New Estimates of Migration
Using the P-VAR Approach
Tackling the Chicken and Egg Problem of
People Versus Jobs
Dr. Frederick Treyz, CEO
Sinan Hastorun, Research Economist
what does REMI say? sm
Migration and Jobs Question
• Do People follow Jobs?
– Labor Demand Factor  Importance of Wages
and Employment Opportunity
OR
• Do Jobs follow People?
– Labor Supply Factor  Migration due to
Amenities, Creative Class, Coolness of Place
• Question tackled for the U.S., Coefficient
Estimates Obtained using State-Level Data
for 1991-2007
what does REMI say? sm
Labor Demand and
Labor Supply Effects
what does REMI say? sm
Distinguishing between
LD Effect vs. LS Effect
• If Labor Demand curve shifts right,
both w↑ and N ↑
• If Labor Supply curve shifts right,
N ↑, but w↓
• If both LD and LS curves shift right,
N↑, but w may go up or down
• Only Original and Final Equilibria are observed
in practice
• Extent of Demand vs. Supply Effects cannot be
determined
what does REMI say? sm
Model Variables
• Net Economic Migration, Relative Wage
Rate and Relative Employment determined
jointly
• ECMG, Δ RWR, Δ REO are all Endogenous
Variables in this Model
• Vector AutoRegression (VAR) technique
ideal for assessing contemporaneous
relationships among a set of possibly
endogenous variables
what does REMI say? sm
The P-VAR Approach
• VAR regresses each variable on its own
lag(s) as well as the lags of all other
variables in the system
• Panel VAR (P-VAR) allows for VAR
Regression Analysis to be conducted over
time and across cases (states), yielding
better estimates than Time-Series, singlestate analysis
what does REMI say? sm
First-order VAR Model
ztk = τ0 + τ1 zt-1k + fk + dt + εt
ztk : 3-variable vector that includes all endogenous variables
τ1 : 3x3 matrix of coefficients to be estimated
fk : vector of country-fixed effects
dt : vector of time-fixed effects
εt : white-noise error term
what does REMI say? sm
Labor Demand
RWRt+1k = RWRtk + δw (LDtk – LFtk)
Δ RWRtk = RWRt+1k - RWRtk
= δw (LDtk – LFtk) = δw Δ REOtk
Δ RWRtk = λw + δw Δ REOtk + εtkd
•
•
•
•
RWRtk: Real Relative Wage Rate in Region k at Time t
REOtk: Relative Employment Opportunity in Region k at Time t
LDtk: Labor Demand in Region k at Time t
LFtk: Labor Force in Region k at Time t
what does REMI say? sm
Labor Supply
Δ LFtk = LFt+1k - LFtk = ECMGtk + (Δ PRSRtk * Ntko)
•
•
•
•
LFtk: Labor Force in Region k at Time t
PRSR tk: Short-Term Participation Rate in Region k at Time t
ECMG tk: Net Economic Migration Rate
Ntko: Population in Region k at Time t
• In the Long-Run
what does REMI say? sm
Δ LFtk = ECMGtk
Individual’s Migration Decision
• Move to Region k if Indirect Utility of k is
Higher than Average National Utility
– if Vtk > Vtu
– Thus, Vtk / Vtu > 1
• Vtk = c (EYtk)ß
• Vtu: Average National Utility at Time t
• EYtk: Expected Income in Region k at Time t
what does REMI say? sm
Indirect Utility Function
Vtk = c (EYtk)ß
= c ( (Etk / LFtk) * (Σ Etk / E * wtk ( RYDtk /YPtk ) ) ß
= c ( REOtk * RWRtk )
ECMGtk = f( gm, RWRtk, REOtk )
•
•
•
•
•
•
Etk: Employment in Region k at Time t
EYtk: Expected Income in Region k at Time t
RYDtk: Real Disposable Income in Region k at Time t
YPtk: Personal Income in Region k at Time t
wtk: Wage Rate in Region k at Time t
gm: long-term trend in Migration
what does REMI say? sm
3- Equation Migration
Model
ECMGtk = a10 – a12 Δ RWRtk – a13 Δ REOtk + ß11
ECMGt-1k + ß12 Δ RWRt-1k + ß13 Δ REOt-1k + εECMGtk
Δ RWRtk = a20 – a21 ECMGtk – a23 Δ REOtk + ß21
ECMGt-1k + ß22 Δ RWRt-1k + ß23 Δ REOt-1k + εRWRtk
Δ REOtk = a30 – a31 ECMGtk – a32 Δ RWRtk + ß31
ECMGt-1k + ß32 Δ RWRt-1k + ß33 Δ REOt-1k + εREOtk
what does REMI say? sm
Matrix Representation
The 3-Equation VAR Model may be expressed as:
βijs: refer to the model coefficients to be
estimated
what does REMI say? sm
VAR Model with 1 Lag
ztk = τ0 + τ1 zt-1k + fk + dt + εt
ztk: the 3-variable vector including all 3 endogenous variables
Net Economic Migration, Relative Wage Rate, and Relative
Economic Opportunity
τ1: the 3x3 matrix of coefficients of contemporaneous relationships
between ECMG, RWR, and REO
what does REMI say? sm
What Does P-VAR* Do?
• Panel Vector AutoRegression Model uses GMM
(General Method of Moments)
• Regresses each endogenous variable on its own
lag(s) as well as the lags of all other variables in
the system
• GMM Estimates for the U.S. are obtained by
using Untransformed (Original) Variables as
Instruments for Helmert-Transformed Variables
(state fixed effects removed)
*PVAR Code for STATA provided by Dr. Inessa Love of the World Bank
what does REMI say? sm
P-VAR Application
• As one system:
• ECMGtk is regressed on ECMGt-1k, Δ RWRt-1k, and Δ REOt-1k
• REOtk is regressed on ECMGt-1k, Δ RWRt-1k, and Δ REOt-1k
• RWRtk is regressed on ECMGt-1k, Δ RWRt-1k, and Δ REOt-1k
• Number of Lags chosen as 1 due to data constraints
• Also, increasing the number of lags does not yield better
estimates – Results for 3 Lags are also provided
• P-VAR run on US 51-region data (50 States + D.C.) for 19912007
what does REMI say? sm
Panel-VAR in STATA
Applying Panel-VAR in STATA requires the following
initial steps prior to estimation due to Panel Data
structure:
1. Time Fixed Effects (dt) removed by “Time-Demeaning” all
3 variables in the system: Done by subtracting from each
variable their means for each year
2. State Fixed Effects (fk) removed by “Helmert
Transformation”: Done by removing the forward mean
for each variable for each state-year
3. Data set as Panel data in STATA by identifying the CrossSection variable and the Time variable
what does REMI say? sm
Lag 1 Results for Economic
Migration (Equation 1)
EQ1: dep.var
L.ECMG
L.lnRWR
L.REO
: ECMG
b_GMM
0.27195261
0.0558211
0.0692154
se_GMM
0.08797128
0.02340918
0.02656291
t_GMM
3.0913794
2.384582
2.6057164
*b refers to coefficient, se to standard error, and t to t-test value
Coefficients for lnRWR and lnREO are both statistically significant:
βECMGRWR = 0.056
βECMGREO = 0.069
βECMGt-1 = 0.272
PREVIOUS MODEL COEFFICIENT ESTIMATES:
βECMGRWR = 0.191
βECMGREO = 0.192
what does REMI say? sm
P-VAR Results with 3 Lags
EQ1: dep.var
: ECMG
b_GMM
se_GMM
t_GMM
L.ECMG
0.26023707
0.08837156
2.9448057
L.lnRWR
0.10060881
0.04270055
2.3561479
L.lnREO
0.10899934
0.05311321
2.0522079
L2.ECMG
0.1907596
0.05117131
3.7278621
L2.lnRWR
-0.06678102
0.04075271
-1.638689
L2.lnREO
-0.04515643
0.06462623
-0.698732
L3.ECMG
-0.00676037
0.0632835
-0.106827
L3.lnRWR
0.01548745
0.02025031
0.7648008
L3.lnREO
-0.05826982
0.03590435
-1.622918
what does REMI say? sm
Variance Decomposition
Analysis
• Percent of Variation in Row Variable
explained by Column Variable (10 Years, 20
Years, and 30 Years Ahead)
• Rows for lnREO provides Variance
Decomposition of Relative Employment
Growth at 10, 20, and 30 Year Intervals for
Migration Labor-Supply, Labor Demand, and
Resident Labor-Supply Shocks
what does REMI say? sm
Variance Decomposition
Detailed Results
ECMG
lnRWR
lnREO
ECMG
lnRWR
lnREO
ECMG
lnRWR
lnREO
s
10
10
10
20
20
20
30
30
30
ECMG
0.74149669
0.21093135
0.12962336
0.72265764
0.2641203
0.15522742
0.72171789
0.26584483
0.15773596
lnRWR
0.0960049
0.7824049
0.2071982
0.1227842
0.715861
0.2320302
0.1236824
0.7113596
0.2328145
lnREO
0.16249841
0.0066638
0.66317843
0.15455817
0.02001874
0.61274237
0.15459968
0.02279554
0.60944959
13% of Employment Growth is explained by Migration Labor Supply
21% of Employment Growth explained by Change in Wage Rate
66% explained by Change in Employment Opportunity
what does REMI say? sm
Impulse-Response Analysis
• Predicted Effect Over Time of Response of
One Variable to a Shock in Another
Variable, holding all others constant
• Response of Economic Migration, Relative
Wage Rate, and Relative Employment in the
51 States to a One Standard Deviation
Shock to Labor Demand, Migration Labor
Supply, and Resident Labor Supply
what does REMI say? sm
Impulse-Response Graphs
what does REMI say? sm
Impulse-Response Results:
95 % Confidence Interval Lines
Response of Employment to a Shock (3rd Row)
• Response of Employment to Migration Flows is
Negative in the 1st Period, but moves slightly
above 0 in later time periods
• Response of Employment to Wage Rate is
Negative Initially, but turns Positive, rising at an
Increasing Rate afterwards
• Response of Employment to Employment
Opportunity is Positive throughout, albeit at a
Declining Trend
what does REMI say? sm