A comparison among partial adjustment,rational expectations and error correction estimates of the canadian demand for money

Starting from a dynamic optimization principle, the currently most popular approaches to modelling money demand functions are derived. The partial adjustment/adaptive expectations, rational expectations, and error correction mechanism formulations are then estimated using a common data set. The error correction mechanism equation is found to dominate the others either because their implicit restrictions are rejected (rational expectations) or by employing the encompassing principle (partial adjustment/adaptive expectations). Surprisingly all three forms have similar long-run solutions. Since the short-run dynamics differ substantially, the results have important implications for the conduct of monetary policy.     

Formulating wald tests of the restrictions implied by the rational expectations hypothesis

In this paper, we examine the small sample properties of alternative formulations of Wald tests of non-linear restrictions implied by the rational expectations hypothesis. A Monte Carlo analysis is presented as well as an example using Canadian aggregate time series data. The evidence indicates that Wald test results are extremely sensitive in small samples to the way in which the non-linear restrictions in such models are parameterized, with a multiplicative form yielding tests of most accurate size. Least squares degrees of freedom adjustments also improve the sample performance of the tests.     

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.     

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.     

Rationality,specification tests,and macroeconomic models

Rational expectation models embody cross-equation restrictions that are implied by the theory of rational expectations. In this paper we illustrate how tests of these restrictions may be implemented in terms of general macroeconomic models by employing the models of Taylor and Sargent as examples. In addition, the more important issue of the proper interpretation of the results of these tests is addressed. We contend that tests for rationality should become part of the model-building process as they are akin to specification tests for models in which rational expectations is treated as the maintained hypothesis. A procedure is suggested when the restriction are inconsistent with data. Special emphasis is placed upon examining how changes in specifications of the model's exogenous variables can influence test results.     

Modelling market fundamentals: A model of the aluminium market

The standard approach to modelling primary commodity markets under rational expectations is to relate the commodity price to the production and consumption ‘surprises’ (i.e. the innovations on the equations). Using the world aluminium market, we show how this approach can be modified so that both the price and stock can be written in terms of one or more market ‘fundamentals’ which reflect the supply—demand balance on the market. This approach allows joint estimation of production, consumption, stock demand and price equations subject to cross-equation restrictions. It may be seen as a formalization of the approach adopted by metals industry analysts.     

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.     

Determinacy,indeterminacy and dynamic misspecification in linear rational expectations models

This paper proposes a testing strategy for the null hypothesis that a multivariate linear rational expectations (LRE) model may have a unique stable solution (determinacy) against the alternative of multiple stable solutions (indeterminacy). The testing problem is addressed by a misspecification-type approach in which the overidentifying restrictions test obtained from the estimation of the system of Euler equations of the LRE model through the generalized method of moments is combined with a likelihood-based test for the cross-equation restrictions that the model places on its reduced form solution under determinacy. The resulting test has no power against a particular class of indeterminate equilibria, hence the non rejection of the null hypothesis can not be interpreted conclusively as evidence of determinacy. On the other hand, this test (i) circumvents the nonstandard inferential problem generated by the presence of the auxiliary parameters that appear under indeterminacy and that are not identifiable under determinacy, (ii) does not involve inequality parametric restrictions and hence the use of nonstandard inference, (iii) is consistent against the dynamic misspecification of the LRE model, and (iv) is computationally simple. Monte Carlo simulations show that the suggested testing strategy delivers reasonable size coverage and power against dynamic misspecification in finite samples. An empirical illustration focuses on the determinacy/indeterminacy of a New Keynesian monetary business cycle model of the US economy.     

Forecasting the exchange rate using nonlinear Taylor rule based models

This research utilises a non-linear Smooth Transition Regression (STR) approach to modelling and forecasting the exchange rate, based on the Taylor rule model of exchange rate determination. The separate literatures on exchange rate models and the Taylor rule have already shown that the non-linear specification can outperform the equivalent linear one. In addition the Taylor rule based exchange rate model used here has been augmented with a wealth effect to reflect the increasing importance of the asset markets in monetary policy. Using STR models, the results offer evidence of non-linearity in the variables used and that the interest rate differential is the most appropriate transition variable. We conduct the conventional out-of-sample forecasting performance test, which indicates that the non-linear models outperform their linear equivalents as well as the non-linear UIP model and random walk.     

Testing Steady‐State Restrictions of Linear Rational Expectations Models when Data are Highly Persistent*

Steady‐state restrictions are commonly imposed on highly persistent variables to achieve stationarity prior to confronting rational expectations models with data. However, the resulting steady‐state deviations are often surprisingly persistent indicating that some aspects of the underlying theory may be empirically problematic. This paper discusses how to formulate steady‐state restrictions in rational expectations models with latent forcing variables and test their validity using cointegration techniques. The approach is illustrated by testing steady‐state restrictions for alternative specifications of the New Keynesian model and shown to be able to discriminate between different assumptions on the sources of the permanent shocks.     

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.     

Parametric continuity in dynamic programming problems

We examine conditions under which the solutions to parametric families of dynamic programming problems are continuous in the parameters. Our main results are that parametric continuity obtains whenever either (a) the family of dynamic programming problems satisfies strong (joint-) continuity properties in the parameter and state or (b) if it satisfies weaker (separate-) continuity requirements, provided these are supplemented by either stronger assumptions on the transition probabilities or by monotonicity restrictions such as are common in economic modelling. The usefulness of our results is illustrated by applying them to some commonly used dynamic economic models.     

BAYESIAN STATE SPACE MODELS IN MACROECONOMETRICS

State space models play an important role in macroeconometric analysis and the Bayesian approach has been shown to have many advantages. This paper outlines recent developments in state space modelling applied to macroeconomics using Bayesian methods. We outline the directions of recent research, specifically the problems being addressed and the solutions proposed. After presenting a general form for the linear Gaussian model, we discuss the interpretations and virtues of alternative estimation routines and their outputs. This discussion includes the Kalman filter and smoother, and precision-based algorithms. As the advantages of using large models have become better understood, a focus has developed on dimension reduction and computational advances to cope with high-dimensional parameter spaces. We give an overview of a number of recent advances in these directions. Many models suggested by economic theory are either non-linear or non-Gaussian, or both. We discuss work on the particle filtering approach to such models as well as other techniques that use various approximations – to either the time state and measurement equations or to the full posterior for the states – to obtain draws.     

A Monte Carlo study of the forecasting performance of empirical SETAR models

In this paper we investigate the multi-period forecast performance of a number of empirical self-exciting threshold autoregressive (SETAR) models that have been proposed in the literature for modelling exchange rates and GNP, among other variables. We take each of the empirical SETAR models in turn as the DGP to ensure that the ‘non-linearity’ characterizes the future, and compare the forecast performance of SETAR and linear autoregressive models on a number of quantitative and qualitative criteria. Our results indicate that non-linear models have an edge in certain states of nature but not in others, and that this can be highlighted by evaluating forecasts conditional upon the regime. Copyright © 1999 John Wiley & Sons, Ltd.     

The behaviour of U.K. export prices of manufactured goods 1970–1983

This paper examines the importance of expectations in the determination of U.K. export prices. Export prices are found to depend upon expectations of total domestic unit costs and foreign prices. The non-linear restrictions implied by the forward-looking model are found to hold and it performs adequately relative to a backward-looking error feedback model. The law of one price is rejected and the evidence is consistent with imperfect competition in export markets.     

Misspecification and Expectations Correction in New Keynesian DSGE Models

This paper focuses on the dynamic misspecification that characterizes the class of small‐scale New Keynesian models currently used in monetary and business cycle analysis, and provides a remedy for the typical difficulties these models have in accounting for the rich contemporaneous and dynamic correlation structure of the data. We suggest using a statistical model for the data as a device through which it is possible to adapt the econometric specification of the New Keynesian model such that the risk of omitting important propagation mechanisms is kept under control. A pseudo‐structural form is built from the baseline system of Euler equations by forcing the state vector of the system to have the same dimension as the state vector characterizing the statistical model. The pseudo‐structural form gives rise to a set of cross‐equation restrictions that do not penalize the autocorrelation structure and persistence of the data. Standard estimation and evaluation methods can be used. We provide an empirical illustration based on USA quarterly data and a small‐scale monetary New Keynesian model.     

EMPIRICAL ESTIMATION OF NON-LINEAR INPUT–OUTPUT MODELS: AN ENTROPY ECONOMETRICS APPROACH

Despite theoretical advances, non-linear input–output models have been empirically applied only to a limited extent. This is mainly due to the fact that the number of parameters to be estimated is much higher than the number of available data points. Taking advantage of the recent proliferation of input–output databases and by applying an estimation strategy that relies on entropy econometrics, this paper suggests a way to estimate the parameters that characterize non-linear relationships between inputs and output. This non-linear modelling allows for considering time-specific input coefficients, instead of fixed ones. Several types of multipliers can be derived from this non-linear model, and the proposed generalized maximum entropy (GME) estimator allows estimating them from time series or cross-sectional datasets of input–output tables. The proposed GME technique is illustrated by means of an empirical application that estimates the parameters that characterize a non-linear input–output model for the Spanish economy over the period 1995–2011.     

Identifiability criteria for Muth-rational expectations models

The authors deal with complete static linear models that contain current Muth-rational expectations. Rank, order and variety conditions for the identifiability of the structural parameter are derived under general restrictions. We also correct statements that appeared in the literature. Our main finding is that, in general, the standard rank and order conditions are sufficient also for the identifiability of the Muth-rational expectations model parameter, whenever there are enough not fully anticipated exogenous variables. If the number of imperfectly forecasted exogenous variables falls short of the number of endogenous variables by g, then g extra restrictions are needed on every equation and the restrictions must meet easily verifiable variety conditions as well as an augmented rank criterion.     

Monotone missing data and pattern-mixture models

It is shown that the classical taxonomy of missing data models, namely missing completely at random, missing at random and informative missingness, which has been developed almost exclusively within a selection modelling framework, can also be applied to pattern-mixture models. In particular, intuitively appealing identifying restrictions are proposed for a pattern-mixture MAR mechanism.