fying a well-fitting model with existing data and statistical methods.7 In summary, the problems posed by high-dimensional estimation, misspecified models, and lack of knowledge of the correct set of explanatory variables seem insurmountable with observational data.
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Much current research in statistics and econometrics is directed at “dimension reduction.” This consists of imposing shape assumptions that are much weaker than those of models like 6.1 and 6.2 but strong enough to reduce the effective number of shapes that must be considered and thereby to increase estimation precision substantially. Although these techniques show considerable promise, they have not yet been developed sufficiently to be applicable to problems like estimation of the effects of right-to-carry laws.