  This paper provides asymptotically valid tests for the null hypothesis of no
treatment effect heterogeneity. Importantly, I consider the presence of
heterogeneity that is not explained by observed characteristics, or so-called
idiosyncratic heterogeneity. When examining this heterogeneity, common
statistical tests encounter a nuisance parameter problem in the average
treatment effect which renders the asymptotic distribution of the test
statistic dependent on that parameter. I propose an asymptotically valid test
that circumvents the estimation of that parameter using the empirical
characteristic function. A simulation study illustrates not only the test's
validity but its higher power in rejecting a false null as compared to current
tests. Furthermore, I show the method's usefulness through its application to a
microfinance experiment in Bosnia and Herzegovina. In this experiment and for
outcomes related to loan take-up and self-employment, the tests suggest that
treatment effect heterogeneity does not seem to be completely accounted for by
baseline characteristics. For those outcomes, researchers could potentially try
to collect more baseline characteristics to inspect the remaining treatment
effect heterogeneity, and potentially, improve treatment targeting.
