Online Technical Appendix: Estimation Details. Following Netzer, Lattin and Srinivasan (2005), the model parameters to be estimated

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1 Onlne Techncal Appendx: Esmaon Deals Followng Nezer, an and Srnvasan 005, he model parameers o be esmaed can be dvded no hree pars: he fxed effecs governng he evaluaon, ncdence, and laen erence componens of he model whch do no vary across ndvduals or producs, ndvdual-specfc devaons from he fxed effecs governng evaluaon and ncdence behavor, and 3 produc-specfc devaons from he fxed effecs n he evaluaon model and laen erence componen. We denoe by ψ he se of fxed effecs from he evaluaon model and η, he ncdence model, δ and δ, and laen erence model θ. We le ζ be a vecor of he ndvdual-specfc devaons from he fxed effecs and. As noed n equaon, ζ ~MVN0,Σ. We le ξ denoe he ndvdual-specfc devaons from η, where ξ ~MVN0,Τ. parameers: The MCMC procedure draws parameers from he condonal dsrbuon of he model ζ,x, ξ,ψ,κ,τ,σ ξ,x,ζ,ψ,κ,τ,τ κ,x,ζ,ξ,ψ,τ,σ κ τ,x,ζ,ξ,ψ,κ,σ τ Σ ζ Τ ξ σ κ κ σ τ τ ψ,x,ζ,ξ,κ,τ where he se of observaons from ncdence decsons z and evaluaon decsons y and X denoes he sae of he rangs envronmen a he me of he observaons.

2 We nex descrbe how we sample he ndvdual-specfc random effecs ζ and ξ, produc-specfc random effecs κ and τ, covarance marces governng he random effecs Σ, Τ, σ κ, and σ τ, and fxed effecs ψ. Generang ndvdual-specfc random effecs for ndvdual fζ,x,ξ,ψ,κ,τ,σ πζ Σ ζ Σ -.5 [.5ζ 'Σ - ζ ] ζ A where πζ Σ s he pror dsrbuon of ζ and ζ s he ndvdual-specfc lkelhood gven by equaon 0. Snce A does no have a closed form, we use a random walk Meropols- Hasngs algorhm wh a Gaussan umpng dsrbuon o draw from he condonal dsrbuon of ζ. eng ζ denoe he value of he vecor on draw, he probably ha of accepng draw + s gven by: ' ] ' ] Pr [.5 accep mn [.5 A The procedure o draw ξ s smlar: fξ,x,ζ,ψ,κ,τ,τ πξ Τ ξ Τ -.5 [.5ξ 'Τ - ξ ] ξ A3 A random walk Meropols-Hasngs algorhm s used o draw from he condonal dsrbuon of ξ, where he probably of accepng a new draw s:

3 ] '.5 [ ] '.5 [ mn accep Pr A4 Generang produc-specfc random effec for produc fκ,x,ζ,ξ,ψ,τ,σ κ πκσ κ κ Πσ κ - [-κ /σ κ ]κ A5 where κ denoes he lkelhood of he daa, derved by akng he produc of he ndvdual-specfc lkelhood n equaon 0 across ndvduals. We use a random walk Meropols-Hasngs algorhm o draw from he condonal dsrbuon of κ. The probably of accepng κ + s: mn Praccep A6 Drawng from he condonal dsrbuon of τ follows a smlar procedure: fτ,x,ζ,ξ,ψ,κ,σ τ πτσ τ τ Πσ τ - [-τ /σ τ ]τ A7 Usng he random walk Meropols-Hasngs algorhm, he probably of accepng draw + s:

4 mn Praccep A8 For effcency, we updae he parameers κ and τ n blocks of mulple producs Chb and Greenberg Updang Covarance Marces Condonal on he values of he ndvdual-specfc random effecs ζ and ξ and he produc-specfc random effecs κ and τ, he correspondng covarance marces can be sampled drecly. We begn by drawng values of Σ condonal on he ndvdual-specfc random effecs ζ. Followng Nezer, an and Srnvasan 005, he condonal dsrbuon of Σ s gven by: N p G N f IW 0 0 ', ~ A9 where IW p denoes an nverse-wshar dsrbuon, p s he lengh of he vecor ζ n our case, p=6, and N s he number of observaons. To assume a dffuse pror, we assume ha f 0 =p+5 and G 0 - s an deny marx of sze p. In he same fashon, he covarance marx Τ s drawn from he condonal dsrbuon Τ ξ, he varance σ κ s drawn from he dsrbuon σ κ κ, and σ τ s drawn from σ τ τ.

5 4 Updang Fxed Effecs The vecor of fxed effecs ψ s drawn n a smlar fashon o he ndvdual-specfc and producspecfc random effecs. The condonal dsrbuon of ψ s gven by: fψ,x,ζ,ξ,κ,τ πψ ψ V -.5 [.5ψ V - ψ]ψ A0 where πψ s he pror dsrbuon of ψ. We assume a dffuse normal pror by seng he mean equal o a vecor of zeros of lengh q, where q s he lengh of ψ, and covarance marx V=5I q. As he condonal dsrbuon gven n A0 does no have a closed form, we use a random walk Meropols-Hasngs algorhm o draw from he condonal dsrbuon. The probably of accepng draw + s gven by: [.5ψ ' V ψ ] ψ Pr accep mn [.5ψ ' V ψ ] ψ A Addonal References Chb, Sddharha and Edward Greenberg 995, Undersandng he Meropols-Hasngs Algorhm, The Amercan Sascan, 49 4, Nezer, Oded, James M. an and V. Srnvasan 008, A Hdden Markov Model of Cusomer Relaonshp Dynamcs, Markeng Scence, 7,