Christopher L. Carter

Instrumental-variables (IV) analysis bridges structural equation modeling and design-based methods for causal inference. In both frameworks, researchers invoke random or as-if random assignment of units to treatment conditions as a way of addressing concerns about confounding variables. Yet, despite areas of convergence, these different approaches to IV analysis rely on distinct underlying assumptions. In this chapter, we discuss areas of overlap and divergence in the modeling strategies. While structural equations embed several core assumptions in linear response schedules, design-based approaches disaggregate and clarify these assumptions. We then use a hypothetical empirical example—price elasticity of demand for coffee—to illustrate these similarities and differences. The chapter concludes with a note of caution on the use of instrumental variables for political science and international relations: whichever framework is invoked, IV analysis generates results that may not generalize beyond the specific intervention that gave rise to the instrument.