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.     

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.     

Limited-dependent rational expectations models with future expectations

This paper examines limited-dependent rational expectations (LD-RE) models containing future expectations of the dependent variable. Limited dependence is of a two-limit tobit variety which may, for example, arise as a result of a policy of imposing limits on the movement of the dependent variable by means of marginal as well as intramarginal interventions. We show that when the forcing variables are serially independent the model has an analytical solution which can be computed by backward recursion. With serially correlated forcing variables, we discuss an approximate solution method, as well as a numerically exact method that, in principle, can be implemented by stochastic simulation, although in practice it is limited by available computational capacity. The paper discusses some properties of the approximate solutions and reports the results of a limited number of Monte Carlo experiments in order to illustrate the computational feasibility of using the exact solution when the fundamentals are serially independent and the approximate solution when they are serially correlated.     

Mitigation of the Lucas critique with stochastic control methods

Lucas (In: Brunner, K., Meltzer, A.H. (Eds.), The Phillips Curve and the Labor Markets, Supplementary Series to the Journal of Monetary Economics, 1976, pp. 19–46) pointed out, that when optimization is performed on a deterministic macro model, the resulting policy may not reflect the true optimal solution. Private agents may react to announced policies and consequently model parameters will start to drift. The aim of this paper is to develop a methodology for deriving an optimal policy in the presence of rational expectations and parameter drift. This drift is captured by a stochastic optimization framework with time-varying parameters. The resulting optimal policy is capable of tracking changes in the parameters due to policy changes. A numerical example illustrates how the methodology provides a way to mitigate the effects of the Lucas critique.     

Adaptive learning,endogenous uncertainty,and asymmetric dynamics

I present a simple model where forecasting confidence affects aggregate demand. It is shown that this model has similar stability properties, under statistical and evolutionary learning, as a model without a confidence affect. From this setup, I introduce “Expectational Business Cycles” where output fluctuates due to learning, heterogeneous forecasting models and random changes in the efficient forecasting model. Agents use one of two forecasting models to forecast future variables while heterogeneity is dictated via an evolutionary process. Increased uncertainty, due to a shock to the structure of the economy, may result in a sudden decrease in output. As agents learn the equilibrium, output slowly increases to its equilibrium value. Expectational business cycles tend to arrive faster, last longer and are more severe as agents possess less information.     

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.     

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.     

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.     

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.     

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.     

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.     

Cohort and target age effects on subjective survival probabilities: Implications for models of the retirement phase

Subjective survival scaling factors are often estimated from one observation of life expectancy and treated as constant to any target age. Using new survey data on subjective survival probabilities, we estimate a model incorporating cohort- and target age-varying beliefs in scaling factors. Both cohort age and target age matter: respondents are pessimistic about overall life expectancy but optimistic about survival at advanced ages, and older respondents are more optimistic than younger. We propose a new theoretical model incorporating cohort- and target age-varying beliefs and illustrate their effects on the perceived value of annuities and on retirement phase consumption plans.     

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.     

影响工学结合开展的因素及对策研究

工学结合是高等职业教育改革的必经之路,本文重点阐释了影响高职院校工学结合的因素,并根据以上因素,结合学校开展校企合作的实践经验总结,提出诸如制定科学的工学结合评价体系等解决方法。     

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.     

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.     

Learning and the dynamics of consumer unsecured debt and bankruptcies

During the Great Moderation, the consumer unsecured debt-to-income ratio nearly doubled and the personal bankruptcy filing rate more than quadrupled. This historically tranquil period ended in 2008 with a severe recession and a protracted credit crunch. We develop a theory of learning in which consumers and lenders adjust their beliefs about the riskiness of the economic environment over time in response to the realized sequence of aggregate shocks and then embed it into an otherwise standard quantitative model of consumer default. Simulations of the model suggest that learning can explain as much as half of the recent boom and bust cycle in consumer unsecured debt and a modest fraction of the rise in bankruptcy filings prior to 2005.     

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 and time-varying macroeconomic volatility

This paper presents a DSGE model in which agents׳ learning about the economy can endogenously generate time-varying macroeconomic volatility. Economic agents use simple models to form expectations and need to learn the relevant parameters. Their gain coefficient is endogenous and is adjusted according to past forecast errors.The model is estimated using likelihood-based Bayesian methods. The endogenous gain is jointly estimated with the structural parameters of the system.The estimation results show that private agents appear to have often switched to constant-gain learning, with a high constant gain, during most of the 1970s and until the early 1980s, while reverting to a decreasing gain later on. As a result, the model can generate a pattern of volatility, which is increasing in the 1970s and falling in the second half of the sample, with a decline that can roughly match the magnitude of the so-called “Great Moderation” in the 1984–2007 period. The paper also documents how a failure to incorporate learning into the estimation may lead econometricians to spuriously find time-varying volatility in the exogenous shocks, even when these have constant variance by construction.     

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.