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.     

Optimal policy in Markov-switching rational expectations models

In this paper we consider the optimal quadratic control problem of Markov-switching linear rational expectation models. These models are general and flexible tools for modelling not only regime but also model or parameter uncertainty. We show, first, how to find the solution of a Markov-switching linear rational expectation model. Based on this solution we then show how to apply dynamic programming to find the optimal time-consistent policy and the resulting Nash-Stackelberg equilibrium. Suitable modifications of the algorithm allow to deal with the (non-RE) case in which the policymaker and the private sector hold different beliefs or probabilities over regime change. We also show how the optimisation procedure can be employed to obtain the optimal policy under commitment. As an illustration we compute the optimal policy in a small open economy subject to stochastic structural breaks in some of its key parameters.     

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.     

Weakly rational expectations

Aumann and Drèze (2008) characterised the set of interim expected payoffs that players may have in rational belief systems, in which there is common knowledge of rationality and a common prior. We show here that common knowledge of rationality is not needed: when rationality is satisfied in the support of an action-consistent distribution (a concept introduced by Barelli (2009)), one obtains exactly the same set of rational expectations, despite the fact that in such ‘weakly rational belief systems’ there may not be mutual knowledge of rationality, let alone common knowledge of rationality. In the special case of two-player zero-sum games, the only expected payoff is the minmax value, even under these weak assumptions.     

Invertible and non-invertible information sets in linear rational expectations models

Rational expectations solutions are usually derived by assuming that all state variables relevant to forward-looking behaviour are directly observable, or that they are “…an invertible function of observables” (Mehra and Prescott, 1980). Using a framework that nests linearised DSGE models, we give a number of results useful for the analysis of linear rational expectations models with restricted information sets. We distinguish between instantaneous and asymptotic invertibility, and show that the latter may require significantly less information than the former. We also show that non-invertibility of the information set can have significant implications for the time series properties of economies.     

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.     

New Political Economy

Alberto Alesina and Nouriel Roubini with Gerald D. Cohen, Political Cycles and the Macroeconomy
Avinash K. Dixit, The Making of Economic Policy: A Transaction-Cost Politics Perspective.
Gordon Pepper, Inside Thatcher's Monetarist Revolution     

The Theory of Exchange Rate Target Zones

The theory of exchange rate target zones focuses on the role of exchange rate expectations in determining exchange rate behaviour and interest rate differentials in currency bands. This paper analyses earlier models of the target zone research programme as well as more recent developments including endogenous realignment expectations, price rigidities and alternative monetary feedback rules by means of a unified approach. Target zones may be the cause of stabilizing or destabilizing exchange rate expectations, the determinants of which crucially depend on the within-band central bank policy as well as the credibility of the central banks' commitment to defend the target zone. The paper closes with a discussion of the relative merits of implementing a target zone and some suggestions for further research.     

A new approach to the existence and regularity of linear equilibrium in a noisy rational expectations economy

This paper gives a new approach to show the existence and regularity of linear equilibrium established by Lou ⓡ al. (2019) for a noisy rational expectations economy. Different from the existing method which essentially requires to find a fixed point of a system of nonlinear algebraic equations, the new approach is operated directly on an alternative form of market-clearing conditions. One main advantage of the new approach is that besides homogeneous-valuation economies, it can also handle the existence of equilibrium in economies with heterogeneous valuations where the existing method for dealing with homogeneous-valuation economies fails to work.     

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.     

Rational expectations equilibria and the ex-post core of an economy with asymmetric information

We study the relationship between the set of rational expectations equilibrium allocations and the ex-post core of exchange economies with asymmetric information.     

The impact of offshore exchange rate expectations on onshore exchange rates: The case of Chinese RMB

This paper examines the impact of offshore RMB exchange rate expectations on onshore RMB (CNY) exchange rates. Employing data for the period of 2005–2018, we show that overall offshore market expectations influence onshore RMB rates, but this effect is significant only for the period after the “Second exchange rate regime reform” in 2010. The non-uniform nature of this impact is also confirmed by the existence of a threshold effect of the expectations in the same period. The study improves our understanding of how the offshore RMB market influences onshore RMB spot rates as a result of the marketization reform of the RMB exchange rate regime.     

A remark on rational expectation equilibria with incomplete markets and real assets

In this note, I established the existence, for a generic set of endowments, of a fully revealing rational expectation equilibrium (REE) in an economy characterized by incomplete markets and real assets.     

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.     

Pooling forecasts in linear rational expectations models

Estimating linear rational expectations models in a limited-information setting requires replacing the expectations of future, endogenous variables either with instrumented, actual values or with forecast survey data. Applying the method of Gottfries and Persson [Empirical examinations of the information sets of economic agents. Quarterly Journal of Economics 103, 251–259], I show how to augment these methods with actual, future values of the endogenous variables to improve statistical efficiency. The method is illustrated with an application to the US hybrid new Keynesian Phillips curve, where traditional, lagged instruments and the median forecast from the Survey of Professional Forecasters both appear to miss significant information used by price-setters, so that forecast pooling with actual values improves the statistical fit to inflation.     

Two-step two-stage least squares estimation in models with rational expectations

The paper develops a two-step estimator for use in rational-expectations models with autocorrelated residuals and predetermined, but not strictly exogenous, instruments. The estimator extends the applicability of McCallum's (1976) error-in-variablesapproach to estimating such models, and is asymptotically efficient in a class of intrumental-variables estimators. As an application we use instrumental-variables techniques to estimate Taylor's (1979) rational-expectations macroeconomic model of the United States.     

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.     

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.     

Linear Decentralized Control with Expectations

In this paper, we consider a decentralized discrete-time control model with expectations. There are as many decision-makers as scalar state (and control) variables, and each decision-maker forms an expectation on the impact that affects him/her. Using rational and naive expectations, we describe the stability conditions of the alternative expectations. Our results generalized earlier ones by Metzler and Lovell, from an inventory control model to an abstract model, and solve the problem of the generation of a feasible normal path presented by Kornai and Martos.     

Minimal state variable solutions to Markov-switching rational expectations models

We develop a new method for deriving minimal state variable (MSV) equilibria of a general class of Markov switching rational expectations models and a new algorithm for computing these equilibria. We compare our approach to previously known algorithms, and we demonstrate that ours is both efficient and more reliable than previous methods in the sense that it is able to find MSV equilibria that previously known algorithms cannot. Further, our algorithm can find all possible MSV equilibria in models. This feature is essential if one is interested in using a likelihood based approach to estimation.