I remember that very many unemployment people rather got into some free job training programs to prolong their time to be electable for unemployment or social security benefits and worked "schwarz" in addition to make themselves an acceptable way of living. Is that still the case?
Yes, the statistics changed January 2005. Till December 2004 the unemployment statistics only included "unemployed" workers. And not the people living on social benefits. That inclusion probably added around 100,000 people?
Some of them might actually earn less if they work in an official job instead of them staying unemployed?
