Advances in the study of partial identification allow applied researchers to learn about parameters of interest without making assumptions needed to guarantee point identification. We discuss the roles that assumptions and data play in partial identification analysis, with the goal of providing information to applied researchers that can help them employ these methods in practice. To this end, we present a sample of econometric models that have been used in a variety of recent applications where parameters of interest are partially identified, highlighting common features and themes across these papers. In addition, in order to help illustrate the combined roles of data and assumptions, we present numerical illustrations for a particular application, the joint determination of wages and labor supply. Finally we discuss the benefits and challenges of using partially identifying models in empirical work and point to possible avenues of future research.

INTRODUCTION

The goal of identification analysis is to determine what can be learned using deductive reasoning through the combination of models (sets of assumptions) and data. Standard approaches to econometric modeling for applied research make enough assumptions to ensure that parameters of interest are point identified. However, it is still possible to learn about such quantities even if they are not.

Econometric models that allow for partial identification, or partially identifying models, make fewer assumptions and use them to generate bounds on the parameters of interest. Such models have a long history, with early papers including Frisch (1934), Reiersol (1941), Marschak and Andrews (1944), and Frechet (1951). The literature on the topic then remained fragmented for several decades, with some further notable contributions such as Peterson (1976), Leamer (1981), Klepper and Leamer (1984), and Phillips (1989). It wasn't until the work of Charles Manski and co-authors beginning in the late 1980s that a unified literature began to emerge, beginning with Manski (1989, 1990). Several influential papers by Elie Tamer and co-authors applying partial identification to a variety of econometric models (e.g., Haile and Tamer, 2003; Honore and Tamer, 2006; Ciliberto and Tamer, 2009) have helped to bring these methods into more common use.