WORKING PAPER SERIES

WORKING PAPER SERIES 08 206 Fsal poly reforms n a general equlbrum model h mperfeons Panagoa Kolous, Naasha Maoul, Aposols Phlppopoulos Πατησίων 76, 04 34 Αθήνα. Tηλ.: 20 8203303 5 / Fax: 20 8238249 76, Passon Sree, Ahens 04 34 Greee. Tel.: (+30) 20 8203303 5 / Fax: (+30) 20 8238249 E mal: eon@aueb.gr /.aueb.gr

Fsal poly reforms n a general equlbrum model h mperfeons Panagoa Kolous *, Naasha Maoul, Aposols Phlppopoulos November, 206 Absra: The debae on he ay of sablzng he eonomy, hrough us n publ spendng or rses n axes, has been nensfed afer he rss n 2008. Ths holds prmarly for he Eurozone perphery ounres. In ve of hgh publ debs, hese ounres have been urged o adop resrve fsal poles hh have furher dampened demand and have orsened he reesson, a leas n he shor erm. I s non ha hn a dynam general equlbrum (DGE) model h a represenave agen a reduon of apal ax raes and he move of he ax burden o labour axes produes soal elfare benefs. Hoever, one should no negle he resulng dsrbuonal mplaons, hh may favour some soal groups vs-à-vs ohers. Suh dsrbuonal mplaons are sgnfanly nfluened by mperfeons n produ and labour mares. Thus, hs paper employs a DGE model ha norporaes heerogeneous agens (enrepreneurs and orers) and mperfely ompeve produ and labour mares, augmened h a relavely rh publ seor, o quanfy he maroeonom and dsrbuonal mplaons of fsal reforms le he above n he euro area. Our man resuls are as follos: Frs, he mos effeve poly for he governmen o boos oupu s o redue he apal ax rae, regardless he poly nsrumen ha adjuss. In addon, f he goal of ax-spendng poly s o promoe elfare, hen should derease he ax rae on labour and nrease he onsumpon ax rae. Fnally, a reduon n any of he ax raes, fnaned by an nrease n apal ax rae, leads o a fall of nequaly beeen he o soal groups. Keyords: rade unons, mare sruure, sruural reforms JEL lassfaon: J5, I. Ahens Unversy of Eonoms and Busness, Ahens Greee CESfo, Munh * Correspondng auhor: Panagoa Kolous, Deparmen of Eonoms, Ahens Unversy of Eonoms and Busness, 76 Passon sr., Ahens 0434, Greee, e-mal: golous@aueb.gr

Inroduon Fsal poly reforms have been ell researhed and here s a long radon n searhng he ays of sablzng he eonomy h he use of a mx of publ spendng and ax poly. Ths debae has been nensfed afer he emergene of he rss n 2008, h mos of Eurozone perphery ounres experene a serous deb rss. In ve of hs fa hese ounres have been urged o adop resrve fsal poles dampenng demand and leadng o severe reesson. So, ssues ha deal h he mx of axes h he reduon of publ deb and smulaon of he eonomy, ae on grea mporane n Europe. I s non ha hn a dynam general equlbrum (DGE) model h a represenave agen a reduon of a onsan apal ax rae and he move of he burden o labour ax produes oupu benefs for he soey. Hoever, one should no negle mporan dsrbuonal mplaons hh favour some groups vs a vs he ohers. These gans and dsrbuonal mplaons are nfluened from he mperfeons n produ and labour mares. In lgh of he above, hs paper employs a DGE model ha norporaes heerogeneous agens (enrepreneurs and orers) and mperfely ompeve produ and labour mares, augmened h a relavely rh publ seor, o examne he quanave maroeonom and elfare mplaons of fsal reforms n Euro Area. I onrbues o he leraure on he effes of ax-spendng poly reforms. In parular, analyses he effes of: () hanges n he omposon of ax raes; and () hanges n publ nvesmen me by adjusmen n one of he dsorng ax rae. I s explored ho hese reforms affe he eonomy boh n long run and along he ranson pah o a ne pos-reform seady sae. A qualave assessmen of he elfare effes assoaed h he alernave poly reform s also provded. Our man resuls are as follos: Frs, he mos effeve poly for he governmen o boos oupu s o redue he apal ax rae, regardless he poly nsrumen ha adjuss. In addon, f he goal of ax-spendng poly s o promoe elfare, hen should derease he ax rae on labour and nrease he onsumpon ax rae. Fnally, a reduon n any of he ax raes, fnaned by an nrease n apal ax rae, leads o a fall of nequaly beeen he o soal groups. We noe ha he resuls qualavely are nuvely and quanavely are small. The res of he paper s organsed as follos: seon 2 presens he heoreal model, seon 3 nludes baselne parameerzaon, seon 4 sudes he ax-spendng reforms and fnally, he las seon onludes he resuls. An Appendx nludes ehnal deals. 2 Model Ths seon ses up a dynam general equlbrum model h mperfe ompeon n produ and labour mares. We sar h an nformal desrpon of he model. 2. Informal desrpon of he model The eonomy onsss of households, frms, rade unons and a governmen. There are o dsn ypes of households, alled enrepreneurs and orers, ho dffer n apal onershp. 2 Enrepreneurs save n he form of physal apal and governmen bonds. They also on he frms and reeve her profs. Worers, on he oher hand, are assumed o fae For he effes of ax-spendng reforms n general equlbrum models h mperfeons, see among ohers Ardagna (2007), Angelopoulos e al. (203). 2 The dsnon beeen apalss and orers follos a long radon n he leraure on eonom poly and soal onfl ha daes ba o e.g. Judd (985). See Lansng (20) for a reve of general equlbrum models h onenraed onershp of apal as a ype of agen heerogeney. 2

ransaons oss for savng or borrong hh prohb her parpaon n fnanal mares; hey hus onsume all her dsposable nome n eah me perod. Worers may be unemployed; n hs ase, hey reeve unemploymen benefs from he governmen. Worers (employed and unemployed) are represened by a rade unon hh bargans h frms over he age rae n a rgh-o-manage unon fashon. On he produon sde, here are fnal and nermedae good frms. Fnal good frms a ompevely and mae zero profs. By onras, nermedae good frms, beng oned by enrepreneurs, enjoy monopoly poer n her on produ mare and mae profs. Fnally, he governmen ssues bonds and axes onsumpon, labour nome and apal nome n order o fnane publ spendng. The laer nludes a unform lump-sum ransfer o all households, publ nvesmen ha augmens publ nfrasruure benefng prvae frms, publ onsumpon ha provdes dre uly o all households and unemploymen benefs reeved by unemployed orers. The me horzon s nfne and he me s dsree. For smply, here s no unerany. 2.2 Populaon Toal populaon, N, s exogenous and onsan over me. There are =, 2,..., N denal enrepreneurs and =,2,..., N denal orers, here N N N =. I s onvenen o defne her populaon shares, N / N n and n = n. For noaonal smply, e assume ha eah enrepreneur ons one of he prof-mang nermedae good frms, N ; hus, he number of hese frms equals he number of enrepreneurs, N = N. 2.3 Households As sad, here are o ypes of households, enrepreneurs and orers. The lfeme uly of eah ype of household, denoed by supersrp j=,, s: ( + ψ ) j β u C G () = 0 here he parameer β ( 0,) s he me preferene rae, j C s j s onsumpon and G s average (per household) governmen spendng on uly-enhanng publ goods and serves. Thus, as n e.g. Chrsano and Ehenbaum (992), governmen onsumpon ψ,. 3 spendng nfluenes prvae uly hrough he value of he parameer [ ] In our numeral soluons, e ll use for he nsananeous uly funon: j ( ψ ) u C + G = j ( C ) + ψg σ σ (2) here σ > s a parameer. 2.3. Households as enrepreneurs 3 Follong he relaed leraure (see e.g. Ardagna, 2007, and Angelopoulos e al., 203), and for smply, e do no allo for endogenous lesure n he uly funon. All agens supply nelasally one un of me hen a or. 3

Eah enrepreneur,, saves n he form of physal apal, I, and governmen bonds, D. He reeves gross nome from one un labour serves suppled nelasally a a age rae,apal holdngs, r K, and governmen bonds, r B. Thus, r denoes he gross reurn o he begnnng-of-perod apal, b r denoes he gross reurn o he begnnng-ofperod governmen bonds, K, and b B. To addonal soures of nome are dvdends pad by frms, π, and average (per household) lump-sum governmen ransfers, budge onsran of eah enrepreneur a me s: G. Thus, he ( + τ ) C + I + D = ( ) ( ) ( ) ( ) = τ e + G e + r K τ r δ K + r B + τ π + G u p b (3) here 0 < s he ax rae on onsumpon, 0 < s he ax rae on labour nome, 0 τ τ p < s he ax rae on nome from apal and dvdends and he parameer δ ( 0,) s he depreaon rae of apal. 4 The las of moon of physal apal and governmen bonds are: K = ( δ ) K + I, K > 0 gven (4) p + 0 τ B = B + D, B > 0gven (5) + 0 Therefore, he enrepreneur s problem s o hoose { C, K+, B+ } = 0 o maxmze () and (2) subje o he budge onsran, (3), and he la of moon of apal and bonds, (4) π =, b and (5), ang mare pres { r, r, }, he employmen rae = 0 { e}, profs = 0 { } 0 u poly varables { } 0 τ, τ, τ, G, G, and nal ondon for K = 0 and B 0 as gven. The frs order ondons nlude he onsrans, (3)-(5), and: p (( + )( r+ ) ) u(.) u+ (.) = β τ δ + ( + τ) C ( + τ+ ) C+ u(.) u+ (.) = β + ( + τ) C ( + τ+ ) C+ b ( r + ) (6a) (6b) hh are he Euler equaons for K + and B + respevely. The opmaly ondons are ompleed h he ermnal ondons, u(.) lm β K 0 + = C and u(.) lm β B 0 + =. C 4 We assume ha apal axes are ne of depreaon and ha he fsal auhores anno mpose separae ax raes on profs and apal nome. We also assume ha reurns o governmen bonds are unaxed. These assumpons are no mporan o our resuls. 4

2.3.2 Households as orers Sne orers are exluded from fnanal mares, he hn-perod budge onsran of eah orer,, s: ( τ ) C ( τ ) ( ) + = e + G e + G (7) u Indvdual orers do no mae any hoes. Gven, hh s deermned by he frm-unon barganng and he assoaed employmen level, e, deermned by frms (see belo), her onsumpon follos resdually from her budge onsran (7). 2.4 Frms and he produon sruure The produon envronmen onsss of o seors: he nermedae good seor and he fnal good seor. Follong Guo and Lansng (999) and many ohers n he leraure on mperfe ompeon n produ mares, e assume ha he fnal good seor s perfely ompeve, hle eah nermedae good frm as as a monopols n s on mare. 2.4. Fnal good frms Assume, for smply, ha he sngle fnal good s produed by one frm. The oupu of hs frm, Y, s produed by a Dx-Sglz ype onsan reurns o sale ehnology: Y N θ θ = λ ( Y ) = (8) here λ denoes he egh aahed o eah npu (e assume λ = o avod sale effes, n equlbrum) and ( 0,] nermedae good produers. 5 The prof of he fnal good produer s defned as: θ s a measure of he monopoly poer enjoyed by N = N Y λpy = Π = (9) here good. P s he pre of eah nermedae good relave o he pre of he sngle fnal The fnal good produer behaves ompevely by hoosng nermedae npus, o maxmze profs, Π. The frs-order ondon yelds he ell-non funon: Y, P Y = Y θ (0) 5 When θ =, nermedae goods are perfe subsues o eah oher n he produon of he fnal goods so ha nermedae good produers have no mare poer. 5

hh gves he demand funon for eah nermedae good, 2.4.2 Inermedae good frms Eah nermedae frm produes a homogeneous produ, npus, apal, produon funon s: 6 K, and orers, Y, used n he nex sep. Y, by hoosng o prvae L, and by usng average (per frm) publ apal, g K N. Is Y α K =Α N g α 2 ( K) ( L) α 3 () here A s oal produvy and,, ( 0,) α α α denoe he oupu elasy of prvae 2 3 apal, labour and publ apal, respevely. We assume onsan reurns o all hree npus and spefally α+ α2+ α3 =. The prof earned by he nermedae good produer a me s: π = PY r K L (2) Tang faor pres, r and as gven, he nermedae good frm hooses g K N, L o maxmze profs, (2), subje o, fnal oupu, Y, and average publ apal, K and s produon funon, (), and he demand funon for s oupu, (0) (see Appendx C for more deals). The frs order ondons are: θα θα 2 θ ( Y) ( Y ) θ r K θ ( Y) ( Y ) θ L = (3a) = (3b) he above ondons equae faor reurns o margnal produs. In urn, he prof of eah nermedae good frm s: θ ( θα θα2)( ) ( ) π = Y Y θ (4) 2.5 Trade unon and age barganng We employ a rgh-o-manage seup here rade unons (represenng orers) and frm federaons (represenng monopols nermedae good frms) bargan over orers age 6 We nlude publ nvesmen, and hene publ apal, beause e sh o have as many fsal poly nsrumens as possble and o be lose o he daa. See e.g. Lansng (998), for a smlar produon funon. 6

rae,. Thus, s hosen so as o maxmze a eghed average of he represenave orer s labour nome and he represenave nermedae good frm s prof: ( τ ) ( ) φ N u u = + π + U n L G n L G r K φ (5) subje o he labour demand funon (3b), and he nermedae frm s produ demand funon, (0), ang he apal so, K, fnal oupu, Y, and he fsal poly varables, { τ,,, u, τ τ G G}, as gven. In he above seup, n L e s he average employmen rae, so ha ( n L ) s he unemploymen rae and φ [ 0,] desrbes he relave barganng poer of he unon, h φ = represenng he monopoly unon ase. The ousde opon for he unon s he u unemploymen benef, G, hle for he frm s he sun os of apal, r K, hh s a onsequene of he assumpon ha he represenave frm aes he average apal aumulaon as gven (see Appendx D for more deals). The frs order ondon s: ( τ ) θα2( Y) ( Y ) ( ) θ φ+ φ α θ = (6) 2.6 Governmen θ 2 u GL θα2 On he revenue sde, he governmen ssues ne bonds, B +, and axes onsumpon, labour nome and apal nome a he raes 0 <, 0 < and 0 < respevely. On τ u he spendng sde, he governmen spends on oal unemploymen benefs, NG ( e ) oal lump-sum ransfers, τ NG, oal publ nvesmen, publ nvesmen) and oal publ onsumpon, budge onsran s: τ NG (e defne, G as he per apa NG. Thus, he hn-perod governmen ( ) ( ) NG + NG + NG + NG e + + r B = u b ( ) p = N τ r δ K + N τπ + Nτ e + N τc + N τ C + B+ (7) Publ nvesmen spendng s used o augmen publ apal used by frms. If e g g K defne he per apa publ apal as, he la of moon s: N g = ( g ) g δ + + G (8) g here he parameer ( 0,) δ s he depreaon rae of publ apal. If e dvde he above aggregae onsran by oal populaon, e have n per apa erms: 7

u b B G + G + G + G ( e ) + ( + r ) = N p B+ = nτ r δ K + nτπ + τ e + n τc + nτ C + N ( ) (9) Thus, n eah perod, here are egh poly nsrumens ( τ,,, u,,, τ τ G G G G, B+ ) ou of hh only seven an be se ndependenly, h he eghh follong resdually o sasfy he governmen budge onsran. Follong mos of he relaed leraure, e assume ha, along he ranson pah, he adjusng nsrumen s he end-of-perod publ deb, B +, so ha he res an be se exogenously by he governmen. A he seady sae, e ll, nsead, se he deb-o-oupu rao as n he daa and allo governmen ransfers o be he resdually deermned publ fnanng nsrumen. For onvenene, onernng he spendng poly nsrumens, e or n erms of her GDP shares: s s NG G =, N Y ny NG G =. N Y ny s NG G =, N Y ny s u u u G ( N N L) G ( n L) G ( e) = = and N Y ny ny u 2.7 Deenralzed dsequlbrum (DD) of he saus quo eonomy We solve for a symmer deenralzed dsequlbrum (DD). Symmery mples Y = Y and P = (see also e.g. Guo and Lansng, 999). Gven he exogenously se poly nsrumens { τ,,, u,,, τ τ s s s s} 0, and nal ondons for he sae varables, K = 0 and B 0, a symmer DD s defned o be an alloaon g b { Y, C, K+, C, e, π, +, r, r,, B+ } = 0 suh ha () households, frms and unons underae her respeve opmzaon problems; () all budge onsrans are sasfed; and () all mares lear exep n he labour mare here e an have devaon from full employmen (full employmen means e = ). Deals are n Appendx. Ths s for any feasble poly. The dynam sysem summarzng hs symmer DD and he resulng sysem n he seady sae are presened n Appendes 2 and 3 respevely. The nex seon solves hs model numerally. 3 Parameerzaon and soluon of he above model Ths seon solves he above model numerally. 3. Parameer values and poly nsrumens Table repors he baselne parameer values for ehnology and preferene, as ell as he values of exogenous poly varables, used o solve he above model eonomy. The me un s mean o be a year. Regardng parameers for ehnology and preferene, e use relavely sandard values ofen employed by he busness yle leraure. Publ spendng and ax rae values are hose of daa averages of he European eonomy over 990-2008. The daa are obaned from OECD, Eonom Ouloo No. 90. 8

Table : Baselne parameer values and poly nsrumens Parameers and poly nsrumens Defnon Value 0 β Rae of me preferene 0.97 0 α Prvae apal share n produon 0.33 0 α Labour share n produon 0.65 2 0 α Publ apal share n produon 0.02 3 p 0 δ Depreaon rae on prvae apal 0.0 g 0 δ Depreaon rae on publ apal 0.0 0 n Populaon share of enrepreneurs 0.30 σ > Relave rs averson oeffen 2 A TFP level ψ Subsuably beeen prvae and 0 publ onsumpon n uly 0 φ Unon poer 0.50 0 θ Produ mare poer 0.90 0 τ Consumpon ax rae 0.936 0 τ Tax rae on apal nome 0.3209 0 τ Tax rae on labour nome 0.3667 u s Unemploymen benefs o oupu rao 0.024 B Υ Publ deb o oupu rao 0.60 s Publ Consumpon o oupu rao 0.20 s Publ Invesmen o oupu rao 0.02 Le us dsuss, brefly, he values summarzed n Table. Worers and enrepreneurs labour shares n he produon funon of he nermedae good frm, α2and α 3, are se a 0.45 and 0.20 respevely. The publ apal share, α 4, s se equal o 0.02, hh s also he GDP share of publ nvesmen n he daa (see e.g. Baxer and Kng, 993, for smlar prae for he US). Gven he values of α 2, α3and α 4, he prvae apal share s α= α2 α3 α4 = 0.33. We normalse he oal faor produvy parameer, Α, o. We also use ommon values for he neremporal elasy of subsuon, σ = 0.5 or σ = 2 and he me dsoun faor, β = 0.97. We assume ha he depreaon rae of physal apal s 0%, hh s he value alulaed by Angelopoulos e al., (2009), and also se he same value for he depreaon rae of publ apal. Noe ha he depreaon raes maer for he long-run value of he nvesmen share n GDP, bu have lle effe on near seady-sae dynams n hs lass of models (see also e.g. Kng and Rebelo, 999). The parameer, ψ, hh measures he degree of subsuably/omplemenary beeen prvae and publ onsumpon n he uly funon, s se equal o 0; as Chrsano and Ehenbaum (992) explan, hs means ha governmen onsumpon s equvalen o a resoure dran n he maro-eonomy. We se he share of enrepreneurs, n, o 0.3. Ths s he share of households, as alulaed by Angelopoulos e al. (203), ho have savngs above 0,000. We hoose a neural value for unon poer, φ= 0.5, hh s n he mddle of he range 9

(.e. 0.4 o 0.6) of values ypally used n he leraure, and a value for he mare poer n he produ mare, θ = 0.9, mplyng ha profs, n equlbrum, amoun o around 0% of GDP. 7, 8 The effeve ax raes on onsumpon, apal and labour n he daa are respevely τ = 0.936, τ = 0.3209 and τ = 0.3667. The values of he oupu shares of publ spendng on onsumpon and unemploymen benefs are respevely s = 0.20 and u s = 0.024. A he seady sae, he publ deb o oupu rao s se a 0.60, hh s lose o he average value n he daa over he sample perod and has also been he Maasrh Treay referene value. In urn, governmen ransfers as a share of oupu, s, follo resdually o lose he governmen budge n hs seady sae soluon. 3.2 Seady sae soluon or he saus quo Gven he parameer and poly nsrumen values n Table, he seady sae soluon of he model eonomy s repored n Table 2. The soluon s meanngful. For nsane, he soluon for he ey raos, le onsumpon and prvae nvesmen as shares of oupu, as ell as he replaemen rae, are lose o hose n he daa. Ths seady sae soluon s ha e all he saus quo or pre-reformed. We also repor ha hs eonomy, hen loglnearzed above s seady sae soluon, s saddle-pah sable. In he nex seon, deparng from hs saus quo seady sae soluon, e ll sudy he mplaons of varous sruural reforms. In he nex seons, deparng from hs saus quo soluon, e sudy he mplaons of fsal poly reforms. Table 2: Pre-reform seady sae CY 0.582 τ 0.3209 I Y 0.979 u= e 0.0807 K Y.9788 0.7600 g K Y 0.2000 ɶ 0.483 B Y 0.6000 r 0.455 s 0.343 rɶ 0.0309 u s 0.0240 C 0.6952 s 0.2000 C.0828 s 0.0200 C 0.529 π Y Toal 0.270 U -.5999 u G 0.4675 U -0.9235 τ 0.3667 τ 0.936 U -.8898 4 Fsal poly reforms Ths seon dsusses he hypoheal reforms suded and hen repors numeral resuls. 7 See e.g. Domej (2005) for a dsusson of he relevan sudes and empral evdene. 8 Ths value approxmaes he magnude ypally employed n Ne Keynesan models o apure he pre mar-up over margnal oss. 0

4. Dsusson of sruural reforms suded Deparng from hs suaon, or ha e have alled he saus quo, e sudy he aggregae and dsrbuonal effes of hangng he ax-spendng mx. We ondu poly expermens n hh he governmen a me =0 underaes a permanen, unanpaed hange n one of he dsorng ax raes or spendng aegores( τ, τ, τ, G, G, G ), ompensaed by a permanen hange n anoher nsrumen ha adjuss o sasfy he neremporal governmen budge onsran (Domej and Heahoe, 2004). In our expermens, e hange only one exogenous poly nsrumen a a me, and allo only one poly nsrumen o adjus a a me, hle eepng all oher nsrumen onsan a her nal seady sae levels. In addon, durng he ranson o he ne seady sae, he end of perod publ deb follos resdually from he hn perod governmen budge onsran n eah me perod. Espeally, e onsder reforms ha hange he omposon of he ax mx as ell as reforms ha aler he omposon of he ax-spendng mx. In parular, o sudy he effes of hanges n he ax mx, e examne poly expermens n hh () a 0% permanen reduon n apal ax rae, τ, s me by a permanen nrease n labour ax rae, (reformed eonomy ), () a 0% permanen reduon n apal ax rae, τ, s me by a permanen nrease n onsumpon ax rae, τ, τ, (reformed eonomy 2), () a 0% permanen reduon n onsumpon ax rae, τ, s me by a permanen nrease n labour ax rae, τ, (reformed eonomy 3), (v) a 0% permanen reduon n onsumpon ax rae, τ, s me by a permanen nrease n labour ax rae, τ,(reformed eonomy 4), (v) a 0% permanen reduon n labour ax rae, τ, s me by a permanen nrease n apal ax rae, τ (reformed eonomy 5). To examne he effes of hanges n he ax-spendng mx, e ondu poly expermen n hh a 0% permanen nrease n publ nvesmen, G, s fnaned by an nrease n labour ax rae, τ,(reformed eonomy 6). We smulae he eonomy for 300 perods and oban he dynam pahs of he endogenous varables along he ranson pah from he pre-reform equlbrum o he ne long run equlbrum assoaed h he assumed reform. 4.2 Ho e or To mplemen a reform and o solve he model, e or as follos. Frs, e solve for he pre-reform seady sae and assume ha he eonomy has been n hs equlbrum unl perod zero. Seond, e solve for he value of he poly nsrumen ha allo adjusng and s onssen h he pos-reform seady sae exogenously hange poly nsrumen and he pre-reform poly nsrumens. In parular, e oban he ne, pos-reform seady sae soluon, by seng he ne value of he exogenously hanged poly nsrumen, holdng all he ohers poly nsrumens a her pre-reform levels and leng one poly nsrumen adjus n he governmen budge onsran n he ne seady sae. Thrd, e mpose he ax reform on he pre-reform equlbrum n perod zero and oban he dynam soluon of he sysem. In parular, e mpose he reform n perod-0 and solve he dynam DD sysem for T=300 perods, eepng he o poly nsrumens ha have been hanged fla over me a her pos reform values and leng s be resdually deermned so ha he governmen b budge onsran s sasfed. The nal ondons for he model's sae varables are gven by he seady sae soluon of he pre-reform eonomy. For he ermnal values of he forard loong varables, e assume ha afer T years he dynam sysem has onverged o s ne seady

sae. Ths mples ha he approprae ermnal ondons are obaned by seng he values for hese varables equal o hose of he preedng perod. The fnal sysem s gven by 6(T+) equaons, hh s solved non-lnearly usng he Malab FSOLVE funon. Ths gves he dynam ranson o he ne seady sae for g b u b T he varables{ K+, +, B+, π, e, C, C, r, r,, Y, G, G, G, G, s}, here e se T = = 0 300 o ensure ha onvergene s aheved (see Appendx 4 for more deals). In all ases, e analyse he ranson from he nal seady sae o he ne one and e sudy boh aggregae and dsrbuonal mplaons. Regardng aggregae ouomes, e loo, for nsane, a oupu, onsumpon, employmen and elfare. 9 Regardng dsrbuon, e ompue separaely he nome and elfare of he represenave member n eah soal group.e. enrepreneurs vs a vs orers. The above values are hen ompared o her respeve values had e reman n he saus quo eonomy permanenly (see also e.g. Cooley and Hansen, 992, Eonomdes e al., 202). 4.3 Seady sae and ranson resuls Ths seon sudes he mplaons of ax-spendng poly reforms n erms of effeny and nome dsrbuon, boh n he seady sae and he ranson. Resuls of seady sae soluons for eah ase, he saus quo and he reformed eonomes, are repored n Table 3a. In Table 3b e presen he seady sae soluons of he reformed eonomes n perenage hanges of he saus quo eonomy. We also alulae he elfare gans/losses from he axspendng reform for eah ype of agen and a he aggregae level, by ompung he onsumpon supplemen requred o mae he agens n he saus quo regme as ell as n he reformed eonomy. We denoe elfare gans or losses for enrepreneurs, orers and he aggregae eonomy asζ, ζ and ζ, =,0,50,300 (see Appendx 5 and Table 4). In addon, e presen he dynam ranson pahs for he mos mporan maroeonom varables n Fgures -6. 9 Aggregae per apa elfare s defned as he eghed average of enrepreneurs and orers elfare. 2

Varable Saus Quo Reformed Eonomy Table 3a: Seady sae soluons levels Reformed Reformed Reformed Eonomy 2 Eonomy 3 Eonomy 4 Reformed Eonomy 5 Reformed Eonomy 6 s poly nsrumen () 0% reduon n τ τ poly nsrumen (2) 0% reduon n τ τ poly nsrumen (3) 0% reduon n τ τ poly nsrumen (4) 0% reduon n τ τ poly nsrumen (5) 0% reduon n τ τ poly nsrumen (6) 0% nrease n s τ poly nsrumen (7) Y 3.98 4.007 4.009 3.97 3.943 3.924 3.9966 ney 0.636 0.6248 0.6360 0.666 0.6253 0.6473 0.632 ney 2.0803 2.2 2.26 2.066 2.078.9960 2.0855 ney ney 3.2937 3.3803 3.3428 3.3436 3.227 3.0834 3.304 C 0.6952 0.6954 0.6967 0.6935 0.6930 0.6939 0.6956 C 0.529 0.5235 0.5265 0.525 0.5325 0.5424 0.5288 C.0828.0966.0939.0865.0676.0474.0846 C / C 2.0464 2.0948 2.0776 2.0692 2.0050.933 2.05 K 7.8779 8.039 8.0469 7.8580 7.644 7.4578 7.9085 g K 0.2389 0.240 0.2405 0.2383 0.2365 0.2353 0.2638 u= e 0.0807 0.0824 0.0807 0.0830 0.0807 0.0766 0.082 0.7600 0.7653 0.7653 0.7600 0.7524 0.7453 0.7634 ɶ 0.483 0.4738 0.4847 0.4667 0.4765 0.4993 0.4803 r 0.455 0.435 0.435 0.455 0.485 0.54 0.455 rɶ 0.0309 0.0309 0.0309 0.0309 0.0309 0.0309 0.0309 τ 0.3667 0.3809 0.3667 0.3860 0.3667 0.3300 0.3708 τ 0.936 0.936 0.2080 0.742 0.742 0.936 0.936 τ 0.3209 0.2888 0.2888 0.3209 0.3629 0.3987 0.3209 s 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 0.0220 3

Varable Reformed Eonomy Reformed Eonomy 2 Table 3b: Seady sae % hanges Reformed Reformed Eonomy 3 Eonomy 4 Reformed Eonomy 5 Reformed Eonomy 6 0% reduon n τ 0% reduon n τ 0% reduon n τ 0% reduon n τ 0% reduon n τ 0% nrease n s τ adjuss () τ adjuss (2) τ adjuss (3) τ adjuss (4) τ adjuss (5) τ adjuss (6) Y 0.52 0.70-0.25 -.00 -.50 0.39 ney -.07 0.70-2.38 -.00 2.50-0.06 ney.53 2.20-0.90-3.00-4.05 0.25 ney ney 2.63.49.52-2.02-6.39 0.32 C 0.03 0.2-0.25-0.32-0.20 0.04 C -.07-0.50-0.77 0.63 2.50-0.06 C.27.02 0.34 -.4-3.27 0.7 C C 2.37.53. -2.02-5.62 0.23 K.96 2.4-0.25-3.00-5.33 0.39 g K 0.52 0.70-0.25 -.00 -.50 0.43 u= e 2. 0.00 2.88 0.00-5.05 0.60 0.70 0.70 0.00 -.00 -.93 0.44 ɶ -.56 0.70-3.04 -.00 3.74-0.2 r -.4 -.4 0.00 2.06 4.05 0.00 rɶ 0.00 0.00 0.00 0.00 0.00 0.00 τ 3.89 0.00 5.25 0.00-0.00. τ 0.00 7.43-0.00-0.00 0.00 0.00 τ -0.00-0.00 0.00 3.09 24.24 0.00 s 0.00 0.00 0.00 0.00 0.00 0.00 4

4.2. Aggregae effes If he goal of ax poly s o smulae he eonomy by hangng he omposon of dsoronary axes, hen should derease he ax rae on apal and nrease he onsumpon ax rae; hs ax reform leads o he hghes nrease n oupu boh n he shor and long run. In he ne long run he oupu nreases by abou 0.70%. The reason s ha he reduon n he apal ax rae nreases n prvae apal, despe ha he nrease n onsumpon ax rae dereases oal onsumpon n he shor run. Ths reduon n he shor run onsumpon s very small n omparson h he nrease n nvesmen, and omes from he larger reduon of he orers onsumpon han he enrepreneurs one n he shor run. Furhermore, n he ase n hh he loer apal ax rae s ompensaed by a hgher labour ax rae, oupu rse due o he nrease n nvesmen, bu hs nrease s less han n he prevous ase beause he nrease n labour ax rae nreases he unemploymen. The nrease n oupu n he long run n hs ase s 0.52%. In onras, hen he derease n he labour ax rae s fnaned by a hgher apal ax rae, here s a delne n oupu n he shor o medum run and n long run, due o he derease n nvesmen and onsumpon, despe he nrease n employmen. The reduon n oupu n he long run s abou.50%, beause a 0% reduon n labour ax rae s ompensaed by a 24.24% nrease n apal ax rae. Also, ax reforms ha redue he onsumpon ax rae have negave effes on oupu boh n he shor and long run, and hs s regardless of he ax rae ha adjuss o ensure fsal solveny. 0 Fnally, a rse n governmen nvesmen o oupu rao fnaned by hgher labour axes smulaes oupu n he long run, bu leads o a fall n oupu over shor-erm-horzons. In hs ase, aes a long perod of me before he posve mpa of publ nfrasruure on he margnal produvy of prvae npus o offse he adverse effes ndued by he loer afer-ax real age. Smlar onlusons an be found n Leeper e al. (200) for he US eonomy. Conernng he effes of he above poles on publ fnanes, he resuls ndae ha, hle a shf of he ax burden from apal axes oards onsumpon axes smulaes he eonomy, produes an nrease n he prmary def-o oupu rao n he shor run. Therefore, onsumpon ax revenues anno mee he loss n apal ax revenues n he early sages of he ax reform. One he oher hand, reduons n onsumpon axes fnaned by hgher nome axes, do no smulae he eonomy, bu onrbue o redung he deb-ooupu rao n he shor run. See subplos (3,) and (6,3) n fgures 2, 3 and 4, here (3,) and (6,3) refer o ro and olumn numbers respevely. Le us no onsder he effes of he alernave ax-spendng sruures on elfare. Table 4 llusraes ha a reduon n any of he ax raes fnaned by an nrease n apal ax rae leads o a elfare gan beeen 0.0059% and 0.0202%, for he aggregae eonomy. In hese ases, he aggregae uly rses along he ranson pah, due o he nrease n oal onsumpon. Enrepreneurs loss n elfare, hh omes from he nrease n apal ax rae and hus he derease n her onsumpon, s smaller han he gan for he orers elfare, n he shor and long run. For all oher ases n Table 4 e noe elfare losses for he aggregae eonomy. To summarse, our resuls sho ha he mos effeve poly for he governmen o boos oupu s o redue he apal ax rae, regardless he poly nsrumen ha adjuss. In addon, f he goal of ax-spendng poly s o promoe elfare, hen should derease he ax rae on labour and nrease he onsumpon ax rae. 0 In he ase ha he reduon of he onsumpon ax rae s fnaned by a hgher labour ax rae he oupu dereases by 0.25% n he long run and hen s fnaned by a hgher apal ax rae he reduon of he oupu n he long run s abou %. The oupu nreases abou 0.39% n he long run. 5

Table 4: Welfare gans and losses over me ζ, ζ, ζ = Reform Reform 2 Reform 3 Reform 4 Reform 5 Reform 6 Capalss = 0.0052 0.0020 0.0043-0.0028-0.033-0.0009 = 0 0.0072 0.004 0.004-0.0057-0.08-0.0007 = 50 0.0099 0.0070 0.0037-0.0097-0.025 0.0002 300 0.005 0.0077 0.0037-0.006-0.0267 0.0005 Worers = -0.067-0.07-0.0068 0.06 0.0429-0.0047 = 0-0.052-0.0099-0.007 0.037 0.0385-0.0039 = 50-0.030-0.0076-0.0074 0.002 0.032-0.0025 = 300-0.025-0.0070-0.0074 0.0094 0.0306-0.002 Aggregae = -0.030-0.0093-0.0049 0.028 0.0327-0.004 = 0-0.04-0.0075-0.005 0.003 0.0282-0.0034 = 50-0.009-0.005-0.0054 0.0067 0.027-0.0020 = 300-0.0086-0.0045-0.0055 0.0059 0.0202-0.007 4.2.2 Dsrbuonal effes Sne here are o dfferen groups of households n he soey orers and enrepreneurs hese nome/elfare gans from eah parular ax-spendng reform may be dsrbued unequally for eah group n soey. Thus, e no urn o ndvdual ouomes or, equvalenly, o dsrbuon. We sar h he ne nome of eah agen, ney and ney. Aordng he resuls he bes poly reform for he orers s o derease labour ax rae and o nrease apal ax rae, bu hs reform has negave mpa on he enrepreneurs ne nome. The oppose effe on ne nomes e noe hen he nverse reform aes plae.e. a reduon of apal ax rae ha s fnaned by an nrease on labour ax rae. Furhermore, an nrease n governmen o oupu rao rases he ne nome of enrepreneurs and deeroraes he ne nome of orers. In he ase n hh he loer onsumpon ax rae s ompensaed by a hgher labour or apal ax rae, ne nomes of he o groups dereases. Benefs for boh groups n soey s noed hen a reduon of apal ax rae s ompensaed by an nrease n onsumpon ax rae. A ey queson no s ho gans more. Even f a poly reform produes a n-n ouome, n he sense ha boh ney and ney rse, relave ouomes an be also mporan. The polal eonoms leraure has poned ou several reasons for hs, nludng polal deology, hab, envy, e. In our model, relave ouomes ll be measured by hanges n he rao of ne nomes, ney / ney. Deparng from he saus quo eonomy, hs rao falls, or nequaly falls, hen a reduon n any of he ax raes s fnaned by an nrease n apal ax rae. The fall s bgger, -6.39%, hen he reduon has o do h he ax rae on labour nsead of -2.02% hen he onsumpon ax rae dereases. In onras, a reduon n any of he ax raes or an nrease n he governmen nvesmen o oupu rao s fnaned by an nrease n labour ax rae deeroraes he equaly beeen he o groups. Agan he rse of nequaly s bgger hen he apal ax rae dereases and hs rse s abou 2.63% n he long run. Fnally, negave resul for he equaly beeen he o groups e have also hen a reduon on apal ax rae s fnaned by an nrease n 6

onsumpon ax rae, despe ha he ne nome of orers and enrepreneurs nreases relave o saus quo eonomy. 5 Conlusons and possble exensons We employed a DGE model ha norporaes heerogeneous agens (enrepreneurs and orers) and mperfely ompeve produ and labour mares, augmened h a relavely rh publ seor, o examne he quanave maroeonom and elfare mplaons of fsal reforms n Euro Area. Frs, e sudy he effes of hanges n he omposon of ax raes, and, seond he effes of hange n publ nvesmen me by adjusmen n one of he dsorng ax rae. Our man resuls are as follos: Frs, he mos effeve poly for he governmen o boos oupu s o redue he apal ax rae, regardless he poly nsrumen ha adjuss. In addon, f he goal of ax-spendng poly s o promoe elfare, hen should derease he ax rae on labour and nrease he onsumpon ax rae. Fnally, a reduon n any of he ax raes, fnaned by an nrease n apal ax rae, leads o a fall of nequaly beeen he o soal groups. We noe ha he resuls qualavely are nuvely and quanavely are small. In fuure ould be neresng o exend our analyss o he ase of a small open eonomy. Ths ould allo us o sudy he effes of alernave fsal poly reforms on exernal mbalanes and nernaonal ompeveness. 7

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Luas R. (990): Supply sde eonoms: an analyal reve, Oxford Eonom Papers, 42, 293-36. Leeper E. M., Waler T. and Yang, S.-C.S. (200): Governmen nvesmen and fsal smulus, Journal of Moneary Eonoms, vol. 57, pp. 000 02. OECD Eonom Ouloo No.90 Pssardes C. (998): The mpa of employmen ax us on unemploymen and ages: he role of unemploymen benefs and ax sruure, European Eonom Reve, vol. 42, pp. 55-83. 9

FIGURES Fgure : From Saus Quo o Reformed Eonomy (0% reduon n τ and τ adjuss) oupu oal onsum pon 4.0 4 3.99 3.98 3.97 0.698 0.696 0.694 0.692 0.69 2.4 onsum pon apalss apal so...09.08 8. 8 7.9 7.8 0.47 onsum pon orers governm en apal 0.535 0.53 0.525 0.52 0.24 0.24 0.239 0.238 0.033 deb 2.4 2.39 2.38 gross neres rae 0.46 0.45 0.44 0.43 ne neres rae 0.032 0.03 0.03 profs gross age governm en nvesm en 0.52 0.5 0.508 0.506 0.504 0.768 0.766 0.764 0.762 0.76 0.024 0.024 0.0239 0.0238 unem ploym en benef ne age governm en ranfers 0.365 0.36 0.355 0.35 0.345 0.49 0.485 0.48 0.475 0.47 0.62 0.65 0.6 0.605 0.6 unem ploym en rae governm en onsum pon share of deb 0.083 0.082 0.08 0.08 0.24 0.24 0.239 0.238 0.604 0.602 0.6 0.598 20

Fgure 2: From Saus Quo o Reformed Eonomy 2 (0% reduon n τ and τ adjuss) oupu 4.0 4.005 4 3.995 3.99 3.985 3.98 onsumpon apalss.096.094.092.09.088.086.084.082 onsumpon orers 0.532 0.53 0.528 0.526 0.524 0.522 oal onsumpon 0.698 0.697 0.696 0.695 0.694 0.693 0.692 0.69 apal so 8. 8.05 8 7.95 7.9 7.85 governmen apal 0.245 0.24 0.2405 0.24 0.2395 0.239 0.2385 deb 2.4 2.405 2.4 2.395 2.39 gross neres rae 0.465 0.46 0.455 0.45 0.445 0.44 0.435 ne neres rae 0.033 0.0325 0.032 0.035 0.03 full model 0.43 0.0305 0.5 0.3585 0.0807 0.5 0.358 profs 0.509 0.508 0.507 0.506 unemploymen benef 0.3575 0.357 0.3565 0.356 0.3555 unemploymen rae 0.0807 0.0807 0.505 0.355 0.0807 0.767 0.486 0.245 gross age 0.766 0.765 0.764 0.763 0.762 0.76 ne age 0.485 0.484 0.483 0.482 governmen onsumpon 0.24 0.2405 0.24 0.2395 0.239 0.76 0.48 0.2385 governmen nvesmen 0.024 0.024 0.024 0.0239 0.0239 0.0239 0.0238 governmen ranfers 0.68 0.66 0.64 0.62 0.6 0.608 0.606 0.604 share of deb 0.602 0.605 0.60 0.6005 0.6 0.5995 2

Fgure 3: From Saus Quo o Reformed Eonomy 3 (0% reduon n τ and τ adjuss) oupu oal onsum pon 3.99 3.985 3.98 3.975 3.97 0.697 0.696 0.695 0.694 0.693 2.39 onsumpon apalss apal so.09.088.086.084.082 7.89 7.88 7.87 7.86 7.85 0.456 onsumpon orers governmen apal 0.532 0.53 0.528 0.526 0.524 0.239 0.2388 0.2386 0.2384 0.2382 0.0309 deb 2.385 2.38 gross neres rae 0.455 0.454 0.453 ne neres rae 0.0309 0.0308 0.0308 0.0307 profs gross age governm en nvesm en 0.507 0.506 0.505 0.504 0.76 0.7605 0.76 0.0239 0.0238 0.0238 governm en ranfers unem ploym en benef ne age 0.37 0.36 0.35 0.34 0.49 0.48 0.47 0.46 0.606 0.604 0.602 0.6 unem ploym en rae governm en onsum pon 0.084 0.083 0.082 0.08 0.08 0.239 0.2388 0.2386 0.2384 0.2382 share of deb 0.49 0.48 0.47 0.46 22

Fgure 4: From Saus Quo o Reformed Eonomy 4 (0% reduon n τ and τ adjuss) oupu 3.99 3.98 3.97 3.96 3.95 3.94 onsumpon apalss.085.08.075.07.065.06 onsum pon orers 0.54 0.538 0.536 0.534 0.532 0.53 0.528 oal onsum pon 0.704 0.702 0.7 0.698 0.696 0.694 0.692 apal so 7.9 7.85 7.8 7.75 7.7 7.65 7.6 governm en apal 0.2395 0.239 0.2385 0.238 0.2375 0.237 0.2365 0.236 deb 2.39 2.385 2.38 2.375 2.37 2.365 gross neres rae 0.49 0.48 0.47 0.46 ne neres rae 0.03 0.0305 0.03 0.0295 full model 2.36 0.45 0.029 0.507 0.357 0.0807 0.506 0.356 profs 0.505 0.504 0.503 0.502 0.50 unem ploym en benef 0.355 0.354 0.353 0.352 unem ploym en rae 0.0807 0.0807 0.5 0.35 0.0807 gross age 0.764 0.762 0.76 0.758 0.756 0.754 0.752 ne age 0.483 0.482 0.48 0.48 0.479 0.478 0.477 0.476 governm en onsum pon 0.2395 0.239 0.2385 0.238 0.2375 0.237 0.2365 0.236 governm en nvesm en 0.0239 0.0239 0.0239 0.0238 0.0237 0.0237 0.0236 governm en ranfers 0.6 0.605 0.6 0.595 0.59 share of deb 0.6 0.598 0.596 0.594 full model 0.585 0.592 23

Fgure 5: From Saus Quo o Reformed Eonomy 5 (0% reduon n τ and τ adjuss) oupu oal onsum pon 4 3.95 3.9 0.72 0.7 0.7 0.69 2.4 onsum pon apalss apal so.2..08.06.04 8 7.8 7.6 7.4 0.55 onsum pon orers governm en apal 0.58 0.56 0.54 0.52 0.24 0.238 0.236 0.234 0.03 deb 2.35 2.3 gross neres rae 0.5 0.45 ne neres rae 0.03 0.029 0.028 0.027 profs governm en nvesm en 0.55 0.5 0.505 0.5 0.495 gross age 0.77 0.76 0.75 0.74 0.024 0.0238 0.0236 0.0234 unem ploym en benef ne age governm en ranfers 0.38 0.37 0.36 0.35 0.52 0.5 0.5 0.49 0.48 0.62 0.6 0.6 0.59 0.58 unem ploym en rae governm en onsum pon share of deb 0.084 0.082 0.08 0.078 0.076 0.242 0.24 0.238 0.236 0.234 0.6 0.595 0.59 0.585 0.58 24

Fgure 6: From Saus Quo o Reformed Eonomy 6 (0% reduon n sand τ adjuss) oupu oal onsum pon 4 3.99 3.98 3.97 0.697 0.696 0.695 0.694 0.693 2.405 ons um pon apalss apal s o.086.084.082.08 7.92 7.9 7.88 7.86 0.46 onsum pon or ers governmen apal 0.532 0.53 0.528 0.526 0.28 0.26 0.24 0.22 0.034 deb 2.4 2.395 2.39 gross neres rae 0.458 0.456 0.454 ne neres rae 0.032 0.03 0.0308 profs 0.509 0.508 0.507 0.506 0.505 unem ploym en benef 0.357 0.356 0.355 0.354 0.353 unem ploym en rae 0.084 0.082 0.08 0.0808 0.0806 gross age governm en nvesm en 0.766 0.764 0.762 0.76 0.027 0.026 0.025 0.024 0.023 ne age governm en ranfers 0.484 0.482 0.48 0.478 0.62 0.65 0.6 0.605 0.6 governm en onsum pon share of deb 0.2405 0.24 0.2395 0.239 0.2385 0.484 0.482 0.48 0.478 25

Appendx : Mare learng ondons The mare learng ondons are: APPENDICES N N N N K = K N K = NK = K = K = = (A.a) N N N = N π = π N π = Nπ π = π = = (A.b) B N + = B+ B+ = N B+ = (A.) N + N N j j e L ( N N ) e NL j= = ( + ) = + = N N e NL N N N N j j N = N, N + N = N Ne N L j = = e e= n L (A.d) Fnally, n he goods mare, he eonomy s per apa resoure onsran s: ( ) θ θ p = + + + ( δ ) K + G + G ny Y nc n C n K (A.f) Appendx 2: The Deenralzed Dsequlbrum I onsss of he follong equaons: The enrepreneur's Euler equaon h respe o apal: ( C ψs ny ) σ ( C ψsny ) σ + + + + p ( + τ ) + ( + τ ) + ( + )( r+ ) = β + τ δ (A.2a) The enrepreneur's Euler equaon h respe o bonds: r ( τ )( r δ ) = (A.2b) b p + + + The orer's budge onsran: ( τ ) C ( τ ) + = e + s ny + sny (A.2) u The nermedae frm's opmaly ondon for L: 26

ny θα 2 = (A.2d) e The nermedae frm's opmaly ondon for K : Y θα = r (A.2e) K The nermedae frm's prof funon: π ( θα θα ) = Y (A.2f) 2 The nermedae frm's produon funon: ny α ( ) ( ) ( ) α n K e 2 α 3 =Α (A.2g) g The unon's opmaly ondon for he age rae: ( ) ( ) 2 u φ+ φ α θ se τ θα2 = θα e 2 (A.2h) The Governmen's Budge Consran: u b ( s + s + s + s ) ny + n ( + r ) B = p = nτ ( r δ ) K + nτπ + τe + n τc + nτ C + n B+ (A.2) The la of moon of publ apal: g = ( g ) g δ + + sny (A.2j) The resoure onsran: p ny = nc + n C + n K+ ( δ ) K + sny + sny (A.2) Therefore, he DD s a sysem of eleven non-lnear dfferene equaons (A.2a)- (A.2) n he pahs of Y,,,,,, g, b, C K+ C e π + r r, and one of he egh poly nsrumens, τ,,, u,,,, τ τ s s s s B+, ha s resdually deermned. Ths equlbrum s gven he pahs of he oher seven ax-spendng poly nsrumens. Appendx 3: The Seady Sae In he long run, varables reman onsan. Thus, x = x = x+ x, here varables hou me subsrp denoe long run values. Then e have he sysem: 27

p ( )( r ) = β + τ δ (A.3a) r ( τ )( r δ ) = (A.3b) b p ( τ ) ( ) ( + τ ) C = e + s u + s ny (A.3) ny θα 2 = (A.3d) e Y K θα = r (A.3e) π ( θα θα ) = 2 Y (A.3f) ny α ( ) ( ) α α n K e 2 3 =Α (A.3g) g ( ) ( ) 2 u φ+ φ α θ s e τ θα2 = θα e ( ) ( ) u b s + s + s + s ny + n r B = 2 = nτ r δ K + nτ π + τ e+ n τ C + nτ C p (A.3h) (A.3) g g δ = sny (A.3j) ( ) p s s ny = nc + n C + n δ K (A.3) Whh s a sysem of eleven equaons (A.3a)-(A.3) n K, g, π, ec,, C, r b, r, Y, and one of he egh poly nsrumens τ, τ, τ, s u, s, s, s, B. Appendx 4: DD for dynam ranson (T=300) To mplemen a ax reform and o solve he model, e or as follos. Frs, e solve for he pre-reform seady sae and assume ha he eonomy has been n hs equlbrum unl perod zero. ne Seond, e solve for he value of τ ha s onssen h he pos-reform zero apal ax seady sae and he pre-reform poly nsrumens. In parular, e oban he ne, pos- reform seady sae soluon, by seng( τ ) = τ 0.0τ, holdng all he ohers poly 28

nsrumens a her pre-reform levels and leng onsran n he ne seady sae. τ adjus n he governmen budge Thrd, e mpose he ax reform on he pre-reform equlbrum n perod zero and oban he dynam soluon of he sysem. In parular, e mpose he ax reform n perod-0 and solve he dynam DE sysem for T=300 perods, eepng τ and τ a over me and leng s be resdually deermned so ha he governmen budge onsran s sasfed. The nal ondons for he model's sae varables are gven by he seady sae soluon of he pre-reform eonomy. For he ermnal values of he forard loong varables, e assume ha afer T years he dynam sysem has onverged o s ne seady sae. Ths mples ha he approprae ermnal ondons are obaned by seng he values for hese varables equal o hose of he preedng perod. The fnal sysem s gven by 6(T+) equaons, hh s solved non-lnearly usng he Malab FSOLVE funon. Ths gves he dynam ranson o he ne seady sae for he g b u b T varables{ K+, +, B+, π, e, C, C, r, r,, Y, G, G, G, G, s}, here e se T = 300 o ensure ha onvergene s aheved. = 0 b ( + τ ) ( + τ ) ( C ) ( C ) σ + + σ ( + )( + ) = β τ r δ +, = 0,,..., T (A.4a) ( τ )( δ) r = r, = 0,,..., T (A.4b) b + + + ( τ ) ( ) u ( + τ ) C = e + G e + G, = 0,,..., T (A.4) θα 2 ny = e, = 0,,..., T (A.4d) θα Y = r K, = 0,,..., T (A.4e) π ( θα θα ) = Y, = 0,,..., T (A.4f) 2 α α α2 2 g α Y =Α ( K ) e, 0,,..., T = n n (A.4g) ( ) ( ) 2 φ+ φ α θ τ θα ny = G e, = 0,,..., T (A.4h) u 2 θα2 ( ) ( ) ( ) G + G + G + G e + n + r B = u b = nτ r δ K + nτπ + τe + n τc + nτ C + n B+, = 0,,..., T (A.4) g g g = ( δ ) + + G, = 0,,..., T (A.4j) 29

ny = nc + n C + n K+ ( δ) K + G + G, = 0,,..., T (A.4) G s = G = syn, = 0,,..., T (A.4l) Yn u u u u u G ( N N L) G ( n L) G( e) u sny s = = = G =, = 0,,..., T N Y ny ny e (A.4m) G s = G = syn, = 0,,..., T (A.4n) Yn B s = B = sy, = 0,,..., T (A.4o) b + b + Y G s = G = syn, = 0,,..., T (A.4p) Yn K K = (A.4q) T+ T B B = (A.4r) T+ T Ths s a sysem of ( ) unnons: 4 T+ + 2T+ 2= 6T+ 6= 6( T+ ) equaons, n 6( T+ ) g b u b T { K+, +, B+, π, e, C, C, r, r,, Y, G, G, G, G, s} g b u { K+, +, B+, π, e, C, C, r, r,, Y, G, G, G, G, s} and seven poly nsrumens: u T u b { τ, τ, τ, s, s, s, s},{ τt, τt, τt, st, st, st, st} = 0 g nal values: { K0, 0, B 0} Appendx 5: Welfare Comparsons The dsouned lfeme uly n he saus quo eonomy (he pre-reformed eonomy): U j sqe = j ( C ) sqe σ T β (A.5a) = 0 σ The dsouned lfeme uly n he reformed eonomy (he pos-reform eonomy): = 0 = T 30

U j re = j ( C ) re, σ T β (A.5b) = 0 σ We follo e.g. Luas (990) and ompue he permanen perenage supplemen n prvae onsumpon requred o mae agens n he saus quo regme as ell as n he reformed eonomy. Ths perenage supplemen s defned as ζ. More spefally, e fnd he value of ζ ha sasfes he follong equaon: U j (( ζ) Csqe) σ T + j U β = 0 ζ = j (A.5) = 0 σ U sqe j re re If ζ > 0 (respevely ζ < 0), here s a elfare gan (respevely loss) of movng from he nal seady sae o he ne reform one. σ 3