In the past 20 years, researchers have begun to embrace the idea that identification is not an all-or-nothing matter and that a set of plausible assumptions that does not deliver point identification can still contain useful information about parameters of interest.This partial identification view has been motivated by the fact that point identification is not the objective by itself and in essence takes us back to Koopmans & Reiersol’s (1950) dictum whereby the specification of a model ought to be based on [A] the underlying economics, [B] prior knowledge (such as the linearity of variable cost that people have established for this industry), or [C] other assumptions with universal or [C*] almost universal acceptance, but [D] should not be geared primarily toward point identifying the parameters. “Scientific honesty demands that the specification of a model be based [B] on prior knowledge of the phenomenon studied and [E] possibly on criteria of simplicity, but not [D] on the desire for identifiability of characteristics that the researcher happens to be interested in” (Koopmans & Reiersol 1950, pp. 169–70). Once the structure is specified, the model can either have no information about the parameter of interest, restrict the parameter of interest to a nontrivial set, or point identify the parameter of interest. This is exactly the domain of identification analysis, with partial identification taking the view that identification is not only about verifying whether the third case holds, but also determining the extent of information contained in the second and linking this to the type of assumptions that the researcher proposes in the model.--Elie Tamer (2010). [Emphasis and Letters added to facilitate discussion. --ES]*
In quoting Koopmans, who won a Nobel in 1975, and Reiersol (hereafter K&R), Tamer calls attention -- en passant -- to the significance of the role of virtue in ordinary scientific practice. It goes beyond general rules of integrity, by appealing to an explicit rule ('do x or y, but not z') in model specification that prevents abuse of a scientific method. The need to articulate the rule suggests that already back in 1950 K&R were aware of the danger of (what we might label) fishing expeditions. While reflecting on the fact that K&R, focus exclusively on individual virtue (and ignore incentives, institutions, and detecting mechanism), I noticed something curious about Tamer's passage.
Criteria [A] through [C*] are neither obviously identical to each other nor identical with [E]. Moreover, criteria [C] and [C*] are together with criteria [B] essentially conservative: appealing to them prevents exploring unusual, unpopular, or wacky ideas. Now, these criteria prevent researcher's personal idiosyncrasies from generating (ad hoc) results, and (useful when computer power was expensive and scarce) focuses the search space. But it also makes it hard for adventurous and speculative research. Now, I was not surprised by this because I had already claimed that Koopmans should be credited for promoting mathematical econometric techniques and tools – and more generally inferential technologies that produce univocal and stable figures in calculating the implications of policy alternatives – within economics and, of course, to policymakers; this made economists attractive as policy experts (as opposed to say, sociologists, lawyers, anthropologists, and historians).
But the plot thickens. I went back to the (1950) K&R paper. There I could not find a clear statement of [A], [B], [C]. [C*]. So, somewhere between the original K&R paper and Tamer's 2010 paper, K&R had become associated with a far more conservative doctrine. (After all, there need not be unanimity over which theory counts as the simpler one.) I wouldn't claim that Tamer made it up, because certainly elsewhere in Koopmans one can find support for versions of [A] & [B]. They are in Koopmans' spirit. But that still leaves [C] and [C*]. Note, too, that there is a straightforward reading of the text in which [A] and [B] are both instances of [C/C*]. This would make the elaborated version of K&R even more conservative than it already is.
What to make of this? The positive spin is that one encourages the econometrician to explore potentially realistic parameters. The negative spin is that one is reinforcing a conservative methodology that prevents econometricians from learning that the world is stranger than thought possible, all in the name of scientific integrity.
*"Identification in econometric models maps prior assumptions and the data to information about a parameter of interest. The partial identification approach to inference recognizes that this process should not result in a binary answer that consists of whether theparameter is point identified."--Tamer.
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