LEY DEL MERCADO DE VALORES

Our model of unionised employment is based on the assumption that workers are able to observe differences in the working conditions and compensation packages offered by unionised and non-unionised firms. That is not to say, however, that unions, particularly through the award system, do not influence the working conditions or remuneration of non-unionised workers. Rather, it assumes that a union presence has an additional impact which is manifested as differences in working conditions or rates of compensation, or both. In particular, our model of unionised employment allows (but does not require) the wage structure to differ between the two sectors.

The union wage differential is conventionally estimated by including a union membership dummy in a wage equation, or by allowing full interactions and estimating separate wage equations for union members and non-members. Throughout the thesis we have argued, at some length, that the wage received by an individual in a unionised plant will be independent of his or her union membership status. However, whether this argument is correct is ultimately an empirical question. Accordingly, in this section, we seek to answer three questions: (i) Is there a wage differential associated with unionised employment? (ii) If so, is the unionised employment differential greater than the conventional union membership differential? and (iii) Do members in unionised establishments receive higher wages than non-members?

Union Coverage and Membership

Modelling Wages and Union Coverage

Recall that we assume that the individual i has a wages function of the form

where Wj is the log hourly wage, and Z, is a vector of human capital and other

wage-determining characteristics. The superscript j indicates the union status

of the worker.^^

If we follow the conventional approach by categorising workers

according to their membership status, and allow only the intercept term to vary

between union members and non-members, the wage equation to be estimated

is

^NU TT/SiU iNU. ^

= 60 - So ) 6 1 + 6 3 .

where Uj is a union membership dummy, Z,"^ contains the same elements as Zj

but excludes the constant, and the 61 is a row vector of parameters excluding

the intercept parameter. The union membership differential, d, is measured by

^^Categorising workers by union membership status: j = U for union members and j = NU for non-union members. Categorising workers by both union membership and unionised employment status: j = U U E for union members, j = N U E for non-union members in unionised establishments, and j = NE for workers in non-unionised employ- ment.

Chapter 4

the coefficient of the union membership dummy (ie.

It is often assumed that there the error term in (4.17), €3; (eji =

and the union membership dummy, conditional on Z,, are correlated. If this is so, the OLS estimate of d (given by the coefficient of the

union membership dummy) is biased. However, consistent estimates may be

obtained by using instrumental variables estimation (Duncan and Leigh, 1985),

or by using the Heckman's (1979) control function approach. For the control

function approach the model to be estimated is

= (4-18)

where Ri = ((/)i(U,-4'i))/(<i'i(l-^i)) is the generalised residual from a reduced form

probit model of union membership (Gourieroux et. al. 1987; Vella and

Verbeek, 1993), and a^ is the covariance between the error term in the

membership probit equation, 6,i, and the error term in the wage equation, 63,.

However, Poirier (1980) has shown that the standard control function

approach is incorrect if the selection mechanism consists of more than one

decision, such as when workers who have secured unionised employment

subsequently choose whether to join the union. Under these circumstances, the

^•^The percentage union-non-union wage differential, D , is given by D = e''-1.

Union Coverage and Membership

full model consists of a wage equation and two selection equations.

v: UE-

w;

; _

_3i

Union Membership Equation Unionised Employment Equation

Wage Equation

(4.19)

Note that the wage equation has been specified so as to allow all of the

parameters to vary for union members, non-members in unionised

employment, and non-unionised workers. Assuming the errors in the model

are trivariate normally distributed with zero mean and covariance matrix^^

1 ^12 ^13

s = _{1 ^23}

^31 ^32 O 3 3

(4.20)

then, following Tunali (1986) and Main and Reilly (1992), the double selection

extension of the conventional control function approach can be derived as

follows.

First, separate wage equations are specified for the three different

25

W e have assumed the usual probit normalisation for the t w o selection equations (ie.

. 2 2

169

Chapter 4

groups of workers. The regression equations to be estimated are^^

E(yv^^\U=\,UE=\)

= Z 6 ^ ^ + £ ( e 3 | f / ' > 0 , f / £ : ' > 0 ) U n i o n M e m b e r s

I ( / = 0 , C / £ = 1 ) =

Z b ^ ^ ^

+ £ ( € 3 1

W < . 0 , UE'>0)

N o n - U n i o n M e m b e r s ( 4 . 2 1 )

Eiw"^^

I

UE=0) = \ UE'^0)

N o n - U n i o n i s e d W o r k e r s

Now, the conditional means of e^, for the three different groups of workers can

be written as

Eie^\U=l,UE=l) = OjjA-j, + o^^X^^

Eie,\U=0,UE=l) =

0,3X2, + (4.22)

E(e,\UE-0) = 0,3X0

where Z—TTT A , - - (4.23) ^21 A o V o N '^•22- P 12) P 12)

^^The subscript i is omitted in order to avoid notational clutter.

Union Coverage and Membership

and

Finally, the conditional mean of the error term for workers in non-unionised workplaces incorporates a standard Mill's ratio term as there is only a single selection mechanism for these workers.

X

. i M l W

(4.25)

Consistent estimation of the wage equations now proceeds by using a modified form of Heckman's (1979) two-step procedure. First, the bivariate probit model of unionised employment and union membership defined by equations (4.1) and (4.10) is estimated. This provides the estimates of jS,, jSj and (7,2 which are necessary to calculate the selection terms in each of the wage equations. The selection terms are included in the wage equations which are then estimated using OLS.

Estimation of the Union Impact on Wages

Using ordinary least squares, we estimate the union wage differential by including a single union status dummy variable in a standard hourly wage

Chapter 4

equation.^^ In fact we separately estimate three union wage differentials - the

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