Further robustness for the estimates comes from regressiounswherre Bauernschuster & Schlotter change the dependent variable to the number of hours worked. In this specification they use the same IV approach and come to results which have rougly the same magnitude as the estimates from LPM described the results section: For both specifications (with and without control variables) the IV yields 14 hours of additional working time per week, yielding 1.4 additional working hours if we assume that childcare attendance increases by 10 percentage points. This is mentionable and statistically significant but in no direction surprising. Therefore this regression adds further credibilty to the IV estimate (having in mind what LATE they identify).

Robustness of the DiD

Besides the control groups used which actually reduce the trust in the estimate of Bauernschuster & Schlotter (see Critical Discussion of the Results), the authors also employ a placebo test to validate that actually identify a causal effect and not a time trend or something which varies over the whole population. Indeed the estimated coefficients are all not distinguishable from zero and therefore support the common trends assumption and the relevance of the introduction of the legal claim.
Decomposing the effect on a year basis shows clearly that before the reform no effects were observable. In contrast to that after the reform the effect gradually increases over time, demonstrating that the reform needed some time to affect womens labor supply decision but clearly affected maternal labor supply five years later considerably. This decomposition first shows the existence of an effect and secondly its evolvement over time. Furthermore it increases the confidence in the common trend assumption.