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.

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.

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.

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.

Model selection (MS) and model averaging (MA) are two popular approaches when many candidate models exist. Theoretically, the estimation risk of an oracle MA is not larger than that of an oracle MS because the former is more flexible, but a foundational issue is this: Does MA offer a substantial improvement over MS? Recently, seminal work by Peng and Yang (2022) has answered this question under nested models with linear orthonormal series expansion. In the current paper, we further respond to this question under linear nested regression models. A more general nested framework, heteroscedastic and autocorrelated random errors, and sparse coefficients are allowed in the current paper, giving a scenario that is more common in practice. A remarkable implication is that MS can be significantly improved by MA under certain conditions. In addition, we further compare MA techniques with different weight sets. Simulation studies illustrate the theoretical findings in a variety of settings.

Recently, Kurisu and Otsu (2022b, Econometric Theory 38(1), 172–193) derived the uniform convergence rates for the nonparametric deconvolution estimators proposed by Li and Vuong (1998, Journal of Multivariate Analysis 65(2), 139–165). This article shows that faster uniform convergence rates can be established for their estimators under the same assumptions. In addition, a new class of deconvolution estimators based on a variant of Kotlarski’s identity is also proposed. It is shown that in some cases, these new estimators can have faster uniform convergence rates than the existing estimators.

This article studies the robustness of quasi-maximum-likelihood estimation in hidden Markov models when the regime-switching structure is misspecified. Specifically, we examine the case where the data-generating process features a hidden Markov regime sequence with covariate-dependent transition probabilities, but estimation proceeds under a simplified mixture model that assumes regimes are independent and identically distributed. We show that the parameters governing the conditional distribution of the observables can still be consistently estimated under this misspecification, provided certain regularity conditions hold. Our results highlight a practical benefit of using computationally simpler mixture models in settings where regime dependence is complex or difficult to model directly.