Some (maybe) unpleasant arithmetic in minimum wage evaluations: The role of power, significance and sample size

In this paper, we discuss the importance of sample size in the evaluation of minimum wage effects. We first show which sample sizes are necessary to make reliable statements about the effects of minimum wages on binary outcomes, and second how to determine these sample sizes. This is particularly important when interpreting statistically insignificant effects, which could be due to (i) the absence of a true effect or (ii) lack of statistical power, which makes it impossible to detect an effect even though it exists. We illustrate this for the analysis of labour market transitions using two data sets which are particularly important in the minimum wage research for Germany, the Integrated Labour Market Biographies (IEB) and the Socio-Economic Panel (SOEP).