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Table 6 Estimation results for the Cox model and RI Logit model

From: Apprenticeship non-completion in Germany: a money matter?

 

Model of Table 3,

  

column 3

Cox

RI Logit

HR

SE

HR

SE

Coef.

SE

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

0.023\(***\)

(0.002)

0.023\(***\)

(0.002)

− 5.189\(***\)

(0.088)

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

0.456\(***\)

(0.028)

0.464\(***\)

(0.028)

− 1.923\(***\)

(0.083)

Female

0.864\(***\)

(0.023)

0.875\(***\)

(0.116)

− 0.598\(***\)

(0.034)

High school diploma

      

(ref:lowest track)

      

   None

0.907\(***\)

(0.027)

0.906\(***\)

(0.023)

− 0.052

(0.032)

   Intermediate track

0.733\(***\)

(0.013)

0.732\(***\)

(0.013)

− 0.365\(***\)

(0.022)

   Academic track

0.590\(***\)

(0.016)

0.588

(0.016)

− 0.651\(***\)

(0.033)

Start. age

2.023\(***\)

(0.116)

2.026\(***\)

(0.116)

0.817\(***\)

(0.071)

Start. age sqr.

0.984\(***\)

(0.001)

0.984\(***\)

(0.002)

− 0.019\(***\)

(0.002)

Start. year

1.187\(***\)

(0.005)

1.180\(***\)

(0.005)

0.180\(***\)

(0.004)

Foreign

1.106\(***\)

(0.031)

1.108\(***\)

(0.031)

0.114\(**\)

(0.037)

Est. size

      

(ref: 1–49 employees)

      

50–249

0.859\(***\)

(0.005)

0.857\(***\)

(0.018)

− 0.012

(0.027)

   250+

0.798\(***\)

(0.023)

0.796\(***\)

(0.023)

0.070

(0.368)

Est. age

0.991\(***\)

(0.001)

0.991\(***\)

(0.001)

− 0.009\(***\)

(0.001)

East Germany

0.975

(0.030)

0.972

(0.030)

− 0.029

(0.039)

Industry

      

(ref: Retail/wholesale/gastronomy)

      

   Farming/fishing/forestry

1.039

(0.079)

1.038

(0.079)

− 0.247\(*\)

(0.097)

   Earths/food/textiles

0.719\(***\)

(0.028)

0.721\(***\)

(0.028)

− 0.0475\(***\)

(0.050)

   Chemical/oil/metal

0.581\(***\)

(0.023)

0.586\(***\)

(0.023)

− 0.453\(***\)

(0.046)

   Electronics/vehicles/misc. prod.

0.617\(***\)

(0.030)

0.618\(***\)

(0.030)

-0.360\(***\)

(0.055)

   Construction/water, energy supply

0.815\(***\)

(0.032)

0.813\(***\)

(0.032)

− 0.071

(0.047)

   Logistics/Postal/Banking

0.961

(0.043)

0.957

(0.042)

0.117\(*\)

(0.054)

   Public/private services

0.843\(***\)

(0.028)

0.845\(***\)

(0.028)

− 0.209\(***\)

(0.040)

   Health/education

1.309\(***\)

(0.038)

1.321\(***\)

(0.038)

0.243\(***\)

(0.037)

   NGOs/culture/sports

1.229\(***\)

(0.044)

1.242\(***\)

(0.044)

0.076

(0.048)

SDR

0.728

(0.123)

0.806

(0.136)

− 1.407\(***\)

(0.217)

MES

1.286\(***\)

(0.058)

1.269\(***\)

(0.057)

0.091

(0.057)

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

0.770\(***\)

(0.013)

0.783\(***\)

(0.013)

− 0.621\(***\)

(0.019)

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

1.438\(***\)

(0.087)

1.389\(***\)

(0.084)

1.605\(***\)

(0.079)

Constant

0.000\(***\)

(0.000)

  

− 359.088\(***\)

(8.193)

\(\theta\)

0.115

0.115

0.266

LR-test

1,509

1,510

1,631

Log likelihood

− 171,485

− 213,676

− 40,600

Wald test

10,821

8,419

9,271

AIC

343,038

427,405

81,257

Observations

641,921

255,403

94,223

  1. \(***\)p < 0.001, \(**\)p < 0.01, \(*\)p < 0.05, n = 94,223 apprenticeships, f = 19,697 non-completion. The table reports conditional hazard ratios (HR) of the fixed component for the Cox model and PWE model and coefficients (coeff.) for the RI logit model. Estimates are adjusted for shared frailties in 35 occupation clusters. SE denotes occupation cluster robust standard errors. The Cox model uses the Efron method for ties. The RI logit specification uses mean-variance adaptive Gauss-Hermite quadrature as integration method. For the Cox model, a partial log likelihood is reported. \(W/W^{(l)}\) refers to the apprenticeship wage in relation to low skilled workers wage, \(ln \text { }W^{(m)}\) to the natural logarithm of daily skilled worker wage, SDR to the supply-demand ratio of apprenticeships, MES to the marginal employment share of the establishment, u to the number of unemployment days, and \(\theta\) to the variance of the shared frailty