Efficient solution techniques for dynamic non-linear rational expectations models

The bifurcation of probability distributions in a non-linear rational expectations model of monetary economy

Some thoughts on rational expectations models, and alternate formulations

Indeterminate equilibrium rational expectations (RE) models are ubiquitous in both theoretical and applied work in dynamic macroeconomics. The issue of characterizing the exact dimension of indeterminacy—i.e. of deriving the full set of causal and stable solutions to linear RE models—has only recently been addressed in the context of general and multivariate settings. This paper complements existing results by identifying bounds on the observable dimension of indeterminacy of linear RE models in the presence of arbitrary initial conditions. Implications for the estimation of indeterminate equilibrium RE models are discussed.

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 "bubbl&' or "bootstrap" effects--ones 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

This note presents a model in which the rational expectations hypothesis does not restrict the number of equilibrium solutions in any meaningful way.1 The techniques and assumptions used to obtain this result, though applied to a very simple duopoly model, are likely to generalize to a variety of rational expectations models. This result suggests that the rationality assumptions often used in economic models may not narrow the range of predicted economic behavior by very much. Such a result is troubling insofar as models that are able to narrow the range of predicted behavior significantly are often the most useful in empirical work. There is a more positive way to state this result, for it suggests a potentially fruitful collaboration between economists and decision psychologists. From the viewpoint of economics, such collaboration may be a source of insight that can help to reduce the number of solutions that rational expectations models of the type presented here seem to generate. From the viewpoint of decision psychology, such collaborative research would provide a framework of equilibrium analysis (or even general equilibrium analysis) that might suggest new forms of experimentation and a broader context for the interpretation of experimental findings. It is worth mentioning in this respect that the feedback implied by the equilibrium framework of economics does not, in and of itself, depend on any rationality assumption but does recognize the effect of the interaction of an aggregation of numerous individual decisions on the individual decision makers themselves. So far as I can tell from my reading of the literature, such feedback from what might be described as the macro implications of the equilibrium process in economics seems to play little or no role in decision psychology. A formal model is presented and discussed in the next section, and

The business cycle analysis of Arthur F. Burns and Wesley C. Mitchell and the National Bureau of Economic Research presumed that aggregate economic variables evolve on a time scale defined by business cycle turning points rather than by months or quarters. Do macroeconomic variables appear to evolve on an economic rather than a calendar time scale? Evidence presented here suggests that they do. However, the estimated economic time scales are only weakly related to business cycle time scales, providing evidence against the view underlying traditional business cycle analysis. Copyright 1987 by University of Chicago Press.

The Application of Observers in the Control of Macroeconometric Systems

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.

Nowadays aircrafts are expected to perform varied and complex tasks which have presented unprecedented control challenges to the aero dynamicists and control engineers. This implies that linear characterization of aircrafts is not well enough to describe the systems characteristics for control purposes and nonlinear modelling techniques are required. Neural network based nonlinear characterization look promising in this regard. This paper investigates into the development of nonlinear modelling paradigms for modern air vehicles with application to a twin rotor multi-input-multi-output system (TRMS). The system is modelled using a nonlinear autoregressive process with external input (NARX) paradigm with a feedforward neural network. Four different types of conjugate gradient algorithms (CGAs) are used in this investigation for supervised learning of the network and their performances are compared in terms of input-output mapping and speed of convergence.

ABSTRACTA rational expectation model with lagged endogenous variables is used to describe how the current price level is influenced by the expectation and historic price level. The time domain of the rational expectation model is extended to a complex discrete time domain which is a collection of points along the real number line. The rational expectation model with lagged endogenous variables is solved in multi-dimensional cases where the agents possess multiple assets, and the current price of each asset is related to the expected price and historical prices. An example about price determination process of storable commodities is given to illustrate the advantages of the rational expectation model on isolate time domain.

The paper is concerned with the role of monetary policy and argues that activist monetary policy can affect the behavior of real output, rational expectations notwithstanding. A rational expectations model with overlapping labor contracts is constructed, with each labor contract being made for two periods. These contracts inject an element of short-run wage stickiness into the model. Because the money stock is changed by the monetary authority more frequently than labor contracts are renegotiated, and, given the assumed form of the labor contracts, monetary policy has the ability to affect the short-run behavior of output, though it has no effects on long-run output behavior.

This survey provides a detailed description of some of the recent theoretical and empirical literature on rational expectations econometrics. The survey pays special attention to non–stationarity of the data, and to the various methods for evaluating rational expectations models that have been developed as alternatives to the classical statistical approach of testing overidentifying restrictions. These methods have become very popular and widely used in empirical research. We provide an illustration using Danish stock market data, and we summarize the many results obtained recently using these measures in areas as diverse as stock prices, the term structure of interest rates, exchange rates, consumption and saving, the balance of payments, tax–smoothing, hyperinflation, and linear quadratic adjustment cost models for inventories, labour demand, and money demand.

Techniques for achieving optimal money supply rules in a rational expectations macroeconomic model

Stackelberg solution for a two-agent rational expectations model

Partial current information and signal extraction in a rational expectations macroeconomic model: A computational solution