Language and Location∗
Andrew John
INSEAD
Boulevard de Constance
Fontainebleu 77305, France
Kei-Mu Yi
International Research
Federal Reserve Bank of New York
33 Liberty St.
New York, NY 10045
April 13, 2001
Abstract
Language is an input into production and trade. In general, a society will possess more production and consumption opportunities when all
its members share a common language. Neighboring societies and communities likewise have a strong incentive to utilize a common language,
and indeed there are countless examples of language assimilation and language loss. The puzzle is that more assimilation has not occurred: history
records numerous examples of communities that coexist with distinct languages and limited economic interaction.
This paper presents a successive-generations model with two languages
and two locations that reconciles assimilation and non-assimilation. Each
generation of agents in each location is initially endowed with one or
both languages. They choose whether to learn the other language, and
whether to move to the other region, and they transmit their final language
∗ This is a revised version of “Language, Learning and Location”. We thank Paul Beaudry,
John Bryant, Russ Cooper, Tina Hickey, Dae Il Kim, Bob King, Ian King, Nobu Kiyotaki,
Narayana Kocherlakota, Kevin Lang, Ed Lazear, Peter Mieszkowski, Joyce Sadka, Robert
Tamura, and seminar participants at Australian National University, Bond University, Georgetown University, University of Hawai’i, University of Helsinki, University of Melbourne, University of New South Wales, University of Texas, Virginia Tech University, the Midwest Macroeconomic Conference, the NBER Winter Economic Fluctuations Conference, and the AEA
Meetings, for very helpful comments. We thank Angela Hung, Fidel Perez, and Dana Rapoport
for excellent research assistance. The views expressed here are those of the authors and are
not necessarily reßective of the Federal Reserve Bank of New York or the Federal Reserve
System.
1
endoment to the next generation in their region. Language facilitates
production: an agent can produce output only in conjunction with others
who share the same location and language. Consequently, there are strong
incentives to locate with others who share the same language, and to learn
the language that others speak. The costs of learning and moving are
endogenous: agents who are learning cannot produce, and agents who
migrate leave behind trading partners. Depending on initial conditions,
the model can deliver assimilation, or equilibria in which location and
language barriers prevent economic interaction from occurring.
1
Introduction
In the last century hundreds of languages have disappeared or fallen into relative
disuse. These include Breton, Cornish, Welsh, and Irish in Europe, non-Swahili
languages in Central sub-Saharan Africa, numerous native North American,
South American and Australian languages, and Ainu in Japan. English is the
official language or “routinely in evidence, publicly accessible in varying degrees,
and part of the nation’s recent or present identity,” in over 75 countries. All told,
about two billion people are now exposed to the English language.1 The reach
of English extends to the Internet, as well, where it has become the dominant
language.
At Þrst glance this phenomenon does not appear difficult to explain with
economics. Language use exhibits network externalities, as argued by Church
and King (1993).2 For an individual, the returns to speaking a language are
increasing in the number of others who speak the same language. Network
externalities generate increasing returns that provide a powerful impetus to the
use of a single language.
A difficulty with this explanation is that — despite the disappearance of hundreds of languages — hundreds of languages and minority language communities
continue to survive and ßourish. The number of Spanish speakers in the United
States has been increasing at least since 1950. French speakers in Canada have
declined, but only very slowly from 29% to 25% in the 35 years between 1951
and 1986. Catalan, a minority language in Spain, shows no signs of diminished
use. Dozens of countries have multiple official languages — India, for example,
has fourteen — and many other countries are to some extent, multilingual. More
generally, there are minority languages within a country, such as Spanish in the
United States, and majority languages that are not global linguae francae, such
as Korean in Korea, that are thriving. A more complete theory of language
1 The
Economist, (12/21/96), p. 78, quoting David Crystal.
see Breton and Mieszkowski (1977), Grenier-Vaillancourt (1983), Lang (1986),
Robinson (1988), Grin (1990), Laitin (1994), Lazear (1995, 1996), and Tamura (1995) for
related work on the economics of language. Marschak (1965) was a pioneering paper on the
evolution of languages and language use. Grin (1996) provides a comprehensive survey of the
literature on the economics of language.
2 Also,
2
use must be able to explain why languages and language communities persist
as well as why they disappear.
Cultural and historical factors also undoubtedly play an important role in the
persistence of languages, but even languages with strong cultural associations
often die out. A focus on such factors alone misses an important part of the
language community dynamics. The existing economic literature on language
use can explain the persistence of a language only by assuming that individuals
have a high (exogenous) cost of learning other languages. But the costs of
learning a language are endogenous: learning takes time, and the opportunity
cost of an individual’s time depends upon that person’s productivity using his
or her current language.
A second way to generate language persistence stems from the recognition
that speakers of a language are geographically isolated.3 Even in a world of
low transportation and communication costs, most economic activity of any
particular individual still tends to occur in relatively localized areas. Intuitively,
it seems clear that it is easier to maintain a language when its speakers are
geographically concentrated, rather than dispersed. This is supported by data
from the 1990 U.S. census, which identiÞes 30 Asian and Hispanic nationalities.
The greater the fraction of a nationality that lives in the center city, the greater
the fraction of households in which no one over the age of 14 speaks English “very
well”.4 But, again, the location choices of individuals are surely endogenous and
depend upon the languages that are spoken in different regions, which in turn
deÞne the (opportunity) cost and beneÞt of migration.
A third explanation of language persistence is government policy. Public policies on language education and use can undoubtedly inßuence language
survival. Until recently, language policies in most countries typically supported
the majority language at the expense both of minority languages and of international linguae francae. In recent decades, this emphasis has changed somewhat,
as governments have increasingly sought to provide some support for minority languages. Public policy has clear limits, however. For example, Irish has
been encouraged and supported in Ireland for most of the 20th century, and yet
English is the dominant language.
We therefore develop a theory of language acquisition and use in which both
the costs of learning and the costs of migration are endogenously determined,
and in which government policies can inßuence language education and use. We
think of language as an essential tool of communication and expression, without
which production is impossible. We think of geographic proximity as likewise
3 Yeh (1995) examines language and location decisions of immigrants, and Benabou (1993,
1996) studies location and human capital acquisition in models of cities and localities.
4 The correlation coefficient is 0.64. The census identiÞes 11 Asian nationalities and 19
Hispanic nationalities. The correlation coefficients for the Asian nationalities is .87, and
for the Hispanic nationalities, .39. This is not surprising given the fact that the Hispanic
nationalities are all speaking variations of one language, while the Asian nationalities are
speaking different languages.
3
being crucial to production. Consequently, in our model, production occurs in
conjunction with other agents who speak the same language and are in the same
location.5 Production can be thought of as arising from random matching in
a search setting or from team production. We assume that there is a network
externality: per capita production of an agent is (weakly) increasing in the
number who speak the same language. As a consequence, each agent wants to
locate with others who speak the same language.
Our model features successive generations of agents in a world with two languages and two locations. Each agent is born in a location and endowed with
one or both languages. In the Þrst period of adult life, individuals choose to
produce or to learn the other language. At the beginning of the second period,
they choose whether to move to the other location. These choices allow the
possibility of remaining in language communities that are geographically isolated. Production also occurs in the second period. Languages are transmitted
across generations in the model: the language endowment of children depends
on the languages spoken by their parents, and on the languages spoken in their
community.
There are strategic complementarities in both the decision to learn and the
choice of location. The opportunity cost of learning the other language depends
on the choices of others in one’s own community. If one’s peers choose to learn,
they are unavailable for production, lowering the opportunity cost of learning.
Conversely, if others choose not to learn, the opportunity cost is higher, and the
incentive to learn is lower. Similarly, the cost of locating in the other community
depends on the choices of others in one’s own community. If one’s peers choose
to migrate, they are available for production in the new community, lowering
the opportunity cost of migrating.
It is not surprising, then, that one equilibrium of the model is assimilation,
in which all agents of one group learn the language of the other group and
everyone moves to the same location. But — depending on the initial endowments of location and language — there can be two other types of equilibrium
in our model: geographic isolation equilibria, in which agents who share common languages are prevented from interacting because of location barriers; and
linguistic isolation equilibria, in which agents who live in the same location are
prevented from interacting because of language barriers. When speakers of different languages live in the same region, assimilation may also occur through
the intergenerational transmission of languages. Children tend to learn the
language that is most widely spoken, and also pass that language on to their
offspring. This process can be self-reinforcing. Such inßuences are absent,
however, when agents are geographically isolated. Thus geographic isolation
5 We take a strong stance on the role of both language and geography in production. We
have chosen to write down a model with strong assumptions on production in order to highlight
the roles of language and location in a stark manner. Evidently, not all production literally
requires geographic proximity or a common language. We discuss relaxing these assumptions
in our concluding remarks.
4
permits minority languages to survive, even in the long run.
Hence, despite the presence of increasing returns, our model generates equilibria in which assimilation does not occur. It can explain the survival, as well
as the disappearance, of languages, and it suggests that a few linguae francae
will not necessarily replace all other languages. Moreover, our model does not
rely on cultural, historical, or other forces — all of which are relevant, but are
not modeled here — to generate our main implication. What is instead crucial is
that location provides a local source of increasing returns that works against the
global increasing returns that encourages full assimilation. A minority language
speaker may be better off not learning, but instead locating and producing with
other non-learning speakers.
We make three additional observations. First, other researchers have suggested that language can be viewed as a metaphor for more general skills that
facilitate economic activity. For example, Lazear (1999) uses the term language
to refer broadly to a set of cultural values. We are quite sympathetic to such interpretations, and view them as consistent with our theoretical model. Indeed,
some of our analysis can be applied even more broadly to other instances of network externalities, such as the simultaneous existence of the metric and imperial
measurement systems, Apple and IBM PC’s, multiple electrical outlet systems,
different credit card networks, or the U.S. and GSM cell phone networks. We
would then interpret bilingualism as dual compatibility, and learning costs as
the costs of attaining such compatibility. (Neither migration nor intergenerational transmission — which play important roles in our analysis — have obvious
parallels in such cases, however.) But, as our review of the sociolinguistics data
attests, our literal focus is language.
Second, our analysis abstracts from the social value of language and considers
it solely as a means of communication. Language is much more than this; it
is a repository of knowledge and of cultural and literary values. Our emphasis
here on the economic causes and consequences of language use should not be
interpreted as a dismissal of such aspects of language. Third, although we
draw attention to the externalities associated with language use, we deliberately
conduct relatively little welfare analysis in the paper. This is because the
normative questions surrounding language use extend well beyond the aspects
of language that we discuss. (See Nettle and Romaine (2000) and Jones (1999)
for two very different normative perspectives on the emergence of a small number
of global languages.)
We begin with an extended discussion of stylized facts on language use from
the sociolinguistics literature. We present the model in Section 3. We then
present four versions of the model: the model with neither learning nor migration (in Section 4); the model with learning only (Section 5); the model with
migration only (Section 6); and the complete model with learning and migration
(Section 7). Section 8 discusses an extension to the model in which there are
inertial agents, and Section 9 concludes.
5
2
Stylized Facts of Language Use
There are approximately 6000 languages spoken in the world today, so it is not
surprising that most countries contain multiple language communities. Some
countries have multiple official languages: for example, both Swedish and
Finnish are official languages in Finland; Irish and English are official languages
in Ireland; French and English are official languages in Canada. In these cases,
multiple languages have legal standing and explicit state support. Some countries also provide support for minority languages: within the European Union,
languages such as Breton, Catalan, Welsh, Sámi and Galician receive aid; likewise there are some attempts to maintain native languages in Australia and the
United States. Nevertheless, most minority languages are under threat of disappearance. Many countries, such as India, Indonesia, or Papua New Guinea are
home to a large number of languages, and many of these languages are at risk
because they have a small number of speakers and limited official protection.
While some languages are conÞned to single locations, many others are spoken in several regions of the world. In addition to the obvious linguae francae
such as English, French and Spanish, languages such as Hindi, Mandarin, and
Urdu are spoken on several continents. In these cases, language communities
may be at risk of disappearing even though the language itself is not at risk.
There may occasionally be government support for such communities (Québec
is an example), but their protection is typically not a priority of government
policy. Indeed, government policies often actively encourage assimilation of such
groups.
In the following subsections, we present some brief case studies of languages
and language communities, in order to highlight some key variables that affect
the survival of language communities. These include the size of the community, its economic signiÞcance, its geographic concentration, and the effects of
schooling and other government policies.
2.1
Welsh in Wales6
In England and Wales, the demand for labor engendered by the Industrial Revolution and subsequent industrialization integrated Wales into the larger English
economy during the Þrst half of the twentieth century.7 Table 1 shows the rapid
decline of Welsh over this period. At the beginning of the century, about half of
the Welsh population spoke Welsh and about 30% of the Welsh speakers were
monolingual. These monolinguals were concentrated in the higher age cohorts.
By 1931 Welsh speakers were only 37 percent of the population, and by 1991,
only 18.5 percent spoke Welsh. (Most of these do not speak Welsh on an every6 Most
of the data for this section are drawn from Hechter (1999) and Price (1984).
is a manufacturing center for the U.K. About 28 percent of Wales’ GDP is manufacturing, compared to 22 per cent for the U.K. as a whole. Wales produces 45 percent of
total UK steel production.
7 Wales
6
Year
1901
1911
1921
1931
1951
1961
1971
1981
1991
Welsh only (000)
281
190
156
98
41
26
33
22
%
15
8.5
6
4
2
1
1
1
Welsh bilinguals (000)
649
787
766
811
674
630
510
487
%
35
35
31
33
27
25
20
18
Total (000)
930
977
922
909
715
656
542
508
%
50
43.5
37
37
29
26
21
19
18.5
Table 1: The Decline of Welsh in the 20th Century
day basis, so the actual number of active users of Welsh is likely much smaller.)
The number of bilinguals rose prior to 1931 and declined thereafter, suggesting that elderly monolinguals were being replaced by younger bilinguals.8 The
data for the latter half of the twentieth century, in turn, indicate that bilinguals
were replaced by English monolinguals. Durkacz (1983, p. 216) has argued that
where parents are monolingual in the minority language, “a high percentage of
their children tend to be bilingual: where parents are bilingual, a high percentage of their children tend to be English monoglots”. Based on data in the 1991
census, 70% of Welsh households are childless, suggesting further erosion in the
future.9
The transition from bilingualism to monolingualism is concretely illustrated
by a survey in 1950 in one Welsh region. Of “over 3500 children from linguistically mixed marriages, only 155” were bilingual; the rest were monolingual
English.10 Similar results were obtained in another survey in 1961. The rate
of decay per generation from Welsh monolingualism to bilingualism was almost
30%. The decline in the Welsh language was exacerbated by English migration
to Wales. Welsh became increasingly conÞned to the rural and mountainous
regions of West and North Wales, and by 1961 only 10% of the population in
8 Much of our paper concerns bilinguals.
The linguistics literature does not give us a
precise deÞnition of bilingualism; Romaine (1995) provides an extensive discussion. It has
been deÞned as narrowly as native-like ßuency in two or more languages, and as broadly as
the ability to utter meaningful phrases in a second language. Under the broader deÞnitions,
it has been estimated that over half the world’s population is bilingual. (Romaine (1995), p.
8.) The extent to which a person is bilingual depends on several factors including speaking,
listening, and writing proÞciency, the frequency with which each language is used, the ability
to alternate between languages, and the ability to keep the languages separate. This latter
category, called ’interference’, is signiÞcant because many bilinguals mix two or more languages
in conversation. In our setup we take a single language as an indivisible construct - we do
not allow for mixing nor for language evolution. We also adopt the narrow deÞnition of
bilingualism: equal ßuency in two languages. Allowing for ßuency in a more continuous way
does not affect our results.
9 See http://users.comlab.ox.ac.uk/geraint.jones/about.welsh.
10 See Price (1984), p. 119.
7
industrial counties spoke Welsh, compared to 45% of the population in nonindustrial counties. (The corresponding Þgures for 1891 were 30% and 62%.).
There are still regions with low population in which Welsh speakers are a
majority — for example, two-thirds of the residents of Anglesey (an island off the
northwest coast) speak Welsh — but in South Wales, which is an industrial part
of the country home to about 70% of the population, 98% of the households now
communicate in English. According to Hindley (1990, p.222), “the territorial
contraction of the Welsh-speaking heartland continues along all the main roads
from English cities and around every coastal and mountain resort, every weekend
cottage, every holiday and retirement home”. It is the “unspectacular and less
attractive interior marginal farming districts which preserve Welsh best”.
Very recent data indicate that the decline of Welsh has halted, at least temporarily: about 20% of the population continue to speak Welsh, and the number
of young speakers has increased. Much of this change is due to government policy — notably the 1993 Welsh Language Act that mandates the teaching of Welsh
in the school system and that requires equal treatment of Welsh and English.
The presence of a Welsh TV channel has undoubtedly played a role also. Nevertheless, it is clear that the vast majority of economic interactions are in English.
Welsh GDP per capita continues to lag behind the rest of the UK; it is currently
about 83% of the UK average and about 80% of the EU average. Indeed, during
the 1990s, the trend has been downward. GDP per head as a percentage of the
UK fell from 87 percent in 1988 to 83 percent in 1996.
2.2
Irish in Ireland11
Henry VIII’s Act for the English Order, Habit and Language decreed that the
Irish “to the utmost of their power, cunning and knowledge, shall use and speak
commonly the English tongue and language”.12 Despite this legal coercion, supported by language policies in schools and churches, the Irish language was still
spoken by a majority of the population as late as around 1840. The mass starvation and emigration precipitated by the Great Famine of 1845-1859 changed
the situation utterly. Just a decade later, in 1851, the number of Irish speakers was a mere 25% percent of the population, with only 5% monolingual Irish
monoglots, and by 1901, Irish was spoken by only 14% of the population, with
Irish monolinguals being only 0.5%. The decline is evident in the numbers of
young speakers: in 1891, only 3.5% of the children under the age of 10 could
speak Irish.
During its decline, the boundaries of the Irish language moved westward.
It was pushed back “toward the peninsulas and islands of the western and
southwestern seaboards, into narrow glens, and up the sides of mountains. By
the Þrst detailed census in 1851, Irish was nearly absent from the eastern half
11 Much
of this section draws from Hindley (1990).
in Nettle and Romaine (2000), p.140.
12 Quoted
8
of the country and was losing ground everywhere except the far western tip”
(Nettle and Romaine (2000), p. 135). The Gaeltacht (the Irish speaking regions)
is now conÞned to the west of Ireland, and is still shrinking. According to the
1991 census, about 71% of the population of the Gaeltacht was Irish-speaking
(versus about 20% of the population as a whole).
Upon independence in 1922, Irish became the Þrst official language, while
English was retained as a second official language. The government actively promoted the teaching of Irish in schools, as well as the use of Irish as a medium
of instruction. The teaching of Irish is compulsory in primary and secondary
schools, and competency in Irish is required for entry into the National University system. The use of Irish as a medium of instruction was more difficult
to achieve. Resistance came from both teachers, many of whom did not speak
Irish, and parents, who did not want their children to learn a language that did
not generate as many economic opportunities as English.
While there are about one million Irish speakers, only about 60,000 of them
are ßuent and use it on an everyday basis.13 English is the primary spoken
language in all but the Gaeltacht. The Irish experience suggests that while
compulsory schooling may prevent language death, it may not be sufficient for
a language to become the primary spoken language. According to Hindley, the
Irish schooling policy and its “almost total failure to make Irish speakers of
the children is a measure of the strength of external environmental pressures
towards English”.14
2.3
Breton in France
Another example of minority language assimilation involves the province of
Bretagne (Brittany) in France. Bretagne has about the same population as
Wales, and like Wales, is below the national average in per capita GDP. From
the time of the French Revolution, France has attempted to impose French on
its population. As late as the 1850s, however, 20% of all Frenchmen could
still not speak French and at the turn of the century, 90 percent of Bretons
spoke Breton.15 According to Coulmas (1992, p. 177), industrialization led to a
halving of the number of speakers by 1952; by 1972 only 25% of the population,
mainly the elderly, used the language in everyday communication. A survey
taken in 1987 indicated that about 8 percent of the population spoke Breton
frequently and about 12 percent spoke it occasionally.16 Today, only about
300,000 speak Breton (about 11% of the population) and of those, only 3%
use Breton as the primary language, and most of these are elderly.17 As with
Welsh and Irish, the majority of Breton speakers tend to be concentrated on
13 Robert
Brummett, “The Irish language”, www.local.ie/content/shtml.
p. 39.
15 The Economist, April 29, 2000.
16 See www.bzh.com/identite˜bretonne/langue/uk-langue bretonne.html.
17 The New York Times, October 17, 1999, and The Economist, April 29, 2000.
14 Hindley,
9
the western coast line of Bretagne.18
A law was passed in 1951 permitting the use of Breton (and other regional
languages, such as Occitan) in schools. This law is largely symbolic, however,
because very few schoolchildren in fact obtain schooling in the language.19 Both
government and non-government promotion of Breton is far weaker than is the
case for Welsh and Irish. Breton’s future looks very shaky.
2.4
Ainu in Japan
The Ainu led an independent life in Northern Japan, sharing neither language
nor location with the rest of Japan until the Meiji restoration of 1868. Subsequently, the Ainu became integrated into the Japanese economy and society.
Replacing subsistence living, wage labor emerged; intermarriages occurred at a
rapid rate. Between 1927 and four decades later the rate of intermarriage increased from 36 percent to 88 percent. Japanese replaced Ainu as the language
of commerce and other everyday communications. The Ainu language is now
extinct.20
2.5
Catalan in Spain
Catalan is an example of a minority language that is ßourishing. According to
the 1996 census, about 79% of the population of Catalonia can speak it, even
though only about half of the population is ethnically Catalan.21 The success
of Catalan is probably due to both political and economic forces. In 1983,
Catalan attained at least equal status with Castilian (Spanish) in schools and
government offices when it was stipulated that Catalan should be the normal
language of education at all levels.22 In 1998, another law was passed that
further tipped the balance to Catalan from Castilian. Also, Catalonia is Spain’s
most economically successful region, with only 13% of the population but 20%
of GDP.23
2.6
French in Canada
Turning to North America, we have the experience of French speakers in Canada.
Here, the issue is not one of language death per se, given that French is spoken in many other locations; rather, the relevant question is the stability of the
language community. Currently, about 14% of the population are monolingual
French, of whom the vast majority are of course in Québec. About two-thirds
speak English only, and most live outside Québec. About 17% are bilingual, of
18 See,
for example, Nettle and Romaine (2000, pp. 136-137).
Economist, April 29, 2000.
20 Coulmas, p. 171.
21 The Economist, September 20, 1997.
22 www.eblul.org/languages/catalan.htm
23 The Economist, December 14, 1996.
19 The
10
whom about half live in Québec province.24 Since the end of World War II, the
percentage of French speakers in Canada has been falling slowly but steadily, despite the fact that the Canadian government has attempted to promote French.
In 1969, the Official Languages Act accorded equal status to French and English. The Official Languages Act of 1982, meanwhile, recognized English and
French as the official languages of all federal institutions.
Alarmed by the continued decline in French speakers, Québec unilaterally
imposed restrictions on English language use and, in 1974, French became the
official language of the province. But a far reaching law in 1977, Bill 101,
the Charter of the French Language, had greater impact.25 English-language
schools “were greatly restricted” by this law. The law also “changed English
place-names and imposed French as the language of business, court judgements,
laws, government regulations, and public institutions”.26
These restrictions led to substantial outmigration from Québec: about a
quarter of a million English-speaking Québecers have left the province over the
last twenty-Þve years.27 In 1986, 90 percent of Canadians whose mother tongue
was French lived in Québec and 83% of the population of Québec reported
French as the mother tongue. Both of these proportions have been increasing.
Conversely, the proportion of Québecois speaking English at home declined
from 15 percent in 1971 to 12 percent in 1986. While the number of bilinguals
in Canada has been increasing, and more than half live in Québec, the province
is still only 35 percent bilingual.
It is estimated that French speakers outside Québec are converting to English
at the rate of about 30% per generation.28 This is why, despite the policy in
Québec, the percentage of French speakers in all of Canada has continued to
fall, reaching 24 percent in 1986.29
2.7
2.7.1
Immigration and Minority Languages in the United
States
Native American Languages
At the time of Columbus, there were approximately 300 languages spoken in
North America. In 1962, there were about 210 languages, of which 89 had
young speakers. Today there are only about 150, and of these, only 20 are
still spoken in homes by children.30 Hence, it is estimated that all but these
20 languages will become extinct by the end of the 21st century. Even the
24 See
www.pch.gc.ca/offlangoff/publicatons/mythes/english/abc.html.
www.pch.gc.ca/offlan...perspectives/english/languages/prov.html.
26 See http://www.linksnorth.com/canada-history/Québecsep.html.
27 New York Times, March 15, 2000.
28 Louise Beaudoin, Quebec language minister, quoted in New York Times, March 15, 2000.
29 Canada Year Book, 1990.
30 Los Angeles Times, January 25, 2000, and Nettle and Romaine (2000, pp.119-120).
25 See
11
most commonly spoken Native American language, Navajo, is facing diminishing numbers. The number of ßuent speakers is apparently half of what it was
a decade ago, and the number of Navajo children speaking only English has
“nearly tripled to almost 30 percent from 1980 to 1990”.31
For decades the Bureau of Indian Affairs actively discouraged the use of
Native American languages in schools. The passage of the Native American
Languages Acts of 1990 and 1992 marked the Þrst time that official government
policy was meant to protect the languages. For many languages, especially those
with no young speakers, this is almost certainly too little, too late. According
to Nettle and Romaine (2000, p. 120), “only a handful of indigenous languages
—Navajo and Dakota in the US, Cree and Ojibwa in Canada — seem promisingly
viable, with thousands of speakers and schooling projects”.
2.7.2
German Immigration in the 19th Century
Waves of immigrants — and their subsequent assimilation — provide another facet
of dynamic language evolution. The signiÞcance of immigration in the history
of the United States sets it apart. One of the best documented immigrant
waves is the mid- and late-19th century inßux of Germans, which was unique
both in its size and its regional concentration. In 1910, according to Kloss
(1966), the German-speaking community peaked at 8.8 million Þrst and second
generation German-Americans — over 9% of the U.S. population. Most lived
in the Midwest. This remains to this day the largest incidence of speakers of a
language other than English in the United States.32
The German-American presence in the Midwestern states was sufficiently
large that local and state governments passed laws mandating that classes be
taught in German. Kloss (1966) documents in Ohio in 1839 what may have
been the Þrst instance of elementary school bilingualism. In the following year
it became mandatory for Cincinnati to provide bilingual schools. Baltimore and
Indianapolis established similar schools in 1874 and 1882, respectively. Many
Midwestern states created “a legal framework for preventing state authorities
from interfering” with the teaching of German during the 1850s, 1860s and
1870s.33 German language schools also included parochial and private nonsectarian schools. By 1900 over 4,000 schools, with over half a million students, taught German and/or taught in German. Up to 10,000 clubs, numerous
churches, and about 500 German language newspapers (with a combined circulation of over 3.4 million), also helped preserve and maintain the language.34
Two World Wars and lower German immigration eventually led to almost
complete English language assimilation within the next half century. As late as
1940, there were still Þve million people in the U.S. with German as the mother
31 ”Indians’
languages near extinction”, Arizona Republic, July 16, 2000.
from the 2000 U.S. Census are not yet available.
33 Kloss, p. 235.
34 See Kloss (in Fishman (1966)) and Fishman, Hayden, and Warshauer in Fishman (1966).
32 Data
12
tongue, including one million third-generation inhabitants, but by 1965, “at
most 50,000 of those under eighteen years of age still speak German natively”
(Kloss (1966, p. 248)).
Most immigrants to the United States assimilated more rapidly. The sheer
size of the community was evidently important for German language maintenance. In addition, Kloss (1966, p. 226) argues that an important factor
was that “a great many German immigrants lived either in language islands
or in monolingual urban sections. They settled in states and territories which
were still in a pioneering stage”. The relative isolation of the Midwest, according to Kloss, also contributed to the relatively slow assimilation of GermanAmericans.35 In fact, in Minnesota, the smallest drop off in the use of German
in the parishes between 1940 and 1950 was in the Minneapolis-St. Paul area,
with presumably the largest number of German-Americans in the state.36
2.7.3
Hispanic and Asian Immigration in the 20th Century
If current trends continue, the numerical importance and geographic concentration of the Spanish speakers in the United States will eclipse that of the
German speakers a century earlier. The large immigrant inßux and the geographic concentration of residences parallel the German experience. By 1976,
the group claiming Spanish as a mother tongue was almost three times as large
(5.7 million) as the German and Italian mother tongue groups.37 According to
the 1990 census, those claiming Spanish as a mother tongue were more than 7
percent of the population, (17.3 million); this is more than eight times larger
than the second largest language group.
More than half of all Hispanics live in California and Texas, although these
states contain less than 20 percent of the total U.S. population. Both foreignborn and native-born Spanish speakers in Arizona, New Mexico, and Texas have
lower rates of English use and higher rates of Spanish monolingualism than their
Spanish speaking counterparts in other regions of the U.S.38 Almost one quarter
of Hispanics live in households in which no person over 14 speaks English very
well.39 It seems clear that this pattern is partially explained by the geographic
proximity of Mexico to these states.
What are the intergenerational language dynamics involving immigrants and
their offspring? Broadly speaking, something similar to the three-generation
pattern discussed earlier applies, but with the conversion to English monolingualism occurring slowly. According to Lopez (1996), drawing from the 1989
35 Lazear (1995) presents evidence that German-speakers in 1900 were less clustered relative
to their size than other immigrant groups. Lazear Þnds that size clearly matters, but it seems
to have mattered less for German-speakers than for other immigrant groups.
36 This information draws from Hofman (in Fishman (1966)).
37 Veltman p. 46.
38 Veltman (1983), p. 71.
39 U.S. Census (1990). In addition, almost one-fourth of Asian immigrants live in households
in which no person speakes English ’very well’. The average for the U.S. is 3.4 percent.
13
Ethnicity and generation
Mexico 1
Mexico 2
Mexico 3
Native Language
88.4
36.4
19.5
Bilingual
9.1
49.1
48.3
English only
2.5
14.5
32.3
Other Hispanic 1
Other Hispanic 2
Other Hispanic 3
69.2
14.4
2.6
25.0
60.3
30.5
5.8
25.3
62.9
Table 2: Language(s) Spoken at Home by Hispanic Immigrants, by Generation
Ethnicity and generation
Asian 1
Asian 2
Asian 3
Native Language
53
4
7
Bilingual
36
19
11
English only
11
77
82
Table 3: Language(s) Spoken at Home by Asian Immigrants, by Generation
CPS, 77% of Þrst generation Hispanic immigrants speak only Spanish and 53%
of second generation immigrants are bilingual. However, only 38% of third generation immigrants are monolingual English and 45% are bilingual.40 Table 2
shows that assimilation occurs more slowly for Mexican immigrants, who constitute the largest Hispanic immigrant sub-group, compared to other Hispanics.
The experience of Asian-speaking immigrants is on the other side of the
three-generation pattern: Asian immigrants often assimilate more quickly. According to Lopez (1996), for Asians between 25 and 44 years old, more than
half of the Þrst generation immigrants are monolingual in their native language,
but 77% of second generation immigrants are monolingual in English (see Table
2). So the bilingual generation often seems to be skipped (although it should
be noted that more than one third of Þrst generation immigrants are already
bilingual).
2.8
What Have We Learned?
In our broad survey of language dynamics, we have considered several cases
where minority languages gradually lost ground to majority languages. One
phenomenon that frequently emerges is what Nettle and Romaine (2000, p. 136)
call the “classic three-generation pattern of language shift” (it is also discussed
in Durkacz (1983)), whereby a language community passes from monolingualism
in the minority language through bilingualism to monolingualism in the majority
language over the course of about three generations. We noted that both Irish
and Welsh appear to exhibit roughly this pattern, as do many immigrant groups
40 Earlier
evidence by Lopez (1982) and Veltman (1983) is also consistent with this work.
14
in the United States. The pace of this adjustment is not constant, however.
Some language communities disappear very fast, such as those of Asian speakers
in the United States. Others disappear more slowly.
The rate at which a language community disappears is apparently linked to
the overall size of that community. The large German-speaking community in
the United States was stable for a long period, and the current large Spanishspeaking community likewise shows no signs of disappearance. Conversely,
smaller immigrant language communities disappeared, and numerous languages
spoken by smaller groups have vanished, including hundreds of Native American
and Australian aboriginal languages, Cornish, and Manx. Not surprisingly,
linguists generally agree that languages (and language communities) with a
small number of speakers are at greater risk of extinction. One rule of thumb
is that any language with fewer than 100,000 speakers is under serious threat
of extinction.41 By this metric, 90% of the world’s 6000 languages are at risk.
Geography evidently plays a signiÞcant role in the disappearance of languages also. The Celtic languages such as Irish, Welsh, Cornish and Breton
were all encroached upon by the majority language. In each case, the boundary between the majority and minority language shifted over time (westward
in each case), so that the speakers of the minority language were increasingly
to be found in isolated rural and coastal regions. Papua New Guinea, which
is mountainous and heavily forested, is estimated to contain about 860 different languages. These languages are able to survive in large part because the
topography and vegetation make it difficult to travel and communicate between
language communities. Similarly, linguists consider Icelandic to be a relatively
secure language, even though it has a relatively small number of speakers.
Economic forces also appear to play an important role. The regions in
which Irish, Welsh and Breton are spoken are remote in the sense that they far
removed from the centers of economic activity. Ainu survived as a language
when the region in which it was spoken was isolated from the rest of Japan; it
disappeared following economic integration. The survival of multiple languages
in Papua New Guinea, meanwhile, is in part due to the fact that islanders
have — at least until recently — seen only limited economic advantage to being
part of a larger economic community.42 Economic forces may now be putting
these languages at risk, as Papua New Guineans are beginning to see economic
gains from speaking languages such as Tok Pisin or, in some cases, English.
Our examples suggest that a minority language must also be associated with
enhanced economic opportunities if it is to be a language of everyday use, as is
evidenced by French in Québec and Catalan in Spain.
41 According to Nettle and Romaine (2000, p. 8), this Þgure of 100,000 has been suggested
by Krauss.
42 As Nettle and Romaine (2000, p. 89) put it, “The local gardens reliably provided for
most basic needs. ... In general, the range of goods and services available outside the local
groups was not sufficient to entice people to enlarge the scale of marketing and economic
specialization.”.
15
This paper is concerned primarily with economic explanations of language
change, but there are of course many other signiÞcant variables that we either
ignore or treat as exogenous in our analysis. Most obviously, politics and policy
have a substantial inßuence on the survival or death of languages. Historically,
colonialism — and the war, disease, and slavery that it brought along — led to
the disappearance of hundreds, perhaps thousands, of languages in Africa, Australasia, and throughout the Americas. Tasmanian disappeared as a language
by the brute fact that its aboriginal speakers were imprisoned and slaughtered.
Smallpox and other diseases introduced by settlers caused the population of
central Mexico to decline by over 90% between 1519 and 1580, causing the loss
of an unknown number of languages.43 Colonialism also led to the imposition of
official state-sanctioned languages, which were then enforced through schooling
and other policies.44
More recently, the focus of policy has shifted in many countries, and policies
have been put in place to aid the survival of threatened languages and language
communities. Recent experience suggests that explicit government policies that
favor minority languages are able to avoid, or at least postpone, the extinction
of the minority language. This appears to have been the case for Irish and
perhaps also Welsh, but came too late for Cornish, Manx, and other languages.
The fate of Breton, Galician, and many other languages is still unknown.
3
The Model
3.1
Preliminaries
We consider a world of successive generations, indexed by t = 0, 1, .... Each
generation’s agents live for three periods: one period of childhood, and two
periods of adult life. In the second period of adult life, the next generation of
children is born, so that the childhood period of generation t + 1 overlaps with
the last period of life of generation t. In childhood, children acquire a language
endowment that depends upon the languages spoken by the previous generation.
Agents only make economic decisions, however, in the two adult periods of their
life. (Because the different generations do not interact economically, we describe
the model as one of successive, rather than overlapping, generations.) We refer
to each date (t) as consisting of the two periods of adult life of generation t.
The world possesses two locations, denoted by {1, 2}, and two languages.45
43 See
Nettle and Romaine (2000, p. 117-118 and p.124).
should also note that a language may die as a simple consequence of linguistic evolution. Latin is no longer spoken not because Latin speakers died out, nor because Latin was
displaced, but simply because it mutated. We do not consider such language evolution in
this paper.
45 Note that we take a language to be a primitive concept. By so doing, we abstract from
issues such as the dynamic evolution of language and the development of dialects and pidgin
languages. We plan to address language evolution in later work.
44 We
16
For expositional purposes, we refer to the languages as English and Spanish.
There is a large, but Þnite, number of agents, and the number of adult agents
is constant over time. We normalize the total mass of agents in each generation
equal to 1, and set the mass of an individual agent equal to ε.46 In any
period, agents are uniquely located either in region 1 or region 2 and are English
monolinguals (indicated by e), Spanish monolinguals (s), or bilinguals (b).47
The number of children of generation t born in location n (n = 1, 2) equals
the total number of agents of generation t − 1 in location n at the end of date
t − 1. The distribution of agents across locations at the beginning of each date
b ; n = 1, 2)
t is given by {e1t , e2t , s1t , s2t , b1t , b2t } ≡ {jnt }, where jnt , (j = e,
Ps,P
jnt = 1∀t.
denotes the mass of agents of type j in location n at date t, and
n
j
We let et ≡ e1t + e2t represent the total mass of English monolinguals at the
beginning of date t, and similarly for st and bt .48
At the beginning of the Þrst period of adult life, monolingual agents make
a decision either to spend the period in production, or to learn the other language. During this period, agents remain in the location in which they were
born. At the beginning of the second period of adult life, agents make a decision either to remain in their current location, or to migrate to the other
location. In the second period of adult life, agents engage in production. After these learning and location decisions have been made, there will in general be a new distribution of agents in the second period, which we denote by
0
}. There is an initial distribution of agents at the
{e01t , e02t , s01t , s02t , b01t , b02t } ≡ {jnt
0
}. Figure 1 shows a timeline of the decisions of agents
end of date t = 0: {jn0
in this economy.
46 These assumptions imply that the total number of agents equals 1/ε. The assumption
that an individual agent has positive mass plays a technical role in some of the lemmata
below. For most purposes, however, the distinction between the number of agents and the
mass of agents is unimportant for our paper, and (with a slight abuse of language) we will
use the terms interchangeably when there is no possibility of confusion. Similarly, for ease of
exposition, we will treat e, s, and b as continuous variables; nothing of substance is affected
by this expository device.
47 It is necessary to be precise about the distinction between monolinguals of a language
and speakers of a language. English monolinguals, of course, speak only English. The total
number of English speakers equals the number of English monolinguals plus the number of
bilinguals.
Also, we treat both Spanish and English symmetrically, that is, they are equally efficient in
economic interaction, all else equal. An alternative framework could include for diglossia, in
which one language is used in the workplace and another language is used at home.
48 We make the assumption, common in overlapping generations models, that each parent
has a single child. In the current setting, this assumption is not completely innocuous, since
many children have parents who speak different languages. We could complicate the model
by, for example, allowing random matching of parents, and specifying different probabilities
for all the different possible combinations of parents’ language skills. For a more complicated
model of cultural transmission across generations, see Bisin and Verdier (2000).
17
3.2
Preferences and Technology
Throughout this subsection we drop the t subscript. The preferences of all
agents are identical, and are assumed to be linear in consumption:
u(c, c0 ) = c + δc0 ,
(1)
where c is consumption in the Þrst period, and c0 is consumption in the second
period. We think of δ as a measure of the amount of time an agent can spend
using a language relative to the amount of time it takes to learn the language.
We do not need to make any assumption on the magnitude of δ, although given
that agents are likely to be able to beneÞt from their language skills for a longer
period than it takes to acquire those skills, it is reasonable to think that δ ≥ 1.
Language and geographical proximity are essential ingredients of production:
output can be produced only when agents are in the same location, and agent
i is more productive when there are more agents in i’s location that share i’s
language. We assume that there are no asset markets and that goods are perishable, so i’s consumption equals i’s production in both periods.49 SpeciÞcally,
we assume that agent i’s consumption in a period is given by
ci
ci
= 0 if agent i is inactive (learning)
= h(Ni , N ) if agent i is active (producing)
(2)
where Ni is the mass of active agents (including agent i) in the region who share
agent i’s language, and N is the total mass of active agents in the region. We
make the following additional assumptions about this technology.
• Assumption A1: h() is continuous and differentiable in both its arguments.
Further, h1 (·, ·) > 0; h11 (·, ·) ≤ 0, where h1 is the partial derivative of
h(., .) with respect to its Þrst argument and h11 is the second derivative
of h(., .) with respect to its Þrst argument.50
• Assumption A2: h2 (·, ·) ≤ 0.
• Assumption A3: Ni h1 (Ni , N ) + N h2 (Ni , N) ≥ 0
• Assumption A4: h(ε, N) = c∀N ; h(x, N ) À h(ε, N )∀x > ε.
• Assumption A5: h(1, 1) = 1
Assumption A1 states that per capita output is increasing and (weakly)
concave in the number of active agents who share agent i’s language. In other
49 Thus
we use the terms production and consumption interchangeably.
the number of agents is Þnite, the domain of h (·, ·) is in fact a set of discrete
points. This of course does not preclude our writing h (·, ·) as a continuous function. We do
so not because continuity and differentiability are required for any of our results, but simply
because it allows us to express the nature of our technology in a compact way.
50 Because
18
words, there is a network externality in the model and this network effect exhibits non-increasing marginal returns. Assumption A2 states that there may
be a congestion externality present, and Assumption A3 implies that there are
non-decreasing returns to scale, so that the congestion externality never outweighs the network externality. When A3 holds with equality, we have constant
returns to scale, and when it is a strict inequality there are increasing returns.51
One interpretation of A3 is that agent i is no worse off if one more speaker of
i’s language enters i’s location.
Assumption A4 implies that even a single agent can produce something;
hence, there is always a positive cost to learning the other language. We can
think of this assumption as home production. However, as indicated in the
second part of the assumption, this production is relatively inefficient (recall
that ε is the mass of an individual agent.) The Þnal assumption (A5) is a
normalization.
The technology described by A1 to A5 is quite general. It encompasses many
special cases, such as the technologies in the models of Church and King (1993)
and Lazear (1999). These cases can include constant returns to scale:
Ni h1 (Ni , N ) + N h2 (Ni , N ) = 0
h(N, N ) = h(1, 1) = 1∀N > ε
¶
µ
Ni
,1 ;
h(Ni , N ) = h
N
(3)
as well as increasing returns to scale:
Ni h1 (Ni , N ) + N h2 (Ni , N ) > 0
h(N, N) strictly increasing in N
h(N, N ) < 1∀N < 1.
(4)
In an economy where all agents can communicate with each other, the degree
of increasing returns to scale governs the extent to which per capita output
rises as the size of the population increases. The concavity of the production
function with respect to its Þrst argument, meanwhile, measures the extent to
which an agent’s output increases as other agents learn that agent’s language
(holding the size of the economy, N, constant). This concavity reßects both the
returns to scale and the congestion effect: in an economy where the congestion
externality is strong, there is a large output effect if agents switch language.
To illustrate, suppose that
µ ¶β
α Ni
= (Ni )α+β N −β .
(5)
h(Ni , N ) = (Ni )
N
51 Our references to ’constant’ and ’increasing’ returns are with respect to location-wide
output, not each agent’s output. That is, under constant returns to scale, h(Ni , N) is homogeneous of degree zero in its arguments, and Ni h(Ni , N)+(N −Ni )h(N −Ni , N) is homogeneous
of degree one.
19
Here, α measures the returns to scale: when α = 0, we have constant returns,
and as α increases, the returns to scale become stronger. Meanwhile, β measures
the size of the congestion externality. For a given degree of overall returns to
scale, a larger value of β implies a larger gain in per capita output of the speaker
of a language when the number who share that language increases. The overall
effect of learning by others in the region (that is, a change in Ni holding N
constant) is given by α+β, which is a measure of the concavity of the production
function with respect to its Þrst argument.52
For our purposes, it is sufficient to specify the technology at this level of
generality of (2), without assuming a speciÞc functional form such as (5) and
without taking a stance on the underlying economic environment and technologies. There are in fact several possible stories that could generate the production
function we have speciÞed. First, we could think of the underlying economic
environment as involving search and matching. In the spirit of Diamond (1982),
imagine that agents can produce goods costlessly, but can carry only one indivisible unit at a time. Agents randomly meet others in their location, and two
agents can swap goods and consume if they can communicate — that is, if they
share a language.53 A second interpretation of our technology is that production takes place in teams, and team production requires both a shared language
and geographical proximity. And, Þnally, we can think of the technology in (2)
as arising in an economy with intermediate goods. For example, imagine that
all agents produce one unit of a specialized intermediate input. Suppose further
that competitive Þnal goods producers in each location purchase goods from one
language group and costlessly assemble goods from these intermediate inputs
using a Dixit-Stiglitz technology.54 Then it is easy to show that we will obtain a
technology satisfying the above restrictions. In a sense, this story decentralizes
the team production structure noted above.
52 Because we have normalized the total number of agents to 1 and we have also normalized
h(1, 1) = 1, output per capita is in general lower (for given Ni , N ) when the returns to scale
are higher. The logic is as follows. In an economy with low returns to scale, most of the
percentage gains from the network externality can be realized even with a small number of
agents, and so an agent can get most of the way to maximum per capita output at a lower
value of Ni . When we interpret our results in the context of real economies, it follows that
we would expect the returns to scale to be lower in larger economies, other things equal.
53 The model here is thus related to work on search-theoretic models of international money
(see, for example, Kiyotaki and Wright (1989, 1993), Matsuyama, Kiyotaki and Matsui (1995),
Trejos and Wright (1995), and Williamson and Wright (1994)). Still, there are many respects
in which language, as modeled here, and money, as modeled in the above papers, are quite distinct. For example, money facilitates transactions, but barter is an alternative. Language (of
some form) is more fundamental; without language there cannot be production/transactions.
Also, the acquisition of a language is a (largely irreversible) human capital investment decision
that has an explicit cost for an individual, and which then yields a stream of beneÞts. There
is no obvious counterpart to this in monetary theory.
54 As used in the trade models of Krugman (1979), Ethier (1982), and others, and the growth
models of Romer (1990) and others.
20
3.3
Evolution of Language Groups Over Time
The language endowments of each new generation of agents in each location
depend upon the Þnal language allocations of the previous generation in that
location. Without loss of generality, we describe this mapping for the case
where all agents are in a single location, and suppress the index n.
We model the evolution of language by assuming that, with some probability,
the children of monolingual parents become bilingual, and with some probability, the children of bilingual parents become monolingual in one or the other
language. These probabilities are assumed in turn to depend upon the relative
frequency with which the two languages are utilized. We refer to this relative
frequency as the “ambient language”. The underlying idea is that the language
or languages acquired by children are inßuenced both by the languages of their
parents and the languages spoken in the society in which they grow up. In other
words, the languages of children can be thought of as pre-determined, rather
than as a choice variable.
SpeciÞcally, we assume
¢
¢
¡
¡
(6)
et = ρ e0t−1 , s0t−1 ; θet−1 e0t−1 + µ e0t−1 , s0t−1 ; θ et−1 b0t−1 ;
¢ 0
¢ 0
¡ 0
¡ 0
s
s
0
0
st = ρ st−1 , et−1 ; θt−1 st−1 + µ st−1 , et−1 ; θt−1 bt−1 ;
bt = 1 − et − st
Thus ρ(e, s; θe ) represents the probability that the child of an English monolingual will also be an English monolingual, and 1 − ρ(e, s; θe ) is the probability
that the child of an English monolingual will instead become bilingual. (We
assume that the child of an English monolingual can always speak English.)
Meanwhile, the child of a bilingual becomes an English monolingual with probability µ(e, s; θe ) and a Spanish monolingual with probability µ(s, e; θs ) (and
is bilingual with probability 1 − µ(e, s; θ e ) − µ(s, e; θs )). The vectors θe and
θs represent other variables that might affect language acquisition, including
schooling policies, prevalent languages in the media, and so on.
We assume that ρ(x, y; θ) and µ(x, y; θ) are homogeneous of degree zero in
x and y, implying that — with a slight abuse of notation — we can write55
µ
µ
¶
¶
e
e
e
e
e
e
; θ ; µ(e, s; θ ) ≡ µ
;θ ;
ρ(e, s; θ ) ≡ ρ
(7)
e+s
e+s
µ
µ
¶
¶
s
s
; θ s ; µ(s, e; θs ) ≡ µ
; θs .
ρ(s, e; θs ) ≡ ρ
(8)
e+s
e+s
In other words, it is the relative proportions of English and Spanish monolinguals that determine the ambient language, and the ambient language is not
55 This
follows from deÞning
ρ(x; θ) ≡ ρ
³
´
x
, 1; θ , µ(x; θ) ≡ µ
1−x
21
³
´
x
, 1; θ .
1−x
affected by the presence of bilinguals. We assume that, over the relevant domain, µ(x; θ) ∈ [0, 1] and ρ(x; θ) ∈ [0, 1]; this guarantees in turn that et and st
lie in the interval [0, 1]. We assume also that these functions are continuous and
differentiable, and that ρ0 (·) > 0, µ0 (·) > 0. Hence if there are relatively more
English monolinguals, then, other things equal, we expect to see more children of
bilinguals become monolingual English and fewer become monolingual Spanish.
Likewise, more children of English monolinguals will themselves be monolingual,
while more children of Spanish monolinguals will become bilingual. Finally, we
assume that
ρ(1; θ) = 1 ∀θ;
µ(0; θ) = 0 ∀θ.
(9)
(10)
The Þrst condition implies that monolingualism is an absorbing state: if at some
date all agents are monolingual speakers of the same language, then this will
be the case at all dates thereafter.56 The second condition rules out spontaneous rebirth of a language: if the number of monolinguals of a given language
equals zero at a given date, there will never be monolinguals of that language
thereafter.57
4
The Model Without Learning or Migration
We build up the behavior of our model in stages. In this section, we focus solely
on the dynamic adjustment of language groups over time, assuming no learning
and no migration. Ignoring agents’ choices about language and location allows
us to establish a benchmark for the dynamics and for the long run effects of
policies such as schooling. In Section 5 we turn to the learning decision: we
examine the model with learning, but assume a single location. In Section 6, by
contrast, we consider the migration decision: we examine the model with two
locations, but with no learning. Section 7 contains results from the full model
with learning and migration.
With no migration and no learning, there is no need to distinguish the two
subperiods at each date. For simplicity, we assume that all agents are in a single
location.58
56 Strictly speaking, this statement anticipates a trivial result on learning also, to the effect
that, when all agents are monolingual, no individual agent will choose to learn in equilibrium.
57 The idea behind this assumption is that a language with no monolinguals will fall into
disuse, since all agents will use the other language for communication. We also impose two
further technical restrictions on the language transmission probabilities, namely,
µ(x; θ) + µ(1 − x; θ)
2µ (·) − ρ (·)
≤
<
1, ∀x ∈ [0, 1] , ∀θ;
1.
The Þrst condition guarantees that the number of bilinguals never becomes negative, and the
second rules out unstable oscillatory dynamics.
58 Completely analogous arguments apply to each individual region if agents are present in
22
4.1
Existence of Steady States
Lemma 1 Existence of steady states. (i) Complete monolingualism (e = 1
and s = 1) are steady states. (ii) There exists at least one interior steady state.
If θe = θs , then there exists a symmetric steady state: e = s.
(Proofs of all results are in the Appendix.)
There are at least three steady states in the model, an English monolingual
steady state, a Spanish monolingual steady state, and one or more interior
steady states with positive numbers of both monolingual groups and bilinguals.
Because of the symmetry of the model, there is an interior steady state with
an equal number of English speakers and Spanish speakers whenever θe = θ s .
Figure 2, panel A, which is based on a mapping deÞned in the proof of Lemma
1, illustrates these steady states. At the level of generality at which we have
speciÞed the ρ (·) and µ (·) functions, we cannot place further restrictions on
the equilibrium number of steady states. That is, it is possible for there to be
multiple interior steady states, as illustrated for example in Figure 2, panel B.
4.2
Stability of Steady State
Lemma 2 (i) If, at some date, there are no monolinguals of one language,
then the economy will tend to a steady-state with only monolinguals of the other
language — that is, bilinguals will disappear. (ii) The monolingual steady states
are locally stable. (iii) Assume that θe = θs . The interior steady state is locally
stable iff
¡1¢! "
¡1¢ 0 ¡1¢ Ã
¡1¢ 0 ¡1¢#
1
−
ρ
ρ
µ
2 ¡ ¢2
¡ ¢2
<
1 − 2 ¡ 1 ¢2
ρ 12
ρ 12
µ 2
Lemma 2 , part (i) tells us that, if initially there are no Spanish monolinguals,
then the economy will head towards the English monolingual steady-state: the
bilingual speakers will gradually disappear. The intuition, of course, is that
Spanish would never be spoken in such a world, and so the ambient language
would be uniquely English. Thus, all children of English monolinguals would
always be monolingual English, whereas only a fraction of children of bilinguals
would themselves be bilingual. Lemma 2, part (ii) indicates that if the economy
gets sufficiently close to monolingualism, it will always tend to the monolingual
steady state.
By contrast, the interior steady state can be either locally stable or locally
unstable. Part (iii) of the lemma shows that the symmetric interior steady state
is less likely to be stable when the elasticity of ρ() and/or the elasticity of µ()
e
) are relatively large. The elasticity
(with respect to the ambient language, e+s
of ρ() governs the extent to which an innovation in, say, the number of current
both. The only difference is that the values of the variables need to be interpreted as fractions
of the total number of agents present in the location.
23
English monolinguals leads to future English monolinguals. The elasticity of
µ() governs the extent to which an innovation in bilinguals will return to being
English monolinguals in the next date. The bigger are these elasticities, the more
likely it is that an innovation in the number of English speakers will be persistent
or self-reinforcing, and the more likely it is that the interior equilibrium will be
unstable. One extreme case is where the two elasticities are zero; that is, the
transition probabilities are independent of the ambient language. Then it is
evident that there will be a stable symmetric interior steady-state. A smaller
value of ρ (1/2) also works in the direction of stability, because it implies that
the children of monolinguals tend not to remain monolinguals: monolingualism
is less likely to become entrenched.59 Panel A of Figure 2 illustrates the case
where the symmetric steady state is unstable. Panel B illustrates the stable
symmetric steady state (note that there are also two unstable steady states).
4.3
Comparative Statics
The intergenerational transmission of languages may be affected by market
forces and government policies. The higher per capita income of English speakers (versus Spanish speakers) in the United States, or the prevalence of Englishlanguage media, including the Internet, throughout the world are examples of
the former. Schooling policies or regulations on the language of commerce and
government are examples of the latter. We introduce these forces in a straightforward way:
Suppose that
¶
µ
¶
µ
θe
e
; θe
= ρ
;
ρ
e+s
θe + s
¶
µ
µ
¶
s
s
; θs
= ρ
ρ
; θ > 1;
e+s
θe + s
and similarly for the µ (·) functions. Here, the number of English monolinguals
have a disproportionate effect on the ambient language; θ captures this disproportionate effect, reßecting the fact that one language is “favored” by markets
and government.
The broken lines in Figure 2 show the effect of an increase in θ. In Panel
B, we observe the intuitive result that the stable symmetric steady state occurs
at a larger value of e/ (e + s). There are relatively fewer Spanish monolinguals
in this steady state. In Panel A, with the unstable interior steady state, we
observe that this steady state now occurs at a lower value of e/ (e + s). This is
again intuitive: it reßects the fact that a larger set of initial conditions would
ultimately result in English monolingualism.
59 Our result contrasts with Bisin and Verdier (2000) who place restrictions on their model
that guarantee that it always possesses an stable interior steady state.
24
4.3.1
The Long-Run Preservation of Minority Languages
Many countries and regions actively pursue policies in order to preserve minority
languages and/or to have multiple official languages. The most prominent policies include the teaching of the language in elementary and secondary school (for
example, Irish in Ireland, Welsh in Wales), regulations requiring the language to
be used in government (and perhaps also private) business (for example, French
in Québec, Catalan in Spain), and provisions for minority language media outlets (for example, Welsh in Wales, Spanish in the United States). Our prior
discussion noted that many of these policies have not succeeded in creating a
true multilingual environment. Our model helps us to understand why this is
so.
Inspection of Figure 2 reveals that there are two distinct issues. First, the
long-run survival of multiple languages within a single region requires that the
economy must have a stable interior steady state, as in Figure 2, Panel B.
Second, it must be the case that the economy is within the basin of attraction
of that steady state. From Lemma 2, a stable interior steady state exists only if
the transition probabilities are relatively insensitive to changes in the ambient
language (that is, the elasticities of µ (·) and ρ (·) must be small). Policies
that make the ambient language less relevant for language acquisition include
the teaching of both languages, requiring both languages to be used on official
documents, etc. Also, policies that encourage the children of monolinguals to
become bilingual — that is, policies that decrease ρ (·) — help ensure the existence
of a stable interior steady state. Finland may be an example of a country which
is successfully maintaining a stable interior steady state, in which there are a
small number of monolingual Finnish or monolingual Swedish speakers, and a
large number of bilinguals.
An insight from our analysis is that it is not sufficient to encourage use
of the minority language (as in Ireland and Wales, for example). One can
imagine many policies that would affect the ambient language prevailing at any
given date. But if the underlying dynamics of the economy are such that there
is no stable interior steady state, such policies will only temporarily prevent
the economy from an inevitable shift to a monolingual steady-state. This is
illustrated by our comparative static experiment above (where we assumed that
the ambient language was given by θe/ (θe + s)). It is evident that local changes
in θ will not affect the stability properties of steady state. Thus even if we
interpret θ as a policy variable, it will ultimately be of no help in preserving a
multilingual society.
Even if an economy does possess a stable interior steady state, it may be on
a transition path to one of the monolingual steady states. Under these circumstances, policies that move the economy into the basin of attraction of the stable
steady-state could help create a bilingual environment. In the United States,
for example, a relatively open immigration policy towards Mexico and other
Spanish-speaking Latin American countries could help push the country away
25
from an English-only steady-state. And Þnally — when we allow for learning —
it is possible that agents within a generation would choose to assimilate, even
if the steady state is stable from the perspective of intergenerational language
transmission.
4.4
Transitional Dynamics
While it is possible for our model to have an interior steady state that is locally
stable, there are reasons to suspect that the unstable dynamics of Figure 2, Panel
A are the more usual case. Most signiÞcantly, this case appears more consistent
with the stylized facts of language evolution in many different countries. Also,
an interior stable steady state is ruled out by fairly mild conditions.60 Much of
our subsequent analysis will therefore focus on the unstable case.
To illustrate the dynamics of our economy, we Þrst note that we can illustrate language groups on a simplex (see Figure 3). In this diagram, any particular point on the simplex represents a mix of English monolinguals, Spanish
monolinguals, and bilinguals. The vertical height from each base represents the
number of each type of agent. Figure 4 shows a phase diagram on this simplex
under the assumption that ρ (·) is linear and µ (·) is quadratic.61
Suppose the economy starts at point A in Figure 4. Here, there are relatively few bilinguals and the numbers of English monolinguals and Spanish
monolinguals are roughly balanced, with English speakers in a slight majority.
Initially, the number of monolinguals of each language declines, and bilingualism increases. Although Spanish is the minority language, the total number
who can speak Spanish (monolinguals and bilinguals) actually increases. At
B, the dynamics change as the number of English monolinguals starts to increase, while the number of Spanish monolinguals continues to decrease. At C,
the number of bilinguals reaches a maximum. English is increasingly becoming
the ambient language. Hence, children of bilinguals are increasingly becoming
English monolinguals, while more and more children of Spanish monolinguals
become bilingual. From this point on, English monolingualism gains at the expense of Spanish monolingualism and bilingualism; the economy is now on an
irreversible path to English monolingualism.62
60 For
example, any of the following is sufficient (not necessary) to rule out local stability
1−ρ( 1
( 1 ) ρ0 ( 1 )
( 1 )ρ0 ( 1 )
( 1 )µ0 ( 1 )
( 1 )µ0 ( 1 )
2)
; 2 1 2 > 2 1 2 >
of the symmetric steady state: 2 1 2 > 1; 2 1 2 >
µ( 2 )
ρ( 2 )
ρ( 1
ρ( 2 )
µ( 2 )
)
2
¡ ¢
1 − ρ 12 .
¡
¢2
e
e
e
e
we assume ρ( e+s
) = e+s
and µ( e+s
) = e+s
.
62 Figure 4 also illustrates another dynamic path, where the economy starts with a large
number of bilinguals, and Spanish has a slight edge over English (point D). Along the dynamic
path, the number of English monolinguals increases for a while, as bilinguals are replaced
by monolinguals of both languages. After point E, however, both bilinguals and English
monolinguals are gradually replaced by Spanish monolinguals.
61 SpeciÞcally,
26
4.4.1
Intergenerational Language Dynamics
This dynamic path is noteworthy because it mirrors the three-generation pattern
of language shift discussed by Nettle and Romaine (2000), Durkacz (1983), and
others. We can also match this path with some of the data that we discussed in
Section 2. For example, Figure 5(A) plots the evolution of Welsh monolinguals,
English monolinguals and bilinguals in Wales (from Table 1 above). It can
be seen that this matches the Þnal stages of the dynamic path in Figure 2.
Figure 5(B) shows the three-generation pattern for Hispanic immigrants to Los
Angeles.63 Again, the observed data match our phase diagram.
5
Learning Only
We now turn to the version of the model in which learning, but not migration,
can occur. We thus retain the assumption that there is only a single location. Our starting point will in general be one with positive numbers of English
monolinguals, Spanish monolinguals, and bilinguals.
Within each date, our equilibrium concept is pure strategy Nash equilibrium.
An equilibrium of our model is two sequences of three-member sets, {jt } , {jt0 },
j = e, s, b, such that, taking the learning choices of other agents as given:
• at each date t, each agent chooses to learn if the gain from learning (extra
second period consumption) exceeds the cost of learning (foregone Þrst
period consumption);
• at each date t, each agent chooses not to learn if the gain from learning is
less than the cost of learning;
• language groups evolve between dates according to (6).
The Þrst two conditions govern how language groups evolve from period
1 to period 2 within a given date, from {et , st , bt } to {e0t , s0t , b0t }. The third
condition governs how language groups evolve between dates, from {e0t , s0t , b0t }
to {et+1 , st+1 , bt+1 } .
5.1
Learning Game
We Þrst consider what outcomes are consistent with equilibrium learning decisions. Two preliminary results are contained in Lemma 3 and Lemma 4.
63 We calculated the data points in Figure 5(B) as follows. First, we set our total population
equal to Hispanics (native and foreign-born) plus native-born non-Hispanics — that is, we
ignored non-Hispanic foreign born. Based on data from the 1990 U.S. Census, this population
is approximately 30% foreign-born Hispanic, 16% native-born Hispanic, and 54% native-born
non-Hispanic. We assumed that the latter are all monolingual English, and we categorized
the other two groups into English monolinguals, Spanish monolinguals, and bilinguals using
the percentages reported in Lopez (1996). We then assumed that the 30% immigrant group
evolved according to the generational data reported in Lopez.
27
Lemma 3 In the learning game, either all agents of a given type learn or none
do.
Lemma 4 Assume b < 1. The allocation where all agents are bilingual is not
an equilibrium of the Þrst-period learning game.
Lemma 3 states that partial learning does not occur. The reason for the
result is the endogenous cost of learning combined with the fact that agents
have positive mass. SpeciÞcally, if one agent of a given type Þnds it worthwhile
to learn, then other agents of the same type must also Þnd learning to be
optimal, since their cost of learning will be lower. Lemma 4 indicates that at
least one of the monolingual groups will choose not to learn. This is intuitive:
if everyone else can speak your language, you have no incentive to learn the
other language. From these two lemmata we can conclude that there are two
possible equilibrium conÞgurations:
• Assimilation: {English, Bilinguals} or {Spanish, Bilinguals}. In these
equilibria, one group of monolinguals learns the other language. All agents
can communicate in the second period.
• Linguistic Isolation: {English, Spanish, Bilinguals} or {English, Spanish}.
In these equilibria, no learning takes place. Some agents are prevented
from trading or producing in the second period by a language barrier.
Bilinguals will be present if and only if they were present at the start of
the date.
We now address what sets of initial conditions at a given date yield each of
the two equilibria.
5.2
5.2.1
Assimilation and Linguistic Isolation
Assimilation {e, s, b} → {e0 , b0 }
For concreteness, consider the case in which the learning is done by the Spanish
monolinguals (that is, e0 = e; b0 = b+s). Given that these Spanish monolinguals
are becoming bilingual, there is clearly no incentive in equilibrium for English
speakers to learn Spanish. Thus, there is a single equilibrium condition: it
must be optimal for Spanish speakers to learn. We consider the deviation of
an individual agent, making the Nash assumption that the behavior of all other
agents is unchanged.
• Spanish want to learn:64 δ − δh(s + b, 1) = δ [1 − h(s + b, 1)] > h(b, e + b).
64 Strictly speaking, the condition is δ [h(1, 1) − h(s + b, 1)] > h(b + ε, e + b + ε), and so the
condition in the text is an approximation. For all of the subsequent analysis, we ignore the ε
terms. Nothing substantive is affected by this.
28
The left hand side of the above inequality represents the gains to learning for
a Spanish monolingual. Given that her peers are learning, she anticipates being
able to communicate with all agents in the second period, and so will obtain
δh(1, 1) = δ. If the agent chooses not to learn, she will not be able to trade with
English monolinguals in the second period, and will obtain δh(s + b, 1). Thus,
the gain from learning is the ability to communicate with English monolinguals
in the second period. The right hand side of the above inequality gives the
cost of learning, which is the foregone output in the Þrst period. Because we
are considering a deviation by one agent - assuming other Spanish agents are
learning - the cost is simply the opportunity to trade with bilinguals in the Þrst
period: h(b, e+b). The inequality is more likely to be satisÞed when the number
of English monolinguals is large and the number of bilinguals is small, because
in this case assimilation brings a large gain and bears a small cost. It is also
more likely to be satisÞed when the number of Spanish monolinguals is small,
because the congestion externality reduces the cost of learning.
5.2.2
Linguistic Isolation {e, s, b} → {e0 , s0 , b0 }
In this equilibrium neither group learns, so e0 = e, s0 = s, and b0 = b. Thus two
conditions need to be met:
• Spanish do not want to learn:
δ
1+δ
< h(s + b, 1)
• English do not want to learn:
δ
1+δ
< h(e + b, 1)
The gain from learning is the same as before, δ [1 − h(s + b, 1)]. The cost of
learning for a Spanish monolingual is the opportunity cost of not communicating
with bilinguals, as well as with other Spanish monolinguals (because the other
Spanish monolinguals are not learning), in the Þrst period. This cost equals
h(s + b, 1). Rearranging, we get the Þrst expression above, and, by analogous
reasoning, we can derive the condition for the English monolinguals to not learn.
The key in each case is that there must be relatively few monolinguals of the
other language, so the gain from learning is small. When both conditions are
satisÞed, linguistic isolation can persist throughout a date.
Figure 6 illustrates the combinations of initial {e, s, b} that are consistent
with assimilation and with non-assimilation (linguistic isolation). For this
illustration we use h(x, y) = x∀x, y and we set δ = 1. The Þgure shows that
assimilation is a possible outcome for a large number of initial distributions.
For example, from point A, the Spanish monolinguals become bilingual, taking
the economy to A0 ; likewise, from point B, the English monolinguals become
bilingual, taking the economy to B 0 . However, as point C shows, assimilation
does not occur when the number of bilinguals becomes sufficiently large. The
presence of bilinguals increases the cost of learning and decreases the beneÞt
from learning, discouraging assimilation.
29
For some initial distributions, it is possible for either the English monolinguals or the Spanish monolinguals to learn: there are multiple equilibria. If the
economy begins at point D in Figure 6, for example, the Spanish monolinguals
might learn, taking the economy to D0 , or the English monolinguals might learn,
taking the economy to D00 . Similarly, there are regions of the diagram where
both assimilation and linguistic isolation are possible. These multiplicities arise
from a strategic complementarity in the learning decision: if an agents’ peers
are learning, they are not available for economic interaction in the Þrst period;
consequently, the opportunity cost of learning is lower when others are also
learning.
Figure 7 combines Figures 4 and 6 to show learning in a dynamic context.
In the simplest case, the economy follows the dynamic path A-B-C-D-E-F. This
corresponds to the path drawn in Figure 4, except that once the economy reaches
point D, assimilation must occur. All the Spanish agents become bilingual at
that date, and in subsequent periods, the bilinguals gradually vanish. So our
model generates a pattern in which, initially, intergenerational transmission
moves the economy gradually and non-linearly towards monolingualism. At
some point, however, the number of speakers of the minority language becomes
too small for the language to survive. Assimilation then occurs rapidly, through
learning, and monolinguals in the minority language vanish. Thereafter, the
bilinguals gradually disappear, and the economy eventually becomes monolingual in the majority language.
Although assimilation occurs for sure at point D, the multiplicities of equilibria imply that such assimilation could occur earlier — either between points
A and B, or between points C and D.65 It is also worth noting that assimilation could arise even in a case where the economy possesses a stable interior
steady state (given that, from Lemma 2, bilinguals will eventually disappear in
an economy with no monolingual speakers of one language).
5.2.3
Assimilation of Immigrant Groups
Evidence from recent U.S. immigration patterns is consistent with a prediction
of the model, namely that relatively small groups are more likely to assimilate.66
Lopez (1996) uses data from the November 1989 CPS, and Þnds that 36% of
Þrst generation Asian immigrants have become bilingual. By contrast only 17%
65 Indeed, in the early stages of adjustment, we know from Figure 6 that it is even possible
that English monolinguals would assimilate.
66 A more precise statement is as follows. Fix the number of bilinguals (b < 1/2). When
the number of English monolinguals is small (and the number of Spanish monolinguals is
therefore large), the only equilibrium outcome is assimilation by the English. As the relative
number of Spanish monolinguals decreases, assimilation by the Spanish (or assimilation by
neither group) also become possible outcomes. When the number of Spanish monolinguals is
sufficiently small, the only equilibrium outcome is assimilation by the Spanish.
30
of Þrst generation Hispanic immigrants, a much larger group, are bilingual.67
A similar pattern holds for sub-groups of the above immigrants as well. Only
10% of Þrst generation Mexican immigrants are bilingual, while 34% of Þrst
generation Chinese are bilingual. Moreover, there is evidence that the greater
is the number of bilingual immigrants, the more rapid is the intergenerational
assimilation into monolingual English speakers. Lopez (1996) Þnds that 77%
of second generation Asian immigrants are monolingual English speakers, compared to just 30% of Hispanic immigrants. This Þts with the dynamic aspects
of our model.
From the inequalities that deÞne assimilation and linguistic isolation, we
can see that an increase in δ encourages assimilation and discourages linguistic
isolation. This is intuitive — when δ increases, the gains from learning rise
relative to the costs of learning. Public policies on language use could also
affect δ. For example, increased government support of the minority language,
such as translations of official documents and bilingual government employees,
would decrease δ and discourage assimilation.
5.2.4
Assimilation in Developing Economies
Our equilibrium conditions also reveal that, with lower returns to scale, the costs
of learning rise and the beneÞt from learning falls, so assimilation becomes a
less likely outcome and linguistic isolation becomes more likely. A smaller
congestion externality has a similar effect. Both imply that h() will be more
concave. When h() is highly concave, most of the network gains are achieved
with a relatively small language group, and the marginal beneÞt of increasing
the language group declines as the language group increases. Recall that the
gains from learning for a Spanish monolingual are given by δ [1 − h(s + b, 1)] .
When h() is very concave, this beneÞt is relatively small even if there is a large
number of English monolinguals. This helps to explain the case of Papua New
Guinea and other societies in which the gains to specialization and assimilation
into a larger economy are perceived to be small.
5.2.5
The Short-Run Preservation of Minority Languages
Earlier, we noted that minority languages could only survive in the long run if
the intergenerational dynamics supported an interior equilibrium. But even this
is not sufficient for language survival, because minority language groups may
choose to learn the majority language and assimilate into the majority culture.
In order for linguistic isolation to be an equilibrium outcome in the short run
(within a date), it must be the case that neither language group is too small
67 It does not matter whether the immigrants learned English before or after they migrated;
all that matters is that they learned English in anticipation of migrating, and understanding
that there were few speakers of their native language in the United States.
31
and that there is a sufficient number of bilinguals. Finland and Switzerland are
examples of countries that probably satisfy these criteria.
6
Migration Only
We now turn to the version of the model in which migration, but not learning,
can occur. Agents choose either to remain in their existing location, or to move
to the other location. Because relocation involves no direct cost, initial location
does not matter for this decision.68 Because there is no learning, e0t = et , s0t = st ,
b0t = bt . As before, our equilibrium concept is pure strategy Nash equilibrium.
0
}, j = e, s, b; n = 1, 2,
An equilibrium of our model is two sequences, {jnt } {jnt
such that, at each date t
• Taking the location choices of others as given, each agent chooses location
such that consumption in that location in period 2 is at least as large as
in the other location;
• Language groups evolve over time in each region according to (6)
6.1
Location Game
In general, there are six types of agents, distinguished by language and location:
English monolinguals, Spanish monolinguals, and bilinguals, in locations 1 and
2. The number of agents of each group can be zero or positive, implying that
there are 26 − 1 = 63 arrangements of the agents by location and language (the
arrangement with zero agents in each location is inadmissible). We will treat
the locations completely symmetrically — for example, we will not distinguish
between an equilibrium where all agents are in location 1 and no agents are in
location 2, and an equilibrium where no agents are in location 1 and all agents
are in location 2. This immediately reduces the number of distinct arrangements
to 35. Many of these 35 can be eliminated by the following lemma:
Lemma 5 (i) Assume that the technology exhibits increasing returns to scale
(see Assumption A3). In any equilibrium of the location game, all English monolinguals will be in one location only, all Spanish monolinguals will be in one
location only, and all bilinguals will be in one location only. (ii) There are 13
distinct equilibrium conÞgurations that satisfy these restrictions.
The intuition for part (i) of Lemma 5 derives from two observations: if
an agent moves from location 1 to location 2, then the number of speakers in
68 As our model is speciÞed, the migration choice is made after the Þrst period, but in a
world without learning, the timing is unimportant; we could equally think of the choice as
being made at the beginning of each date. For this reason, the value of δ is irrelevant in this
section.
32
location 2 increases; and, in general, an agent is strictly better off when there are
more speakers in her location with whom she can communicate. The exception
arises under constant returns, when any agent who can communicate with all
others receives second-period consumption equal to 1, and this is unaffected by
the arrival of more agents. We address this in Lemma 6.
Lemma 6 Assume that the technology exhibits constant returns to scale. (i) If
e > 0, s > 0, b > 0, then, in any equilibrium of the location game, all English
monolinguals will be in one location only, all Spanish monolinguals will be in
one location only, and bilinguals may be present in both locations. (ii) If either
e = 0 or s = 0, location is irrelevant.
For ease of exposition, we will assume henceforth in this section that the
economy exhibits some (possibly very small) amount of increasing returns. From
part (ii) of Lemma 5, we know that the number of distinct arrangements is
reduced to 13. Moreover, in this section we are only interested in cases where
there are both English and Spanish monolinguals present; otherwise the location
decision is uninteresting.69 Lemma 7 shows that this restriction reduces the
number of distinct arrangements to six. The lemma also shows that one of
these six is not an equilibrium, leaving us with Þve equilibrium allocations.70
Lemma 7 Assume e0 > 0 and s0 > 0. The location game has 5 equilibria:
The possible equilibrium conÞgurations in this case are:
• Linguistic Isolation: {English, Spanish, Bilinguals},{φ} or {English, Spanish}, {φ}. All agents would be able to trade or produce with each other,
but for a language barrier.
• Geographic Isolation: {English, Bilinguals}, {Spanish}, or {Spanish, Bilinguals}, {English}, or {Spanish}, {English}. One of the monolingual groups
would be able to produce or trade with bilinguals but for a geographic
barrier — that is, the bilinguals are in the other location. English monolinguals cannot produce or trade with Spanish monolinguals, because of
both a language and a geographic barrier.
We can use our simplex diagram to represent geographic isolation; Figure 8
illustrates. As before, the large simplex represents the total number of agents.
Suppose that point A indicates the mix of agents in the overall economy. We
then represent the two regions by drawing two smaller simplexes around point
A. Each triangle is displaced from the bases of the larger simplex by an amount
69 The
appendix provides a version of Lemma 6 that covers all cases
following analysis assumes that the number of bilinguals is strictly positive, since the
equilibria without bilinguals are special cases. To analyze these cases, simply set b = 0 and
eliminate any conditions on moving by bilinguals.
70 The
33
equal to the number of agents of that type who are in the other location. Point
A then also correctly represents the mix of agents within each region.71
Because there is no learning and no explicit cost of migration, the initial
conditions (that is, the locations of agents in the Þrst period) are not relevant
for this version of the model. All that matters is the total number of agents of
each type. We thus examine the conÞgurations of agents that are consistent
with geographic isolation and with linguistic isolation.
6.2
Linguistic Isolation → {e0 , s0 , b0 }{φ}
It is trivial to show that linguistic isolation is possible for all initial conditions.
If all agents have decided to live in a single location, no individual agent will
have any incentive to deviate.
6.2.1
Ghost Towns
This rather stark conclusion is due to the fact that we assume all agents of
each language group are identical; we relax this condition in Section 8, where
we consider the possibility that some agents behave inertially. Also, when
we allow for learning as well as migration, linguistic isolation will not always
be an equilibrium because, under some circumstances, agents will choose to
assimilate by learning the other language. Nevertheless, linguistic isolation
without learning does have a counterpart in reality. If agents were initially
present in both locations, then complete outmigration from one location could
correspond to ghost towns in the west of the United States, or emigration from
the Scottish Highlands and Islands.
6.3
Geographic Isolation → {e0 , b0 }{s0 }
For concreteness, consider the case where the Spanish monolinguals are geographically isolated. The Spanish are unable to trade with the bilinguals because of a geographic barrier. In a Nash equilibrium, the following equilibrium
conditions must hold.
• Bilinguals locate with English monolinguals: h(s, s) < h(e + b, e + b) ⇒
s < 1/2;
• Spanish locate with other Spanish: h(b, e + b) < h(s, s)
The Þrst condition tells us that the number of Spanish agents must be less
than Þfty percent of the population, because otherwise bilinguals would Þnd
71 Thus, in Figure 8, the number of bilinguals in region 1 equals b and the number of
1
bilinguals in region 2 equals b2 . Hence the simplex for region 2 is displaced by b1 from the
b = 0 axis, and the simplex for region 1 is displaced by b2 from that axis. Inspection makes
it clear that the geometry works: the total number of bilinguals equals b1 + b2 .
34
it more proÞtable to locate in the Spanish-speaking community. The second
condition ensures that Spanish speakers do not wish to locate with bilinguals:
the gain from interacting with bilinguals, h(b, e + b), must be smaller than the
gains from interacting with other Spanish monolinguals, h(s, s). In Figure 9
we illustrate the initial conditions consistent with geographic isolation.72
Geographical isolation provides a means for minority languages to survive
even in the face of the dynamic tendencies toward monolingualism outlined in
Section 4. This is illustrated in Figure 10. Suppose that at some date point
A represents the total number of agents in the economy, and that Spanish
monolinguals are geographically isolated. Point A lies inside the region deÞned
by the two inequalities above, so it is an equilibrium for agents not to migrate.
Note that point A lies at the vertex of the region-2 triangle, indicating that,
in region 2, all agents are monolingual Spanish. Point A also lies on the s =
0 boundary of the region-1 triangle, indicating that region 1 is inhabited by
English monolinguals and bilinguals.
Over time, our dynamic adjustment tells us that the mix of agents in region 1
will shift, as relatively fewer in each generation are bilingual. Thus the triangle
for region 2 will “slide down” the edge of the region-1 triangle. Eventually,
the economy will reach point C, where there are English monolinguals only in
region 1, and Spanish monolinguals only in region 2.73 This outcome can persist
indeÞnitely.
Although Figure 10 reveals that geographic isolation can play a role in the
survival of minority languages, there are still two curious features of that Þgure.
First, the geographic isolation equilibrium could break down at any time — that
is, at any date, it would be an equilibrium outcome for the entire isolated group
to move to the other location. In Section 8, we show that this conclusion is no
longer true once some agents behave inertially. Second, according to Figure 10,
it is possible for arbitrarily small language communities to survive. Section 7
shows that, while this is true in the economy with migration only, it no longer
holds once we allow for both learning and migration in the same model.
6.3.1
Geographic Isolation and the Survival of Minority Languages
Our review of the sociolinguistics evidence makes it clear that geographic concentration and isolation plays a critical role in the survival of many languages.
In Europe, almost all of the monolingual speakers of the minority languages,
including Welsh, Irish, Basque, and Breton, are located on the coasts or in
72 For the functional forms and parameters that we have chosen, this Þgure resembles Figure
6. This is coincidental, as can be seen from inspection of the underlying equations.
73 Starting from geographic isolation of one language group, it is also possible that the outcome will be that the other language group will be isolated. This requires that the bilinguals
move. Thus, suppose that, originally, English monolinguals are isolated, and then the bilinguals move: {e}, {s, b} → {e, b}, {s}. The conditions for this to be an equilibrium are identical
to the case discussed in the text.
35
mountainous areas. Moreover, the evolution of the monolingual speaking regions over time follows a pattern in which the regions closest to the economic
core disappear by becoming bilingual, and the regions furthest from the core
remain monolingual. Cornish is a language that used to be spoken on the southwestern peninsula of England. The last region to lose its monolingual speakers
was at the very tip of the peninsula, furthest from London.
Papua New Guinea is remote from the rest of the world, so it is no surprise that its native languages continue to ßourish. But, as discussed above,
Papua New Guinea is also remote from itself, with a dense collection of rain
forests, mountains and rivers. As a consequence, Papua New Guinea possesses
the greatest linguistic diversity on the planet. Moreover, the largest languages
belong to the groups of people in the interior highlands, where geographic isolation is the lowest. The smallest languages are in the coastal lowlands which
contain rainforests and swamps.74
7
The Complete Model
In this section, we consider the complete model, in which agents make both a
location decision and a learning decision. In general, in the Þrst period at any
date, there may be English monolinguals, Spanish monolinguals, and bilinguals
present in each location. On the basis of Lemma 5, however, we can conclude
that such a situation cannot persist for more than one period. We thus focus
solely on the cases where the initial conditions are either linguistic isolation
or geographic isolation. We also do not provide a complete characterization
of equilibria here, as many of our results would duplicate our Þndings from
Sections 5 and 6. Instead, we look only at the cases where the interaction of the
learning decision and the migration decision leads to outcomes that differ from
our earlier analysis.
7.1
Geographic Isolation → Assimilation
{e, b}{s} → {e0 , b0 }{φ}
Starting from geographic isolation, assimilation of the geographically isolated
group is possible for all initial distributions of agents. The reason is straightforward: if all Spanish agents are learning and moving, there is obviously no
incentive for a single agent to deviate. The introduction of learning does not
alter the Þnding from the previous model that an equilibrium with geographic
isolation is fragile, in the sense that it is always an equilibrium outcome for the
74 To the extent that some of these different groups trade with each other, there are people
in each group who are bilingual or multilingual. So economic interaction and bilingualism go
hand-in-hand; the groups that do not trade tend not to share a language. This is consistent
with the assumptions underlying our model.
36
isolated group to migrate and assimilate. In Section 8 we show that inertial
agents can reduce the fragility of this equilibrium.75
7.1.1
Industrialization and Assimilation
We saw in Section 2 a number of examples of language disappearance occurring
side-by-side with industrialization. In the model, assimilation of a geographically isolated group can happen for no reason other than a shift in expectations:
assimilation is an optimal strategy if others are also assimilating. In practice, it
seems likely that some exogenous shock would serve to shift the focal point of the
economy from isolation to assimilation. One contender is industrialization: an
industrialized economy is likely to possess stronger increasing returns to scale,
which increases the gains to assimilation. The experience of the Ainu in Japan
might be an example of such a shift from geographic isolation to assimilation.
Industrialization also is associated with lower transport and communication
costs, which may, in effect, integrate a region that was previously geographically
isolated. In this case, a language group that was previously geographically
isolated would Þnd itself linguistically isolated instead. Agents would then fact
two options: assimilation, or migration to a new, more isolated region. This
scenario captures the gradual pushing back of such languages like Welsh, Irish,
and Breton to the most remote and isolated parts of their region, as the English
and French economies expanded.
7.2
Geographic Isolation → Geographic Isolation
{e, b}{s} → {e0 , b0 }{s0 }
We next consider the case where geographic isolation persists. For this to
be a Nash equilibrium, the following conditions must hold.
• Bilinguals do not want to move: s < 1/2;
• Spanish do not want to move: h(b, e + b) < h(s, s);
• Spanish do not want to learn and move: δ [h(e + b, e + b) − h(s, s)] <
h(s, s).
75 Assimilation may also occur where the non-isolated group chooses to learn
({e, b}{s} → {s0 , b0 }{φ}). For example, if the Spanish group are isolated, then the English
monolinguals may choose to learn Spanish, and the Spanish agents migrate. Of course, the
English monolinguals learn Spanish in anticipation of the fact that Spanish monolinguals will
then be attracted to the location by the large number of bilinguals. There is a cost to learning
for the English speakers, even if all of their peers are learning, because English speakers forego
Þrst-period trade with bilinguals. The condition for this equilibrium is that:
• English want to learn: δ [h(1, 1) − h(e + b, 1)] > h(b, e + b).
This condition requires that the number of Spanish agents (the payoff to learning for the
English monolinguals) is large relative to the number of bilinguals (the cost to learning for
the English monolinguals).
37
Compared to the model without learning, geographic isolation is less likely
to arise, in the sense that there is a smaller set of initial conditions that are
consistent with this outcome. The Þrst two conditions are the same as before,
but there is now a third condition that ensures that Spanish monolinguals do
not want to assimilate. For no learning and assimilation to occur, there must
be a sufficiently large number of Spanish agents. By contrast, in the model
without learning, geographic isolation of Spanish agents was possible even when
the number of Spanish agents was very small, provided that the number of
bilinguals was correspondingly small. For the benchmark technology that we
have used in our illustrations, geographic isolation of the Spanish cannot be an
equilibrium if Spanish monolinguals are less than 25% of the population. 76
7.2.1
The Survival of Small Language Groups
Although geographic isolation can play a key role in the survival of minority
languages, it is still necessary for isolated language groups to be of sufficient size.
Only the largest monolingual groups will be able to forestall assimilation into a
larger language group. The historical evidence supports our result. The Welsh,
Breton, Galician, and Cornish populations were and are less than 5 percent of
the relevant population, and each of the remaining Native American groups in
the United States is considerably less than 0.1 percent of the population.
We have conducted our analysis as if the economic possibilities are determined purely by the numbers of agents, but it is often the case that one language
is associated with superior production possibilities. Political forces may have
established a particular language as the language of power, spoken by the cultural and educated élite, as is the case for English, Spanish and French in many
former European colonies. In such cases, we might want to assume a different
technology in the different regions, in order that language groups receive appropriate economic weight. For example, the Catalan population in GDP-weighted
terms is 20 percent of the country, implying that Catalan is more valuable than
the number of its speakers would suggest.
As an illustration, suppose that h(Ni , N ) = (Ni )α (Ni /N )β , and suppose
that δ = 1. Suppose also that, in the initial equilibrium, α = 1/2. Geographic
76 It is also possible that the equilibrium outcome is that the other language group will be
isolated. This requires that there is no learning, and that the bilinguals move: {e, b}{s} →
{e0 }{s0 , b0 }. The conditions are:
• Bilinguals want to move: h(s + b, s + b) > h(e, e) ⇒ e < 1/2;
• English do not want to move: h(b, s + b) < h(e, e);
• English do not want to learn and move: δ [h(s + b, s + b) − h(e, e)] < h(e + b, e + b)
The key difference, relative to the case in the text, is in the third condition. For English
monolinguals, the cost of learning is inßuenced by the number of bilinguals, since English
agents who learn must forego the opportunity to trade with these bilinguals in the Þrst period.
As a consequence, there is actually a larger set of initial conditions that are consistent with
this outcome than with the previous case.
38
isolation can be sustained as an equilibrium provided that s > 1/5. But now
suppose that industrialization increases the returns to scale, so that α = 1.
Following this change, geographic isolation is only sustainable if s > 1/3. (We
would obtain a similar result if we instead considered an increase in δ, which
represents an increase in the gains to learning. A large enough increase in δ
could eliminate geographic isolation as an equilibrium, leading to assimilation.)
When the number of bilinguals is small, it is easier to support geographic
isolation than linguistic isolation. We have already noted the geographic concentration of immigrant groups: Germans in the Midwest, Asians in cities on
the west coast, Latinos in Texas and California, and so on. Immigrant groups
that are sufficiently large and sufficiently geographically concentrated are able
to maintain their language communities for signiÞcant periods of time. In the
United States, there are fewer Asians than Hispanics, and the Hispanic groups
typically speak variations on one language, Spanish, while the Asian groups
speak different languages. Hence, the model implies that the Asian households
should be relatively more geographically isolated (implying a higher correlation
of the percentage of households for each language group that do not speak English very well and the percentage of households that live in the center city) than
Hispanic households. We indeed Þnd evidence supporting this implication, as
footnote 5 indicates.
7.2.2
Canada and Québec
Assimilation, while an equilibrium outcome, need not be welfare-improving — at
least for the generation that makes the transition. To take a simple example,
suppose that there are no bilinguals, and suppose that we begin from geographic
isolation. If the Spanish assimilate, they gain the possibility of trading with
English monolinguals in the second period, but they forego output in the Þrst
period. Assimilation thus decreases their welfare if
δ [h (1, 1) − h(s, s)]
<
h(s, s)
δ
> h(s, s).
⇒
1+δ
(11)
(12)
If the returns to scale are relatively low (so h(s, s) is large) and/or if δ is relatively
small, then assimilation is actually a bad idea for the Spanish monolinguals. (Of
course, assimilation bestows positive externalities on English monolinguals, so
they unambiguously prefer that the Spanish agents assimilate.)
We can think of Canada as divided into two regions, Québec and the Rest-ofCanada, in a geographic isolation equilibrium: French monolinguals and bilinguals in Québec; English monolinguals in the Rest of Canada.77 In this setting,
both geographic isolation and full assimilation may be equilibrium outcomes.
77 An alternative interpretation, given that the Rest-of-Canada (especially Ontario) also
contains a large number of bilinguals, is that we have geographic isolation with bilinguals in
both locations. We saw in Section 5 that this equilibrium can occur under constant returns
39
Furthermore, it may be the case that it would be an equilibrium outcome for
French monolinguals to become bilingual, but that this equilibrium is undesirable from the point of view of French speakers. That is, assimilation could be
a coordination failure outcome for this language group. (Recall that, because
Québec is a relatively large economy, our technology is likely to exhibit low
returns to scale.)
Our model allows us to interpret the passage of French-only laws in Québec
in 1977 and forward as an equilibrium selection device, in which the geographic
isolation equilibrium can be legislated and implemented. It is perfectly possible
that these laws allow Québec to maintain equilibrium with geographic isolation,
and that this equilibrium is the preferred outcome for Québecers. Over time,
our model suggests that Québec would tend to become increasingly monolingual
French, which is consistent with the facts that we reported in Section 2.
7.3
Geographic Isolation → Linguistic Isolation
{e, b}{s} → {e0 , s0 , b0 }{φ}
Now consider the circumstances when agents’ decisions may move the economy from geographic isolation to linguistic isolation. For this to be an equilibrium, the following must be true:
• Spanish do not want to learn: δ [h(1, 1) − h(s + b, 1)] < h(s, s)
• English do not want to learn: δ [h(1, 1) − h(e + b, 1)] < h(e + b, e + b)
The Þrst learning decision says that the cost of learning for the Spanish
(lack of trade with other Spanish in the Þrst period) must outweigh the beneÞt
of learning (ability to communicate with English monolinguals in the second
period). Thus this condition says that the number of Spanish agents must be
sufficiently large relative to the number of English agents. The second condition
states that the number of Spanish agents must not be too large, otherwise
English monolinguals will want to learn Spanish.
7.3.1
German Immigration and Assimilation
The move from geographic isolation to linguistic isolation corresponds to “regular migration”, such as immigrants who came to the United States but did not
learn English. If the immigrant group is small relative to the overall population, as is usually the case, it is unlikely that the home population will Þnd it
worthwhile to learn the immigrants’ language, and so the second condition will
be satisÞed. Meanwhile, immigrants will choose not to learn if their language
community is sufficiently large or if δ is small. This is consistent with the fact
to scale. The argument for this interpretation is that both Québec and the Rest of Canada
are large enough that any increasing returns have already been exploited and the regions are
now, at the margin, constant returns.
40
that older immigrants are more likely to remain monolingual than are younger
immigrants.
During the wave of German immigration in the 19th century, the Germanspeaking group was so large that immigrants had little need to assimilate.
Moreover, continued immigration (in the mid and late 19th century) helped
to forestall the dynamic adjustment that eventually pushes these monolinguals
into bilingualism. (As we have noted elsewhere, geographic concentration also
played a signiÞcant role.) In fact, there was some concern at the time that the
immigration wave was so large that it would tip the economy to a monolingual
German path. This explains some of the backlash against German language
instruction that occurred beginning in the late19th century. World War I, decreased German immigration, and increased non-German immigration, can all
be viewed as shocks that lowered the cost of assimilating, so that full assimilation
eventually occurs. We argue that this Þts well with Kloss’s (1966) description
of the German-American experience in the Midwest.
7.3.2
Spanish-speakers in the United States
In Section 2 we described the geographic concentration of Spanish speakers in
the United States. One way to think of this concentration is as an example of a
geographic isolation equilibrium: Spanish speakers locate in the Southwest and
English speakers everywhere else. Yet this does not seem to capture the extent of
Latino integration in many U.S. metropolitan areas, such as New York, Chicago,
Los Angeles, Houston and Miami. These and similar metropolitan areas might
better be described as a linguistic isolation equilibrium where Spanish speakers,
English speakers and bilinguals coexist and interact. Such an equilibrium can
be supported as long as the number of monolingual of either tongue is not too
large. Larger numbers of bilinguals make it easier to maintain this equilibrium.
Our model suggests that, over time, linguistic isolation is likely to give way
to monolingualism, as bilingual parents end up with monolingual children. Ongoing immigration, however, can have an offsetting effect. For example, consider
the path starting at A in Figure 11. In the early stages of adjustment, the number of Spanish monolinguals declines while the number of English monolinguals
and bilinguals increases. But immigration of Spanish speakers would of course
adjust the balance in precisely the opposite direction.
In the United States at present, the number of Spanish-speaking agents is so
large that it is very plausible that immigrants see little value to learning English.
Indeed, in some parts of the country, we are more likely to see a violation of the
second condition. An inability to speak Spanish could be a signiÞcant economic
handicap in Miami or Houston, for example. Again, continued immigration is
one of the forces that is slowing the assimilation process.
41
7.4
Linguistic Isolation → Geographic Isolation
({e, s, b}{φ} → {e0 , b0 }{s0 })
Finally, consider the shift from linguistic isolation to geographic isolation.
For this to be an equilibrium, the following conditions must be satisÞed.
• Spanish want to move: h(s, s) > h(b, e + b)
• Bilinguals do not want to move: h(e + b, e + b) > h(s, s)
• Spanish do not want to learn: δ [h(e + b, e + b) − h(s, s)] < h(s + b, 1).
Compared to the model with no learning, there is now an additional condition. This condition guarantees that an individual Spanish speaker will prefer
to migrate and join other Spanish speakers rather than assimilate by learning
English. These three conditions are sufficient, because it is obvious that English speakers do not want to move without learning, while the condition that
bilinguals do not want to move is sufficient to ensure that English speakers will
not want to learn (that is, become bilingual) and then move.
Figure 11, which can be contrasted with Figure 9, shows the conÞgurations of
initial conditions consistent with equilibrium. Figure 11 also makes it clear that
migration allows a language to persist under circumstances where — in a single
location — assimilation would be the only equilibrium outcome. For example,
at point A, linguistic isolation cannot persist. If the economy had only one
location, agents would assimilate. But the presence of a second location opens
up the alternative possibility of migration.
7.4.1
The Origin of Nations
The late 20th century saw several examples of the dissolution of larger countries
and the formation of smaller ones (often reversing previous agglomerations).
Examples include the former Soviet Union, the former Yugoslavia, Czechoslovakia, and East Timor. It is, we think, not too far-fetched to interpret such
events in the context of our model as shifts from linguistic isolation to geographic
isolation. Of course, the quest for political independence involves much more
than a desire to maintain a language; it is a desire to maintain a culture and
national identity. Still, a unique language is very often a vital part of such
identity. It is certainly noteworthy that Timorese languages were suppressed
in Indonesia, as were native languages in the former Soviet Union.
7.5
The Complete Model: A Summary
Figure 12 presents a schematic summary of the possible outcomes in our model
within a date. The starting points at the beginning of a date are linguistic
isolation and geographic isolation. Possible outcomes are linguistic isolation,
42
geographic isolation, and assimilation. The Þgure indicates the real-world phenomena that we believe are captured by each possibility, together with some
examples of the relevant language communities.
8
8.1
Extensions
Inertial Agents
Our model exhibits very strong strategic complementarities in terms of both
learning and location decisions. If all agents in a location are learning in the
Þrst period, then there is evidently no incentive for any agent to deviate and
not learn. Similarly, if all agents have chosen to locate in one place, there is no
incentive for any agent to deviate. We deliberately made the model stark, in
order to highlight the fact that, even with such strong forces for assimilation,
other outcomes are possible.
Of course, we do not literally believe that all agents truly make location
or learning decisions simultaneously. In reality, this is a more gradual process.
If such adjustment takes place within a generation, then our model may be a
good approximation. But migration decisions and assimilation decisions may
take place across several generations. One way to capture this idea is to assume
that, at each date, only a fraction of agents actually make language and location
decisions, while the remaining agents are inertial. SpeciÞcally, suppose that a
fraction γ of all agents of a given type actually make language and location
decisions at each date. The other (1 − γ) are available as production/trading
partners, but do not learn the other language, and remain in the same location
for both periods.
8.1.1
Learning Only
Consider Þrst the case of the learning decision only.78 The conditions for linguistic isolation to persist are unchanged, because they are conditions for not
learning to be an equilibrium action. But assimilation is less likely to occur
when there are inertial agents. As before, we need to verify that Spanish agents
to want to learn. In addition, because assimilation does not occur completely
within a period, we also need to verify that English agents do not want to learn.
Figure 13 illustrates the possibility of assimilation for γ = 1/3. Comparison
with Figure 6 shows that assimilation can occur only from a smaller set of initial allocations. To illustrate, if the number of English and Spanish speakers
is equal, then assimilation is only possible if the number of bilinguals is less
than 1/7. In the previous case, assimilation was possible provided the number
of bilinguals was less than 1/3. Also, there is a much smaller region where
multiple equilibrium outcomes are possible.
78 A
detailed analysis is contained in the Appendix.
43
The eventual adjustment to full assimilation in this economy comes about
both because of the intergenerational adjustment and the learning within a
generation. This is illustrated in the adjustment path shown in Figure 13.
8.1.2
Migration Only
In our earlier model, the initial distribution of agents was irrelevant when we
considered migration without learning. With inertial agents, the initial distribution matters. If agents are initially all in one location (linguistic isolation),
then we are less likely to see geographic isolation emerging as an equilibrium
outcome. The more interesting case is when the economy initially exhibits some
geographic isolation. Previously, we observed that it was always an equilibrium
outcome for the geographically isolated agents to migrate to the other region,
leading to linguistic isolation. The reason was that, if all other agents migrate,
no individual agent will remain. But if some agents will remain no matter
what, this extreme conclusion no longer holds.
Suppose that, initially, Spanish agents are isolated (that is, we start from
{e, b}, {s}). Spanish agents will only be willing to migrate to the other region
if the gain from dealing with the bilinguals offsets the loss from interactions
with those agents that stay behind. Thus, migration of the Spanish is not
necessarily an equilibrium response, in contrast to the earlier analysis. Finally,
note that the conditions for geographic isolation to persist are unchanged from
the previous analysis. If all agents are choosing not to move, then it does not
matter that some agents cannot move.
Figure 14 shows all the possible outcomes starting from geographic isolation,
assuming γ = 1/3. Broadly speaking, if the number of Spanish monolinguals
is small, then those who can will deÞnitely migrate, leaving behind a smaller
geographically isolated group. Conversely, if the number of Spanish monolinguals is large, then bilinguals will start to move to join the Spanish speaking
agents. There is also a region (with few bilinguals and a large number of English monolinguals) where no migration occurs. Finally, there are some regions
where there are multiple equilibria: it is possible, but not certain, that either
Spanish monolinguals or bilinguals will choose to migrate.79
A dynamic path with no migration, such as indicated in Figure 10, is still
possible in this case; we show the same path (A-B-C) in Figure 14, but omit
the simplexes for the individual regions. In contrast to Figure 10, we see
that, at point B, the economy reaches a region where geographic isolation is the
only equilibrium. Thus, with a sufficiently large number of inertial agents, we
Þnd that not only is it possible that geographic isolation will persist, but that,
under some circumstances, this is the only equilibrium outcome. If the economy
79 If migration occurs, then the analysis at subsequent dates becomes more complicated,
since we now have to consider the decisions of four (or more) groups of agents. In addition,
of course, we have to consider how the language groups evolve between dates.
44
reaches point B, geographic isolation is permanent, and the long-run equilibrium
(at point C) involves two geographically isolated groups of monolinguals.
8.2
Vehicular Languages
Nowadays, if a Chinese businesswoman is negotiating with a Spanish businessman, they will almost certainly communicate using English. One limitation
of our framework is that we have only considered a world with two languages,
and so cannot directly model this phenomenon of “vehicular languages”. We
can, however, consider a simple variant of our model that captures the essential
idea.
Suppose that we have two language groups as before, but suppose that each
group faces a choice about learning, not the other language, but a third, vehicular language. For example, imagine that e indicates Estonian monolinguals, s
indicates Swahili monolinguals, and they are considering whether to learn English as a vehicular language. “Bilinguals”, in this setting, are those who already
know the vehicular language.
It is only worth learning a vehicular language if others already know the language, or if you anticipate that others will learn the language. To illustrate this
idea, suppose that δ = 1, γ = 1/3, and suppose that existing bilinguals speak
neither Swahili nor Estonian. In our basic model, the analysis was simpliÞed
by the fact that it was never an equilibrium for both groups of monolinguals
to learn. Here, there are four possible equilibrium outcomes: learning by
both; learning by Swahili speakers only; learning by Estonian speakers only;
and learning by neither.
Figure 15 shows the equilibrium outcomes. When there is a large number of
bilinguals — that is, speakers of the vehicular language — the incentive to learn
is also large, and so learning by both groups is an equilibrium. Conversely,
neither group will learn if there is a small number of bilinguals. Learning by
only one group is also a possibility. If (for example), there are relatively few
Swahili monolinguals, and a relatively large number of Estonian monolinguals,
then it is an equilibrium for only the Swahili speakers to learn. Finally, there
are some regions with multiple equilibrium outcomes. The gain to learning the
vehicular language is evidently greater when speakers of the other language are
also learning. Hence, even if the existing speakers of the vehicular language
(that is, existing bilinguals) are relatively few, it can be an equilibrium for both
groups to learn. For example, if the number of Estonian and Swahili speakers
is the same, then learning by both is an equilibrium when b > 1/7. For the
parameters we have chosen, there is even a small region where all four outcomes
are possible.
45
9
Conclusions
In their fascinating and comprehensive analysis of contemporary language extinction, Nettle and Romaine (2000) argue that economic and political forces
lie behind the disappearance of language diversity in the modern world. Along
the way, they criticize a view that they call “benign neglect”.
According to the benign neglect position, language death comes
about because people make a free choice to shift to another language.
As people are rational beings who may reasonably be expected to
know where their self-interest lies, we, as outside observers, cannot
condemn such choices. Seen from an economist’s perspective the
arena of languages is just another free market, and as economists
are fond of pointing out, it can be shown that a free competitive
market in any activity should produce an optimal distribution of
that activity for all concerned. The wane of some languages is
simply a side effect of countless individual choices, and thus is no
more or less morally signiÞcant than a change in the price of Þsh.
Our earlier examples have undermined the basis of this argument. We have shown that in many cases of language death, the
shift occurred not because of an increase in the available choices,
but because of a decrease in choice brought about by the exercise of
undemocratic power. [Nettle and Romaine (2000, p. 154)]
In contrast to Nettle and Romaine, we contend that economic forces, and
rational decisions about language use, do play a signiÞcant role in the evolution
of languages and language communities. But, like them, we question the logic
of benign neglect. In our view, the ßaw with this view is not so much that it
ignores political realities, but that it is not good economics. As we argue here,
and others have argued before us, language acquisition and language use are
choices that are riddled with externalities, and there can be no presumption
that individual decisions will generate socially optimal outcomes.80
We have illustrated how economic incentives affect language use and acquisition in a general model that highlights the importance of geographic location.
Location matters if there are costs to producing across locations, so agents want
to live where other agents live. Language matters if there are costs to producing across languages, so agents want to speak the language that others speak.
Our model examines both short and long run language dynamics. The language acquisition of children depends on the languages spoken by their parents,
and the ambient language in their community. Under plausible assumptions,
80 Indeed, language death could arise as a coordination failure, whereby people abandon a
language simply because everyone else is doing the same thing, even if everyone would prefer
to maintain the language instead. That said, we do not deny that there are powerful efficiency
arguments for the adoption of a standard language. See Jones (1999) for a forceful expression
of some of these.
46
and in the absence of government policy, there is a long run tendency towards
monolingualism. This matches the experience of many language communities.
Meanwhile, within a generation, agents in our model make learning and migration decisions. There are strong incentives for agglomeration and assimilation
in the world described in this paper. Individuals wish to locate where they can
communicate with others, and they have an incentive to learn in order to be able
to communicate with a larger number of people. Thus our model does indeed
contain the ingredients that lead to assimilation. At the same time, it is possible
to obtain equilibrium outcomes in which assimilation does not occur, and separate languages instead persist. In our model we can explain both assimilation,
and linguistic and geographic isolation, without any underlying heterogeneity
among agents other than their initial language and location endowment.
Our model is based in part on the decision to acquire a second language.
One might legitimately ask to what extent language acquisition is actually a
conscious decision made by adults. Do adults explicitly consider the costs and
beneÞts of learning another language, or do parents, schools, and public policy
completely dictate the languages a child learns and carries with him or her
into adulthood? While we acknowledge that most adults do not learn another
language, we remind the reader that this is an equilibrium outcome: adults
are choosing not to learn. Further, in the United States and other countries,
immigration as well as national language policies mean that choice of language
is a critically important decision for many adults. For people thinking of moving
to Québec, the cost of learning French is certainly a part of the calculus. For
these reasons we (as well as many of the authors we cite) have chosen to model
language acquisition in addition to intergenerational language transmission.
Most of our discussion has interpreted language literally, and a primary goal
of the model is to shed light on the sociolinguistics data. Other research has
suggested that language can also be viewed as a metaphor for more general skills
that facilitate economic activity. Language serves as a repository of knowledge,
for example. In Lang (1986) language is viewed as just a vehicle for communication between agents, and Lazear (1996) uses culture as his metaphor. We
are quite sympathetic to these interpretations, and indeed would offer others.
For example, we think language models could be used to shed light on communication across scientiÞc disciplines: interdisciplinary work is costly because it
requires investment in the language of the other discipline.81
Two natural extensions of our model involve allowing agents some possibilities to trade across locations and produce across languages. The former could
be accomplished by introducing more than one good and by incorporating ‘iceberg’ transportation costs of the type that have been used in the international
trade literature. Our intuition suggests that introducing multiple goods will
increase the likelihood that linguistic and/or geographic isolation is an equilibrium. Producing across languages could involve introducing translators that
81 See
Katz and Matsui (1996) for a model of language as a standard of behavior.
47
serve as intermediaries, as in Yavas (1994), or introducing multiple technologies,
some of which require a single language, and others which do not.
10
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51
1
1.1
Appendix
Proofs of Lemmata
Lemma 1 Existence of steady states. (i) Complete monolingualism (e = 1 or
s = 1) is a steady state. (ii) There exists at least one interior steady state. If
θe = θs , then there exists a symmetric steady state: e = s.
Proof. (i) Immediate from conditions (5) and (6) in the text. . (ii) From the
expressions for the evolution of language groups, the following two equations
deÞne the dynamic adjustment of the model between t − 1 and t:
µ
µ
¶
¶
¡
¢
e0t−1
e0t−1
e
e
0
1 − e0t−1 − s0t−1 ;
; θ et−1 + µ 0
;θ
et = ρ 0
0
0
et−1 + st−1
et−1 + st−1
µ
µ
¶
¶
¡
¢
s0t−1
s0t−1
s
s
0
st = ρ 0
1 − e0t−1 − s0t−1 .
;
θ
+
µ
;
θ
s
t−1
0
0
0
et−1 + st−1
et−1 + st−1
(The value for bt is determined residually.) DeÞne
ψ(x; θ) ≡
µ(x; θ)
.
1 − ρ(x; θ)
It is easy to show that at an interior steady state, the steady-state values of
{e, s, b} are given by
´
³
e
; θe
ψ e+s
´
³
´;
³
e =
e
s
1 + ψ e+s
; θe + ψ e+s
; θs
´
³
s
ψ e+s
; θs
´
³
´;
³
s =
e
s
1 + ψ e+s
; θs + ψ e+s
; θe
b =
1+ψ
Hence it follows that
e
e+s
=
ψ
=
³
³
ψ
³
e
e
e+s ; θ
1
´
+ψ
³
e
e
e+s ; θ
´
e
e+s ; θ
e
´
+ψ
³
³
s
s
e+s ; θ
s
s
e+s ; θ
´
e
ψ e+s
; θe
´
³
³
e
ψ e+s
; θe + ψ 1 −
1
´
´
s
e
e+s ; θ
(1)
´.
e
e
The right hand side of this expression equals 0 at e+s
= 0 and equals 1 at e+s
=
e
e
1. Moreover, it is easy to show that it has slope zero at e+s = 0 and e+s = 1.
e
∈ (0, 1) such
Since the right hand side is a continuous function, there exists e+s
that the equation is satisÞed. Further, it is immediate from inspection that,
e
= 1/2 solves this expression.
when θe = θ s , e+s
Lemma 2 (i) If, at some date, there are no monolinguals of one language,
then the economy will tend to a steady-state with only monolinguals of the other
language — that is, bilinguals will disappear. (ii) The monolingual steady states
are locally stable. (iii) Assume that θe = θs . The interior steady state is locally
stable iff
¡ ¢! "
¡1¢ 0 ¡1¢#
¡1¢ 0 ¡1¢ Ã
1 − ρ 12
ρ 2
µ
2 ¡
¢ <
¡ ¢
1 − 2 ¡ 1 ¢2
ρ 12
ρ 12
µ 2
Proof. (i) Immediate from conditions (5) and (6) in the text. (ii) Consider
a monolingual steady state. Linearizing the dynamic equations around this
steady state, we Þnd that the characteristic equation has roots {1 − µ(1), ρ(0)}.
Both roots lie between zero and one, and so the system is locally stable. (iii)
Linearizing the dynamic equations around the steady state, we get the characteristic equation
2
(α − λ) − β 2
= 0;
µ
¶µ 0¶
ρ0
1−e−s
µ
α = ρ+ −µ+
;
4
e
4
µ
¶
µ
¶
1−e−s
ρ0
µ0
+µ+
β =
4
e
4
where all variables are evaluated at steady state. The two roots are given by
λ = {α + β, α − β} .
If α < 0, the dominant root is α − β, which (by B7)
is less than
´´in absolute
³ one
¡1¢ ³ 0
µ0
value. If α > 0, the dominant root equals ρ+ 2 ρ + (1 − ρ) µ . Stability
requires that this root be less than unity. Rearranging, we can express this
condition in terms of elasticities, as in the statement of the lemma
Lemma 3 In the learning game, either all agents of a given type learn or none
do.
Proof. Suppose not. That is, suppose we have an equilibrium where some
number N L engage in learning, and some number N N of agents of the same
type do not engage in learning. Let C L denote the cost of learning for an agent
who has chosen to learn, and let C N be the cost that a non-learner would incur,
were she instead to choose to learn. Then C L > C N , because, were one of the
2
non-learners to choose to learn, she would be giving up the opportunity to trade
with N N − ε agents, whereas learners give up the opportunity to trade with N N
agents. Similarly, the gain to learning for a non-learner is at least as great as
the gain to a learner. But then, if it is worthwhile for learning agents to learn,
then it must a fortiori be worthwhile for a non-learner to learn. Thus we have
a contradiction.
Lemma 4 Assume b < 1. The allocation where all agents are bilingual is not
an equilibrium of the Þrst-period learning game.
Proof.
If all other agents are bilingual, then the gain from learning for
an English or Spanish monolingual is zero, and the cost of learning is strictly
positive. Thus at least one monolingual would choose not to learn.
Lemma 5 (i) Assume that the technology exhibits increasing returns to scale
(see Assumption A3). In any equilibrium of the location game, all English monolinguals will be in one location only, all Spanish monolinguals will be in one
location only, and all bilinguals will be in one location only. (ii) There are 13
distinct equilibrium conÞgurations that satisfy these restrictions.
Proof. (i) Consider an allocation where agent i (English, Spanish, or bilingual)
has optimally chosen to be in location 1. Then, by revealed preference:
h(Ni1 , N 1 ) ≥ h(Ni2 + ε, N 2 + ε)
where the superscripts denote location. This implies, by the assumption of
increasing returns, that
h(Ni1 , N 1 ) > h(Ni2 , N 2 )
Now assume that an agent of the same type as agent i has optimally chosen to
be in location 2. Then it similarly follows that
h(Ni1 , N 1 ) < h(Ni2 , N 2 )
Thus, we have a contradiction. (ii) This is established by inspection of the
possible conÞgurations of agents.
Lemma 6 Assume that the technology exhibits constant returns to scale. (i) If
e > 0, s > 0, b > 0, then, in any equilibrium of the location game, all English
monolinguals will be in one location only, all Spanish monolinguals will be in
one location only, and bilinguals may be present in both locations. (ii) If either
e = 0 or s = 0, location is irrelevant.
Proof. As in Lemma 5, consider an allocation where agent i (English, Spanish, or bilingual) has optimally chosen to be in location 1. Then, by revealed
preference:
h(Ni1 , N 1 ) ≥ h(Ni2 + ε, N 2 + ε)
3
This implies that
h(Ni1 , N 1 ) > h(Ni2 , N 2 )
unless Ni2 = N 2 . Now assume that an agent of the same type as agent i has
optimally chosen to be in location 2. Then it similarly follows that
h(Ni1 , N 1 ) < h(Ni2 , N 2 )
unless Ni1 = N 1 . Thus we have a contradiction unless Ni1 = N 1 , and Ni2 = N 2 .
These two conditions imply that all agents in location 1 can communicate with
each other, and that all agents in location 2 can communicate with each other.
To prove (i), suppose that, without loss of generality, there is an English speaker
in location 1. Then there can be no Spanish speakers in location 1, and so all
the Spanish speakers must be in location 2. But then there can be no English
speakers in location 2, and so all the English speakers must be in location 1.
Bilinguals, by deÞnition, can communicate with all agents. Under constant
returns to scale, they receive consumption equal to 1 in either location, and so
are indifferent about their choice of location. To prove (ii), simply note that, if
either monolingual English or monolingual Spanish are absent, then all agents
in the economy can communicate with each other. All agents then receive
consumption equal to 1 irrespective of location. The model makes no prediction
about location in this case.
Lemma 7 Assume e0 > 0 and s0 > 0. The location game has 5 equilibria:
Proof.
The assumption that e0 > 0 and s0 > 0 immediately reduces the
number of admissible arrangements to six. Now consider the allocation
{e, s}, {b}
For the English speakers to be locating optimally, it follows that
h(e, e + s) ≥ h(b, b).
For the bilinguals in location 2 to be locating optimally, we have
h(b, b) ≥ h(e + s, e + s).
Now h(·, ·) is strictly increasing in its Þrst argument, so we have
h(e + s, e + s) > h(e, e + s)
so we have a contradiction.
The following lemma analyzes the general location game without the assumption that e > 0 and s > 0.
4
Lemma 8 The location game has 10 equilibria: (i) Geographic Isolation
{English, Bilinguals} , {Spanish}
{Spanish, Bilinguals} , {English}
{English} , {Spanish}
(ii) Linguistic Isolation
{English, Spanish, Bilinguals} , {φ}
{English, Spanish} , {φ}
(iii) Assimilation/Monolinguallism
{English, Bilinguals} , {φ}
{Spanish, Bilinguals} , {φ}
{English} , {φ}
{Spanish} , {φ}
(iv) Universal Bilingualism
{Bilinguals} , {φ}
Proof. From Lemma 5, there are 13 admissible arrangments. Similar arguments to that in Lemma 7, combined with our assumption of increasing returns,
allow us to rule out {{e, s} , {b}}, {{e} , {b}} and {{s} , {b}} . This leaves ten
cases that can be equilibria of the location game.
1.2
Inertial Agents
Here we set out the conditions used in the paper for the model with inertial
agents. A fraction γ of all agents of a given type actually make language
and location decisions at each date. The other (1 − γ) are available as production/trading partners, but do not learn the other language, and remain in the
same location for both periods.
1.2.1
Learning Only
Consider Þrst the case of the learning decision only. The conditions for linguistic
isolation to persist are unchanged, because they are conditions for not learning
to be an equilibrium action. Assimilation is an equilibrium if:1
1 In the presence of inertial agents, it is also possible to have assimilation by both monolingual groups at once. The conditions are
• Spanish want to learn: δ [h(1, 1) − h(γe + s + b, 1)] > h((1 − γ)s + b, 1)
• English want to learn: δ [h(1, 1) − h(e + γs + b, 1)] > h((1 − γ)e + b, 1)
For the parameters we have been considering (in particular, δ = 1), this outcome is not
possible, however.
5
• Spanish want to learn: δ [h(1, 1) − h(s + b, 1)] > h((1 − γ)s + b, 1)
• English do not want to learn: δ [h(1, 1) − h(e + γs + b, 1)] < h(e + b, 1)
(For the parameters we have been considering, the second expression is in
fact implied by the Þrst.)
1.2.2
Migration Only
Starting from linguistic isolation, geographic isolation of the Spanish is an equilibrium if 2
• Spanish want to move: h(γs, γs) > h((1 − γ)s + b, (1 − γ)s + e + b)
• Bilinguals do not want to move: h(e+(1−γ)s+b, e+(1−γ)s+b) > h(γs, γs)
Under our benchmark parameters and technology, γ > 1/2 is necessary for
this outcome to be possible at all.3
Starting from geographic isolation ({e, b}, {s}), the conditions for geographic
isolation to persist are unchanged from the previous analysis:
• Bilinguals do not want to move: h(s, s) < h(e + b, e + b);
• Spanish do not want to move: h(b, e + b) < h(s, s)
If the following condition holds, then it is an equilibrium outcome for Spanish
monolinguals to migrate:
• Spanish want to move: h(γs + b, e + γs + b) > h((1 − γ)s, (1 − γ)s).
Another possibility from these initial conditions is that a fraction γ of bilinguals migrate away from the English monolinguals and join the Spanish monolinguals. This is possible if:4
2 It is possible that both English and Spanish speakers might choose to migrate. The initial
conditions supporting this possibility are defined by
• Spanish want to move: h (γs, γ (e + s)) > h ((1 − γ)s + b, (1 − γ)(s + e) + b)
• English want to move: h (γe, γ (e + s)) > h ((1 − γ)e + b, (1 − γ)(s + e) + b)
• Bilinguals do not want to move:
h (γ (e + s) , γ (e + s))
h ((1 − γ) (e + s) + b, (1 − γ) (e + s) + b)
>
3 If we observe a transition from linguistic isolation towards geographic isolation at date t,
then, in general, we would expect there to be Spanish agents in both locations at date t + 1.
Our analysis thus far has not considered initial conditions where one type of agent is initially
present in both locations.
4 If migration occurs, then the analysis at subsequent dates becomes more complicated,
since we now have to consider the decisions of four (or more) groups of agents. In addition,
we have to consider how the language groups evolve between dates.
6
• Bilinguals want to move: h(s + γb, s + γb) > h(e + (1 − γ)b, e + (1 − γ)b)
• English don’t want to move: h(γb, s + γb) < h(e + (1 − γ)b, e + (1 − γ)b).
Yet another possibility is that both bilinguals and English monolinguals want
to migrate. If the English want to move, then bilinguals will want to move a
fortiori. Hence this is an equilibrium outcome if:
• English want to move: h(γ(b+e), γ(b+e)) > h((1−γ)(b+e), (1−γ)(b+e)).
7
Figure 1: A Timeline
Migrate?
Acquire
initial
language(s)
Childhood
Learn/
Work
Period 1
Work
Period 2
Migrate?
Acquire
initial
language(s)
Childhood
Learn/
Work
Period 1
Work
Period 2
Migrate?
Acquire
initial
language(s)
Childhood
Date t-1
Date t
Learn/
Work
Period 1
Date t+1
Work
Period 2
Figure 2: Existence and Stability of
Steady States
1
1/2
1
e
e+s
A: Unstable Symmetric Steady State
1
1/2
1
B: Stable Symmetric Steady State
e
e+s
Figure 3: The Language Simplex
b=1
e
s
b
e=1
s=1
Monolingual Steady States
Figure 4: Transitional Dynamics
b=1
e=0
D
s=0
E
b=0
C
B
A
e=1
s=1
Figure 5(A): Language Decline in
Wales
b=1
1931
1911
1901
1921
1951
1961
1971
1981
e=1
Welsh = 1
Figure 5(B): Assimilation of Hispanics
in Los Angeles
b=1
Generation 2
Generation 3+
Generation 1.5
Generation 1
e=1
s=1
Figure 6: Assimilation
b=1
Non-assimilation;
assimilation by
English
Non-assimilation
C
D’
D”
Nonassimilation;
assimilation by
Spanish
A
D
Assimilation by
English or Spanish
e=1
B
Assimilation
by English
Assimilation
by Spanish
A’
B’
Non-assimilation;
assimilation by
English or
Spanish
Assimilation by
English or Spanish
s=1
Figure 7: Assimilation in the Dynamic
Economy
b=1
E
C
D
B
A
F
e=1
s=1
Figure 8: Multiple Locations
b=1
b1 =1
b2 =1
A
b1
e1 =1
b2
s1 =1
b2
e2 =1
e=1
s2 =1
b1
s=1
Figure 9: Geographic Isolation
b=1
Geographic
isolation of
English
Geographic
isolation of
Spanish
Geographic isolation
of English or
Spanish
Geographic isolation
of Spanish
e=1
Geographic isolation
of English
s=1
Figure 10: Geographic Isolation and
Survival of Minority Languages
b=1
Region 2
(Spanish
only)
A
B
Region 1
(English and
Bilinguals)
C
e=1
s=1
Figure 11: Linguistic Isolation to
Geographic Isolation
b=1
Geographic
isolation of
English
Geographic
isolation of
Spanish
Geographic isolation
of English or
Spanish
A
Geographic
isolation
of Spanish
e=1
Geographic
isolation
of English
s=1
Figure 12: Equilibrium Outcomes in
the Complete Model
TO
Geographic
Isolation
Linguistic Isolation
Assimilation
• Survival of small
language communities
• Migration without
learning
• Economic integration
• Ghost towns
• Disappearance of
small language
communities
• Papua New Guinea
• Quebec
• Iceland
• Irish Gaeltacht
•First-generation
immigration to U.S.
•Emigration from
Ireland,
• Emigration from
Scottish Highlands
• Ainu
• Cornish
• Manx
• Native American
languages
• Origin of Nations
• Survival of large
language communities
• Disappearance of
large language
communities
• Assimilation of
immigrant groups
• Yugoslavia
• East Timor
• German immigrants in
U.S (19th C.).
• Hispanic immigrants
in U.S.
• Swedish in Finland
• German immigrants in
U.S. (20th C.)
• Asian immigrants in
U.S.
FROM
Geographic
Isolation
Linguistic
Isolation
Figure 13: Assimilation with Inertial
Agents
b=1
Non-assimilation;
assimilation by
Spanish
Non-assimilation;
assimilation by
English
Non-assimilation
Non-assimilation;
assimilation by
English or Spanish
Assimilation
by Spanish
e=1
Assimilation by
English or Spanish
Assimilation
by English
s=1
Figure 14: Migration with Inertial
Agents, Starting From {e, b}, {s}
b=1
b: No
s: Yes
b: Maybe
s: Maybe
A
b: No
s: Maybe
B
b: Yes
s: No
b: No
s: No
C
e=1
b: Maybe
s: No
s=1
Figure 15: Equilibrium Outcomes with
a Vehicular Language
b=1
Key:
{e,s}:
{e}:
{s}:
{φ}:
e and s learn
e learn; s do not
s learn; e do not
neither learn
{e,s}
{e,s}, {s}
{e,s}, {e}
{e,s},
{φ}
{s}
{φ}, {s}
{e,s}, {e},
{e,s}, {s},
{φ}
{φ}
{e,s},{φ}
{e}
{φ}, {e}
{φ}
e=1
s=1