Econometrics

30 pages, 583 KiB

Open AccessArticle

When It Counts—Econometric Identification of the Basic Factor Model Based on GLT Structures

Sylvia Frühwirth-Schnatter

Darjus Hosszejni

and

Hedibert Freitas Lopes

Econometrics 2023, 11(4), 26; https://doi.org/10.3390/econometrics11040026 - 20 Nov 2023

Viewed by 284

Abstract

Despite the popularity of factor models with simple loading matrices, little attention has been given to formally address the identifiability of these models beyond standard rotation-based identification such as the positive lower triangular (PLT) constraint. To fill this gap, we review the advantages of variance identification in simple factor analysis and introduce the generalized lower triangular (GLT) structures. We show that the GLT assumption is an improvement over PLT without compromise: GLT is also unique but, unlike PLT, a non-restrictive assumption. Furthermore, we provide a simple counting rule for variance identification under GLT structures, and we demonstrate that within this model class, the unknown number of common factors can be recovered in an exploratory factor analysis. Our methodology is illustrated for simulated data in the context of post-processing posterior draws in sparse Bayesian factor analysis. Full article

(This article belongs to the Special Issue High-Dimensional Time Series in Macroeconomics and Finance)

► Show Figures

Figure 1

28 pages, 580 KiB

Open AccessArticle

On the Proper Computation of the Hausman Test Statistic in Standard Linear Panel Data Models: Some Clarifications and New Results

Julie Le Gallo

and

Marc-Alexandre Sénégas

Econometrics 2023, 11(4), 25; https://doi.org/10.3390/econometrics11040025 - 08 Nov 2023

Viewed by 595

Abstract

We provide new analytical results for the implementation of the Hausman specification test statistic in a standard panel data model, comparing the version based on the estimators computed from the untransformed random effects model specification under Feasible Generalized Least Squares and the one computed from the quasi-demeaned model estimated by Ordinary Least Squares. We show that the quasi-demeaned model cannot provide a reliable magnitude when implementing the Hausman test in a finite sample setting, although it is the most common approach used to produce the test statistic in econometric software. The difference between the Hausman statistics computed under the two methods can be substantial and even lead to opposite conclusions for the test of orthogonality between the regressors and the individual-specific effects. Furthermore, this difference remains important even with large cross-sectional dimensions as it mainly depends on the within-between structure of the regressors and on the presence of a significant correlation between the individual effects and the covariates in the data. We propose to supplement the test outcomes that are provided in the main econometric software packages with some metrics to address the issue at hand. Full article

► Show Figures

Figure 1

32 pages, 10108 KiB

Open AccessArticle

Dirichlet Process Log Skew-Normal Mixture with a Missing-at-Random-Covariate in Insurance Claim Analysis

and

Econometrics 2023, 11(4), 24; https://doi.org/10.3390/econometrics11040024 - 12 Oct 2023

Viewed by 488

Abstract

In actuarial practice, the modeling of total losses tied to a certain policy is a nontrivial task due to complex distributional features. In the recent literature, the application of the Dirichlet process mixture for insurance loss has been proposed to eliminate the risk of model misspecification biases. However, the effect of covariates as well as missing covariates in the modeling framework is rarely studied. In this article, we propose novel connections among a covariate-dependent Dirichlet process mixture, log-normal convolution, and missing covariate imputation. As a generative approach, our framework models the joint of outcome and covariates, which allows us to impute missing covariates under the assumption of missingness at random. The performance is assessed by applying our model to several insurance datasets of varying size and data missingness from the literature, and the empirical results demonstrate the benefit of our model compared with the existing actuarial models, such as the Tweedie-based generalized linear model, generalized additive model, or multivariate adaptive regression spline. Full article

► Show Figures

Figure 1

11 pages, 276 KiB

Open AccessArticle

A New Matrix Statistic for the Hausman Endogeneity Test under Heteroskedasticity

Alecos Papadopoulos

Econometrics 2023, 11(4), 23; https://doi.org/10.3390/econometrics11040023 - 10 Oct 2023

Viewed by 469

Abstract

We derive a new matrix statistic for the Hausman test for endogeneity in cross-sectional Instrumental Variables estimation, that incorporates heteroskedasticity in a natural way and does not use a generalized inverse. A Monte Carlo study examines the performance of the statistic for different heteroskedasticity-robust variance estimators and different skedastic situations. We find that the test statistic performs well as regards empirical size in almost all cases; however, as regards empirical power, how one corrects for heteroskedasticity matters. We also compare its performance with that of the Wald statistic from the augmented regression setup that is often used for the endogeneity test, and we find that the choice between them may depend on the desired significance level of the test. Full article

Journal Menu

Journal Browser

Econometrics, Volume 11, Issue 4 (December 2023) – 4 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI