= Thomas J. Rothenberg
{c}
\b[Thomas J. Rothenberg] is a mathematical econometrician whose work concerns <statistical inference> and the <identifiability> of models. The American Economic Association's 2015 citation recognizes his contributions to identification and inference and identifies him as a professor emeritus at Berkeley.<Thomas Rothenberg, Distinguished Fellow 2015 by the American Economic Association>[Award citation and institutional identification]{ref}
His primary paper <Identification in Parametric Models by Thomas J. Rothenberg>, published in 1971, develops identification criteria beyond one model considered in isolation. It connects local identification with the information matrix under regularity conditions and treats identification of individual parameters separately from that of the full vector.<Identification in Parametric Models by Thomas J. Rothenberg>[First-page abstract; §5, Theorem8]{ref} The distinction is useful when a scientifically relevant combination is recoverable even though the entire parameterization is not; <identifiability from linear observations> gives an explicit example.
An original counterexample explains why the regularity qualifications matter. Consider one observation with <normal distribution>
$$
Y\sim N(\theta^3,1),\qquad \theta\in\mathbb R.
$$
The mean map is one-to-one, so distinct parameters have distinct observable distributions. Nevertheless its <Fisher information> is
$$
\mathcal I(\theta)=\left(\frac{d\theta^3}{d\theta}\right)^2=9\theta^4,
$$
which vanishes at zero. The information rank changes there, so a nonsingularity criterion cannot be applied without its assumptions. <Nonregular identification at a flat mean map> separates exact distinguishability from first-order sensitivity: a zero derivative does not by itself establish that two different parameter values produce the same law.
The example illustrates a broader contribution of identification theory. Before asking an estimator for a precise answer, determine whether the observations can distinguish the proposed quantities and whether the local approximation used for inference is valid.
\Image[https://www.aeaweb.org/honors_awards/bios/images/Thomas_Rothenberg.gif]
{title=Thomas J. Rothenberg in the American Economic Association award portrait}
{description=Externally hosted image identified by the society's named Distinguished Fellow citation.}
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