Instrumental Variable Estimation in Demographic Studies: The LATE interpretation of the IV estimator with heterogenous effects

Heterogeneous effects of treatment on an outcome is a plausible assumption to make about the vast majority of causal relationships studied in the social sciences. In these circumstances the IV estimator is often interpreted as yielding an estimate of a Local Average Treatment Effect (LATE): a marginal change in the outcome for those whose treatment is changed by the variation of the particular instrument in the study. Our aim is to explain the relationship between the LATE parameter and its IV estimator by using a simple model which is easily accessible to applied researchers, and by relating the model to examples from the demographic literature. A focus of the paper is how additional heterogeneity in the instrument – treatment relationship affects the properties and interpretation of the IV estimator. We show that if the two kinds of heterogeneity are correlated, then the LATE parameter combines both the underlying treatment effects and the parameters from the instrument – treatment relationship. It is then a more complicated concept than many researchers realise.

Instrumental variable estimation of truncated local average treatment effects

Instrumental variable (IV) analysis is used to address unmeasured confounding when comparing two nonrandomized treatment groups. The local average treatment effect (LATE) is a causal estimand that can be identified by an IV. The LATE approach is appealing because its identification relies on weaker assumptions than those in other IV approaches requiring a homogeneous treatment effect assumption. If the instrument is confounded by some covariates, then one can use a weighting estimator, for which the outcome and treatment are weighted by instrumental propensity scores. The weighting estimator for the LATE has a large variance when the IV is weak and the target population, i.e., the compliers, is relatively small. We propose a truncated LATE that can be estimated more reliably than the regular LATE in the presence of a weak IV. In our approach, subjects who contribute substantially to the weak IV are identified by their probabilities of being compliers, and they are removed based on a pre-specified threshold. We discuss interpretation of the proposed estimand and related inference method. Simulation and real data experiments demonstrate that the proposed truncated LATE can be estimated more precisely than the standard LATE.

Estimation of local treatment effects under the binary instrumental variable model

Instrumental variables are widely used to deal with unmeasured confounding in observational studies and imperfect randomized controlled trials. In these studies, researchers often target the so-called local average treatment effect as it is identifiable under mild conditions. In this paper, we consider estimation of the local average treatment effect under the binary instrumental variable model. We discuss the challenges for causal estimation with a binary outcome, and show that surprisingly, it can be more difficult than the case with a continuous outcome. We propose novel modelling and estimating procedures that improve upon existing proposals in terms of model congeniality, interpretability, robustness and efficiency. Our approach is illustrated via simulation studies and a real data analysis.

Instruments with Heterogeneous Effects: Bias, Monotonicity, and Localness

In Instrumental Variables (IV) estimation, the effect of an instrument on an endogenous variable may vary across the sample. In this case, IV produces a local average treatment effect (LATE), and if monotonicity does not hold, then no effect of interest is identified. In this paper, I calculate the weighted average of treatment effects that is identified under general first-stage effect heterogeneity, which is generally not the average treatment effect among those affected by the instrument. I then describe a simple set of data-driven approaches to modeling variation in the effect of the instrument. These approaches identify a Super-Local Average Treatment Effect (SLATE) that weights treatment effects by the corresponding instrument effect more heavily than LATE. Even when first-stage heterogeneity is poorly modeled, these approaches considerably reduce the impact of small-sample bias compared to standard IV and unbiased weak-instrument IV methods, and can also make results more robust to violations of monotonicity. In application to a published study with a strong instrument, the preferred approach reduces error by about 19% in small (N ≈ 1, 000) subsamples, and by about 13% in larger (N ≈ 33, 000) subsamples.

Intangible Capital and Leverage

We investigate the causal effect of intangible capital on leverage. To address endogeneity, we exploit patent invalidations by a U.S. court in which judges are randomly assigned to cases. Differences in judge leniency provide exogenous variation in the probability that firms’ patents are invalidated. Using this probability as an instrument for exogenous losses in intangible capital, we find a patent invalidation leads to a 14.1% reduction in leverage, suggesting that intangible capital causally supports leverage. This local average treatment effect is stronger in firms that use patents as loan collateral and in less creditworthy as well as smaller firms.

Profiling Compliers and Noncompliers for Instrumental-Variable Analysis

Instrumental-variable (IV) estimation is an essential method for applied researchers across the social and behavioral sciences who analyze randomized control trials marred by noncompliance or leverage partially exogenous treatment variation in observational studies. The potential outcome framework is a popular model to motivate the assumptions underlying the identification of the local average treatment effect (LATE) and to stratify the sample into compliers, always-takers, and never-takers. However, applied research has thus far paid little attention to the characteristics of compliers and noncompliers. Yet, profiling compliers and noncompliers is necessary to understand what subpopulation the researcher is making inferences about and an important first step in evaluating the external validity (or lack thereof) of the LATE estimated for compliers. In this letter, we discuss the assumptions necessary for profiling, which are weaker than the assumptions necessary for identifying the LATE if the instrument is randomly assigned. We introduce a simple and general method to characterize compliers, always-takers, and never-takers in terms of their covariates and provide easy-to-use software in R and STATA that implements our estimator. We hope that our method and software facilitate the profiling of compliers and noncompliers as a standard practice accompanying any IV analysis.