Jean-Marie Dufour

Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models

General characterizations of valid confidence sets and tests in problems involving (locally almost) unidentified (LAU) parameters are presented. In particular, any valid confidence set for an unbounded LAU parameter must be unbounded with positive probability. Consequently, almost surely bounded confidence sets, like Wald-type confidence sets, have zero coverage probability and Wald-type test statistics cannot be pivotal functions. The results are applied to simultaneous equations (weak instruments), regressions with autoregressive errors, long-run multipliers, and cointegrating vectors. For such models, Wald-type procedures are not recommended while LR procedures can be shown to be valid.

Short Run and Long Run Causality in Time Series: Theory

Causality in Grangers sense is defined in terms of predictibility one period ahead. The notion of causality is generalized by considering causality at any given horizon 1 (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)

Identification, weak instruments, and statistical inference in econometrics

We discuss statistical inference problems associated with identification and testability in econometrics, and we emphasize the common nature of the two issues. After reviewing the relevant statistical notions, we consider in turn inference in nonparametric models and recent developments on weakly identified models (or weak instruments). We point out that many hypotheses, for which test procedures are commonly proposed, are not testable at all, while some frequently used econometric methods are fundamentally inappropriate for the models considered. Such situations lead to ill-defined statistical problems and are often associated with a misguided use of asymptotic distributional results. Concerning nonparametric hypotheses, we discuss three basic problems for which such difficulties occur : (1) testing a mean (or a moment) under (too) weak distributional assumptions; (2) inference under heteroskedasticity of unknown form; (3) inference in dynamic models with an unlimited number of parameters. Concerning weakly identified models, we stress that valid inference should be based on proper pivotal functions —a condition not satisfied by standard Wald-type methods based on standard errors — and we discuss recent developments in this field, mainly from the viewpoint of building valid tests and confidence sets. The techniques discussed include alternative proposed statistics, bounds, projection, split-sampling, conditioning, Monte Carlo tests. The possibility of deriving a finite-sample distributional theory, robustness to the presence of weak instruments, and robustness to the specification of a model for endogenous explanatory variables are stressed as important criteria assessing alternative procedures.

Recursive stability analysis of linear regression relationships: An exploratory methodology

The problem of the instability of econometric relationships over time has been recognized by several econometricians [e.g. Chow (1960), Duesenberry and Klein (1965), Cooley and Prescott (1976)]. Parameter stability is especially important when one wants to use a model for forecasting and policy simulations. For example, the assessment of the stability of the demand for money is of crucial importance in decisions about the role of monetary policy. Generally, when using an econometric model to study the effect of a policy change, it is essential that the parameters of the model be invariant with respect to the change contemplated. In this respect, Lucas (1976) has shown that, since the parameters of econometric models reflect the optimal decision rules of economic agents and these integrate knowledge about policy decision rules, changes in policies are likely to induce changes in the parameters of the relationships. Assessing the importance of such possible instabilities may be particularly relevant in the context of policy simulation studies. A fairly general way of interpreting the instability of econometric relationships over time is to assume the presence of some sort of misspecification (omitted variables, incorrect functional forms, etc.). One could also speak of ‘structural changes’ in the economy but it can always be argued that the ‘structural parameters’ one has in mind are changing because the variables which determine them are omitted from the model, and that

Inflation dynamics and the New Keynesian Phillips Curve: An identification robust econometric analysis

In this paper, we use identification-robust methods to assess the empirical adequacy of a New Keynesian Phillips Curve (NKPC) equation. We focus on the Gali and Gertler’s (1999) specification, on both U.S. and Canadian data. Two variants of the model are studied: one based on a rationalexpectations assumption, and a modification to the latter which consists in using survey data on inflation expectations. The results based on these two specifications exhibit sharp differences concerning: (i) identification difficulties, (ii) backward-looking behavior, and (ii) the frequency of price adjustments. Overall, we find that there is some support for the hybrid NKPC for the U.S., whereas the model is not suited to Canada. Our findings underscore the need for employing identificationrobust inference methods in the estimation of expectations-based dynamic macroeconomic relations.

Short Run and Long Run Causality in Time Series: Inference

We propose methods for testing hypotheses of non-causality at various horizons, as defined in Dufour and Renault (1998, Econometrica). We study in detail the case of VAR models and we propose linear methods based on running vector autoregressions at different horizons. While the hypotheses considered are nonlinear, the proposed methods only require linear regression techniques as well as standard Gaussian asymptotic distributional theory. Bootstrap procedures are also considered. For the case of integrated processes, we propose extended regression methods that avoid nonstandard asymptotics. The methods are applied to a VAR model of the U.S. economy.

Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary or nonstationary AR(1) errors

Abstract Inference on the autocorrelation coefficient ϱ of a linear regression model with first-order autoregressive normal disturbances is studied. Both stationary and nonstationary processes are considered. Locally best and point-optimal invariant tests for any given value of ϱ are derived. Special cases of these tests include tests for independence and tests for unit-root hypotheses. The powers of alternative tests are compared numerically for a number of selected testing problems and for a range of design matrices. The results suggest that point-optimal tests are usually preferable to locally best tests, especially for testing values of ϱ greater than or equal to one.

NONLINEAR HYPOTHESES, INEQUALITY RESTRICTIONS, AND NON-NESTED HYPOTHESES: EXACT SIMULTANEOUS TESTS IN LINEAR REGRESSIONS

In the classical linear model, comparison of two arbitrary hypotheses on the regression coefficients is considered. Problems involving nonlinear hypotheses, inequality restrictions, or non-nested hypotheses are included. Exact bounds on the null distribution of likelihood ratio statistics are derived (based on the central Fisher distribution). As a special case, a bounds test similar to the Durbin-Watson test is proposed. Multiple testing problems are studied: the bounds obtained for a single pair of hypotheses are shown to enjoy a simultaneity property that allows combination of any number of tests. This result extends to nonlinear hypotheses a well-known result given by H. Scheffe for linear hypotheses. A method of building bounds-induced tests is suggested. Copyright 1989 by The Econometric Society.

Simulation‐Based Finite Sample Normality Tests in Linear Regressions

In the literature on tests of normality, much concern has been expressed over the problems associated with residual-based procedures. Indeed, the specialized tables of critical points which are needed to perform the tests have been derived for the location-scale model; hence reliance on available significance points in the context of regression models may cause size distortions. We propose a general solution to the problem of controlling the size normality tests for the disturbances of standard linear regression, which is based on using the technique of Monte Carlo tests.

Exact Inference Methods for First-Order Autoregressive Distributed Lag Models

Exact tests and confidence sets are obtained for general transformations of the coefficients in linear first-order autoregressive models with exogenous variables and i.i.d. disturbances. The tests proposed have known level and are either similar (constant rejection probability under all processes consistent with the null hypothesis) or use bounds which are free of nuisance parameters. Correspondingly, the confidence sets are either similar with known size or conservative. These exact methods are asymptotically valid under weak regularity conditions. Their usefulness is illustrated by power comparisons and by applications to a dynamic trend model of money velocity and a model of money demand.(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)