β Scribed by J. Stoye
No coin nor oath required. For personal study only.
Few econometricians have recently impacted the way we think about our field as much as Charles Manski. The main channel by which he has accomplished this is through study of partial identification, or bounds. For a simple example, consider the distribution of employment status in a population of interest. Say that 90% of this population report their status when prompted; of these, 80% are employed and 10% are unemployed. But 10% of the population refuse to answer questions on employment. Then the population probability of employment is not identified-no survey of any size will reveal it. However, these numbers imply that between 10% and 20% of the population are unemployed. A large sample will reveal these bounds with arbitrary precision. Also, they can be tightened by imposing identifying assumptions. If one is willing to assume that nonresponders entirely resemble the responders other than by not responding, then one can conclude that the unemployment rate is 11%. Less restrictive assumptions will lead to less sharp conclusions, illustrating what Manski calls the 'Law of Decreasing Credibility.'
In a nutshell, the idea of bounds is that this type of reasoning can be fruitfully applied to a huge range of problems. This insight did not exactly change the game overnight. Some readers may be surprised to learn that Manski's first explicit 'bounds' paper was published precisely two decades ago (Manski, 1989). Ten years later, partial identification was still a niche enterprise. Today, things look much different: The theoretical literature on partial identification has assumed such a pace that this reviewer is behind on readings despite attending two specialized meetings in 2008 alone. Bounds are incorporated throughout a recent textbook on causal inference (Morgan and Winship, 2007) that was not even written by economists. Perhaps most tellingly, it is not unusual these days to hear the phrase 'point identified' in place of 'identified'-in talks that do not even feature any bounds.
Identification for Prediction and Decision (Harvard University Press 2007; IPD henceforth) is Manski's new monograph, and there is no denying that much of it is about bounds. Yet a monograph on bounds already exists (Manski, 2003). How does IPD differ? First, it has a much wider scope. Manski's recent projects (including bounds, the measurement of expectations, and treatment choice) are held together by a specific worldview that would be somewhat trivialized by reducing it to bounds. His agenda in IPD is to present the coherent whole, from bounds via
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