Handling multiple proxies

Abstract Substituting a proxy for an unobservable variable without further ado is common practice in applied econometric work. When more than one proxy is available, the question arises how to best handle them. Although the case often occurs in practice, the literature on this question is scarce. It started with Lubotsky and Wittenberg (2006) and was later on expanded by Bollinger and Minier (2015). We extend their work in various ways. We present an alternative derivation of their results by rearranging the elements in the regression, we prove the optimality of the approach, we propose a different normalization that facilitates interpretation, we propose a new estimator for the factor loadings, and we discuss a test for whether the proxies span a single latent dimension. A small numerical example demonstrates the theory. By way of empirical illustration, we consider the case of the size of a firm, which often enters models that analyze firm behavior. We provide some simple advice to practitioners.