# A NOTE ON THE ANALYSIS OF TRADE UNIONS AND RELATIVE WAGES

 Publication Date 01 August 1979 DOI http://doi.org/10.1111/j.1468-0084.1979.mp41003005.x Author JOHN CREEDY Date 01 August 1979 A NOTE ON THE ANALYSIS OF
By JOHN CREEDY*
I. INTRODUCTION
The purpose of this note is to examine the method used by a number of recent
studies which have attempted to estimate the effect of trade unions on relative
wages within occupations in Great Britain.' These studies raise many difficult
problems associated with data and the interpretation of results, but this note is
confined to some statistical aspects of the work.2 The estimation of the union/non-
union differential is examined in section (II), while section (III) then considers some
further difficulties where hours of work are variable.
II. ESTIMATION OF THE AVERAGE UNION/NON-UNION DIFFERENTIAL
The fundamental problem is, of course, raised by the fact that direct information
about differentials is not available from published data.3 The usual estimates are
obtained from a single equation model which is based on a simple identity which
decomposes the average wage within the jth occupation, w,, into a weighted average
of the average union wage wj and the average non-union wage w, where the
weights depend on the proportion of workers who are 'covered' by the union
negotiated wage, t» Thus z=tz+ (1 _1)iC (1)
A similar decomposition is obviously available for the logarithms of wages, where
w etc. are re-defined in terms of the respective logarithms of the geometric means.4
An immediate problem is raised if average hourly earnings are approximated by
the ratio of average weekly earnings to average weekly hours, since the latter is not
equal to the former and the discrepancy will be different in each occupation.
To simplify notation it is convenient to drop the subscripts and rewrite equation
(l)as z=tx+(lt)y (2)
where the definitions of z, x and y are obvious by comparison with (1). The usual
method then proceeds by rewriting (2) as
z=y+ID (3)
* I should like to thank K. Mayhew for comments on an earlier version of this note.
'These include Pencavel (1974), Mulvey (1976, 1977, 1978), and Layard et. al. (1978), who describe
their results as 'relatively reliable' and 'very approximate' in the same paragraph (ibid, p. 287).
2A survey of some of the difficulties is given in Metcalf (1977). Particularly important are problems
of dealing with different levels of skill (especially where unions influence labour training), and the effect
of size of establishment.
Mulvey (1978, p. 106) actually makes the strange assertion that the non-union wage is 'obviously
not directly observable', but this is only true if by 'non-union' is meant the wage in complete absence of
any unions.
In fact only arithmetic means are available, a problem which has been considered in a different
context in Prais and Houthakker (1955, p. 14).
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