Manski introduced an important notion of *partial* identification,
which happens when perfect data is not enough to pin a parameter down to a
single point value, but can impose non-trivial bounds on it. The degree to
which a parameter is identifiable, in this sense, depends on the class of
models one is willing to consider, i.e., on the strength of the assumptions one
is willing to make. The stronger those assumptions, the narrower the bounds,
in some cases yielding full or point-identification. This book is an
introduction to work by Manski and co-authors on partial identifiability in
social-scientific and policy-making problems. The main themes are that (1)
many parameters are only very poorly identified with credible assumptions, due
to the ubiquity of missing data; but (2) non-trivial partial-identification
bounds, based on not-too-strong assumptions, do exist; while (3) the
traditional assumptions used to point-identify parameters (e.g., linear
homogeneous demand-and-supply curves in economics, plus instrumental variables)
are very strong, sometimes completely unfalsifiable, and have little or no
basis in established or even conjectural theory. Finally, (4) it is important
for both social science and policy to admit to the uncertainty or ambiguity
this leaves us with, rather than simply making stuff up so as to be
definite. [1]

Manski is quite serious about the "decision" part of his title. The reason
we want to know the kinds of things he's been concerned with is that they tell
us what will happen (or tend to happen) when we take different sorts of action
in the world. If there is uncertainty about consequences, then there is
uncertainty about policy, too. (In this vein, a later paper of Manski's on
"actualist
rationality" is very much worth reading.) Like many writers, he admires
Wald's
notion of "statistical decision functions", rules which tell the policy maker
what action to take in new cases, as a function of training data; Manski is
particularly taken with the idea that a good rule will minimize the maximum
regret one will experience as a consequence of using it rather than some other
decision function. There are some interesting results here on the implications
of partial identifiability for decision functions. There is also a lament that
this style of decision theory went out of fashion in the 1960s, in favor of
more cut-and-dried Bayesian decision analysis. To my mind, though, this sort
of work is still being done, only it's being called
"statistical learning theory." When we say
that a learning algorithm is "probably approximately correct", for instance, we
mean that, with arbitrarily high confidence, using the rule the algorithm gives
us to make decisions about new data will have a risk arbitrarily close to the
best possible rule, *no matter what* the distribution of the data. (The
importance of minimizing regret becomes even clearer in
the online-learning
literature.) Trading exact optimality for practical non-parametrics seems like
a reasonable deal to me. In any case, it would be very cool if anything could
be done with this connection.

The book should be accessible to anyone with a working knowledge of
probability and statistics, including linear regression; it's largely
self-contained beyond that, and the writing is quite clear, and technicalities
studiously avoided. (I particularly found his discussion of identification in
linear simultaneous equation models *much* better than the usual
treatment in econometrics books.) While the numerical examples are more
detailed than I really needed, they also seem like they would actually help
many readers.

[1]: Aside/quibble: Manski is a bit unfair to Herbert Simon in his last chapter. (Of course, I am not exactly objective where the latter is concerned.) Simon's founding papers on bounded rationality were essentially making computational complexity arguments, i.e.,mathematicalarguments that we cannot, and therefore do not, act like expected utility maximizers in any non-trivial setting. This was followed by an extensive series of experimental investigations into how we make decisions, not just left hanging there...

368 pp., a few line diagrams, bibliography, index

Probability and Statistics; Economics; Sociology

Currently in print as a hardback, ISBN 978-0-674-02653-7 [Buy from Powell's], US$58

5 August 2009