Table 8 Estimated hazard ratios for the piecewise exponential model of the apprenticeship non-completion hazard for different censoring dates

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

0.023\(***\)

(0.002)

0.022\(***\)

(0.002)

0.016\(***\)

(0.001)

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

0.456\(***\)

(0.028)

0.463\(***\)

(0.029)

0.437\(***\)

(0.028)

Time

(ref: (547–1000] days)

   (0–60]

0.985

(0.027)

0.931\(*\)

(0.026)

0.865\(***\)

(0.027)

   (60–121]

1.536\(***\)

(0.038)

1.451\(***\)

(0.036)

1.351\(***\)

(0.038)

   (121–212]

1.296\(***\)

(0.031)

1.222\(***\)

(0.030)

1.148\(***\)

(0.031)

   (212–425]

0.933\(**\)

(0.020)

0.880\(***\)

(0.019)

0.833\(***\)

(0.021)

   (425–547]

0.983

(0.026)

0.928\(***\)

(0.025)

0.885\(***\)

(0.026)

Female

0.864\(***\)

(0.023)

0.871\(***\)

(0.023)

0.865\(***\)

(0.024)

High school diploma

(ref: lowest track)

   None

0.907\(***\)

(0.027)

0.900\(***\)

(0.023)

0.899\(***\)

(0.024)

   Intermediate track

0.733\(***\)

(0.013)

0.737\(***\)

(0.013)

0.741\(***\)

(0.014)

   Academic track

0.590\(***\)

(0.016)

0.587\(***\)

(0.016)

0.590\(***\)

(0.017)

Start. age

2.023\(***\)

(0.116)

1.995\(***\)

(0.115)

1.998\(***\)

(0.121)

Start. age sqr.

0.984\(***\)

(0.001)

0.985\(***\)

(0.001)

0.984\(***\)

(0.002)

Start. year

1.187\(***\)

(0.005)

1.185\(***\)

(0.005)

1.195\(***\)

(0.005)

Foreign

1.106\(***\)

(0.031)

1.101\(**\)

(0.032)

1.113\(***\)

(0.033)

Est. size

(ref: 1–49 employees)

   50–249

0.859\(***\)

(0.005)

0.861\(***\)

(0.018)

0.858\(***\)

(0.019)

   250+

0.798\(***\)

(0.023)

0.800\(***\)

(0.023)

0.801\(***\)

(0.025)

Est. age

0.991\(***\)

(0.001)

0.991\(***\)

(0.001)

0.990\(***\)

(0.001)

East Germany

0.975

(0.030)

0.980

(0.030)

0.979

(0.032)

Industry

(ref: Retail/wholesale/gastronomy)

   Farming/fishing/forestry

1.039

(0.079)

1.032

(0.079)

1.086

(0.086)

   Earths/food/textiles

0.719\(***\)

(0.028)

0.709\(***\)

(0.028)

0.696\(***\)

(0.029)

   Chemical/oil/metal

0.581\(***\)

(0.023)

0.581\(***\)

(0.023)

0.576\(***\)

(0.025)

   Electronics/vehicles/misc. prod.

0.617\(***\)

(0.030)

0.613\(***\)

(0.030)

0.592\(***\)

(0.031)

   Construction/water, energy supply

0.815\(***\)

(0.032)

0.810\(***\)

(0.032)

0.821\(***\)

(0.035)

   Logistics/Postal/Banking

0.961

(0.043)

0.959

(0.043)

0.885\(*\)

(0.043)

   Public/private services

0.843\(***\)

(0.028)

0.849\(***\)

(0.029)

0.859\(***\)

(0.031)

   Health/education

1.309\(***\)

(0.038)

1.301\(***\)

(0.038)

1.256\(***\)

(0.038)

   NGOs/culture/sports

1.229\(***\)

(0.044)

1.226\(***\)

(0.044)

1.198\(***\)

(0.045)

SDR

0.728

(0.123)

0.779

(0.133)

0.697\(*\)

(0.126)

MES

1.286\(***\)

(0.058)

1.293\(***\)

(0.059)

1.335\(***\)

(0.063)

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

0.770\(***\)

(0.013)

0.774\(***\)

(0.013)

0.753\(***\)

(0.013)

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

1.438\(***\)

(0.087)

1.413\(***\)

(0.086)

1.482\(***\)

(0.095)

Constant

0.000\(***\)

(0.000)

0.000\(***\)

(0.000)

0.000\(***\)

(0.000)

\(\theta\)

0.115

0.117

0.134

LR-test of \(\theta\)

1,509

1,493

1,510

Log pseudolikelihood

− 171,485

− 168,037

− 150,392

Wald test

10,821

10,276

9,497

AIC

343,038

336,142

300,852

Observations

641,921

641,122

599,852

Apprenticeships

94,223

94223

94,223

Non-completion

19,697

19,362

17,495