Public policy setting often involves quantitative choices with quantitative outcomes. Yet unqualified statements about the precise consequences of alternative choices characterize much of the policy analysis bearing on these decisions. Public Policy in an Uncertain World: Analysis and Decisions by Charles F. Manski characterizes and richly illustrates the nature of this unwarranted certitude. It details specific constructive alternatives on which the economics profession has achieved varying degrees of consensus. Those in our profession charged with the education of future policy analysts should consider using it and how to round out its presentation of decision making from their own perspective.

Methods for the systematic application of Monte Carlo integration with importance sampling to Bayesian inference are developed. Conditions under which the numerical approximation converges almost surely to the true value with the number of Monte Carlo replications, and its numerical accuracy may be assessed reliably, are given. Importance sampling densities are derived from multivariate normal or student approximations to the posterior density. These densities are modified by automatic rescaling along each axis. The concept of relative numerical efficiency is introduced to evaluate the adequacy of a chosen importance sampling density. Applications in two illustrative models are presented.

[Structural and stochastic neutrality have refutable implications for aggregate economic time series only in conjunction with other maintained hypotheses. Simple and commonly employed maintained hypotheses lead to restrictions on measures of feedback and their decomposition by frequency. These restrictions also suggest an empirical interpretation of the notional long and short runs. It is found that a century of annual U.S. data, and postwar monthly data, consistently support structural superneutrality of money with respect to output and the real rate of return and consistently reject its superneutrality with respect to velocity. A quantitative characterization of the long run is suggested.]

In this paper the concept of approximate slope, introduced by R. R. Bahadur, is used to make asymptotic global power comparisons of econometric tests. The approximate slope of a test is the rate at which the logarithm of the asymptotic marginal significance level of the test decreases as sample size increases, under a given alternative. A test with greater approximate slope may therefore be expected to reject the null hypothesis more frequently under that alternative than one with smaller approximate slope. Two theorems, which facilitate the computation and interpretation of the approximate slopes of most econometric tests, are established. These results are used to undertake some illustrative comparisons. Sampling experiments and an empirical illustration suggest that the comparison of approximate slopes may provide an adequate basis for evaluating the actual performance of alternative tests of the same hypothesis.

[The regression relation between regularly sampled Y(t) and X"19t),..., X"N(t) implied by an underlying model in which time enters more generally is studied. The underlying model includes continuous distributed lags, discrete models, and stochastic differential equations as special cases. The relation between parameters identified by regular samplings of Y and X"j and those of the underlying model is characterized. Sufficient conditions for identification of the underlying model in the limit as disaggregation over time proceeds are set forth. Empirical evidence presented suggests that important gains can be realized from temporal disaggregation in the range of conventional measurement frequencies for macroeconomic data.]

Models are the venue for much of the work of the economics profession. We use them to express, compare and evaluate alternative ways of addressing important questions. Applied econometricians are called upon to engage in these exercises using data and, often, formal methods whose properties are understood in decision-making contexts. This is true of work in other sciences as well. There is an enormous literature on alternative formal approaches to these tasks, and in particular on the relative advantages of Bayesian and frequentist methods. By “Bayesian ” I mean statistical inference that reaches a conclusion by means of a conditional distribution of unknown quantities given known quantities and model specifications. This conditional distribution follows from applying Bayes’s theorem to the joint distribution of known and unknown quantities in the model specifications. Known quantities, including data, are treated as observed values of random variables. Unknown quantities, including functions of parameters and as yet unobserved data, are treated as unobserved random variables. Formal methods of model expression, comparison and evaluation that do not have these attributes are non-Bayesian. By “frequentist ” I mean a particular

The Lucas critique of econometric policy evaluation (1976) argues that, to the extent econometric models do not capture the primitive parameters of tastes and technology, their coefficients can be expected to vary with changes in policy regimes. Several econometricians have undertaken empirical work that separates the parameters of tastes, technology, and policy, estimating models that are in principle immune from this critique. Exemplary contributors to this effort have been Thomas Sargent (1978) and Sargent and Lars Hansen (1980). The empirical work inspired by the Lucas critique has proceeded using representative agent models and aggregate data. The treatment of expectations and dynamic optimization has been careful, although at times necessarily limited by the analytical requirements of attaining closed-form solutions for dynamic programming problems under uncertainty. Potential problems due to have usually been ignored, although when preferences and technology are quadratic it appears that they can be disposed of quickly: assuming a representative firm is only a convenience, as the model admits a tidy theory of aggregation (Sargent, 1978, p. 1016). It is ironic that a paradigm that emphasizes the isolation of the primitive parameters of tastes and technology has led to empirical work that has ben conducted almost exclusively with aggregate data. (There are exceptions: T. MaCurdy, 1983; J. Biddle, 1984.) There are several difficulties with this development. First, the fact that representative agent models with exact can be constructed is unrelated to whether or not these models are adequate; we can also construct models in which agents' behavior is unaffected by the policy regime. To exclusively model and test one but not the other appears to be a misplacement of emphasis. Second, some of this work has proceeded using representative agents whose behavior cannot be aggregated exactly (see, M. Eichenbaum, Hansen, and Kenneth Singleton, 1984, for an example). There is a third and most fundamental objection to empirical work which seeks to avoid the Lucas critique, yet uses aggregate data. Whenever econometric policy evaluation is undertaken using models estimated with aggregate data, it is implicitly presumed that the aggregator function is structural with respect to the policy intervention in question. Formally, aggregator functions are no more structural than are within-regime, reducedform relations of endogenous to policy variables. As a modeling strategy, ignoring the sensitivity of aggregators to policy changes seems no more compelling than ignoring the dependence of expectations on the policy regime. This paper describes a very modest econometric model in which the effects of ignoring and of ignoring expectations, each within the context of several representative agent models, can be appreciated. Objective functions are quadratic and prices are disparate across agents; in these respects the model's assumptions are in the mainstream of Lucas and subsequent empirical work. The model is carefully contrived so that exact is always possible. This is not essential to the argument in any way, but it drastically reduces the number of circumstances to be examined in constructing numerical examples. The example pertains to neoclassical production, and in each case there are three distinct representative agents: one for production, one for factor demand, *Professor of Economics, Duke University, Durham, NC 27706. Financial support from NSF Grant SES8318778 and a Sloan Research Fellowship are gratefully acknowledged. A more detailed version of this paper is available on request from the author.

[This article provides an exact Bayesian framework for analyzing the arbitrage pricing theory (APT). Based on the Gibbs sampler, we show how to obtain the exact posterior distributions for functions of interest in the factor model. In particular, we propose a measure of the APT pricing deviations and obtain its exact posterior distribution. Using monthly portfolio returns grouped by industry and market capitalization, we find that there is little improvement in reducing the pricing errors by including more factors beyond the first one.]