arXiv subjects

Hugo Kruiniger

Publications and source records attributed to Hugo Kruiniger.

5 recordsLinked to original sources

arXiv2025

A further look at Modified ML estimation of the panel AR(1) model with fixed effects and arbitrary initial conditions

In this paper we consider two generalizations of Lancaster's (Review of Economic Studies, 2002) Modified Maximum Likelihood estimator (MMLE) for the panel AR(1) model with fixed effects, arbitrary initial conditions, and strictly exogenous covariates when the time dimension of the panel, T, is fixed. When the autoregressive parameter rho=1, the limiting modified profile log-likelihood function for this model has a stationary point of inflection, and rho is first-order underidentified but second-order identified. We show that, unlike the Random Effects and Transformed MLEs for this type of model, the generalized MMLEs are uniquely defined in finite samples w.p.1. for any value of |rho|=<1. When rho=1, the rate of convergence of the MMLEs is N^{1/4}, where N is the cross-sectional dimension of the panel. We derive the limiting distributions of the MMLEs when rho=1. They are generally asymmetric. We also show that Quasi LM tests that are based on the modified profile log-likelihood function and use its expected rather than observed Hessian for hypotheses that include a restriction on rho, and confidence sets that are based on inverting these tests have correct asymptotic size in a uniform sense when |rho|=<1. Finally, we investigate the finite sample properties of the MMLEs and the QLM test in a Monte Carlo study.

econ.EM↗

arXiv2025

Uniform Quasi ML based inference for the panel AR(1) model

Maximum Likelihood (ML) offers attractive alternatives to Generalized Method of Moments (GMM) estimators for dynamic panel data models. However, to date no identification-robust inference methods exist that can be used in conjunction with the ML estimators for these models. In this paper we propose ML based inference methods for panel AR(1) models with arbitrary initial conditions and heteroskedasticity that are robust to the strength of identification. We show that (Quasi) Lagrange Multiplier (LM) tests and confidence sets (CSs) that use the expected Hessian rather than the observed Hessian of the log-likelihood function have correct asymptotic size and coverage probability in a uniform sense, respectively. Such Quasi LM tests and CSs are also robust to misspecification of the distribution of the data and to heterogeneity, including heteroskedasticity. We derive the power envelope of a Fixed Effects version of such an LM test for hypotheses involving the autoregressive parameter when the average information matrix is estimated by a centered OPG estimator and the model is only second-order identified, and show that it coincides with the maximal attainable power curve in the worst-case setting. We also study the empirical size and power properties of these (Quasi) LM tests and find that the hypothesis that the (Quasi) LM test has correct size cannot be rejected.

econ.EM↗

arXiv2023

Large sample properties of GMM estimators under second-order identification

Dovonon and Hall (Journal of Econometrics, 2018) proposed a limiting distribution theory for GMM estimators for a p - dimensional globally identified parameter vector {\phi} when local identification conditions fail at first-order but hold at second-order. They assumed that the first-order underidentification is due to the expected Jacobian having rank p-1 at the true value {\phi}_{0}, i.e., having a rank deficiency of one. After reparametrizing the model such that the last column of the Jacobian vanishes, they showed that the GMM estimator of the vector comprising the first p-1 parameters, {\phi}_{1}, converges at rate T^{-1/2} and the GMM estimator of the remaining parameter, {\phi}_{p}, converges at rate T^{-1/4}. They also provided a limiting distribution of T^{1/4}({\phi}_{p}-hat-{\phi}_{0,p}) subject to a (non-transparent) condition which they claimed to be not restrictive in general. However, as we show in this paper, their condition is in fact only satisfied when {\phi} is overidentified and the limiting distribution of T^{1/4}({\phi}_{p}-hat-{\phi}_{0,p}), which is non-standard, depends on whether {\phi} is exactly identified or overidentified. In particular, the limiting distributions of the sign of T^{1/4}({\phi}_{p}-hat-{\phi}_{0,p}) for the cases of exact and overidentification, respectively, are different and are obtained by using expansions of the GMM objective function of different orders. Unsurprisingly, we find that the limiting distribution theories of Dovonon and Hall (2018) for Indirect Inference (II) estimation under two different scenarios with second-order identification where the target function is a GMM estimator of the auxiliary parameter vector, are incomplete for similar reasons. We discuss how our results for GMM estimation can be used to complete both theories. We also derive the optimal weight matrices for {\phi}_{1}-hat and {\phi}_{p}-hat, respectively.

econ.EM↗

arXiv2021

Root-n-consistent Conditional ML estimation of dynamic panel logit models with fixed effects

In this paper we first propose a root-n-consistent Conditional Maximum Likelihood (CML) estimator for all the common parameters in the panel logit AR(p) model with strictly exogenous covariates and fixed effects. Our CML estimator (CMLE) converges in probability faster and is more easily computed than the kernel-weighted CMLE of Honor\'e and Kyriazidou (2000). Next, we propose a root-n-consistent CMLE for the coefficients of the exogenous covariates only. We also discuss new CMLEs for the panel logit AR(p) model without covariates. Finally, we propose CMLEs for multinomial dynamic panel logit models with and without covariates. All CMLEs are asymptotically normally distributed.

econ.EM↗

arXiv2020

Further results on the estimation of dynamic panel logit models with fixed effects

Kitazawa (2013, 2016) showed that the common parameters in the panel logit AR(1) model with strictly exogenous covariates and fixed effects are estimable at the root-n rate using the Generalized Method of Moments. Honor\'e and Weidner (2020) extended his results in various directions: they found additional moment conditions for the logit AR(1) model and also considered estimation of logit AR(p) models with p>1. In this note we prove a conjecture in their paper and show that for given values of the initial condition, the covariates and the common parameters 2^{T}-2T of their moment functions for the logit AR(1) model are linearly independent and span the set of valid moment functions, which is a 2^{T}-2T-dimensional linear subspace of the 2^{T}-dimensional vector space of real valued functions over the outcomes y element of {0,1}^{T}. We also prove that when p=2 and T element of {3,4,5}, there are, respectively, 2^{T}-4(T-1) and 2^{T}-(3T-2) linearly independent moment functions for the panel logit AR(2) models with and without covariates.

econ.EM↗