"What does the German minimum wage do?" is published by baua: Preprint and can be viewed as a PDF here.

Abstract
In this article, we examine structural changes in minimum-wage and low-wage labour after the introduction and first increase of the German minimum wage. Changes in the risks workers face of earning gross hourly wages below the minimum-wage or low-wage thresholds are identified by comparing individual, company-level and sectoral characteristics based on the Structure of Earnings Surveys (SESs) 2014 and 2018. The SES is a mandatory survey of companies that provides information on wages and working hours for approximately 1 million jobs and nearly 70,000 companies from all industries. Using these rich data, we present the first systematic analysis of how structural changes in individual-, company-, and industry-level determinants affect minimum- and low-wage workers. Using a descriptive analysis, we first summarize the changing pattern in jobs, companies, and industries after the minimum wage introduction. Second, we use random intercept-only models to estimate the explanatory power of the individual, company, and industry levels in the years 2014 and 2018 respectively. Third, we perform logistic and linear regression estimations to assess the changing risks of having a minimum- or low-wage job and the distance between a worker’s actual earnings and the minimum and low-wage thresholds. We conclude that the minimum wage had an elevator effect regarding minimum-wage labour. However, compositional effects regarding the minimum-wage and low-wage workforce were evident in terms of individual and company factors. There was a selective redistribution of minimum-wage employees into slightly higher wage ranges. Furthermore, convergence seems to have occurred predominantly among sectors, as their explanatory power for lower wages declined.