Partial Identification in Econometrics

Abstract

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 the parameter is point identified. Rather, given the data, the partial identification approach characterizes the informational content of various assumptions by providing a menu of estimates, each based on different sets of assumptions, some of which are plausible and some of which are not. Of course, more assumptions beget more information, so stronger conclusions can be made at the expense of more assumptions. The partial identification approach advocates a more fluid view of identification and hence provides the empirical researcher with methods to help study the spectrum of information that we can harness about a parameter of interest using a menu of assumptions. This approach links conclusions drawn from various empirical models to sets of assumptions made in a transparent way. It allows researchers to examine the informational content of their assumptions and their impacts on the inferences made. Naturally, with finite sample sizes, this approach leads to statistical complications, as one needs to deal with characterizing sampling uncertainty in models that do not point identify a parameter. Therefore, new methods for inference are developed. These methods construct confidence sets for partially identified parameters, and confidence regions for sets of parameters, or identifiable sets.non-point-identified models, sensitivity analysis, robust inference, bounds

The identification power of smoothness assumptions in models with counterfactual outcomes

“…Furthermore, we may conduct sensitivity analysis by looking at different values of b. In Section 4.3, we provide an example of sensitivity analysis (for general discussions on sensitivity analysis, see Leamer (1985), Tamer (2010), and others).…”

“…For example, see monographs by Manski (2003Manski ( , 2007, a recent review by Tamer (2010), and references therein. One important branch of this literature is concerned with bounding the distribution of the counterfactual outcomes or bounding the average treatment effects.…”

Understanding the Past: Statistical Analysis of Causal Attribution

“…The literature divides into two approaches, depending on whether to focus on the confidence regions that cover the entire bounds (e.g. Chernozhukov, Hong and Tamer, 2007;Imai and Soneji, 2007) or those that contain the true value with a certain confidence level (see Tamer, 2010, for a recent review). In the empirical applications in this paper, I use the symmetric and uniformly convergent confidence interval by Imbens and Manski (2004).…”

Moment inequalities in the context of simulated and predicted variables

“…Recently, estimating with moment inequalities rather than traditional equalities has proven increasingly popular (Tamer, 2010). Even in contexts when a model is difficult or even impossible to compute exactly, economic theory may provide inequalities that are amenable to estimation.…”