Demonstration of the need for invariance of parameters with
respect to classes of manipulations to answer classes of questions.
One theme developed in my paper is that major limitations
tant social science questions. These limitations are not surprising since
the statistical treatment effect literature is an offshoot of the experi-
mental design literature in biostatistics. My essay shows that ‘‘techni-
cal’’ assumptions invoked in the statistical treatment effect literature
have unappealing implications for social science.
Two cornerstone assumptions: SUTVA and Strong Ignorability
(SI) are especially unappealing. SUTVA is a version of an invariance
assumption developed in econometrics some 40–50 years ago
and formalized in the Hurwicz (1962) paper I cite. In the form
advocated by Sobel and many other statisticians, it precludes social
interactions and general equilibrium effects, and so precludes the
evaluation of large scale social programs. The SI assumption,
by ruling out any role for unobservables in self selection, justifies
matching by assuming away any interesting behavior of the agents
being studied. While Sobel criticizes econometrics for making
various assumptions, he ignores the fact that the approach that
he favors makes implicit assumptions that are stronger and
less tenable. The econometric approach is explicit about its
Sobel does not acknowledge any intellectual priority for early
work by economists that precedes the ‘‘Rubin model’’ as exposited by
Holland (1986). Selection models defined over potential outcomes
with explicit treatment assignment mechanisms were presented by
Gronau (1974) and Heckman (1974, 1976, 1978) in the economics
literature. The econometric discrete choice literature (McFadden
1974, 1981) used counterfactual utilities as did its parent literature
in mathematical psychology (Thurstone 1927, 1959). Unlike the
Rubin model, these models do not start with the experiment as an
ideal point of departure, but they start with well-posed, clearly
This notion is in the early Cowles Commission work. See Marschak
(1962) as cited in my paper. Rubin’s SUTVA is a special case of the invariance
condition formalized by Hurwicz.
behavioral theory where the unobservables that underlie the selection
and evaluation problem are made explicit.
Rubin’s 1978 model of treatment choice came later and only
implicitly accounts for the unobservables that drive the selection
problem. His point of departure is randomization and the analysis
of his 1976 and 1978 papers is a dichotomy between randomization
(ignorability) and nonrandomization, not an explicit treatment of
particular selection mechanisms in the nonrandomized case as devel-
oped in the econometrics literature.
Sobel dismisses the value of making clear the assumptions
about model unobservables that produce selection and evaluation
problems when he dismisses ‘‘structural’’ models. In this regard
he follows Angrist, Imbens, and Rubin (1996) and Holland (1986).
Sobel equates structural models (economic models) with LISREL
type models and standard simultaneous equations models despite
the greater generality of the structural models (see, e.g., Matzkin
make explicit the assumptions required to identify parameters in any
particular problem. The treatment effect literature does not make
fewer assumptions; it is just much less explicit about its assumptions.
Like many statisticians, Sobel prefers to be implicit about many of his
assumptions. This approach begs serious questions about the best way
to model the severe problems that arise in making sound policy
My essay is about:
Clearly defining the policy problem being addressed;
Asking what parameter is required to answer the problem;
Discussing minimal identification conditions; and
Analyzing the properties of various estimators.
While Sobel’s discussion claims to show that there are dimensions
along which the econometric literature is lacking relative to the statistical
literature on treatment effects, his arguments are based on misstatements
and misunderstandings of the econometrics literature that are prevalent in
the statistical treatment effect literature. For example, he makes the claim,
like Rubin and many other statisticians, that econometric selection
REJOINDER: RESPONSE TO SOBEL
He claims that economists, and I in
claim made by Rubin.
Sobel clearly has not read or understood the
potential outcomes and treatment assignment rules long before Rubin’s
My 1974–1976 papers are not ‘‘informal’’ and they present
wages) and outcome selection mechanisms. The switching regression
model of Quandt (1958, 1972) describes a model of potential outcomes
and develops various regime (potential outcome) selection rules.
Detached readers would be advised to compare the level of formality in
these papers with the relative informality of Rubin’s papers, especially his
informal 1974 paper which Sobel cites. In that paper, there is no systema-
tic discussion of treatment assignment rules whereas, by 1974, the econo-
metric literature had systematically developed and analyzed such rules.
The early econometric work clearly separates the definition of
parameters from their identification in a fashion not found in the statistics
literature. Heckman and Robb (1985, 1986) present comprehensive ana-
lyses of outcome equations, selection mechanisms and unobservables
using economic theory. We had no need to draw on the ‘‘Rubin Model’’
which was a special case of economic models that were formulated prior
to Rubin’s work. A more accurate description of Rubin’s contribution is
that he exposited aspects of econometric models to statisticians.
2. WHAT IS NEW IN MY PAPER AND
NOT DISCUSSED BY SOBEL
Sobel does not discuss my extension of the treatment effect literature
to the identification of non-recursive systems. The literature on
Heckman (1980, 1990), Heckman and Robb (1985, 1986), Heckman
others, have relaxed the normality assumption made in the early 1970’s literature.
See Heckman and Vytlacil (2005, 2006b) for a survey. It is far from clear that in
practice normality is a poor assumption in many applications. See Heckman
The Roy model (1951) is a clear predecessor as are the switching
models of Quandt (1958, 1972).