Table 9 Estimated hazard ratios for the piecewise exponential model of the apprenticeship non-completion hazard accounting for interaction effects

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

0.022\(***\)

(0.004)

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

0.618\(***\)

(0.059)

Time

(ref: (547–1000] days)

   (0–60]

144.807\(***\)

(57.156)

   (60–121]

27.609\(***\)

(9.923)

   (121–212]

2.289\(*\)

(0.841)

   (212–425]

7.326\(***\)

(2.419)

   (425–547]

1.142

(0.476)

Female

0.349\(***\)

(0.094)

high school diploma

(ref: lowest track)

   None

1.340

(0.492)

   Intermediate track

1.374

(0.364)

   Academic track

0.983

(0.408)

Start. age

1.990\(***\)

(0.114)

Start. age sqr.

0.985\(***\)

(0.001)

Start. year

1.188\(***\)

(0.005)

Foreign

1.105\(***\)

(0.031)

Est. size

(ref: 1–49 employees)

   50–249

0.771

(0.236)

   250+

0.647

(0.222)

Est. age

0.991\(***\)

(0.001)

East Germany

0.965

(0.030)

Industry

(ref: Retail/wholesale/gastronomy)

   Farming/fishing/forestry

1.036

(0.079)

   Earths/food/textiles

0.710\(***\)

(0.028)

   Chemical/oil/metal

0.581\(***\)

(0.023)

   Electronics/vehicles/misc. prod.

0.620\(***\)

(0.030)

   Construction/water, energy supply

0.803\(***\)

(0.032)

   Logistics/Postal/Banking

0.966

(0.043)

   Public/private services

0.838\(***\)

(0.029)

   Health/education

1.295\(***\)

(0.038)

   NGOs/culture/sports

1.219\(***\)

(0.044)

SDR

0.698\(*\)

(0.119)

MES

1.291\(***\)

(0.058)

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

0.766\(***\)

(0.013)

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

1.430\(***\)

(0.087)

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

(ref: (547–1000] days)

   (0–60]

0.356\(***\)

(0.087)

   (60–121]

0.671

(0.143)

   (121–212]

0.820

(0.171)

   (212–425]

0.114\(***\)

(0.022)

   (425–547]

0.609\(*\)

(0.148)

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

2.128\(***\)

(0.297)

High school diploma\(\times W/W^{(l)}\)

(ref: lowest track)

   None

0.810

(0.185)

   Intermediate track

0.811

(0.128)

   Academic track

3.345\(***\)

(0.693)

Est. size\(\times W/W^{(l)}\)

(ref: 1–49 employees)

   50–249

1.288

(0.208)

   250+

2.010\(***\)

(0.361)

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

(ref: (547–1000] days)

   (0–60]

0.332\(***\)

(0.030)

   (60–121]

0.525\(***\)

(0.042)

   (121–212]

0.894

(0.073)

   (212–425]

0.721\(***\)

(0.053)

   (425–547]

1.005

(0.093)

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

1.168\(*\)

(0.071)

High school diploma\(\times ln \text { }W^{(m)}\)

(ref: lowest track)

   None

0.923

(0.077)

   Intermediate track

0.875\(*\)

(0.052)

   Academic track

0.810\(*\)

(0.074)

Est. size\(\times ln \text { }W^{(m)}\)

(ref: 1–49 employees)

   50–249

1.005

(0.070)

   250+

0.999

(0.081)

Constant

0.000\(***\)

(0.000)

\(\theta\)

0.118

LR-test of \(\theta\)

1536

Log pseudolikelihood

− 171,247

Wald test

11,449

AIC

342,607