Inferring Latent Preferences from Network Data

Transcription

1 Inferring Latent Preferences from Network John S. Ahlquist 1 Arturas 2 1 UC San Diego GPS 2 NYU 14 November 2015

2 very early stages Methodological extend latent space models (Hoff et al 2002) to partial observability 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 evaluate effects (Rosendorff & Shin 2012) Existing empirical models of BIT formation fail to account for network dependencies Observed treaty network and preferences for BITs may evolve dynamically and endogenously Identify treaties likely to be breached or to have trouble in ratification

3 Partial observability zij : i s net (unobserved) payoff for signing a BIT with j BIT ij observed iff zij > 0 z ji > 0 Z* ij > 0 Z* ji < 0 Z* ij > 0 Z* ji > 0 no BIT observed Observed BIT Z* ji no BIT observed Z* ji < 0 Z* ij < 0 no BIT observed Z* ji < 0 Z* ij > 0 Z* ij

4 Observed and latent networks nondirectional observed network and directional latent relations Observed network G Associated latent networks G 1, G 2, G 3 C C A B A B C C A B A B

5 Random utility & latent variables z ij = systematic random {}}{{}}{ µ ij + ɛ ij ɛ ij = a i + b j }{{} + u iv j }{{} 2nd order dependence 3rd order dependence µ ij = β (s) x (s) i µ ji = β (s) x (s) y ij = y ij = y ji = yij yji j + β (r) x (r) j + β (r) x (r) i { 1 if zij 0, 0 otherwise + β (d) x (d) ij + β (d) x (d) ji

6 Model assumptions & structure Bayesian model, diffuse priors on hyperparameters, MCMC estimation ( z ij zji ( ai b i ) ( [ µij + a N i + b j 1 ρ 2, µ ji + a j + b i ρ 1 ) ( [ 0 σ N 2 0, 2 a σ ab σ ab σb 2 ]) ( u + i v j u j v i ), (1) ]), (2) u i N K (0, σ 2 ui ), (3) v i N K (0, σ 2 v I ). (4)

7 BIT network 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

8 Convergence Convergence problems in sparse networks bd.1 bd , density = 0.03 bs3 bs bd.1 bd , density = 0.15 Intercept bd br2 br1 bs3 bs Intercept bd br2 bs1 br Time bs Time Time Time

9 Regression weights over time gdp.r exports out[, 2] out[, 2] : :2014 uds.r proximity out[, 2] out[, 2] : :2014

10 Latent preferences and BITs Germany Probability DEU is demanded as treaty partner DEU 2000 PRT ISR COD CUB CMR ARM CHN ARG BGD BGR CPV BRA HRV CHL BOL DZA CZE AZE BLR ALB BIH BEN ECU COG GHA GEO HUN EGY KAZ EST IND BRB SLV IDN CIV PRK KOR THA VNM LBR LAO MDG MNG VEN KWT UGA MEX OMN ZWE MDA TCD CRI CYP AGO BFA GAB KGZ MKD MAR URY ROU MYS UKR PER SVN UZB TUR RUS KEN JAM HND JOR LBN MLT LTU NGA SEN TUN PRY POL SVK TZA PHL PAN ZAF LKA PAK NIC YEM ARE LVA MLI BDI RWA ZMB SGP GIN GRC TJK TGO TKM MRT ESP NAM MOZ GNB AUT KHMMUS ETH NER IRN SDN STP BWA PNG FRA CAF GMB GUY SLE LSO NPL TTO REU DMA LCA QAT ATG SYR HTI DOM SOM GTM COL PSE FIN SAU SWZ VCT GNQ ERI LBY AUS DNK ISL BLZ GRD BHR TON CHE NLD BRN ITA CAN NOR GBR LIE SWE SYC IRL SMR DJI MCO SURMWI AND IRQ AFG MDV BHS KNA NZL COM MMR NRU BTN USA MHL PLW FSM WSM KIR TWN VUT JPN SLB FJI DEU Probability DEU is demanded as treaty partner FRA ESP AND USA LIE MCO BTN MDV KNA SWE NRU FSM PLW WSM SLB KIR TUV FJI NZL AUS DEU BRN AUT FIN JPN DEU 2010 GRC AFG GRD IRQ ATG DMA HTI NPLKGZ COD BHR IRN COG GEO TCD AZE OMN CMR BEN ARM BGD CHN ARG BGR EGY HRV BRA DZA BOL CHL CZE ETH BLR EST ALB CIV BIH GUY KOR KWT HUN JOR KEN KAZ LBN IND LVA LSO MUS MDA MNG MAR MOZ LTU CAF BDI MDG MEX PAK PSE LCA SLE RWA TKM SYR TJK TTO SDN ARE YEM ROU UKR RUS SEN TUN TUR URY PER SVN UZB POL SVK GAB BRB JAM IDN LBR MYS PHL ZAF LKA TGO VNM TZA PAN NIC SOM MKD GHA NER ZWE VEN PNG MRT UGA CUB LAO MLT TLS AGO NGA ZMB GTM ECU PRY QAT LBY BFA GNQ BWA NAM SAU CRI ISR SLV TON HND CPV KHM GIN DJI VUT SGP THA BHS DOM MNE CYP COL GMB MLI SWZ ITA STP BLZ PRK REU CHE COM PRT ERI MWI NLD SUR GBR IRL VCT ISL DNK CAN NOR GNB SYC SMR MMR TWN MHL Probability DEU demands treaty from the other Probability DEU demands treaty from the other

11 Latent preferences and BITs Brazil Probability BRA is demanded as treaty partner BRA 2000 CUB EGY CHN PRT DZA TUN MAR FIN MYS JAM ROU AUT SUR IDN KOR PER YEM SDN VEN QAT ECU SEN TUR MLI NOR LBY GIN GHA ZAF PRY SYR ZWE CZE AUS GRC JOR CPV BOL GMB MRT LBN POL OMN PAK BGR BHR NER TCD CIV BRB HRV SLV ETH COL BFA KWT MOZ GUY PRK IRN TGO GAB BIH HUN ARE IND MLT TTOMUS RUS AGO MKD BLR PAN CRI BWA ALB DOM CMR GRD NAMTHASVK UKR ZMB ERIJPN GTM ISR BHS COG COM DMA BGD CAF ATG DJI GNB IRQ NGA HTI HND MDG MCO KHM MDV NRU FSM AND BRN GNQ AFG BRA KEN BEN BTN LSO MWI LAO LBR BDI KIR LIE FJI BLZ ARM KGZ AZE GEO IRL EST COD KAZ MHL MMR NPL MNG NZL KNA NIC PNG PLW RWA PSE LCA VCT STP TKM UZBVNM UGA SVN WSM SOM LKA SMR SWZ SLB SLE SAU PHLSGP TJK TON VUT TZA SYCISL MDA LTUMEX CYP LVA CHE DEU ITA NLD GBR FRA ARG SWE DNK REU CHL USA ESP CAN URY TWN Probability BRA is demanded as treaty partner BRA 2010 GIN USA BFA MLI MUS BEN COM MRT TCD PRT CUB GHA DNK CHN GMB BDI BRB CAN EGY MAR GNB KNA CMR QAT SUR BWA TUN ZAF GBR DEU CHE REU ITA NLD FRA SWE FIN ESP CHL JAM DZA ARG KOR AUT LBY GUY ZWE VEN BHS IRN CPV NOR NER PER PRY DMA ERI LBNSEN MYS ECU LCA ATG GAB JPN KEN TGO UGA AND COL ROU MCO CIV AUS COG SMR HTI LIE CRI CAF GRD AGO IDN KWT STP BOL CZE GNQ ISL DOM NPL IRQ CYP BRN GRC IND SLV KIRETH PRK NGA SYR ZMB MDG RWA SWZ MWI TZA VCTSDN BGR MDV AFG BTN FJI BGD BHR BLZ HRV NRU FSM BRA LSO LBR LAO KHM DJI IRL COD MLT HND MHL MOZ NAM MMR OMNZL PAK RUS TWN WSM SOM PSE SLE YEM TUR URY PNG PLW SYC SGP TON TUV VUT SLB TLS LKA TKM PHLARE MNG TJKSAU THAKGZ JOR BIH ALB ARM TTO MKD VNMNE KAZ NICUZB BLR SVKSVN AZE GTM ESTGEO HUN MDA PAN UKR MEX POL ISRLVA LTU Probability BRA demands treaty from the other Probability BRA demands treaty from the other

12 Latent preferences and BITs China Probability CHN is demanded as treaty partner CHN CHN 2000 PRK BGD HUN MYS EGY KOR DEU POL CZE PAK BGR FRA PHL IND IDN KWT MNG ITA PRT OMN DNK REU AUS DZA FIN QAT TUN ROU VNM CHE MAR LKA TUR RUS THA YEM LAO NLD SWE HRV GBR UKR UZB AUT CUB ARG SVK ZWEARE KAZ ZAF SGP JOR ALB IRN LTU SDN LBN TJK SYR ESP KGZ ISR CHL LVA BIH KHM BLR MKD GRC SVN TKM ETH PER MLT BHR JPN MUS BRN USA GEO ARM PNG MDA TCD NOR AZE JAM GHASEN MOZ MLI LBY TWN EST CIV CAN NER CPVCMR GAB UGA VEN NPL GIN ZMB MRT ERI TZA TGO BFA BOL MEX SOM MDG AGO CYP NGA PRY KEN DJI ECU SLV NAM BWA COD PSE IRQ MMRSAU URY NZL GMB AFG COG CAF RWA BTN BRA MDV BRB PLW TON STP NIC SWZ SUR COMBDI CRI BEN NRU FSM PAN VUT GNB ISL MWI GTM HND GUY KIR LSO LBRCOL SMR TTO WSM SLB DOMMHL SLE HTI SYC MCO IRL LIE FJI GNQ DMA GRD AND BHS VCT ATG LCA BLZ KNA Probability CHN is demanded as treaty partner MDV AND LIE MCO GRDSLB DMA LCA ATG BTN FSM NRU LSO BDI PLW PSE SOM SLE HTI WSM TUV FJI KIR LBR KNA BHS CHN TGO TON CAF CHN 2010 RWA COM BEN TLSIRQBFA CIV NER BRB GUY STP GNB IRL SUR TCD CMRAFG NPL COG BRN BHR DZA BGD ARM BGR EGY ETH BLR AZE AUT REU KHM FRA DEU HRV CZE GIN KEN USA SDN MUS MOZ MAR SYR YEM TUNTUR OMN LBN IRN IDN IND GHA GRC JPN JOR MNG KWT KGZ MYS KOR LAO HUN PRK PAK MRT MDG PNG ZAF ARE QAT ROU RUS FIN KAZ PHL SEN ESP LKA CHE SGP SVK POL TJK TZA TKM GBR VNM UKR UZB THA ZWELTU ITA MLI UGA LBY SWE LVA CUB ALB BWA BIH COD GEO MDA NLD VUT GAB JAM ARG ZMB AGO AUS SVN MEX ISR DJI PRT MKD CYP ERI PER NGA DNK CHL GMB EST GNQ MLT TTO SAU CAN NAM BRA SWZ VEN CPV BOL NZL ECU URY NOR PAN SLV MWI MMR CRI PRY MNE NIC SYC GTM ISL HND DOM COL SMR BLZ MHL TWN VCT Probability CHN demands treaty from the other Probability CHN demands treaty from the other

13 Examining the predicted network 2014 subset HND USA JPN RUS MAR TUR PER NLD CHN ZAF MEX IND MYS GHA DEU NGA NZL BWA

14 suggest benefits in learning about latent preferences Even a poorly fitting network model able to recover interesting changes Still to do: gather more covariates (US interest rate, transparency) out of sample forecasting comparison dynamic estimation benchmarking against existing models