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Modeling migration flows: Modeling migration flows: explanations and policy implications explanations and policy implications
(the case of Luxembourg)(the case of Luxembourg)
CMTEA 2008The future of Europe in a world of uncertainties
Romania, Iaşi, September 25-27, 2008
Paris
Luxembourg in Europe
The context (1)
• Migration– migration = change of place of residence and workplace
( residential move)– functional labour market areas (flma) administrative
areas– crossing borders: internal vs international
• Cross-border commuting– travel daily or weekly from residence to workplace, not
necessarily, but generally within flma• Luxembourg: commuters cross-border workers (CBW)
The context (2)• Importance of migrations and commuting for
Luxembourg– average population growth: 0.9%
• net migration flows explain 60% of demographic growth
• today, 40% of the 0.5 million inhabitants are foreigners
– average employment growth: 2.6%• commuters take 2/3 of net newly created jobs and make up
40% of total employment
• As a result, 60% of employed workers are foreigners
• Another illustration: pop. aged 15-64: 322 000
total employment: 319 000
The context (3)• This research takes place in the context of the
overall modelling of the Luxembourg economy– estimated standard macro-model– endogenize labour supply through modelling of
migrations and commuters
• Stylized facts– net earnings and unemployment differentials with
neighbouring countries • net earnings are higher, about 40%
• unemployment is lower, some 5 percentage points
– housing prices are higher in (and around) Lux. (>100%)• other living costs (food, cothing) are less different
• Why this research might be interesting (for others)?– not so many time series studies in the migration context (factors
influencing migrations)
– few time series studies that apply cointegration testing and error correction techniques
– not many studies that compare factors affecting simultaneously migrations and commuting
– this work could easily be extended to other regions/countries, experiencing high in/out-flows of labour
• NB it is ongoing work, paper not finalised…
The context (4)
Literature review (1)
• Causes of migration– gravity models– human capital – income / leisure– job search + matching– equilibrium / disequilibrium
• Consequences of migration– wages– productivity– demographic trends
Literature review (2)• Gravity models
– based on the Newtonian law of gravitation – not derived from theoretical modelling of economic
behaviour– but widely used, with good results, can be estimated
• Mij = G * Pi0 * Pj
1 * Dij 2
– Mij = migration from i to j
– G = constant term
– Pi = population of origin («weight»)
– Pj = population in destination area
– Dij = distance between both destinations
Literature review (3)
• Modified gravity models– include variables linked to economic behaviour– no formal derivation but taken from other theories
• Mij = G * Pi0 * Pj
1 * Dij 2 * Xi
3 * Xj 4
– Xi, Xj = economic and other variables related to regions i and j
– Job opportunities, earnings, unemployment, housing prices, risk, geographic characteristics (amenities), political situation, etc...
The model (1)
• Data 1980-2006, yearly
• Test / impose restrictions on model coefficients– taking ratios of independent variables: (Xi/ Xj)
reduction of the number of parameters to be estimated
• Other simplifications– drop Pi (foreign population) and Dij (distance)
• foreign population varies much less
• two “countries”: Luxembourg and “the rest of the world” (ROW, to be defined) aggregate flows
The model (2)• ln(Mk/P) = 0
k + 1k * ln(L/P) + 2
k * ln(Yj/Yi) + 3k *
ln(Uj/Ui) + 4k * ln(HPj/HPi) + k
– j = Lux; i = ROW– k = in, out, com:
• in: in-migration (flow)
• out: out-migration (flow)
• com: commuters (stock)
• L = tot. labour demand in Lux.: 1in, com > 0; 1
out = 0
• Y = relative earnings: 2in, com >0; 2
out<0
• U = rel. unempl. rates: 3in, com < 0; 3
out > 0
• HP = rel. house prices: 4in < 0; 4
out, com > 0
The model (3)• Some precisions on the variables
– Migrations (Min, out, com):• in, out = total (gross) flow
• com(muters) = stock of foreign workers travelling daily or weekly from B, F, D to L
– Labour demand (L) = total domestic employment in Lux.– Per capita earnings (Y):
• B, F, D (country wise); source = OECD (“Taxing wages”) after taxes and social transfers
– Unemployment rate (U):• neighbouring regions (from B, F, D), Nuts3; source =Eurostat
– House prices (HP):• neighbouring regions (from B, F, D), different sources
Estimation results (1)
• Order of integration– all variables (ratios) entering the equations are I(1)
• Estimation of level equations (1st step of Engle-Granger two step procedure)– OLS, stationarity of residuals cointegration?– Results fail to confirm cointegrating relationship
(McKinnon critical values) but residuals “optically” stationary…
-0. 25
-0. 20
-0. 15
-0. 10
-0. 05
0. 00
0. 05
0. 10
0. 15
RES_MI GRI N_OLS
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
RES_MIGRIN_OLS2
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
RES_MIGROUT _OLS
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
RES_FRIN_OLS
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
RES_FRIN_OLS2
Estimation results (2)• Error correction models
– Dynamic ECM only works for CBW: cointegration clearly confirmed by t-test on error-correction parameter (Banerjee 1998)
– Others: retain static LR parameters ↔ Engle-Granger two-step (or Zivot 2000)
• Endogeneity bias:– to what extent the immigration rate does it cause (some
of) the independent variables (for example house prices)? to be studied
– other non-tackled issues: small sample bias, outliers…
Estimation results (3)Table: Migration equations (elasticities*)
Dependent var.1 Lagg
ed d
ep.
Lagg
ed im
mig
ratio
n
Em
ploy
men
t
Rel
. rev
enue
s3
Une
mp.
rat
io4
Rel
. hou
se p
rices
5
Em
ploy
men
t
Rel
. rev
enue
s
Une
mp.
rat
io
Rel
. hou
se p
rices
Dum
mie
s (n
umbe
r)
Val
ue
Stu
dent
F-s
tat.
(join
t sig
nific
ance
)
LM te
st s
tat.
In-migration 0.35 n.a. 0.64 0.27 -0.09 n.s. 1.00 0.66 -0.25 n.s. 0 -0.45 -2.95 0.23 0.06 0.45 0.34Out-migration n.s. 0.34 n.a. n.s. 0.06 0.07 n.a. n.s. 0.05 0.12 2 -0.25 -1.60 0.45 0.06 0.51 0.35
Cross-border workers6 n.s. n.a. 1.17*** 0.19* -0.09*** 0.06 1.00 1.75 -1.33*** 1.67*** 0 -0.12 -6.39 0.93 0.01 0.32 0.16
* All variables in log-form
3 Revenues Lux. / Rev. abroad4 Unemployment Lux. / Ue abroad5 House prices Lux. / H. p. abroad
7 n.a. = not applicable
Long run
2 Coefs on indep. variables are elasticities; *=10% significance level; **=5%; ***=1%; No * ==> not significant (n.s.) at the 10% level (short run) except for the first two equations where the long-run part is calibrated.
6 Contrary to the other equations, the cross-border equation is estimated in one step (dynamic ECM), hence significance levels on variables in the long run part (no * ==> not significant)
1 All migration variables are expressed as migration rates , i.e. migration flow divided by total population; the stock of cross.border workers is divided by total employment
Independent variables5
Error correction
term
Short run (variables in first difference)
Test statistics
Aju
sted
R-s
quar
ed
S.E
. re
gres
sion
Serial correlation of residuals (p
values)
Estimation results (4)
Final long-run specifications:
log(Min) = log(L) + 0.66*log(Yj/Yi) – 0.25*log(Uj/Ui)
log(Mout) = log(P) + 0.05*log(Uj/Ui) + 0.12*log(HPj/HPi)
log(Mcom) = log(L) + 1.75*log(Yj/Yi) – 1.33*log(Uj/Ui)
+1.67*log(HPj/HPi)
Simulations (1)• Set up a model linking the labour market with
population dynamics:– 3 migration equations– population dynamics (linked to migrations)– unemployment
• 2 simultanous feedback variables: population + unemployment
• But: partial model– no feedback from unemployment to prices/wages– total domestic employment (L) = exogenous
Simulations (2)
Rel. Disp. income
Rel. House prices
Rel. unempl. rate
Commuters
Net MigrationsTotal
populationNatural
movement
Labour force(act. pop.)
Labour demand /
Total empl.
Resident employment
Resident unempl.
Exogenous var.
Endogenous var., (behavioural)
Definition var.
Simulations (3)
• Integrate the “new” migration equations into a complete macro-model:– wage equation (WS-PS), depending i.a. on UE– wage-price spiral– price-competitiveness– employment is endogenous– capacity constraints– etc…
• Simulate the same shocks in both set-ups (partial and complete)
Simulations (4)
• Simulations: generate shocks to main RHS variables:– domestic labour demand and unemployment– foreign unemployment, house prices and labour
earnings
• Rationality of the shocks:– test impact of national policies acting on the labour
market: higher employment, lower unemployment– reproduce stylized facts: higher unemployment in
bordering regions, lower net wages and house prices
Simulations (5)
• 10% increase in labour demand (in Lux.)– increases resident employment and commuters (CBW)
• impact on CBW stronger (except for the two first years in partial model) for a transition period, but, in the LR, convergence towards increase of 10%
– part in newly created jobs: 2/3 commuters; 1/3 resident– resident unemployment only decreases initially
• decrease in resident unemployment attracts new foreign workers unsustainable
– Full model: multiplier effects impact on total employment > 10% decrease in resident UE a little stronger
Complete modelPartial model
-10
-5
0
5
10
15
20
25
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
In-migration
CBW
Out-migration
-10
-5
0
5
10
15
20
25
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
In-migration
CBW
Out-migration
-3.5
-2.5
-1.5
-0.5
0.5
1.5
2.5
3.5
4.5
2007
2010
2013
2016
2019
2022
2025
2028
Unemployment rate (%points)
Migration rate (% oftot. pop.)
Activity rate
-3.5
-2.5
-1.5
-0.5
0.5
1.5
2.5
3.5
4.5
2007
2010
2013
2016
2019
2022
2025
2028
Unemployment rate (%points)
Migration rate (% oftot. pop.)
Activity rate
Complete modelPartial model
0
5
10
15
20
25
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
Cross-borderemployment (CBW)
Total employment
Resident employment
0
5
10
15
20
25
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
Cross-borderemployment (CBW)
Total employment
Resident employment
20
30
40
50
60
70
80
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
% of new jobs takenby res. employment
% of new jobs takenby CBW
20
30
40
50
60
70
80
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
% of new jobs takenby res. employment
% of new jobs takenby CBW
Complete model
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
2007
2010
2015
2020
2030
GDP (vol.)
National demand (vol.)
Exports (vol.)
GDP deflator
-2
0
2
4
6
8
10
12
14
16
18
2007
2010
2015
2020
2030
Oth
er e
xpo
rts
Exports of goods (vol.)
Exports of services(vol.)
Consumption of non-residents (vol.)
Simulations (6)
• 1 ppt decrease in domestic unemployment (UE)– the initial decrease in domestic UE increases foreign
labour supply…– …which pushes up UE in L
• there is a 1:1 substitution between resident workers and CBW
– as a result, the decrease in UE is almost completely reversed
• only in the complete model is there a sligthly bigger decrease in resident UE, because migrations increase less…
• …due to lower net wages (overall negative demand shock)
Complete modelPartial model
-0.75
-0.50
-0.25
0.00
0.25
0.5020
07
2010
2013
2016
2019
2022
2025
2028
Unemployment rate (%points)
Activity rate (% of tot.pop.)
-0.75
-0.50
-0.25
0.00
0.25
0.50
2007
2010
2013
2016
2019
2022
2025
2028
Unemployment rate (%points)
Activity rate (% of tot.pop.)
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
In-migration
CBW
Out-migration
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
In-migration
CBW
Out-migration
Complete modelPartial model
§
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
Cross-borderemployment (CBW)
Resident employment
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
Cross-borderemployment (CBW)
Total employment
Resident employment
-1.0
-0.5
0.0
0.5
1.0
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
GDP (vol.)
National demand (vol.)
GDP deflator
Simulations (7)
• Modifiy (foreign, exogenous) variables that act on foreign labour supply:– unemployment – earnings– house prices
• Modifiy these variables in a way to emphasize stylized facts:– higher UE, lower earnings and lower house prices in the
neighbouring regions
Simulations (8)
• Results:– in all cases, increased foreign labour supply depresses
resident employment and increases res. UE– the initial negative impact on GDP reverses after some
periods, due to the favorable evolution of price competitiveness (fall in domestic prices)
– in case of a fall in foreign house prices, the negative demand shock lasts longer (although the amplitude of the results of the shocks on the national variables can generally not be compared)
Impact on in-migration
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
Increase in foreign UE,partial
Increase in foreign UE,complete
Decrease in foreign netw ages, partial
Decrease in foreign netw ages, complete
Decrease in foreign houseprices, partial
Decrease in foreign houseprices, complete
Impact on cross-border employment
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
Increase in foreign UE,partial
Increase in foreign UE,complete
Decrease in foreign netw ages, partial
Decrease in foreign netw ages, complete
Decrease in foreign houseprices, partial
Decrease in foreign houseprices, complete
Impact on resident employment
-9.0
-8.0
-7.0
-6.0
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
Increase in foreign UE,partial
Increase in foreign UE,complete
Decrease in foreign netw ages, partial
Decrease in foreign netw ages, complete
Decrease in foreign houseprices, partial
Decrease in foreign houseprices, complete
Impact on resident UE
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
Increase in foreign UE,partial
Increase in foreign UE,complete
Decrease in foreign netw ages, partial
Decrease in foreign netw ages, complete
Decrease in foreign houseprices, partial
Decrease in foreign houseprices, complete
Impact on GDP (vol.), complete model
-0.5
0.0
0.5
1.0
1.5
2.0
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
Increase in foreign UE (+1% point)
Decrease in foreign netw ages (-5%)
Decrease in foreign houseprices (-10%)
Impact on total employment, complete model
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
Increase in foreign UE (+1% point)
Decrease in foreign netw ages (-5%)
Decrease in foreign houseprices (-10%)
Impact on GPD deflator, complete model
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
Increase in foreign UE (+1% point)
Decrease in foreign netw ages (-5%)
Decrease in foreign houseprices (-10%)
Impact on national demand, complete model
-1.5
-1.0
-0.5
0.0
0.5
1.0
2007
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
Increase in foreign UE (+1% point)
Decrease in foreign netw ages (-5%)
Decrease in foreign houseprices (-10%)
Conclusions (1)
• Econometric evidence confirms the importance of earnings, unemployment and house prices for explaining cross-border worker’s (commuters) movements
• Estimations of migration equations are less robust (econometrically), but the obtained coefficients are sensible
Conclusions (2)
• A positive demand shock on the national economy, having an impact on employment and/or unemployment, increases foreign labour supply, possibly as much as to reverse, partially or totally, the positive initial impact of the favourable shock
• Increased foreign labour supply, due to unfavourable exogenous causes (negative shocks on foreign economies), is generally positive for the domestic economy, after some lags, with the exception of unemployment, that increases
Thank you very much for your Thank you very much for your attentionattention
Questions?Questions?
