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.     

Testing rational expectations by the use of overidentifying restrictions

A simple econometric test for rational expectations in the case in which unobservable, rationally expected variables appear in a structural equation is presented. Using McCallum's instrumental variable estimator as a base, a test for rational expectations per se and a joint test of rational expectations and hypotheses about the structural equation are presented. The new test is shown to be a new interpretation of Basmann's test of overidentifying restrictions. As an illustration, the hypothesis that the forward exchange rate is the rationally expected future spot exchange rate is tested and rejected.     

Expectation formation of older married couples and the rational expectations hypothesis

This paper tests the Rational Expectations (RE) hypothesis regarding retirement expectations of older married American couples, controlling for sample selection and reporting biases. In prior research we found that individual retirement expectation formation was consistent with the Rational Expectation hypothesis, but in that work spousal considerations were not analyzed. In this research we take advantage of panel data on expectations to test the RE hypothesis among married individuals as well as joint expectations among couples. We find that regardless of whether we assume that married individuals form their own expectations taking spouse's information as exogenous, or the reports of the couple are the result of a joint expectation formation process, their expectations are consistent with the RE hypothesis. Our results support a wide variety of models in economics that assume rational behavior of married couples.     

Identification of rational expectations models

This paper deals with the problem of the identification of simultaneous Rational Expectations (RE) models. In the case of RE models with current expectations of the endogenous variables, the necessary and sufficient conditions for the global identification are derived explicitly in terms of the structural parameters and the linear homogenous identifying restrictions. It is shown that in the absence of a priori restrictions on the processes generating the exogenous variables and the disturbances, RE models and general distributed lag models are ‘observationally equivalent’. In the case of RE models with future expectations of the endogenous variables, a general solution that highlights the ‘non-uniqueness’ problem and from which other solutions such as forward or backward solutions can be obtained, is derived. It is shown that untestable and often quite arbitrary restrictions are needed if RE models with future expectations are to be identifiable. Certain order conditions similar to those obtained for the identification of RE models with current expectations are also derived for this case.     

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.     

Predictions of short-term rates and the expectations hypothesis

This paper emphasizes that traditional tests of the EH are based on two assumptions: the expectations hypothesis (EH) per se and an assumption about the expectations generating process (EGP) for the short-term rate. Arguing that conventional tests of the EH need to assume EGPs that may be significantly at odds with the true EGP, we investigate this possibility by analyzing the out-of-sample predictive performances of several models for predicting interest rates, including a few models which assume that the EH holds in its functional form that relates long- to short-term yields. Using US riskless yield data for a 1970–2016 monthly sample and testing methods that take into account the parameter uncertainty, the null hypothesis of an equal predictive accuracy of each model relative to the random walk alternative is hardly ever rejected at intermediate and long horizons. This confirms that, at least at a practical level, the main difficulty with the EH is represented by the effective prediction of short-term rates. We discuss the relevance of these findings for central banks’ use of forward guidance.     

Estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments

A well-known difficulty in estimating conditional moment restrictions is that the parameters of interest need not be globally identified by the implied unconditional moments. In this paper, we propose an approach to constructing a continuum of unconditional moments that can ensure parameter identifiability. These unconditional moments depend on the “instruments” generated from a “generically comprehensively revealing” function, and they are further projected along the exponential Fourier series. The objective function is based on the resulting Fourier coefficients, from which an estimator can be easily computed. A novel feature of our method is that the full continuum of unconditional moments is incorporated into each Fourier coefficient. We show that, when the number of Fourier coefficients in the objective function grows at a proper rate, the proposed estimator is consistent and asymptotically normally distributed. An efficient estimator is also readily obtained via the conventional two-step GMM method. Our simulations confirm that the proposed estimator compares favorably with that of Domínguez and Lobato (2004, Econometrica) in terms of bias, standard error, and mean squared error.     

On the impossibility of insider trade in rational expectations equilibria

Existing no trade results are based on the common prior assumption (CPA). This paper identifies a strictly weaker condition than the CPA under which speculative trade is impossible in a rational expectations equilibrium (REE). As our main finding, we demonstrate the impossibility of speculative asset trade in an REE whenever an insider is involved who knows the asset's true value. To model insider trade as an equilibrium phenomenon an alternative equilibrium concept than the REE is thus required.     

The heterogeneous expectations hypothesis: Some evidence from the lab

This paper surveys learning-to-forecast experiments (LtFEs) with human subjects to test theories of expectations and learning. Subjects must repeatedly forecast a market price, whose realization is an aggregation of individual expectations. Emphasis is given to how individual forecasting rules interact at the micro-level and which structure they cocreate at the aggregate, macro-level. In particular, we focus on the question wether the evidence from laboratory experiments is consistent with heterogeneous expectations.     

Generalized runs tests for the IID hypothesis

We provide a family of tests for the IID hypothesis based on generalized runs, powerful against unspecified alternatives, providing a useful complement to tests designed for specific alternatives, such as serial correlation, GARCH, or structural breaks. Our tests have appealing computational simplicity in that they do not require kernel density estimation, with the associated challenge of bandwidth selection. Simulations show levels close to nominal asymptotic levels. Our tests have power against both dependent and heterogeneous alternatives, as both theory and simulations demonstrate.     

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.     

Generalized spectral tests for the martingale difference hypothesis

This article proposes a test for the martingale difference hypothesis (MDH) using dependence measures related to the characteristic function. The MDH typically has been tested using the sample autocorrelations or in the spectral domain using the periodogram. Tests based on these statistics are inconsistent against uncorrelated non-martingales processes. Here, we generalize the spectral test of Durlauf (1991) for testing the MDH taking into account linear and nonlinear dependence. Our test considers dependence at all lags and is consistent against general pairwise nonparametric Pitman's local alternatives converging at the parametric rate n^-1/2,$n^{-1/2},$ with n$n$ the sample size. Furthermore, with our methodology there is no need to choose a lag order, to smooth the data or to formulate a parametric alternative. Our approach could be extended to specification testing of the conditional mean of possibly nonlinear models. The asymptotic null distribution of our test depends on the data generating process, so a bootstrap procedure is proposed and theoretically justified. Our bootstrap test is robust to higher order dependence, in particular to conditional heteroskedasticity. A Monte Carlo study examines the finite sample performance of our test and shows that it is more powerful than some competing tests. Finally, an application to the S&P 500 stock index and exchange rates highlights the merits of our approach.     

Full information estimation and stochastic simulation of models with rational expectations

A computationally feasible method for the full information maximum-likelihood estimation of models with rational expectations is described in this paper. The stochastic simulation of such models is also described. The methods discussed in this paper should open the way for many more tests of the rational expectations hypothesis within macroeconomic models.     

Spectral tests of the martingale hypothesis for exchange rates

A new family of spectral shape tests was proposed recently by Durlauf (1991) for testing the martingale hypothesis. Unlike the widely used variance ratio test, spectral shape tests are consistent against all stationary non-white-noise alternatives from the martingale null. In this paper we examine the finite sample properties of the spectral shape tests and find that the tests have good size and power properties even for small samples. We apply the tests to examine the martingale hypothesis for five major currencies vis-à-vis the US dollar for the period 1974–89. The results indicate that most currencies violate the martingale hypothesis. It appears that some rejections are due to long-memory influences.     

Examining bias in estimators of linear rational expectations models under misspecification

Most rational expectations models involve equations in which the dependent variable is a function of its lags and its expected future value. We investigate the asymptotic bias of generalized method of moment (GMM) and maximum likelihood (ML) estimators in such models under misspecification. We consider several misspecifications, and focus more specifically on the case of omitted dynamics in the dependent variable. In a stylized DGP, we derive analytically the asymptotic biases of these estimators. We establish that in many cases of interest the two estimators of the degree of forward-lookingness are asymptotically biased in opposite direction with respect to the true value of the parameter. We also propose a quasi-Hausman test of misspecification based on the difference between the GMM and ML estimators. Using Monte-Carlo simulations, we show that the ordering and direction of the estimators still hold in a more realistic New Keynesian macroeconomic model. In this set-up, misspecification is in general found to be more harmful to GMM than to ML estimators.     

Alternation of parties in power and economic volatility: testing the rational partisan hypothesis and policy learning hypothesis

Right and left parties have distinct macroeconomic preferences that could create different levels of volatility during their executive tenures. But rational partisan theory argues that, because actors in the economy anticipate ruling party behavior, partisan differences only matter when election outcomes are uncertain. We argue that policy risk from ruling parties extends beyond elections, leading to important variation in growth volatility that occurs during a ruling party’s tenure. Building on theories of policy risk and learning, we argue that after elections, economic actors still face uncertainty about the policies of new ruling parties. With time in power, new ruling parties build policy track records, reducing policy risk and, thus, volatility. We estimate a learning curve model of ruling party duration’s effect on the variation in quarterly GDP growth rates. Using data from 44 democracies between 1981 and 2009, we find that learning processes extend beyond the conclusion of uncertain elections.     

Kalman filtering estimation of unobserved rational expectations with an application to the German hyperinflation

The assumption that rational expectations always lie on a convergent path is subject to an empirical test using the German hyperinflation data. The estimation technique employs a Kalman filtering algorithm. After presenting a brief background for the convergent expectations problem and a derivation of the various model specifications, a generalized expectations model and its attendant Kalman filtering estimation technique are discussed. Additional estimation details and empirical results are then presented. Based on an assumption of normally distributed errors, the null hypothesis of convergent paths is rejected in all situations involving a deterministic specification of the evolution of the unobserved parameter which characterizes the convergent path. The same null hypothesis is rejected in four of the six cases corresponding to a stochastic specification of the evolution of the unobserved parameter which characterizes the convergent path. A discussion of these findings, their economic significance, and suggestions for further research concludes the paper.     

Semiparametric tests of conditional moment restrictions under weak or partial identification

We propose two new semiparametric specification tests which test whether a vector of conditional moment conditions is satisfied for any vector of parameter values θ₀. Unlike most existing tests, our tests are asymptotically valid under weak and/or partial identification and can accommodate discontinuities in the conditional moment functions. Our tests are moreover consistent provided that identification is not too weak. We do not require the availability of a consistent first step estimator. Like Robinson [Robinson, Peter M., 1987. Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form. Econometrica 55, 875–891] and many others in similar problems subsequently, we use k-nearest neighbor (knn) weights instead of kernel weights. The advantage of using knn weights is that local power is invariant to transformations of the instruments and that under strong point identification computation of the test statistic yields an efficient estimator of θ₀ as a byproduct.     

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.