Convergence Between Black Immigrants and Black Natives Across ...

w i,g = k + cx i + dy g + Jm e i,g + e i (3)
where m e i,g denotes the expected average of other people’s decisions in the group,
m e i,g = 1 n  j2gE(w j |F i ). (4)
As in Manski’s original formulation, y g = ¯x g , where ¯x g = 1 n g
 i2g x i denotes the average across i of x i
within a given g. Coefficient vector c and scalar J capture contextual and endogenous effects. 24 Under the
assumption y g = ¯x g , every contextual effect is the average of a corresponding individual characteristic
m g = k +(c + d) y g
1 J
We see that m g is linearly dependent on the other regressors, i.e. the constant and y g . This linear
dependence implies that the identification of the full set of structural parameters fails. For this study, the
parameter of interest is a (to be introduced), and not c or J. Hence, this paper will not further deal with
conditions that could be put in place to restore identification of all parameters. 25
What group g do first generation immigrants belong to? In other words, which individuals affect their
decision to participate in the labor force? Figures 10a and 10b showed that an immigrant’s labor force
participation decision varies considerably by age of immigration. This suggests that immigrants assimilate
with natives to varying degrees.
Consequently, I represent an immigrant’s choice by a mixture of two
choices, the choice of individual i in group 1 and that of individual i in group 2. Group 1 represents all
natives of the same racial group and group 2 represents a different group.
(5)
It is not clear how to cleanly define group 2, and the following two sections will go through two possibilities.
w i,g1,2 = a i w i,g1 +(1 a i )w i,g2 (6)
Case 1: Group 2 Members Are only Affected by own Characteristics
Let’s assume that g 1 evolves as the baseline model in (3) while members of group 2 are only affected by
their own characteristics. In other words,
After some algebra, we get 26
24 Assumptions on the error terms are discussed in Appendix C.
25 See Blume et al. (2010) for a detailed discussion and ways to restore identification.
26 Section C provides an explicit derivation of the model.
w i,g2 = k + cx i + e i (7)
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