Wage Inequality and Human Capital Formation
Akira Shimada*
Faculty of Economics, Nagasaki University
Abstract
We investigate the effects of wage inequality between skilled and unskilled workers on humancapital formation in a home country when the workers in the home country can migrate to aforeign country. In contrast to the previous analyses on brain drain, we pay attention to the factthat resources for human capital formation, such as education, are not necessarily suppliedelastically and free. For this reason, we include a resource market in our model and consider its
transactions explicitly. We show that even if workers have to pay pecuniary costs to form humancapital, both skilled and unskilled workers in the home country always attempt to migrate whensome of them can be accepted in a foreign country. We also show that brain gain and brain draintake place simultaneously. In particular, if wage inequality is larger in the foreign country than in
the home country, skilled workers experience brain gain whereas unskilled workers experience
brain drain. In contrast, if wage inequality is larger in the home country, skilled workers
experience brain drain, whereas unskilled workers experience brain gain. Our results suggest thathow migration possibilities affect human capital formation of different types of workers is closely
related to differences in wage inequality between the home and foreign countries.

JEL Classification: F22; J24; J31; O15
Keywords: Wage inequality; Migration; Brain drain; Brain gain*

Email address for correspondence: shimada@nagasaki-u.ac.jp
11. Introduction
We investigate how wage inequality between skilled and unskilled workers in a home country
and a foreign country affects human capital formation of the home country’s workers when someof them can be accepted in the foreign country. For this purpose, we consider that the resources
necessary for human capital formation, such as education, cannot always be supplied elasticallyand that workers generally cannot obtain such resources free of cost.
Wage inequality between skilled and unskilled workers has been a serious problem in many
countries, especially in developing countries (Wood 1995, 1997; Marjit et al. 2001). Against ourstandard theoretical presumption, the recent liberalisation in trade did not necessarily alleviate it(Marjit and Beladi 2002; Marjit et al. 2004). On the contrary, in Latin America and South Asia,
including India, trade liberalisation has increased wage inequality. Undoubtedly, trade is not the
only factor that affects wage inequality. However, wage inequality does not seem to disappear
easily.
This suggests that in an analysis on brain drain, we cannot ignore this reality because theanalysis is often associated with skilled and unskilled labour and different wage inequalities in thelabour-sending and labour-receiving countries. As shown by Yabuuchi and Chaudhuri (2007) andBeladi et al. (2008), migration and other factor motility affect wage inequality. However, we inferthat wage inequality will also affect migration. But the effects of wage inequality on emigrationand human capital formation have received little attention so far.
There can be two cases of wage inequality in a labour-sending country (often a developing
country) and a labour-receiving country (often a developed country). One possibility is that wage
inequality in the labour-sending country becomes smaller than that in the labour-receiving country
as a result of, for example, trade liberalisation. Another possibility is that the labour-sending
country would still have a larger wage inequality than the labour-receiving country. Therefore, we
2assume these two cases and examine the effects of migration possibilities on human capitalformation.
There is another weakness in previous studies on brain drain. Although the research has a long
history, until now it has not paid sufficient attention to the fact that the supply of resources forhuman capital formation, such as education, cannot always meet the demand instantaneously andwithout cost.1 Stark et al. (1997, 1998) assumed that an individual worker develops his humancapital to maximise his utility derived from wages minus non-pecuniary costs of human capital

1

According to Docquier and Rapoport (2009), the research history comprises three generations.

Although a survey of the research is not the aim here, a brief overview is as follows: The term
“brain drain” gained wide usage in the late 1960s when the migration of skilled workers fromdeveloping to developed countries accelerated. The first-generation research, which includes
Grubel and Scott (1966) and Berry and Soligo (1969), generally emphasized the benefits of freemigration to the world economy. While the first-generation research assumed a competitive
economy, Bhagwati and Hamada (1974), Hamada and Bhagwati (1975), and Bhagwati andRogriguez (1975), which formed the second-generation research, introduced more realistic
institutional settings and emphasized the negative effects of skilled emigration. After the
mid-1990s the third-generation research, which includes Mountford (1997), Stark et al. (1997,1998), and Beine et al. (2001, 2008), emerged. They took emigration of skilled workers to bebeneficial not only to the labour-receiving country but also to the labour-sending country on the
grounds that migration possibilities may send a positive signal and motivate others in thelabour-sending country to acquire more resources, such as education. This will result in a larger
average amount of acquired human capital of the labour-sending country. In the next section, webuild a model in line with this argument.
3

formation. No constraint was assumed for human capital formation and no pecuniary costs were
included.2 Accordingly, we can assume that in their models the resource for human capitalformation is being supplied to meet the demand instantaneously and without any pecuniary costs.
These premises also apply to Mountford (1997) and Beine et al. (2001, 2008).
However, such assumptions are not realistic. In a short period, resources used for human capitalformation, such as education, cannot be supplied elastically with changes in demand. If a large
number of people are willing to attend school, it will take some time before all of them can attend
school. It goes without saying that this is because the supply of education cannot be increased in ashort period. In such a case, we naturally consider that demand will be equalized to supply givenchanges in the price of the resource. If this is the case, it will be difficult to rule out the market for
the resource and pecuniary costs related to human capital formation.
Therefore, we incorporate into the model the resource market and consider transactions of theresource explicitly.
Once the resource market and its transactions are introduced in the analysis, even if skilled andunskilled workers’ wages are given independently, human capital formation for these two types ofworkers becomes interdependent through the resource market. This is another advantage ofincluding the resource market.
We will derive the following results: When skilled and unskilled workers in the home country
have migration possibilities to a foreign country, both always have an incentive to migrate even if
they need to pay pecuniary costs to form human capital. If the wage inequality between skilled
and unskilled workers is larger in the foreign country than in the home country, migration

2

Stark et al. (1998, footnote 1) stated explicitly that they disregard direct outlays in connection

with human capital investment.
4

possibilities raise the average acquired human capital of skilled workers in the home country, but
lower the average acquired human capital of unskilled workers in the home country. In otherwords, the skilled workers experience brain gain and unskilled workers experience brain drain. In
contrast, if wage inequality is larger in the home country than in the foreign country, skilledworkers experience brain drain and unskilled workers experience brain gain.
The remainder of this paper is organised as follows: Section 2 models a two-country economy
with skilled and unskilled workers. We assume that the home country and the foreign country
have different wage inequalities and that there is a resource market for human capital formation in
the home country. We also assume that some of the home country’s workers can migrate to theforeign country. Section 3 examines the effects of wage inequality on human capital formation of
the home country’s workers. Section 4 presents concluding remarks.

2. The Model
We assume two countries, a home country and a foreign country. The foreign country has alarger capital stock than the home country. There are skilled and unskilled workers in bothcountries. Both types of workers in the home country have migration possibilities to the foreigncountry. Migrants do not send remittances to the home country. Firms in the foreign country do
not distinguish between skilled (unskilled) native workers and skilled (unskilled) migrant workers.
This implies that skilled (unskilled) native and skilled (unskilled) migrant workers are paid thesame wage in the foreign country. Moreover, we assume that there is no unemployment in either
country.
In the home country, there are N skilled workers and (1   ) N unskilled workers, where  ,0    1, is a constant and denotes the fraction of skilled workers in the initial labour endowment

before migration. N is a positive constant and denotes the initial labour endowment. We assume5

that skilled and unskilled workers have the same migration possibility  , 0    1, that is given
exogenously and defined as the probability for an individual skilled (unskilled) worker to be
accepted as a (an) skilled (unskilled) migrant into the foreign country, although in the benchmark
case, they are assumed to have no migration possibilities, i.e.   0.
The productivity of an individual worker depends on capital stock, innate talent, and acquired
human capital. Since the capital stock is assumed to be larger in the foreign country, a worker ismore productive in the foreign country than in the home country if he has the same level of innate
talent and acquired human capital in the two countries. By nature, a skilled worker can beconsidered more talented than an unskilled worker. Accordingly, we assume that a skilled worker
has higher productivity than an unskilled worker if he is equipped with the same level of capitalstock and acquired human capital. Needless to say, by capturing more resources, an individual
worker forms more human capital and, other things being equal, the worker with more acquired
human capital is more productive.
To ensure that the model reflected these considerations, we included the following assumptions:
An individual skilled worker acquires human capital by ln eS if he captures the resources by
eS ( 1). Needless to say, under this assumption acquired human capital increases with its
resources. He earns hS ln eS in the home country and f S ln eS in the foreign country, which isdetermined to be equal to the skilled native workers’ wages in that country wS* , where hS  f S ,implying that capital is more abundant in the foreign country.3 An individual unskilled worker

3

In general, wages in the labour-sending country will not be independent from emigration, andwages in the labour-receiving country will not be independent from immigration. However, toavoid complicating the analysis, we consider that effects of emigration and immigration on wages
are not significant, and assume that wages in the home country are independent from emigration
6

forms human capital by ln eU by capturing the resource by eU ( 1). He earns hU ln eU in thehome country and fU ln eU in the foreign country, which is determined to equal the unskilled
native workers’ wages in that country wU* , where hU  fU . We also assume that hU  hS andfU  f S since skilled workers (migrants) are more talented than unskilled workers (migrants).
We define the home country’s wage inequality between skilled and unskilled workers as
hS ln eS hU ln eU , and the foreign country’s wage inequality as wS* wU* . Under these definitions,wage inequality is larger in the home country than in the foreign country if
hS
f
 S,
hU
fS
and wage inequality is larger in the foreign country than in the home country if
hS
f
 S.
hU f S
Both skilled and unskilled workers in the home country attempt to capture the same resource todevelop human capital. However, as mentioned, it is difficult for the supply of the resource toinstantaneously meet demand. We assume that the home country’s total supply of the resource
remains unchanged throughout the analysis and denote it with a positive constant E , which is
given exogenously. We also assume that the resource price p is determined competitively in the
resource market. The resource is traded at the equilibrium price.
There is an argument against these assumptions. It goes without saying that education is themost important resource for human capital formation, but it is often financed by taxes and we do
not pay its costs directly, although Commander et al. (2004) pointed out that in the last decadeand wages in the foreign country are independent from immigration. We also assume that humancapital accumulated in the home country does not ‘depreciate’ even after migration.

7

there has been an increase in the provision of private educational services in many developing
countries. The price of such services does not seem to be adjusting demand and supply. This istrue for primary and secondary education. However, we must note that primary and secondary
education is usually compulsory. As a result, there will be no differences between skilled andunskilled workers in receiving these levels of education. In the context of our model, the same
duration of primary and secondary education can be included in both eS and eU , purchased at aresource price of zero. The difference in the demand for education will emerge for tertiary
education, which is becoming more market-oriented (Johnstone et al., 1998).4 Accordingly, thedemand for tertiary education will be more price-dependent and given the market price, skilled
and unskilled workers will demand different amounts of tertiary education. This will cause eS
and eU to have different values. These observations allow us to assume a resource market that
allocates the resource among the skilled and unskilled workers according to the price.
Under migration possibilities for both types of workers, an individual skilled worker in the~ ~home country demands the resource to maximise his net earnings WSS ,U that are equal to skilledworkers’ expected wages minus pecuniary costs for realising such wages, i.e.
~ ~WSS ,U  f S ln eS  (1   )hS ln eS  peS .
Similarly, an individual unskilled worker in the home country demands the resource to maximise~ ~his net earnings WUS ,U that are equal to unskilled workers’ expected wages minus pecuniary costs
for realising such wages, i.e.
~ ~WUS ,U  fU ln eU  (1   )hU ln eU  peU .
In contrast to Stark et al. (1997, 1998), non-pecuniary costs are not included by implicitly

4

According to Dahlman and Aubert (2001) and Zeng and Wang (2007), private provision for

tertiary education has been growing rapidly in China.
8

assuming that such costs are fixed.

3. The Brain Gain and the Brain Drain

In this section, we examine the effects of migration possibilities on human capital formation ofskilled and unskilled workers. In particular, we examine whether skilled and unskilled workers in
the home country increase or decrease their average acquired human capital when some of them
are accepted in the foreign country.
As a benchmark, we first deal with the case where neither type of worker has migration
possibilities, i.e.   0. An individual skilled worker demands the resource to maximise his net
earnings hS ln eS  peS (  WSS ,U ), and skilled workers’ total demand for the resource is(hS p ) N , which decreases with the resource price. Similarly, an individual unskilled worker

demands the resource to maximise his net earnings hU ln eU  peU (  WUS ,U ), and unskilledworkers’ total demand for the resource is ( hU p )(1   ) N , which also decreases with theresource price.
For the resource market to be in equilibrium, the total demand for the resource must be equal toits supply:hShN  U (1   ) N  E ,pp
and the resource price is determined as follows:p   {hS   hU (1   )}(  p S ,U ),where   N E is assumed to be sufficiently small so that net earnings and the average acquired
human capital are positive.
By substituting resource price into net earnings, we derive net earnings of an individual skilledworker and an individual unskilled worker under no migration possibilities:
9



hS
WS  hS ln 1 ( WSS ,U ),  {hS   hU (1   )} 

(1)



hU
WU  hU ln 1 ( WUS ,U ).
  {hS   hU (1   )} 

(2)

Accordingly, in the benchmark case, the average acquired human capitals of skilled workers andunskilled workers are, respectively,lnhS( AAHCSS ,U ), {hS   hU (1   )}

(3)

ln

hU
(  AAHCUS ,U ).
 {hS   hU (1   )}(4)

The average acquired human capital is larger for skilled workers than for unskilled workers since
an individual skilled worker demands more resources than an individual unskilled worker.
We next deal with the usual case where both types of workers have migration possibilities, i.e.
~ ~

  0. From WSS ,U eS  0 , we find that skilled workers demand the resource by~ ~[{f S  (1   )hS } p ]N , and from WUS ,U eU  0 , we find that unskilled workers demand theresource by [{fU  (1   )hU } p](1   ) N .
The resource price is determined as follows:~ ~p   [{f S  (1   )hS }  {fU  (1   )hU }(1   )]( p S ,U ).
~ ~The resource price is higher when migration possibilities are non-zero, i.e. p S ,U  p S ,U . This isbecause migration possibilities raise the total demand for the resource.
Under non-zero migration possibilities, an individual skilled worker and an individual unskilledworker have the following net earnings:~ ~f S  (1   )hS
WS  {f S  (1   )hS }ln
 1 ( WSS ,U ). (5)  [{f S  (1   )hS }  {fU  (1   )hU }(1   )] 

10

~ ~


fU  (1   )hU
WU  {fU  (1   )hU }ln
 1 ( WUS ,U ). (6)  [{f S  (1   )hS }  {fU  (1   )hU }(1   )] Accordingly, the average acquired human capital for skilled and unskilled workers are,respectively,ln~ ~f S  (1   )hS(  AAHC SS ,U ).
 [{f S  (1   )hS }  {fU  (1   )hU }(1   )]

(7)

ln

~ ~
fU  (1   )hU(  AAHCUS ,U ).
 [{f S  (1   )hS }  {fU  (1   )hU }(1   )](8)

As in the benchmark case, the average acquired human capital is larger for skilled workers thanfor unskilled workers.
We are now in a position to compare the usual case with the benchmark case to derive theeffects of migration possibilities on human capital formation. Inspection of Equations (7) and (3)shows that~ ~sign( AAHCSS ,U  AAHCSS ,U )
f S  (1   )hShS sign   [{f S  (1   )hS }  {fU  (1   )hU }(1   )]  {hS   hU (1   )}  , sign (hU f S  hS fU ),and inspection of Equations (8) and (4) shows that~ ~sign ( AAHCUS ,U  AAHCUS ,U )hU
fU  (1   )hU sign   [{f S  (1   )hS }  {fU  (1   )hU }(1   )]  {hS   hU (1   )}  sign ( hU f S  hS fU ).

These equations suggest that if
f S fU  hS hU ( hU f S  hS fU  0),
11

then,

(9)
~ ~

~ ~

AAHCSS ,U  AAHCSS ,U and AAHCUS ,U  AAHCUS ,U .
According to Equation (9), if wage inequality is larger in the foreign country than in the homecountry, the average acquired human capital of skilled workers is larger under non-zero migration
possibilities than under zero migration possibilities, whereas the average acquired human capitalof unskilled workers is smaller under non-zero migration possibilities than under zero migration
possibilities. Thus, under non-zero migration possibilities, it is likely that the skilled workers
experience brain gain and the unskilled workers experience brain drain.
Whether the brain gain and the brain drain materialise depends on whether workers in the homecountry actually attempt to migrate to the foreign country. Even with non-zero migration
possibilities, workers do not attempt to migrate if they cannot obtain larger net earnings by doing
so. By comparing Equations (5) and (1) and Equations (6) and (2), we find that if
~ ~

~ ~

f S fU  hS hU , WSS ,U  WSS ,U , whereas we cannot determine which of WUS ,U and WUS ,U islarger. Accordingly, skilled workers certainly attempt to migrate, but unskilled workers may not
attempt to migrate since unskilled workers do not necessarily obtain larger net earnings by~ ~migration. However, even if WUS ,U  WUS ,U is possible, they will attempt to migrate to the foreigncountry because their net earnings would be much smaller if they choose to remain in the home
~ ~

~

~

country when skilled workers are attempting to migrate, i.e. WUS ,U  WUS ,U , where WUS ,U is the net
earning of an individual unskilled worker who does not attempt to migrate when skilled workers
are attempting to migrate.5 Thus, both types of workers certainly attempt to migrate.
Therefore, if the foreign country’s wage inequality is larger than that of the home country,
skilled workers experience brain gain and unskilled workers experience brain drain. This result is

5~

WUS ,U  hU ln hU  [{f S  (1   )hS }  hU (1   )]  hU .
12

independent from the value of  .
In contrast, if
f S fU  hS hU ( hU f S  hS fU  0),
(10)

then,
~ ~

~ ~

AAHCSS ,U  AAHCSS ,U and AAHCUS ,U  AAHCUS ,U .
According to Equation (10), if wage inequality is larger in the home country than in the foreigncountry, it is likely that skilled workers decrease the average acquired human capital and unskilledworkers increase the average acquired human capital given non-zero migration possibilities. Thissuggests that skilled workers may experience brain drain and unskilled workers may experience
brain gain.
To examine whether brain gain and brain drain actually occur, we compare net earnings. We
~ ~

~ ~

~ ~

find that WUS ,U  WUS ,U , whereas WSS ,U  WSS ,U as well as WSS ,U  WSS ,U are possible. Accordingly,
unskilled workers certainly attempt to migrate, but skilled workers do not always attempt to
~ ~

~

~

migrate. However, we also find that WSS ,U  WSS ,U , where WSS ,U is the net earning of an individual
skilled worker who does not attempt to migrate when unskilled workers are attempting tomigrate.6 As in the previous case, workers who lose by not attempting to migrate will attempt tomigrate. Thus, both types of workers certainly attempt to migrate.
Therefore, if the home country’s wage inequality is larger than that of the foreign country,
unskilled workers experience brain gain and skilled workers experience brain drain. This result isalso independent from the value of  .
When there is no difference in wage inequality between the two countries, i.e. f S fU  hS hU ,both types of workers attempt to migrate. However, neither brain gain nor brain drain occurs. In

6~

WSS ,U  hS ln hS  [hS   {fU  (1   )hU }(1   )]  hS .

13other words, if
f S fU  hS hU ( hU f S  hS fU  0),
then,
~ ~

~ ~

WSS ,U  WSS ,U and WUS ,U  WUS ,U ,
~ ~

~ ~

AAHCSS ,U  AAHCSS ,U and AAHCUS ,U  AAHCUS ,U .

To summarise the results derived in this section, even if workers have to pay pecuniary costs toobtain the resource to develop human capital, both skilled and unskilled workers attempt tomigrate to the foreign country. If the home country’s wage inequality is smaller, skilled workers
experience brain gain and unskilled workers experience brain drain. In contrast, if the homecountry wage inequality is larger, unskilled workers experience brain gain and skilled workers
experience brain drain.

4. Concluding Remarks

Migration possibilities affect the incentive structure of workers and change their human capitalformation. Although it has been considered that emigration of skilled workers has negative
impacts on the labour-sending country, recent studies have found that skilled workers’ emigration
may increase average acquired human capital of the labour-sending country. In other words, thelabour-sending country may experience brain gain as well as brain drain.
To examine the effects of migration possibilities on human capital formation in a more realistic
situation, we explicitly took account of differences in wage inequality in the labour-sending andlabour-receiving countries and the limited availability of the resource for human market formation.
Previous analyses on the brain drain have paid little attention to these facts, which seem tostrongly affect skilled worker emigration and human capital formation.
We found that both skilled and unskilled workers always attempt to migrate to the foreign
14

country even if they have to pay pecuniary costs to obtain the resource and that how the brain gain
and the brain drain occur depends on differences in wage inequality between home and foreigncountries.
Our analysis can be extended in several directions by modifying the assumptions. We assumed
that the resource market is competitive. As a first attempt to introduce the resource market, suchan assumption is appropriate, but in reality, the resource is allocated in a non-competitive manner.
If we change the assumption of the competitive resource market, the results are likely to bedifferent. We also assumed that the resource is financed privately. We can extend the analysis byassuming that a part of the resource is financed publicly. The results would also be affected
depending on how workers pay taxes and how the government provides the resource. Moreover,
we assumed that the budget constraint of an individual worker is not binding and that his net
earnings are always positive. We can include the case where an individual worker cannot demand
the resource as much as he wants at the market price given the budget constraint. Incorporatingsuch a case will significantly improve our analysis.

15

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