The importance of owner-managed SMEs and regional apprenticeship activity: evidence from the German Mittelstand

Empirical Research in Vocational Education and Training

Table 3 Manski model

	Direct effects	Indirect effects	Total effects
Share of Mittelstand firms	0.0218*	− 0.0849*	− 0.0631
Unemployment rate	0.0273	0.0280	0.0553
Unemployed potential trainees	0.0580***	0.2556***	0.3136***
Medium-skilled potential trainees	0.6358	− 8.1262	− 7.4904
High-skilled potential trainees	− 0.6437	1.0097	0.3660
Size of universities	− 0.0666	− 0.5825	− 0.6491
Distance to universities	0.0066***	0.0028	0.0094
Small firms	0.0916*	− 0.0758	0.0158
Large firms	0.0040	0.7407	0.7447
Working-age population	0.0103	0.1370	0.1474
Population density	0.0000	0.0002	0.0002
GDP per capita	− 0.0162**	0.0132	− 0.0030
CDU/CSU/FDP	0.0306***	− 0.0389	− 0.0083
Other parties	0.0309	− 0.0799	− 0.0489
N	326
Nagelkerke	0.8386
\(\rho\)	0.5222 (0.0000)
\(\lambda\)	− 0.7407 (0.0000)

Industrial sectors and occupations are further controls not reported in this table. Additional file 1: Table S6 reports the results of the Manski model including sectors and occupations
*** p < 0.01, ** p < 0.05, * p < 0.1.