We show how correctly to extend known methods for generating error bands in reduced form VAR's to overidentified models. We argue that the conventional pointwise bands common in the literature should be supplemented with measures of shape uncertainty, and we show how to generate such measures. We focus on bands that characterize the shape of the likelihood. Such bands are not classical confidence regions. We explain that classical confidence regions mix information about parameter location with information about model fit, and hence can be misleading as summaries of the implications of the data for the location of parameters. Because classical confidence regions also present conceptual and computational problems in multivariate time series models, we suggest that likelihood-based bands, rather than approximate confidence bands based on asymptotic theory, be standard in reporting results for this type of model.

Econometrics

A multivariate regime-switching model for monetary policy is confronted with U.S. data. The best fit allows time variation in disturbance variances only. With coefficients allowed to change, the best fit is with change only in the monetary policy rule and there are three estimated regimes corresponding roughly to periods when most observers believe that monetary policy actually differed. But the differences among regimes are not large enough to account for the rise, then decline, in inflation of the 1970s and 1980s. Our estimates imply monetary targeting was central in the early 1980s, but also important sporadically in the 1970s.

Is credit expansion a sign of desirable financial deepening or the prelude to an inevitable bust? We study this question in modern US data using a structural VAR model of 10 monthly frequency variables, identified by heteroskedasticity. Negative reduced-form responses of output to credit growth are caused by endogenous monetary policy response to credit expansion shocks. On average, credit and output growth remain positively associated. “Financial stress” shocks to credit spreads cause declines in output and credit levels. Neither credit aggregates nor spreads provide much advance warning of the 2008–2009 crisis, but spreads improve within-crisis forecasts. (JEL C51, E23, E31, E43, E44, E52, G01)

This paper considers estimation and hypothesis testing in linear time series when some or all of the variables have (possibly multiple) unit roots. The motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as regressors. Parameters that can be written as coefficients on mean zero, nonintegrated regressors have jointly normal asymptotic distribution, converging at the rate of T(superscript "one-half") In general, the other coefficients (including the coefficient on polynomials in time), and associated t and F test statistics, have nonstandard asymptotic distributions. Copyright 1990 by The Econometric Society.

Abstract Individuals are constantly processing external information and translating it into actions. This draws on limited resources of attention and requires economizing on attention devoted to signals related to economic behaviour. A natural measure of such costs is based on Shannon’s “channel capacity”. Modelling economic agents as constrained by Shannon capacity as they process freely available information turns out to imply that discretely distributed actions, and thus actions that persist across repetitions of the same decision problem, are very likely to emerge in settings that without information costs would imply continuously distributed behaviour. We show how these results apply to the behaviour of an investor choosing portfolio allocations, as well as to some mathematically simpler “tracking” problems that illustrate the mechanism. Trying to use costs of adjustment to explain “stickiness” of actions when interpreting the behaviour in our economic examples would lead to mistaken conclusions.