We introduce a new test for a two-sided hypothesis involving a subset of the structural parameter vector in the linear instrumental variables (IVs) model. Guggenberger, Kleibergen, and Mavroeidis (2019, Quantitative Economics, 10, 487–526; hereafter GKM19) introduce a subvector Anderson–Rubin (AR) test with data-dependent critical values that has asymptotic size equal to nominal size for a parameter space that allows for arbitrary strength or weakness of the IVs and has uniformly nonsmaller power than the projected AR test studied in Guggenberger et al. (2012, Econometrica, 80(6), 2649–2666). However, GKM19 imposes the restrictive assumption of conditional homoskedasticity (CHOM). The main contribution here is to robustify the procedure in GKM19 to arbitrary forms of conditional heteroskedasticity. We first adapt the method in GKM19 to a setup where a certain covariance matrix has an approximate Kronecker product (AKP) structure which nests CHOM. The new test equals this adaptation when the data are consistent with AKP structure as decided by a model selection procedure. Otherwise, the test equals the AR/AR test in Andrews (2017, Identification-Robust Subvector Inference, Cowles Foundation Discussion Papers 3005, Yale University) that is fully robust to conditional heteroskedasticity but less powerful than the adapted method. We show theoretically that the new test has asymptotic size bounded by the nominal size and document improved power relative to the AR/AR test in a wide array of Monte Carlo simulations when the covariance matrix is not too far from AKP.

This paper proposes a robust moment selection method aiming to pick the best model even if this is a moment condition model with mixed identification strength, that is, moment conditions including moment functions that are local to zero uniformly over the parameter set. We show that the relevant moment selection procedure of Hall et al. (2007, Journal of Econometrics 138, 488–512) is inconsistent in this setting as it does not explicitly account for the rate of convergence of parameter estimation of the candidate models which may vary. We introduce a new moment selection procedure based on a criterion that automatically accounts for both the convergence rate of the candidate model’s parameter estimate and the entropy of the estimator’s asymptotic distribution. The benchmark estimator that we consider is the two-step efficient generalized method of moments estimator, which is known to be efficient in this framework as well. A family of penalization functions is introduced that guarantees the consistency of the selection procedure. The finite-sample performance of the proposed method is assessed through Monte Carlo simulations.

This paper studies control function (CF) approaches in endogenous threshold regression where the threshold variable is allowed to be endogenous. We first use a simple example to show that the structural threshold regression (STR) estimator of the threshold point in Kourtellos, Stengos and Tan (2016, Econometric Theory 32, 827–860) is inconsistent unless the endogeneity level of the threshold variable is low compared to the threshold effect. We correct the CF in the STR estimator to generate our first CF estimator using a method that extends the two-stage least squares procedure in Caner and Hansen (2004, Econometric Theory 20, 813–843). We develop our second CF estimator which can be treated as an extension of the classical CF approach in endogenous linear regression. Both these approaches embody threshold effect information in the conditional variance beyond that in the conditional mean. Given the threshold point estimates, we propose new estimates for the slope parameters. The first is a by-product of the CF approach, and the second type employs generalized method of moment (GMM) procedures based on two new sets of moment conditions. Simulation studies, in conjunction with the limit theory, show that our second CF estimator and confidence interval for the threshold point together with the associated second GMM estimator and confidence interval for the slope parameter dominate the other methods. We further apply the new estimation methodology to an empirical application from international trade to illustrate its usefulness in practice.

This paper studies the non-Gaussian pseudo maximum likelihood (PML) estimation of a spatial autoregressive (SAR) model with SAR disturbances. If the spatial weights matrix $M_{n}$ for the SAR disturbances is normalized to have row sums equal to 1 or the model reduces to a SAR model with no SAR process of disturbances, the non-Gaussian PML estimator (NGPMLE) for model parameters except the intercept term and the variance $\sigma _{0}^{2}$ of independent and identically distributed (i.i.d.) innovations in the model is consistent. Without row normalization of $M_{n}$, the symmetry of i.i.d. innovations leads to consistent NGPMLE for model parameters except $\sigma _{0}^{2}$. With neither row normalization of $M_{n}$ nor the symmetry of innovations, a location parameter can be added to the non-Gaussian pseudo likelihood function to achieve consistent estimation of model parameters except $\sigma _{0}^{2}$. The NGPMLE with no added parameter can have a significant efficiency improvement upon the Gaussian PML estimator and the generalized method of moments estimator based on linear and quadratic moments. We also propose a non-Gaussian score test for spatial dependence, which can be locally more powerful than the Gaussian score test. Monte Carlo results show that our NGPMLE with no added parameter and the score test based on it perform well in finite samples.

We study large sample properties of likelihood ratio tests of the unit-root hypothesis in an autoregressive model of arbitrary order. Earlier research on this testing problem has developed likelihood ratio tests in the autoregressive model of order 1, but resorted to a plug-in approach when dealing with higher-order models. In contrast, we consider the full model and derive the relevant large sample properties of likelihood ratio tests under a local-to-unity asymptotic framework. As in the simpler model, we show that the full likelihood ratio tests are nearly efficient, in the sense that their asymptotic local power functions are virtually indistinguishable from the Gaussian power envelopes. Extensions to sieve-type approximations and different classes of alternatives are also considered.

This paper considers testing for unit roots in Gaussian panels with cross-sectional dependence generated by common factors. Within our setup, we can analyze restricted versions of the two prevalent approaches in the literature, that of Moon and Perron (2004, Journal of Econometrics 122, 81–126), who specify a factor model for the innovations, and the PANIC setup proposed in Bai and Ng (2004, Econometrica 72, 1127–1177), who test common factors and idiosyncratic deviations separately for unit roots. We show that both frameworks lead to locally asymptotically normal experiments with the same central sequence and Fisher information. Using Le Cam’s theory of statistical experiments, we obtain the local asymptotic power envelope for unit-root tests. We show that the popular Moon and Perron (2004, Journal of Econometrics 122, 81–126) and Bai and Ng (2010, Econometric Theory 26, 1088–1114) tests only attain the power envelope in case there is no heterogeneity in the long-run variance of the idiosyncratic components. We develop a new test which is asymptotically uniformly most powerful irrespective of possible heterogeneity in the long-run variance of the idiosyncratic components. Monte Carlo simulations corroborate our asymptotic results and document significant gains in finite-sample power if the variances of the idiosyncratic shocks differ substantially among the cross-sectional units.