Despite an abundance of semiparametric estimators of the transformation model, no procedure has been proposed yet to test the hypothesis that the transformation function belongs to a finite-dimensional parametric family against a nonparametric alternative. In this article, we introduce a bootstrap test based on integrated squared distance between a nonparametric estimator and a parametric null. As a special case, our procedure can be used to test the parametric specification of the integrated baseline hazard in a semiparametric mixed proportional hazard model. We investigate the finite sample performance of our test in a Monte Carlo study. Finally, we apply the proposed test to Kennan’s strike durations data.

Functional linear regression has gained popularity as a statistical tool for studying the relationship between function-valued variables. However, in practice, it is hard to expect that the explanatory variables of interest are strictly exogenous, due to, for example, the presence of omitted variables and measurement error. This issue of endogeneity remains insufficiently explored, in spite of its empirical importance. To fill this gap, this article proposes new consistent FPCA-based instrumental variable estimators and develops their asymptotic properties in detail. Simulation experiments under a wide range of settings show that the proposed estimators perform considerably well. We apply our methodology to estimate the impact of immigration on native labor market outcomes in the US.

Diffusion over a network refers to the phenomenon of a change of state of a cross-sectional unit in one period leading to a change of state of its neighbors in the network in the next period. One may estimate or test for diffusion by estimating a cross-sectionally aggregated correlation between neighbors over time from data. However, the estimated diffusion can be misleading if the diffusion is confounded by omitted covariates. This paper focuses on the measure of diffusion proposed by He and Song (2022, Preprint, arXiv:1812.04195v4 [stat.ME]), provides a method of decomposition analysis to measure the role of the covariates on the estimated diffusion, and develops an asymptotic inference procedure for the decomposition analysis in such a situation. This paper also presents results from a Monte Carlo study on the small sample performance of the inference procedure.

This paper studies large N and large T conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the interactive fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of) interactive fixed effects. It also allows the number of covariates to grow slowly with N and T. We derive an error bound on the estimator that holds uniformly in the quantile level. The order of the bound implies uniform consistency of the estimator and is nearly optimal for the low-rank component. Given the error bound, we also propose a consistent estimator of the number of interactive fixed effects at any quantile level. We demonstrate the performance of the estimator via Monte Carlo simulations.

This paper shows that if the errors in a multiple regression model are heavy-tailed, the ordinary least squares (OLS) estimators for the regression coefficients are tail-dependent. The tail dependence arises, because the OLS estimators are stochastic linear combinations of heavy-tailed random variables. Moreover, tail dependence also exists between the fitted sum of squares (FSS) and the residual sum of squares (RSS), because they are stochastic quadratic combinations of heavy-tailed random variables.

Only in the last few years has the history of econometrics become established as an accepted field of research, with its own doctoral students and sessions at professional meetings. Yet, the first written histories of econometrics appeared as far back as the 1950s, when Carl Christ [4] reviewed the first 20 years' econometric work of the Cowles Commission and George Stigler [37] surveyed the early econometric analyses of consumer demand. Contributions in the intervening years have been sparse, with historical accounts such as Stigler [38], Humphrey [23], and Cargill [3] providing helpful landmarks, and additional insights coming from papers such as Gold-berger [16] and Griliches [17]. Now we have a new monograph on the history of the Cowles Commission by Hildreth [22], a number of journal articles, and Roy Epstein's 1987 book, A History of Econometrics, as further contributions to this small but rapidly expanding field.

We consider the Breitung (2002, Journal of Econometrics 108, 343–363) statistic ξn, which provides a nonparametric test of the I(1) hypothesis. If ξ denotes the limit in distribution of ξn as n → ∞, we prove (Theorem 1) that 0 ≤ ξ ≤ 1/π2, a result that holds under any assumption on the underlying random variables. The result is a special case of a more general result (Theorem 3), which we prove using the so-called cotangent method associated with Cauchy's residue theorem.

It is undoubtedly desirable that econometric models capture the dynamic behavior, like trends and cycles, observed in many economic processes. Building models with such capabilities has been an important objective in the continuous time econometrics literature, for instance, the cyclical growth models of Bergstrom (1966); the economy-wide macroeconometric models of, for example, Bergstrom and Wymer (1976); unobserved stochastic trends of Harvey and Stock (1988 and 1993) and Bergstrom (1997); and differential-difference equations of Chambers and McGarry (2002). This paper considers continuous time cyclical trends, which complement the trend-plus-cycle models in the unobserved components literature but could also be incorporated into Bergstrom type systems of differential equations, as were stochastic trends in Bergstrom (1997).

Karanasos (1998) presented a new method for computing the theoretical autocovariance function (acf) of the following univariate autoregressive moving average (ARMA) model:

Φ(L)yt = Θ(L)εt

where

Φ(L) = 1 − φ1L − … − φpLp, Θ(L) = 1 − θ1L − … − θqLq

The Econometric Society Australasian Meeting in 1997 was hosted by the economics department at the University of Melbourne on July 2 to 4 with Peter Bardsley (economics) and Vance L. Martin (econometrics) as cochairpersons. Special features consisted of a star-studded lineup of invited speakers, the inaugural E.J. Hannan lecture, a range of special seminars in economic theory and econometric theory, and a number of nonacademic but spirited special events that took place both during and after the conference.

In this article, we consider binary response models with linear quantile restrictions. Considerably generalizing previous research on this topic, our analysis focuses on an infinite collection of quantile estimators. We derive a uniform linearization for the properly standardized empirical quantile process and discover some surprising differences with the setting of continuously observed responses. Moreover, we show that considering quantile processes provides an effective way of estimating binary choice probabilities without restrictive assumptions on the form of the link function, heteroskedasticity, or the need for high dimensional nonparametric smoothing necessary for approaches available so far. A uniform linear representation and results on asymptotic normality are provided, and the connection to rearrangements is discussed.

This paper considers a generalized panel data transformation model with fixed effects where the structural function is assumed to be additive. In our model, no parametric assumptions are imposed on the transformation function, the structural function, or the distribution of the idiosyncratic error term. The model is widely applicable and includes many popular panel data models as special cases. We propose a kernel-based nonparametric estimator for the structural function. The estimator has a closed-form solution and is easy to implement. We study the asymptotic properties of our estimator and show that it is asymptotically normally distributed. The Monte Carlo simulations demonstrate that our new estimator performs well in finite samples.

In many important textbooks the formal statement of the spectral representation theorem is followed by a process version, usually informal, stating that any stationary stochastic process {ξ(t), t ∈ T} is the limit in quadratic mean of a sequence of processes {S(n,t), t ∈ T}, each consisting of a finite sum of harmonic oscillations with stochastic weights. The natural issues, whether the approximation error ξ(t) − S(n,t) is stationary or whether at least it converges to zero uniformly in t, have not been explicitly addressed in the literature. The paper shows that in all relevant cases, for T unbounded the process convergence is not uniform in t (so that ξ(t) − S(n,t) is not stationary). Equivalently, when T is unbounded the number of harmonic oscillations necessary to approximate ξ(t) with a preassigned accuracy depends on t. The conclusion is that the process version of the spectral representation theorem should explicitly mention that in general the approximation of ξ(t) by a finite sum of harmonic oscillations, given the accuracy, is valid for t belonging to a bounded subset of the real axis (of the set of integers in the discrete-parameter case).The author is grateful for very useful suggestions to Francesco Battaglia, Gianluca Cubadda, Domenico Marinucci, Enzo Orsingher, Dag Tjøstheim, and Umberto Triacca and also to an anonymous referee and the Econometric Theory co-editor Benedikt M. Pötscher.

This paper derives the limit distribution of the rescaled sum of the reciprocal of the positive part of a random walk with continuously distributed innovations, and of the rescaled sum of the reciprocal of the absolute value of a random walk with continuously distributed innovations. It also considers this statistic for the case of a simple random walk, and shows that the limit distribution is different for this case.

It is a challenging task to review the research carried out by Professor Sargan which has covered such a broad range of areas and which offers general and unifying approaches to tackling problems and to obtaining results.I can only apologize for my audacity in accepting to deliver this laudatio. In order to remedy the limitation of my resources, I have benefited from Manuel Arellano's help and I have used the papers by David Hendry and Ken Wallis (1984), Peter Phillips (1985), and Esfandiar Maasoumi (1988a, 1988b). These papers review and summarize the works of the common master, who is considered to be one of the major contributors to Econometrics; in the words of Professor T.W. Anderson: “one of the most distinguished econometricians of our generation.” I am grateful to Peter Phillips and Grayham Mizon for their comments in preparing the English version of this laudatio.