Richard Goldstein and Yan Cheng--
Partha Deb claims (correctly, from my point of view) in another thread
that various reduced form approaches are often better regarded than a
structural equations approach, usually because the theoretical and
statistical assumptions required for identification are somewhat more
palatable. With a binary "intervening variable" whose causal impact is
of primary interest, and some complicated theoretical "path diagrams"
of causation, the usual Stata command for reduced form models is
-treatreg- and for other models where the variable of interest is not
binary, see -ivreg2- (from -ssc install ivreg2-). In Richard's
example, suppose instead of a "causal diagram" like
b --> d --> h
we have
b --- h
\ /
\ /
d
with arrows ending like so:
b --> h
b--> d --> h
so e.g. b increases d which increases h, and b also directly increases
h. (I don't think the original diagram really captures causation of
heart rates, nor does my revised diagram, but that is why I am using
letters instead of names--assume the causation really does flow as
shown.) Then (especially if the correct model is linear) you can
regress h on b and d and get the partial effect of b and d (two of the
three arrows). If you want the total effect of b on h, then you
regress h on b and leave d out of the model. Neither of these
approaches estimates all three arrows at once--hence they are "reduced
form" rather than "structural equations" models.
If instead we have arrows ending like so:
b --> h
d --> b
d --> h
we have the classic "omitted variables" problem if we leave d out of
the regression. It is usually the case that when a variable like d in
this example cannot be directly measured (latent ability, unknown
genotype, etc.) people fall back on Instrumental Variables, finding
another variable z that satisfies z--> b but not z--> h on the causal
diagram (and satisfying various other statistical assumptions) and
then use -ivreg2 h (b=z)- to estimate.
On 3/5/07, Austin Nichols <austinnichols@gmail.com> wrote:
Richard Goldstein and Yan Cheng--
Any discussion of intervening variables or path analysis could touch
on hundreds of different sets of terminology from numerous
disciplines, but a seach on "structural equations models" should
encompass much of the relevant literature [in Stata, the first hit
should be on -reg3- probably, and see gllamm.org for complicated
models]. This thread is certainly a long one in economics, and no
short answer is likely to satisfy.
On 3/5/07, Partha Deb <partha.deb@hunter.cuny.edu> wrote:
If you take the approach and specify the treatment equation as a reduced form,
then you have the lower burden of defending the structure of the outcome
equation, and are implicitly admitting you don't have much confidence in
whatever structural form might underly the treatment process. It's safe to
say this is currently the more popular approach.
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