  Weighting methods are used in observational studies to adjust for covariate
imbalances between treatment and control groups. Entropy balancing (EB) is an
alternative to inverse probability weighting with an estimated propensity
score. The EB weights are constructed to satisfy balance constraints and
optimized towards stability. We describe large sample properties of EB
estimators of the average causal treatment effect, based on the
Kullback-Leibler and quadratic R\'enyi relative entropies. Additionally, we
propose estimators of their asymptotic variances. Even though the objective of
EB is to reduce model dependence, the estimators are generally not consistent
unless implicit parametric assumptions for the propensity score or conditional
outcomes are met. The finite sample properties of the estimators are
investigated through a simulation study. In an application with observational
data from the Swedish Childhood Diabetes Register, we estimate the average
effect of school achievements on hospitalization due to acute complications of
type 1 diabetes mellitus.
