Results of the DiD approach

The coefficient of interest \(\delta\) can easily be taken from Table 2 as the coefficient related to the interaction term in equation (3). The three specifications yield quantitatively significant effects and vary only slightly. Bauernschuster & Schlotter estimate that through the reform the employment of the respective mothers was increased by 5 percentage points according the the specification in which the authors use the mothers of 10 and 11 year old children as control group and up to 8 percentage points when all 29 to 36 year old women without children. To make this estimates comparable to those obtained in the IV estimation, it is crucial to know that between 1996 and 2001 the childcare attendance rate of three and four year old children in the sample increased by 17 percentage points from 53 to 70 percent. This means that an increase calulated for an 10 percentage point increase in the attendance rate results in a 3 percentage point increase in maternal employment (if we again assume linearity here). This estimate is nearly the same point estimate as the coefficient for the iV estimate. This result is a first indication that both approaches identify the true effect of public childcare on maternal employment. 
However it must be stated that this interpretation of Bauernschuster & Schlotter seems rather sloppy if one considers the following two imprecisions. Firstly the effect has almost the same magnitude if we take the 10 and 11 year old children but this is only one of three control groups and yields the lowest estimate of all three different specifications. If someone would for example calculate the effect obtained for the second control group the effect would be larger with 4.7 percentage points per 10 percentage points increase in availability. Even more staggering is the wrong computation of the effect in the preferred specification of Bauernschuster & Schlotter. To calculate the effect of a ten percentage points expansion of public childcare they randomly state that the increase in childcare attendance was from 55 to 70 percent instead of the 53 and 70 percent the authors present their readers one page before. Thereby the effect observed changes from 3.0 (true value) to 3.4 (what the authors report) percentage points per ten percentage points increase in kindergarten attendance. Although that might be not significant it is a mentionable inaccuracy of the paper.