Alain Guay

A Survey of Alternative Methodologies for Estimating Potential Output and the Output Gap

In this paper, the authors survey some of the recent techniques proposed in the literature to measure the trend component of output or potential output. Given the reported shortcomings of mechanical filters and univariate approaches to estimate potential output, the paper focusses on three simple multivariate methodologies: the multivariate Beveridge-Nelson methodology (MBN), Cochranes methodology (CO), and the structural VAR methodology with long-run restrictions applied to output (LRRO). The foundation of these methodologies is first discussed and then applications to U.S. output and consumption data are considered. The LRRO estimates provide significant evidence of a diffusion process for shocks to potential output. This suggests that permanent shocks have more complex dynamics than a random walk, which is the basic assumption of the CO and MBN approaches. However, it is also found that the estimation of the output gap on the basis of an estimated VAR is imprecise, which is consistent with results obtained by Staiger, Stock and Watson (1996) with a different methodology. The spectra of the transitory components (output gaps) resulting from the empirical applications of the CO, MBN and LRRO methodologies differ from one another. Indeed, only the LRRO transitory component has a peak at business-cycle frequencies, i.e., cycles lasting between 6 and 32 quarters.

Predictive tests for structural change with unknown breakpoint

This paper considers predictive tests for structural change in models estimated via Generalized Method of Moments. Our analysis extends earlier work by Ghysels and Hall (1990a) by allowing for the instability to occur at an unknown point in the sample. We analyze various statistics based on continuous mappings of the sequence of predictive tests calculated for a set of possible breakpoints in the sample. The limiting distribution of these statistics is derived under both the null hypothesis and local alternatives. Percentiles are reported for the distribution under the null. A side product of our analysis is that we can illuminate the power properties of the predictive test and also compare its properties to those of the Wald, LR and LM tests for parameter variation. We study those power properties both via local asymptotic analysis and Monte Carlo. Cette etude generalise la procedure proposee par Ghysels et Hall (1990a) pour tester le changement structurel pour des modeles estimes par la methode de moments generalisee. Nous ne supposons plus le point de rupture comme etant connu et proposons plusieurs statistiques predictives avec changement structurel inconnu. Comme les distributions asymptotiques sont non standard, nous fournissons les valeurs critiques. Finalement, nous etudions la puissance des tests et faisons des comparaisons avec des tests du type Wald, LM et LR.

What do interest rates reveal about the functioning of real business cycle models

Abstract This paper begins by documenting the extent to which the predictions of standard Real Business Cycle (RBC) models are incompatible with observed movements in real interest rates. The main finding of the paper is that extending the baseline model to include habit persistence in consumption and adjustment costs to capital significantly improves the models empirical performance. In our evaluation of the models performance, we take special care of estimating and testing predictions of the model using both moments drawn directly from the data and moments calculated after identifying shocks to the stochastic trend.

Indirect Inference, Nuisance Parameter, and Threshold Moving Average Models

We analyze the modifications that occur in indirect inference when a nuisance parameter is not identified under the null hypothesis. We develop a testing procedure adapted to this simulation-based estimation method, and detail its use for detecting the threshold effect in threshold moving average models with contemporaneous and lagged asymmetries. In contrast to existing threshold models, these models allow taking into account the presence of asymmetric effects of current and lagged random shocks. We use them to measure the persistence of shocks to U.S. output.

Identification of Technology Shocks in Structural VARs

The usefulness of SVARs for developing empirically plausible models is actually subject to controversies in macroeconomics. We propose a two-step SVARs-based procedure which consistently estimates the effect of permanent technology shocks on aggregate variables. Simulation experiments from a standard business cycle model and a sticky prices model show that our approach outperforms standard SVARs. The two-step procedure, when applied to actual data, predicts a significant short-run decrease of hours after a technology improvement followed by a hump-shaped positive response. Additionally, the rate of inflation and the nominal interest rate displays a significant decrease after this shock.

A Data-Driven Nonparametric Specification Test For Dynamic Regression Models

The paper introduces a new nonparametric specification test for dynamic regression models. The test combines chi-square statistics based on Fourier series regression. A data-driven choice of the regression order, which uses the square root of the number of Fourier coefficients, is proposed. The benefits of the new test are (1) the selection procedure produces explicit and chi-square critical values that give a finite-sample size close to the nominal size; (2) the test is adaptive rate-optimal and detects local alternatives converging to the null with a rate that can be made arbitrarily close to the parametric rate. Simulation experiments illustrate the practical relevance of the new test.The first author acknowledges financial support from the Fonds QuA©bA©cois de la Recherche sur la SociA©tA© et la Culture (FQRSC). The second author acknowledges financial support from LSTA.

Optimal Predictive Tests

Abstract This paper develops optimal tests based on sequential predictive moment conditions. We show that an appropriate weighting version of the predictive test achieves the same power as optimal structural change tests proposed by Sowell (1996a) Optimal tests for parameter instability in the generalized method of moments framework. Econometrica64:1085–1107 and (1996b) Tests for Violations of MOMENT conditions. Manuscript.Graduate School of Industrial Administration, Carnegie Mellon University. Consequently, we can apply directly Sowells results. Optimal predictive tests for parameter instability and overidentifying restriction stability are proposed. The finite sample properties of LM, Wald, LR‐type and predictive tests for parameter instability are studied via a simulation study.

Robust adaptive rate-optimal testing for the white noise hypothesis

A new test is proposed for the weak white noise null hypothesis. The test is based on a new automatic selection of the order for a Box–Pierce (1970) test statistic or the test statistic of Hong (1996). The heteroskedasticity and autocorrelation-consistent (HAC) critical values from Lee (2007) are used, allowing for estimation of the error term. The data-driven order selection is tailored to detect a new class of alternatives with autocorrelation coefficients which can be o(n−1/2) provided there are sufficiently many of such coefficients. A simulation experiment illustrates the good statistical properties of the test both under the weak white noise null and the alternative.

Structural change tests for GEL criteria

ABSTRACT This article examines structural change tests based on generalized empirical likelihood methods in the time series context, allowing for dependent data. Standard structural change tests for the Generalized method of moments (GMM) are adapted to the generalized empirical likelihood (GEL) context. We show that when moment conditions are properly smoothed, these test statistics converge to the same asymptotic distribution as in the GMM, in cases with known and unknown breakpoints. New test statistics specific to GEL methods, and that are robust to weak identification, are also introduced. A simulation study examines the small sample properties of the tests and reveals that GEL-based robust tests performed well, both in terms of the presence and location of a structural change and in terms of the nature of identification.

Using Implied Probabilities to Improve Estimation with Unconditional Moment Restrictions

In this paper, we investigate the information content of implied probabilities (Back and Brown, 1993) to improve estimation in unconditional moment conditions models. We propose and evaluate two 3-step euclidian empirical likelihood estimators and their bias-correction versions for weakly dependent data. The first one is the time series extension of the 3S-EEL proposed by Antoine, Bonnal and Renault (2007).The second one is new and uses in contrast only an estimator of the weighting matrix at an efficient 2-step GMM estimator, while leaving unrestricted the Jacobian matrix. Both estimators use implied probabilities to achieve higher-order improvements relative to the traditional GMM estimator. A Monte-Carlo study reveals that the finite and large sample properties of the (bias-corrected) 3-step estimators compare very favorably to the existing approaches: the 2-step GMM and the continuous updating estimator. As an application, we re-assess the empirical evidence regarding the New Keynesian Phillips curve in the US.