Spatial autoregressive (SAR) and related models offer flexible yet parsimonious ways to model spatial and network interactions. SAR specifications typically rely on a particular parametric functional form and an exogenous choice of the so-called spatial weight matrix with only limited guidance from theory in making these specifications. Also, the choice of a SAR model over other alternatives, such as spatial Durbin (SD) or spatial lagged X (SLX) models, is often arbitrary, raising issues of potential specification error. To address such issues, this paper develops a new specification test within the SAR framework that can detect general forms of misspecification including that of the spatial weight matrix, the functional form and the model itself. The test is robust to the presence of heteroskedasticity of unknown form in the disturbances and the approach relates to the conditional moment test framework of Bierens ([1982, Journal of Econometrics 20, 105–134], [1990, Econometrica 58, 1443–1458]). The Bierens test is shown to be inconsistent in general against spatial alternatives and the new test introduces modifications to achieve test consistency in the spatial setting. A central element is the infinite-dimensional endogeneity induced by spatial linkages. This complexity is addressed by introducing a new component to the omnibus test that captures the effects of potential spatial matrix misspecification. With this modification, the approach leads to a simple pivotal test procedure with standard critical values that is the first test in the literature to have power against misspecifications in the spatial linkages. We derive the asymptotic distribution of the test under the null hypothesis of correct SAR specification and prove consistency. A Monte Carlo study is conducted to study its finite sample performance. An empirical illustration on the performance of the test in modeling tax competition in Finland is included.

We propose a test for anticipated changes in spot volatility, either due to continuous or discontinuous price moves, at the times of realization of event risk in the form of pre-scheduled releases of economic information such as earnings announcements by firms and macroeconomic news announcements. These events can generate nontrivial volatility in asset returns, which does not scale even locally in time. Our test is based on short-dated options written on an underlying asset subject to event risk, which takes place after the options’ observation time and prior to or after their expiration. We use options with different tenors to estimate the conditional (risk-neutral) characteristic functions of the underlying asset log-returns over the horizons of the options. Using these estimates and a relationship between the conditional characteristic functions with three different tenors, which holds true if and only if continuous and discontinuous spot volatility does not change at the event time, we design a test for this hypothesis. In an empirical application, we study anticipated individual stocks’ volatility changes following earnings announcements for a set of stocks with good option coverage.

Tests based on heteroskedasticity robust standard errors are an important technique in econometric practice. Choosing the right critical value, however, is not simple at all: conventional critical values based on asymptotics often lead to severe size distortions, and so do existing adjustments including the bootstrap. To avoid these issues, we suggest to use smallest size-controlling critical values, the generic existence of which we prove in this article for the commonly used test statistics. Furthermore, sufficient and often also necessary conditions for their existence are given that are easy to check. Granted their existence, these critical values are the canonical choice: larger critical values result in unnecessary power loss, whereas smaller critical values lead to overrejections under the null hypothesis, make spurious discoveries more likely, and thus are invalid. We suggest algorithms to numerically determine the proposed critical values and provide implementations in accompanying software. Finally, we numerically study the behavior of the proposed testing procedures, including their power properties.

In this paper, we develop methods for statistical inferences in a partially identified nonparametric panel data model with endogeneity and interactive fixed effects. Under some normalization rules, we can concentrate out the large-dimensional parameter vector of factor loadings and specify a set of conditional moment restrictions that are involved with only the finite-dimensional factor parameters along with the infinite-dimensional nonparametric component. For a conjectured restriction on the parameter, we consider testing the null hypothesis that the restriction is satisfied by at least one element in the identified set and propose a test statistic based on a novel martingale difference divergence measure for the distance between a conditional expectation object and zero. We derive a tight asymptotic distributional upper bound for the resultant test statistic under the null and show that it is divergent at rate-N under the global alternative. To obtain the critical values for our test, we propose a version of multiplier bootstrap and establish its asymptotic validity. Simulations demonstrate the finite sample properties of our inference procedure. We apply our method to study Engel curves for major nondurable expenditures in China by using a panel dataset from the China Family Panel Studies.

In this paper, we generalize the concept of functional dependence (FD) from time series (see Wu [2005, Proceedings of the National Academy of Sciences 102, 14150–14154]) and stationary random fields (see El Machkouri, Volný, and Wu [2013, Stochastic Processes and Their Applications 123, 1–14]) to nonstationary spatial processes. Within conventional settings in spatial econometrics, we define the concept of spatial FD measure and establish a moment inequality, an exponential inequality, a Nagaev-type inequality, a law of large numbers, and a central limit theorem. We show that the dependent variables generated by some common spatial econometric models, including spatial autoregressive (SAR) models, threshold SAR models, and spatial panel data models, are functionally dependent under regular conditions. Furthermore, we investigate the properties of FD measures under various transformations, which are useful in applications. Moreover, we compare spatial FD with the spatial mixing and spatial near-epoch dependence proposed in Jenish and Prucha ([2009, Journal of Econometrics 150, 86–98], [2012, Journal of Econometrics 170, 178–190]), and we illustrate its advantages.

It is common to assume in empirical research that observables and unobservables are additively separable, especially when the former are endogenous. This is because it is widely recognized that identification and estimation challenges arise when interactions between the two are allowed for. Starting from a nonseparable IV model, where the instrumental variable is independent of unobservables, we develop a novel nonparametric test of separability of unobservables. The large-sample distribution of the test statistics is nonstandard and relies on a Donsker-type central limit theorem for the empirical distribution of nonparametric IV residuals, which may be of independent interest. Using a dataset drawn from the 2015 U.S. Consumer Expenditure Survey, we find that the test rejects the separability in Engel curves for some commodities.

We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of commonly used predictive comparison statistics. Our approach continues to rely on the out of sample mean squared error loss differentials between the two competing models, leads to nuisance parameter-free Gaussian asymptotics, and is shown to remain valid under flexible assumptions that can accommodate heteroskedasticity and the presence of mixed predictors (e.g., stationary and local to unit root). A local power analysis also establishes their ability to detect departures from the null in both stationary and persistent settings. Simulations calibrated to common economic and financial applications indicate that our methods have strong power with good size control across commonly encountered sample sizes.

Since Bai (2009, Econometrica 77, 1229–1279), considerable extensions have been made to panel data models with interactive fixed effects (IFEs). However, little work has been conducted to understand the associated iterative algorithm, which, to the best of our knowledge, is the most commonly adopted approach in this line of research. In this paper, we refine the algorithm of panel data models with IFEs using the nuclear-norm penalization method and duple least-squares (DLS) iterations. Meanwhile, we allow the regression coefficients to be individual-specific and evolve over time. Accordingly, asymptotic properties are established to demonstrate the theoretical validity of the proposed approach. Furthermore, we show that the proposed methodology exhibits good finite-sample performance using simulation and real data examples.

This paper extends the spurious factor analysis of Onatski and Wang (2021, Spurious factor analysis. Econometrica, 89(2), 591–614.) to high-dimensional data with heterogeneous local-to-unit roots. We find a spurious factor phenomenon similar to that observed in the data with unit roots. Namely, the “factors” estimated by the principal components analysis converge to principal eigenfunctions of a weighted average of the covariance kernels of the demeaned Ornstein–Uhlenbeck processes with different decay rates. Thus, such “factors” reflect the structure of the strong temporal correlation of the data and do not correspond to any cross-sectional commonalities, that genuine factors are usually associated with. Furthermore, the principal eigenvalues of the sample covariance matrix are very large relative to the other eigenvalues, creating an illusion of the “factors”capturing much of the data’s common variation. We conjecture that the spurious factor phenomenon holds, more generally, for data obtained from high frequency sampling of heterogeneous continuous time (or spacial) processes, and provide an illustration.

We demonstrate that a large class of discrete choice models of demand can be approximated by real analytic demand models. We obtain this result by combining (i) a novel real analytic property of the mixed logit and the mixed probit models with any distribution of random coefficients and (ii) an approximation property of finite mixtures of Gumbel and Gaussian distributions. To illustrate some of the implications of this result, we discuss how real analyticity facilitates nonparametric and semi-nonparametric identification, extrapolation to hypothetical counterfactuals, numerical implementation of demand inverses, and numerical implementation of the maximum likelihood estimator.

This paper introduces a new class of time-varying vector moving average processes of infinite order. These processes serve dual purposes: (1) they can be used to model time-varying dependence structures, and (2) they can be used to establish asymptotic theories for multivariate time series models. To illustrate these two points, we first establish some fundamental asymptotic properties and use them to infer the trending term of a vector moving average infinity process. We then investigate a class of time-varying VARX models. Finally, we demonstrate the empirical relevance of the theoretical results using extensive simulated and real data studies.

We consider local level and local linear estimators for estimation and inference in time-varying parameter (TVP) regressions with general stationary covariates. The latter estimator also yields estimates for parameter derivatives that are utilized for the development of time invariance tests for the regression coefficients. Our theoretical framework is general enough to allow for a wide range of stationary regressors, including stationary long memory. We demonstrate that neglecting time variation in the regression parameters has a range of adverse effects in inference, in particular, when regressors exhibit long-range dependence. For instance, parametric tests diverge under the null hypothesis when the memory order is strictly positive. The finite sample performance of the methods developed is investigated with the aid of a simulation experiment. The proposed methods are employed for exploring the predictability of SP500 returns by realized variance. We find evidence of time variability in the intercept as well as episodic predictability when realized variance is utilized as a predictor in TVP specifications.

This paper proposes a novel method of algorithmic subsampling (data sketching) for multiway cluster-dependent data. We establish a new uniform weak law of large numbers and a new central limit theorem for multiway algorithmic subsample means. We show that algorithmic subsampling allows for robustness against potential degeneracy, and even non-Gaussian degeneracy, of the asymptotic distribution under multiway clustering at the cost of efficiency and power loss due to algorithmic subsampling. Simulation studies support this novel result, and demonstrate that inference with algorithmic subsampling entails more accuracy than that without algorithmic subsampling. We derive the consistency and the asymptotic normality for multiway algorithmic subsampling generalized method of moments estimator and for multiway algorithmic subsampling M-estimator. We illustrate with an application to scanner data for the analysis of differentiated products markets.

This paper proposes a subsampling inference method for extreme conditional quantiles based on a self-normalized version of a local estimator for conditional quantiles, such as the local linear quantile regression estimator. The proposed method circumvents difficulty of estimating nuisance parameters in the limiting distribution of the local estimator. A simulation study and empirical example illustrate usefulness of our subsampling inference to investigate extremal phenomena.

Extreme propensity scores arise in observational studies when treated and control units have very different characteristics. This is commonly referred to as limited overlap. In this paper, we propose a formal statistical test that helps assess the degree of limited overlap. Rejecting the null hypothesis in our test indicates either no or very mild degree of limited overlap and hence reassures that standard treatment effect estimators will be well behaved. One distinguishing feature of our test is that it only requires the use of a few extreme propensity scores, which is in stark contrast to other methods that require consistent estimates of some tail index. Without the need to extrapolate using observations far away from the tail, our procedure is expected to exhibit excellent size properties, a result that is also borne out in our simulation study.

This paper presents an asymptotic theory for recurrent jump diffusion models with well-defined scale functions. The class of such models is broad, including general nonstationary as well as stationary jump diffusions with state-dependent jump sizes and intensities. The asymptotics for recurrent jump diffusion models with scale functions are largely comparable to the asymptotics for the corresponding diffusion models without jumps. For stationary jump diffusions, our asymptotics yield the usual law of large numbers and the standard central limit theory with normal limit distributions. The asymptotics for nonstationary jump diffusions, on the other hand, are nonstandard and the limit distributions are given as generalized diffusion processes.

This paper considers semiparametric sieve estimation in high-dimensional single index models. The use of Hermite polynomials in approximating the unknown link function provides a convenient framework to conduct both estimation and variable selection. The estimation of the index parameter is formulated from solutions obtained by the routine penalized weighted linear regression procedure, where the weights are used in order to tackle the unbounded support of the regressors. The resulting index parameter estimator is shown to be consistent and sparse, and the asymptotic normality for the estimators of both the index parameter and the link function is established. To perform variable selection in the ultra-high dimension case, we further suggest a forward regression screening method, which is shown to enjoy the sure independence screening property. This screening procedure can be used before the penalized variable selection to reduce the burden of dimensionality. Numerical results show that both the variable selection procedures and the associated estimators perform well in finite samples.

This paper provides nonparametric specification tests for the commonly used homogeneous and stable coefficients structures in panel data models. We first obtain the augmented residuals by estimating the model under the null hypothesis and then run auxiliary time series regressions of augmented residuals on covariates with time-varying coefficients (TVCs) via sieve methods. The test statistic is then constructed by averaging the squared fitted values, which are close to zero under the null and deviate from zero under the alternatives. We show that the test statistic, after being appropriately standardized, is asymptotically normal under the null and under a sequence of Pitman local alternatives. A bootstrap procedure is proposed to improve the finite sample performance of our test. In addition, we extend the procedure to test other structures, such as the homogeneity of TVCs or the stability of heterogeneous coefficients. The joint test is extended to panel models with two-way fixed effects. Monte Carlo simulations indicate that our tests perform reasonably well in finite samples. We apply the tests to re-examine the environmental Kuznets curve in the United States, and find that the model with homogenous TVCs is more appropriate for this application.

Systemic risk measures have been shown to be predictive of financial crises and declines in real activity. Thus, forecasting them is of major importance in finance and economics. In this paper, we propose a new forecasting method for systemic risk as measured by the marginal expected shortfall (MES). It is based on first de-volatilizing the observations and, then, calculating systemic risk for the residuals using an estimator based on extreme value theory. We show the validity of the method by establishing the asymptotic normality of the MES forecasts. The good finite-sample coverage of the implied MES forecast intervals is confirmed in simulations. An empirical application to major U.S. banks illustrates the significant time variation in the precision of MES forecasts, and explores the implications of this fact from a regulatory perspective.