General characterizations of valid confidence sets and tests in problems which involve locally almost unidentified (LAU) parameters are provided and applied to several econometric models. Two types of inference problems are studied: (1) inference about parameters which are not identifiable on certain subsets of the parameter space, and (2) inference about parameter transformations with singularities (discontinuities). When a LAU parameter or parametric function has an unbounded range, it is shown under general regularity conditions that any valid confidence set with level 1 \Gamma ff for this parameter should be unbounded with probability close to 1 \Gamma ff in the neighborhood of nonidentification subsets and should as well have a non-zero probability of being unbounded under any distribution compatible with the model: no valid confidence set which is bounded with probability one does exist. These properties hold even if "identifying restrictions" are imposed. Similar results also ob...

Abstract: In the first half of this century, special attention was given to two features of the business cycle: the comovement of many individual economic series and the different behavior of the economy during expansions and contractions. Recent theoretical and empirical research has revived interest in each attribute separately, and we survey this work. Notable empirical contributions are dynamic factor models that have a single common macroeconomic factor and nonlinear regime-switching models of a macroeconomic aggregate. We conduct an empirical synthesis that incorporates both of these features. It is desirable to know the facts before attempting to explain them; hence, the attractiveness of organizing business-cycle regularities within a model-free framework. During the first half of this century, much research was devoted to obtaining just such an empirical characterization of the business cycle. The most prominent example of this work

We introduce reprojection as a general purpose technique for characterizing the observable dynamics of a partially observed nonlinear system. System parameters are estimated by method of moments wherein moments implied by the system are matched to moments implied by the transition density for observables that is determined by projecting the data onto its Hermite representation. Reprojection imposes the constraints implied by the system on the transition density and is accomplished by projecting a long simulation of the estimated system onto the Hermite representation. We utilize the technique to assess the dynamics of several diffusion models for the short-term interest rate that have been proposed and compare them to a new model that has feedback from the interest rate into both the drift and diffusion coefficients of a volatility equation. This effort entails the development of new graphical diagnostics.

We describe three methods for analyzing the dynamics of a nonlinear time series that is represented by a nonparametric estimate of its one-step ahead conditional density. These strategies are based on examination of conditional moment profiles corresponding to certain shocks; a conditional moment profile is the conditional expectation evaluated at time t of a time invariant function evaluated at time t + j regarded as a function of j. The first method, which compares conditional moment profiles to baseline profiles, is the nonlinear analog of conventional impulse-response analysis. The second assesses the significance of a profile by comparing its sup-norm confidence band to a null profile. The third examines profile bundles for evidence of damping or persistence. Experimental designs for choosing an appropriate set of shocks are discussed. These methods are applied to a bivariate series comprised of daily changes in the Standard and Poor's composite price index and daily NYSE transactions volume from 1928 to 1987. The findings from these data are: (i) The multi-step ahead conditional volatility profile exhibits a symmetric response to both positive and negative price shocks. In contrast, the conditional volatility profile of the univariate price change process exhibits an asymmetric response. (ii) The one-step ahead response of volume to price shocks is different than the multi-step ahead response. Price shocks produce an increase in volume one-step ahead but decrease it in subsequent steps. (iii) There is little evidence for long-term persistence in either the conditional mean or volatility of the bivariate process. o 1

The tendency for changes in the federal funds rate to be implemented gradually has been considered evidence of an interest-rate smoothing objective for the Federal Reserve. This paper investigates whether gradual movements in the federal funds rate can be explained by the dynamic structure of the economy and the uncertainty that the Fed faces regarding this structure, without recourse to including an ad-hoc interest rate smoothing argument in the objective function of the Fed. The analysis calculates the optimal funds rate policy given the structural form of the economy estimated in a VAR. In the absence of parameter uncertainty, the calculated policy responds more aggressively to changes in the economy than the observed policy, resulting in a substantially higher volatility of the funds rate than observed. Parameter uncertainty, however, limits the willingness of the Fed to deviate from the policy rule that has been previously implemented. Because the Fed has historically smoothed interest rates, the calculated policy under parameter uncertainty can account for a considerable portion of the gradualism observed in funds rate movements.

Abstract: This paper uses a simple New Keynesian monetary DSGE model as a prior for a vector autoregression and shows that the resulting model is competitive with standard benchmarks in terms of forecasting and can be used for policy analysis. JEL classification: C11, C32, C53

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This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We apply these methods to several example economies.

: FRB/US is a large-scale quarterly econometric model of the U.S. economy, developed to replace the MPS model. Most behavioral equations are based on specifications of optimizing behavior containing explicit expectations of firms, households, and financial markets. Although expectations are explicit, the empirical fits of the structural descriptions of macroeconomic behavior are comparable to those of reduced-form time series models. In most instances, tests do not reject overidentifying restrictions of rational expectations or the hypothesis of serially independent residuals. As modeled, private sector expectations of policy constitute a major transmission channel of monetary policy. Keywords: Macroeconomic models, private sector learning, rational expectations, vector autoregressions. Edited by F. Brayton and P. Tinsley. Authors of sections are: F. Brayton (section 1); P. Tinsley (sections 2 and 4); A. Bomfim, D. Reifschneider, and P. von zur Muehlen (section 3); B. Tetlow and J. W...

We develop a framework for modeling conditional loss distributions through the introduction of risk factor dynamics. Asset value changes of a credit portfolio are linked to a dynamic global macroeconometric model, allowing macro effects to be isolated from idiosyncratic shocks from the perspective of default (and hence loss). Default probabilities are driven primarily by how firms are tied to business cycles, both domestic and foreign, and how business cycles are linked across countries. The model is able to control for firm-specific heterogeneity as well as generate multi-period forecasts of the entire loss distribution, conditional on specific macroeconomic scenarios. The approach can be used, for example, to compute the effects of a hypothetical negative equity price shock in South East Asia on the loss distribution of a credit portfolio with global exposures over one or more quarters. The approach has several other features of particular relevance for risk managers, such as the exploration of scale and symmetry of shocks, and the effect of non-normality on credit risk. We show that the effects of such shocks on losses are asymmetric and non-proportional, reflecting the highly non-linear nature of the credit risk model. Non-normal innovations such as Student t generate expected and unexpected losses which increase the fatter the tails of the innovations.