A Cautionary Tale About Control Variables in IV Estimation

Abstract

Many instrumental variable (IV) regressions include control variables to justify(conditional) independence of the instrument and the potential outcomes. The plausibility of conditional IV independence crucially depends on the timing when the control variables are determined. This paper systemically works through different IV models and discusses the (conditions for the) satisfaction of conditional IV independence when controlling for covariates measured (a) prior to the instrument, (b) after the treatment, or (c) both. To illustrate these identification issues, we consider an empirical application using the Vietnam War draft risk as instrument either for veteran status or education to estimate the effects of these variables on labor market and health outcomes.

Candidates’ Education and Turnout: Evidence from Italyn Municipal Elections

“… Our findings do not change when we include candidates’ characteristics, two measures of the degree of political competition (number of candidates standing for a mayoral position and the electoral margin) in the electoral race and a dummy for concomitant national elections among controls. However, since these variables are endogenous, we prefer not to consider them among our main specifications (see Deuchert and Huber, ). …”

Gifted Identification and the Role of Gifted Education

“…These omissions compromise the implication of the findings for gifted education. Moreover, from a methodological point of view, questions arise concerning the rigor of the study, given the importance of control variables for justifying the independence of the instrument and the potential outcomes in typical instrumental variable (IV) estimations (see Deuchert & Huber, 2014, for a detail discussion of this issue). Although some of these issues might be related to the tradition of economic research or simply due to page restrictions, many in gifted education would appreciate more details to fully understand, interpret, and apply the findings.…”

Direct and Indirect Effects Based on Difference-in-Differences With an Application to Political Preferences Following the Vietnam Draft Lottery

“…1 On the other hand, low draft numbers may have not only increased the risk to be drafted but also the likelihood to voluntarily join the army (Angrist, 1991). The draft avoiding behaviour makes the use of the lottery as an instrumental variable doubtful (Deuchert and Huber, 2014).…”

“…Furthermore, note that if was a valid instrument for that satisfied the exclusion restriction, as for instance assumed in Angrist (1990) in the context of the Vietnam draft lottery, any direct effect ( ) would be zero and the indirect 1 (1) = 1 (0) = 1 would correspond to the so-called intention to treat effect. In our empirical application outlined below, we do not impose this strong assumption, which has for instance been challenged in Deuchert and Huber (2014), but explicitly allow for direct effects.…”

“…Our mediator of interest is military service during the Vietnam War. We note that a subset of individuals (compliers) was induced by the lottery to serve in the army either through being drafted or "voluntarily" joining the military in case of an unfavourable lottery outcome (Angrist, 1991), while others avoided the draft (never takers) for instance through college deferments (Card and Lemieux, 2001;Kuziemko, 2010;Deuchert and Huber, 2014), or would have served in any case (always takers). We aim at estimating the direct effects of the draft lottery on the never takers, as well as the direct and indirect effect (via military service) on the compliers.…”