This paper develops asymptotic distribution theory for generalized method of moments (GMM) estimators and test statistics when some of the parameters are well identified, but others are poorly identified because of weak instruments. The asymptotic theory entails applying empirical process theory to obtain a limiting representation of the (concentrated) objective function as a stochastic process. The general results are specialized to two leading cases, linear instrumental variables regression and GMM estimation of Euler equations obtained from the consumption-based capital asset pricing model with power utility. Numerical results of the latter model confirm that finite sample distributions can deviate substantially from normality, and indicate that these deviations are captured by the weak instruments asymptotic approximations.

In this paper, we propose a parametric spectral estimation procedure for constructing heteroskedasticity and autocorrelation consistent (HAC) covariance matrices. We establish the consistency of this procedure under very general conditions similar to those considered in previous research, and we demonstrate that the parametric estimator converges at a faster rate than the kernel-based estimators proposed by Andrews and Monahan (1992) and Newey and West (1994). In finite samples, our Monte Carlo experiments indicate that the parametric estimator matches, and in some cases greatly exceeds, the performance of the prewhitened kernel estimator proposed by Andrews and Monahan (1992). These simulation experiments illustrate several important limitations of non-parametric HAC estimation procedures, and highlight the advantages of explicitly modeling the temporal properties of the error terms. Wouter J. den Haan Andrew Levin Depa.

In this paper, we study the short-run and long-run comovement between prices and real activity in the G7 countries during the postwar period using VAR forecast errors and frequency domain filters. We find that there are several patterns of the correlation coefficients that are the same in all countries. In particular, the correlation at the 'long-run' horizon is virtually always negative and the correlation at the 'short-run' horizon is typically substantially higher. Although there is evidence of positive 'short-run' correlations for some countries it is not very robust to the choice of the price and output variables. In addition, we propose a more efficient method to calculate the covariances of VAR forecast errors and - in contrast to claims made in the literature - we show that band-pass filters isolate the desired set of frequencies not only when the series are stationary but also when they are first or second-order integrated processes.

In this paper, I present two different methods that can be used to obtain a concise set of descriptive results about the comovement of variables. The statistics are easy to interpret and capture important information about the dynamics in the system that would be lost if one focused only on the unconditional correlation coefficient of detrended data. The methods do not require assumptions about the order of integration. That is, the methods can be used for stationary as well as integrated processes. They do not require the types of assumptions needed for VAR decompositions either. Both methods give similar results. In the postwar period, the comovement between output and prices is positive in the During the same period, the comovement between hours and real wages is negative in the that a model in which demand shocks dominate in the short run and supply shocks dominate in the long run can explain the empirical results, while standard sticky-price models with only demand shocks cannot.

We investigate, by Monte Carlo methods, the finite sample properties of GMM procedures for conducting inference about statistics that are of interest in the business cycle literature. These statistics include the second moments of data filtered using the first difference and Hodrick-Prescott filters, and they include statistics for evaluating model fit. Our results indicate that, for the procedures considered, the existing asymptotic theory is not a good guide in a sample the size of quarterly postwar U.S. data.

This paper explains the divergent behavior of European and US unemployment rates using a job market matching model of the labor market with an interaction between shocks and institutions. It shows that a reduction in TFP growth rates, an increase in real interest rates, and an increase in tax rates leads to a permanent increase in unemployment rates when the replacement rates or initial tax rates are high, while no increase in unemployment occurs when institutions are 'employment friendly.' The paper also shows that an increase in turbulence, modeled as an increased probability of skill loss, is not a robust explanation for the European unemployment puzzle in the context of a matching model with both endogenous job creation and job destruction.

This paper analyzes the performance of heteroskedasticity-and-autocorrelation-consistent (HAC) covariance matrix estimators in which the residuals are prewhitened using a vector autoregressive (VAR) filter. We highlight the pitfalls of using an arbitrarily fixed lag order for the VAR filter, and we demonstrate the benefits of using a model selection criterion (either AIC or BIC) to determine its lag structure. Furthermore, once data-dependent VAR prewhitening has been utilized, we find negligible or even counter-productive effects of applying standard kernel-based methods to the prewhitened residuals; that is, the performance of the prewhitened kernel estimator is virtually indistinguishable from that of the VARHAC estimator.