An Empirical Justification for the Use of Draft Lottery Numbers as a Random Treatment in Political Science Research

Over the past several years, there has been growing use of the draft lottery instrument to study political attitudes and behaviors (see, e.g., Bergan 2009; Erikson and Stoker 2011; Henderson 2012; Davenport 2015). Draft lotteries, held in the United States from 1969 to 1972, provide a potentially powerful design; in theory, they should provide true randomization for the "treatment" of military service or behavioral reactions to the threat of such service. However, the first draft lottery conducted in 1969 was not conducted in a random manner, giving those citizens born in the fourth quarter of the year disproportionately higher chances of being drafted. In this note, we describe the randomization failure and discuss how this failure could in theory compromise the use of draft lottery numbers as an instrumental variable. We then use American National Election Studies data to provide support for the conclusion that individuals most affected by the randomization failure (those born in the fourth quarter of the year) largely do not look statistically distinct from those born at other times of the year. With some caveats, researchers should be able to treat the 1969 draft numbers as if they were assigned at random. We also discuss broader lessons to draw from this example, both for scholars interested in using the draft lottery as an instrumental variable, and for researchers leveraging other instruments with randomization failures. Specifically, we suggest that scholars should pay particular attention to the sources of randomization failure, sample attrition, treatment and dependent variable selection, and possible failure of the exclusion restriction, and we outline ways in which these problems may apply to the draft lottery instrument and other natural experiments.