A Linear Estimator for Factor-Augmented Fixed-T Panels with Endogenous Regressors

Supplementary Materials: The supplementary appendix to this article provides additional results about the method developed in the present article. In particular, Section S1 analyses several extensions of the model analyzed in the main text, including unbalanced panels, observed factors, and consistency of the GMM estimator under an alternative set of assumptions, in which the factor loadings are treated as a sequence of constants. Section S2 provides descriptive statistics for the data used in the empirical illustration. Section S3 reports additional Monte Carlo results. Finally, Section S4 provides proofs of the main theoretical results put forward in the article. The supplemental materials are available online at: https://ndownloader.figstatic.com/files/22658501 .Copyright © 2020 The Authors.. A novel method-of-moments approach is proposed for the estimation of factor-augmented panel data models with endogenous regressors when T is fixed. The underlying methodology involves approximating the unobserved common factors using observed factor proxies. The resulting moment conditions are linear in the parameters. The proposed approach addresses several issues which arise with existing nonlinear estimators that are available in fixed T panels, such as local minima-related problems, a sensitivity to particular normalization schemes, and a potential lack of global identification. We apply our approach to a large panel of households and estimate the price elasticity of urban water demand. A simulation study confirms that our approach performs well in finite samples.NWO VENI grant number 451-17-002; Australian Research Council, under research grant number DP-170103135

New results on asymptotic properties of likelihood estimators with persistent data for small and large T

Data Availability Statement: Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.Copyright © The Author(s) 2023. This paper revisits the panel autoregressive model, with a primary emphasis on the unit-root case. We study a class of misspecified Random effects Maximum Likelihood (mRML) estimators when T is either fixed or large, and N tends to infinity. We show that in the unit-root case, for any fixed value of T, the log-likelihood function of the mRML estimator has a single mode at unity as N→ ∞ . Furthermore, the Hessian matrix of the corresponding log-likelihood function is non-singular, unless the scaled variance of the initial condition is exactly zero. As a result, mRML is consistent and asymptotically normally distributed as N tends to infinity. In the large-T setup, it is shown that mRML is asymptotically equivalent to the bias-corrected FE estimator of Hahn and Kuersteiner (Econometrica 70(4):1639–1657, 2002). Moreover, under certain conditions, its Hessian matrix remains non-singular