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THE INTERACTION BETWEEN THE WELFARE STATE AND MIGRATION:
POLITICO-ECONOMIC THEORY AND EVIDENCE
A generous welfare state acts as a magnet for unskilled migrants, but may repel skilled
ones (Section I). At the same time, migrants may change the political power balance between the
pro “big” and pro “small” government; depending on how active the migrants are in the political
process, and whether or not they inflict some fiscal costs or benefits on the native-born voters and
the magnitude of these costs and benefits. Thus, migration has important implications for the size
of the welfare state (Section II). The net fiscal burden of skilled and unskilled migration and its
welfare implications will be rigorously revisited (Section III). Migration can affect the politicoeconomic sustainability of old-age social security, and vice versa (Section IV).
I. The Welfare State as a Host for Skilled and Unskilled Migration
A generous welfare state acts as a magnet for low-skill migrants. But it may repel highskill (potential) migrants. We propose to study analytically (Subsection I.a) and empirically
(Subsection I.b) the selection-formation of pairs, each consisting of a representative potential
migrant (within each skill category) from a source country to a potential host country, and the
corresponding magnitudes of migration.
I.a. A General Equilibrium Model of Skilled and Unskilled Migration
To highlight the factors that shape the attractiveness of the welfare state to skilled and
unskilled migrants, consider a stylized benchmark model of migration. Assume a potential host
country, where there are nh and nl exogenously given, native-born, skilled and unskilled
workers, respectively. The size of the native-born population is normalized to one ( nh + nl = 1).
We simplify by assuming perfect substitution between skilled and unskilled labor: a skilled
worker provides one unit of effective labor, whereas an unskilled worker provides only q < 1
units of effective labor. Aggregate output (Y ) is given by a standard concave, constant-returns-to
scale production function Y  F K , L , where K is a (fixed) stock of capital and L is aggregate
labor supply:
(1)
L  nh  mh  q( nl  ml ) ,
where mh and ml are the number of skilled and unskilled migrants, respectively. Assuming that
their opportunity income at the source country is constant, wh* and wl* , respectively, we can
write the following migration equilibrium equations:
(2a)
(1   )qw  b  wl*
(2b)
(1   )w  b  wh* ,
(3)
w  FL K , L
where
is the competitive wage rate,  is the exogenous, flat, income tax rate, and b is the uniform
transfer (demogrant), all in the host country. The static budget constraint is given by (assuming,
for simplicity, zero depreciation rate for capital):
(4)
b1  m2    Y ,
where m2 = ml + mh is the total number of migrantsi. Eqs. (2a) and (2b) can be solved for b and
w:
(5)
b
we*  qwh*
,
1 q
(6)
w
wh*  we*
.
(1   )(1  q )
Substituting Eqs. (1) and (5) into Eq. (4) we get
 we*  qwh* 


 1  q (1  m2 )  F K , nh  qnl  m1   R( , m1 ),


(7)
where R( , m1 ) is tax revenues, and m1  mh  qml is the total labor supply of migrants in
efficiency units. Substituting Eqs. (6) and (1) into Eq. (3) yields
wh*  wl*  (1   )(1  q)FL K , nh  qnl  m1 .
(8)
The latter two equations constitute the fundamental equilibrium conditions of this model. They
can be solved for the labor supply m1  and the number m2  of the migrants as functions of the
tax rate
  . Total differentiation of Eq. (8) with respect to 
yields:
dm1
 FL [(1   )FLL ]1  0 .
d
On inspection of Eq. (7) we can see that
 dm2 
 dR 
  sign 
.
 d 
 d 
sign 
Assuming that supply-side economics does not prevail; that is, dR / d  0 (which is always
true for small  ’s), then dm2 / d  0 . Thus, we have plausibly established that the labor supply
of the immigrants m1  falls while their number ( m2 ) rises when the host country's tax rate
 
is raised. This can happen only if dml / d  0 and dmh / d  0. Thus, more taxes (and
transfers) attract additional low-skill migrants but fewer high-skill migrants.
We propose to extend this stylized model as follows. First, the host country is taken here
as a small open economy in the sense that the economic features of the source country (such as
wages and the tax-transfer policies) are exogenous. For the empirical analysis of the determinants
of migration within pairs of host-source countries, we would like to investigate also the
implications of the source country policy (e.g. the tax-transfer parameters) on migration
decisions. We intend to do this in the proposed research. Indeed, our international, cross-section,
bilateral dataset motivates us to carry out such multi-country analysis of migration decisionsii.
Second, we plan to supplement our neo-classic model with wage rigidities and imperfect
competition in the labor market, so as to allow for unemployment, especially migration-generated
one. Third, to confront the predictions of the model with data, we propose to introduce into it
world-wide and country-specific productivity shocks which have strong implications for the labor
market and migration.
2
I.b. An Empirical Investigation of the Formation of Migrant-Host Country pairs in an
International Cross-Section Dataset
Our dataset contains stocks of immigrants, based on census and register data, for the
years 1990 and 2000, within 21 European countriesiii. Immigrants are at working age (25+),
defined as foreign born. The stock of immigrants is specified by their country of origin and their
education classes. There are three classes of education: low-skilled (0-8 schooling years),
medium-skilled (9-12 schooling years) and high-skilled (13+ schooling years). The data also
contains the non-movers, that is, the stock of the domestic-born labor force. The explanatory
variables are specified in the data description within section II.b.
A first look at the data will be done with a baseline specification of OLS-gravity
equations as follows:
(9)
mig s ,h,e   0  1welfare s   2 welfareh   3GDPPCs   4GDPPCh 
 5 X s , h, e   s , h, e
The dependent variable ( mig s , h,e ) is the stock of immigrants, with education level e, originated
in source country s and residing in host country h, as a share of their source country respective
population. The main variable of interest is the variable “welfare” which refers to some
parameters characterizing a typical welfare state (such as, for instance, the average labor tax rate).
Naturally, migration is affected also by economic variables that capture some push-pull factors,
such as the GDP per capita (GDPPC) in the source and host countries, which may be good
proxies for the income opportunities in these countries. We will use also a vector of some other
explanatory variables X s , h,e , such as the geographical distance between the pair of countries


and whether or not they use a common language. Clearly, there may arise a problem of
endogeneity between the welfare and migration variables, as the stock of migrants in the host
country may influence the desire and need of that country for more welfare spending. Thus, we
may need to use some instrument for welfare h . One may think of using defense spending, which
is negatively correlated with welfareh , or the size of the public sector work force which is
positively correlated with welfareh . These may be good instruments because there is no
presumption that they are correlated with the immigration stock.
Assume that the simple gravity equation looks like that:
(9’)
m( s, h, e)  X ( s, h)  (e)  W ( s, h)   (e)
where m (s,h,e) is the emigration stock rate from country s to country h of individuals with
education level e; X(s,h) is a vector of determinants - including welfare benefits -  b is a vector
of parameters ; W(s,h) is the countries specific disturbance, and
specific disturbance.
 (e)
is the education-level
The obvious shortcoming of this cross section equation is that it can never control for all country
specific, nor countries-pair specific, variables. In other words, W and X are inevitably correlated.
So, for instance, in order to accurately describe the impact of the welfare benefits, one needs to
control for all other country-specific properties which are correlated both with migration and the
welfare rate (or, alternatively, come up with IV - which are almost always debatable).
Since what we are interested is examining whether there is a difference impact over different skill
3
levels, Yona suggested to focus over the "difference-in-difference" effect. That is, if, for instance,
if the parameter  high (s ) is the coefficient of welfare in the host countries in the high-skilled
 low (u ) is the coefficient of welfare in the host countries in the low-skilled equation,
then it is better to look only at  high ( s )   low (u ) (which is the "difference-in-difference"
equation, and
estimator).
I took this idea a step forward (or maybe it took me a while to understand what Yona actually
meant...). Instead of estimating b1(s) and b1(u) from two different equations, one for the skilled
and one for the unskilled (or, using dummy variables in a single estimation), I can estimate the
difference between the two equations (skilled minus unskilled):
(9’’) D m( s, h)  X ( s, h) D  D
where "D" stands for the skill difference. This ways, in the example above,
D   high ( s)   low (u ) is in fact the estimated coefficient. Hence I can test directly and simply
the hypothesis suggested by theory:
D   high ( s)   low (u )  0 .
More importantly, the main advantage of this "difference-in-difference" (or "DID") approach is that
equation (9’’) gets rid of all country specific unobserved items, as well as from all countries-pair
specific unobserved items (the term w in (9’)).
All that left in the error term is unobserved elements which are skill-dependent
(u). First, these elements are much less likely to affect the determinants of X, since X has only
(s,h) index - it is not skill dependent (it contains variables like GDP per worker, welfare benefits
etc.). Secondly, even if some element in u is correlated with X, it will still generate unbiased
estimators insofar the correlation of the omitted variable with X is skill invariant. Thirdly, even if
the omitted variable is correlated with X differently across skills, it will work against the hypothesis
from D   high ( s )   low (u )  0 - as long as the impact of X over the skilled-omitted variable is
higher than the impact over the unskilled-omitted variable. This can be justified, since the skilled
"market" is smaller than the unskilled "market", thus normally greatly affected by macro-economic
variables. In the latter case, the "DID" estimator is biased upward, which works against the
hypothesis: D   high ( s )   low (u )  0 .
On top of that, of course, We shall use lagged values of the welfare benefits and conduct some
robustness tests using instrumental variables..
The above specification takes the choice of people from country s to migrate to country h
as exogenous. It did not look at the possibility of potential migrants from country s to migrate into
third countries. Thus, it may be possible that people from country s did not migrate to country h,
not because the latter is not more attractive than the former, but because third countries were even
more attractive than country h. Therefore, the regression coefficients may be biased. Put
differently, one would like to look at the factors that determines the formation of the pair (s,h)
with country s as a source and country h as a host. To do this, we employ a conditional-logit
migration model, following Davies, Greenwood and Li (2001). Assume that there are N countries.
In each country there is a representative individual (for each skill-level e  1,2,3, denoting the
education level, respectively). Each individual of skill level e, has a discrete choice to make; that
is, where to live. Denote the choice of a representative individual from source country s with skill
4
level e, by Ys , e  1,2,..., N. Assume that the (latent) utility gain of such individual is specified
by:
(10)
U s ,h,e  U s ,e (Ys ,e  h)   X s ,h,e   s ,h,e ,
where Xe ,.,. is a vector of characteristics for the “source-host” country pair (s,h). Note that this
specification allows for the possibility that some of the coefficients of the explanatory variables
are different across skill levels. Assume that an individual from source country s will migrate to
some host country h, if, and only if, the utility gain there is the highest, given her N possibilities
(including, of course, not moving):
(11)
Ps ,h,e  Probability (Ys ,e  h) = Probability (U s , h, e  U s , h' ),
h'  h ,
Assume that the disturbances in (10) are independent and identically distributed, and has a
Gumbel-type distribution. Thus, the probability for choosing a certain host country is the
cumulative logistic function:
(12)
Ps ,h,e 
exp(  X s ,h,e )
,
 exp(  X s, j ,e )
j
The log-likelihood estimated function for skill level e is thereforeiv:
(13)
log Le    Mig s ,h,e log( Ps ,h,e ) ,
s
h
where Mig s , h, e is the stock of immigrants of skill level e from source country s into host country
h.
Naturally, among the explanatory variables we plan to focus on the tax-transfer variables.
As there may be an endogeneity problem associated with these variables of interest, we will treat
the problem by a standard two-stage procedure. That is, we first regress these potentially
endogenous tax-transfer variables on the other exogenous variables and some instruments. As
mentioned before, these instruments could be defense spending, or the size of the public sector
work force. In the second stage, we plan to run the conditional logit model, where the fitted
values of the potentially endogenous variables replace their observed values; see, e.g., Woolridge
(2002, p.474).
The discrete-choice model method has been scarcely employed within the field of
international migration. One prominent advantage that this method posses, is that it would enable
us to estimate the influence of third countries' properties and policies over the migration
movements between any pair of source-host countries.
II. Implications of Migration for the Size and Structure of the Welfare State
In the preceding section we took the welfare state policy variables as exogenous, and
studied migration of different skill types as endogenously determined in equilibrium. In this
section we treat migration of different skill types as exogenous, and study the size and structure
of the welfare state as endogenously determined in a politico-economic equilibrium. Additionally,
migration quotas (either of skilled or unskilled individuals) may be endogenized, so as to render
them as choice variables in the politico-economic equilibrium. The analytical framework is
5
studied in Subsections II.a-II.b, and key predictions of this study are confronted with data in
Subsection II.c.
II.a. A Politico-Economic Model of the Evolution of the Welfare State with and without
Skilled and Unskilled Migration
Consider a benchmark, static model of politico-economic determination of the size of the
welfare state, as in Razin and Sadka (2001). Migrants are all unskilled and their supply (m) is
exogenous. There are two levels of work skill, low (unskilled) and high (skilled). The latter can
be obtained by investing e units of time. Each native-born individual is endowed with one unit of
time, so that if she invests e units of time to become skilled, then she works for the remaining
time, 1-e, and has a productivity of one. If she does not acquire skill, then she spends all of her
unit of time at work; but her productivity is only q<1. There is also a pecuniary cost,  , of
acquiring skillv. The parameter e is distributed uniformly over the unit interval [0,1]. Under these
circumstances, there is a cutoff level, e * , of the time-cost of education, given by
(14)
e*  1  q 

,
(1   ) w
such that all individuals with e below e * become skilled, and all the rest – unskilled; where  is
the flat income tax rate and w is the wage rate. The size of the native-born population is
normalized to one. The production function is linear so that F ( K , L)  rK  wL , where factor
prices, r and w, are fixed. Total labor supply is given by
(15)
1
L  e *  ( e * ) 2  (1  e *  m )q.
2
Tax revenues are used to finance a uniform transfer (b) given by:
(16)
b
 ( wL  rK )
1 m
.
Note that this transfer is accorded to migrants too. For any tax rate  and exogenously given
migration quota m, Eqs. (14)-(16) determine e * , L, and b as functions of  and m: e * =
The number of migrants (m) is
e * (  ,m), L = L( ,m), and b = b(  ,m).
*
exogenous. But we nevertheless write e , L, and b as functions of m, because we wish to explore
the effect of m on these variables. Consumption is a strictly decreasing function of the parameter
e for the native-born skilled individuals, then constant for the native-born unskilled individuals. It
is also constant for the migrants, but at a lower level than for the native-born unskilled
individuals, because the migrants do not own any capital. This function is given by:
(17)
(1   ) w(1  e )    [1  (1   ) r ]K  b( , m ), 0  e  e * ( , m ),

c(e, , m)  
(1   ) wq  [1  (1   ) r ]K  b( , m ), e  e * ( , m ),

(1   ) wq  b( , m ), 1  e  1  m

where, for ease of exposition, we artificially attribute a parameter value for e between 1 and 1+m
to the migrants, simply in order to indicate that their consumption is below that of the native-born
unskilled individuals. With this consumption schedule, the median voter is a decisive voter in a
6
majority-voting system. Denote the time-cost of education parameter of the median voter by eM.
Suppose plausibly that the new migrants are entitled to vote. Hence:
(18)
e M (m) 
1 m
.
2
The politico-economic equilibrium  (denoted by  0 (m ) ) maximizes the consumption of the
median voter, that is,
(19)
 0 ( m)  arg max ce M m, , m .
We are interested in exploring how migration (m) affects the size of the welfare state (  0 ), that is,
we look for the sign of d 0 / dm. It can be shown that:
(20)
 signwq  m   rK , e M  e *

d
sign( 0 )   sign rK , e *  e M  1
dm

0, e M  1

Consider first the case in which the median voter is skilled, that is, e M  e * . As can be
seen from Eq. (20), the sign of d 0 / dm is not determined a priori: an increase in the number of
migrants can either raise or lower the politico-economic equilibrium tax rate and demogrant.
Consider next the case in which the median voter is a native-born unskilled individual, that is,
e *  e M  1 : an increase in the number of migrants unambiguously lowers the politicoeconomic equilibrium tax rate and demogrant. In the extreme case in which the median voter is
an (unskilled) migrant, an increase in the number of migrants has no effect on the size of the tax
rate and demogrant. The rationale for this result is as follows. Begin with the case in which the
median voter is a native-born unskilled individual. Then the majority of the voters are unskilled
and they are certainly pro-tax. This majority has already pushed the tax rate upward to the limit
(constrained by the efficiency loss of taxation). A further increase in the number of migrants who
join the pro-tax coalition does not change the political-power balance, which is already dominated
by the pro-tax coalition. However, the median voter who is a native-born member of this coalition
(and, in fact, all the unskilled native-born individuals) would now lose from the “last” (marginal)
percentage point of the tax rate, because a larger share of the revenues generated by it would
“leak” to the migrants whose number has increased. (Recall that, before more migrants arrived,
this median voter was indifferent with respect to the marginal percentage point of the tax rate.)
Therefore, the median voter and all unskilled native-born individuals now support a lower tax
rate. This is also why d 0 / dm = 0 in the case in which the median is an unskilled migrant,
because the “leakage” element does not exist. In this case, an increase in the number of migrants
does not change the politico-economic equilibrium tax rate and demogrant. Turn now to the case
in which the median voter is a native-born skilled individual. The leakage element, as in the case
in which the median voter was a native-born unskilled individual, work for lowering the tax rate
when m increases. However, now an increase in m tilts the political-power balance toward a
median voter who is less able (with a higher value of e) and has a lower income; she benefits
more from a tax hike than the original median voter. Thus, an increase in m generates two
conflicting effects on the politico-economic equilibrium tax rate. Therefore, we cannot
unambiguously determine the effect of m on  and b.
7
We propose to extend this stylized model in several directions. First, we propose to allow
also for skilled migrants. This may undermine the unimodality of the decision-making process
and may therefore necessitate the application of some other political-economy mechanisms, such
as probabilistic voting. Second, in this section the policy of each country is determined
independently of other countries. As a result, in a sample of cross section, the number of
observations is equal to the number of countries in the sample, which may be too small. Hence,
we would like to employ panel data. In such a case, it is suitable to introduce some dynamics to
the model, paying attention to the fact that political systems often make it hard to change taxes
frequently. Third, we would like also to consider the implications of migration for the structure of
taxation (e.g., between labor and capital) and expenditures (e.g., among transfers, public services,
and public goods).
II.b. A Panel Data Investigation of the Effects of Migration on the Size and Structure of
the Welfare State
The benchmark model of the preceding subsection alludes to the existence of a “fiscal
leakage” factor that may cause a negative effect of unskilled migration on the size of the welfare
state. Indeed, a first look at panel data comprised of 20 OECD countries over various periods
between 1974 and 2004 reveals a negative effect of the total stock of all immigrants, as a share of
the source countries population, on the size of the average labor tax rate (which is the main source
of finance of the benefits of the welfare state). This result is described in Table A which presents
the coefficient values obtained when regressing the average labor tax rate over migrants' share
within all source countries and on other explanatory variables. The latter include, among others,
the ratio of the average income in the bottom quintile to the average income in the middle
quintile, and the ratio of the average income in the top quintile to the average income in the
middle quintile. These are some measures of the skewedness of the income distribution. Indeed,
as Meltzer and Richards (1981) argue, Table A suggests that a more skewed distribution calls for
more redistribution. Arguably, as the migrants’ share may itself be affected by the labor tax rate,
it is useful to instrument it. We chose as an instrument for each country the average population
size, or, GDP per capita, for all other countries in the sample, which we expect to be negatively
correlated with the migrants’ share. At the same time, this instrument is not expected to be
correlated with the error term.
We propose to follow up on this initial “finding” of a fiscal leakage effect, and confront
some key predictions from the proposed extended model of the preceding subsection with a more
detailed panel data. For instance, even to analyze empirically the predictions of the benchmark
static model more carefully, we have to break down the stock of immigrants into skill categories.
Also, because unskilled migration may create some effects that counteract the fiscal leakage
effect, such as the tilt of the preferences of the median voter toward more taxes, we would like to
isolate the latter effect by controlling for the preferences of the (income) median voter. Similarly,
the predictions of the extended model will be addressed, paying attention to the relative rigidity of
the political system with respect to frequent tax changes.
III. The Net Fiscal Benefits and Costs of Skilled and Unskilled Migration to the
Welfare State
We mentioned in the preceding section that migration may generate fiscal costs or
benefits. In this section we focus on the study of this issue. In particular, we distinguish between
the short-run (static) and the long-run (dynamic) costs, and between skilled and unskilled
migration..
8
Consider a simple overlapping generations model, as in Razin and Sadka (1999), in order
to highlight the distinction between the static (short-run) and the dynamic (long-run) analysis of
the net fiscal costs, and between skilled and unskilled migration. This background will guide us in
the case-study of Israel in the next subsection. Each generation lives for two periods. In each
period, a new generation with a continuum of individuals is born. Each individual brings 1+n
children in the first period of her life. The human-capital formation of this model is similar to that
of Subsection II.a, except that we drop out the pecuniary cost   of education, for simplicity.
There is a pay-as-you-go (PAYG) pension system, which employs a flat payroll tax (  ) on the
young in order to finance a uniform benefit (b) to the aged. Suppose that at some period (say,
period zero), a one-shot wave of m unskilled, working age, migrants are allowed in. They grow
up in the same rate (n) as the native-born population, and the ability parameter (e) of their
offspring, who have access to the same education system as the native born is distributed
according to the same c.d.f. G on the unit interval [0,1]. Consider now the following thought
experiment. Suppose that the government continues to maintain the pre-migration social-security
contribution rate,  , intact. We then ask what pension benefit (b) can be paid to retirees in our
PAYG system. One can show that the pension that will be paid to the old, living at the time when
the wave of unskilled, working-age migration takes place, (i.e. period 0), is:
(21)


 e*



b0  w (1  n)  (1  e )dG(e )  q[1  G (e*)]   qm  ,


0



whereas the pension paid to all future generations of retirees is (including the immigrants):
(22)
 e*

b1  b2  b3  ...  (1  n)w   (1  e )dG (e )  q[1  G (e*)]  .
0

Upon inspection of Eq. (21), one can observe that b0increases with the number of unskilled
migrants. Therefore, the old generation in period 0 is clearly better-off with migration. Upon
inspection of Eq. (22), one can observe that b1 = b2 = b3 = … are unaffected by the migration. In
particular, and somewhat surprising, the young generation at the time in which the unskilled
migrants arrives is not adversely affected by the migration. Thus, the existing population will
welcome this unskilled, working-age migration. Furthermore, by creating some surplus in the
pension system (to be invested in a social security fund) during the period of migration (that is, by
lowering b0 just a little bit) the gains that accrue only to the current old, could be spread out to the
current young as well as to all future generations. In other words, unskilled, working-age
migration is a Pareto-improving change with respect to migrants and existing current and future
native-born generations. Strikingly, this result obtains even though the unskilled migrants may
well inflict a net fiscal burden (cost), in the sense that the present value of their pension benefits
exceeds their pension contributions. To demonstrate this point, we calculate the present value of
the life-time net fiscal cost (NFC) of a representative unskilled migrant:
(23)
NFC 

1  n  e*
w  (1  e )dG ( e )  q[1  G ( e*)]   qw .
1 r  0

One can see that the fiscal cost is positive, if:
9
_
(24)
G ( e*)( e *  e ) r  n

,
1 e *
1 n
_
_
where e is the skilled population mean of e. Note that e * is greater than e , because the former is
the upper bound of e for the skilled population, whereas the latter is the mean. Thus, the left-hand
side of condition (24) is definitely positive. Consider the plausible case where r > n, in which the
economy is dynamically efficient. If a large share of the native-born population is skilled, then
condition (24) could be satisfied. In this case, NFC is positive, and, at the same time, unskilled,
working-age migration is a Pareto-improving change for the migrants and the native-born
population. This illustrates the distinction between the static and dynamic aspects of the net fiscal
costs or benefits.
This benchmark overlapping generations model will be extended and refined to allow for
many overlapping generations; several kinds of benefits, some general and some age related;
distortionary taxes and benefits; etc. This novel consumption-advancing mechanism of
immigration lends itself to an elaborate calibration analysis.
Table A: Labor Tax Rate Determinants
OLS
IV
Labor tax rate
Labor tax rate
-3.224012
-2.206926
(0.508922)***
(1.009515)**
25.451420
25.679007
(17.107175)
(8.126642)***
0.000001
0.000001
(0.000000)**
(0.000000)***
6.550313
6.468997
(7.026670)
(2.514344)**
-26.121411
-25.515669
(15.241788)
(7.248268)***
-0.127474
-0.126829
(0.034528)***
(0.016283)***
13.781162
14.021105
(4.322360)***
(5.259318)***
0.326496
0.325693
(0.113020)***
(0.043701)***
Observations
316
316
Number of countries
20
20
Migrants/Total source population
Government jobs share
Old population
Rich/middle income share quintiles
Poor/middle income share quintiles
Trade openness
Growth GDP per capita
Year
R-squared
0.489
10
Robust standard errors in parentheses
* significant at 10%; ** significant at 5%; *** significant at 1%
IV. Political Economy Migration Policy, and Sustainability of Social Security
System Through Migration
Suppose that the economy is populated by overlapping generations of identical
individuals who live for two periods. When young, the representative individual works and makes
labor-leisure and consumption-savings decisions. When old, the individual retires, and receives
social security benefits, and income from private savings. As before, the tax-transfer system is
"pay as you go", where in every period the government levies a flat tax on the young's wage
income, which fully finances the social security benefits paid to the old. Immigrants enter the
economy when young, and gain the right to vote only in the next period, when old. They have the
same preferences as those of the native born, except from having a higher population growth rate.
Immigrants are fully integrated into the social security system upon arrival into the country.
Offspring of immigrants are like native born in all respects (in particular, they have the same rate
of population growth). In this model, the old individual prefers that the migration quota will be
as large as possible, because the larger the current immigration is, the larger is the total amount of
tax collected, and thus the social security benefits she receives. The old preferable tax rate is the
"Laffer point" tax rate, where the tax revenues are maximized. The young individual prefers
naturally that the current tax rate is as low as possible, but regarding migration quota her
preferences are ambiguous. A larger migration quota increases next period social security benefits
per old individual, because migrants have population growth rate which is higher than that of the
native born. On the other hand, larger migration quota typically influences the identity (old or
young) of next period decisive voter. This strategic consideration results from the fact that a
higher current migration quota not only increases the number of current young which will be the
old voters in the next period but also increases the number of young voters (some of these are
offspring of the current migrants) in the next period. Since the immigrants’ fertility rate is higher
than that of the native born, a higher migration quota will increase the number of young voters by
more than the number of old voters in the next period. Thus, the current young voter tends to
favor the most liberal migration policy. When this consideration dominates, it may lead to an
equilibrium where the decisive voter identity alternate over time from young to old, to young.
We propose to employ a subgame-perfect Markov equilibrium of perfect foresight, as our
equilibrium concept (see, e.g., Krusell and Rios-Rull (1996)). The fixed-point condition requires
that if next period policy outcome is derived by the vector of policy decision rules, the
maximization of the indirect utility of the current decisive voter will reproduce the same law of
motion.
We begin with a baseline model in which a perishable consumption good is produced using
only labor as an input; transfers from young to old (paid by flat rate tax on labor income) are the
only means of guaranteeing old-age consumption. Each generational cohort lives two periods,
supplying labor inelastically when young, and deriving utility from consumption in both periods
of life. If there were not to be immigration, it is a standard outcome in this framework that if the
population growth rate is positive, young always outnumber the old. Therefore, a pay-as-you-go
social security system cannot be sustained under majority voting. If, however, population growth
is negative, so that the old outnumber the young, then the pay-as-you-go system can be sustained
11
with a constant tax rate that maximize the social security benefits ( the preferred point of old
cohort at each period). Now introduce immigration into the standard framework. Immigrants
arrive young but cannot vote until they are old. Their children, who are identical to young native
born, can vote when young. Moreover, immigrants (though not their offspring) have a birth rate
that is larger from the native born rate. Immigration policy can be described by a endogenously
determined quota variable. We restrict the feasible choices of the quota with doubling the
population being an upper bound on immigration. The central tension faced by today's young in
thinking about policy is that both the ratio of young to old in the next period, and the ratio of
taxpayers to old dependents in the next period increase in the present period immigration quota. A
higher value of the latter this period will raise the number of young tax payers per old dependent
next period, but also increase the voting power of the young next period, perhaps putting them in
the majority. If the native born and the immigrants' birth rate are positive (while by assumption
the latter rate exceeds the former), then young voters always outnumber old voters, and the payas-you-go social security system will not be sustainable as a Markov equilibrium. So immigration
is of no help in this case. On the other hand, if the native-born birth rate is negative, then the
social security system is sustainable absent immigration. In this case the question is not whether
immigration helps sustain social security, but whether it threatens its sustainability. Assuming
that birth rate of natives is negative, the sort of equilibrium that arises depends on the sum of
native-born and immigrants birth rates. If the sum of native-born and immigrants' birth rates is
negative, admitting no immigrants today guarantees an old majority tomorrow. Even if current
young choose the maximum allowable immigration so as to maximize next period benefits, there
will still be a majority of the old tomorrow. Both current old and current young agree on letting in
the maximal amount of immigrants, and except perhaps for \ the initial period, the majority of
voters will always be old. Therefore the tax rate is set at the "Laffer " rate. Immigration does not
yet add much to the survival of the social security system in this case. But when the sum of
native-born and immigrants' birth rates is positive and the native-born birth rate is negative,
immigration adds an interesting twist. It in essence poses a threat to social security that in the
absence of migration will be assured. In this case the numbers of old and young next period are
equal and by assumption ties are decided in favor of the old. Then current young's desire for
higher immigration, to maximize their old-age benefits, is constrained by their desire to maintain
old majority next period. If the young are currently in the majority the set the current tax rate
equal zero (implying no benefits for the current old) and set immigration quota at an intermediate
level that barely makes the old majority in the next period. Next period, the old median voter sets
the tax at the "laffer" rate and the immigration quota at the maximum level. The latter guarantees
that the young will be in majority in subsequent period; and the cycle repeats itself. We propose
to extend the base-line model to include private saving and capital accumulation, giving
individuals two sources of consumption in old age (social security benefits and private savings).
We preliminarily find a similar collection of equilibrium exists. The extended model has an
additional collection of equilibria. As in Forni (2005), in the case of a positive native-born birth
rate, when the young are always in the majority, a pay-as-you-go social security system is
sustained by a tax rate as a function of the capital stock (a second state variable in addition to the
state variable in the base-line model which is the ratio of old to young). The tax rate is decreasing
in the capital stock. In the case in which the fertility rates of the native born and immigrant
populations are positive, the number of next period young voters exceeds the number of next
period old voters, which means that the decisive voter is always young. Therefore, if the capital
per native-born work force is in the critical range than the optimal strategy of the young is always
to vote for a positive tax rate and maximum migration quota, thus sustaining both migration and
the social security system. The size of the social security system depends on the capital per
native-born worker, and on the exogenously given ceiling on migration quotas. Thus the politicaleconomy sustainable migration boosts up the size of the social security's tax revenue.
12
In the extended model we examine the conventional hypothesis that the decision or median
voter opts to keep out political migrants, so as to keep her wage from falling. These many, some
conflicting, considerations concerning immigration call for a thorough theoretical investigation;
and to a challenging empirical question whether a PAYG social security system tilts the politicoeconomic equilibrium toward more liberal migration policies. A time-series analysis of the U.S.
spanning over the last two centuries, which witnessed a switch from free to restricted migration
regimes, changes in migration quotas, and the establishment and evolution of many ingredients of
the welfare state, will serve as a good test ground.
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i
We assume that
mh , ml  0 which implies that prior to their moving, the reservation income in
the source country is lower than their prospect income in the host country.
ii As our cross-section dataset does not allow drawing conclusions about dynamics, it is not our
first priority to try to introduce dynamics into our static setting.
iii This dataset was employed in Docquier and Marfouk (2006) and was kindly provided to us by
them.
iv Alternatively, due to insufficient observations, one may wish to pull together all the equations for
e=1,2,3 into a single likelihood function log L   log Le .
e
v
This pecuniary cost is essential, as it serves to render the income tax distortive, thereby putting
a limit to taxation.
16