(i) It does not always keep the normative analysis of decision-making distinct from its descriptive analysis, losing sight of the fact that these methods are appealing shortcut approximations, not improvements on, decision-making based on the Savage axioms. (ii) In all the existing applications to monetary policy it analyzes uncertainty about relatively unimportant aspects of models, while making strong, but actually uncertain, assumptions about other, more important aspects.

Christopher A. Sims, Uncertainty in the Monetary Aggregates: Sources, Measurement and Policy: Discussion, The Journal of Finance, Vol. 36, No. 2, Papers and Proceedings of the Thirty Ninth Annual Meeting American Finance Association, Denver, September 5-7, 1980 (May, 1981), pp. 515-517

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.

Particularly under the assumption of rational expectations, a model may have serially correlated errors and those errors may be uncorrelated with contemporaneous and lagged values of a predetermined instrument, yet the instruments may not be strictly exogenous. This paper proposes a method for transforming such a model to one without serial correlation, while keeping the instrument predetermined. Standard theory of instrumental variables estimation then applies. Furthermore, it turns out that for transformations of the class proposed, asymptotic distribution theory is the same whether the serial correlation properties of the errors are known a priori or estimated. As the number of lagged values of the predetermined variables used as instruments increases, the asymptotic variance of the standard instrumental variables estimator applied to the transformed model approaches that of the optimal estimator proposed by Hansen and Sargent [8]. IN A NUMBER of recently developed macroeconomic models behavioral equations arise in which error terms can be asserted on the basis of economic arguments to be uncorrelated with some set of instrumental variables at a certain set of dates, but not to be uncorrelated with the instruments at all dates. Examples of such

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.

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.