Example 3LC4. Event history, cloglog link model: time to fill vacancies of firms (9556 vacancies in 4121 firms)

This is a study of the length of time (level 1, observed at the weekly level) needed to fill vacancies (level 2) by employers (level 3) in the vacancy data set vwks4emp_vars.dat.  We estimate a stock model of the duration of the vacancy; in addition to the firm’s characteristics and those of the vacancy, we use covariates which represent the stock of the labour market at the current duration, i.e. the total number of job-seekers (logged) and the total number of vacancies (logged) in the local labour market.

We use a 10-piece non-parametric baseline hazard for spell duration (t) with 8 covariates (loguu, logvv, nonman, written, size, wage, grade, dayrel).  Many of the baseline dummy variables coefficients are similar. The level-2 random effect standard deviation (sclev2) is 1.5825   (SE=0.81508E-01), and the level-3 random effect standard deviation (sclev3) is 0.82271 (SE=0.55584E-01).

Reference

Andrews, M., Bradley, S., Stott, D., Upward, R.,  (2007), Testing theories of labour market matching, http://ideas.repec.org/p/ecj/ac2003/209.html

Data description

Number of observations = 137223 (weeks)

Number of level-2 cases (‘vacref’ = identifier for vacancy) = 9556

Number of level-3 cases (‘empref’ = identifier for firm) =  4121

The variables are:

match = 1 if vacancy filled, 0 otherwise in a particular week

nonman = 1 if a non-manual vacancy, 0 otherwise

written = 1 if vacancy required a written method of application, 0 otherwise

size = firm size of the vacancy

wage = log wage of the vacancy

vacref = vacancy reference (a number)

empref = employer reference (a number)

dayrel = 1 if day release available to the post, 0 otherwise

t = vacancy duration (see below)

loguu = log of stock of job-seekers in the local labour market

logvv = log of stock of vacancies in the local labour market

The covariate (t) for the baseline hazard is defined as follows:

t=1, week 1

t=2, week 2

t=3, weeks 3-4

t=4, weeks 5-6

t=5, weeks 7-8

t=6, weeks 9-13

t=7, weeks 14-26

t=8, weeks 27-39

t=9, weeks 40-52

t=10, weeks 53+

The first few lines and columns of vwks4emp_vars.dat look like:

Sabre commands

out vwks.log

data match nonman written size wage vacref grade empref dayrel t loguu logvv

case first=vacref second=empref

yvar match

fac t ft

mass first=36 second=36

ari a

fit ft loguu logvv nonman written size wage grade dayrel

dis m

dis e

stop

Sabre log file

<S> data match nonman written size wage vacref grade empref dayrel t loguu logvv

137223 observations in dataset

<S> case first=vacref second=empref

<S> yvar match

<S> fac t ft

<S> mass first=36 second=36

<S> ari a

<S> fit ft loguu logvv nonman written size wage grade dayrel

Initial Homogeneous Fit:

Iteration       Log. lik.       Difference

__________________________________________

1          -135728.40

2          -30135.093       0.1056E+06

3          -16451.118       0.1368E+05

4          -12818.836        3632.

5          -11849.767        969.1

6          -11645.414        204.4

7          -11625.888        19.53

8          -11625.385       0.5024

9          -11625.383       0.2028E-02

10          -11625.383       0.6999E-07

Iteration       Log. lik.         Step      End-points     Orthogonality

length    0          1      criterion

________________________________________________________________________

1          -11490.967        1.0000    fixed  fixed       86.522

2          -11448.769        1.0000    fixed  fixed       416.96

3          -11344.893        1.0000    fixed  fixed       84.301

4          -11326.158        1.0000    fixed  fixed       70.470

5          -11319.106        1.0000    fixed  fixed       254.56

6          -11312.097        1.0000    fixed  fixed       58.089

7          -11225.904        1.0000    fixed  fixed       5.9514

8          -11217.031        1.0000    fixed  fixed       4.3284

9          -11216.895        1.0000    fixed  fixed       36.100

10          -11216.894        1.0000    fixed  fixed       30.277

11          -11216.894        1.0000    fixed  fixed

<S> dis m

X-vars            Y-var             Case-var

________________________________________________

ft                match             vacref

loguu                               empref

logvv

nonman

written

size

wage

dayrel

Univariate model

Standard complementary log-log

Gaussian random effects

Number of observations             =  137223

Number of level 2 cases            =    9556

Number of level 3 cases            =    4121

X-var df           =    18

Scale df           =     2

Log likelihood =     -11216.894     on  137203 residual degrees of freedom

<S> dis e

Parameter              Estimate         Std. Err.

___________________________________________________

ft          ( 1)       -9.0599          0.57617

ft          ( 2)       -8.9999          0.56647

ft          ( 3)       -9.0236          0.56146

ft          ( 4)       -9.2420          0.56123

ft          ( 5)       -9.6414          0.56567

ft          ( 6)       -9.8594          0.56298

ft          ( 7)       -9.5458          0.56487

ft          ( 8)       -9.5306          0.57795

ft          ( 9)       -9.3870          0.59536

ft          (10)       -9.9367          0.61382

loguu                  0.86470          0.63310E-01

logvv                 -0.73230E-01      0.48542E-01

nonman                -0.35115          0.75405E-01

written               -0.83641          0.94974E-01

size                  -0.34307E-01      0.23184E-01

wage                  -0.17708E-02      0.38449E-01