Download 3. Simulations and Results

Modelling Migration in an OLG Framework:
the Case of UK Migration Policy
by
Katerina Lisenkova
National Institute of Economic and Social Research
Marcel Mérette
University of Ottawa
May 2013
Abstract
This paper uses an OLG CGE model for the UK to illustrate the long-term effect on migration
on the macroeconomy. As an illustration we use current UK government’s migration target
to reduce net migration “from hundreds of thousands to tens of thousands”. Achieving this
target would require to reduce recent net migration numbers by a factor of 2. In our
simulations we compare the impact of demographic shock based on the principal ONS
population projections with the lower migration scenario, which assumes that migration
rates are reduced by 50%. Our results show that such a significant reduction in net
migration has strong negative effect on the economy. Both level of GDP and GDP per capita
fall during the simulation period. Moreover this policy has significant negative impact on
public finances. As a result of growing gap between government revenues and spending,
public debt increases by 8 percentage points of GDP in case or lower migration.
(*) Financial support from the Economic and Social Research Council under the grant: “A
dynamic multiregional OLG-CGE model for the study of population ageing in the UK” is
gratefully acknowledged.
1. Introduction
International migration is a growing phenomenon – between 1990 and 2010 the stock of
international migrants has increased from 155 m to 214 m (United Nations, 2012). It has
significant economic impact on both sending and receiving countries. From the point of view
of developed economies, which usually play the role of host country, there are two
distinctive views on the impacts of increased immigration.
The first perspective is to look at immigration as one potential solution for challenges
presented by population ageing. Over the past 50 years, the proportion of the UK
population aged 65 and above has increased from 12 to 17 per cent, and by 2060 it will
reach 26 per cent1. Changes in population structure are determined by three demographic
processes: fertility, mortality and migration. While fertility and mortality generally adjust
slowly and thus have a long-term impact on demographic structure, migration can change
rapidly and produce a strong impact in the short run. It is also most dependent on policy.
That is why many countries in the developed world use migration as a policy tool to address
demographic challenges. The rationale behind this “remedy” is that migrants are usually
younger than the native population, and therefore will be able to substitute falling working
age population during the transition period.
The second perspective on the impact of immigrants on the host economy looks at the
situation through the prism of competition. The argument is that immigrant workers
compete with natives for jobs which results in higher unemployment and lower pay for
native workers. Immigrants also apply for welfare benefits and use free (or subsidised)
public services and thus have negative impact on public purse. Although there is no
evidence that expansion of migration leads to negative labour market effects of native-born
workers (Dustman et al, 2008; Lemos and Portes, 2008), this view is often popular with the
press.
In this paper we disentangle these two views to provide a quantitative assessment of the
long-term impact of migration on macroeconomy. As an experiment, we chose the
migration policy target set by the current UK government, which aims to reduce the level of
net migration from “hundreds of thousands to tens of thousands”. As Figure 1 shows net
1
2010-based principal ONS projections
migration in “hundreds of thousands” is a relatively recent phenomenon in the UK, and
traditionally it experienced negative net migration. The recent large influx of immigrants
after the accession of the Eastern-European countries to the EU (so-called A8 countries) in
2004 raised tensions within society and brought migration policy to the front pages of the
newspapers. Tightening of the migration rules, which was introduced by the current
government, has started to show results. According to the most recent estimates of net
migration, during the year ending in July of 2012 net migration was 163 thousands – the
lowest level since 2003.
Figure 1. Net migration, UK, 1964-2011
300,000
250,000
200,000
150,000
100,000
50,000
0
-50,000
2010
2008
2006
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
-100,000
Source: ONS
The principal assumption about net migration in the most recent 2010-based population
projections by ONS is that it will remain at two hundred thousand per year over the next 50
years. Thus, if current government succeeds in achieving its migration target, the net
migration has to be reduced by more than half. We attempt to model the impact of this
policy.
In a recent study, Dustman et al. (2010) estimated the fiscal impact of A8 migration in the
UK. They showed that this wave of immigrants had a positive net contribution to public
finances. This study is very useful in providing a static assessment of the past events. We
want to provide a dynamic assessment of the future changes in immigration policy. For this
we employ a dynamic overlapping generations computable general equilibrium model (OLGCGE), which is widely acknowledged as the best tool for modelling issues associated with
demographic change. The age-disaggregated structure of an OLG-CGE model makes it
possible to study age-specific behaviour and the impact of changes in age structure of the
population on the economy.
The model is in the Auerbach and Kotlikoff (1987) tradition and introduces age-specific
mortality following Borsch-Supan et al. (2006). It incorporates variation in life expectancy
with a perfect annuity market, through which unintentional bequests are implicitly
distributed. The theoretical description of this approach was first presented in Yaari (1965).
This modification allows precise replication of the population structure from the population
projections and dramatically improves the accuracy of demographic shocks.
There are several approaches to modelling migrants in an OLG-CGE framework. One
approach is to assume that immigrants are identical to natives, i.e. they have the same level
of assets, qualification and productivity. An alternative approach is to assume that
immigrants differ from natives at least on some of the dimensions. One dimension that
seems important is the level of immigrants’ assets. Intuitively, if immigrants bring assets
(debt) when they come this can have positive (negative) impact on the level of capital in the
host country. If they come without assets, they increase labour supply, while simultaneously
decreasing the level of productivity due to capital dilution.
Fehr et al. (2004) and Chojnicki et al. (2011) assume that immigrants have the same level of
assets as natives of the same age and qualification, while Storesletten (2000) assumes that
immigrants have no assets when they come. Chojnicki et al. (2011) state that the choice
with respect to this assumption should not make much difference, due to the young age of
most migrants. In this paper we follow the first approach.
This paper is organised as follows. In section 2, we give a description of the model. In section
3, we outline the calibration procedure. Section 4 describes performed simulations and
presents results for two policy alternatives. And section 5 concludes with a brief discussion.
2. The Model
The model presented in this section is designed to analyse the long-term economic and
labour market implications of demographic change in the UK. The UK is modelled as a small
open economy. The rest of the world is not explicitly modelled. It is present in the model
mainly to close the government budget constraint and the current account of the UK. Below
we describe the demographic structure of the model and outline the main features of the
production, household and government sectors. The demographic process is superimposed
on the OLG model and provides the exogenous shock or driving force behind the simulations
results.
2.1 Demographic Structure
The population is divided into 21 generations or age groups (i.e., 0-4, 5-9, 10-14, 15-19, …,
100-104). Population projections represent an exogenous shock. In other words,
demographic variables such as fertility, mortality and net-migration are assumed to be
exogenous. This is a simplifying assumption given that such variables are likely endogenous
and affected by, for example, differences in economic growth. Every cohort is described by
two indices. The first is t, which denotes time. The second is g, which denotes a specific
generation or age group.
The size of the cohort, Pop, belonging to generation g+k in period t is given by two laws of
motion:
(1)
𝑃𝑜𝑝𝑡,𝑔+𝑘 = {
𝑃𝑜𝑝𝑡−1,𝑔+𝑘+5 𝑓𝑟𝑡−1
𝑓𝑜𝑟 𝑘 = 0
𝑃𝑜𝑝𝑡−1,𝑔+𝑘−1 (𝑠𝑟𝑡−1,𝑔+𝑘−1 + 𝑚𝑟𝑡−1,𝑔+𝑘−1 ) 𝑓𝑜𝑟 𝑘 ∈ [1,20]
The first law of motion simply implies that the number of children born at time t (age group
g+k = g, i.e. age group 0-4) is equal to the size of the first adult age group (g+k+5=g+5, i.e.
age group 20-24) at time t-1 multiplied by the “fertility rate”, fr, in that period. If every
couple on average has two children, the fertility rate is approximately equal to 1 and the
size of the youngest generation g at time t is approximately equal to the size of the first
adult generation g+5, one year in the past.
The second law of motion gives the size of any age group g+k beyond the first generation, g,
as the size of this generation a year ago multiplied by the sum of age specific conditional
survival rate, sr, and net migration rate, mr, at time t-1. In this model survival and net
migration rates vary across time and age. For the final generation the age group 100-104
(k=20), the conditional survival rate is zero. This means that for the oldest age group at the
end of the period, everyone dies with certainty.
Demographic change is assumed to be exogenous. Time variable fertility and time/age
variable net migration and conditional survival rates are calibrated based on the population
projections. This allows precise modelling of demographic shock of any configuration within
the model. This feature of this model makes it ideal for studying of the impact of
demographic change.
2.2 Production Sector
A representative firm produces at time t a single good using a Cobb-Douglas technology. The
firm hires labour and rents physical capital. The production function is:
(2)

1
Yt  AKt Lt
where Y is output, K is physical capital, L is effective units of labour, A is a scaling factor
and  is the share of physical capital in value added. A firm is assumed to be perfectly
competitive and factor demands follow from profit maximization:



 1
(3)
K
ret  A t
 Lt
(4)
K
wt  (1   ) A t
 Lt




where re is the rental rate of capital and w is the wage rate.
In the model there are four types of labour, qual = 1, 2, 3 and 4. Three are defined in terms of
skill-level: “high-skilled workers” (qual=1), “medium-skilled workers” (qual=2) and “lowskilled workers” (qual=3). The fourth type of labour is “non-working individuals” (qual=4).
A firm transforms its demand for labour, L, into a demand for skills, Lqual, based on a
constant-elasticity-of-substitution (CES) function:
(5)
Lqual,t
 w
  qual  t
w
 qual,t
L

 Lt


where wqual is the wage rate for a specific type of skills,  is the share of skill level and  L is
the skill substitution elasticity. The composite wage rate, w of the firm’s aggregate labour
input is related to skill-specific market wages wqual by the following optimization expression:
(6)
1 L
wt
   qual wqual,t
1 L
qual
2.3 Household Behaviour
Household behaviour in the model is captured by 21 representative households in an AllaisSamuelson overlapping generations structure representing each of the age groups (as
described above). Individuals enter the labour market at the age of 20, retire (on average) at
age 65, and die at the latest by age 104. Younger generations (i.e. 0-4, 5-9, 10-14 and 15-19)
are fully dependent on their parents and play no active role in the model. However, they do
influence the age dependent components of public expenditure such as health and
education. An exogenous age/time-variable survival rate determines life expectancy.
Adult generations (i.e. age groups 20-24, 25-29, …, 100-104) optimise their
consumption/saving patterns. A household’s optimization problem consists of choosing a
profile of consumption over the life cycle by maximizing a CES type inter-temporal utility
function that is subject to lifetime budget constraint. Inter-temporal preferences of an
individual born at time t are given by:
k

1
20  1 
U
 km0 srt m, g m (Ct k , g k )1
 
1   k 4 1   

(7)


0<θ<1

where C denotes consumption,  is the pure rate of time preference and θ is the inverse of
the constant inter-temporal elasticity of substitution. Future consumption is also discounted
by unconditional survival rate,  k srt k ,g k , which is the probability of survival up to the age
g+k and period t+k. It is a product of the age/time-variable conditional survival rate between
periods t+k and t+k+1 and between ages g+k and g+k+1 denoted srt+k,g+k.
In is important to note that a “period” in the model corresponds to five years and a unit
increment in the index, k, represents both the next period, t+k, and, for this individual, a
shift to the next age group, g+k.
The household is not altruistic. It does not leave intentional bequests to children. However,
it leaves unintentional bequests due to uncertainty of life duration. The unintentional
bequests are distributed through a perfect annuity market, as described theoretically by
Yaari (1965). This idea was implemented in an OLG context by Boersch-Supan et al. (2006).
Given the assumption of a perfect annuity market, the household’s dynamic budget
constraint takes the following form:
(8)
HAqual,t 1, g 1 
Y
L
qual,t , g
1  
1

srt . g
L
qual,t

 
 
 Ctrt  Pensqual,t , g  TRFqual,t , g  1  1   tK Rit HAt , g  Ct , g

where Ri is the rate of return on physical assets, τK is the effective tax rate on capital, τ” is
the effective tax rate on labour, Ctr is the contribution to the public pension system, YL is
labour income and Pens is pension benefits. The intuition behind the term 1/sr is that the
assets of those who die during the period t are distributed equally between their peers.
Therefore, if the survival rate at time t in age group g is less than one, then at time t+1
everyone in their group has more assets. That is, they all receive an unintentional bequest
through the perfect annuity market.
Labour income is defined as:
L
Yqual
,t , g  wqual,t EPqual, g LS qual, g
(9)
where LSqual is the exogenous supply of a specific type of labour, where skill is proxied by
educational qualifications obtained (as discussed below) . It is assumed that qualificationspecific labour income is a function of the individual’s age-specific productivity. In turn, it is
assumed that these age-specific productivity differences are captured in qualification-specific
age-earnings profiles. These profiles, EPqual,g,
are quadratic functions of age:
EPqual, g   qual  (qual ) g  ( qual ) g 2 , γ, λ, ψ ≥ 0
(10)
with parametric values estimated from micro-data (as discussed below). Retirees’ pension
benefits are assumed to be the same across all generations and qualification groups and stay
constant in real terms.
Differentiating the household utility function with respect to its lifetime budget constraint
yields the following first-order condition for consumption, commonly known as Euler’s
equation:
(11)
Cqual,t 1, g 1
 

 1  1   tK1 Rit 1

 (1   qual )


1

Cqual,t , g
It is important to note that survival probabilities are present in both the utility function and
the budget constraint. Therefore, they cancel each other out and are not present in the Euler’s
equation.
2.3 Investment and Asset Returns
Migrants in any period are assumed to own the same level of assets the domestic
population of the same age and the same skill-level. This implies that when net-migration is
positive, migrants’ assets add to the stock of capital. Therefore the motion law of capital
stock, Kstock, takes into account depreciation and assets of newly arrived migrants:
(12)
Kstockt 1  Invt  (1   ) Kstockt  qual g HAqual,t 1, g 1 NM qual,t 1, g 1
where Inv represents investment, δ is the depreciation rate of capital, HA is the level of
household assets and NM is the level of net-migration.
Financial markets are fully integrated implying that financial capital is undifferentiated so
that interest rate parity holds. Let Ri be the rate of return on physical assets. It can be
defined as the rental rate minus the depreciation rate:
1  Ri t  ret  (1   )
(13)
2.4 Government Sector
The Government can run a fiscal deficit, Def, and has to service public debt, Debt.
Consequently its budget constraint is defined as:

(14)

 Ctrt wqual,t EPqual, g LS qual, g    tC Pt C, g Ct , g   Def t
g
iqual

 Govt   Popt , g TRFt , g  Penst , g   Ri t Debt t ,
 Pop   
t,g
L
qual,t



g
where C is the effective tax rate on consumption and Gov is public consumption. The lefthand side of this equation shows tax revenues from different sources and government
borrowing. The right hand side of the equation refers to government expenditures, transfers
to households and servicing of the public debt. Note that the representative household of
generation g at time t represents a specific cohort of size, Popt , g . The size of each cohort
must be taken into account when computing total tax revenues and transfers to households
in a specific period of time. Note that the pension program is a part of the overall
government budget.
Public debt is accumulated according to the following rule:
(15)
Debtt+1 = Debtt + Deft
Public expenditures per capita, GEPC, are assumed to be fixed per-person and hence total
expenditure, Gov, depends only on the size of the total population, TPop.
(18)
𝐺𝑜𝑣𝑡 = 𝑇𝑃𝑜𝑝𝑡 𝐺𝐸𝑃𝐶
2.5 Market and Aggregation Conditions
The model assumes that all markets are perfectly competitive. The equilibrium condition for
the goods market is that UK’s output, together with return on foreign assets, FA, and
borrowing from the rest of the world, Def, must be equal to total demand originating from
consumption, investment and government spending:
(19)
Yt  Ri t FAt  Def t   Popt , g Ct , g  Invt  Govt
g
The demand for labour of a specific skill-level is equal to the supply of this skill:
(20)
Lqual,t   Popt , g LS qual, g EPqual, g
g
and the stock of capital accumulated in period t is equal to the demand expressed by a firm:
(21)
Kstockt  K t
The capital market is assumed to be in equilibrium. The total stock of private wealth, HA,
accumulated at the end of period t must be equal to the value of the total stock of capital
and foreign assets at the end of period t:
(22)
 Pop
t,g
HAt , g Kstockt  FAt
g
Note that the current account can be derived from this model as the difference between
national savings and domestic investment:
(23)

 

CAt    Popt 1, g 1 HAt 1, g 1   Popt , g 1 HAt , g 1    Kstockt 1  Kstockt 


g
g

 
Private Savings
Domestic Investment
Alternatively, the current account is either given as the trade balance plus the interest
revenues from net foreign asset holdings, or as the difference between nominal GNP (i.e.
GDP including interest revenues on net foreign assets) and domestic absorption.
3. Calibration
The aggregate side of the model is calibrated using 2010 data for the UK. The data for
demographic shock is taken from the “official” population projections carried out by the
Office of National Statistics (discussed further below). Population projections are used for
calibration of fertility, survival and migration rates used in the model.
Data on public finances and GDP are taken from ONS and HM Treasury. Effective wage
income and consumption tax rates are calculated from the corresponding government
revenue categories and calibrated tax base i.e. total employment income and aggregate
consumption. The total amount of pensions is taken from the Government Actuarial
Department (GAD); other transfers from Department for Work and Pensions. Based on this
information the effective pension contribution rate and the average size of pension benefits
are calculated. For effective pension contribution rate calculation it is assumed that the
same contribution rate is paid on all wage income. For average size of pension benefits the
total amount of pension benefits is divided by the total number of people of pension age.
For simplicity it is assumed that both males and females start receiving pension benefits at
age 65.
The source of the labour market data is the Quarterly Labour Force Survey (QLFS). To avoid
single observation biases data for three quarters is used (i.e. Q1:2008, Q1:2009 and
Q1:2010). From these pooled data, parameters of the age-specific productivity (earnings)
profiles by qualification are estimated. These data are also used to calculate age-specific
labour force participation rates and the distribution of the labour force by qualification. For
age-specific productivity profiles, Mincer age-earnings regressions are estimated (Mincer,
1958).
Capital share of the output (α) is set to 0.3. The (5-year) intertemporal elasticity of
substitution (1/γ) is set to 1.25 and (5-year) and interest rate at 0.04 (2% a year).
The calibration procedure contains four steps. In the first step, available labour market data
on the distribution of workers’ skill is used to calibrate the composition of the population
accordingly. This first step ensures that labour demand equals labour supply for each skill.
The second step consists of using the information on output, capital and labour demands
and the first-order conditions of the firm problem to calibrate the scaling parameter for the
productivity function, plus wage and rental rates.
The third step is the most challenging involving equations pertaining to the household’s
optimisation problem, the equilibrium conditions in the assets and goods markets to
calibrate the rate of time preference and government expenditures on sectors other than
health and education (Gov). In other words, the (5-year) rate of time preference is solved
endogenously in the calibration procedure in order to generate realistic consumption
profiles and capital ownership profiles per age group, for which no data are easily available.
Capital ownership profiles must also satisfy the equilibrium condition on the asset market.
Public expenditures on other sectors (Gov) is endogenously determined to close the budget
constraint of the government and ensures the equilibrium on the goods market. Note that
the rate of time preference and the intertemporal elasticity of substitution together
determine the slope of the consumption profiles across age groups in the calibration of the
model (when the population is assumed to be stable). This is also the slope of the
consumption profile of an individual across his lifetime in the simulated model in the
absence of demographic shocks or economic growth.
The fourth and final step uses the calibration results of the first three steps to verify the
model is able to replicate the observed data corresponding to the initial equilibrium. Only
when the initial equilibrium is perfectly replicated with the calibration solution can the
model be used to evaluate the consequences of demographic shocks associated with
population ageing.
3. Simulations and Results
The population projections act as an exogenous demographic shock to the model. For the
baseline scenario we use the 2010-based principal population projections for the UK. Figure
2 illustrates this projection by showing changes in different age groups over the next 50
years. The fastest growing age group is 65+. By the end of projection period it increases by
over 100%. The number of children (0-19) and working age adults (20-64) also increases but
much slower – by 19% and 16% respectively. Total population increases by 31 %.
Figure 2. Projected Change in Scottish Population by Age Groups, 2010-2060
120%
0-19
100%
20-64
65+
Total
80%
60%
40%
20%
0%
2010
2015
2020
2025
2030
2035
2041
2046
2051
2056
2060
Source: 2010-based principal ONS population projection
To illustrate the effect of immigration on macroeconomy we use a thought experiment that
reflects the current government’s migration policy target – to reduce net migration “from
hundreds of thousands to tens of thousands”. As was noted before, the principal scenario of
the ONS population projections assumes long-term net migration of 200 thousand per year.
This means that net migration has to decrease by a factor greater than 2 to achieve the
stated target. For simplicity, for the lower migration scenario we just reduce migration rates
by a factor of two, i.e. we assume that migration in every age group reduces by the same
proportion. This simplifying assumption allows a quick illustration of the effects of this
migration policy. The results presented in the following figures show the percentage
difference of the lower migration scenario relative to the baseline scenario.
Figure 3 shows the difference in factors of production and the levels of output between two
scenarios. Reduction in labour supply is exogenous and driven by population projections. In
the scenario with the lower level of migration by 2060, the productivity adjusted level of
labour supply (taking into account age-productivity profiles and qualifications) is 12% lower
than in the baseline scenario. The same is true regarding the level of output and capital.
Output per person reduces much less as higher net migration leads to a general increase in
population. Nevertheless output per person is almost 3% lower in the lower migration
scenario.
Figure 3. Output and factors of production
0%
2010
2015
2020
2025
2030
2035
2040
2045
2050
2055
2060
-2%
-4%
-6%
-8%
-10%
-12%
-14%
Output
Labour
Capital
Output per person
Source: simulation results
We make an assumption that government spending per capita stays fixed. This means that
government spending on one immigrant is the same as on one native born person.
According to many researchers, this assumption makes our results weaker, as immigrants
have been shown to claim fewer benefits, use less health services and participate less in
other social programs (Dustman et al, 2010). In addition most of them come as young adults
and require no spending on school education, and many of them pay for their further and
higher education in the UK. Our simulations disregard all of this and thus overestimate the
reduction in government spending in the lower migration scenario relative to the baseline.
Nonetheless, as Figure 4 shows, government revenues decline faster than government
spending in the case of reduced net migration.
Figure 4. Government spending and revenues
2%
0%
2010
2015
2020
2025
2030
2035
2040
2045
2050
2055
2060
-2%
-4%
-6%
-8%
-10%
Government spending
Governemnt revenues
-12%
Source: simulation results
The difference between the response of government revenues and spending to a reduction
in the level of net migration results in widening of government budget deficit, presented in
Figure 5. Unlike previous figures, it shows the simple difference in government deficit and
public debt expressed as a share of GDP between the two scenarios. By the end of the
simulation period, deficit is 1.5 percentage points of GDP higher in the scenario with lower
migration. This leads to public debt which is almost 8 percentage points of GDP higher.
Figure 5. Government budget deficit and public debt as a share of GDP
8%
7%
Government budget deficit
Public Debt
6%
5%
4%
3%
2%
1%
0%
2010
2015
2020
2025
2030
2035
2040
2045
2050
2055
2060
-1%
Source: simulation results
Conclusions
In this paper we use an OLG CGE model for the UK to illustrate the long-term effect on
migration on the macroeconomy. As an illustration we use current UK government’s
migration target to reduce net migration “from hundreds of thousands to tens of
thousands”. Achieving this target would require to reduce recent net migration numbers by
a factor of 2. In our simulations we compare the impact of demographic shock based on the
principal ONS population projections with the lower migration scenario, which assumes that
migration rates are reduced by 50%.
Our results show that such a significant reduction in net migration has strong negative effect
on the economy. Both level of GDP and GDP per capita fall during the simulation period.
Moreover this policy has significant negative impact on public finances. As a result of
growing gap between government revenues and spending, public debt increases by 8
percentage points of GDP in case or lower migration.
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