John DiNardo 143
have employed to analyze the question:
- Ashenfelter (1978) constructs control groups based on industry, race, and worker
type (that is, craftsmen, operatives, laborers).
- Freeman (1984) compares wage rates for the same individual atdifferent points in
time.At one point in time the worker is in a unionized job; at a different point
in time the worker is in a non-unionized job.
- Lemieux (1998) compares wage rates for the same individual who holdstwo jobs,
one of which is unionized, the other which is not.
- Krashinsky (2004) compares wage rates ofidentical twins, one who is unionized
and one who is not.
- Card (1992) constructs control groups, based on observable characteristics,
which tend to receive the same wage in the non-union sector, as well as con-
trolling for differences in permanent characteristics (that is, person-specific fixed
effects).
- DiNardo and Lemieux (1997) and Cardet al.(2003) compare US and Canadian
workers, exploiting differential timing in the decline of unionization in the two
countries.
Depending on the precise context, the union wage effect as measured in these
studies ranges from 5% to 45%, with the vast majority of studies being at the higher
end. All of the aforementioned studies adopt a distinctly non-Bayesian approach
to the econometric analysis. The variety of research designs was not motivated
by an attempt to “refine” posterior beliefs, but to put the hypothesis that unions
raise wages to the most severe test possible with existing data. Each of the papers
described above tried to “rule out” other explanations for the difference in union
and non-union wages. (Perhaps this is why the posterior distribution of estimates
of the union wage effect are as tight as they are – a survey of labor economists
found remarkable unanimity on the average size of the effect (Fuchset al.,1998).
The posterior mode of the economists surveyed was that unions raised wages 15%
relative to similar non-union workers.)
What is also useful about this example is that there exists at least one Bayesian
analysis, Chib and Hamilton (2002), which helpfully contrasts some unsophisti-
cated non-Bayesian estimates from a small sample of workers. These non-Bayesian
estimates vary from about 16% to 25%. If one treats these as “average treatment
effects on the treated (ATOT),” these estimates are similar to their Bayesian posterior
distributions.^62
To put it a bit too simply, the basic empirical model has long been some variant
of the following:
logwi = Xβ 0 +αi+
0 ifUi= 0
= Xβ 1 +ψαi+
1 ifUi= 1
P(Ui= 1 ) = F(Zγ),
