Methodology for Analyzing State Tax Policy By Orphe Pierre Divounguy, PhD, Revised by Andrew J. Kidd, PhD (May 2018)

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1 Mhodology for Analyzing Sa Tax Policy By Orph Pirr Divounguy, PhD, Rvisd by Andrw J. Kidd, PhD (May 2018) Inroducion To analyz how changs o ax policy impacs no only govrnmn rvnus bu also conomic aciviy and dcisions mad by businsss and ciizns, conomiss a Th Bucky Insiu s Economic Rsarch Cnr (ERC) dvlopd a dynamic scoring modl ha prdics h ffcs of policy changs on gross domsic produc, jobs craion or loss, and rvnu. Bucky s dynamic scoring modl is in kping wih currn conomic pracics a h fdral lvl, which uss dynamic analysis and dynamic scoring o analyz major fdral ax policy proposals. This modling simulas changs in h conomy ha rsul from changs in ax policy and shows how hos changs impac ax rvnus. Using his dynamic scoring modl, calibrad for Louisiana wih publically availabl daa, conomiss wih h ERC ar abl o prdic how proposals by policymakrs will impac h sa s conomy and sa rvnus. A proposal analyzd using h modl ss how h policy affcs h choics of housholds and businsss in h conomy. For xampl, h proposal o incras h sals ax in Louisiana rducs how much h ciizns spnd on goods and srvics. As a rsul of popl spnding lss, businsss hir fwr workrs. This inracion canno b capurd using a saic analysis. Each scion of h modl incorporas h proposd ax policy and rvals h rsuling changs in bhavior of popl and businsss. Th dynamic procss allows h modl o simula how a policy affcs all aspcs of h conomy. Th Basic Modl Tim is discr and lass forvr. Evry priod, h conomy is populad by hrognous housholds spcializd in h producion of on of ( s) yps of goods. Sinc h Burau of Economic Analysis rpors macroconomic daa for US sas in yarly inrvals, a priod is assumd o b a yar in his framwork. Each scor ( s) is populad by a larg numbr of idnical firms. Th conomy also faurs a govrnmn scor ha collcs axs and purchass goods from all scors. A shar q (0, 1 ) of housholds has arning abiliy = { 1,, E }.

2 Ths shars ar such ha h oal populaion is rquird skills o work in scor s is μ,s (0, 1) such ha μ,s = 1. q = 1. Th shar of housholds wih h Th Houshold Problm Each houshold chooss consumpion c,, savings k, (s), how much o borrow d, (s) and mark hours (s), o solv h following problm: l, 1 (1+ ) V, (s) = max c (s),l (s),k (s) U(c ) l (s) E[V (s)],,,, φ σ, + β,+1 subjc o h following consrains: c d, = ζ (1 + τ ) S (s) + ( 1 ζ) S (s) + S x, (s) + ( 1 + i r, 1 )d, 1 + τ k S k, 1 (s) + [ ϕ 2 ( S (s) S (s) c, c, k, (s) = x, (s) + ( 1 δ)k, 1 (s) c, (s) 0, l, (s) [0, 1 ], k,0 (s) 0, k,t +1 (s) = 0 ) = S ln(c (s)) U(c, α s, k, whr δ is h dprciaion ra of capial V, (s) dfins xpcd uiliy discound a a pain facor β [0, 1 ]. As in Mndoza (1991) ϕ dnos a capial adjusmn cos. Housholds wigh consumpion goods according o α s (0, 1 ). Th paramr ha rgulas h Frisch lasiciy of labor supply is dnod σ and φ is a scaling facor ha hlps mach hours workd obsrvd in h daa. Th rurn on capial ln o firms is r (s). Th wag paid o workrs in scor s is w (s). Consumpion is dnod c (s), x (s) dnos gross invsmn, and k (s) dnos physical capial ln o firms in scor s. i r, dnos h inrs ra a which domsic rsidns can borrow from inrnaional marks in priod, and d is houshold db. W assum i r, = i r,w + η(xp (D D ) 1) whr i r,w is h world inrs ra facd by domsic agns and is assumd o b consan, η and D ar also consan paramrs. η(xp (D D ) 1) is h sa spcific inrs ra prmium ha incrass wih h lvl of db. Th assumpion of a db lasic inrs ra is akn from Schmi-Grohé and Urib (2003). D rprsns h aggrga lvl of db. is h ax on houshold consumpion purchass. ζ is h shar of consumpion goods subjc o h sals ax, and τ i,s is h individual incom ax collcd by h sa. τ i,f is h individual τ c, incom ax collcd by h fdral govrnmn. Incom ax ras dpnd on h individual k corp arning abiliy. τ is a ax on fixd asss ownd by housholds. τ is h corpora incom ax o facd by h ownrs of capial. τ is h shar of incom paid o all ohr axs, fs, and rvnu sourcs for h sa govrnmn no includd spcifically in h modl., k, 1

3 Individuals choos { c,, x,, l,, k,+1, d, } =0 so as o maximiz h uiliy funcion subjc o h rsourc consrain and a no-ponzi schm consrain ha implis ha h houshold s db posiion mus b xpcd o grow a a ra lowr han h inrs ra in h long-run. Firms In ach scor s, a larg numbr of compiiv firms produc goods according o h following producion funcion: θs y (s) = a (k 1 (s)) ( z l,(s) ) Ths firms solv h following profi maximizaion problm: (1 θ ) s ca θs Π = ( 1 τ )a (k 1(s)) ( z l,(s) ) w, (s)l, (s) r (s)k 1 (s) whr a is oal facor produciviy (TFP), θ is associad wih h capial shar of oal oupu. z is labor produciviy spcific o a houshold mmbr s arning abiliy. I is imporan o no ca ha h dmand for labor is scor s spcific. τ is a commrcial aciviy ax, modld as a ax on a firm s rvnus. (1 θ ) s Th rprsnaiv firm in scor s hirs labor according o h following condiion: (1 τ ca θs )(1 θ s )a (k 1(s)) ( z l,(s) ) z = w, (s), whr w. (s) is h wag ra for group in scor ( s). Th dmand for capial is such ha: ( θ ) s ca θs 1 ( 1 τ )a (k 1(s)) ( z l,(s) ) = r (s), W assum a follows a saionary man zro auorgrssiv procss of ordr 1 in h log. Th shock innovaion is drawn from a sandard normal disribuion. ϵ A, (a ) = ρ A (a 1 ) + ϵ A, Th Govrnmn Scor Th govrnmn conribuions o h rainy-day fund { RF } is h xcss of ax rvnu plus fdral govrnmn ransfrs n of govrnmn spnding addd o h prvious priod s balanc. (1 θ ) s RF = T + F F g Dficis - ngaiv conribuions - o h rainy-day fund rduc h fund s balanc.

4 Th sa govrnmn s ax rvnus T ar givn by: T = E S s ca c (τ y (s) + τ ζc (s) + τ ζc (s) + τ i,s w (s)l (s) r (s)k (s) k (s)+ y (s) ), + τ i,s k o, 1 + τ 1 τ Govrnmn spnding policy is assumd o volv according o: κ 1 )(κ) (κ ) = ( ρ g,h + ρ g,h 1 + ϵ g whr κ is h sa shar of incom spn by h govrnmn scor in h long-run, h sady-sa quilibrium. This spcificaion implis ha g = κy which mans ha h siz of govrnmn rflcs changs in GDP. I also implis ha govrnmn is assumd o grow as h conomy grows. Variabls wihou h im subscrip dno sady-sa valus. Th ax insrumns follow h xognous procsss: τ i,s = ( 1 ρ )τ i,s i,s τ i,s + ρ + ϵ i,s 1 i,s τ c = ( 1 ρ )τ c c c + ρ c τ 1 + ϵ c τ = ( 1 ρ )τ + ρ τ 1 + ϵ τ corp = ( 1 ρ )τ corp τ corp + ρ corp corp 1 + ϵ corp τ ca = ( 1 ρ )τ ca ca ca + ρ ca τ 1 + ϵ ca τ k = ( 1 ρ )τ k k k + ρ k τ 1 + ϵ k τ o = ( 1 ρ )τ o o o + ρ o τ 1 + ϵ o i,f τ = ( 1 ρ )τ i,f i,f τ i,f + ρ + ϵ i,f 1 i,f As in Schmi-Grohé and Urib, w wri h rad balanc o GDP raio (TB) in sady-sa as: [c+x+g] T B = 1 y Th Compiiv Equilibrium A compiiv quilibrium is such ha givn h s of xognous procsss, housholds solv h houshold uiliy maximizaion problm, firms solv h profi maximizaion problm, h capial and labor marks clar. Th Drminisic Sady-Sa Th characrizaion of h drminisic sady sa is of inrs for wo rasons. Firs, h sady-sa facilias h calibraion of h modl. This is bcaus, o a firs approximaion, h drminisic sady-sa coincids wih h avrag posiion of h modl conomy. In urn, maching avrag valus of ndognous variabls o hir obsrvd counrpars (.g., maching prdicd and obsrvd avrag valus of h labor shar, h consumpion shars, or h radbalanc-o-oupu raio) can rval informaion abou srucural paramrs ha can b xploid

5 in h calibraion of h modl. Scond, h drminisic sady-sa is ofn usd as a convnin poin around which h quilibrium condiions of h sochasic conomy ar approximad (s Schmi-Groh and Urib, 2003). For any variabl, w dno is sady-sa valu by rmoving h im subscrip. Using h soluion from h housholds and firms choic problms, h sady-sa implis ha: 1 = β[(1 τ i,s τ o τ i,f τ corp )r + 1 δ τ k ] y = k θs l (1 θ s ) k ( ) θ s 1 = r Ths xprssions dlivr h sady-sa capial-labor raio, which w dno ω Th sady-sa lvl of capial is: θ s ω k l = ( ) l 1 β 1+δ+τ i,s o i,f corp θ (1 τ τ τ τ ) s k = ω l k 1/(θ 1) s Finally, h sady-sa lvl of consumpion can b obaind by valuaing h rsourc consrain a h sady-sa: which implis: y = c + x + g + T By c = y δk g T By As for h paramr ha dicas housholds prfrnc for lisur: φ = α s c i,s o i,f,, (1 τ τ τ )w (1+τ +τ )c, (s) 1 (1+ )l (s) Calibraion Typically, a calibraion assigns valus o h modl paramrs by maching firs and scond momns of h daa ha h modl aims o xplain. Th dprciaion ra of capial δ and h world inrs ra i r,w ar basd on paramr valus widly usd in h rlad businss-cycl liraur and on h avrag annual dprciaion ra akn from h Burau of Economic Analysis, δ = 0.1 and i r,w = Th scor spcific paramr θ s is s o mach h obsrvd avrag labor shars for ach of nin producion scors in Louisiana. In h prsn modl, h labor shar is givn by h raio of labor incom o oupu which is 1 θ s a all ims. σ,, 1 σ (s)

6 Th paramr D is s o mach h obsrvd avrag rad-balanc o oupu raio in Louisiana sinc T B = i r,w D/y

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