JEL No. C10 The major contributions of twentieth century econometrics to knowledge were the definition of causal parameters when agents are constrained by resources and markets and causes are interrelated, the analysis of what is required to recover causal parameters from data (the identification problem), and clarification of the role of causal parameters in policy evaluation and in forecasting the effects of policies never previously experienced. This paper summarizes the development of those ideas by the Cowles Commission, the response to their work by structural econometricians and VAR econometricians, and the response to structural and VAR econometrics by calibrators, advocates of natural and social experiments, and by nonparametric econometricians and statisticians.

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acknowledges the support for this work by staff in the Division of Research and Statistics including

Ancestral graph models, introduced by Richardson and Spirtes (2002), generalize both Markov random fields and Bayesian networks to a class of graphs with a global Markov property that is closed under conditioning and marginalization. By design, ancestral graphs encode precisely the conditional independence structures that can arise from Bayesian networks with selection and unobserved (hidden/latent) variables. Thus, ancestral graph models provide a potentially very useful framework for exploratory model selection when unobserved variables might be involved in the data-generating process but no particular hidden structure can be specified. In this paper, we present the Iterative Conditional Fitting (ICF) algorithm for maximum likelihood estimation in Gaussian ancestral graph models. The name reflects that in each step of the procedure a conditional distribution is estimated, subject to constraints, while a marginal distribution is held fixed. This approach is in duality to the well-known Iterative Proportional Fitting algorithm, in which marginal distributions are fitted while conditional distributions are held fixed. 1

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Covariance matrices which can be arranged in tridiagonal form are called covariance chains. They are used to clarify some issues of parameter equivalence and of independence equivalence for linear models in which a set of latent variables influences a set of observed variables. For this purpose, orthogonal decompositions for covariance chains are derived first in explicit form. Covariance chains are also contrasted to concentration chains, for which estimation is explicit and simple. For this purpose, maximum-likelihood equations are derived first for exponential families when some parameters satisfy zero value constraints. From these equations explicit estimates are obtained, which are asymptotically efficient, and they are applied to covariance chains. Simulation results confirm the satisfactory behaviour of the explicit covariance chain estimates also in moderate-size samples.

: The goal of this study is the derivation and application of a direct characterization of the inverse of the covariance matrix central to portfolio analysis. As argued below, such a specification, in terms of a few primitive constructs, provides new and illuminating expressions for such key concepts as the optimal holding of a given risky asset and the slope of the risk-return efficiency locus faced by the individual investor. The building blocks of the inverse turn out to be the regression coefficients and residual variance obtained by regressing the asset's excess return on the set of excess returns for all other risky assets. Keywords: portfolio analysis, covariance matrix, inverse matrix. * The author is a Senior Economist in the Division of International Finance, Board of Governors of the Federal Reserve System. The views in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reser...

Key classical macroeconomic hypotheses specify that permanent changes in nominal variables have no effect on real economic variables in the long run. The simplest “long-run neutrality ” proposition specifies that a permanent change in the money stock has no long-run consequences for the level of real output. Other classical hypotheses specify that a permanent change in the rate of inflation has no long-run effect on unemployment (a vertical long-run Phillips curve) or real interest rates (the long-run Fisher relation). In this article we provide an econometric framework for studying these classical propositions and use the framework to investigate their relevance for the postwar U.S. experience. Testing these propositions is a subtle matter. For example, Lucas (1972) and Sargent (1971) provide examples in which it is impossible to test long-run neutrality using reduced-form econometric methods. Their examples feature rational expectations together with short-run nonneutrality and exogenous variables that follow stationary processes so that the data generated by these models do not contain the sustained changes necessary to directly test long-run neutrality. In the context of these models, Lucas and Sargent argued that it was necessary to construct fully articulated behavioral models to test the neutrality propositions. McCallum (1984) extended these arguments and showed that lowfrequency band spectral estimators calculated from reduced-form models were also subject to the Lucas-Sargent critique. While these arguments stand on firm logical ground, empirical analysis following the Lucas-Sargent prescriptions has not yet yielded convincing evidence on the neutrality propositions. This undoubtedly reflects a lack of consensus among macroeconomists on the appropriate behavioral model to use for the investigation.

The liquidity premium on U.S. government securities is quantitatively estimated and tabulated, using maturities from 1 month to 30 years. Unbiased forecasting by the market is assumed in order to get at expectations. The premium is estimated, first allowing it to take any shape and then constraining it to conform to a functional form which implies that the "normal " shape of the yield curve is monotonically increasing toward an asymptote. Tests for constancy of the premium over the post-Accord period, normality of the forecasting errors, and monotonicity of the premium with respect to maturity are performed, and the dependence of the premium on the level of interest rates is discussed. I.