IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

Inferring Latent Preferences from Network Data

John S. Ahlquist1 Arturas Rozenas2

1UC San Diego GPS 2NYU

14 November 2015

IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

Motivationvery early stages

Methodological

• extend “latent space” models (Hoff et al 2002) to “partialobservability” in binary, non-directed graphs

• Build on mixture model approach (Ward et al. 2013)

• Generate improved forecasting and case selection tools

Substantive

• Need convincing model of treaty formation to evaluateeffects (Rosendorff & Shin 2012)

• Existing empirical models of BIT formation fail to accountfor network dependencies

• Observed treaty network and preferences for BITs mayevolve dynamically and endogenously

• Identify treaties likely to be breached or to have trouble inratification

IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

Partial observability

z∗ij : i ’s net (unobserved) payoff for signing a BIT with jBITij observed iff z∗ij > 0 ∧ z∗ji > 0

Z*ij

Z* ji

Z*ij > 0

Z*ji > 0

Observed BIT

Z*ij > 0

Z*ji < 0

no BIT observed

Z*ij < 0

Z*ji < 0

no BIT observed

Z*ij > 0

Z*ji < 0

no BIT observed

IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

Observed and latent networksnondirectional observed network and directional latent relations

A B

C

Observed network G

A B

C

A B

C

A B

C

Associated latent networks G∗1 ,G∗2 ,G∗3

IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

Random utility & latent variables

z∗ij =

systematic︷︸︸︷µij +

random︷︸︸︷εij

εij = ai + bj︸ ︷︷ ︸2nd order dependence

+ u′ivj︸︷︷︸3rd order dependence

µij = β(s)x(s)i + β(r)x

(r)j + β(d)x

(d)ij

µji = β(s)x(s)j + β(r)x

(r)i + β(d)x

(d)ji

y∗ij =

{1 if z∗ij ≥ 0,

0 otherwise

yij = yji = y∗ij y∗ji

IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

Model assumptions & structureBayesian model, diffuse priors on hyperparameters, MCMC estimation

(z∗ijz∗ji

)∼ N2

(µij + ai + bjµji + aj + bi

,

[1 ρρ 1

])+

(u′ivju′jvi

), (1)(

aibi

)∼ N2

(00,

[σ2a σabσab σ2b

]), (2)

ui ∼ NK (0, σ2uI ), (3)

vi ∼ NK (0, σ2v I ). (4)

IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

DataBIT network 1990-2014

• BIT signing data from UNCTAD

• BITs assumed to remain in place permanently

• Estimated independently for each year

• Covariates: exports, imports, distance, GDP, population,UDS

• One-dimensional latent space assumed.

• Missing covariate data imputed as part of MCMC

IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

ConvergenceConvergence problems in sparse networks

−0.

20.

00.

2

bd.1

−0.

10.

10.

3

bd.2

−0.

7−

0.5

−0.

3

bd.3

−3.

4−

2.8

−2.

2

Inte

rcep

t

−0.

20.

20.

6

0 200 400 600 800 1000

bs1

Time

−0.

60.

00.

4

bs2

0.0

0.4

bs3

−0.

40.

00.

4

br1

−0.

50.

51.

0

0 200 400 600 800 1000

br2

Time

1990, density = 0.03

−0.

15−

0.05

0.05

bd.1

0.00

0.10

0.20

bd.2

−0.

80−

0.70

bd.3

−1.

6−

1.2

−0.

8

Inte

rcep

t

−0.

40.

00.

4

0 200 400 600 800 1000bs

1Time

−0.

20.

2

bs2

−0.

30.

00.

2

bs3

−0.

40.

00.

4

br1

−0.

40.

00.

4

0 200 400 600 800 1000

br2

Time

2010, density = 0.15

IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

Regression weights over time

1990 1995 2000 2005 2010

-0.6

-0.2

0.2

0.4

gdp.r

1990:2014

out[,

2]

1990 1995 2000 2005 2010

-0.15

-0.05

0.05

0.15

exports

1990:2014

out[,

2]

1990 1995 2000 2005 2010

-0.6

-0.2

0.20.4

uds.r

1990:2014

out[,

2]

1990 1995 2000 2005 2010

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

proximity

1990:2014

out[,

2]

IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

Latent preferences and BITsGermany

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

DEU 2000

Probability DEU demands treaty from the other

Pro

babi

lity

DE

U is

dem

ande

d as

trea

ty p

artn

er

AFG

ALBDZA

AND

AGO

ATG

ARGARM

AUS

AUT

AZE

BHS

BHR

BGDBRBBLR

BLZ

BEN

BTN

REU

BOLBIH

BWA

BRA

BRN

BGRBFABDICPV

KHM

CMR

CAN

CAF

TCDCHLCHN

COL

COM

COGCODCRICIVHRVCUB

CYP

CZE

DNK

DJI

DMADOM

ECUEGYSLV

GNQ ERI

EST

ETH

FJI

FIN

FRA

GAB

GMB

GEO

DEU

GHA

GRC

GRD

GTM

GINGNB

GUY

HTI

HNDHUN

ISL

INDIDN

IRN

IRQ

IRL

ISR

ITA

JAM

JPN

JORKAZKEN

KIR

PRKKORKWT

KGZLAOLVALBN

LSO

LBR

LBY

LIE

LTUMKDMDG

MWI

MYS

MDV

MLIMLT

MHL

MRTMUS

MEX

FSM

MDA

MCO

MNGMAR

MOZ

MMR

NAM

NRU

NPL

NLD

NZL

NIC

NER

NGA

NOR

OMNPAK

PLW

PSE

PAN

PNG

PRYPERPHLPOLPRT

QAT

ROURUS

RWA

KNA

LCA

VCT

WSM

SMR

STP

SAU

SEN

SYC

SLE

SGPSVKSVN

SLB

SOM

ZAF

ESP

LKA

SDN

SUR

SWZ

SWE

CHE

SYR

TWN

TJK

TZATHA

TGO

TON

TTO

TUNTUR

TKMUGAUKRARE

GBR

USA

URYUZB

VUT

VENVNMYEM

ZMB

ZWE

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

DEU 2010

Probability DEU demands treaty from the other

Pro

babi

lity

DE

U is

dem

ande

d as

trea

ty p

artn

er

AFG ALBDZA

AND AGO

ATG ARGARM

AUS

AUT

AZE

BHS

BHRBGDBRBBLR

BLZ

BEN

BTN

REU

BOLBIH

BWA

BRABRN

BGR

BFA

BDI

CPVKHM

CMR

CAN

CAFTCDCHLCHN

COL

COM

COGCOD

CRI

CIVHRV

CUB

CYP

CZE

DNK

DJI

DMA

DOM

ECU

EGY

SLVGNQ

ERI

ESTETH

FJI

FIN

FRA GAB

GMB

GEO

DEU

GHAGRC GRD

GTM

GIN

GNB

GUYHTI

HND

HUN

ISL

INDIDNIRNIRQ

IRL

ISR

ITA

JAM

JPN

JORKAZKEN

KIR

PRK

KORKWTKGZ

LAO

LVALBNLSO LBR

LBYLIE

LTU

MKDMDG

MWI

MYS

MDV

MLI

MLT

MHL

MRT

MUSMEX

FSM

MDA

MCO

MNG

MNE

MARMOZ

MMR

NAM

NRU

NPL

NLD

NZL

NIC

NERNGA

NOR

OMNPAK

PLW

PSE PAN

PNGPRY

PERPHLPOL

PRT

QAT

ROURUSRWA

KNA

LCA

VCT

WSM

SMR

STP

SAU

SEN

SYC

SLE

SGP

SVKSVN

SLB

SOM

ZAFESP

LKASDN

SUR

SWZ

SWE

CHE

SYR

TWN

TJKTZA

THA

TLS

TGO

TON

TTOTUNTURTKM

TUV

UGA

UKRARE

GBR

USA

URYUZB

VUT

VENVNM

YEM

ZMBZWE

IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

Latent preferences and BITsBrazil

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

BRA 2000

Probability BRA demands treaty from the other

Pro

babi

lity

BR

A is

dem

ande

d as

trea

ty p

artn

er

AFG

ALB

DZA

AND

AGO

ATG

ARG

ARM

AUS

AUT

AZEBHS

BHR

BGD

BRB

BLR

BLZBENBTN

REU

BOL

BIH

BWA

BRABRN

BGR

BFA

BDI

CPV

KHM

CMR

CAN

CAF

TCD

CHL

CHN

COL

COMCOG COD

CRI

CIVHRV

CUB

CYP

CZE

DNK

DJIDMA

DOM

ECU

EGY

SLV

GNQ

ERI

EST

ETH

FJI

FIN

FRA

GAB

GMB

GEO

DEU

GHA

GRC

GRD GTM

GIN

GNB

GUY

HTI HND

HUN

ISL

IND

IDN

IRN

IRQIRL

ISR

ITA

JAM

JPN

JOR

KAZKENKIR

PRK

KOR

KWT

KGZLAO LVA

LBN

LSOLBR

LBY

LIE LTU

MKD

MDGMWI

MYS

MDV

MLI

MLT

MHL

MRT

MUS

MEXFSM MDAMCOMNG

MAR

MOZ

MMR

NAM

NRUNPL

NLD

NZL NIC

NER

NGA

NOR

OMNPAK

PLWPSE

PAN

PNG

PRY

PER

PHL

POL

PRT

QAT

ROU

RUS

RWAKNALCAVCTWSMSMRSTPSAU

SEN

SYCSLE SGP

SVK

SVNSLBSOM

ZAF

ESP

LKA

SDN

SUR

SWZ

SWE

CHE

SYR

TWNTJK

TZA

THA

TGO

TON

TTO

TUN

TUR

TKMUGA

UKR

ARE

GBR

USA

URY

UZB

VUT

VEN

VNM

YEM

ZMB

ZWE

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

BRA 2010

Probability BRA demands treaty from the other

Pro

babi

lity

BR

A is

dem

ande

d as

trea

ty p

artn

er

AFG ALB

DZA

AND

AGO

ATG

ARG

ARM

AUS

AUT

AZE

BHS

BHRBGD

BRB

BLRBLZ

BEN

BTN

REU

BOL

BIH

BWA

BRABRN BGR

BFA

BDI

CPV

KHM

CMR

CAN

CAF

TCD

CHL

CHN

COL

COM

COG

COD

CRICIV

HRV

CUB

CYPCZE

DNK

DJI

DMA

DOM

ECU

EGY

SLVGNQ

ERI

ESTETH

FJI

FIN

FRA

GAB

GMB

GEO

DEU

GHA

GRCGRD

GTM

GIN

GNB

GUY

HTI

HND HUN

ISL INDIDN

IRN

IRQ

IRL ISR

ITA

JAM

JPN

JOR KAZ

KEN

KIRPRK

KOR

KWT

KGZLAO LVA

LBN

LSOLBR

LBY

LIE

LTUMKDMDGMWI

MYS

MDV

MLI

MLTMHL

MRT

MUS

MEXFSM MDA

MCO

MNG MNE

MAR

MOZMMR NAMNRU

NPL

NLD

NZL NIC

NER

NGA

NOR

OMNPAK

PLWPSE PANPNG

PRYPER

PHL POL

PRT

QAT

ROU

RUSRWA

KNA

LCA

VCTWSM

SMRSTP

SAU

SEN

SYCSLE SGP SVKSVNSLBSOM

ZAF

ESP

LKA

SDN

SUR

SWZ

SWE

CHE

SYRTWN

TJK

TZA

THATLS

TGO

TON TTO

TUN

TURTKMTUV

UGA

UKRARE

GBRUSA

URYUZBVUT

VEN

VNMYEM

ZMB

ZWE

IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

Latent preferences and BITsChina

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

CHN 2000

Probability CHN demands treaty from the other

Pro

babi

lity

CH

N is

dem

ande

d as

trea

ty p

artn

er

AFG

ALBDZA

AND

AGO

ATG

ARG

ARM

AUSAUT

AZE

BHS

BHR

BGD

BRB

BLR

BLZ

BEN

BTN

REU

BOL

BIH

BWA

BRA

BRN

BGR

BFA

BDI

CPV

KHM

CMR

CAN

CAF

TCD

CHL

CHN

COL

COM

COG

COD

CRI

CIV

HRVCUB

CYP

CZE

DNK

DJI

DMA

DOM

ECU

EGY

SLV

GNQ

ERI

EST

ETH

FJI

FINFRA

GAB

GMB

GEO

DEU

GHA

GRC

GRD

GTM

GIN

GNB

GUY

HTI

HND

HUN

ISL

INDIDN

IRN

IRQ

IRL

ISR

ITA

JAM

JPN

JORKAZ

KEN

KIR

PRKKORKWT

KGZ

LAO

LVALBN

LSO LBR

LBY

LIE

LTU

MKD

MDG

MWI

MYS

MDV

MLI

MLT

MHL

MRT

MUS

MEX

FSM

MDA

MCO

MNGMAR

MOZ

MMRNAM

NRU

NPL

NLD

NZL

NIC

NER

NGA

NOR

OMNPAK

PLW

PSE

PAN

PNG

PRY

PER

PHLPOLPRTQAT

ROURUS

RWA

KNALCAVCT

WSMSMR

STP

SAU

SEN

SYCSLE

SGPSVK

SVN

SLB

SOM

ZAF

ESP

LKA

SDN

SURSWZ

SWE

CHE

SYR

TWN

TJK

TZA

THA

TGO

TON

TTO

TUNTUR

TKM

UGA

UKRAREGBR

USA

URY

UZB

VUT

VEN

VNMYEM

ZMB

ZWE

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

CHN 2010

Probability CHN demands treaty from the other

Pro

babi

lity

CH

N is

dem

ande

d as

trea

ty p

artn

er

AFG

ALB

DZA

ANDAGO

ATG

ARG

ARM

AUS

AUTAZE

BHS

BHR BGD

BRB

BLR

BLZ

BENBTN REU

BOL

BIHBWA

BRA

BRN BGRBFABDI

CPV

KHMCMR

CAN

CAF

TCD

CHL

CHN

COL

COM COG

COD

CRI

CIV

HRVCUB

CYP

CZE

DNKDJI

DMA

DOM

ECU

EGY

SLV

GNQ

ERIEST

ETH

FJI

FINFRA

GAB

GMB

GEO

DEUGHA GRC

GRD

GTM

GIN

GNB

GUY

HTI

HND

HUN

ISL

INDIDNIRNIRQ

IRL

ISR

ITA

JAM

JPNJORKAZKEN

KIR

PRKKORKWTKGZLAOLVA

LBN

LSO

LBR

LBY

LIE

LTU

MKD

MDG

MWI

MYSMDV MLI

MLT

MHL

MRTMUS

MEX

FSMMDA

MCO

MNG

MNE

MARMOZ

MMR

NAM

NRU

NPL

NLD

NZL

NIC

NER

NGA

NOR

OMNPAK

PLWPSE

PAN

PNG

PRY

PER

PHLPOL

PRT

QATROURUSRWA

KNA

LCA

VCT

WSM

SMR

STP

SAU

SEN

SYC

SLE

SGPSVK

SVN

SLB

SOMZAFESPLKASDN

SUR

SWZ

SWECHESYR

TWN

TJKTZA THATLS

TGOTON

TTO

TUNTURTKM

TUV

UGA

UKRAREGBRUSA

URY

UZB

VUT

VEN

VNMYEM

ZMB

ZWE

IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

Examining the predicted network2014 subset

USA

DEU

MEX

PER

CHN

IND

TUR

MAR

ZAF

BWA

NGA

NZL

NLD

GHA

HND

RUS

JPN

MYS

IPES

Ahlquist &Rozenas

Motivation

The model

Data

Preliminaryresults

Conclusion

Conclusion

• Preliminary results suggest benefits in learning aboutlatent preferences

• Even a poorly fitting network model able to recoverinteresting changes

• Still to do:• gather more covariates (US interest rate, transparency)• out of sample forecasting comparison• dynamic estimation• benchmarking against existing models