Robust Econometrics

The concepts and measures of robustness are introduced first (Section 1),
followed by a most common types of estimation methods and their properties
(Section 2). Various econometric methods based on these common estimators
are discussed later in Section 3, covering tasks from time series regression over
GMM estimation to simulation-based methods.

1 Measures of robustness

Robustness properties can be formulated within two frameworks: qualitative
and quantitative robustness. Qualitative robustness is concerned with the
situation in which the shape of the underlying (true) data distribution devi-
ates slightly from the assumed model. It focuses on questions like stability
and performance loss over a family of such slightly deviating distributions.
Quantitative robustness considers the situation in which the sensitivity of
estimators to a proportion of aberrant observations is studied.

A simple example can make this clear. Suppose one has collected a sam-
ple on an individual’s income (after say 10 years of schooling) and one is
interested in estimating the mean income. If {xi}_iⁿ₌₁ denotes the logarithm
of this data and we suppose that they have a cumulative distribution func-
tion (cdf) F, assumed to be N(μ,σ2), the maximum likelihood estimator
(MLE) is x = R udF_n(u) = T(F_n), where F_n(u) = n^-1 Pnn=₁1(χ_i ≤ u), and
μ = R udF(u) = T(F). Qualitative robustness asks here the question: how
well will μ be estimated if the true distribution is in some neighborhood of

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