Identification in Econometrics: A Way to Get Causal Information from Observations? Damien Fennell, LSE UCL, May 27, 2005

Aims Larger Goal Make explicit causal concepts assumed in certain econometric methods. Why? (Ultimately) to better understand how econometrics can/should inform policy Goal of this Paper To focus on a small aspect of econometric method: identification. How? Herbert Simon claims can get from observed functional relations to causal relations using concepts of experiment and identifiability I claim this fails Simon’s causal semantics & identifiability ≠> causal relations

Structural Models and Identification Structural models in econometrics, e.g. Are supposed to tell us what happens given interventions.  Equations are to be read using some causal semantics Econometrician’s aim: To infer coefficients in such models from observations An established condition for this is that the model must be identifiable i.e. be able to calculate values for coefficients from observations.

So, intuitive to assume that: A tested structural identifiable model yields information about causal connections. But what is involved in this? The classic method for finding out about causal connections is experimentation. So one question I ask is Is there a connection between identification and experiments? If so, what is it? Structural Models and Identification II

Also, economists (even philosophical ones) often think identifiability takes care of causes, e.g. “what Simon (1953b) showed was that linear system of equations was identified if and only if it was causally ordered” (Hoover, 2001, p. 147). Is this right? To address all these issues, turn to Simon Simon explicitly connects causal order, experiments and identifiability. Another reason: As quote shows, Simon is influential. Structural Models and Identification III

Given a linearly independent set of equations, solvable for the internal variables in terms of external variables. Simon’s causal order is the order in which the internal variables can be solved for block recursively. For example Simon’s Formal Order x 1,x 2 - external variables p, q – internal variables So system has causal order: {p}  {q}

Simon’s Causal Semantics Experimenter/Nature can choose value of external factors freely  external variables variation free Mechanisms are invariant to ‘changes’ in the values of factors  equations invariant. Formal LanguageMetalanguage External variableExternal factor (directly controllable by experimenter/nature) Internal variableInternal factor (indirectly controllable by experimenter/nature) EquationMechanism Key point The idea of an experiment is captured in the assumption that directly controllable factors are variation free

Simon’s Causal Order Causal Interpretation of Formal Order If a factor precedes another in causal order then, if it changes value then the latter factor changes (in line with equations for mechanisms). While factors that are not causally subsequent (to a factor that changes) do not change. If x changes: If x causally precedes y => y changes If z doesn’t causally succeed any such x => z doesn’t change

How does this connect with identification? Perhaps this theorem can help Theorem: An equation is identifiable (from exclusions alone) if and only if it is possible for any two variables in the equation to vary (relative to each other) while all other variables in the equation remain constant. The last part of the theorem sounds like an experiment, so it is tempting to jump to An equation is identifiable if and only if an ‘experiment’ is possible between any two variables in it. This view of experiment matches Simon’s: it is based on a variation free concept Identification and Experiments

So far we have Simon’s causal semantics with its view of experiments AND A theorem linking experiments and identification Can these be used to get causal relations from observations? A Quick Recap

Case 1 – Rearranged Variables Problem Simon’s notes a problem (also Glymour 83, Cartwright 89): Can rearrange formal order by moving variables around Problem: two mathematically equivalent systems with different causal orders -Here Simon’s semantics do not ensure unique causal order - Moreover both systems are identifiable So requiring identifiability doesn’t help with unique causal order

Case 2 – Another Example: Changed External Variables Problem Two more mathematically equivalent systems: different causal orders, both identifiable

So, what does Identification get us from Observations? If an identifiable system with known functional form holds, then unknown parameters can be inferred from observations, this can be interpreted using the ‘experiments’ theorem - Inferring a parameter from observations can be read as working out from non experimental data, how two variables would have changed together if only these had changed. But Case 1 and 2 show can have mathematically equivalent systems that are identifiable but which have distinct causal orders. So, our ‘experiments’ that are possible by identification - do not allow one to measure causal strength, only strength of functional relations from observations

Some Conclusions 1. Variation free is too weak a concept for causal order or experiments. 2. Leads to Simon’s causal semantics not ensuring unique causal order 3. Experiments that are possible by identifiability are at the level of functional not causal relations. Lesson1: Identifiable functional relations, can be inferred from observed variable values, but this does not in itself give causal connections. Knowledge of causal content of functional relations must come from elsewhere. Lesson2: Beware of those who claim identifiability takes care of causes, at semantic or epistemic levels! Particularly those who rely on Simon in doing so.