On non-uniqueness in rational expectations models: An attempt at perspective

Many macroeconomic models involving rational expectations give rise to an infinity of solution paths, even when the models are linear in all variables. Some writers have suggested that this non-uniqueness constitutes a serious weakness for the rational expectations hypothesis. One purpose of the present paper is to argue that the non-uniqueness in question is not properly attributable to the rationality hypothesis but, instead, is a general feature of dynamic models involving expectations. It is also argued that there typically exists in a very wide class of linear rational expectations models, a single solution that excludes ‘bubble’ or ‘bootstrap’ effects — one that occur only because they are arbitrarily expected to occur. A systematic procedure for obtaining solutions free from such effects is introduced and discussed. In addition, this procedure is used to interpret and reconsider several prominent examples with solution multiplicities, including ones developed by Fischer Black and John B. Taylor.     

Rational expectations and monetary models of exchange rate determination: An empirical examination

One asset model of exchange rate determination that has received substantial attention in the literature is the monetary model. As with other asset models, expectations of future exchange rates play a key role. Usually these expectations are assumed to be formed rationally. However, to date there has been no attempt to empirically estimate a complete monetary model with rational expectations. In this paper, such a model is estimated and the restrictions implicity imposed by the rational expectation hypothesis tested. The results suggest that both the parameter constraints associated with the monetary model and those implied by the REH are consistent with recent exchange rate behavior.     

Instrumental variables procedures for estimating linear rational expectations models

This paper illustrates how to use instrumental variables procedures to estimate the parameters of a linear rational expectations model. These procedures are appropriate when disturbances are serially correlated and the instrumental variables are not exogenous. We compare our procedures to some alternative estimators that estimate free parameters from restrictions implied by the Euler equations. The procedures are applicable to a variety of linear rational expectations models, several examples of which we cite.     

Switching regime models in the Spanish inter-bank market

Nonlinear present value models are adjusted to data from the Spanish inter-bank market between 1986 and 1992, with the ultimate objective of testing the rational expectations hypothesis of the term structure of the interest rates. The nonlinearity stems from using models with two stochastically switching regimes. The models are submitted to various specification tests and are compared with linear present value models. Very clearly differentiated regimes are identified, the analysis of the results in the light of the institutional, political and economic events that affected the Spanish economy during the period of study demonstrates the usefulness of this type of models. The expectation hypothesis is, however, rejected.     

Using Survey Data of Inflation Expectations in the Estimation of Learning and Rational Expectations Models

Does survey data contain useful information for estimating macroeconomic models? We address this question by using survey data of inflation expectations to estimate the New Keynesian model by Smets and Wouters ( 2007 ) and compare its performance under rational expectations and adaptive learning. The survey information serves as an additional moment restriction and helps us to determine the learning agents' forecasting model for inflation. Adaptive learning fares similarly to rational expectations in fitting macro data, but clearly outperforms rational expectations in fitting macro and survey data simultaneously. In other words, survey data contain additional information that is not present in the macro data alone.     

A volatility model based on adaptive expectations: An improvement on the rational expectations model

Investment expectations affect stock price volatility, making asset pricing more difficult. Correctly capturing investment expectations can help alleviate this problem. In this paper, we analyze the rational expectations properties of existing volatility models. Second, we explore a volatility model based on adaptive expectations by using mathematical methods and the applicable conditions and continuity feature of the adaptive expectations volatility model. Third, under the assumption of adaptive expectations, we construct adaptive expectations GARCH (ADGARCH) and LSTM-ADGARCH models. Using daily trading data from the Shanghai stock index and SPX500 for the period 2015–2021, we find that the volatility model based on adaptive expectations has more explanatory power than one based on rational expectations.     

Rational expectations and corporate dividend policy

The problem of expectations formation has been either ignored or treated with very restrictive assumptions in traditional dividend adjustment models. Since these models are typically used to explain the dividend decisions of individual firms, a more satisfactory treatment of the process of expectations formation is needed. In order to analyze the dynamic dividend adjustment process, this article proposes a model, more general than previous ones, that is consistent with the rational expectations hypothesis. A nonlinear regression method is used to estimate the parameters of the model and to test the validity of the rational expectations hypothesis in dividend decisions making. The partial adjustment model with rational expectations explains dividend adjustments reasonably well. The overall results suggest that firms make use of available earnings information to form optimal future earnings forecasts; specifically, a firm's dividend adjustment process is completed in about two and a half quarters. This article also finds that the fourth-order serial correlation problem disappears after a generalized Tobit model is used for the parameter estimation.     

An integrated view of tests of rationality,market efficiency and the short-run neutrality of monetary policy

This paper analyzes an important class of models in which expectations play an important role. Topics included in the analysis are tests of: (1) rationality of forecasts in either market or survey data, (2) capital market efficiency, (3) the short-run neutrality of monetary policy and, (4) Granger causality in macroeconometric models. The common elements of these tests are highlighted. In particular, cross-equation tests for rationality or the short-run neutrality of money are shown to be equivalent to more common regression tests in the literature. These results demonstrate that the exact specification of the relevant information set used in rational forecasts is not necessary for the cross-equation tests to have desirable asymptotic properties. Also discussed are the conditions for identification of coefficients and testability of hypotheses.     

Estimating the Euler equation for output

New Keynesian macroeconomic models have generally emphasized that expectations of future output are a key factor in determining current output. The theoretical motivation for such forward-looking behavior relies on a straightforward generalization of the well-known Euler equation for consumption. In this paper, we use maximum likelihood and generalized method of moments (GMM) methods to explore the empirical importance of output expectations. We find little evidence that rational expectations of future output help determine current output, especially after taking into account the small-sample bias in GMM.     

Can perpetual learning explain the forward-premium puzzle?

Under rational expectations and risk neutrality the linear projection of exchange-rate change on the forward premium has a unit coefficient. However, empirical estimates of this coefficient are significantly less than one and often negative. We show that replacing rational expectations by discounted least-squares (or “perpetual”) learning generates a negative bias that becomes strongest when the fundamentals are strongly persistent, i.e. close to a random walk. Perpetual learning can explain the forward-premium puzzle while simultaneously replicating other features of the data, including positive serial correlation of the forward premium and disappearance of the anomaly in other forms of the test.     

Multiple-solution indeterminacies in monetary policy analysis

A sizeable fraction of recent research on monetary policy has been concerned with issues relating to analytical “indeterminacies”—i.e. multiple solutions in rational expectations (RE) models. Most of the literature features sophisticated RE analysis conducted within dynamic models that reflect optimizing behavior by individual agents and incorporate Taylor-style policy rules. A few papers have suggested that some of the particular indeterminacy arguments are misleading or irrelevant. For the most part, however, there has been little dissent from the position that these indeterminacies present a genuine problem for monetary policy makers. The purpose of the present paper, by contrast, is to argue that conclusions based on multiple-solution indeterminacy findings are of dubious merit rather generally.     

Recent developments in the theory of inflation and unemployment

The paper examines the theoretical literature of the past decade on the causes of inflation and unemployment. The basic theme is the pervasive impact of sluggish price adjustment on the validity and relevance of recent models. The insulation of real output from anticipated monetary changes, derived in the recent rational expectations literature, loses its validity when prices adjust slowly to changes in demand. The search literature explains only part of unemployment when layoffs rather than wage cuts are the major tool of employment adjustment in recessions. The ‘new-new’ microeconomics of implicit contracts, idiosyncratic exchange, and default penalties is reviewed, as are the implications of sluggish price adjustment for both ‘domestic monetarism’ and for the monetary approach to balance-of-payments theory.     

Tests of financial models in the presence of overlapping observations

A general approach to testing serial dependence restrictionsimplied from financial models is developed. In particular, wediscuss joint serial dependence restrictions imposed by randomwalk, market microstructure, and rational expectations modelsrecently examined in the literature. This approach incorporatesmore information from the data by explicitly modeling dependenciesinduced by the use of overlapping observations. Because theestimation problem is sufficiently simple in this framework,the test statistics have simple representations in terms ofonly a few unknown parameters. As a result, relatively goodsize properties are attained in small samples. In addition,the benefit to overlapping observations and the advantage ofexamining multiperiod time series are explicitly quantified.     

Adaptive expectations,rational expectations,and money demand in hyperinflation Germany

In the recent literature Sargent and Wallace (IER, June, 1973) have estimated the demand equation for money in hyperinflation under the restriction that the adaptive formula of Phillip Cagan yields rational inflation expectations in the sense of John Muth. The present paper finds evidence to reject for the Germany case the proposition that adaptive expectations are rational. The procedure employed is basically to overfit the stochastic representation for the inflation rate implied by the ‘adaptive-is-rational’ hypothesis. The paper also puts forward and applies a two-step procedure to estimate the important money demand elasticity in hyperinflation. The procedure returns reasonable results with large estimated standard errors.     

Structural Error Correction Models: A System Method for Linear Rational Expectations Models and an Application to an Exchange Rate Model

This paper develops a system instrumental variable method to estimate the speed of adjustment coefficient in the long-run equilibrium of structural error correction models for a class of linear rational expectations models. This method is applied to an exchange rate model with sticky prices, in which the speed of adjustment coefficient governs the half-life of the real exchange rate. Compared to single equation methods, the system method gives smaller half-life estimates with sharper standard errors.     

Macroeconometric testing of the rational expectations and structural neutrality hypotheses for the United States

Empirical tests of the neutrality of money growth found in recent literature are tests of the joint hypothesis of rational expectations and structural neutrality. Although tests of this joint hypothesis are informative, it is also important to gain information on the accuracy of its constituents. This paper presents the application of a methodology capable of providing information on the empirical validity of the rational expectations, structural neutrality, and joint hypotheses. Tests of these hypotheses are performed on the basis of FIML estimation of an extended version of a model recently presented by Robert Barro, using U.S. data for 1946–1973.     

Estimation of an adaptive stock market model with heterogeneous agents

Standard asset pricing models based on rational expectations and homogeneity have problems explaining the complex and volatile nature of financial markets. Recently, boundedly rational and heterogeneous agent models have been developed and simulated returns are found to exhibit various stylized facts, such as volatility clustering and fat tails. Here, we are interested in how well the proposed models can explain all the properties seen in real data, not just one or a few at a time. Hence, we do a proper estimation of some simple versions of such a model by the use of efficient method of moments and maximum likelihood and compare the results to real data and more traditional econometric models. We discover two main findings. First, the similarities with observed data found in earlier simulations rely crucially on a somewhat unrealistic modeling of the noise term. Second, when the stochastic is more properly introduced the models are still able to generate some stylized facts, but the fit is generally quite poor.     

The Dependency of Rent-to-Price Ratio on Appreciation Expectations: An Empirical Approach

Using two unique datasets from different neighborhoods in Houston, TX, which provide us data for houses with similar structure (or even same house), we test the standard model of housing values to determine how the formation of households’ expectations regarding price appreciations affects housing market prices. Using these datasets we are able to address previously encountered problems in the literature such as the lack of adjustment for quality differences, the connection between prices and rents for the different type of housing, and the spatial distribution of housing. We test whether consumer behavior leads to potentially unstable market conditions with price bubbles. Our results suggest that appreciation expectations are based on past price appreciation but at the same time they depend on the fundamental factors such as, locational and structural. These findings show a hybrid consumer behavior of rational and adaptive expectations. Finally, we show how these expectations could sometimes lead to unstable price levels.     

Further evidence on the rationality of interest rate expectations

This paper extends the limited work on interest rate expectations to a previously unexploited data set that covers a broad range of EMS and non-EMS foreign currency deposits. We corroborate the earlier finding in the literature that interest rate forecasts are not rational and that agents do not use all available information in an efficient manner; this finding applies to the post-1990 period, thus questioning the assertion of Frankel and Froot [Frankel, J.F., Froot, K.A., 1987a. Using survey data to test standard propositions regarding exchange rate expectations. American Economic Review 77, 151] that “the nature of the rejection of rational expectations strongly depends on the sample period”. Although forecast errors on EMS rates are smaller and less volatile than errors on non-EMS rates, expectations on EMS rates are nevertheless biased.