Beyond LATE: Estimation of the Average Treatment Effect with an Instrumental Variable

Abstract

Political scientists frequently use instrumental variables (IV) estimation to estimate the causal effect of an endogenous treatment variable. However, when the treatment effect is heterogeneous, this estimation strategy only recovers the local average treatment effect (LATE). The LATE is an average treatment effect (ATE) for a subset of the population: units that receive treatment if and only if they are induced by an exogenous IV. However, researchers may instead be interested in the ATE for the entire population of interest. In this article, we develop a simple reweighting method for estimating the ATE, shedding light on the identification challenge posed in moving from the LATE to the ATE. We apply our method to two published experiments in political science in which we demonstrate that the LATE has the potential to substantively differ from the ATE.

Bounded, Efficient and Multiply Robust Estimation of Average Treatment Effects Using Instrumental Variables

“…To see their differences, note that, under different sets of identification assumptions described above,where the second equality in expression (2) is due to Abadie (), theorem 3.1. We can also see from expression (2) that, with a causal IV, in the case where assumption 5(a) and assumption 5(b) are incorrect but the monotonicity assumption is correct, our estimand E X [ δ ( X )] can still be interpreted as the LATE for a complier population whose covariate distribution matches that of the full study population (Aronow and Carnegie, ); similarly for the case where only the no current treatment value interaction assumption is correct.…”

“…It is interesting that, with a causal IV, δ ( X ) may also be interpreted as LATE( X )= E [ Y (1)− Y (0)| D (1)=1, D (0)=0, X ] under the monotonicity assumption that D (1)⩾ D (0), almost everywhere (Imbens and Angrist, ). Hence, with a causal IV, the monotonicity assumption and assumption 5 together imply the latent ignorability assumption LATE( X )=ATE( X ) (Frangakis and Rubin, ; Angrist and Fernandez‐Val, ; Aronow and Carnegie, ). Similarly, under a no current treatment value interaction assumption, δ ( X ) can also be interpreted as ETT( X )= E [ Y (1)− Y (0)| D =1, X ] (Hernán and Robins, ).…”

“…As a result, the LATE would in general differ from the ATE, which is arguably the causal parameter of interest in most observational studies (Imbens, ). We refer interested readers to Deaton (), Heckman and Urzua (), Pearl () and Aronow and Carnegie () for additional discussions on whether the LATE is of genuine scientific interest.…”

“…To the best of our knowledge, to date there has only been limited work focusing on the ATE in the context of an IV, while successfully maintaining identification and estimation assumptions clearly separated. Before our work, Angrist and Fernandez‐Val () and Aronow and Carnegie () assumed that, conditionally on a covariate profile, the ATE is the same as the LATE, so it can be identified under a monotonicity assumption, provided that the causal effect of the IV on the treatment is not confounded. Hernán and Robins () and Vansteelandt and Didelez () instead assumed absence of treatment effect modification by the instrument among the treated and untreated population respectively.…”

Compared to what? Variation in the impacts of early childhood education by alternative care type

“…In high dimensions, however, this is impractical. Instead, we recommend a simple data augmentation strategy, due to Ibrahim (1990) and applied to causal inference by, among others, Aronow and Carnegie (2013) and Hsu and Small (2014). The essential idea is to use the same model as in Section B.3, except without any outcomes:…”