Labor market characteristics and cultural choice

• Date: 01 September 2020
• Published date: 01 September 2020
• Author: Jiabin Wu,Christopher Ellis,Jon C. Thompson
• DOI: http://doi.org/10.1111/jpet.12449

J Public Econ Theory. 2020;22:1584–1617.wileyonlinelibrary.com/journal/jpet1584

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© 2020 Wiley Periodicals LLC

Received: 25 January 2019

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Accepted: 10 May 2020

DOI: 10.1111/jpet.12449

ORIGINAL ARTICLE

Labor market characteristics and cultural

choice

Christopher Ellis

1

|Jon C. Thompson

2

|Jiabin Wu

1

1

Department of Economics, University of

Oregon, Eugene, Oregon

2

Atkinson Graduate School of

Management, Willamette University,

Salem, Oregon

Correspondence

Jiabin Wu, Department of Economics,

University of Oregon,

Eugene 97403‐1285, OR.

Email: jwu5@uoregon.edu

Abstract

We develop a model of cultural selection based on the

labor market characteristics of different cultural types.

Following Borjas (1994, 1995) we assume that cultural

heterogeneity increases labor productivity due to skill

complementarities, however following Jackson and

Xing (2014) we also assume that cultural heterogeneity

hampers communication. We model this as a game in

which individuals from two cultural types first engage

in random matching, then once matched play a co-

ordination game. Other‐type matches are thus poten-

tially more productive, but also less likely to coordinate.

We show that these two labor market characteristics

serve as important primitives in determining if a

cultural minority persists. Essentially, when the pro-

ductivity advantages from a cross‐cultural match suffi-

ciently outweigh the disadvantages of coordination

problems then the cultural minority will persist. If not it

will be assimilated. Further, we obtain results con-

cerning the efficient size of the cultural minority, the

effects of tax and welfare programs on the size and

welfare of the cultural minority, and the relationship

between the intensity of social interaction and size and

welfare of the cultural minority.

1|INTRODUCTION

The presence of a minority cultural group that coexists within a majority culture has long led to

frictions. In the USA from Henry Cabot Lodge commenting on immigration during the “age of

mass migration”to Donald Trump in the present day, there have been those that argue for

immigration restrictions. These arguments are usually based on the notion that some cultural

groups are either “too slow”to assimilate into the majority culture or indeed do not assimilate

at all.

1

This obviously presumes that assimilation is desirable and/or the time path of cultural

change is inefficient. The analysis we present below speaks to both of these questions. We

develop a novel model of cultural choice which gives us insights into when a minority culture

exists in equilibrium and describes the time path to that equilibrium. Unlike earlier theoretical

work on cultural selection we are able to employ standard criteria to examine the welfare

properties of the equilibrium and the time path. Further we are able to identify any in-

efficiencies present and evaluate remedial policies.

Our simple model of cultural selection is based on the labor market characteristics of

different cultural types. Our approach is inspired by early observations made by Borjas

(2003)andLazear(1999a,b), first that immigrants may bring skills to the labor market

complementary to those possessed by natives, and, second, they may introduce costs via

difficulties in communication. We base our model of cultural choice on these observations

in a very natural way. We assume that agents in an economy consist of one of two types,

these types are culturally distinct and possess complementary skills. The agents in the

economy are randomly matched in pairs, and once matched play a coordination game.

2

If the players coordinate on an equilibrium, then a surplus is realized and allocated between

the participants via Nash bargaining. An agent's cultural type effects their expected payoffs

and ultimately the steady‐state equilibrium distribution of types in three ways: first the

types have complementary skills such that cross‐cultural “other‐type”matches are poten-

tially more productive than “own‐type”matches, second the probability of equilibrium

coordination is lower for other‐type matches versus own‐type matches reflecting commu-

nication problems due to their cultural dissimilarities, and third and finally the types

possess different threat points that effect the distribution of surplus following successful

coordination. A steady‐state equilibrium is characterized by the proportion of the types in

the population, which for either type may be zero, one, or some intermediate value in-

dicating the persistence of a minority.

3

Our work is closely related to the extensive literature on intergenerational cultural trans-

mission, the modern version of which was pioneered by Bisin and Verdier (2000,2001) and is

surveyed in Bisin and Verdier (2010). The key idea in this literature is imperfect empathy

whereby an altruistic parent uses their own preferences to evaluate the utility of their offspring.

Imperfect empathy provides an incentive for a parent to incur a cost so as to socialize a child to

share their own cultural traits. The alternative to parental socialization is for the offspring to be

socialized by a randomly chosen role‐model from the general population. Bisin and Verdier

(2001) show that imperfect empathy plays an important role in explaining the persistence of

1

See Henry Cabot Lodge's speech in the US Senate in 1896 https://www.nationalists.org/library/america/henry‐lodge‐

speech‐1896.html or Donald Trump's interview with Tucker Carlson on Fox News in 2016 https://niskanencenter.org/

blog/muslim‐immigrants‐assimilate/.

2

For a survey of matching functions see Petrongolo and Pissarides (2001).

3

That a good theory of cultural selection must admit equilibria characterized both by full integration of a minority, and

by the minority's persistence, is highlighted nicely by counterposing the examples given by Bisin and Verdier (2000)

and Giusta, Hashimzade, and Myles (2016). The former motivates their analysis by pointing to the continued existence

and cultural distinctiveness of the Orthodox Jewish community in the US. The latter motivate their analysis by pointing

to the complete assimilation of the Jewish community in the East End of London in the late nineteenth and early

twentieth centuries.

ELLIS ET AL.

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cultural minorities.

4

,

5

We employ a different approach and do not assume imperfect empathy.

The main contribution of our work is to build a cultural selection model based on the em-

pirically established labor market characteristics of cultural diversity in the workforce. This

model allows us to propose explanations for when cultural minorities assimilate and when they

remain distinct. It also allows us to make welfare statements concerning whether a market

mechanism will lead to efficiency in terms of the steady‐state size of a cultural minority and

along the time path to the steady state. That is whether assimilation is too fast or too slow.

These questions are difficult to address using the Bisin and Verdier approach where it is unclear

how to specify a social welfare function. However, our model does not rely on imperfect

empathy and parents are altruistic in the standard sense so standard welfare statements are

quite possible.

The paper is organized as follows. In Section 1.1, we present a brief literature review to

better place our contribution in the existing research. In Section 2we develop our basic model,

derive the steady‐state distribution of types that would be chosen by a benevolent planner and

compare this to a market solution where the agents type is chosen so as to maximize expected

payoffs. We explore when the steady‐state equilibrium is interior and when it is at a corner,

giving us insights into when a minority will be assimilated and when they will persist. We show

that for an interior steady‐state equilibrium the market solution involves too few agents

choosing the minority culture relative to the social welfare optimum. This follows from ex-

ternalities in matching. In choosing to be minority‐type agents individuals do not internalize

the effect of their choices on the expected payoffs of other agents they are potentially matched

with. The failure of agents choosing to be the minority type to internalize the effects of their

choices on the probability of highly productive cross‐cultural matches is the key externality

behind our results.

In Section 3we develop the models dynamics in an overlapping generation's structure

where altruistic parents may choose their children's culture, and where changes in culture from

parents to children involve increasing convex costs. We show that the dynamic always involves

convergence to the interior steady‐state equilibrium when it exists, then examine the welfare

properties of the convergence path. Two distortions are present along the dynamic path, first a

dynamic version of the matching externality, and second a failure of individual agents to

internalize the effects of their choice of their child's type on the adjustment costs faced by other

agents.

In Section 4we introduce some extensions to our model. We first explore the implications of

the intensity of social interaction for the interior steady‐state equilibrium proportions of the two

cultural types and for the welfare properties of the interior steady‐state equilibrium. We model

greater social interaction by allowing for multiple rounds of matching per period. We show that

the intensity of social interaction is important for determining both whether the minority is

assimilated in equilibrium, that is, whether there is a corner solution, and if the equilibrium is

interior, the size of the minority in that equilibrium. These results arises because multiple

4

The intuition is as follows. As the proportion of the population that is not of the minority approaches 100% a minority

child will almost certainly become a member of the majority if socialized by a random stranger, hence a cultural

minority parent who is culturally intolerant will choose to socialize the child themselves, ensuring the continued

existence of the minority.

5

There are different cultural transmission mechanisms based on imperfect empathy in the literature. Bisin and Verdier

(2000) consider homogamous marriages. Giusta et al. (2016) argue that parents from an immigrant population must

trade off the labor market advantages of schooling and the cultural costs arising from the schools socializing their

children in the host culture.

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