We conduct Monte Carlo simulations to evaluate the use of information criteria (Akaike information criterion [AIC] and Schwarz information criterion [SC]) as an alternative to various probability-based tests for determining cointegrating rank in multivariate analysis. First, information criteria are used to determine cointegrating rank given the lag order in a levels vector autoregression. Second, information criteria are used to determine the lag order and cointegrating rank simultaneously. Results show that AIC has an advantage over trace tests for cointegrated or stationary processes in small samples. AIC does not perform well in large samples. The performance of SC is close to that of the trace test. SC shows better large sample results than AIC and the trace test, even if the series are close to nonstationary series or they contain large negative moving average components. We also find evidence that supports the joint estimation of lag order and cointegrating rank by the SC criterion. We conclude that information criteria can complement traditional parametric tests.We are grateful to Peter C.B. Phillips and an anonymous referee for their comments, which significantly improved the paper.

Standard econometric model selection methods are based on four conceptual errors: parametric vision, the assumption of a true data generating process, evaluation based on fit, and ignoring the impact of model uncertainty on inference. Instead, econometric model selection methods should be based on a semiparametric vision, models should be viewed as approximations, models should be evaluated based on their purpose, and model uncertainty should be incorporated into inference methods. These problems have been examined individually but not jointly, and my view is that future research into econometric model selection should attempt to address all four issues.This research was supported by the National Science Foundation. I thank Peter Phillips and a referee for helpful comments that greatly improved the arguments and exposition.

We consider asymmetric kernel density estimators and smoothed histograms when the unknown probability density function f is defined on [0,+∞). Uniform weak consistency on each compact set in [0,+∞) is proved for these estimators when f is continuous on its support. Weak convergence in L1 is also established. We further prove that the asymmetric kernel density estimator and the smoothed histogram converge in probability to infinity at x = 0 when the density is unbounded at x = 0. Monte Carlo results and an empirical study of the shape of a highly skewed income distribution based on a large microdata set are finally provided.We thank O. Linton and the three referees for constructive criticism and M.P. Feser and J. Litchfield for kindly providing the Brazilian data. We are grateful to I. Gijbels, J.M. Rolin, and I. Van Keilegom for their stimulating remarks and to participants at the workshop on statistical modeling (UCL 2002), LAMES (Sao Paulo 2002), L1 Norm conference (Neuchatel 2002), Geneva econometrics seminar, and KUL econometrics seminar for their comments. Part of this research was done when the second author was visiting THEMA and IRES. The first, resp. second, author gratefully acknowledges financial support from the “Projet d'Actions de Recherche Concertées” grant 98/03-217, and from the IAP research network grant P5/24 of the Belgian state, resp. the Swiss National Science Foundation through the National Centre of Competence in Research: Financial Valuation and Risk Management (NCCR-FINRISK).

This paper develops optimal tests for model selection between two nested models in the presence of underlying parameter instability. These are joint tests for both parameter instability and a null hypothesis on a subset of the parameters. They modify the existing tests for parameter instability to allow the parameter vector to be unknown. These test statistics are useful if one is interested in testing a null hypothesis on some parameters but is worried about the possibility that the parameters may be time varying. The paper provides the asymptotic distributions of this class of test statistics and their critical values for some interesting cases.I thank M. Watson for the idea of this paper and for numerous discussions, suggestions, comments, and teaching. I am grateful to T. Clark, G. Chow, R. Gallant, F. Sowell, N. Swanson, E. Tamer, and A. Tarozzi and also to the co-editor and two referees and to seminar participants at the University of Virginia, ECARES Université Libre de Brussels, the 2001 Triangle Econometrics Conference, the 2002 NBER Summer Institute, the 2003 Summer Meetings of the Econometric Society, and the 2003 EC2 Conference for comments. Financial support from IFS Summer Research, Princeton University, is gratefully acknowledged. All mistakes are mine.

This paper introduces a test for the comparison of multiple misspecified conditional interval models, for the case of dependent observations. Model accuracy is measured using a distributional analog of mean square error, in which the approximation error associated with a given model, say, model i, for a given interval, is measured by the expected squared difference between the conditional confidence interval under model i and the “true” one.

When comparing more than two models, a “benchmark” model is specified, and the test is constructed along the lines of the “reality check” of White (2000, Econometrica 68, 1097–1126). Valid asymptotic critical values are obtained via a version of the block bootstrap that properly captures the effect of parameter estimation error. The results of a small Monte Carlo experiment indicate that the test does not have unreasonable finite sample properties, given small samples of 60 and 120 observations, although the results do suggest that larger samples should likely be used in empirical applications of the test.The authors express their gratitude to Don Andrews and an anonymous referee for providing numerous useful suggestions, all of which we feel have been instrumental in improving earlier drafts of this paper. The authors also thank Russell Davidson, Clive Granger, Lutz Kilian, Christelle Viaroux, and seminar participants at the 2002 UK Econometrics Group meeting in Bristol, the 2002 European Econometric Society meetings, the 2002 University of Pennsylvania NSF-NBER time series conference, the 2002 EC2 Conference in Bologna, Cornell University, the State University of New York at Stony Brook, and the University of California at Davis for many helpful comments and suggestions on previous versions of this paper.

This paper considers estimation and inference in panel vector autoregressions where (i) the individual effects are either random or fixed, (ii) the time-series properties of the model variables are unknown a priori and may feature unit roots and cointegrating relations, and (iii) the time dimension of the panel is short and its cross-sectional dimension is large. Generalized method of moments (GMM) and quasi maximum likelihood (QML) estimators are obtained and compared in terms of their asymptotic and finite-sample properties. It is shown that the asymptotic variances of the GMM estimators that are based on levels in addition to first differences of the model variables depend on the variance of the individual effects, whereas by construction the fixed effects QML estimator is not subject to this problem. Monte Carlo evidence is provided showing that the fixed effects QML estimator tends to outperform the various GMM estimators in finite sample under both normal and nonnormal errors. The paper also shows how the fixed effects QML estimator can be successfully used for unit root and cointegration tests in short panels.We are grateful to Karim Abadir, Stephen Bond, Jinyong Hahn, Marc Nerlove, Ingmar Prucha, and, especially, Manuel Arellano, Peter Schmidt, Peter Phillips (the editor), and four anonymous referees for helpful and constructive comments. We have also benefited from useful suggestions by participants at various seminars and conferences.

When Stephen Perez and I first began our Monte Carlo studies of the efficacy of general-to-specific search methodologies in 1995, we were keenly aware of our limited ability to capture the tacit knowledge of the skilled time-series econometrician operating in the London School of Economics (LSE) tradition (Hoover and Perez, 1999a, 1999b). Econometrics, we believed, was an art, and our algorithm was not intended to replace the artist. David Hendry and Hans-Martin Krolzig's subsequent development of PcGets did not, in fact, eliminate the art of econometrics. Power tools did not eliminate the art of the cabinetmaker but changed where his value added lay and—importantly—made new things possible. PcGets is likewise a new, powerful tool, useful in the hands of a skilled craftsman.I thank Peter Phillips, Selva Demiralp, Stephen Perez, and an anonymous referee for helpful comments on an earlier draft.

A new first-order asymptotic theory for heteroskedasticity-autocorrelation (HAC) robust tests based on nonparametric covariance matrix estimators is developed. The bandwidth of the covariance matrix estimator is modeled as a fixed proportion of the sample size. This leads to a distribution theory for HAC robust tests that explicitly captures the choice of bandwidth and kernel. This contrasts with the traditional asymptotics (where the bandwidth increases more slowly than the sample size) where the asymptotic distributions of HAC robust tests do not depend on the bandwidth or kernel. Finite-sample simulations show that the new approach is more accurate than the traditional asymptotics. The impact of bandwidth and kernel choice on size and power of t-tests is analyzed. Smaller bandwidths lead to tests with higher power but greater size distortions, and large bandwidths lead to tests with lower power but smaller size distortions. Size distortions across bandwidths increase as the serial correlation in the data becomes stronger. Overall, the results clearly indicate that for bandwidth and kernel choice there is a trade-off between size distortions and power. Finite-sample performance using the new asymptotics is comparable to the bootstrap, which suggests that the asymptotic theory in this paper could be useful in understanding the theoretical properties of the bootstrap when applied to HAC robust tests.We thank an editor and a referee for constructive comments on a previous version of the paper. Helpful comments provided by Cliff Hurvich, Andy Levin, Jeff Simonoff, and seminar participants at NYU (Statistics), U. Texas Austin, Yale, U. Montreal, UCSD, UC Riverside, UC Berkeley, U. of Pittsburgh, SUNY Albany, U. Aarhus, Brown U., NBER/NSF Time Series Conference, and 2003 Winter Meetings of the Econometrics Society are gratefully acknowledged. We gratefully acknowledge financial support from the National Science Foundation through grant SES-0095211. We thank the Center for Analytic Economics at Cornell University.

Jan Kmenta is the author of the internationally respected text The Elements of Econometrics [1] and co-editor of several books related to econometric model building. His published research over 40 years relates to many facets of econometric theory and practice, including the estimation of production functions, the evaluation of structural econometric models, and estimation in the face of missing data. This work has appeared in the leading journals of the profession. A 1966 paper [11] is of historical interest for being the second econometric model constructed of the Australian economy. In his work, through both constructive contributions and methodological critique, he has always sought to highlight and advance the evidently close connection between economics and econometrics.

Kmenta was born on January 3, 1928, in Prague, the Czech Republic. He was educated at the Jirasek State Gymnasium in Prague (1939–47) and the Czech University of Technology in Prague (1947–49). At the University of Sydney (1952–55), Australia, he graduated with a Bachelor of Economics degree (First Class Honors). He obtained a Master of Arts degree (1959) and a Doctor of Philosophy degree (1964) from Stanford University with a doctoral dissertation entitled “Australian Postwar Immigration: An Econometric Study.” After teaching stints in Australia, Stanford, and Wisconsin, he taught at Michigan State from 1965 to 1973 and at the University of Michigan from 1973 to 1993. He is currently Professor Emeritus of Economics and Statistics, University of Michigan, and Visiting Professor, CERGE-EI, Charles University, Prague.

His various academic awards and prizes include the Alexander von Humboldt Foundation Award for Senior U.S. Scientists, the Michigan Economic Society Best Professor Award, the Royal Economic Society Lecturer at the University of Leicester, and the Karel Englis Medal of the Academy of Sciences of the Czech Republic. He was awarded an honorary doctorate from the University of Saarland, Germany, and served as associate editor, Journal of the American Statistical Association (1973–1979 and 1985–1992), associate editor, Review of Economics and Statistics (1975–1992), and associate editor, Metrika (1981–1985). Kmenta was listed as 40th among all economists ranked by the total number of citations (Medoff 1989).

This is an edited transcript of two tape-recorded interviews conducted with Professor Kmenta in Sydney on March 12, 2004, as he visited the University of New South Wales to present the seminar Econometrics: A Failed Science? I am indebted to one of Kmenta's former students, Eric Sowey, for suggesting this project and for his enthusiasm and support throughout.

This paper establishes various results involving functions of integrated processes. Two theorems—which improve similar results by Park and Phillips—are proved for averages of functions of an integrated process that has not been rescaled by the square root of sample size. In addition, two results are given that characterize asymptotic behavior of averages of nonintegrable functions of rescaled integrated processes; the observations close to the pole take over asymptotic behavior in that case. Throughout, we make the assumption that the innovations of the integrated process are a linear process.

Conditions ensuring a central limit theorem for strongly mixing triangular arrays are given. Larger samples can show longer range dependence than shorter samples. The result is obtained by constraining the rate growth of dependence as a function of the sample size, with the usual trade-off of memory and moment conditions. An application to heteroskedasticity and autocorrelation consistent estimators is proposed.

We develop general conditions for rates of convergence and convergence in distribution of iterative procedures for estimating finite-dimensional parameters. An asymptotic contraction mapping condition is the centerpiece of the theory. We illustrate some of the results by deriving the limiting distribution of a two-stage iterative estimator of regression parameters in a semiparametric binary response model. Simulation results illustrating the computational benefits of the first-stage iterative estimator are also reported.We thank a co-editor and two referees for comments and criticisms that led to significant improvements in this paper. We also thank Roger Klein for providing us with Gauss code to compute his estimator.

Teaching graduate econometrics means covering three different kinds of subject matter: a grounding in the theory of econometrics, a long laundry list of available econometric techniques, and an introduction to the fact that the practice of linking models and data is every bit as untidy as mathematical statistics is neat. I assign Econometric Theory and Methods (ETM) as a primary text in our first Ph.D. econometrics course. ETM is in charge of getting the students their theoretical grounding. I also assign Greene's excellent Econometric Analysis (2003) for its coverage of a long list of techniques. My laptop, EViews, and I, together with a whole lot of real data, are responsible for being untidy.

We consider the Gaussian ARFIMA(j,d,l) model, with spectral density and an unknown mean . For this class of models, the n−1-normalized information matrix of the full parameter vector, (μ,θ), is asymptotically degenerate. To estimate θ, Dahlhaus (1989, Annals of Statistics 17, 1749–1766) suggested using the maximizer of the plug-in log-likelihood, , where is any n(1−2d)/2-consistent estimator of μ. The resulting estimator is a plug-in maximum likelihood estimator (PMLE). This estimator is asymptotically normal, efficient, and consistent, but in finite samples it has some serious drawbacks. Primarily, none of the Bartlett identities associated with are satisfied for fixed n. Cheung and Diebold (1994, Journal of Econometrics 62, 301–316) conducted a Monte Carlo simulation study and reported that the bias of the PMLE is about 3–4 times the bias of the regular maximum likelihood estimator (MLE). In this paper, we derive asymptotic expansions for the PMLE and show that its second-order bias is contaminated by an additional term, which does not exist in regular cases. This term arises because of the failure of the first Bartlett identity to hold and seems to explain Cheung and Diebold's simulated results. We derive similar expansions for the Whittle MLE, which is another estimator tacitly using the plug-in principle. An application to the ARFIMA(0,d,0) shows that the additional bias terms are considerable.Research on this topic commenced during 2000–2002, while the author was visiting the Cowles Foundation for Research in Economics at Yale University. The author is most grateful to the Cowles Foundation for their generous hospitality and to Donald Andrews and Peter Phillips for numerous helpful comments.

This note discusses the (dis-)similarities between automated inference and computer-aided decisions, at the interface of econometrics and economics. It is argued that computer-aided decisions are best suited for scientific communication. For the future, the topic of learning is singled out as one of the most promising areas of integration of econometric techniques and economics.I thank Peter Phillips and an anonymous referee for useful remarks on a previous version of this comment. The usual disclaimer applies.

We investigate the issue of the uniqueness of the cross-validation selected smoothing parameters in kernel estimation of multivariate nonparametric regression or conditional probability functions. When the covariates are all continuous variables, we provide a necessary and sufficient condition, and when the covariates are a mixture of categorical and continuous variables, we provide a simple sufficient condition that guarantees asymptotically the uniqueness of the cross-validation selected smoothing parameters.We thank a referee for the constructive comments.

In this note we show that, when the true data generating process is a stationary one around a constant term with a break, the stationarity test of Kim (2000, Journal of Econometrics 95, 97–116) against the alternative hypothesis of change of persistence rejects the null of stationarity asymptotically with probability one.I am grateful to an anonymous referee for his useful comments, which have helped to improve the content and presentation of this note. I acknowledge financial support from Ministerio de Ciencia y Tecnología, project SEC2003-09205.

This paper generalizes the intuition of Hausman and Taylor (1981, Econometrica 49, 1377–1398) and develops a method of dealing with a time-invariant regressor in nonlinear panel models with fixed effects. We illustrate the usefulness of our result by discussing the implication for some nonlinear models of social interactions.We are grateful to Dan Ackerberg and Jerry Hausman for helpful comments. The first author gratefully acknowledges financial support from NSF grant SES-0313651.

We give a brief introduction to the vector autoregressive model for cointegrated I(2) variables and show how some plausible economic relations can be formulated in the I(2) framework in such a way that likelihood ratio tests for their validity are asymptotically χ2 distributed.The authors thank Paolo Paruolo for helpful comments and the ESF for financial support in the framework of the EMM network.

Infinite order vector autoregressive (VAR) models have been used in a number of applications ranging from spectral density estimation, impulse response analysis, and tests for cointegration and unit roots, to forecasting. For estimation of such models it is necessary to approximate the infinite order lag structure by finite order VARs. In practice, the order of approximation is often selected by information criteria or by general-to-specific specification tests. Unlike in the finite order VAR case these selection rules are not consistent in the usual sense, and the asymptotic properties of parameter estimates of the infinite order VAR do not follow as easily as in the finite order case. In this paper it is shown that the parameter estimates of the infinite order VAR are asymptotically normal with zero mean when the model is approximated by a finite order VAR with a data dependent lag length. The requirement for the result to hold is that the selected lag length satisfies certain rate conditions with probability tending to one. Two examples of selection rules satisfying these requirements are discussed. Uniform rates of convergence for the parameters of the infinite order VAR are also established.Very helpful comments by the editor and two referees led to a substantial improvement of the manuscript. I am particularly indebted to one of the referees for pointing out an error in the proofs. All remaining errors are my own. Financial support from NSF grant SES−0095132 is gratefully acknowledged.