On the consistency of the logistic quasi-MLE under conditional symmetry

Jeffrey Wooldridge

Economics Letters, 2020, vol. 194, issue C

Abstract: For estimating the parameters of a linear conditional mean, I show that the quasi-maximum likelihood estimator (QMLE) obtained under the nominal assumption that the error term is independent of the explanatory variables with a logistic distribution is consistent provided the conditional distribution of the error term is symmetric. No other restrictions are required for Fisher consistency; in particular, the error and covariates need not be independent, and so general heteroskedasticity of unknown form is allowed. Importantly, the influence function of the logistic quasi-log likelihood is bounded, making it more resilient to outliers than ordinary least squares. Inference using the logistic QMLE is straightforward using a robust asymptotic variance–covariance matrix estimator.

Keywords: Quasi-maximum likelihood estimation; Logistic distribution; Robust estimation; Influence function; Robust variance–covariance matrix; Outlier (search for similar items in EconPapers)
JEL-codes: C13 C21 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecolet:v:194:y:2020:i:c:s0165176520302317

DOI: 10.1016/j.econlet.2020.109363

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