What does REMI say? sm New Estimates of Migration Using the P-VAR Approach Tackling the Chicken and...

what does REMI say? sm

New Estimates of Migration Using the P-VAR Approach

Tackling the Chicken and Egg Problem of People Versus Jobs

Dr. Frederick Treyz, CEOSinan Hastorun, Research Economist


Migration and Jobs Question

• Do People follow Jobs? – Labor Demand Factor Importance of Wages

and Employment OpportunityOR

• 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


Labor Demand and Labor Supply Effects


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


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


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, single-state analysis


First-order VAR Model

ztk = τ0 + τ1 zt-1

k + fk + dt + εt

ztk : 3-variable vector that includes all endogenous variables

τ1 : 3x3 matrix of coefficients to be estimatedfk : vector of country-fixed effectsdt : vector of time-fixed effectsεt : white-noise error term


Labor Demand

RWRt+1k = RWRt

k + δw (LDtk – LFt

k)

Δ RWRtk = RWRt+1

k - RWRtk

= δw (LDtk – LFt

k) = δw Δ REOtk

Δ RWRtk = λw + δw Δ REOt

k + 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


Labor Supply

Δ LFtk = LFt+1

k - LFtk = ECMGt

k + (Δ PRSRtk * Nt

ko)

• 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 Δ LFtk = ECMGt

k


Individual’s Migration Decision

• Move to Region k if Indirect Utility of k is Higher than Average National Utility– if Vt

k > Vtu

– Thus, Vtk / Vt

u > 1

• Vtk = c (EYt

k)ß

• Vtu: Average National Utility at Time t

• EYtk: Expected Income in Region k at Time t


Indirect Utility FunctionVt

k = c (EYtk)ß

= c ( (Etk / LFt

k) * (Σ Etk / E * wt

k ( RYDtk /YPt

k ) ) ß

= c ( REOtk * RWRt

k )

ECMGtk = f( gm, RWRt

k, 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


3- Equation Migration Model

ECMGtk = a10 – a12 Δ RWRt

k – a13 Δ REOtk + ß11

ECMGt-1k + ß12 Δ RWRt-1

k + ß13 Δ REOt-1k + εECMGt

k

Δ RWRtk = a20 – a21 ECMGt

k – a23 Δ REOtk + ß21


k + ß23 Δ REOt-1k + εRWRt

k

Δ REOtk = a30 – a31 ECMGt

k – a32 Δ RWRtk + ß31


k + ß33 Δ REOt-1k + εREOt

k


Matrix Representation

The 3-Equation VAR Model may be expressed as:

βijs: refer to the model coefficients to be estimated


VAR Model with 1 Lag

ztk = τ0 + τ1 zt-1

k + 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 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


P-VAR Application

• As one system:• ECMGt

k is regressed on ECMGt-1k, Δ RWRt-1

k, and Δ REOt-1k

• REOtk is regressed on ECMGt-1

k, Δ RWRt-1k, and Δ REOt-1

k

• RWRtk is regressed on ECMGt-1

k, Δ RWRt-1k, and Δ REOt-1

k

• 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

1991-2007


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 Cross-Section variable and the Time variable


Lag 1 Results for Economic Migration (Equation 1)

*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

EQ1: dep.var : ECMGb_GMM se_GMM t_GMM

L.ECMG 0.27195261 0.08797128 3.0913794L.lnRWR 0.0558211 0.02340918 2.384582L.REO 0.0692154 0.02656291 2.6057164


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


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


Variance Decomposition Detailed Results

s ECMG lnRWR lnREOECMG 10 0.74149669 0.0960049 0.16249841lnRWR 10 0.21093135 0.7824049 0.0066638lnREO 10 0.12962336 0.2071982 0.66317843ECMG 20 0.72265764 0.1227842 0.15455817lnRWR 20 0.2641203 0.715861 0.02001874lnREO 20 0.15522742 0.2320302 0.61274237ECMG 30 0.72171789 0.1236824 0.15459968lnRWR 30 0.26584483 0.7113596 0.02279554lnREO 30 0.15773596 0.2328145 0.60944959

13% of Employment Growth is explained by Migration Labor Supply21% of Employment Growth explained by Change in Wage Rate66% explained by Change in Employment Opportunity


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


Impulse-Response Graphs


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 New Estimates of Migration Using the P-VAR Approach Tackling the Chicken and...

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