  Applied analysts often use the differences-in-differences (DID) method to
estimate the causal effect of policy interventions with observational data. The
method is widely used, as the required before and after comparison of a treated
and control group is commonly encountered in practice. DID removes bias from
unobserved time-invariant confounders. While DID removes bias from
time-invariant confounders, bias from time-varying confounders may be present.
Hence, like any observational comparison, DID studies remain susceptible to
bias from hidden confounders. Here, we develop a method of sensitivity analysis
that allows investigators to quantify the amount of bias necessary to change a
study's conclusions. Our method operates within a matched design that removes
bias from observed baseline covariates. We develop methods for both binary and
continuous outcomes. We then apply our methods to two different empirical
examples from the social sciences. In the first application, we study the
effect of changes to disability payments in Germany. In the second, we
re-examine whether election day registration increased turnout in Wisconsin.
