**Exercise L10, bivariate model, linear and binary**

Vella and Verbeek (1998) analysed the male data from the Youth Sample of the US National Longitudinal Survey for the period 1980-1987. The number of young males in the sample is 545. The version of the data set (wagepan.dat) we use was obtained from Wooldridge (2002). The same data were used for modelling the wages and for separately modelling trade union membership by Rabe-Hesketh and Skrondal (2005, exercises 2.7 and 4.7). We start by re-estimating the separate models for log(wages) and for trade union membership. We then estimate a joint model thus allowing trade union membership to be endogenous in the wage equation.

**Data description**

Number of observations (rows): 4360

Number of variables (columns): 44

Description of the sub-set of variables we are going to use in this exercise:

nr= person identifier

year=1980 to 1987

black=1 if respondent is black,0 otherwise

exper=labour market experience (age-6-educ)

hisp=1 if respondent is Hispanic, 0 otherwise

poorhlth=1 if respondent has a health disability, 0 otherwise

married=1 if respondent is married, 0 otherwise

nrthcen=1 if respondent lives in the Northern Central part of the

nrtheast=1 if respondent lives in the North East part of the

rur=1 if respondent lives in a rural area, 0 otherwise

south=1 if respondent lives in the
South of the

educ=years of schooling

union=1 if the respondent is a member of a trade union, 0 otherwise

lwage=log of hourly wage in US dollars

d8m=1 if the year is 198m, 0 otherwise, m=1,…,7

The first few rows and columns of the data for the univariate models look like:

Start Sabre and specify transcript file:

out union-wage.log

data nr year agric black bus construc ent exper fin hisp poorhlth hours &

manuf married min nrthcen nrtheast occ1 occ2 occ3 occ4 occ5 occ6 occ7 &

occ8 occ9 per pro pub rur south educ tra trad union lwage d81 d82 d83 &

d84 d85 d86 d87 expersq

read wagepan.dat

**Suggested exercise**

Wage equation

(1) Estimate a linear model for lwage (log of hourly wage) with the covariates (educ, black, hisp, exper, expersq, married, union, d8m, m=1,2,…,7) and the respondent identifier (nr) random effect. Is this random effect significant? Use 64 quadrature points to estimate this model?

Trade Union membership

(2) Estimate a logit model for trade union membership (union), with the covariates. (black, hisp, exper, educ, poorhlth, married, rur,nrthcen, nrtheast, south and allow for the respondent identifier (nr) random effect. Is this random effect significant? How many quadrature points should we use to estimate this model?

Joint Model

We have stacked the data for this part (union-wage.dat), the first few columns and rows look like

To read this data you need:

out union-wage.log

data ij r nr year agric black bus construc ent exper fin hisp poorhlth &

hours manuf married min nrthcen nrtheast occ1 occ2 occ3 occ4 occ5 &

occ6 occ7 occ8 occ9 per pro pub rur south educ tra trad union y d81 &

d82 d83 d84 d85 d86 d87 expersq r1 r2

read union-wage.dat

(3) Using the model specifications for log(wages) and trade union membership you have just used, estimate a joint model of the determinants of log(wages) and trade union membership. What is the magnitude and significance of the correlation between the random effects for log(wages) and union membership? How does the magnitude and significance of the direct effect of union in the wage equation change? What are the reasons for this? Have any other features of the models changed? What does this imply?

Below are the commands we used

case nr

yvar y

model b

rvar r

family second=g

constant first=r1 second=r2

trans r1_black r1 * black

trans r1_hisp r1 * hisp

trans r1_exper r1 * exper

trans r1_educ r1 * educ

trans r1_poorhlth r1 * poorhlth

trans r1_married r1 * married

trans r1_rur r1 * rur

trans r1_nrthcen r1 * nrthcen

trans r1_nrtheast r1 * nrtheast

trans r1_south r1 * south

trans r2_educ r2 * educ

trans r2_black r2 * black

trans r2_hisp r2 * hisp

trans r2_exper r2 * exper

trans r2_expersq r2 * expersq

trans r2_married r2 * married

trans r2_union r2 * union

trans r2_d81 r2 * d81

trans r2_d82 r2 * d82

trans r2_d83 r2 * d83

trans r2_d84 r2 * d84

trans r2_d85 r2 * d85

trans r2_d86 r2 * d86

trans r2_d87 r2 * d87

nvar 11

mass second=64

fit r1_black r1_hisp r1_exper r1_educ r1_poorhlth r1_married r1_rur &

r1_nrthcen r1_nrtheast r1_south r1 &

r2_educ r2_black r2_hisp r2_exper r2_expersq r2_married r2_union &

r2_d81 r2_d82 r2_d83 r2_d84 r2_d85 r2_d86 r2_d87 r2

dis m

dis e

stop

**References**

Rabe-Hesketh, S., and Skrondal, A., (2005), Multilevel and Longitudinal Modelling using Stata, Stata Press, Stata Corp, College Station, Texas

Vella, F., and Verbeek, M., (1998), Whose wages do unions raise? A dynamic model of unionism and wage rate determination for young men. Journal of Applied Econometrics, 13, 163-183.

Wooldridge, J, M., (2002), Econometric Analysis of Cross
Section and Panel Data, MIT Press,