Exact Rational Expectations, Cointegration, and Reduced Rank Regression

We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important role in the calculation of maximum likelihood estimation of the restricted parameters.

Estimating change in a proportion by combining measurements from a true and a fallible classifier

Consider a binary classification of a large population at two points in time. The classification is observed with error for the whole population using a fallible classifier and without error for a random sample using an accurate classifier. Following Tenenbein (1970), the population proportions are estimated by poststratification according to the fallible classifier for both the time points. Assuming a multinomial probability model, the joint asymptotic normality of the two estimators is demonstrated. Comparison is made with the estimator based on the survey data only. In particular the importance of including the same items in the samples at both time points is discussed

Interpreting the evidence for new Keynesian models of inflation dynamics

Abstract We present a framework for interpretation of the empirical results of New Keynesian models of in ‡ation dynamics. Both the rational expectations solution of the structural New Keynesian Phillips curve, NKPC, and the reduced form VAR analysis of the multivariate time series properties give insight about the joint implications of the evidence in the NKPC literature. For example, we show that the unit-root form of non-stationary may be implied for in ‡ation even though the econometric model initally assumed stationarity. The uniqueness and form of a rational expectations solution may depend on whether dynamic (in)homogeneity is present, and on the size of the forward-coe¢ cient in the NKPC

Interpreting the evidence for new Keynesian models of inflation dynamics

Abstract We present a framework for interpretation of the empirical results of New Keynesian models of in ‡ation dynamics. Both the rational expectations solution of the structural New Keynesian Phillips curve, NKPC, and the reduced form VAR analysis of the multivariate time series properties give insight about the joint implications of the evidence in the NKPC literature. For example, we show that the unit-root form of non-stationary may be implied for in ‡ation even though the econometric model initially assumed stationarity. The uniqueness and form of a rational expectations solution may depend on whether dynamic (in)homogeneity is present, and on the size of the forwardcoe¢ cient in the NKPC

Testing rational expectations in vector autoregressive models

Assuming that the solutions of a set of restrictions on the rational expectations of future values can be represented as a vector autoregressive model, we study the implied restrictions on the coefficients. Nonstationary behavior of the variables is allowed, and the restrictions on the cointegration relationships are spelled out. In some interesting special cases it is shown that the likelihood ratio statistic can easily be computed.publishedVersio

A note on the power of bootstrap unit root test

In this note we consider the asymptotic power functions of some bootstrap unit root tests under local alternatives and show that they are in fact the same as for ordinary unit root tests. This is regardless of whether the differences of the observations, i.e. the so-called restricted residuals, or the ordinary least squares residuals are used to construct the resampled observations. We also consider models containing a constant and a linear trend and the DF-GLS tests proposed by Elliot et al.(1996). A small Monte Carlo experiment is included