Matching and Inverse Propensity Weighting Estimates of the Union Wage Premium: Evidence from Canada, 1997–2014

• Published date: 01 January 2018
• Author: Michele Campolieti
• DOI: http://doi.org/10.1111/irel.12202
• Date: 01 January 2018

Matching and Inverse Propensity Weighting

Estimates of the Union Wage Premium:

Evidence from Canada, 1997–2014

*

MICHELE CAMPOLIETI

I estimate the union wage premium for private-sector workers using Canadian

data from Statistics Canada’s Labour Force Survey from 1997 to 2014, examining

the trend and gender differences in the premium. I obtain my estimates using

matching and inverse propensity weighting estimators, which form counterfactuals

for union workers. These estimators create better covariate balance and can also

be used to address the bias that arises from the log transformation of wages.

Introduction

There has been an extensive literature exploring the effects of unions on

wages. Freeman and Medoff (1984) conceptualized the effects of unions on

wages as well as different aspects of employment via the two faces of unionism:

the monopoly face and the collective voice face. Through their monopoly face,

unions seek rents and bargain for higher wages over competitive levels for their

members. In his overview of the union wage premium literature, Lewis (1986)

made a distinction between the absolute wage gain and relative wage gap of

unions. The absolute wage gain can be thought of as the difference in wages

between union workers in the actual economy and union workers in a hypotheti-

cal economy in which unions do not necessarily have monopoly power. In con-

trast, the relative wage gap of unions reflects the observed difference in wages

between union and nonunion workers with actual data.

The literature estimating the union wage premium has focused on the rela-

tive wage gap of unions and has used ordinary least squares (OLS) to obtain

estimates of this premium. However, an alternative approach to obtain esti-

mates of the union wage premium, i.e., the relative wage gap, is to use estima-

tors that form estimates of counterfactuals, i.e., what would union workers

*The author’saffiliation is University of Toronto, Toronto, Ontario, Canada. E-mail: campolie@

chass.utoronto.ca.

JEL Codes: J01, C11, C38

INDUSTRIAL RELATIONS, Vol. 57, No. 1 (January 2018). ©2017 Regents of the University of California

Published by Wiley Periodicals, Inc., 350 Main Street, Malden, MA 02148, USA, and 9600 Garsington

Road, Oxford, OX4 2DQ, UK.

101

earn if they were not unionized. These approaches have been used in labor

economics to examine wages and the distribution of wages as well as other

outcome measures. For example, DiNardo, Fortin, and Lemieux (1996) used

reweighting approaches, which relied on kernel estimators to generate weights,

to construct counterfactual wage distributions to examine the effects of a num-

ber of factors (e.g., unions and minimum wages) on the U.S. wage distribution

and how these effects change over time. Matching and inverse propensity

weighting estimators of causal effects are another approach for constructing

counterfactuals. These estimators have been used extensively in the evaluation

of training and other active labor-market support programs to construct coun-

terfactuals for participants in these programs (e.g., see Heckman, LaLonde,

and Smith [1999] for a comprehensive survey). Matching and inverse propen-

sity weighting estimators can also be used to construct a counterfactual for

union workers and estimate the union wage premium. After matching or

reweighting, union and nonunion workers should have the same observable

characteristics (on average).

Two earlier studies used matching estimators to estimate the union wage

premium (Bryson 2002; Eren 2007). However, since these papers have

appeared an important methodological issue, covariate balance, i.e., whether

the treated and the untreated groups are similar on the basis of observable

characteristics, has been addressed. While matching and inverse propensity

weighting estimators should induce covariate balance, there is no guarantee

that they do. Consequently, the recent methodological literature has developed

estimators that optimize and ensure covariate balance as well as doing so in a

more straightforward fashion (e.g., among others, Iacus, King, and Porro 2011;

Diamond and Sekhon 2013; and Imai and Ratkovic 2014).

Another benefit of the matching and reweighting estimators is that they can

be used to avoid the retransformation problem that occurs with logged depen-

dent variables. This retransformation problem is well known in the health eco-

nomics literature (e.g., among others, Duan 1983; Manning 1998; Mullahy

1998; Manning and Mullahy 2001) and it involves accounting for the fact that

the marginal effect of a variable on a logged outcome measure must take into

account the distribution of the error term. Not making this adjustment can lead

to substantial biases in the estimates. Blackburn (2007) recognized that this

issue could also arise in estimates of log wage equations, like those estimating

the union wage premium because the log-wage variance among union workers

would be less than that for nonunion workers.

1

Blackburn (2007) suggested

1

If w N(l,r²) then log(w) is log normally distributed with mean elþ1

2r2and variance e2lþr2½er21.

More generally, Blackburn (2007) shows that EðelogðwÞjxÞ¼ex0bþdUnion EðeujxÞand that E(e

u

|x) 6¼ 1, even

if E(u |x) =0, where E(|x) denotes the expected value conditional on x.

102 / MICHELE CAMPOLIETI