Interdependence in Comparative International Political Economy by stevenTerrell

VIEWS: 21 PAGES: 77

									        Spatial Econometric Models
            of Interdependence
  Theory & 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
                            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: i‘s actions depend on j‘s. Examples.
   – Theory:
      • General: externalitiesstrategic policy complements/substitutesrace-to-
        bottom/top/elseearly/late-mover advantagesstrategic delay/rush-for-1st
      • Specific: a model of inter-jurisdictional tax-competition (P&T ch. 12)
   – Empirics: ―Galton‘s Problem‖; Estimation, Inference,
     Interpretation, & Presentation
             A Motivating Context:
  Globalization & Domestic-Policy Autonomy
• Standard Argument:
   – ↑ capital mobility & trade integration sharpen capital‘s 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 nec‘ly) 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 C&IPE to notice & incorporate explicitly
• Interdependence (def): yi=f(yj≠i); note: not merely that yi & yj≠i corr
        The Broad Range of Spatial Interdependence
• Theoretical Contexts (ubiquitous):                             • (Simmons et al.‘s 06) Mechanisms:
    –   ANY Strategic Decision-making: sisj                        –   Competition
    –   Externalities & Spillovers                                  –   Coercion
    –   Learning/Emulation, Demonstration                           –   Learning
    –   Networks/Epistemic Communities                              –   Emulation
    –   Literal Diffusion, Contagion, Migration                     –   [Migration/Contagion (F&H Add)]
• Substantive Contexts (ubiquitous):
                                                                   – Policy, instit‘s, regimes diffusion:
    – Security Policy (e.g., alliances, wars)                           • Policy: Schneider&Ingram‗88, Rose ‗93,
    – Environmental (e.g., air-pollution reg)                             Meseguer ‗04,‗05, Gilardi ‗05
    – Regulatory (e.g., telecomm stds)                                  • Institutional or regime: Implicit/Informal:
                                                                          Dahl‘s Polyarchy, Starr‘s Democratic Dominoes,
    – Legis reps‘ votes depend on others‘                                 Huntington‘s 3rd Wave. Explicit/Formal:
                                                                          O‘Loughlin et al. ‗98, Brinks & Coppedge ‗06,
    – Elects., cand. qualities or strategies                              Gleditsch & Ward ‗06, ‘07
    – p(∙)&outs coups (Li&Thompson 75), riots                      – Int‘l diffusion of liberalization:
      (Govea&West 81), revolts (Brinks&Copp 06)                         • Simmons&Elkins 04, 06a, 06b, Eising 02,
    – Contextual effects in micro-behavior:                               Brune et al. 04, Brooks 05…
         •   Braybeck&Huckfeldt 02ab, Cho 03, Huckfeldt et al.     – Globalization & interdependence:
             05, Cho&Gimpel 07, Cho&Rudolph 07, Lin et al 06
                                                                        • Genschel 02, Basinger&Hallerberg 04, Knill
                                                                          05, Jahn 06, Swank 06, F&H 06,07, Kayser 07
• Tobler’s 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)
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:
  –   Dahl’s 1971 Polyarchy (1 of 8 causes dem listed); center-stage Starr’s 1991 ‚Democratic Dominoes‛; Huntington’s 1991 Third Wave; Beissinger 2007;
      Bunce & Wolchik 2006, 2007; et al. in E. Eur. Transitions; Hagopian & Mainwaring 2005 et al. in LA; O’Loughlin 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.

•C&IPE, e.g. globalization≈interdependence:
  – 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.
Substantive & Theoretical Ubiquity & Centrality (2)
• Representatives’ votes (Lacombe & Shaughnessy 2005), citizens’ votes (Huckfeldt & Sprague 1991; O’Laughlin 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: interdep≈definition 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; O’Loughlin 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).
           Policy Interdependence:
 A General Theoretical Model (Brueckner ‘03)
• i‘s utility depends pi & pj b/c interdep (& vv): U i  U i  pi , p j 
• Accordingly, i‘s optimal policy, pi*, depends j‘s action, pj:
                        p ,p                                             0          R p j 
                                                                                   1
       Max U
         pi
                   i
                         i   j     U     i
                                          pi    0    p  U       *
                                                                     i
                                                                            i
                                                                            pi
              pj

• So slope best-response function depends on effect of pj on
  marginal utility of pi: p* R  p j  U ip p           1
                                      i
                                               nd
                                                               i   j
                                                                         ; 2 -order cond.  -                 0
                                   p j         p j        U   i
                                                                pi pi                             U   i
                                                                                                      pi pi

• Therefore: Diminishing returns and…
                                                                                                  pi*
   – …negative externalities =>strategic complements: U                              i
                                                                                              0      0
                                                                                                  p j
                                                                                     pi p j
       • Positive slope: positive feedback/same-signed reactions
   – …positive externalities => strategic substitutes:                                            pi*
                                                                                 U   i
                                                                                              0      0
                                                                                                  p j
                                                                                     pi p j
       • Negative slope: neg. feedback/opposite-signed reactions
           Policy Interdependence:
  General Theory & Substantive Implications
• Dimin returns & neg externalities  Strategic Complements
   –  Race-to-Bottom (RTB) (or -Top). Examples:
      • Tax Competition         j     Uii j (  marg cost  i )   i
      • 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:  S j  Uii j (b/c  securityi )  Si
      • E.g., ALMP:  ALMPj  U A A (b/c  Empi )  ALMPi
                                    i
                                           i   j

   –  Late-mover advantage  strategic delay & Wars of Attrition
• DimRet & both +&– externs:  R j  environi                      Ri (Free - Ride)
   – Environmental Reg‘s (& CHIPs?):  R j   cost Ri   Ri (RTB)
      Figure 2. Best Response Functions: Strategic Substitutes
•p2




                                      p 2  R( p1 )




                     p1  R ( p 2 )




                                                                 •p1
 An International Tax-Competition Model as a
Specific Substantive Example of Interdependence
• Stylized Theoretical Model Cap-Tax Comp. (P&T ‗00, ch.12)
     – 2 jurisdicts, dom & for cap-tax, τk & τk* to fund fixed spend. For-invest mobility costs, M.
     – Inds‘ lab-cap endow, ei, & choose lab-leisure, l & x, & save-invest, s=k+f to max
       ω=U(c1)+c2+V(x), over l, c1, & c2, s.t. time-c., 1+ei=l+x, & b.c.‘s, 1–ei=c1+k+f+≡c1+s
       & c2=(1–τk)k+(1–τk*)f–M(f)+(1–τl)l.
     –  equilibrium economic choices of citizens: s  S ( k )  1  Uc (1   k )
                                                                                   1


                                   f  F ( k , k )  M 1 ( k   k ) k  K ( k , k )  S ( k )  F ( k , k )
                                                 *
                                                         f
                                                                     *                 *                          *

     –  indirect utility, W, defined over policy variables, τl, τk, & τk*:
                                                                                              
W ( l , k )  U 1  S ( k )   1   k  S ( k )   k   k F ( k , k ) M F ( k , k )  1   l  L( l )  V 1  L( l ) 
                                                                  *           *               *


     – 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:

                 S ( kp )  e p                      L( lp )  e p             S ( kp )  2 F* ( kp* , kp ) k 
                                 1   l ( kp )                             1                                    
                    S ( kp )                         L( lp )                             S ( kp )               
•  Best-Response Functions: τk=T(eP,τk*) & τk*=T*(eP*,τk) for dom & for pm.
     – Slopes: ∂T/∂τk* & ∂T*/∂τk, pos or neg b/c ↑τk*  cap-inflow; can use ↑tax-base to ↓τk or
       to ↑τk (seizing upon ↓elasticity base).
     – Background of this slide plots case both positively sloped; illustrated comparative static
       is of leftward shift of domestic government.
      Empirical Models of Interdependence:
         Galton’s Problem in C&IPE
• Interdependence  yi=f(yj)
• Generic (linear) dynamic spatial-lag model of C&IPE:
                                        yit    wij y jt  d βd  sβs   d  s  βds   it
                                                              it      t        it   t
                                                j i

• Galton’s Problem: Extremely difficult disting why C(yi,yj) b/c...
   – 1. Correlated domestic/unit-level conditions, d (CPE)
   – 2. Common/corr’d 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 C&IPE
   – 4. Interdependence/diffusion/contagion: yi=f(yj,CC-CPE), substance C&IPE
• Upshot Empirically (Franzese & Hays ‗03,‗04,‗06ab,‗07abcd,‗08ab):
   – ° omit or mis-specify CPE, tend over-estimate IPE (interdependence) & v.v.
   – yiyj => textbook endogeneity/simultaneity problem w/ spatial lag; analogous:
       • ° fail redress endog sufficiently  mis-est (usu. over-est.) ρ  (under)mis-est. β
   – Most Important Conclusion: Model It!TM Insofar as omit or rel‘ly 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 >> simultaneity bias in any of practical examples we‘ve
         considered, & S-OLS did OK our MCs provided interdep remained modest (|ρ|<.3±).
                 The Terms of Galton’s Problem:
           Omitted-Variable vs. Simultaneity Biases in
           Spatial- and Spatio-Temporal-Lag Models
               y  Qδ  ε, where Q   Wy x and δ                                       
• OVB (rel. mis-spec.) v. simultaneity:
                              ˆ              cov( Wy, x)
     – OVB        (OLS): plim OLS                  ;                OLS  0
                                                                          ˆ
                                               var(x)
     – SimB (S-OLS):plim δ
                         ˆ                          1  cov  Wy, ε   var( x )                        QQ 
                                                                                      where Ψ  plim      
                                                    Ψ   cov  Wy, ε   cov( Wy, x ) 
                                       S-OLS
                                                                                                            n 
     – In S-T, little more complicated, but:                                                        
                                                                                 
                                                                                 ˆ           0
                                                                                                     
                                                                                ˆ 
y  Qδ  ε where Q   Wy My X  and δ     β                       OVB:        FMy,X  
                                                                                               Wy

                                                                                                   1
                     QQ  Qε 
                               1
                                                                               β 
                                                                                 β   FMy,X  
        ˆ
 plim δ  δ  plim                  , which, with X = x,                     ˆ             Wy
                             
                     n  n 
                                                                                                 2

                      cov  Wy , ε   var  My   var  x      With all positive S-T dep, ρ
                   1                                                
 plim δ     
        ˆ
              Ψ      cov  Wy, ε   cov  Wy, My   var  x   space-dep over-est‘d & 
             
                     cov  Wy , ε   cov  Wy, x   var  My   time-dep & β under-est‘d
                                                                    
Estimating Spatial/Spatio-Temporal-Lag Models
• Inconsistent Estimators:
  – Omit spatial-dep (e.g., OLS): bad idea if ρ non-negligible
  – Ignore simultaneity (e.g., S-OLS): could be OK (in MSE)
    if ρ 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
 Estimating Spatial- & Spatio-Temporal-
       Dynamic Models by S-ML
• S-ML for Spatial-Lag Model:                                                     NT

                                                                        1       εε 
                                                                                   2

         y   Wy  XB  ε  ε   I   W  y  Xβ  Ay  Xβ  L(ε)   2  exp   2 
                                                                         2    2 
  – Std, but ε → y by |A| not 1  computational issues, plus
                                                           NT

                                                     1 2     1                            
                                       L(y ) | A |  2  exp   2  Ay  Xβ   Ay  Xβ  
                                                      2    2                           
• Conditional S-ML S-T (ie., given 1stobs, Nx1 form);
  (unconditional is messy but exists; won‘t show):
                                     1
                                     2
                                                      2                            1 T
        ln f yt ,yt1 ,...,y 2 y1   N T  1  ln 2  T  1  ln I   W  2  εεt
                                                                                   2 t  2
                                                                                               t


        where εt  y t   WN y t  Xt β   I N y t 1 ; was just: ε t  y t   WN y t  Xt β
• Stationarity (if row-stdzd, & ρ,>0): ρ+<1
• Spatial Probit: complicated but doable (show if time)
• m-STAR & Est‘d W; endog W: doable (show if…)
           Figure 1: Estimated Bias in  Plotted Against True 
                                       ˆ
              Across Representative NxT Sample-Dimensions




Notes: Dashed Line: S-OLS. Dotted Line: S-2SLS-IV. Dashed-Dotted Line: S-ML
                                             ˆ
                        Figure 2: Estimated  S Plotted Against True 
                        Across Representative NxT Sample-Dimensions




  Notes: Solid Line: Non-spatial OLS. Dashed Line: S-OLS. Dotted Line: S-2SLS-IV. Dashed-
Dotted Line: S-ML. Non-Spatial OLS results plotted against the larger-scale 2nd y-axis on the right.
      Figure 3: RMSE  Plotted Against True  Across Representative
                      ˆ
               NxT Sample-Dimensions (BIAS+EFFICIENCY)




Notes: Dashed Line: S-OLS. Dotted Line: S-2SLS-IV. Dashed-Dotted Line: S-ML.
                              ˆ
             Figure 4: RMSE  S Plotted Against True  Across Representative
                       NxT Sample-Dimensions (BIAS+EFFICIENCY)




Notes: Solid line: Non-spatial OLS. Dashed Line: S-OLS. Dotted Line: S-2SLS-IV. Dashed-Dotted
   Line: S-ML. Non-spatial OLS results plotted against the larger-scale 2nd y-axis on the right.
                Figure 5: Standard-Error  Accuracy Plotted Against True 
                                         ˆ
                       Across Representative NxT Sample-Dimensions




Notes: Dashed Line: S-OLS. Dotted line: S-2SLS-IV. Dashed-Dotted Line: S-ML. Standard error
accuracy is gauged by the ratio of the average estimated standard error to the true standard deviation
of the sampling distribution. Values less than one indicate overconfidence.
                                        ˆ
              Figure 6: Standard-Error  S Accuracy Plotted Against True 
                      Across Representative NxT Sample-Dimensions




Notes: Solid Line: Non-spatial OLS. Dashed Line: S-OLS. Dotted line: S-2SLS-IV. Dashed-
Dotted Line: S-ML. Standard error accuracy is gauged by the ratio of the average estimated
standard error to the sampling-distribution standard deviation. Values less than one indicate
overconfidence.
                            APPLICATIONS
• Globalization, Tax Competition, & Domestic Policy
   – Replicates: Swank&Steinmo 02, Hays 03, Basinger&Hallerberg 04
• ALMP: Active-Labor-Market Policy in EU (F&H ‗06)
   – DepVar: LMT spend per unemployed worker
   – Hypoth: Positive spillovers (@ 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: Hypoth—―states as laboratories‖≈diffusion by learning
       • DepVar: max monthly AFDC benefit
       • Ind Vars: state‘s 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: Hypoth—―states as laboratories‖≈diffusion by learning
       • DepVar: 1 if state‘s CHIP includes monthly premium; IndVars same.
 Practical Model Specification & Estimation
• Most convenient to work in (Nx1) vector form:
                                                                   y t   y t 1   Wy t  Xt β  εt
• WN=an NxN of (time-invariant) spatial wts, wij, & WNIT gives W.
• E.g., 15x15 binary-contiguity from ALM paper:
                              AUT   BEL   DEN   FIN   FRA DEU GRE   IRE   NTH   NOR   PRT   ESP   SWE CHE   GBR
                        AUT    0     0     0     0     0   1   0     0     0     0     0     0     0   1     0
                        BEL    0     0     0     0    1    1   0     0     1     0     0     0     0   0     1
                        DEN    0     0     0     0    0    1   0     0     0     0     0     0     1   0     0
                        FIN    0     0     0     0    0    0   0     0     0     1     0     0     1   0     0
                        FRA    0     1     0     0    0    1   0     0     0     0     0     1     0   1     1
                        DEU    1     1     0     0    1    0   0     0     1     0     0     0     0   1     0
                        GRE    0     0     0     0    0    0   0     0     0     0     0     0     0   0     0
                   W
                        IRE    0     0     0     0    0    0   0     0     0     0     0     0     0   0     1
                        NTH    0     1     0     0    0    1   0     0     0     0     0     0     0   0     1
                        NOR    0     0     0     1    0    0   0     0     0     0     0     0     1   0     0
                        PRT    0     0     0     0    0    0   0     0     0     0     0     1     0   0     0
                        ESP    0     0     0     0    1    0   0     0     0     0     1     0     0   0     0
                        SWE    0     0     1     1    0    0   0     0     0     1     0     0     0   0     0
                        CHE    1     0     0     0    1    1   0     0     0     0     0     0     0   0     0
                        GBR    0     1     0     0    1    0   0     1     1     0     0     0     0   0     0
   – N.b., row-stdz typ., convenient, but not nec‘ly subst‘ly neutral
   – Ideally, substance, which not nec‘ly  geography, in W.
• Beware of extant software: critical bug in LeSage‘s MatLab code;
  likelihood in some third-party Stata SAR code seems flat wrong.
 Swank & Steinmo APSR ’02 Replication
                     Table 2. Reanalysis of Swank and Steinmo (2002, Appendix Table 2)
                                        Effective Tax Rate on Capital                    Effective Tax Rate on Labor
                                Swank and        Reanalysis     Reanalysis       Swank and       Reanalysis     Reanalysis
                                 Steinmo              (1)            (2)          Steinmo             (3)            (4)
      Temporal Lag                0.809**          0.808**        0.864**          0.671**          0.66**       0.711**
                                                    (0.05)        (0.048)                          (0.054)        (0.054)
        Spatial Lag                                 0.104*        0.126**                           0.017           0.05
                                                   (0.054)        (0.054)                          (0.058)        (0.055)
      Liberalization               1.146            1.235*         0.629           -.261**        -0.255**        -0.168*
                                                   (0.725)        (0.702)                          (0.102)        (0.091)
          Trade                    -0.018           0.009          0.005            -0.009          0.001          -0.001
                                                   (0.064)        (0.061)                          (0.023)        (0.023)
 Structural Unemployment         -1.147**         -1.218**       -1.033**         -0.359**         -0.38**         -0.148
                                                   (0.306)        (0.283)                          (0.189)        (0.189)
    Public Sector Debt            0.089**          0.099**         0.046           0.053**         0.056**       0.038**
                                                   (0.036)        (0.032)                          (0.014)        (0.013)
    Elderly Population            1.264**           1.011          -0.08            -0.018           0.03          0.171
                                                   (0.615)        (0.481)                           (0.23)        (0.184)
          Growth                  0.230*            0.242         0.307**           -0.008          -0.009         0.009
                                                   (0.151)        (0.147)                          (0.051)        (0.051)
 Percent Change in Profits        0.127**          0.136**        0.174**
                                                   (0.055)        (0.054)
   Domestic Investment             0.066            0.045          0.059
                                                   (0.055)        (0.049)
         Inflation                                                                0.115**         0.115**           0.063
                                                                                                   (0.05)          (0.043)
      Unemployment                                                                0.280**         0.296**          0.144*
                                                                                                  (0.084)          (0.079)
     Left Government             0.018**          0.018*            0.012         0.008**         0.008**          0.007*
                                                   (0.01)           (0.01)                        (0.004)          (0.004)
Christian Dem. Government        0.041**           0.035             0.01           0.001          0.002            0.009
                                                  (0.028)          (0.026)                        (0.011)           (0.01)
       Fixed Effects
          Country                   Yes             Yes              Yes              Yes            Yes              Yes
                                                        1                                                1
            Year                    Yes             Yes               No              Yes           Yes               No
             R2                     .928            .922             .914             .989          .989             .988
1
  Biannual Period Effects. Parentheses contain standard errors. **Significant at the 5% Level; *Significant at the 10% Level.
                               Hays IO ‘03 Replication
Table 1. Capital Tax Rates and International Capital Mobility (Capital Account Openness)
                                 Capital Account       Capital Account      Capital Account     Capital Account   Capital Account   Capital Account
Independent Variables              Openness              Openness             Openness            Openness          Openness          Openness

Capital Mobility                     1.918**               2.223**              2.159**              1.620*           1.695*            1.729*
                                      (.919)                (.930)              (1.045)              (.859)           (.996)            (1.013)
Capital Mobility
 Interacted with:

     Capital Endowment                -.070*                -.069*              -.069**               -.033           -.0425             -.048
                                        (.040)              (.040)               (.033)              (.039)           (.030)              (.040)

     Consensus Democracy               .484                 .746*                 .691              1.245***         1.053**           1.121**
                                       (.431)               (.434)                (.472)              (.428)          (.485)            (.534)

     Corporatism                      -1.186                -2.229               -2.008             -3.047**         -2.578*             -2.453
                                       (1.339)             (1.359)                (1.399)            (1.318)         (1.357)            (1.641)

     Left Government                  .370*                  .286                 .304                .304             .321              .331
                                      (.196)                (.195)                (.209)             (.186)           (.196)             (.215)

     Population                      -1.79e-07           -9.77e-06**           -7.74e-06*           5.79e-07         3.88e-07            .001
                                    (3.49e-06)            (3.98e-06)           (4.03e-06)          (3.30e-06)       (3.60e-06)           (.004)

     European Union                   -.204                -.465***             -.410**             -.520***         -.440**           -.442***
                                       (.161)                (.170)              (.185)               (.161)          (.176)             (.168)

Temporal Lag                         .834***               .754***              .771***             .686***          .723***           .706***
                                      (.034)                (.039)               (.028)              (.043)           (.031)            (.038)

Spatial Lag                                                    .280***             .221***            .316***        .237***           .267***
                                                                (.066)               (.048)            (.049)         (.035)            (.044)
Obs.                                      465                    465                 465                465            465               465
Estimation                        Non-spatial OLS           Spatial OLS         Spatial 2SLS        Spatial OLS    Spatial 2SLS       Spatial ML
Diffusion                                                      Uniform            Uniform          Non-uniform     Non-uniform       Non-uniform
Notes: The regressions were estimated with fixed country effects. (Coefficients for country dummies not shown.)
Parentheses for the OLS estimates contain panel corrected standard errors.
Parentheses for the 2SLS estimates contain robust standard errors clustered by year.
Parentheses for the ML estimates contain robust standard errors.
** * Significant at 1%, ** Significant at 5%, * Significant at 10%
Basinger & Hallerberg APSR ’04 Replication
      Table 1. Replication and Reanalysis of Basinger and Hallerberg
                              APSR
       Partisanship            -2.17          -1.83            -1.83             -1.71
                              (1.58)         (2.05)           (1.93)            (1.91)
   Partisanship world        -11.2**        -11.88*          -11.87*           -10.23*
                              (3.39)         (5.32)           (5.01)            (5.03)
     Capital controls          1.30           1.84             1.84               2.02
                              (2.70)         (2.49)           (2.34)            (2.32)
  Capital controls world      6.35*         27.15*           27.27*             23.18*
                              (3.50)        (13.39)          (12.53)           (12.53)
   Ideological distance      -3.05**          -2.47            -2.47            -2.85*
                              (1.46)         (1.77)           (1.67)            (1.67)
Ideological distance world    9.11*           2.65             2.63               2.55
                              (4.72)         (3.30)           (3.10)            (3.07)
Change in capital taxation      .20*           .03              .02               .10*
 in competitor countries       (.09)          (.28)            (.18)             (.05)

    Control Variables
        Intercept            16.94**         18.18**          18.16**           17.42**
                              (3.05)          (3.40)           (3.19)            (3.17)
      Tax Ratet-1             -.29**          -.29**           -.29**            -.29**
                               (.06)           (.04)            (.04)              (.04)
       Growtht-1              .27**           .32**            .33**              .30**
                               (.10)           (.12)            (.11)              (.11)
      Inflationt-1              -.00            -.00             -00                -.00
                               (.01)           (.02)            (.01)              (.01)
           N                    269             269              269                269
        R2 / LL                 .34             .32           -670.83           -668.99
       Estimator             S-OLS           S-OLS             S-ML              S-ML
                            Incorrect        Correct          Correct            Binary
     Weights Matrix            GDP             GDP              GDP            Contiguity
                             Weights         Weights          Weights           Weights
        Notes: The country dummy variable   coefficients are omitted to save space.
Beck, Gleditsch, Beardsley ISQ ‘06 Replication
                              Beck et al.       Beck et al.     Reanalysis (1)           Reanalysis (2)         Reanalysis (3)
                                0.03**            0.02**            -0.001                  0.029**                0.028*
       LN GDP A
                                 (.01)             (.01)            (.012)                   (.015)                 (.016)
                                0.04**            0.03**            -0.001                   -0.015                 -0.003
       LN GDP B
                                 (.01)             (.01)            (.012)                   (.015)                 (.016)
                                 0.02             0.04**           0.064**                   0.012                  0.056
       LN POP A
                                 (.02)             (.02)            (.023)                    (.06)                 (.065)
                                 0.02              0.03            0.056**                   0.031                  0.059
       LN POP B
                                 (.02)             (.02)            (.023)                   (.055)                 (.059)
                               -0.03**           -0.04**          -0.043**                   0.014                  -0.004
      LN Distance
                                 (.01)             (.01)            (.009)                   (.073)                 (.072)
                                0.13**             0.11              0.05                    -0.053                 -0.063
       LN Tau-b
                                 (.06)             (.06)            (.058)                    (.06)                  (.06)
                                0.13**            0.14**           0.155**                  0.143**                0.089**
     LN Democracy
                                 (.03)             (.03)            (.031)                   (.034)                 (.037)
                               -0.20**           -0.20**           -0.19**                 -0.186**               -0.157**
        LN MID
                                 (.04)             (.04)            (.037)                   (.039)                 (.039)
                               -0.30**           -0.28**          -0.229**                 -0.157**                 -0.055
     LN Multipolar
                                 (.05)             (.05)            (.053)                   (.053)                 (.056)
                                 -0.06             -0.04            -0.011                   0.054                  0.032
       LN Bipolar
                                 (.05)             (.05)            (.048)                   (.053)                 (.055)
                                0.92**            0.91**           0.901**                  0.795**                0.825**
     Temporal Lag
                                 (.01)             (.01)            (.007)                    (.01)                  (.01)
                                                  0.02**            0.07**                   0.18**                .097**
       Spatial Lag
                                                   (.01)            (.012)                   (.014)                 (.039)
      Fixed Effects:             No                 No                No                      Dyad                Dyad, Yr
   Contemporaneous
                                 No                No                Yes              Yes              Yes
       Spatial Lag
        Estimator               OLS               OLS                ML               ML                ML
      Observations              2565              2565              2565             2565              2565
     Log-Likelihood              —                 —                31.57           140.71            282.68
       LR Statistic                                                               218.28**          283.94**
 Notes: Parentheses contain standard errors. **, * = significant at 5%, 10% levels, respectively. The Likelihood
 Ratio (LR) Statistics evaluate the null hypotheses that the coefficients on the dyad dummies (41) and year
 dummies (67) are jointly zero with 5% critical values of 56.94 (    d . f . 41 ) and 87.11 (  d . f .67 ) respectively.
                                                                      2                           2
Franzese & Hays EUP ‘06
             Volden AJPS ‘06 AFDC Replication
                          Table 1. State Welfare Policy (Maximum AFDC Benefit)
                                       Spatial AR Lag     Spatial AR Lag      Spatial AR Lag     Spatial AR Lag      Spatial AR Error
ependent Variables          OLS           (S-OLS)           (S-2SLS)            (S-GMM)            (S-MLE)              (S-MLE)
         Constant         54.519           -246.76            -422.09             -500.05           -156.282             676.120
                        (531.830)         (450.75)           (437.74)            (413.02)          (429.130)            (471.965)
      Poverty Rate         -6.560            8.04              13.205               7.29               3.657               3.239
                         (11.262)         (10.022)            (9.977)             (8.452)             (8.917)            (10.062)
       Retail Wage          -.121            .016                .089               -.008               -.025               -.344
                           (.226)           (.193)             (.187)              (.201)              (.181)              (.243)
vernment Ideology           1.513           1.397              1.359*            1.655**              1.432*             1.696**
                          (1.030)           (.863)             (.825)              (.761)              (.806)              (.822)
-party Competition      621.799**           368.65             286.98            438.9**           444.677*              263.887
                        (290.871)         (250.55)           (243.72)            (197.47)          (226.911)            (238.419)
        Tax Effort       3.357**            2.022               1.553              2.397              2.423*             2.936**
                          (1.587)          (1.364)            (1.328)             (1.493)             (1.262)             (1.213)
     Federal Share         -4.405           -5.818             -6.012              -3.654              -5.393             -6.882*
                          (5.001)           (4.20)            (4.014)             (3.415)             (3.901)             (4.099)
        Spatial AR                        .767***           1.069***             .840***             .537***             .565***
                                            (.178)             (.232)              (.237)              (.122)              (.131)
  Moran I-statistic     3.312***

            LM        12.322***

             LM        11.606***
                *
             LM         6.477**

             LM        5.845***
                *
             LM           .716
    Log-likelihood                                                                                    -270.763             -272.728
            Adj.-R2         .461              .622               .595                .606                .510                .588
                Obs.         48                48                  48                 48                  48                  48
s: The spatial lags are generated with a binary contiguity weighting matrix. All the spatial weights matrices are row-standardized.
                 ***Significant at the 1% Level; **Significant at the 5% Level; *Significant at the 10% Level.
         Volden AJPS ‘06 CHIPs Replication
le 2. State Welfare Policy (Monthly CHIP Premium)
                                      Probit                  Probit               Spatial AR              Spatial AR
 Independent Variables                 MLE                   MCMC                  Lag Probit              Error Probit
             Constant                 -4.978                  -5.163                  -5.606                   -5.531
                                     (6.260)                 (6.292)                (10.159)                  (7.337)
           Poverty Rate                -.244                 -.265**                 -.374**                   -.243*
                                      (.153)                  (.156)                  (.231)                   (.157)
            Retail Wage                .004                    .004*                   .006*                    .004*
                                      (.003)                  (.003)                  (.004)                   (.003)
 Government Ideology                   .011                     .011                    .014                     .014
                                      (.013)                  (.013)                  (.020)                   (.014)
Inter-party Competition               2.174                    2.108                   1.473                    2.636
                                     (3.388)                 (3.478)                 (6.134)                  (3.794)
              Tax Effort               -.014                   -.014                   -.020                    -.017
                                      (.019)                  (.019)                  (.034)                   (.021)
          Federal Share                .045                     .048                    .065                     .043
                                      (.063)                  (.064)                  (.095)                   (.066)
              Spatial AR               .079                     .102                .200***                  .297***
                                      (.798)                  (.815)                  (.148)                   (.196)
              Pseudo-R2                .222                     .220                    .607                     .574
                   Obs.                  48                      48                      48                       48
  Notes: In the first two columns, the models are estimated assuming the spatial lags are exogenous. The model in the first
  column is estimated using standard ML techniques. The parentheses in this column contain estimated standard errors and
  the hypothesis tests assume that the asymptotic t-statistics are normally distributed. The models in columns two through
  four are estimated using MCMC methods with diffuse zero-mean priors. The reported coefficient estimate is the mean of
  the posterior density based on 10,000 observations after a 1000 observation burn-in period. The number in parentheses is
  the standard deviation of the posterior density. The p-values are also calculated using the posterior density. The last two
  models are estimated with true spatial estimators described in the text. In third column, 30 of the 10,000 spatial AR
  coefficients sampled from the posterior distribution were negative. In the fourth column, none of the 10,000 sampled
  spatial AR coefficients were negative. ***p-value <.01, **p-value<.05, *p-value <.10.
 Interpreting Spatial/Spatio-Temporal Effects
• The Model: y             Wy   My  Xβ  ε
   – 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:
                                y t   WN y t   y t 1  Xt β  ε t
   – Coefficients, βx are just pre-spatial, pre-temporal—and
     wholly unobservable!—impulse from some x to y.
• Spatio-Temporal Effects:
   – Post-spatial, pre-temporal “instantaneous effect” of x:
    I N   WN   Xt β  εt  xi for some (set of) i; i.e.,  I N   WN  xciβ
                   1                                                           1
                                                                                   k

                                                    y t   I N   WN 
                                                                    y t 1  Xt β  εt 
                                                                       1
   – Spatio-Temporal Response Paths:
   – LR Multiplier/LR-SS:y t   Wy t   y t  Xt β  εt    W   I  y t  Xt β  εt
                              I N   W   I N   Xt β  ε t 
                                                   1
Presenting Spatial/Spatio-Temporal Effects
• Standard Errors (Confidence Intervals &
  Hypothesis Tests) of Effects:
                                 ˆ ˆ
                               si  k      si  k 
                                                ˆ ˆ
                      
                    ˆ ˆ
  – Delta Method: V si  k   
                                    ˆ
                                 θ 
                                           
                                           ˆ
                                        V θ  ˆ 
                                             θ 
  – …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
Swank & Steinmo APSR ’02 Replication
Swank & Steinmo APSR ’02 Replication
  Figure 2. Spatio-Temporal Effects on the German Capital Tax Rate from a Positive One-Unit
             Counterfactual Shock to Structural Unemployment in Germany (with a 90% C.I.)
    0.2


     0


   -0.2


   -0.4


   -0.6
                                                      Cumulative 15-Period Effect: -6.523
   -0.8


     -1


   -1.2


   -1.4


   -1.6


   -1.8


     -2
          1    2     3    4     5     6    7     8     9     10     11     12     13        14   15
Swank & Steinmo APSR ’02 Replication
 Figure 3. Spatio-Temporal Effects on the French Capital Tax Rate from a Positive One-Unit
            Counterfactual Shock to Structural Unemployment in Germany (with a 90% C.I.)
    0.1




   0.05




     0

                                                      Cumulative 15-Period Effect: -.943

  -0.05




   -0.1




  -0.15




   -0.2
          1    2    3     4     5    6     7     8     9     10     11     12     13       14   15
Basinger & Hallerberg APSR ’04 Replication
     Table 2. Conditional Coefficients for the Effects of a Change in Tax
     Rates on Capital in Competitor Countries Given Domestic
     Ideological Distance (Mendoza et al. Tax Rates, GDP Weights)
     Ideological Distance                      APSR
     Regression Coefficients
     Coefficient, change in competitor         .24*      .38       -.13      .15*
     countries                                 (.12)    (.28)     (.29)      (.08)
     Coefficient, change in competitor          -.52    -1.12      .86        -.24
     countries*distance, party, cap controls   (.60)   (1.08)    (1.31)      (.29)

     Conditional Coefficients
     0 distance                                .24*      .38       -.13      .15*
     (United Kingdom, 1980-97)                 (.12)    (.28)     (.29)      (.08)
     0.1 distance                              .19*      .27       -.04      .13*
     (Denmark, 1991-92)                        (.08)    (.22)     (.21)      (.06)
     0.2 distance                              .14*      .16       .04       .10*
     (Netherlands, 1982-88)                    (.08)    (.20)     (.19)      (.05)
     0.3 distance                                .09     .04       .13        .08
     (Italy, 1981)                             (.11)    (.24)     (.25)      (.06)
     0.5 distance                               -.02     -.18      .30        .03
     (Finland, 1996-97)                        (.21)    (.40)     (.47)      (.10)

     Estimator                                 S-OLS     S-OLS    S-ML       S-ML
                                             Incorrect Correct   Correct    Binary
     Weights Matrix                             GDP       GDP     GDP      Contiguity
                                              Weights Weights    Weights    Weights
     Notes: See Basinger and Hallerberg (2004), Table 3.
 Basinger & Hallerberg APSR ’04 Replication
Table 3. Conditional Coefficients for the Effects of a Change in Tax
Rates on Capital in Competitor Countries Given Domestic
Partisanship Level (Mendoza et al. Tax Rates, GDP Weights)
Partisanship                              APSR
Regression Coefficients
Coefficient, change in competitor          -.24   1.39*       -.83       -.11
countries                                 (.40)    (.71)     (.89)      (.21)
Coefficient, change in competitor           .67   -2.13*     1.47         .40
countries*distance, party, cap controls   (.63)   (1.21)    (1.52)      (.37)

0 partisanship                             -.24   1.39*       -.83       -.11
(no country)                              (.40)   (.71)      (.89)      (.21)
0.2 partisanship                           -.10    .96*       -.54       -.03
(Norway, 1989)                            (.27)   (.48)      (.60)      (.14)
0.4 partisanship                            .03    .53*       -.24        .05
(Netherlands, 1982-88)                    (.16)   (.28)      (.32)      (.07)
0.6 partisanship                          .16*      .10       .05       .13*
(Austria, 1987-97)                        (.07)   (.21)      (.19)      (.06)
0.8 partisanship                          .30*     -.32       .35       .21*
(Ireland, 1990-92)                        (.13)   (.36)      (.39)      (.11)
                                                                                   Table 4. Conditional Coefficients for the Effects of a Change in Tax
Estimator                               S-OLS       S-OLS    S-ML       S-ML       Rates on Capital in Competitor Countries Given Domestic Use of
                                       Incorrect Correct    Correct    Binary      Capital Controls (Mendoza et al. Tax Rates, GDP Weights)
Weights Matrix                           GDP         GDP     GDP      Contiguity   Capital Controls                          APSR
                                        Weights Weights     Weights    Weights     Regression Coefficients
Notes: See Basinger and Hallerberg (2004), Table 4.                                Coefficient, change in competitor         .26*      .11       .16        .08
                                                                                   countries                                 (.10)    (.28)     (.21)      (.06)
                                                                                   Coefficient, change in competitor          -.96     .60      -1.88       .20
                                                                                   countries*distance, party, cap controls   (.76)   (1.86)    (1.51)      (.33)

                                                                                   0 capital controls                        .26*      .11        .16       .08
                                                                                   (United States, 1980-97)                  (.10)    (.28)     (.21)      (.06)
                                                                                   0.25 capital controls                       .02     .26       -.31      .13*
                                                                                   (France, 1980-89)                         (.14)    (.35)     (.33)      (.07)
                                                                                   0.5 capital controls                       -.22     .41       -.78       .18
                                                                                   (Portugal, 1980-85)                       (.32)    (.77)     (.68)      (.14)
                                                                                   0.75 capital controls                      -.46     .56      -1.25       .23
                                                                                   (Greece, 1981)                            (.50)   (1.23)    (1.05)      (.22)

                                                                                   Estimator                                S-OLS      S-OLS   S-ML        S-ML
                                                                                                                           Incorrect Correct   Correct    Binary
                                                                                   Weights Matrix                            GDP        GDP     GDP      Contiguity
                                                                                                                           Weights Weights     Weights    Weights
                                                                                   Notes: See Basinger and Hallerberg (2004), Table 5.
  Beck, Gleditsch, Beardsley ISQ ‘06 Replication
Figure 1: Temporal Effects with Spatial Feedback (E.g., US Exports to Russia response to US-Russia MID)


       0


   -0.05


    -0.1


   -0.15


    -0.2


   -0.25
             1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
 Beck, Gleditsch, Beardsley ISQ ‘06 Replication
Figure 2: First Order Spatio-temporal Effects (E.g., US Exports to Germany response to US-Russia MID)


    0.001
   0.0005
        0
  -0.0005
   -0.001
  -0.0015
   -0.002
  -0.0025
   -0.003
  -0.0035
   -0.004
  -0.0045
               1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
  Beck, Gleditsch, Beardsley ISQ ‘06 Replication
Figure 3: 2nd-Order Spatio-temporal Effects (E.g., German Exports to Russia response to US-Russia MID)


    6.00E-04
    4.00E-04
    2.00E-04
   0.00E+00
   -2.00E-04
   -4.00E-04
   -6.00E-04
   -8.00E-04
   -1.00E-03
   -1.20E-03
   -1.40E-03
   -1.60E-03
                   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
                                   Franzese & Hays EUP ‘06
Table 2. Short-Run Spatial Effects of Labor Market Training Expenditures in Europe (Binary Contiguity Weights Matrix)
          AUT          BEL        DEN          FIN         FRA         DEU         IRE        NTH          NOR          PRT         ESP         SWE         CHE         GBR
                     0.005*       0.006       0.000      0.020*      -0.135*      0.000      0.006*        0.000       0.000       -0.001      -0.001     -0.140*      -0.002
AUT                  (.0019)     (.0031)     (.0001)     (.0095)     (.0317)     (.0001)     (.0029)      (.0001)     (.0002)     (.0009)     (.0007)     (.0338)     (.0015)
         0.002*                  0.003*       0.000      -0.066*     -0.064*     0.005*      -0.065*       0.000      -0.001*     0.004*       0.000       0.006*     -0.064*
BEL     (.0010)                  (.0014)     (.0000)     (.0152)     (.0142)     (.0021)     (.0144)      (.0000)     (.0004)     (.0019)     (.0003)     (.0029)     (.0142)
         0.006       0.006*                  0.012*      0.006*      -0.148*      0.000      0.007*       0.012*       0.000       0.000      -0.148*      0.006*      -0.001
DEN (.0031)         (.0029)                  (.0058)     (.0030)     (.0383)     (.0001)     (.0033)      (.0058)     (.0001)     (.0003)     (.0387)     (.0026)     (.0011)
         0.000       0.000      0.012*                    0.000       -0.002      0.000       0.000       -0.134*      0.000       0.000      -0.129*       0.000       0.000
FIN     (.0001)     (.0083)     (.0058)                  (.0001)     (.0013)     (.0000)     (.0001)      (.0314)     (.0000)     (.0000)     (.0294)     (.0001)     (.0000)
         0.008*     -0.053*      0.002        0.000                  -0.051*     0.004*      0.010*        0.000      0.009*      -0.061*      0.000      -0.057*     -0.057*
FRA     (.0038)     (.0122)     (.0012)      (.0000)                 (.0120)     (.0020)     (.0049)      (.0000)     (.0044)     (.0164)     (.0003)     (.0143)     (.0144)
        -0.045*     -0.043*     -0.049*      -0.001*      -0.043*                -0.001      -0.046*      -0.001*      0.000      0.003*       0.007      -0.040*      0.010*
DEU (.0106)         (.0095)     (.0128)      (.0004)      (.0100)                (.0005)     (.0114)      (.0004)     (.0003)     (.0012)     (.0036)     (.0081)     (.0049)
         0.000       0.018*      0.000        0.000       0.020*        -0.004               0.020*        0.000       0.000       -0.001      0.000       -0.001     -0.294*
IRE     (.0003)     (.0084)     (.0002)      (.0000)      (.0099)      (.0031)               (.0097)      (.0000)     (.0002)     (.0009)     (.0000)     (.0007)     (.0755)
         0.004*     -0.086*      0.004        0.000       0.017*       -0.093*     0.007*                  0.000       0.000       -0.001     -0.001*      0.003*     -0.093*
NTH (.0020)         (.0192)     (.0022)      (.0001)      (.0082)      (.0227)     (.0032)                (.0001)     (.0001)     (.0007)     (.0005)     (.0010)     (.0231)
         0.000       0.000      0.012*       -0.134*       0.000        -0.002      0.000        0.000                 0.000       0.000      -0.129*       0.000       0.000
NOR (.0001)         (.0001)     (.0058)      (.0314)      (.0001)      (.0013)     (.0000)      (.0001)               (.0000)     (.0000)     (.0294)     (.0001)     (.0000)
         0.000       -0.002      0.000        0.000        0.043        -0.002      0.000        0.000      0.000                 -0.298*      0.000       -0.002      -0.002
PRT     (.0003)     (.0016)     (.0001)      (.0000)      (.0220)      (.0016)     (.0002)      (.0004)    (.0000)                (.0788)     (.0000)     (.0018)     (.0018)
         -0.001      0.008*      0.000        0.000       -0.152*      0.008*      -0.001*       -0.002     0.000     -0.149*                  0.000        0.008       0.008
ESP     (.0009)     (.0038)     (.0003)      (.0000)      (.0411)      (.0037)     (.0004)      (.0011)    (.0000)    (.0394)                 (.0001)     (.0043)     (.0043)
        -0.001*     -0.001*     -0.099*      -0.086*      -0.001*       0.014       0.000       -0.001*    -0.086*     0.000        0.000                 -0.001*       0.000
SWE (.0005)         (.0004)     (.0258)      (.0196)      (.0004)      (.0073)     (.0000)      (.0005)    (.0196)    (.0000)      (.0000)                (.0004)     (.0001)
        -0.093*      0.009*     0.004*        0.000       -0.095*      -0.080*      0.000        0.003      0.000      -0.001      0.006*      -0.001*                 0.005*
CHE     (.0225)     (.0039)     (.0017)      (.0000)      (.0238)      (.0161)     (.0002)      (.0010)    (.0000)    (.0006)      (.0029)     (.0004)                (.0021)
         -0.001     -0.064*      -0.001       0.000       -0.071*       0.015      -0.074*      -0.070*     0.000     -0.001*       0.004       0.000       0.003
GBR (.0007)         (.0142)     (.0005)      (.0000)      (.0180)      (.0073)     (.0189)      (.0173)    (.0000)    (.0004)      (.0021)     (.0001)     (.0016)
Notes: The off-diagonal elements of the table report the effect of a one-unit increase in the column country‘s labor-market-training expenditures on its European counterparts.
These numbers are calculated using the spatial multiplier matrix (I  ρW) 1 and thus reflect all feedback effects. Parentheses contain standard errors calculated by the delta
method.
                               Franzese & Hays EUP ‘06
Table 3. Steady-State Spatial Effects of labor Market Training Expenditures in Europe (Binary Contiguity Weights Matrix)
                AUT         BEL       DEN         FIN        FRA        DEU        IRE        NTH        NOR           PRT        ESP      SWE       CHE        GBR
                           0.027      0.052      0.002      0.159     -0.530*     0.005      0.050       0.002         0.006    -0.021    -0.016   -0.557*     -0.033
AUT                       (.0136)    (.0296)    (.0024)    (.0914)    (.1588)    (.0050)    (.0292)    (.0024)       (.0067)   (.0189)   (.0134)   (.1663)    (.0277)
                 0.013                0.023      0.001     -0.254*    -0.238*     0.033     -0.236*      0.001        -0.009     0.033    -0.007     0.047    -0.237*
BEL             (.0068)              (.0125)    (.0010)    (.0723)    (.0636)    (.0167)    (.0581)    (.0010)       (.0079)   (.0204)   (.0058)   (.0237)    (.0636)
                 0.052       0.047               0.094      0.051     -0.640*     0.003      0.056       0.094         0.002    -0.007   -0.648*    0.039*     -0.025
DEN             (.0407)    (.0346)              (.0505)    (.0305)    (.2218)    (.0038)    (.0335)    (.0505)       (.0022)   (.0062)   (.2271)   (.0183)    (.0211)
                 0.002       0.002     0.094                0.002      -0.028     0.000      0.002     -0.520*         0.000     0.000   -0.493*     0.002     -0.001
FIN             (.0785)    (.0640)   (.0739)               (.0570)    (.2043)    (.0096)    (.0621)    (.0076)       (.0057)   (.0149)   (.0403)   (.0266)    (.0489)
                0.064*     -0.203*     0.020       0.001              -0.207*     0.034      0.082*      0.001       0.080*    -0.286*    -0.006   -0.240*    -0.247*
FRA             (.0031)    (.0027)   (.0505)     (.2121)              (.0228)    (.0002)    (.0026)    (.1477)       (.0001)   (.0004)   (.1402)   (.0016)    (.0014)
               -0.177*      -0.158   -0.213*      -0.009      -0.173             -0.012     -0.191*     -0.009        -0.006     0.023     0.065    -0.133     0.083
DEU             (.0502)    (.0864)   (.0122)     (.0010)     (.2112)             (.0209)    (.0466)    (.0010)       (.0514)   (.1164)   (.0054)   (.0808)    (.0910)
                 0.009       0.132     0.007       0.000       0.172      -0.069             0.163       0.000         0.006    -0.023    -0.002    -0.015    -1.257*
IRE             (.0131)    (.0928)   (.0075)     (.0005)     (.1045)     (.0576)            (.0940)    (.0005)       (.0074)   (.0212)   (.0029)   (.0127)    (.4242)
                 0.033     -0.314*     0.038       0.002       0.137     -0.382*      0.054              0.002         0.005    -0.018    -0.011     0.011    -0.390*
NTH             (.0267)    (.1186)   (.0223)     (.0018)     (.0777)     (.1241)    (.0313)            (.0018)       (.0057)   (.0161)   (.0099)   (.0007)    (.1319)
                 0.002       0.002     0.094     -0.520*       0.002      -0.028      0.000       0.002                0.000     0.000   -0.493*     0.002     -0.001
NOR             (.0031)    (.0027)   (.0505)     (.1477)     (.0024)     (.0228)    (.0002)     (.0026)              (.0001)   (.0004)   (.1402)   (.0016)    (.0014)
                 0.012      -0.037     0.004       0.000       0.398      -0.038      0.006       0.015     0.000              -1.345*    -0.001    -0.044     -0.045
PRT             (.0175)    (.0424)   (.0044)     (.0003)     (.2572)     (.0341)    (.0074)     (.0171)   (.0003)              (.5073)   (.0016)   (.0398)    (.0425)
                -0.021       0.067    -0.007       0.000     -0.714*       0.068     -0.011      -0.027     0.000      -0.672*             0.002     0.079     0.082
ESP             (.0252)    (.0559)   (.0062)     (.0004)     (.2910)     (.0448)    (.0106)     (.0242)   (.0004)      (.2537)           (.0025)   (.0524)    (.0566)
                -0.011      -0.009   -0.432* -0.329*          -0.010       0.129     -0.001      -0.011   -0.329*        0.000    0.001             -0.008     0.005
SWE             (.0119)    (.0103)   (.1514)     (.0935)     (.0090)     (.0805)    (.0010)     (.0099)   (.0935)      (.0005)   (.0016)           (.0059)    (.0056)
               -0.371*       0.062     0.026       0.001     -0.400* -0.266*         -0.005       0.011     0.001       -0.015    0.053      -0.008            0.037
CHE             (.1644)    (.0439)   (.0122)     (.0011)     (.1346)     (.0532)    (.0042)     (.0007)   (.0011)      (.0133)   (.0350)    (.0059)           (.0217)
                -0.017     -0.237*    -0.012      -0.001     -0.309*       0.125    -0.314* -0.293*        -0.001       -0.011    0.041       0.004      0.028
GBR             (.0185)    (.0959)   (.0105)     (.0007)     (.1137)     (.0734)    (.1061)     (.0989)   (.0007)      (.0106)   (.0283)    (.0042)     (.0163)
                                                                       -unit increase in the column country‘s labor-market-training expenditures on its European
Notes: The off-diagonal elements of the table report the effect of a one
                                                                                                                
counterparts. These numbers are calculated using the long-run spatio-temporal-multiplier matrix I  (I  W) 1  I  W1 . Parentheses contain standard errors
                                                                                                                    1


calculated by the delta method.
                     Some Other Presentations (3)
Figure 1. Short-run Spatial Effects of a Positive One-   Figure 2. Steady-state Spatial Effects of a Positive One-
          unit Shock to German LMT Expenditures                    unit Shock to German LMT Expenditures
Volden AJPS ‘06 AFDC Replication
Table 4. Spatial Effects on AFDC Benefits from a $100
Counterfactual Shock to Monthly Retail Wages in Missouri
                                      Immediate             Long-Run Steady
Neighbor                             Spatial Effect            State Effect
                                           .51                      4.26
Arkansas                                [.16,.87]               [1.01,7.52]
                                           .62                      5.11
Illinois                               [.19,1.04]               [1.25,8.97]
                                          0.52                      4.37
Iowa                                    [.15,.88]               [.99, 7.75]
                                          0.77                      6.38
Kansas                                 [.23,1.31]              [1.60,11.17]
                                          0.44                      3.68
Kentucky                                [.13,.75]                [.87,6.50]
                                          0.52                      4.44
Nebraska                                [.15,.89]                [.99,7.90]
                                          0.52                      4.47
Oklahoma                                [.15,.89]                [.96,7.98]
                                          0.38                      3.21
Tennessee                               [.12,.65]                [.75,5.67]
Notes: Effects calculated using estimates from the spatial AR lag model in
Table 3. Brackets contain a 95% confidence interval.
     Volden AJPS ‘06 AFDC Replication
    Figure 1. Spatio-Temporal Effects on AFDC Benefits in Missouri from a
$100 Counterfactual Shock to Monthly Retail Wages in Missouri (with 95% C.I.)
30




25




20




15




10

                                               Cumulative 10-Period Effect: $55.75



5




0
      1      2      3       4      5       6          7              8               9   10
      Volden AJPS ‘06 AFDC Replication
   Figure 2. Spatio-Temporal Effects on AFDC Benefits in Nebraska from a
$100 Counterfactual Shock to Monthly Retail Wages in Missouri (with 95% C.I.)
1.4




1.2




 1




0.8

                                                      Cumulative 10-Period Effect: $4.11


0.6




0.4




0.2




 0
       1     2      3       4      5       6      7          8              9              10
                          Conclusion
• Spatial & Spatio-Temporal Interdependence
   – Important & Appreciable Substance (e.g., globalization & int‘l
     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 ρ 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 Galton‘s 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 C&IPE
    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
                        yi*    wij y*  Xβ   i ; p  yi  1    yi* 
                                       j
• The Challenge:                  j i
   – Not n indep., unidimensional CDF std normals, so (log-)likelihood=product
     (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 & Slade’s 1998: two-step GMM estimator (for spatial-error probit).
                The Econometric Problem (2)
• Structural Model: y*   Wy *  Xβ  ε
                               y*  (I   W) 1 Xβ  u
• Reduced Form:
                               where u  (I   W) 1 ε

• Measurement Equation: yi  1 if yi *  0
                             
                                               0 if yi *  0
•   Probability:                          
                 p( yi  1| X)  p (I   W) 1 Xβ   (I   W) 1 ε   0
                                                    i                 i       
                               
    – Or: p( yi  1| xi )  p ui  (I   W) 1 Xβ   i
                                                   i      
                              
           where u ~MVN 0,[(I   W)(I   W)]1      
• For Spatial-Error-Probit:
                                                   
 y*  Xβ  u; with u  (I   W) 1 ε, so u ~MVN 0,[(I   W)(I   W)]1   
  p( yi  1| xi )  p  ui  xi β  i 
            The Econometric Problem (3)
• Comments:
                                                           ˆ
                                                          Dp
                                           ˆ
  – Notice that, when we come to interpret p &                 , we face the
                                                          DX
    same MVN integration
     • We haven’t 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 subst’ly/thry’ly, but cf. Swank on capital-
       tax competition, e.g., where argues US exclusively leads & omits US.
  – Having y, not y*, on RHS may seem subst’ly or thry’ly
    desirable in some cases, but gen’ly 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)
  The Estimators: Bayesian Gibbs-MH Sampler (1)
• Basic Idea (See Gill’s 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 gen’l 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 cond’l 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
  The Estimators: Bayesian Gibbs-MH Sampler (2)
• Bayesian Gibbs-MH (MCMC) Sampler for Spatial Probit:
                                                               1                           1
                                                                                                     εε 
   – Likelihood: L y * , W |  , β,  2                                    In   W e       2 2
                                                                                                              , with
                                             2                 2( n /2)


                    ε   I n   W  y *  Xβ in s-lag; ε   I n   W   y *  Xβ  in s-err
   – Diffuse Priors => Joint Posterior:
                                             p   , β,  | y , W   I n   W                                  ( n 1)  2 2  ε ε 
                                                                                                                              1      
                                                                     *
                                                                                                                          e
   – Conditional Priors:
                                 ( n 1)  2 2  ε ε 
                                                    
           p  |  , β   
                                             1

       •                                 e                 , so  2 ~  n , which is std, so Gibbs
                                                                        2


             p  β |  ,   ~ N β,  2 ( XCCX) 1 
                                                      
       •
             with C  I n and β  ( XX) -1 X  I n   W  y * for s-lag, and, for s-err:
             C   I n   W  & β  ( X(I n   W)(I n   W) X) 1 X(I n   W)(I n   W)y *
                                          ( n 1)  2 2  ε ε 
                                                             
       p   | β,    I n   W 
                                                      1

                                                             e              ,
   –
       w/ ε for s-lag & s-err as before. Non-std, so Metropolis-Hastings.
            i         
       • f z |  , β,  ~ N ( y* ,  2 ), left- or right-truncated at 0 as y  1 or 0
                              ˆi i                                          i
The Estimators: Freq. Recursive Import. Smplr (RIS) (1)
                                                                x0
• Basic Idea:
     – To approx. n-dim. cumulative std-norm.,
                                                      
                                                           p       f n (x) dx
     – Re-express as a mean by mult & divide by std dist. truncated
       to support of desired integral, (=the Importance dist.): g n  x 
                                                                  c

             x0
             f n ( x) c
     – p  c        g n (x) dx
            g ( x)                                f n ( x)  1 R f n ( x r )
           n                             p E c   c
                                            ˆ
    – This gives probability, p, sought as:       g n (x)  R r 1 g n (x r )
•   We want:                                 
               p(u  v), with u ~ MVN 0, (I   W)(I   W) 1 ,      
                  v  Q  I   W  Xβ, with Q a diag mat having qi  2 yi  1
                                  1


     – So, Imp. dist. is n-dim. MVN truncated at v. (uh-oh! but<)
     – V-Cov u being pos-def => Cholesky decomposition exists s.t.:
         Σ 1  AA, with A upper-triangular and η  Au independent!
         So substituting u  A -1 η  Bη gives: p  Bη  v   p  η  B 1 v 
                                                                             
The Estimators: Freq. Recursive Import. Smplr (RIS) (2)
• So we want to calc. this set of indep. cum. std.norms:
                                             b1,11 b1,2
                                                     1     1
                                                           b1,3        b1, n   v1 
                                                                         1

                                                    1                         
                                              0 b2,2                           
  p  Bη  v   p  η  B v  , where B v   0
                   
                          1
                             
                                        1
                                                                      bn  2,n   
                                                                       1

                                                                       1        
                                                                     bn 1,n   
                                             0                        bn ,1  vn 
                                                                         
                                                           0     0        n      
• 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, υ (!)
   – Repeat R times & avg => RIS est. of the log-likelihood to max:
                                   n
                          ˆ       R
                               R
                          l            j ,r 
                             r 1  j 1      
        Evaluating the Estimators (One Quick MC)
• DGF: (n.b., same W, diff. coeffs. For x & y)
   y   I n   W   xβ  ε  , where x   I n   W  z and z, ε ~ N  0,1
    *               1                                    1


• Conditions:
    – Row-stdzd contig. wts U.S. 48; =0.5, =1.0, n={48,144},θ={0.0, 0.5}
                                                                       ML with Wy ML with Wy* Bayesian Gibbs
• You can’t see this, but:
                                                                                                      
    –   Rel’ly poor bias perf. BG Experiment #1: n=48, =0.0
                                       Mean Coefficient Estimate       1.02   0.32   1.13   0.74   1.23   0.30
    –   In fact, std ML w/ Wy            Actual SD of Estimates        0.33   0.69   0.41   0.36   0.28   0.16
    –   seems dominate, but this          Mean of Reported SE          0.30   0.41   0.35   0.30   0.42   0.21

    –   b/c 2 biases, meas./spec.    Experiment #2: n=48, =0.5
                                       Mean Coefficient Estimate       1.22   0.35   1.13   0.69   1.21   0.28
    –   err & simult. Simult incr        Actual SD of Estimates        0.56   0.76   0.61   0.33   0.24   0.14
                                          Mean of Reported SE          0.36   0.46   0.42   0.29   0.39   0.20
    –   in , meas-err decr or flat
    –   in n, so over- to under-est. Experiment #3: n=144, =0.0
                                       Mean Coefficient Estimate       0.94   0.42   1.01   0.68   1.14   0.34
    –   (Checked & it’s true) B&V ‘04 Actual SD of Estimates           0.17   0.27   0.19   0.16   0.15   0.10
                                          Mean of Reported SE          0.16   0.22   0.18   0.15   0.22   0.12
    –   do MC like #2 for RIS & find
                                     Experiment #4: n=144, =0.5
    –   =-18%, =+10%, so better. Mean Coefficient Estimate           1.08   0.48   0.97   0.64   1.13   0.32
                                              Actual SD of Estimates   0.19   0.29   0.21   0.16   0.14   0.09
                                               Mean of Reported SE     0.18   0.23   0.20   0.15   0.21   0.12
             Calculating & Presenting Effects (1)
• If confine discussion to y*, then as prev. F&H:
y*   Wy  Xβ  ε  (I n   W)-1 ( Xβ  ε)
                                                                      1
      1           w1,2                             w1,n 
      w          1                                             
           2,1                                                   
                                                                         Xβ  ε   S  Xβ  ε 
                                                                 
                                      1             w( n 1),n 
        wn ,1                   wn ,( n 1)        1         
                                                                 
• And s.e.’s/c.i.’s by delta method as:
               ˆ ˆ
             si  k       si  k 
                               ˆ ˆ            ˆ         ˆ ˆ         ˆ ˆ
                                                         si  k   si  k                       
   
  ˆ ˆ
V si  k   
                  ˆ     ˆ               ˆ
                       V θ  ˆ  , where θ   ˆ  and  ˆ                                   ˆ
                                                                                                 si 
             θ            θ              k      θ          ˆ                         
          Calculating & Presenting Effects (2)
• But we (should) want to discuss:
  p( yi  1)            (I   W) 1 X1β                (I   W) 1 X0β     
                                             i     p  ui                   i
                  p  ui                                                             
     X                            i                                i             
                                                                                    
• Note: given probit, must know xi; given spatial
  interdependence, must know X (!).
                             ˆ
• Given interdep, calc these p will req. MVN cdf!
 p
 X
     Φn (I   W)1 X1β    i1   Φn (I   W)1 X0β    i1 
                                
                                                                      
• Or< better idea?
                                                     ˆ ˆ
        Calculate y1 & y * at some X1 & X0 , & draws β,  , ε.
                  ˆ* ˆ0
                                                   ˆ        ˆ
        Apply measurement rule to convert these to y1 and y 0 .
                          ˆ                         ˆ
        Avg difference=E(dy/dX), & var(diff)=E(V(E(dy/dX))).
  An Example Application: US State CHIP Premia
                            Probit-         Probit-        Spatial-Lag          Spatial-Error   Spatial-Lag
                               ML           MCMC          Probit (Gibbs)        Probit (Gibbs)  Probit (RIS)
                             -4.978          -5.163            -5.606                -5.531         -5.186
       Constant
                            (6.260)         (6.292)          (10.159)               (7.337)        (5.944)
                              -.244         -.265**           -.374**                -.243*          -.171
    Poverty Rate
                             (.153)          (.156)            (.231)                (.157)         (.125)
                               .004           .004*             .006*                 .004*          .004*
     Retail Wage
                             (.003)          (.003)            (.004)                (.003)         (.002)
                               .011            .011              .014                  .014          -.004
Government Ideology
                             (.013)          (.013)            (.020)                (.014)         (.116)
      Inter-party             2.174          2.108              1.473                 2.636           1.27
     Competition            (3.388)         (3.478)           (6.134)               (3.794)        (31.94)
                              -.014           -.014             -.020                 -.017           .005
      Tax Effort
                             (.019)          (.019)            (.034)                (.021)         (.017)
                               .045            .048              .065                  .043           .041
    Federal Share
                             (.063)          (.064)            (.095)                (.066)         (.056)
 Spatial lag or error-         .079            .102          .200***               .297***            .243
          lag                (.798)          (.815)            (.148)                (.196)         (.252)
                 2
      Pseudo-R                 .222            .220              .607                  .574            NA
    Observations                48              48                48                    48             48
Notes: The first two columns‘ estimators assume the spatial lags exogenous. The first column gives the standard
 Notes: 1. Informative U(0,1) prior on  standard-errors, and its hypothesis tests assume asymptotic
probit ML estimates. Its parentheses contain estimatedhelps. We’ve qualms.
               calculated t-statistics. The models in columns two significance also.
normality of 2. Difference in Bayesian vs. frequentistthrough four apply MCMC methods with diffuse
priors, except for a Uniform(0,1) prior on ρ. The reported coefficient estimateshave dom’d heremeans based on
              3. Note measurement/specification-error seem to are posterior-density for ML.
   Example Estimated Spatial Effect, with
Certainty Estimate, in Binary-Outcome Model
         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<
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 Est‘d-W
 • A Simple Spatial-Econometric Proposal:
   – Estimated W ≈ Multiple W (m-STAR)
   – Endogenize W means W(y)=>S-IV in m-STAR
Spatial Econometrics                            Network Analysis
• Economists & Political                     • Sociologists & Political
  Economists                                   Sociologists
• Core Question:                             • Core Questions:
   – How alters‘ actions affect                   – How do nets form?
     ego‘s via network & v.v.?                    – What expl. net struct.?
   – Contagion v. Common                          – How ego‘s position in net
     Exposure (Galton‘s Problem)                    & net struct affect?
• Core Tools:                                • Core Tools
   – SAR, STAR, S-QualDep…                        – Net stats (measures),
   – S-GMM, S-ML                                    graphics, ERGMs, …
 • INTERDEPENDENCE
    – Definition: yi=f(yj≠i); i‘s actions depend on j‘s.
    – 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)
 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., C&IPE) 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) suffice=>causal prec.
 Leenders’ (1997) Co-evolution Model
• Selection:
  – Arc forms or not in continuous time Markov process:
    0ij  0  0 dij ; 1ij  1  1dij ...e.g, dij  yi ,t 1  y j ,t 1
• Contagion:
  – =STAR model           y   Wy   y t 1  Xβ  ε
• => Co-Evolution Model:
  – Identification strategy: time lag
  – Findings of MC‘s
      • Coarse obs periodicity => big biases
      • If selection & model contagion => big biases
      • If contagion & model selection => biases, less big
    Snijders’ (‘97-‘07) Co-evolution Model
•   Steglich et al. (‗07): two threefold empirical challenges
     – contagion, selection, context (1st+3rd=Galton‘s Problem; 2nd=coevolution => similar implications)
          • In gen., any omissions or inadequacies in modeling one tends against that & favor others looks most like it
     – coarse periodicity, alternative mech‘s & 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 @ one time; Can parameterize the rate; Conditionally independent
     – When opp act, multinomial w/ N network options—change 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)
     – Estimated by simulated method of moments; recently, by simulated likelihood
•   Identification: (IIA and…)
     – Assume temporal precedence implies causal precedence, in particular condition on first obs
     – Each actor‘s action or opp to act takes all else as given, i.e., conditional independence
     – In gen., strategy seems: control for (condition on) possible sources dependence; no stochastic dep.
        Issues from C&IPE 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.
Multi-Parametric Spatio-Temporal (AR) Lag Model
      y  1W1y   2 W2 y  ...   R WR y   My  Xβ  ε
                                                                         R
          Wy   My  Xβ  ε, where W    r Wr
                                                                        r 1

         yi  1  wij y j   2  wij y j  ...   R  wij y j   yi ,t 1   xk  k   i
                    1                2                     R                       i

                      j               j                  j                      k


                                                   
                1wij   2 wij  ...   R wij y j   xk  k   i
                     1         2                R          i

                  j                                          k

                           R      
                   R wij  y j    xk  k   i
                                            i

                j  r           k
                                                                                                  1
                              ln L(ρ,  , β,  ; y, X)  ln(2 2 )  NT /2  ln A                       ee
                                                                                                 2   2

                                 A  I NT  W            e  Ay   My  Xβ
                                                                  R
                                                    W    r Wr
                                                    ˆ     ˆ
                                                                 r 1


         var(W(i , j ) )   W1(i , j ) W2(i , j ) ...WRi , j )  Ωρ  W1(i , j ) W2(i , j ) ...Wmi , j ) 
             ˆ
                           
                                                       (          ˆ
                                                                 ˆ
                                                                                                 (
                                                                                                          
 Co-Evolution Models in m-STAR Format
• Wr = covariates expected explain network
• Co-evolution models=models with W=f(y): larger challenges.
   – Our first cut: same poor man’s exogeneity, time-lag the y in W=f(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 (1+q) 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).
Active Labor Market Program Expenditures in OECD Countries, 1981-2002
Dependent variable                                     Total ALM                                    LMT                                   SEMP
                                               (1)          (2)           (3)          (4)           (5)          (6)           (7)          (8)         (9)
Temporal Lag                               0.875***     0.880***      0.892***     0.872***      0.873***     0.865***      0.830***     0.833***    0.822***
                                            (0.028)      (0.026)       (0.026)      (0.029)       (0.028)      (0.028)       (0.035)      (0.034)     (0.034)
Real GDP Growth Rate                       1.365***     1.339***        -0.032       0.269         0.312        -0.445        0.036        0.040       -0.890
                                            (0.430)      (0.423)       (1.105)      (0.210)       (0.204)      (0.640)       (0.196)      (0.189)     (0.620)
Standerdized Unem. Rate                      -0.070       -0.074        -0.338       0.361         0.412        0.452         -0.169       -0.187      -0.580
                                            (0.826)      (0.794)       (0.867)      (0.465)       (0.445)      (0.508)       (0.457)      (0.438)     (0.491)
Union Density                              0.888***     0.918***      0.814***       0.205         0.205        0.161       0.567***     0.584***    0.575***
                                            (0.315)      (0.303)       (0.302)      (0.174)       (0.167)      (0.171)       (0.176)      (0.168)     (0.173)
Deindustrialization                          1.259        1.249         0.771        0.106         0.114        -0.220     1.4260***     1.413***    1.100**
                                            (0.820)      (0.783)       (0.776)      (0.469)       (0.448)      (0.454)       (0.455)      (0.437)     (0.442)
Trade Openness                            -0.522***    -0.484***        -0.307       -0.187       -0.168*       -0.037        0.018        0.022       0.064
                                            (0.176)      (0.169)       (0.196)      (0.101)       (0.097)      (0.114)       (0.108)      (0.103)     (0.120)
Working Age Population                       0.946        0.916         0.090      2.239**       2.210***     1.819**         -0.139       -0.140      -0.366
                                            (1.561)      (1.497)       (1.571)      (0.888)       (0.861)      (0.925)       (0.866)      (0.828)     (0.885)
Left Cabinet Seats                           -0.024       -0.016        -0.015       0.035         0.036       0.042*       -0.049**     -0.046**      -0.040
                                            (0.041)      (0.039)       (0.038)      (0.023)       (0.022)      (0.022)       (0.023)      (0.022)     (0.021)
Christian Dem. Cabinet Seats                 -0.160      -0.173*        -0.146       -0.070        -0.074       -0.056        -0.032       -0.036      -0.019
                                            (0.099)      (0.095)       (0.092)      (0.056)       (0.054)      (0.054)       (0.055)      (0.052)     (0.052)
Left Libertarian Vote                        -0.285       -0.293        -0.421       -0.316        -0.325       -0.399        -0.248       -0.241      -0.274
                                            (0.650)      (0.621)       (0.603)      (0.371)       (0.354)      (0.028)       (0.361)      (0.345)     (0.342)

Spatial Weights:
Borders                                                   -0.004        -0.006                     -0.007       -0.008                     0.001       -0.002
                                                         (0.007)       (0.007)                    (0.007)      (0.007)                    (0.007)     (0.007)

European Union Membership                               -0.033***    -0.032***                  -0.033***     -0.033***                  -0.036***   -0.035***
                                                         (0.012)      (0.012)                    (0.012)       (0.012)                    (0.013)     (0.013)

Trade Shares                                              0.018         0.025                      0.027       0.030*                      0.004       0.013
                                                         (0.017)       (0.018)                    (0.017)      (0.018)                    (0.017)     (0.017)

ALM Program Expenditures                                  0.008         -0.004                     -0.009       -0.015                     0.019       0.005
                                                         (0.016)       (0.017)                    (0.015)      (0.016)                    (0.015)     (0.016)

                                           22.176     21.184*** 19.960***          12.604      12.028*** 11.664***          12.324      11.765*** 11.328***
                                                        (0.785)   (0.739)                        (0.452)   (0.436)                        (0.436)   (0.419)

Log-Likelihood                            -1646.410     -1642.34      -1620.8      -1438.49      -1434.31     -1423.27      -1430.23     -1425.92    -1411.92

Note
All regressions include fixed country effects. In addition to the country fixed effects, Model (3), (6) and (9) also include fixed year effects.
                                                         The
All the spatial weights matrices are row-standardized. parentheses contain standard errors.
*** Significant at the .01 level; ** Significant at the .05 level; * Significant at the .10 level.
                 Table 3: First-Period Spatial Effects of Union Density on Logged LMT per Capita (2000 PPP$)
         AUS       AUT       BEL      CAN       DNK         FIN      FRA      GER       GRC        IRE       ITA       JPN       NTH      NWZ       NOR        PRT       ESP      SWE       CHE       GBR        USA
AUS    58.4***     0.03      0.21      0.02      0.05      0.09      0.11       0.1        0       0.13     0.07*      0.09     0.05*      0.08      0.01    0.02**      0.11      0.08     0.04*      0.02      0.06
       (16.83)    (0.03)    (0.17)    (0.02)    (0.04)    (0.07)    (0.08)    (0.07)      (0)     (0.11)    (0.04)    (0.31)    (0.03)    (0.33)      (0)     (0.01)    (0.09)    (0.06)    (0.03)    (0.08)    (0.25)
AUT      0.03    58.4***     0.05      0.01      -0.1*     -0.07     -0.04     0.05    -0.16**     -0.03     -0.06     0.03     -0.11*     0.02      0.01    -0.14**     -0.05     -0.08     0.07    -0.15**     0.02
        (0.02)   (16.83)    (0.14)    (0.01)    (0.06)    (0.07)    (0.06)    (0.34)    (0.07)     (0.1)    (0.09)    (0.02)    (0.06)    (0.02)      (0)     (0.07)    (0.08)    (0.06)     (0.1)    (0.07)    (0.05)
BEL      0.04    -0.12**   58.4**      0.01      -0.09     -0.05     0.02        0     -0.16**       0       -0.07     0.03      -0.06     0.02      0.01      -0.13     -0.03     -0.06     0.06      -0.12     0.02
        (0.03)    (0.06)   (16.83)    (0.01)    (0.07)    (0.08)    (0.09)    (0.11)    (0.07)    (0.11)    (0.06)    (0.02)    (0.09)    (0.02)    (0.01)    (0.06)    (0.08)    (0.07)    (0.04)    (0.08)    (0.07)
CAN      0.03      0.03      0.21    58.4**      0.05      0.09      0.11      0.09        0       0.13      0.06      0.03      0.04      0.02      0.01    0.02**      0.11      0.08      0.05      0.01      0.23
        (0.02)    (0.03)    (0.17)   (16.83)    (0.04)    (0.07)    (0.08)    (0.06)      (0)     (0.11)    (0.05)    (0.05)    (0.03)    (0.02)    (0.01)    (0.01)    (0.09)    (0.06)    (0.04)    (0.03)    (0.58)
DNK      0.03      -0.12     0.06      0.01    58.4**      -0.06     -0.04     0.01    -0.16**     -0.02     -0.09     0.03       -0.1     0.02      0.02    -0.14**     -0.05     -0.03    0.05*      -0.13     0.02
        (0.02)    (0.06)    (0.14)    (0.01)   (16.83)    (0.06)    (0.06)    (0.12)    (0.07)     (0.1)    (0.06)    (0.03)    (0.07)    (0.02)    (0.06)    (0.07)    (0.08)    (0.13)    (0.03)    (0.12)    (0.06)
 FIN     0.04    -0.12**     0.06      0.01      -0.09   58.4**      -0.03     -0.03   -0.16**     -0.02     -0.08     0.03      -0.1*     0.02      0.04    -0.14**     -0.04     -0.02    0.05*      -0.13     0.03
        (0.02)    (0.06)    (0.14)    (0.01)    (0.06)   (16.83)    (0.07)    (0.14)    (0.07)     (0.1)    (0.06)    (0.04)    (0.06)    (0.02)    (0.16)    (0.07)    (0.08)    (0.12)    (0.03)    (0.12)    (0.09)
FRA    0.03**    -0.12**     0.09      0.01      -0.1*     -0.06   58.4**      -0.01   -0.16**     -0.02     -0.06     0.03      -0.1*     0.02      0.01    -0.14**     -0.02     -0.07     0.06      -0.12     0.03
        (0.03)    (0.06)    (0.13)    (0.01)    (0.06)    (0.08)   (16.83)    (0.12)    (0.07)     (0.1)    (0.07)    (0.03)    (0.06)    (0.02)    (0.01)    (0.06)    (0.07)    (0.07)    (0.06)    (0.08)    (0.09)
GER      0.03      -0.1*     0.08      0.01      -0.09     -0.06     -0.01   58.4**    -0.16**     -0.02     -0.07     0.03      -0.08     0.02      0.01    -0.14**     -0.04     -0.07     0.07      -0.13     0.03
        (0.02)    (0.06)    (0.14)    (0.01)    (0.09)    (0.07)    (0.07)   (16.83)    (0.07)     (0.1)    (0.08)    (0.04)    (0.06)    (0.02)    (0.02)    (0.06)    (0.07)    (0.06)    (0.05)    (0.11)     (0.1)
GRC      0.03    -0.12**     0.05      0.01      -0.1*     -0.07     -0.03     -0.02   58.4**      -0.03     -0.06     0.03       -0.1     0.02      0.01    -0.14**     -0.05     -0.08    0.05*      -0.14     0.02
        (0.02)    (0.06)    (0.13)    (0.01)    (0.06)    (0.07)    (0.07)    (0.19)   (16.83)     (0.1)    (0.06)    (0.04)    (0.07)    (0.02)      (0)     (0.07)    (0.07)    (0.06)    (0.03)    (0.09)    (0.06)
 IRE     0.04    -0.12**     0.08      0.01      -0.1*     -0.06     -0.03     -0.04   -0.16**   58.4**      -0.08     0.03      -0.1*     0.02      0.01    -0.14**     -0.04     -0.07     0.05      -0.03     0.04
        (0.03)    (0.06)    (0.14)    (0.01)    (0.06)    (0.08)    (0.07)    (0.08)    (0.07)   (16.83)    (0.06)    (0.04)    (0.06)    (0.02)    (0.01)    (0.07)    (0.08)    (0.07)    (0.04)    (0.23)    (0.160
 ITA     0.03       -0.1     0.06      0.01      -0.1*     -0.07       0       -0.02   -0.16**     -0.02   58.4**      0.03       -0.1     0.02      0.01    -0.14**     -0.04     -0.08     0.07      -0.14     0.03
        (0.02)    (0.13)    (0.13)    (0.01)    (0.06)    (0.08)    (0.08)     (0.2)    (0.07)     (0.1)   (16.83)    (0.02)    (0.06)    (0.02)    (0.01)    (0.06)    (0.06)    (0.06)    (0.11)     (0.1)    (0.09)
 JPN     0.05      0.03      0.21      0.02      0.05      0.09      0.11      0.11        0       0.13     0.07*    58.4**     0.05*      0.02      0.01    0.02**      0.11      0.08     0.05*      0.01      0.12
        (0.06)    (0.02)    (0.17)    (0.05)    (0.04)    (0.07)    (0.08)    (0.08)      (0)     (0.11)    (0.04)   (16.83)    (0.03)    (0.02)    (0.01)    (0.01)    (0.09)    (0.06)    (0.03)    (0.06)    (0.53)
NTH      0.03    -0.12**      0.1      0.01      -0.1*     -0.07     -0.03     0.01    -0.16**     -0.02     -0.09     0.03    58.4**      0.02      0.01    -0.14**     -0.04     -0.08    0.05*      -0.12     0.02
        (0.02)    (0.06)    (0.13)    (0.01)    (0.06)    (0.07)    (0.08)    (0.16)    (0.07)     (0.1)    (0.06)    (0.02)   (16.83)    (0.02)    (0.01)    (0.07)    (0.07)    (0.06)    (0.03)    (0.09)    (0.07)
NWZ      0.14      0.03      0.21      0.02      0.05      0.09      0.11       0.1*       0       0.13     0.07*      0.07      0.04    58.4**      0.01    0.02**      0.11      0.08      0.05      0.02      0.05
        (0.24)    (0.03)    (0.17)    (0.02)    (0.04)    (0.07)    (0.08)    (0.06)      (0)     (0.11)    (0.04)    (0.19)    (0.03)   (16.83)      (0)     (0.01)    (0.09)    (0.06)    (0.04)    (0.08)    (0.21)
NOR      0.03      0.03      0.21      0.02      0.06      0.12      0.12      0.12        0       0.13     0.07*      0.03      0.06      0.02    58.4**    0.02**      0.11      0.13     0.05*      0.05      0.02
        (0.03)    (0.02)    (0.16)    (0.03)    (0.05)     (0.2)    (0.08)    (0.13)      (0)      (0.1)    (0.04)    (0.03)    (0.07)    (0.02)   (16.83)    (0.01)    (0.08)    (0.13)    (0.03)     (0.2)    (0.08)
PRT      0.03    -0.12**     0.05      0.01      -0.1*     -0.07     -0.02     -0.03   -0.16**     -0.03     -0.08     0.03     -0.11*     0.02      0.01    58.4**      0.04      -0.08    0.05*      -0.13     0.02
        (0.02)    (0.06)    (0.13)    (0.01)    (0.06)    (0.07)     (0.1)    (0.14)    (0.07)     (0.1)    (0.06)    (0.02)    (0.06)    (0.02)    (0.01)   (16.83)    (0.27)    (0.06)    (0.03)    (0.11)    (0.05)
 ESP     0.03    -0.12**     0.07      0.01      -0.1*     -0.06     0.03      -0.03   -0.16**     -0.02     -0.07     0.03      -0.1*     0.02      0.01       -0.1   58.4**      -0.07     0.05      -0.13     0.02
        (0.03)    (0.06)    (0.14)    (0.01)    (0.06)    (0.08)    (0.11)    (0.14)    (0.07)     (0.1)    (0.09)    (0.03)    (0.06)    (0.02)    (0.01)    (0.16)   (16.83)    (0.07)    (0.03)    (0.11)    (0.08)
SWE      0.03    -0.12**     0.06      0.01      -0.07     -0.04     -0.04     -0.03   -0.16**     -0.02     -0.09     0.03       -0.1     0.02      0.04    -0.14**     -0.04   58.4**     0.05*      -0.13     0.03
        (0.02)    (0.06)    (0.14)    (0.01)     (0.1)    (0.12)    (0.06)    (0.14)    (0.07)     (0.1)    (0.06)    (0.03)    (0.07)    (0.02)    (0.08)    (0.07)    (0.08)   (16.83)    (0.03)    (0.12)    (0.09)
CHE      0.03      0.05      0.22      0.01      0.06      0.09     0.15*      0.17        0       0.14       0.1      0.03      0.05      0.02      0.01    0.02**      0.11      0.08    58.4**      0.02      0.03
        (0.02)    (0.08)    (0.16)    (0.01)    (0.04)    (0.07)    (0.09)    (0.22)    (0.01)    (0.11)    (0.07)    (0.04)    (0.04)    (0.02)      (0)     (0.01)    (0.08)    (0.06)   (16.83)    (0.07)     (0.1)
GBR      0.03    -0.12**     0.07      0.01      -0.1*     -0.07     -0.02     -0.04   -0.16**     -0.01     -0.09     0.03      -0.09     0.02      0.01    -0.14**     -0.05     -0.08    0.05*    58.4**      0.04
        (0.02)    (0.06)    (0.16)    (0.02)    (0.06)    (0.07)    (0.07)    (0.13)    (0.07)    (0.11)    (0.06)    (0.04)    (0.07)    (0.01)    (0.02)    (0.07)    (0.07)    (0.06)    (0.03)   (16.83)    (0.16)
USA    0.04**      0.03      0.21      0.13      0.05      0.09      0.11       0.1        0       0.13     0.07*      0.07     0.05*      0.02      0.01    0.02**      0.11      0.08     0.05*      0.02    58.4**
        (0.02)    (0.02)    (0.16)    (0.24)    (0.04)    (0.07)    (0.07)    (0.08)      (0)      (0.1)    (0.04)    (0.21)    (0.03)    (0.02)    (0.01)    (0.01)    (0.08)    (0.06)    (0.03)    (0.08)   (16.83)
Notes: The cells report the first-period spatial effect of a 1% increase in the column country‘s union density on its
own subsidized employment expenditures (     100) and the expenditures (  100) of its OECD counterparts (identified
by the rows) based on the model (8) estimates.
       Table 4: Estimated ALM-Policy Interdependencies/Network in 1981
      AUS     CAN      FIN    FRA       NTH    NWZ ESP SWE         GBR    USA
AUS   0.000   0.019   0.456 0.022       0.075  0.617 0.09* 0.706 0.225 0.179
      0.000   0.086   0.336 0.099      0.051   0.646 0.053 0.514 0.219 0.806
CAN   0.002   0.000   0.451 0.005       0.064  0.481 0.084 0.697 0.176 0.428
      0.009   0.000   0.348 0.023      0.041   0.373 0.062 0.537 0.107 1.135
FIN   0.008   0.007   0.000 0.044       0.118  0.627 0.126* 1.092 0.300 0.066
      0.035   0.032   0.000 0.199      0.143   0.486 0.074 0.758 0.315 0.297
FRA   0.005   0.009   0.458 0.000      -1.675  0.481 0.202 0.712 -1.49*** 0.093
      0.021   0.042   0.332 0.000      0.605   0.372 0.206 0.500 0.569 0.415
NTH   0.004   0.006   0.476 -1.69**     0.000  0.496 0.114 0.744 -1.435** 0.079
      0.018   0.027   0.335 0.702      0.000   0.386 0.103 0.499 0.669 0.354
NWZ   0.243   0.013   0.602 0.013      0.089* 0.000 0.115 0.931 0.265 0.118
      0.464   0.060   0.461 0.058       0.051  0.000 0.077 0.703 0.174 0.529
ESP   0.003   0.005   0.477 0.249      0.102   0.503 0.000 0.739 0.250 0.060
      0.014   0.024   0.351 0.478       0.147  0.389 0.000 0.533 0.291 0.270
SWE   0.008   0.009   0.836 0.052       0.150  0.751 0.148* 0.000 0.353 0.082
      0.034   0.041   0.787 0.235      0.212   0.581 0.085 0.000 0.351 0.366
GBR   0.011   0.016   0.504 -1.67*** -1.621*** 0.528 0.121 0.784 0.000 0.122
      0.048   0.071   0.356 0.620      0.608   0.401 0.110 0.535 0.000 0.547
USA   0.014   0.311   0.454 0.031       0.082  0.483 0.092* 0.704 0.217 0.000
      0.062   0.672   0.342 0.139      0.077   0.367 0.052 0.518 0.189 0.000
Note: Dependent variable: SEMP. Actual weights multiplied them by 100 (and
standard errors adjusted accordingly) to improve table formatting. [XXXX: These are
for c-dums, no t-dums model]
1981
                                   Table 5: Estimated ALM-Policy Interdependencies/Network in 1991
        AUS     BEL      CAN      DEN      FIN    FRA     DEU     IRE      ITA     JPN     NTH    NWZ NOR          PRT       ESP      SWE     CHE        GBR     USA
AUS    0.000    0.458   0.022     0.201   0.312 0.070 0.126 0.130         0.040   0.160    0.036  0.215 0.115      0.025     0.218   0.101    0.008      0.047   0.105
       0.000    0.339   0.041    0.150    0.233 0.045 0.091 0.093         0.056   0.523   0.026   0.578 0.085     0.017     0.159    0.062    0.023     0.137    0.426
BEL    0.029    0.000   0.018*   -0.140   0.401 -0.232 -0.165 -0.227 -0.345** 0.060       -0.275  0.139 0.149   -0.365***   -0.110   0.131    0.009   -0.320**   0.040
       0.018    0.000   0.010    0.203    0.303 0.192 0.208 0.144         0.138   0.037   0.194   0.107 0.107     0.131     0.190    0.079    0.025     0.152    0.121
CAN    0.023*   0.453   0.000     0.199   0.309 0.062 0.108 0.128         0.029* 0.059 0.032* 0.107 0.115       0.024***     0.215   0.096    0.004      0.025   0.401
       0.013    0.345   0.000    0.152    0.238 0.037 0.065 0.097         0.017   0.073   0.018   0.082 0.082     0.018     0.164    0.070    0.006     0.039    0.982
DEN    0.025*   0.111   0.016     0.000   0.353 -0.311** -0.153 -0.255* -0.353*** 0.058 -0.342** 0.119 0.150     -0.370*    -0.155   0.196    0.010    -0.341*   0.035
       0.015    0.343   0.010    0.000    0.236 0.131 0.223 0.144         0.135   0.052   0.145   0.091 0.096     0.132     0.179    0.207    0.033     0.199    0.108
 FIN   0.029    0.544   0.018     0.251   0.000 0.093 0.191 0.153         0.048   0.065    0.055  0.127 0.188   0.031***     0.262   0.210    0.011      0.064   0.047
       0.017    0.383   0.014    0.151    0.000 0.089 0.281 0.108         0.072   0.068   0.081   0.097 0.316     0.018     0.175    0.201    0.035     0.202    0.158
FRA    0.023*   0.115   0.016    -0.192   0.318 0.000 -0.199 -0.264* -0.311* 0.054 -0.345** 0.110 0.121         -0.369***   -0.134   0.104    0.030   -0.329**   0.047
       0.014    0.281   0.014    0.170    0.238 0.000 0.246 0.138         0.166   0.048   0.144   0.084 0.079     0.131     0.148    0.062    0.070     0.153    0.165
DEU    0.024*   0.121   0.016    -0.167   0.328 -0.262 0.000 -0.261* -0.330       0.060 -0.309** 0.112 0.126    -0.370***   -0.158   0.111*   0.042    -0.343*   0.052
       0.014    0.317   0.013    0.228    0.238 0.172 0.000 0.138         0.197   0.070   0.149   0.086 0.078     0.131     0.151    0.063    0.080     0.196    0.190
 IRE   0.024*   0.099   0.016    -0.184   0.330 -0.310** -0.250 0.000 -0.359*** 0.058 -0.348** 0.114 0.124      -0.373***   -0.163   0.107    0.010     -0.175   0.072
       0.014    0.309   0.013    0.174    0.248 0.139 0.162 0.000         0.130   0.060   0.137   0.087 0.084     0.134     0.172    0.066    0.031     0.405    0.278
 ITA   0.025    0.075   0.017    -0.195   0.313 -0.230 -0.199 -0.268*     0.000   0.051 -0.347** 0.108 0.116    -0.371***   -0.160   0.102    0.062   -0.350**   0.047
       0.015    0.289   0.016    0.167    0.234 0.212 0.386 0.140         0.000   0.039   0.142   0.083 0.083     0.131     0.140    0.061    0.259     0.174    0.166
 JPN   0.047    0.464   0.031     0.204   0.315 0.072 0.136 0.132         0.035   0.000    0.041  0.113 0.117      0.025     0.221   0.100    0.009      0.037   0.214
       0.107    0.339   0.078    0.149    0.237 0.051 0.122 0.092         0.036   0.000   0.042   0.075 0.084     0.016     0.159    0.065    0.030     0.089    0.916
NTH    0.023    0.139   0.015    -0.193   0.315 -0.300* -0.156 -0.267* -0.352** 0.050      0.000  0.108 0.120   -0.372***   -0.173   0.105*   0.009   -0.315**   0.039
       0.014    0.284   0.009    0.163    0.231 0.176 0.310 0.138         0.141   0.037   0.000   0.084 0.076     0.133     0.160    0.060    0.030     0.173    0.131
NWZ    0.212    0.480   0.022     0.210   0.325 0.070* 0.125 0.135        0.037   0.117 0.035* 0.000 0.120         0.026     0.228   0.104    0.006      0.047   0.089
       0.399    0.352   0.036    0.157    0.248 0.040 0.077 0.101         0.039   0.322   0.021   0.000 0.090     0.018     0.168    0.067    0.014     0.133    0.356
NOR    0.023    0.486   0.024    0.234*   0.375 0.089 0.164 0.138         0.039   0.055    0.060  0.113 0.000     0.028*     0.232   0.191    0.006      0.092   0.039
       0.015    0.344   0.046    0.132    0.435 0.103 0.222 0.094         0.047   0.047   0.121   0.087 0.000     0.016     0.160    0.208    0.016     0.333    0.131
PRT    0.022    0.070   0.015    -0.195   0.313 -0.287 -0.226 -0.269* -0.345** 0.048 -0.348** 0.108 0.119          0.000    -0.027   0.103*   0.010   -0.345**   0.029
       0.014    0.299   0.009    0.166    0.233 0.223 0.272 0.144         0.156   0.032   0.139   0.083 0.077     0.000     0.470    0.060    0.033     0.190    0.087
 ESP   0.025    0.119   0.016    -0.174   0.347 -0.209 -0.215 -0.253* -0.325      0.056 -0.348*** 0.120 0.129     -0.310     0.000   0.112    0.010   -0.343**   0.040
       0.015    0.337   0.010    0.182    0.260 0.222 0.268 0.143         0.206   0.043   0.134   0.092 0.092     0.291     0.000    0.069    0.030     0.190    0.132
SWE    0.025*   0.489   0.017     0.264   0.373 0.085 0.175 0.136         0.043   0.055    0.056  0.112 0.181     0.028*     0.232   0.000    0.011      0.060   0.047
       0.015    0.325   0.015    0.206    0.295 0.090 0.275 0.094         0.065   0.049   0.102   0.086 0.150     0.016     0.155    0.000    0.035     0.192    0.165
CHE    0.023*   0.462   0.015     0.202   0.310 0.131 0.254 0.131         0.093   0.056    0.047  0.107 0.114     0.026*     0.222   0.102    0.000      0.044   0.048
       0.013    0.316   0.012    0.142    0.230 0.132 0.382 0.088         0.131   0.064   0.069   0.082 0.083     0.015     0.145    0.060    0.000     0.125    0.174
GBR    0.026    0.095   0.020    -0.194   0.314 -0.277* -0.234 -0.230 -0.351** 0.057 -0.315** 0.109 0.124*      -0.371***   -0.170   0.107*   0.015      0.000   0.071
       0.020    0.349   0.032    0.161    0.226 0.142 0.243 0.175         0.144   0.066   0.149   0.079 0.071     0.132     0.150    0.061    0.054     0.000    0.273
USA    0.029    0.459   0.224     0.200   0.309 0.076 0.133 0.132         0.039   0.125    0.041  0.108 0.115      0.025     0.219   0.100    0.010      0.045   0.000
       0.029    0.327   0.409    0.149    0.234 0.065 0.119 0.086         0.052   0.367   0.045   0.079 0.081     0.016     0.154    0.063    0.031     0.128    0.000
Note: Dependent variable: SEMP. Actual weights multiplied them by 100 (and standard errors adjusted accordingly)
to improve table formatting. [XXXX: These are for c-dums, no t-dums model]
1991
                                      Table 6: Estimated ALM-Policy Interdependencies/Network in 2001
       AUS        AUT     BEL      CAN        DEN       FIN     FRA      DEU       GRE         IRE       ITA     JPN       NTH     NWZ       NOR        PRT       ESP      SWE      CHE    GBR    USA
AUS    0.000      0.060   0.359   0.028       0.094    0.156    0.194   0.174*     0.001      0.228   0.120*    0.157    0.080*    0.142    0.009*      0.034     0.189    0.136   0.084   0.039 0.103
       0.000     0.042    0.262   0.039      0.067    0.111    0.119    0.103      0.003     0.169     0.068    0.521     0.046    0.559    0.005      0.024     0.136    0.089    0.051  0.139 0.423
AUT    0.055      0.000   0.088   0.021*    -0.180*   -0.120   -0.073    0.086   -0.274***   -0.048    -0.104   0.048   -0.189**   0.035    0.010    -0.241***   -0.082   -0.138   0.127 -0.253** 0.028
       0.039     0.000    0.240   0.012      0.096    0.123    0.108    0.590      0.095     0.172     0.145    0.040     0.083    0.026    0.007      0.090     0.129    0.103    0.169  0.104 0.087
BEL    0.065   -0.204**   0.000   0.024*     -0.164   -0.093    0.030    0.004   -0.274***   -0.002    -0.130   0.053     -0.104   0.042    0.012    -0.234***   -0.045   -0.113   0.099 -0.208 0.037
       0.046     0.090    0.000   0.014      0.103    0.141    0.147    0.185      0.095     0.184     0.090    0.034     0.155    0.031    0.010      0.088     0.141    0.111    0.061  0.128 0.120
CAN    0.054      0.058   0.350   0.000       0.091    0.151    0.183    0.154     0.001      0.222     0.107   0.056      0.075   0.035    0.010       0.033     0.183    0.130   0.079   0.017 0.399
       0.037     0.043    0.265   0.000      0.069    0.115    0.128    0.099      0.001     0.171     0.072    0.073     0.050    0.026    0.008      0.024     0.139    0.096    0.056  0.041 0.979
DEN    0.057   -0.212**   0.096   0.021*      0.000   -0.108   -0.067    0.010   -0.273***   -0.042   -0.151*   0.052    -0.177*   0.036    0.033    -0.240***   -0.079   -0.053   0.088* -0.228 0.033
       0.038     0.088    0.240   0.012      0.000    0.104    0.109    0.204      0.095     0.169     0.086    0.051     0.100    0.027    0.107      0.089     0.133    0.217    0.051  0.185 0.107
 FIN   0.061   -0.209**   0.109   0.023     -0.162*    0.000   -0.061   -0.048   -0.273***   -0.035   -0.147*   0.057   -0.179**   0.037    0.063    -0.238***   -0.071   -0.042   0.091* -0.223 0.044
       0.036     0.086    0.247   0.015      0.084    0.000    0.111    0.245      0.095     0.175     0.086    0.068     0.089    0.028    0.276      0.089     0.132    0.205    0.052  0.202 0.155
FRA    0.059   -0.209**   0.155   0.023     -0.173*   -0.110    0.000   -0.020   -0.273***   -0.030    -0.101   0.053    -0.174*   0.038    0.013    -0.235***   -0.032   -0.130   0.112 -0.214 0.045
       0.040     0.088    0.223   0.015      0.097    0.130    0.000    0.214      0.095     0.174     0.109    0.047     0.097    0.028    0.019      0.087     0.122    0.107    0.096  0.129 0.162
DEU    0.059    -0.179*   0.139   0.022      -0.158   -0.111   -0.016    0.000   -0.272***   -0.034    -0.126   0.056     -0.145   0.037    0.015    -0.237***   -0.065   -0.128   0.118 -0.231 0.048
       0.039     0.097    0.239   0.014      0.143    0.123    0.122    0.000      0.094     0.171     0.136    0.065     0.100    0.028    0.027      0.088     0.119    0.098    0.079  0.171 0.176
GRE    0.053   -0.214**   0.084   0.020*   -0.180**   -0.123   -0.061   -0.039     0.000     -0.054    -0.100   0.055     -0.176   0.035    0.010    -0.242***   -0.082   -0.142   0.085* -0.239 0.031
       0.038     0.085    0.218   0.011      0.090    0.118    0.125    0.336      0.000     0.164     0.275    0.073     0.111    0.025    0.007      0.091     0.114    0.100    0.048  0.145 0.102
 IRE   0.061   -0.210**   0.132   0.023     -0.171*   -0.106   -0.049   -0.070   -0.275***    0.000    -0.147   0.057    -0.175*   0.039    0.013    -0.238***   -0.064   -0.127   0.094* -0.061 0.071
       0.041     0.093    0.242   0.014      0.098    0.133    0.115    0.136      0.096     0.000     0.088    0.060    0.090*    0.029    0.016      0.091     0.140    0.110    0.055  0.401 0.276
 ITA   0.058     -0.179   0.106   0.023     -0.177*   -0.117    0.006   -0.028   -0.269***   -0.041     0.000   0.048     -0.179   0.036    0.010    -0.238***   -0.063   -0.136   0.127 -0.237 0.044
       0.036     0.218    0.224   0.015      0.095    0.127    0.143    0.345      0.095     0.171     0.000    0.037     0.094    0.027    0.008      0.088     0.111    0.106    0.177  0.151 0.158
 JPN   0.079      0.060   0.358   0.036       0.095    0.154    0.194    0.182     0.002      0.227   0.114*    0.000    0.084*    0.039*   0.010       0.034     0.188    0.134   0.085* 0.028 0.211
       0.097     0.040    0.256   0.076      0.064    0.112    0.116    0.124      0.005     0.166     0.066    0.000     0.049    0.022    0.008      0.023     0.133    0.091    0.049  0.092 0.909
NTH    0.056   -0.213**   0.163   0.021*    -0.177*   -0.118   -0.052    0.014   -0.273***   -0.044    -0.148   0.047      0.000   0.035    0.014    -0.240***   -0.078   -0.135   0.086* -0.200 0.037
       0.039     0.087    0.224   0.012      0.091    0.122    0.131    0.281      0.095     0.166     0.089    0.036     0.000    0.027    0.024      0.089     0.125    0.098    0.050  0.151 0.129
NWZ    0.242      0.059   0.357   0.027       0.093    0.153    0.189   0.168*     0.002      0.225   0.115*    0.112      0.077   0.000    0.009*      0.034     0.187    0.134   0.081   0.038 0.087
       0.397     0.042    0.257   0.034      0.067    0.114    0.122    0.095      0.005     0.171     0.066    0.321     0.047    0.000    0.005      0.024     0.136    0.090    0.053  0.136 0.354
NOR    0.053      0.060   0.356   0.029       0.114    0.199   0.205*    0.204     0.002      0.225   0.115*    0.049      0.101   0.035    0.000      0.036*     0.188    0.218   0.081   0.082 0.038
       0.038     0.039    0.244   0.044      0.088    0.341    0.119    0.212      0.005     0.161     0.065    0.047     0.109    0.026    0.000      0.020     0.126    0.215    0.052  0.334 0.130
PRT    0.054   -0.215**   0.090   0.020*    -0.180*   -0.122   -0.042   -0.057   -0.275***   -0.051    -0.144   0.045   -0.182**   0.035    0.013       0.000     0.064   -0.139   0.085* -0.231 0.028
       0.038     0.089    0.222   0.011      0.093    0.123    0.174    0.247      0.096     0.169     0.103    0.031     0.093    0.026    0.021      0.000     0.459    0.100    0.049  0.175 0.087
 ESP   0.059   -0.209**   0.118   0.022*    -0.174*   -0.109    0.043   -0.045   -0.273***   -0.030    -0.118   0.051   -0.179**   0.038    0.011      -0.179     0.000   -0.130   0.091* -0.230 0.038
       0.041     0.088    0.245   0.013      0.099    0.130    0.192    0.243      0.095     0.176     0.154    0.042     0.087    0.028    0.010      0.276     0.000    0.108    0.054  0.174 0.130
SWE    0.059   -0.210**   0.110   0.023      -0.124   -0.066   -0.063   -0.051   -0.274***   -0.038   -0.150*   0.052   -0.175**   0.037    0.070    -0.239***   -0.075    0.000   0.090* -0.225 0.045
       0.037     0.087    0.231   0.016      0.166    0.202    0.110    0.237      0.095     0.172     0.085    0.048     0.099    0.027    0.133      0.089     0.133    0.000    0.052  0.194 0.163
CHE    0.057      0.095   0.372   0.021       0.098    0.158   0.249*    0.293     0.003      0.233     0.166   0.054    0.091*    0.036    0.010      0.036*     0.197    0.139   0.000   0.035 0.046
       0.037     0.128    0.249   0.013      0.063    0.113    0.135    0.369      0.008     0.168     0.107    0.060     0.063    0.027    0.007      0.021     0.127    0.088    0.000  0.122 0.166
GBR    0.058   -0.216**   0.112   0.026    -0.179**   -0.122   -0.035   -0.067   -0.274***   -0.014    -0.150   0.054     -0.150   0.036    0.018      -0.240    -0.080   -0.137   0.089* 0.000 0.069
       0.033     0.089    0.274   0.030      0.089    0.115    0.121    0.218      0.095     0.198     0.091    0.066     0.114    0.023    0.043      0.088     0.113    0.093    0.052  0.000 0.270
USA    0.060      0.059   0.355   0.228       0.092    0.151   0.196*    0.179     0.001      0.226   0.117*    0.121      0.084   0.036    0.010    0.034***     0.186    0.133   0.084* 0.037 0.000
       0.035     0.040    0.246   0.407      0.066    0.111    0.112    0.121      0.003     0.158     0.066    0.365     0.050    0.023    0.010      0.023     0.129    0.087    0.049  0.131 0.000
Note: Dependent variable: SEMP. Actual weights multiplied them by 100 (and standard errors adjusted accordingly)
to improve table formatting. [XXXX: These are for c-dums, no t-dums model]
2001
                             Conclusion
• Spatial & Spatiotemporal Interdependence
   – Important & Appreciable Substance (e.g., globalization & int‘l 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 ρ 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 Galton‘s 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 C&IPE

								
To top