Spatial Econometric Models of Interdependence Theory

1
Spatial Econometric Modelsof InterdependenceThe
ory Substance Empirical Specification,
Estimation, Evaluation Substantive
Interpretation Presentation

• Talk prepared for Blalock Lecture on
• 7 August 2008 at the ICPSR Summer School
• based on the joint work of
• Robert J. Franzese, Jr., The University of
  Michigan
• Jude C. Hays, The University of Illinois

2
Overview

• Motivation Integration Domestic
  Policy-Autonomy
• Does economic integration constrain govts from
  redistributing income, risk, opportunity
  through tax spending policies?
• In answering this related questions, scholars
  have overlooked spatial interdependence of
  domestic policies as important evidence.
• Economic integration generates externalities
  across political jurisdictions, which implies
  strategic policy interdependence, so policy of
  one govt will be influenced by policies of its
  neighbors.
• Interdependence Substance, Theory, Empirics
  Use contexts econ integration ( related) to
  explore explain
• Substance is actions depend on js. Examples.
• Theory
• General externalities?strategic policy
  complements/substitutes?race-to-bottom/top/else?ea
  rly/late-mover advantages?strategic
  delay/rush-for-1st
• Specific a model of inter-jurisdictional
  tax-competition (PT ch. 12)
• Empirics Galtons Problem Estimation,
  Inference, Interpretation, Presentation

3
A Motivating ContextGlobalization
Domestic-Policy Autonomy

• Standard Argument
• ? capital mobility trade integration sharpen
  capitals threat vs. domestic govts to flee
  excessive/inefficient tax public policy forces
  welfare-state retrench tax shift from more-mob.
  cap. (esp. finance) to less-mob. lab. (esp.
  skilled-man.)
• Recent counter-arguments findings
• Some empirical Q whether constrained or
  constraint from trade/capital integ.
• Counter-arguments (e.g.)
• Rodrik (Cameron) Demand (contra supply) SocPol
  may ? w/ integ ? indeterminate
• Garrett 98/Boix 98 Left/active govt more/as
  efficient ? capital not flee
• Hall-Soskice 01/Franzese-Mosher 02 comparative
  institutional advantage ? trade-integ foster
  divergence (liquid) cap-integ may foster race to
  bottom (not necly) zero
• Swank 02 ( many others) political economic
  barriers /or advantages ? considerable
  maneuvering room
• Standard all counter arguments ? spatial
  interdependence b/c whatever pressures may arise
  from globalization depend on what neighbors,
  competitors, partners, substitutes, complements
  do
• Accordingly, appropriate model places others
  policies on right-hand side
• Basinger-Hallerberg 04 maybe 1st in CIPE to
  notice incorporate explicitly
• Interdependence (def) yif(yj?i) note not
  merely that yi yj?i corr

4
The Broad Range of Spatial Interdependence

• Theoretical Contexts (ubiquitous)
• ANY Strategic Decision-making si?sj
• Externalities Spillovers
• Learning/Emulation, Demonstration
• Networks/Epistemic Communities
• Literal Diffusion, Contagion, Migration

• (Simmons et al.s 06) Mechanisms
• Competition
• Coercion
• Learning
• Emulation
• Migration/Contagion (FH Add)

• Substantive Contexts (ubiquitous)
• Security Policy (e.g., alliances, wars)
• Environmental (e.g., air-pollution reg)
• Regulatory (e.g., telecomm stds)
• Legis reps votes depend on others
• Elects., cand. qualities or strategies
• p()outs coups (LiThompson 75), riots
  (GoveaWest 81), revolts (BrinksCopp 06)
• Contextual effects in micro-behavior
• BraybeckHuckfeldt 02ab, Cho 03, Huckfeldt et al.
  05, ChoGimpel 07, ChoRudolph 07, Lin et al 06

• Policy, instits, regimes diffusion
• Policy SchneiderIngram88, Rose 93, Meseguer
  04,05, Gilardi 05
• Institutional or regime Implicit/Informal
  Dahls Polyarchy, Starrs Democratic Dominoes,
  Huntingtons 3rd Wave. Explicit/Formal
  OLoughlin et al. 98, Brinks Coppedge 06,
  Gleditsch Ward 06, 07
• Intl diffusion of liberalization
• SimmonsElkins 04, 06a, 06b, Eising 02, Brune et
  al. 04, Brooks 05
• Globalization interdependence
• Genschel 02, BasingerHallerberg 04, Knill 05,
  Jahn 06, Swank 06, FH 06,07, Kayser 07

• Toblers Law I invoke the first law of
  geography everything is related to everything
  else, but near things are more related than
  distant things (1970).
• Plus Space More Than Geography (Beck,
  Gleditsch, Beardsley 2006)

5
Substantive Theoretical Ubiquity Centrality
(1)

• US State Policy-innovation diffusion deep roots
  much contemporary interest, sustained
  attention between
• Crain 1966 Walker 1969, 1973 Gray 1973 Knoke
  1982 Caldiera 1985 Lutz 1987 Berry Berry
  1990 Case et al. 1993 Berry 1994 Rogers 1995
  Mintrom 1997ab Brueckner 1998 Mintrom Vergari
  1998 Mossberger 1999 Berry Berry 1999 Godwin
  Schroedel 2000 Balla 2001 Mooney 2001
  Wejnert 2002 Coughlin et al. 2003 Bailey Rom
  2004 Boehmke Witmer 2004 Daley Garand 2004
  Grossback et al. 2004 Mencken 2004 Berry
  Baybeck 2005 Garrett et al. 2005 Costa-Font
  Ons-Novell 2006 Karch 2006 Rincke 2006 Shipan
  Volden 2006 Volden 2006 Werck et al. 2006
  Woods 2006 Volden et al. 2007.
• Similar policy-learning mechanisms underlie some
  comparative studies of policy diffusion
• Schneider Ingram 1988 Rose 1993 Bennett 1997
  Dolowitz Marsh 2000 True Mintrom 2001 Tews
  et al. 2003 Jensen 2004 Meseguer 2004, 2005
  Brooks 2005, 2007 Gilardi 2005 Gilardi et al.
  2005 Murillo Schrank 2005 Weyland 2005 Braun
  Gilardi 2006 Linos 2006 Parys 2006 Ermini
  Santolini 2007 Moscone et al. 2007.
• Institutional or regime diffusion likewise
  long-standing recently much reinvigorated
• Dahls 1971 Polyarchy (1 of 8 causes dem listed)
  center-stage Starrs 1991 Democratic Dominoes
  Huntingtons 1991 Third Wave Beissinger 2007
  Bunce Wolchik 2006, 2007 et al. in E. Eur.
  Transitions Hagopian Mainwaring 2005 et al. in
  LA OLoughlin et al. 1998, Brinks Coppedge
  2006, Gleditsch Ward 2006, 2007 estimated
  empirically extent, paths, /or patterns dem
  diffuse. Kelejian et al. 2007 give institutional
  diffusion general theoretical empirical
  treatment.
• CIPE, e.g. globalizationinterdependence
• Diffusion of Liberalization Related Simmons
  Elkins 2004, Simmons et al. 2006, Eising 2002
  Brune et al. 2004 Brooks 2005, 2007 Jordana
  Levi-Faur 2005 Way 2005 Lazer 2006 Prakash
  Potoski 2006 Brune Guisinger 2007 and many
  others.
• Glob/Interdep/TaxComp Dom Policy Auton
  Genschel 2002 Guler et al. 2002 Franzese Hays
  2003, 2004b, 2005a, 2007abc, 2008c Badinger et
  al. 2004 Basinger Hallerberg 2004 Heichel et
  al. 2005 Henisz et al. 2005 Holzinger Knill
  2005 Knill 2005 Polillo Guillén 2005 Elkins
  et al. 2006 Jahn 2006 Lee Strang 2006 Manger
  2006 Swank 2006 Baturo Grey 2007 Cao 2007
  Cao et al. 2007 Coughlin et al. 2007 Garretsen
  Peeters 2007 Mosley Uno 2007 Mukherjee
  Singer 2007.

6
Substantive Theoretical Ubiquity Centrality
(2)

• Representatives votes (Lacombe Shaughnessy
  2005), citizens votes (Huckfeldt Sprague 1991
  OLaughlin et al. 1994 Pattie Johnston 2000
  Beck et al. 2003 Calvo Escolar 2003 Kim et
  al. 2003 Schofield et al. 2003 Lacombe
  Shaughnessy 2007), election outcomes (Shin
  Agnew 2002, 2007 Hiskey Canache 2005 Wing
  Walker 2006 Kayser 2007), candidate qualities,
  contributions, or strategies (Goldenberg et al.
  1986 Mizruchi 1989 Krasno et al. 1994 Cho
  2003 Gimpel et al. 2006)
• Probabilities outcomes of coups (Li Thompson
  1975), riots (Govea West 1981), civil wars
  (Murdoch Sandler 2004, Buhaug Rød 2006) /or
  revolutions (Brinks Coppedge 2006)
• IR interdepdefinition of subject
• States entry into wars, alliances, treaties
  (Murdoch et al. 2003), or organizations.
• Empirical attention to inherent spat-dep IR
  greatest in Shin Ward 1999 Gleditsch Ward
  2000 Gleditsch 2002 Ward Gleditsch 2002 Hoff
  Ward 2004 Gartzke Gleditsch 2006 Salehyan
  Gleditsch 2006 Gleditsch 2007, and, in different
  way, Signorino 1999, 2002, 2003 Signorino
  Yilmaz 2003 Signorino Tarar 2006
• In micro-behavioral work, too, long-standing
  surging interest contextual or neighborhood
  effects
• Huckfeldt Sprague 1993 review, some of which
  stress interdep Straits 1990 OLoughlin et al.
  1994 Knack Kropf 1998 Liu et al. 1998
  Braybeck Huckfeldt 2002ab Beck et al. 2002
  McClurg 2003 Huckfeldt et al. 2005 Cho Gimpel
  2007 Cho Rudolph 2007. Sampson et al. 2002 and
  Dietz 2002 review the parallel large literature
  on neighborhood effects in sociology
• At beyond other disciplinary borders, subjects
  include
• Social-movements McAdam Rucht 1993 Conell
  Cohn 1995 Giugni 1998 Strang Soule 1998
  Biggs 2003 Browning et al. 2004 Andrews Biggs
  2006 Holmes 2006 Swaroop Morenoff 2006.
• Microeconomic preferences Akerloff 1997
  Postlewaite 1998 Glaeser Scheinkman 2000
  Manski 2000 Brock Durlauf 2001 Durlauf 2001
  Glaeser et al. 2003 Yang Allenby 2003 Sobel
  2005 Ioannides 2006 Soetevent 2006
• Macroeconomic performance Fingleton 2003 Novo
  2003 Kosfeld Lauridsen 2004 Maza Villaverde
  2004 Kelejian et al. 2006 Mencken et al. 2006
• Technology, marketing, and other firm strategies
  Abramson Rosenkopf 1993 Geroski 2000 Strang
  Macy 2001 Holloway 2002 Bradlow 2005
  Autant-Berard 2006 Mizruchi et al. 2006
• Violence and crime Grattet et al. 1998 Myers
  2000 Baller et al. 2001 Morenoff et al. 2001
  Villareal 2002 Baker Faulkner 2003
  Oberwittler 2004 Bhati 2005 Mears Bhati 2006
  Brathwaite Li 2008
• Fertility, birthweight, child development,
  child poverty Tolnay 1995 and Montgomery
  Casterline 1996 Morenoff 2003 Sampson et al.
  1999 Voss et al. 2006
• Not to mention public health and epidemiology
  (contagion!).
• More exotic topics ordainment of women (Chaves
  1996), right-wing extremism (Rydgren 2005),
  marriage (Yabiku 2006), national identity (Lin et
  al. 2006), faculty (Weinstein 2007).

7
Policy InterdependenceA General Theoretical
Model (Brueckner 03)

• is utility depends pi pj b/c interdep ( vv)
• Accordingly, is optimal policy, pi, depends js
  action, pj
• So slope best-response function depends on effect
  of pj on marginal utility of pi
• Therefore Diminishing returns and
• negative externalities gtstrategic complements
• Positive slope positive feedback/same-signed
  reactions
• positive externalities gt strategic substitutes
• Negative slope neg. feedback/opposite-signed
  reactions

8
Policy InterdependenceGeneral Theory
Substantive Implications

• Dimin returns neg externalities ? Strategic
  Complements
• ? Race-to-Bottom (RTB) (or -Top). Examples
• Tax Competition
• Labor Regulation
• Trade Barriers (politically)
• ? Early-mover advantage ? race to go first
• E.g. Exch.Deprec., tech.stds. ( other focal
  pts. in coord. or battle sexes)
• Dimin returns pos externalities ? Strategic
  Substitutes
• ? Free-Riding Incentives
• E.g., Alliance Security
• E.g., ALMP
• ? Late-mover advantage ? strategic delay Wars
  of Attrition
• DimRet both externs
• Environmental Regs ( CHIPs?)

9
Figure 2. Best Response Functions Strategic
Substitutes

• p2

• p1

10
An International Tax-Competition Model as a
Specific Substantive Example of Interdependence

• Stylized Theoretical Model Cap-Tax Comp. (PT
  00, ch.12)
• 2 jurisdicts, dom for cap-tax, tk tk to fund
  fixed spend. For-invest mobility costs, M.
• Inds lab-cap endow, ei, choose lab-leisure, l
  x, save-invest, skf to max ?U(c1)c2V(x),
  over l, c1, c2, s.t. time-c., 1eilx,
  b.c.s, 1eic1kfc1s c2(1tk)k(1tk)fM(
  f)(1tl)l.
• ? equilibrium economic choices of citizens
• ? indirect utility, W, defined over policy
  variables, tl, tk, tk
• Besley-Coate (97) citizen-candidate(s) face(s)
  electorate w/ these prefs.
• Stages 1) elects, 2) cit-cand winners set taxes,
  3) all private econ decisions made.
• Ebm win cand has endow eP such that desires
  implement this Modified Ramsey Rule
• ? Best-Response Functions tkT(eP,tk)
  tkT(eP,tk) for dom for pm.
• Slopes ?T/?tk ?T/?tk, pos or neg b/c ?tk ?
  cap-inflow can use ?tax-base to ?tk or to ?tk
  (seizing upon ?elasticity base).
• Background of this slide plots case both
  positively sloped illustrated comparative static
  is of leftward shift of domestic government.

11
Empirical Models of InterdependenceGaltons
Problem in CIPE

• Interdependence ? yif(yj)
• Generic (linear) dynamic spatial-lag model of
  CIPE
• Galtons Problem Extremely difficult disting why
  C(yi,yj) b/c...
• 1. Correlated domestic/unit-level conditions, d
  (CPE)
• 2. Common/corrd exposure exog-external
  shocks/conditions, s (open-CPE)
• 3. Responses to these 2 may be context-conditional
  , s?d (CC-CPE)
• 40. Correlated stochastic component (Beck-Katz),
  nuisance CIPE
• 4. Interdependence/diffusion/contagion
  yif(yj,CC-CPE), substance CIPE
• Upshot Empirically (Franzese Hays
  03,04,06ab,07abcd,08ab)
• omit or mis-specify CPE, tend over-estimate IPE
  (interdependence) v.v.
• yi?yj gt textbook endogeneity/simultaneity
  problem w/ spatial lag analogous
• fail redress endog sufficiently ? mis-est (usu.
  over-est.) ? ? (under)mis-est. ß
• Most Important Conclusion Model It!TM Insofar as
  omit or relly mis-spec spatial interdep, tend
  over-est impact domestic exog-ext factors
  v.v. ? most crucial, regardless of CPE/IPE
  emphasis well-spec model measure both.
• S-OLS may suffice. OVB gtgt simultaneity bias in
  any of practical examples weve considered,
  S-OLS did OK our MCs provided interdep remained
  modest (?lt.3).

12
The Terms of Galtons ProblemOmitted-Variable
vs. Simultaneity Biases inSpatial- and
Spatio-Temporal-Lag Models

• OVB (rel. mis-spec.) v. simultaneity
• OVB (OLS)
• SimB (S-OLS)
• In S-T, little more complicated, but

With all positive S-T dep, ? space-dep over-estd
? time-dep ß under-estd
13
Estimating Spatial/Spatio-Temporal-Lag Models

• Inconsistent Estimators
• Omit spatial-dep (e.g., OLS) bad idea if ?
  non-negligible
• Ignore simultaneity (e.g., S-OLS) could be OK
  (in MSE) if ? not too large sample-dims
  benevolent
• Simplest Option, if Available
• Time-Lagged Spatial-Lag OLS easy unbiased iff
• No contemporaneous (i.e., w/in obs period)
  interdependence.
• Model of temporal dynamics sufficiently accurate
  (see Achen)
• 1st obs pre-determined if not, spatial-Hurwicz
  bias (order 1/T)
• Consistent Estimators
• S-IV/2SLS/GMM Use WX to instrument Wy, etc.
• S-ML Specify system for Max-Likelihood estimation

14
Estimating Spatial- Spatio-Temporal-Dynamic
Models by S-ML

• S-ML for Spatial-Lag Model
• Std, but e ? y by A not 1 ? computational
  issues, plus
• Conditional S-ML S-T (ie., given 1stobs, Nx1
  form) (unconditional is messy but exists wont
  show)
• Stationarity (if row-stdzd, ?,?gt0) ??lt1
• Spatial Probit complicated but doable (show if
  time)
• m-STAR Estd W endog W doable (show if)

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APPLICATIONS

• Globalization, Tax Competition, Domestic Policy
• Replicates SwankSteinmo 02, Hays 03,
  BasingerHallerberg 04
• ALMP Active-Labor-Market Policy in EU (FH 06)
• DepVar LMT spend per unemployed worker
• Hypoth Positive spillovers (_at_ borders) effective
  member-state ALMP ? free-riding underinvest.
  Appreciable?
• IndVars rGDPpc, UE, UDen, Deindustrialization
  (Iversen-Soskice), Trade, FDI, Pop65, LCab,
  CDemCab, LLibVote, GCons
• MIDs Trade Beck, Gleditsch, Beardsley 06
• DepVar Directed trade data
• Hypoth MIDs affect trade in beyond dyad
• IndVars GDPab, POPab, Distance, tau-b,
  MutualDem, MID, Bi/MultiPoleSys
• AFDC CHIPs in U.S. States (Volden 06)
• AFDC Hypothstates as laboratoriesdiffusion
  by learning
• DepVar max monthly AFDC benefit
• Ind Vars states poverty rate, avg monthly wage
  in retail, govt ideology (0-100, R-L), º
  interparty competition (.5-1.0, comp-non), tax
  effort (rev as tax capacity), AFDC bens
  paid by fed govt.
• CHIPs Hypothstates as laboratoriesdiffusion
  by learning
• DepVar 1 if states CHIP includes monthly
  premium IndVars same.

22
Practical Model Specification Estimation

• Most convenient to work in (Nx1) vector form
• WNan NxN of (time-invariant) spatial wts, wij,
  WN?IT gives W.
• E.g., 15x15 binary-contiguity from ALM paper
• N.b., row-stdz typ., convenient, but not necly
  substly neutral
• Ideally, substance, which not necly ? geography,
  in W.
• Beware of extant software critical bug in
  LeSages MatLab code likelihood in some
  third-party Stata SAR code seems flat wrong.

23
Swank Steinmo APSR 02 Replication
24
Hays IO 03 Replication
25
Basinger Hallerberg APSR 04 Replication
26
Beck, Gleditsch, Beardsley ISQ 06 Replication
27
Franzese Hays EUP 06
28
Volden AJPS 06 AFDC Replication
29
Volden AJPS 06 CHIPs Replication
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Interpreting Spatial/Spatio-Temporal Effects

• The Model
• Model may look linear, but is not as in all
  beyond purely linear-additive, coefficients
  effects very different things!
• Convenient, for interpretation, to write model
  this way too
• Coefficients, ßx are just pre-spatial,
  pre-temporaland wholly unobservable!impulse
  from some x to y.
• Spatio-Temporal Effects
• Post-spatial, pre-temporal instantaneous effect
  of x
• Spatio-Temporal Response Paths
• LR Multiplier/LR-SS

31
Presenting Spatial/Spatio-Temporal Effects

• Standard Errors (Confidence Intervals
  Hypothesis Tests) of Effects
• Delta Method
• or Simulate!
• Upshot Cannot see substance clearly from only
  the estimated coefficients their standard
  errors
• Effective Presentational Options
• SR/LR-Response Grids
• Spatio-Temporal Response-Paths
• Maps

32
Swank Steinmo APSR 02 Replication
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Swank Steinmo APSR 02 Replication
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Swank Steinmo APSR 02 Replication
35
Basinger Hallerberg APSR 04 Replication
36
Basinger Hallerberg APSR 04 Replication
37
Beck, Gleditsch, Beardsley ISQ 06 Replication
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Beck, Gleditsch, Beardsley ISQ 06 Replication
39
Beck, Gleditsch, Beardsley ISQ 06 Replication
40
Franzese Hays EUP 06
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Franzese Hays EUP 06
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Some Other Presentations (3)
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Volden AJPS 06 AFDC Replication
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Volden AJPS 06 AFDC Replication
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Volden AJPS 06 AFDC Replication
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Conclusion

• Spatial Spatio-Temporal Interdependence
• Important Appreciable Substance (e.g.,
  globalization intl cap-tax compete seems quite
  real does constrain), not Nuisance.
• Therefore Model them. Interpret them.
• How specify estimate models?
• If space-lag is time-lagged, not problem but if
  thry substance says immediate (w/in an
  observational period), can handle that too
• S-OLS not a bad strategy even then, if ? not too
  big smpl-dims right S-ML, in some regards
  IV-based strategies, seem effective
• Spatio-Temporal Effects not directly read from
  coefficients use graphs maps grids
• Information-demands of Galtons Problem severe ?
• Standard errors of effects tend big. Suspect
  delta-method lin-approx. maybe part problem plan
  explore performance bootstrap.
• Max effort care theory, measure, specification,
  to both CIPE

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Spatial QualDep The Econometric Problem (1)

• Spatial Qualitative/Categorical/Lmtd-Dep-Var
  Models in the Lit
• Spatial probit McMillen 1992,1995 Bolduc et.
  al. 1997 Pinkse Slade 1998 LeSage 1999, 2000
  Beron et al. 2003 Beron Vijverberg 2004
• Spatial logit Dubin 1997 Lin 2003
  Autant-Bernard 2006
• Spatial sample-selection (i.e., s-Tobit/Heckit)
  McMillen 1995, Smith LeSage 2004,
  Flores-Lagunes Schnier 2006
• Spatial multinomial-probit McMillen 1995, Bolduc
  et al. 1997
• Spatial discrete-duration Phaneuf Palmquist
  2003
• Survival w/ spatial frailty Banerjee et al.
  2004, Darmofal 2007
• Spatial count Bhati 2005, including ZIP Rathbun
  Fei 2006
• The Challenge
• Not n indep., unidimensional CDF std normals, so
  (log-)likelihoodproduct (sum) thereof, but 1
  n-dimensional CDF of non-std (heterosked.)
  normals
• Spatial Latent-Variable Models Estimation
  Strategies
• McMillen 1992 EM algorithm, rendered spatial
  probit estimable, but no std-errs arb.
  parameterization of induced heteroscedasticity.
• McMillen 1995, Bolduc et. al. 1997
  simulated-likelihood strategies to estimate
  spatial-MNP
• Beron et al. 03, Beron Vijverberg 04
  recursive-importance-sampling (RIS) estimator
• LeSage 1999, 2000 Bayesian strategy of
  Markov-Chain-Monte-Carlo (MCMC) by
  Metropolis-Hastings-within-Gibbs sampling.
• Fleming 2004 simpler, if approximate, strategies
  allowing interdep. in (non)linear probability
  models, estimable by NLS, GLM, or GLMM
• Pinkse Slades 1998 two-step GMM estimator
  (for spatial-error probit).

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The Econometric Problem (2)

• Structural Model
• Reduced Form
• Measurement Equation
• Probability
• Or
• For Spatial-Error-Probit

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The Econometric Problem (3)

• Comments
• Notice that, when we come to interpret
  , we face the same MVN integration
• We havent seen such substantive interpretation
  yet attempted fully in the literature, but we
  suggest an easier way to do it.
• If can order dependence pattern ensure only
  antecedent y appear on RHS, then std probit ML
  w/ a spatial-lag works
• We think usu. indefensible substly/thryly, but
  cf. Swank on capital-tax competition, e.g., where
  argues US exclusively leads omits US.
• Having y, not y, on RHS may seem substly or
  thryly desirable in some cases, but genly not
  logically possible
• Problem would be that outcome, yi, would
  indirectly (via spatial feedback) determine yi,
  but then yi would directly determine yi. The
  stochastic difference b/w them will thus ? a
  logical inconsistency.
• Notice similar MVN issue w/ time lags suggests
  similar strategies (but simpler b/c ordered) may
  allow model temp dynamics directly rather than
  nuisance (e.g., BKT splines)

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The Estimators Bayesian Gibbs-MH Sampler (1)

• Basic Idea (See Gills intro Bayesian textbook,
  e.g.)
• Monte Carlo (MC) Given likelihood/posterior, can
  sample to estimate any quantity of interest,
  including density, e.g.
• Markov Chain (MC)MC
• Each draw depends on previous, so need only
  conditional like./post.
• Some theorems indicate, under fairly genl
  conditions, distribution parameter draws
  converges to distribution under true like./post.
• Gibbs Sampler simplest of MCMC family
• Express each parameter like./post. conditional on
  others.
• Cycle to draw each conditional on others starts
  or previous draw
• After some sufficient burn-in, all subsequent
  param-vector draws follow true multivariate
  likelihood/posterior.
• Metropolis-Hastings useful when condl
  param-dist non-std
• Draws from a seed or jump distribution are
  accepted or rejected as the next sampled
  parameters, depending on how they compare to a
  suitably transformed expression of the target
  distribution

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The Estimators Bayesian Gibbs-MH Sampler (2)

• Bayesian Gibbs-MH (MCMC) Sampler for Spatial
  Probit
• Likelihood
• Diffuse Priors gt Joint Posterior
• Conditional Priors

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The Estimators Freq. Recursive Import. Smplr
(RIS) (1)

• Basic Idea
• To approx. n-dim. cumulative std-norm.,
• Re-express as a mean by mult divide by std
  dist. truncated to support of desired integral,
  (the Importance dist.)
• This gives probability, p, sought as
• We want
• So, Imp. dist. is n-dim. MVN truncated at v.
  (uh-oh! but)
• V-Cov u being pos-def gt Cholesky decomposition
  exists s.t.

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The Estimators Freq. Recursive Import. Smplr
(RIS) (2)

• So we want to calc. this set of indep. cum.
  std.norms
• Can do so recursively, beginning w/ last obs.
• First, calculate upper bound for truncated-normal
  dist. of nth
• Draw from this dist use it to calc upper bound
  for (n-1)th
• Since indep., probability of sample observed
  (0,1) is product of n univariate cumulative std.
  norms at these bounds, (!)
• Repeat R times avg gt RIS est. of the
  log-likelihood to max

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Evaluating the Estimators (One Quick MC)

• DGF (n.b., same W, diff. coeffs. For x y)
• Conditions
• Row-stdzd contig. wts U.S. 48 ?0.5, ?1.0,
  n48,144,?0.0, 0.5
• You cant see this, but
• Relly poor bias perf. BG
• In fact, std ML w/ Wy
• seems dominate, but this
• b/c 2 biases, meas./spec.
• err simult. Simult incr
• in ?, meas-err decr or flat
• in n, so over- to under-est.
• (Checked its true) BV 04
• do MC like 2 for RIS find
• ?-18, ?10, so better.

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Calculating Presenting Effects (1)

• If confine discussion to y, then as prev. FH
• And s.e.s/c.i.s by delta method as

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Calculating Presenting Effects (2)

• But we (should) want to discuss
• Note given probit, must know xi given spatial
  interdependence, must know X (!).
• Given interdep, calc these will req. MVN cdf!
• Or better idea?

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An Example Application US State CHIP Premia
Notes 1. Informative U(0,1) prior on ? helps.
Weve qualms. 2. Difference in Bayesian vs.
frequentist significance also. 3. Note
measurement/specification-error seem to have
domd here for ML.
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Example Estimated Spatial Effect, with Certainty
Estimate, in Binary-Outcome Model
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In lieu of conclusions

• S-QualDep (latent-y) models hard, doable
• We have a lot of work yet to do
• Illustrate calculation of effects s.e.s
• Explore estimator properties systematically
• Compare non-spatial probit spatial-lag
  ML-probit approximate specifications
• Next Crucial Extensions
• Extend to other QualDep models
• Estimated-W models (see next for a start)
• System-of-Equations in Space

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The m-STAR Model as an Approach to Modeled,
Dynamic, Endogenous Interdependence

• Spatial Econometrics and (Political) Economy
  Network Analysis and (Political) Sociology
• Co-Evolution Models in Network Analysis
• (Node) Behaviors/Attributes Network (Edges)
• Spatial-Statistical Approaches to Estd-W
• A Simple Spatial-Econometric Proposal
• Estimated W Multiple W (m-STAR)
• Endogenize W means W(y)gtS-IV in m-STAR

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Spatial Econometrics
Network Analysis

• Economists Political Economists
• Core Question
• How alters actions affect egos via network
  v.v.?
• Contagion v. Common Exposure (Galtons Problem)
• Core Tools
• SAR, STAR, S-QualDep
• S-GMM, S-ML

• Sociologists Political Sociologists
• Core Questions
• How do nets form?
• What expl. net struct.?
• How egos position in net net struct affect?
• Core Tools
• Net stats (measures), graphics, ERGMs,

• INTERDEPENDENCE
• Definition yif(yj?i) is actions depend on
  js.
• Seems subset of Network Effects, which also
• Effects of structure network per se (e.g.,
  transitive triplets)
• Effects of position i in network per se. (e.g.,
  betweenness i)

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Where Spatial Econometrics Needs to Go ( Network
Analysis is or Needs to Go also)

• Two Things Always Asked Do Next
• Qualitative Limited Dependent Variables
• Bigger estimation challenges because
• Cannot place y itself on RHS, can only place y.
• N-dimensional integration to get probabilities
• Considerable progress S-Probit/Tobit etc.,
  S-MNP, S-
• Estimate/Parameterize , ideally, Endogenize W
• This essence of network analysis
• However, challenges in many contexts (e.g.,
  CIPE) differ
• W not always (or usually) binary or categorical
• W not always (or usually) observed.
• T not always (or usually) very long.
• Temporal precedence not always (or usually)
  sufficegtcausal prec.

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Leenders (1997) Co-evolution Model

• Selection
• Arc forms or not in continuous time Markov
  process
• Contagion
• STAR model
• gt Co-Evolution Model
• Identification strategy time lag
• Findings of MCs
• Coarse obs periodicity gt big biases
• If selection model contagion gt big biases
• If contagion model selection gt biases, less big

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Snijders (97-07) Co-evolution Model

• Steglich et al. (07) two threefold empirical
  challenges
• contagion, selection, context (1st3rdGaltons
  Problem 2ndcoevolution gt similar implications)
• In gen., any omissions or inadequacies in
  modeling one tends against that favor others
  looks most like it
• coarse periodicity, alternative mechs paths,
  net dependence precludes assume independence.
• Observed Data
• N actors connected by observed, binary,
  endogenous, time-variant connectivity matrix
• Vector of N observed, ordinal behaviors
• Further exogenous explanators may exist at unit
  or dyadic level
• Model Components
• Exponential (constant hazard-rate) model of opp
  to act
• One change (or not) by one person _at_ one time Can
  parameterize the rate Conditionally independent
• When opp act, multinomial w/ N network
  optionschange tie or none
• Compares objective with current behaves net to
  current behaves net w/ 1 switch his row
  non-strategic
• Can parameterize, including as function of
  actions Conditionally independent
• When opp act, could instead change
  behavior/attribute
• Compares object w/ current net behaves to his
  alternative behave, w/ switch of 1,0-1 only
  non-strategic
• Can parameterize, including as function network
  /or of others actions Conditionally
  independent
• Parameters to Estimate
• Coefficients of hazard-rate model and of the two
  multinomial logits (n.b., IIA)

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Issues from CIPE Perspective

• Many behaviors or attributes of interest as
  dependent variables, relative connectivity
  between units less likely binary or ordinal.
• Strengths of relative connectivity not always
  observed, or even observable, directly.
• Under these conditions, for estimation purposes,
  the left-hand side of the selection component of
  the model would have no data. Could only estimate
  them off implications for behavior.
• Temporal precedence often not suffice assure
  causal precedence
• Strategic interdep often operates literally
  simultaneously or even E(future)
• In estimation, simultaneous generally means
  within an observational period many contexts
  high frequency behavior relative to obs
  periodicity.
• Time lagging suffices only if insofar as
  spatiotemporal dynamics fully properly
  specified in model (1st non-stoch, not w/in
  period simult).
• Condition on 1st obs needs T large for efficiency
  for small-sample bias.

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Multi-Parametric Spatio-Temporal (AR) Lag Model
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Co-Evolution Models in m-STAR Format

• Wr covariates expected explain network
• Co-evolution modelsmodels with Wf(y) larger
  challenges.
• Our first cut same poor mans exogeneity,
  time-lag the y in Wf(y)
• Our plan two-step estimation-procedure.
• First, apply spatial-GMM (see, e.g., Anselin
  2006, Franzese Hays 2008b) to obtain by spatial
  instrumentation consistent estimates of
  endogenous wij and their estimated
  variance-covariance.
• Then draw from that estimated multivariate
  distribution of instrumented W estimates to
  insert in the conditional or unconditional m-STAR
  likelihood.
• Maximize likelihood under each of q draws from
  that first-stage S-GMM instrumented estimated
  distribution of W estimates.
• Point estimates of parameters then just average
  of q 2nd stage S-ML estimates
• Estimated variance-covariance of
  parameter-estimates is average of estimated
  variance-covariance matrices from each iteration
  plus (1q) times sample variance-covariance in
  the point estimates across iterations (King et
  al. 2001).
• First stage consistent, asymptotically
  efficient, so estimator should inherent nice
  properties of S-ML and S-GMM, but no proof yet.
• Monte Carlo assessment will follow so will
  direct comparison to Snijders et al. approach
  (near as two models can approx each other).

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1981
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1991
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2001
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Conclusion

• Spatial Spatiotemporal Interdependence
• Important Appreciable Substance (e.g.,
  globalization intl cap-tax compete seems quite
  real does constrain), not Nuisance.
• Therefore Model them. Interpret them.
• How specify estimate models?
• If space-lag is time-lagged, maybe not problem
  but if thry substance says immediate (w/in an
  observational period), can/should handle that
  too
• S-OLS not a bad strategy even then, if ? not too
  big smpl-dims right S-ML, , in some regards,
  IV-based strategies seem effective
• Spatiotemporal Effects not directly read from
  coefficients use graphs response-plots maps
  grids
• Info-demands Galtons Problem big, Coevolution
  ? REALLY big
• Standard errors of effects tend big. Suspect
  delta-method lin-approx. maybe part problem plan
  explore performance sim/boot/jack.
• Max effort care theory, measure, specification,
  to both CIPE

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Thank You!