Robust Econometrics

As a generalization of S-estimation, the τ -estimators include S-estimators
as a special case for ρ₁ = ρ₂ because then τ² (z, θ) = θs² (z, θ). On the other
hand, if ρ₂(t) = t², τ²(z, θ) = η²(z, θ)dF_n(z) is just the standard deviation
of model residuals. Compared to S-estimators, the class of τ estimators can
improve in terms relative Gaussian efficiency because its breakdown depends
only on function ρ₁ , whereas its asymptotic variance is function of both ρ₁
and ρ2. Thus, ρ1 can be defined to achieve the breakdown point equal to 0.5
and ρ2 consequently adjusted to reach a pre-specified relative efficiency for
Gaussian data (e.g., 95%).

3 Methods of robust econometrics

The concepts and methods of robust estimation discussed in Sections 1 and 2
are typically proposed in the context of a simple location or linear regression
models, assuming independent, continuous, and identically distributed ran-
dom variables. This however rarely corresponds to assumptions typical for
most econometric models. In this section, we therefore present an overview of
developments and extensions of robust methods to various econometric mod-
els. As the M -estimators are closest to the commonly used LS and MLE,
most of the extensions employ M -estimation. The HBP techniques are not
that frequently found in the economics literature (Zaman et al., 2001; Sapra,
2003) and are mostly applied only as a diagnostic tool.

In the rest of this section, robust estimation is first discussed in the

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