4 4 slides dynamical models for migration projections

8/12/2019 4 4 Slides Dynamical Models for Migration Projections

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Dynamical models

for migration projections

Violeta Calian

Statistics Iceland

Joint Eurostat UNECE Work Session on Demographic Projections

Rome,October 29-31, 2013

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Introduction

Goal

migration forecast during unstable economical condi-

tions

Statistical problem

modelling with auto-correlated and non-stationary time

series

uncertainty control

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Our solution

dynamical models =

auto-regressive distributed lag (ARDL

) models, where:

the dependent variable at time t is modelled as a func-

tion of its own values at different time lags and of the

values of several simultaneous or lagged predictor vari-

ables.

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Main points

1. why do we use dynamical models

2. what are the mathematical conditions for a reliablestatistical inference and whether they are fulfilled

by our data and models

3. how are our models for all migration componentsbuilt and how do they perform

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Data

the number of Icelandic immigrants/emigrants, men

the number of Icelandic immigrants/emigrants, women

the number of immigrants/emigrants, women of

foreign citizenship

the number of foreign immigrants/emigrants, men

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Data

the unemployment rate

a measure of GDP

the number of graduating students, men and womenrespectively

a dummy variable coupled to the Icelandic economic

boom

a dummy variable which mirrors the re-sizing of the

EEA

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Data analysis

Statistical tests for all time series:

stationarity: augumented Dickey-Fuller and Kwiatkowski-

Philips-Schmidt-Shin (KPSS)

auto-correlation of first and higher order, by using

Durbin-Watson and Breusch-Gofrey tests

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unemployment rate

Time

x

4

1970 1980 1990 2000 2010

0

4

8

change in unemployment rate

Time

diff(x4)

1980 1990 2000 2010

0

4

GDP

Time

x

8

1970 1980 1990 2000 2010

40

1

00

change in GDP

Time

diff

(x8)

1980 1990 2000 2010

5

5

number of graduate students, women

Time

x

6

1970 1980 1990 2000 2010

500

2000

change in number of graduate students, women

Time

diff(x6)

1980 1990 2000 2010

100

150

number of graduate students, men

x5

1970 1980 1990 2000 2010

400

1200

change in number of graduate students, men

diff(x5)

1980 1990 2000 2010

100

100

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change in number of Icelandic immigrant men

Time

diff(y1)

1980 1990 2000 2010

400

0

2

00

change in number of Icelandic emmigrant men

Time

diff(y2)

1980 1990 2000 2010

400

0

400

800

change in number of Icelandic immigrant women

Time

diff(y3)

1980 1990 2000 2010

300

0

200

change in number of Icelandic emmigrant women

Time

diff(y4)

1980 1990 2000 2010

200

200

600

change in number of foreign immigrant women

Time

diff(y7)

1980 1990 2000 2010

1000

0

1000

change in number of foreign emmigrant women

Time

diff(y8)

1980 1990 2000 2010

400

0

400

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Conditions for valid inference

consistent model selection for the structure and the

order of the model

independent and identically distributed residuals

non-biased and consistent point estimates

correct and optimal calculation of confidence/prediction

intervals

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ARDL Models

y(t)

n=;i=0 y(t i) +

pi=1 y(t i)

+ mk;j=0

xk(tj)

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y1(t) y1(t 1) + x4(t) + x4(t 1) + y2(t 1)

y2(t) y2(t 1) + y2(t 2) + x5(t 2)

y3(t) y3(t 1) + x4(t) + x8(t) + x4(t 1) + x8(t 1)

y4(t) y4(t 1) + y4(t 2) + x6(t 2)

y7(t) y7(t 1) +boom(t) +eea(t) + x4(t) + x8(t) +

x4(t 1) + x8(t 1)

y8(t) y8(t 1) +y7(t) +y7(t 1) +x4(t) +x8(t) +

x4(t 1) + x8(t 1)

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Interpretation

The interpretation and model diagnostics when using

ARDL is very different from the classical so-called static

models (see collinearity, short and long term effects)

One way to apply the classical notions is to transforma dynamical model into the equivalent error correction

model (ECM):

y(t)

y(t) +k

xk(t)

+

y(t 1)

y(t 1) +

kxk(t 1)

+ ...

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Behaviour of residuals and model fit

Stationarity of residuals:

KPSS tests do not reject the hypothesis of sta-

tionarity (all p-values 0.1)

augumented Dickey-Fuller tests reject non-stationarity

(all p-values 0.01)

Normality of residuals: Jacques-Bera tests do notreject normality of model residuals - distributions.

( all p values 0.1). Histograms.

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Behaviour of residuals and model fit

Autocorrelation of residuals:

Box-Ljung tests do not reject the hypothesis of

random residuals

direct calculation of autocorrelation for residuals

(see Figure A1)

Goodness of fit: rainbow tests

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0 5 10 15

0.2

0.2

0

.6

1.0

Lag

ACF

residuals of model 1

0 5 10 15

0.2

0.2

0

.6

1.0

Lag

ACF


0 5 10 15

0.2

0.2

0.6

1.0

Lag

ACF


0 5 10 15

0.2

0.2

0.6

1.0

Lag

ACF


0 5 10 15

0.2

0.2

0.6

1.0

Lag

ACF


0 5 10 15

0.2

0.2

0.6

1.0

Lag

ACF


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1980 1990 2000 2010

500

1000

1500

time

y1

1980 1990 2000 2010

500

1500

2500

time

y2

1980 1990 2000 2010

500

1000

1500

time

y3

1980 1990 2000 2010

500

15

00

2500

time

y4

1980 1990 2000 2010

0

1000

2

000

3000

time

y7

1980 1990 2000 2010

0

500

1000

2000

time

y8

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2013 2014 2015 2016 2017

1000

2000

time

y1

2013 2014 2015 2016 2017

1000

2000

3

000

time

y2

2013 2014 2015 2016 2017

1200

1600

2000

time

y3

2013 2014 2015 2016 2017

1500

2500

time

y4

2013 2014 2015 2016 2017

500

1500

2500

time

y7

2013 2014 2015 2016 2017

200

600

1000

1400

time

y8

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2013 2014 2015 2016 2017

1000

0

100

0

2000

time

netmigrationnumbe

rs

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New and old predictions (with permission, from Omar Hardarson)

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Conclusions and Discussion

Good performance of ARDL models

Limitations: regressor forecast, registration process

Coverage and type II errors

Vector ARDL models: how realistic

External factors

4 4 slides dynamical models for migration projections

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