Table 3 Estimated hazard ratios for the piecewise exponential models of the apprenticeship non-completion hazard

\(W/W^{(l)}\)

0.019\(***\)

(0.001)

0.022\(***\)

(0.002)

0.023\(***\)

(0.002)

\(ln \text { }W^{(m)}\)

0.538\(***\)

(0.017)

0.441\(***\)

(0.027)

0.456\(***\)

(0.028)

Time

(ref: (547–1000] days)

   (0–60]

1.372\(***\)

(0.036)

1.088\(**\)

(0.029)

0.985

(0.027)

   (60–121]

2.094\(***\)

(0.049)

1.691\(***\)

(0.040)

1.536\(***\)

(0.038)

   (121–212]

1.616\(***\)

(0.038)

1.382\(***\)

(0.033)

1.296\(***\)

(0.031)

   (212–425]

1.112\(***\)

(0.023)

0.984

(0.029)

0.933\(**\)

(0.020)

   (425–547]

1.107\(***\)

(0.029)

1.020

(0.027)

0.983

(0.026)

Female

0.944\(**\)

(0.021)

0.864\(***\)

(0.023)

High school diploma

(ref: lowest track)

   None

0.908\(***\)

(0.023)

0.907\(***\)

(0.027)

   Intermediate track

0.734\(***\)

(0.013)

0.733\(***\)

(0.013)

   Academic track

0.596\(***\)

(0.016)

0.590\(***\)

(0.016)

Start. age

1.986\(***\)

(0.113)

2.023\(***\)

(0.116)

Start. age sqr.

0.985\(***\)

(0.001)

0.984\(***\)

(0.001)

Start. year

1.134\(***\)

(0.003)

1.187\(***\)

(0.005)

Foreign

1.098\(**\)

(0.031)

1.106\(***\)

(0.031)

Est. size

(ref: 1–49 employees)

   50–249

0.846\(***\)

(0.018)

0.859\(***\)

(0.005)

   250+

0.787\(***\)

(0.023)

0.798\(***\)

(0.023)

Est. age

0.991\(***\)

(0.001)

0.991\(***\)

(0.001)

East Germany

0.831\(***\)

(0.021)

0.975

(0.030)

Industry

(ref: Retail/wholesale/gastronomy)

   Farming/fishing/forestry

1.046

(0.080)

1.039

(0.079)

   Earths/food/textiles

0.724\(***\)

(0.028)

0.719\(***\)

(0.028)

   Chemical/oil/metal

0.586\(***\)

(0.023)

0.581\(***\)

(0.023)

   Electronics/vehicles/misc. prod.

0.627\(***\)

(0.031)

0.617\(***\)

(0.030)

   Construction/water, energy supply

0.817\(***\)

(0.032)

0.815\(***\)

(0.032)

   Logistics/Postal/Banking

0.964

(0.043)

0.961

(0.043)

   Public/private services

0.848\(***\)

(0.029)

0.843\(***\)

(0.028)

   Health/education

1.260\(***\)

(0.036)

1.309\(***\)

(0.038)

   NGOs/culture/sports

1.218\(***\)

(0.043)

1.229\(***\)

(0.044)

SDR

0.728

(0.123)

MES

1.286\(***\)

(0.058)

\(u^{(l)}/u^{(m)}\)

0.770\(***\)

(0.013)

\(u^{(h)}/u^{(m)}\)

1.438\(***\)

(0.087)

Constant

0.012\(***\)

(0.002)

0.000\(***\)

(0.000)

0.000\(***\)

(0.000)

\(\theta\)

0.216

0.125

0.115

LR-test of \(\theta\)

3,610

1,912

1,509

Log pseudolikelihood

− 174,247

− 171,639

− 171,485

Wald test

5,534

10,542

10,821

AIC

348,513

343,338

343,038