Microeconomic theory often yields models with multiple nonlinear equations, nonseparable unobservables, nonlinear cross equation restrictions, and many potentially multicolinear covariates. We show how statistical dimension reduction techniques can be applied in models with these features. In particular, we consider estimation of derivatives of average structural functions in large consumer demand systems, which depend nonlinearly on the prices of many goods. Utility maximization imposes nonlinear cross equation constraints including Slutsky symmetry, and preference heterogeneity yields demand functions that are nonseparable in unobservables. The standard method of achieving dimension reduction in demand systems is to impose strong, empirically questionable economic restrictions such as separability. In contrast, the validity of statistical methods of dimension-reduction such as principal components has not hitherto been studied in contexts like these. We derive the restrictions implied by utility maximization on dimension-reduced demand systems and characterize the implications for identification and estimation of structural marginal effects. We illustrate the results by reporting estimates of the effects of gasoline prices on the demands for many goods, without imposing any economic separability assumptions.

This note re-investigates the smooth tests for the equality of distributions introduced by Bera et al. (2013, Econometric Theory 29, 419–446) and provides a modified smooth test which works for the general case with two sample sizes m and n. Asymptotic properties of the proposed test statistic under both the null and the alternative hypothesis are studied.

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).

We examine the identifiability of a nonlinear state space system under general assumptions. The discrete time evolution of the state is generated by a recurrent Elman network. For a large set of Elman networks we determine the class of observationally equivalent minimal systems, i.e., minimal systems that exhibit the same input-output behavior.The authors are grateful for discussions with M. Deistler and D. Bauer. A.A. Al-Falou was funded by the ERNSI network within the European Union program Training and Mobility of Researchers (TMR). D. Trummer was funded by the FWF (Austrian Science Fund). We thank an anonymous referee for helpful comments and suggestions.

We examine a test for weak stationarity against alternatives that covers both local-stationarity and break point models. A key feature of the test is that its asymptotic distribution is a functional of the standard Brownian bridge sheet in [0,1]2, so that it does not depend on any unknown quantity. The test has nontrivial power against local alternatives converging to the null hypothesis at a T−1/2 rate, where T is the sample size. We also examine an easy-to-implement bootstrap analogue and present the finite sample performance in a Monte Carlo experiment. Finally, we implement the methodology to assess the stability of inflation dynamics in the United States and on a set of neuroscience tremor data.

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.

Conditional value-at-risk (CVaR) and conditional expected shortfall (CES) are widely adopted risk measures which help monitor potential tail risk while adapting to evolving market information. In this paper, we propose an approach to constructing simultaneous confidence bands (SCBs) for tail risk as measured by CVaR and CES, with the confidence bands uniformly valid for a set of tail levels. We consider one-sided tail risk (downside or upside tail risk) as well as relative tail risk (the ratio of upside to downside tail risk). A general class of location-scale models with heavy-tailed innovations is employed to filter out the return dynamics. Then, CVaR and CES are estimated with the aid of extreme value theory. In the asymptotic theory, we consider two scenarios: (i) the extreme scenario that allows for extrapolation beyond the range of the available data and (ii) the intermediate scenario that works exclusively in the case where the available data are adequate relative to the tail level. For finite-sample implementation, we propose a novel bootstrap procedure to circumvent the slow convergence rates of the SCBs as well as infeasibility of approximating the limiting distributions. A series of Monte Carlo simulations confirm that our approach works well in finite samples.

The literature on regression kink designs develops identification results for average effects of continuous treatments (Nielsen et al., 2010, American Economic Journal: Economic Policy 2, 185–215; Card et al., 2015, Econometrica 83, 2453–2483), average effects of binary treatments (Dong, 2018, Jump or Kink? Identifying Education Effects by Regression Discontinuity Design without the Discontinuity), and quantile-wise effects of continuous treatments (Chiang and Sasaki, 2019, Journal of Econometrics 210, 405–433), but there has been no identification result for quantile-wise effects of binary treatments to date. In this article, we fill this void in the literature by providing an identification of quantile treatment effects in regression kink designs with binary treatment variables. For completeness, we also develop large sample theories for statistical inference, present a practical guideline on estimation and inference, conduct simulation studies, and provide an empirical illustration.

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.

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.

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.