rational expectation hypothesis. Tests directly based on qualitative data are not powerful because of the nature of the data. An alternative method is proposed in this paper. We apply the usual orthogonality conditions of rationality to the unobservable variables which are assumed to trigger the categorical responses of surveys when they cross certain thresholds. To implement the test, an original estimation method for latent variable models using indicators is required. The results show that the Hypothesis is not always rejected for the expectations of changes in demand drawn from surveys of French manufacturing industry.     

Yield curve responses to market sentiments and monetary policy

Central banks recently started to target longer term interest rates. The empirical failure of the rational expectations theory of the yield curve, however, limits its applicability to monetary policy analysis. The success of agent-based behavioral asset pricing models and behavioral macroeconomic models in replicating statistical regularities of empirical data series motivates to apply them to yield curve modeling. This paper analyses how the interaction of monetary policy and market sentiments shape the yield curve in a behavioral model with heterogeneous and bounded-rational agents. One result is that the behavioral model replicates empirical facts of term structure data. Moreover, it overcomes one major deficiency of rational expectations models of the yield curve in explaining the empirically observed uncertain responses of longer term yields to changes in the central bank rate. These are explained by the behavioral model’s ability to generate different responses of market sentiments to shocks at different times which lead to a variety of interest rate responses. Further results of this paper can be used as policy advice on how central banks can target the level, slope and curvature of the yield curve by targeting market sentiments about inflation and the business cycle.     

Testing the restrictions implied by the rational expectations hypothesis

The nature and form of the restrictions implied by the rational expectations hypothesis are examined in a variety of models with expectations and the properties of appropriate test statistics are analyzed with Monte Carlo evidence. Specifically, we consider the implications of lagged variables, simultaneous equations, and future period expectations upon the number and functional form of the rational expectations restrictions. Two asymptotically equivalent test statistics — a likelihood ratio and a Wald test — are available for implementing a test of these restrictions. Monte Carlo evidence is offered to provide a comparison between the properties of the alternative test statistics in small samples.     

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.     

The analysis of seasonal economic models

Many important insights can be obtained about economic relationships and seasonality when an economic model contains an explicit specification of the mechanism generating seasonality in the endogenous variables. Unfortunately, determining the correct structure is difficult. The purpose of this paper is to outline a methodology for the analysis of seasonal economic models. In particular, several ways of incorporating seasonality into a structural model are considered and the implications for the behavior of the endogenous variables are derived. Finally, a rational expectations version of Cagan's money demand function is analyzed to demonstrate some of the important aspects of the techniques and seasonal economic models in general.