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)

grade = grade required by the vacancy

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

read /scratch/hpc/22/stott/vwks4emp_vars.dat

case first=vacref second=empref

yvar match

link c

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

<S> read /scratch/hpc/22/stott/vwks4emp_vars.dat

 

     137223 observations in dataset

 

<S> case first=vacref second=empref

<S> yvar match

<S> link c

<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

    grade

    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

    grade                 -0.11449          0.42496E-01

    dayrel                -0.47149          0.95122E-01

    sclev2                  1.5825          0.81508E-01

    sclev3                 0.82271          0.55584E-01

 

<S> stop