The exact likelihood function for a prototypal job search model is analyzed. The optimality condition implied by the dynamic programming framework is fully imposed. Using the optimality condition allows identification of an offer arrival probability separately from an offer acceptance probability. The estimation problem is nonstandard. The geometry of the likelihood function in finite samples is considered, along with asymptotic properties of the maximum likelihood estimator.

In this paper, we examine the performance of the predictive risk of the Steinrule (SR) and positive-part Stein-rule (PSR) estimators when relevant regressors are omitted in the specified model. The exact formula of the predictive risk of the PSR estimator is derived, and the sufficient condition for the PSR estimator to dominate the SR estimator under a specification error is given. It is shown by numerical computation that the PSR estimator seems to be the best choice among the OLS, SR, and PSR estimators even when there are omitted variables.

For long memory time series models with uncorrelated but dependent errors, we establish the asymptotic normality of the Whittle estimator under mild conditions. Our framework includes the widely used fractional autoregressive integrated moving average models with generalized autoregressive conditional heteroskedastic-type innovations. To cover nonstationary fractionally integrated processes, we extend the idea of Abadir, Distaso, and Giraitis (2007, Journal of Econometrics 141, 1353–1384) and develop the nonstationarity-extended Whittle estimation. The resulting estimator is shown to be asymptotically normal and is more efficient than the tapered Whittle estimator. Finally, the results from a small simulation study are presented to corroborate our theoretical findings.

We consider the problem of estimating a nonparametric regression model containing categorical regressors only. We investigate the theoretical properties of least squares cross-validated smoothing parameter selection, establish the rate of convergence (to zero) of the smoothing parameters for relevant regressors, and show that there is a high probability that the smoothing parameters for irrelevant regressors converge to their upper bound values, thereby automatically smoothing out the irrelevant regressors. A small-scale simulation study shows that the proposed cross-validation-based estimator performs well in finite-sample settings.

Procedures for computing the full information maximum likelihood (FIML) estimates of the parameters of a system of simultaneous regression equations have been described by Koopmans, Rubin, and Leipnik, Chernoff and Divinsky, Brown, and Eisenpress. However, all of these methods are rather complicated since they are based on estimating equations that are expressed in an inconvenient form. In this paper, a transformation of the maximum likelihood (ML) equations is developed which not only leads to simpler computations but which also simplifies the study of the properties of the estimates. The equations are obtained in a form which is capable of solution by a modified Newton-Raphson iterative procedure. The form obtained also shows up very clearly the relation between the maximum likelihood estimates and those obtained by the three-stage least squares method of Zellner and Theil.

We investigate the convergence in distribution of integrals of stochastic processes satisfying a functional limit theorem. We allow a large class of continuous Gaussian processes in the limit. Depending on the continuity properties of the underlying process, local Lebesgue or Riemann integrability is required.We are grateful to the referees and Benedikt Pötscher for their helpful and constructive comments. The research of the first author was partially supported by OTKA grants T37668 and T43037 and NSF-OTKA grant INT-0223262. The research of the second author was partially supported by NATO grant PST.EAP.CLG 980599 and NSF-OTKA grant INT-0223262.

In this paper we propose a bootstrap version of the Wald test for cointegration in a single-equation conditional error correction model. The multivariate sieve bootstrap is used to deal with dependence in the series. We show that the introduced bootstrap test is asymptotically valid. We also analyze the small sample properties of our test by simulation and compare it with the asymptotic test and several alternative bootstrap tests. The bootstrap test offers significant improvements in terms of size properties over the asymptotic test, while having similar power properties. The sensitivity of the bootstrap test to the allowance for deterministic components is also investigated. Simulation results show that the tests with sufficient deterministic components included are insensitive to the true value of the trends in the model and retain correct size.

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter to ensure that the corresponding counting process N(t) satisfies Var N(t) ~ Ct2d+1 (C > 0) as t → ∞, with the same memory parameter that was assumed for the durations. Thus, these conditions ensure that the memory parameter in durations propagates to the same memory parameter in the counts. We then show that any autoregressive conditional duration ACD(1,1) model with a sufficient number of finite moments yields short memory in counts, whereas any long memory stochastic duration model with d > 0 and all finite moments yields long memory in counts, with the same d. Finally, we provide some results about the propagation of long memory to the empirically relevant case of realized variance estimates affected by market microstructure noise contamination.

We establish asymptotic normality of weighted sums of linear processes with general triangular array weights and when the innovations in the linear process are martingale differences. The results are obtained under minimal conditions on the weights and innovations. We also obtain weak convergence of weighted partial sum processes. The results are applicable to linear processes that have short or long memory or exhibit seasonal long memory behavior. In particular, they are applicable to GARCH and ARCH(∞) models and to their squares. They are also useful in deriving asymptotic normality of kernel-type estimators of a nonparametric regression function with short or long memory moving average errors.

Considering the contribution of the Cowles research institute to the development of econometrics, one has little choice in this address and must mainly focus attention on one major achievement, namely, the building of the simultaneous equation methodology. One does not need to demonstrate the indisputable fact that this methodology was conceived and elaborated at the Cowles Commission in the forties. Neither does one need to insist on the long standing significance of this achievement nor on its central place in any education or reflection concerning statistical inference about economic phenomena. More interesting is the question of how research at Cowles during the first 15 years of its existence led to this result and how further econometric research here during the last 30 years relates to the simultaneous equation achievement. Also relevant is the following question: how does the message that was sent out by the Cowles people to the world in 1950 stand today? Should it be replaced by another different one? Or should it simply be somewhat amended and supplemented?

To do full justice to the research work and achievements of the many econometricians that were associated with Cowles through the years would require a much longer paper than the present one. But one must at least try also to summarize here those main concerns that stood outside the simultaneous equation methodology.

Recent literature shows that embedding fractionally integrated time series models with spectral poles at the long-run and/or seasonal frequencies in autoregressive frameworks leads to estimators and test statistics with nonstandard limiting distributions. However, we demonstrate that when embedding such models in a general I(d) framework the resulting estimators and tests regain desirable properties from standard statistical analysis. We show the existence of a local time domain maximum likelihood estimator and its asymptotic normality—and under Gaussianity asymptotic efficiency. The Wald, likelihood ratio, and Lagrange multiplier tests are asymptotically equivalent and chi-squared distributed under local alternatives. With independent and identically distributed Gaussian errors and a scalar parameter, we show that the tests in addition achieve the asymptotic Gaussian power envelope of all invariant unbiased tests; i.e., they are asymptotically uniformly most powerful invariant unbiased against local alternatives. In a Monte Carlo study we document the finite sample superiority of the likelihood ratio test.I am grateful to Bent Jesper Christensen, Niels Haldrup, Pentti Saikkonen (the co-editor), and two anonymous referees for many useful comments and suggestions that significantly improved this paper. This work was done while the author was at the University of Aarhus, Denmark.

We derive exact finite-sample expressions for the biases and risks of several common pretest estimators of the scale parameter in the linear regression model. These estimators are associated with least squares, maximum likelihood and minimum mean squared error component estimators. Of these three criteria, the last is found to be superior (in terms of risk under quadratic loss) when pretesting in typical situations.

We consider quadratic forms of martingale differences and establish a central limit theorem under mild and easily verifiable conditions. By approximating Fourier transforms of stationary processes by martingales, our central limit theorem is applied to the smoothed periodogram estimate of spectral density functions. Our results go beyond earlier ones by allowing a variety of nonlinear time series and by avoiding strong mixing and/or summability conditions on joint cumulants.We thank the two reviewers for their detailed comments, which led to substantial improvements. The work is supported in part by NSF grant DMS-0478704.

We investigate the finite-sample bias of the quasi-maximum likelihood estimator (QMLE) in spatial autoregressive models with possible exogenous regressors. We derive the approximate bias result of the QMLE in terms of model parameters and also the moments (up to order 4) of the error distribution, and thus a feasible bias-correction procedure is directly applicable. In some special cases, the analytical bias result can be significantly simplified. Our Monte Carlo results demonstrate that the feasible bias-correction procedure works remarkably well.

This paper determines the properties of standard generalized method of moments (GMM) estimators, tests, and confidence sets (CSs) in moment condition models in which some parameters are unidentified or weakly identified in part of the parameter space. The asymptotic distributions of GMM estimators are established under a full range of drifting sequences of true parameters and distributions. The asymptotic sizes (in a uniform sense) of standard GMM tests and CSs are established.

The paper also establishes the correct asymptotic sizes of “robust” GMM-based Wald, t, and quasi-likelihood ratio tests and CSs whose critical values are designed to yield robustness to identification problems.

The results of the paper are applied to a nonlinear regression model with endogeneity and a probit model with endogeneity and possibly weak instrumental variables.

Following the approach proposed by Gregoir and Laroque (1993, Econometric Theory 9, 329–342), we consider a class of multivariate processes that, when differenced enough, yields covariance stationary processes whose determinant of the matrix series associated with their Wold representation has various unit roots with various orders of multiplicity we restrict to be integers. A representation theorem is provided that involves different polynomial error correction terms at each frequency associated with each unit root. An identification criterion for each set of error correction terms is proposed.

In this paper, I derive the efficiency bound of the structural parameter in a linear simultaneous equations model with many instruments. The bound is derived by applying a convolution theorem to Bekker's (1994, Econometrica 62, 657–681) asymptotic approximation, where the number of instruments grows to infinity at the same rate as the sample size. Usual instrumental variables estimators with a small number of instruments are heuristically argued to be efficient estimators in the sense that their asymptotic distribution is minimal. Bayesian estimators based on parameter orthogonalization are heuristically argued to be inefficient.

We discuss the limiting behavior of the serial correlation coefficient in mildly explosive autoregression, where the error sequence is in the domain of attraction of an α-stable law, α ∈ (0,2]. Therein, the autoregressive coefficient ρ = ρn > 1 is assumed to satisfy the condition ρn → 1 such that n(ρn − 1) → ∞ as n → ∞. In contrast to the vast majority of existing literature in the area, no specific form of ρ is required. We show that the serial correlation coefficient converges in distribution to a ratio of two independent stable random variables.The authors thank P.C.B. Phillips and two anonymous referees for a very careful reading of the manuscript, pointing out several mistakes, and providing shorter and simpler proofs. This research was partially supported by NATO grant PST.EAP.CLG 980599 and NSF-OTKA grant INT-0223262. This work was done while the first author was at the University of Utah.

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.