In his 2005 article "The Scientific Model of Causality" (Sociological Methodology, vol. 35 (1) page 40,) Jim Heckman reviews the historical development of causal notions in econometrics, and paints an extremely complimentary picture of the current state of this development.
As an illustration of econometric methods and concepts, Heckman discusses the classical problem of estimating the causal effect of Y2 on Y1 in the following systems of equations
Y1 = a1 + c12Y2 + b11X1 + b12 X2 + U1 (16a)
Y2 = a2 + c21Y1 + b21X1 + b22 X2 + U2 (16b)
where Y1 and Y2 represent, respectively, the consumption levels of two interacting agents, and X1, X2, the levels of their income.
Unexpectedly, on page 44, Heckman makes a couple of remarks that almost threw me off my chair; here they are:
"Controlled variation in external (forcing) variables is the key to defining causal effects in nonrecursive models. It is of some interest to readers of Pearl (2000) to compare my use of the standard simultaneous equations model of econometrics in defining causal parameters to his. In the context of equations (16a) and (16b), Pearl defines a causal effect by "shutting one equation down" or performing "surgery" in his colorful language."
"He implicitly assumes that "surgery," or shutting down an equation in a system of simultaneous equations, uniquely fixes one outcome or internal variable (the consumption of the other person in my example). In general, it does not. Putting a constraint on one equation places a restriction on the entire set of internal variables. In general, no single equation in a system of simultaneous equation uniquely determines any single outcome variable. Shutting down one equation might also affect the parameters of the other equations in the system and violate the requirements of parameter stability."
I wish to bring up for blog discussion the following four questions:
- Is Heckman right in stating that in nonrecursive systems one should not define causal effect by surgery?
- What is the causal effect of Y2 on Y1 in the model of Eqs. (16a -16b) ??
- What does Heckman mean when he objects to surgery as the basis for defining causal parameters?
- What did he have in mind when he offered "… the standard simultaneous equations model of econometrics" as an alternative to surgery "in defining causal parameters"?
The following are the best answers I could give to these questions, but I would truly welcome insights from other participants, especially economists and social scientists (including Jim Heckman, of course).