Optimal policy rules in an export-oriented economy

Transcription

1 Humbld Universi in Berlin Insiue f Ecnmic Plic I & Schumeer Insiue Macrecnmics, Mne and Caial Markes Oimal lic rules in an exr-riened ecnm in Pursui f he Degree Maser f Science in Ecnmics and Managemen a he Schl f Business and Ecnmics Humbld-Universi Berlin Presened b Aamanchuk Maria 5263 [email protected] Examiner: Prfessr Harald Uhlig, Ph.D. Berlin, 6h Jul 27

2 Affidavi/saur declarain I herewih declare, in lieu f ah, ha I have reared his aer n m wn, using nl he maerials (devices menined. Ideas aken, direcl r indirecl, frm her surces, are idenified as such. This wrk has n been submied in equal r similar frm anher examinain ffice and has n been ublished. Berlin, Jul 6, 27 signaure

3 Absrac esearch is deermined b he necessi f finding he se f imal feedback cefficiens f fiscal and mnear licies wihin an exr-riened ecnm wih emhasis n he il indusr such as ussia. T address his issue we build he en ecnm general equilibrium mdel ha can be seen as BC mdel augmened wih sme addiinal feaures. As a benchmark we ake he mdel f Schmi-Grhe and Uribe (24. We exand heir mdel b including he exernal secr, nn-rducing il secr and a fund fr accumulaing he huge revenues frm il exr ur analsis. We calibrae he ecnm fr he case f ussia. Our main findings are: under il rice shck imal mnear lic rule feaures a significan resnse uu; he cefficien f nminal ineres rae varies significanl fr differen shcks; cnsidering sabilizain fund under assive fiscal lic wih liabili argeing each value f liabili argeing cefficien culd eiher rduce n deviain frm sead sae given an value f inflain feedback cefficien r cause a deviain which is exacl he same. 2

4 Cnens. Inrducin 4 2. Lieraure 6 Benchmark aer 8 3. Facs 4. The Mdel 2 5. Mdel Analsis 33 Equilibrium 33 Lg-linearizain 34 Sead-sae 36 Calibrain 38 Technical eculiariies f rgram imlemenain 4 6. Mdel esuls Discussin 5 8. Summar and cncluding remarks 53 eferences 55 Aendix 58 Aendix. 58 Aendix 2. 6 Aendix 3. MATLAB cde fr majr rgram 63 Aendix 4a. MATLAB cde fr searching 3 feedback cefficiens 73 Aendix 4b. MATLAB cde fr searching 2 feedback cefficiens 74 3

5 . Inrducin During he las few ears searching fr he imal rules f he gvernmen and he cenral bank has araced significan ineres. As such, he are crucial in deermining macrecnmic licies in he Eurean Unin (he imal lic rules f he Eurean Cenral Bank and he EU gvernmens, he bes licies f he cenral bank and he gvernmen aimed a he sabilizain f deb and inflain, and in deermining he influence f macrecnmic licies n inflain, rducin, ec. Alhugh he search fr imal fiscal and mnear lic rules in Wesern ecnmic lieraure has been sudied in deail, man f he resuls cann be direcl alied he curren siuain in ussia s ecnm. There are w majr reasns fr his: he exr-riened characer f he ussian ecnm and sme secific characerisics, such as a significan rle f he sabilizain fund, which have an imac n finding he imal feedback rules cefficiens and n suding heir influence n he ecnm. esearch is deermined b he necessi f finding he imal feedback cefficiens f fiscal and mnear licies wihin an exr-riened ecnm wih emhasis n he il indusr such as ussia. In he ecnm wih nminal rigidiies cnsidered in his research under differen fiscal ririies he efficienc f mnear lic als wuld be differing. If he gvernmen is mainl riened n balanced budge argeing, hen he imal feedback cefficiens f mnear lic rule culd var dramaicall wih he siuain f liabili argeing. Hwever, ur aim des n cnsis in deermining a single imal rule fr all saes f he wrld. Bu we d clarif he ssible se f imal feedback cefficiens under a aricular shck in he ecnm. Obviusl, when a echnlg shck ccurs, hen gvernmen lic shuld differ frm he ne under an il shck. Thus, we deermine a se f cefficiens ha saisf he requiremen f imal lic in an exr-riened ecnm wih emhasis n he il indusr. A ha we rel n he fllwing crieria f imali: he imal lic rule is deermined hrugh minimizain f variables deviains frm heir sead-sae. The racical cnribuin f ur wrk als cnsiss in rviding he rgram based n a Tlki rgram fr MATLAB imlemenain. I culd answer he quesin abu he imali f a aricular lic. I means ha under values f feedback cefficiens which are cerain (wih ssibl ne uncerain value, he imulse resnses culd be easil fund. In case f mre uncerainies he rgram shws deviains frm sead sae under all ssible varians f feedback cefficien cmbinains in a aricular mmen. Fr he rgram deails see Uhlig (997 4

6 T address he issue ulined abve we build a general equilibrium mdel fr an exrriened ecnm. As a benchmark we ake Schmi-Grhe and Uribe (24, wh cmue imal fiscal and mnear lic rules in a mdified real business ccle mdel. One f he ke elemens f ur mdel cnsiss in analzing he ecnm wih huge il revenues, ar f which is accumulaed in a sabilizain fund, avid high inflain, amng her reasns. We calibrae he ecnm fr he case f ussia. T d his we cnduc exensive research f he ussian ecnm wihin he erid frm 2 he beginning f 27 and frmulae slized facs n basis f i. We build imulse resnses and calculae deviains frm sead-saes under echnlg, gvernmen urchases, il flw and il rices shcks. Our main findings are: under il rice shck imal mnear lic rule feaures a significan resnse uu; he cefficien f nminal ineres rae varies significanl fr differen shcks; cnsidering sabilizain fund under assive fiscal lic wih liabili argeing each value f liabili argeing cefficien culd eiher rduce n deviain frm sead sae given an value f inflain feedback cefficien r cause a deviain which is exacl he same. The remainder f he aer cnsiss f seven secins. Secin 2 resens a brief surve f he lieraure suding he search fr imal fiscal and mnear lic rules. Secin 3 elucidaes he aricular facs f he ussian ecnm ha were used build and calibrae he mdel. The mdel and is analsis are resened in Secin 4 and 5, resecivel. Secin 6 rvides he resuls we have bained. Secin 7 cnains he discussin f he achieved resuls. Secin 8 cncludes. 5

7 2. Lieraure A cnsiderable amun f analsis seeking imal mnear and fiscal lic rules has aken lace ver he las 2 ears. Alernaive mnear rules as well as fiscal lic arges were develed in a number f cunries invesigains. The sueriri f rules was iniiall shwn b ber Hall (984, Benne McCallum (984, Jhn Talr (986a. In he resen ears, in ms f his lieraure mnear lic rule resumed have a frm f an ineres-rae feedback rule ha cnsiders he nminal ineres rae as a funcin f inflain and sme characerisics f aggregae acivi (usuall, uu. The aer b Talr (993 was grundbreaking: he auhr suggesed simle and racable ineres rae rule fr Cenral Bank. Owing ha he racice f using Talr-e rules became widesread in ecnmic mdeling. Iniiall, his rule was elabraed fr indusrialized cunries. Hwever, he exerience f he advanced emerging markes researches shwed ha ineres rae rules describe he lic seing behavir f he mnear auhri raher quali (see, fr insance, Caldern and Schmid-Hebbel, 23, Mhan and Klau, 23, Minella e al., 23, Trres Garcia, 23. Cnsidering an exr-riened ecnm and describing sme f he eculiariies f he ussian ecnm, we als rel n Talr rule. The firs research n he imal rule fr mnear lic in ussia was rduced b Drbshevsk and Kzlvska (22. Fllwing Clarida, Gali and Geler (998 he auhrs used he GMM mehdlg fr searching fr he imal ineres rae resnse bu failed incrrae uu in he analsis. Hwever, Vdvichenk, Vrnina (24 als seeking fr he imal mnear rule analzed ussian ecnm wihin he s crisis erid, , aking his lessn in accun. Using ecnmeric mdeling, he esimaed differen mnear lic rules, as well as Talr-e rule, and fund u ha ineres rae lic f he Bank f ussia has been raher adaive and ha he mne sul insrumen erfrmed he sabilizing rle. Succeed als he aciviss f including uu in mnear lic crierin funcin, Hall (984 and Talr (986a, we d n exclude GDP frm mnear rule in ur analsis. Esanv, Merkl, Vinhas de Suza (24 searching fr he imal mnear rule analzed he erid f in ussia and fund u ha Tailr rule did n crresnd he ecnmic rcesses rerl. Hwever, he made he emirical esimain f lic rules, her han we exand he hereical general equilibrium mdel wih il secr and sabilizain fund. 6

8 We d analze he exr-riened ecnm wih emhasis il indusr b he examle f he subsequen erid f ussian ecnm ha differs dramaicall frm Cnsidering differen shcks we are mainl ineresed in he he influence f he il rice shck n he ecnm. This quesin fr a number f differen cunries was als sudied in Bernake e al. (997, Eswd (982, Fr and Lilien (986. The reacin f mnear and fiscal lic il shcks, , in 55 develing and develed cunries, was sudied b las-named auhrs, wh fund ha accmmdain f mnear lic can even reduce uu grwh in he lng run erid. The lnger he ime f accmmdain he less effecive is siive lic influence n uu. The exansinar fiscal lic rduces he same resuls. Tw ssible sraegies fr mnear lic under il shck f 99 were suggesed b Talr (993. If il shck is emrar, hen ssibl i is beer n increase ineres rae (hugh in reali, Cenral Bank did, bu hen he deviain in lic rule is required. The her varian rses n change lic a all. Searching he answer he issue f desirable lic sraegies under he il shck, we sud differen lic arges and seek fr he imal se f lic cefficiens. In addiin he siuain f acive mnear lic ur analsis includes he cnsiderain f he acive fiscal lic influence n he rice index. There are sudies in lieraure f he cndiins under which inflain is deermined slel eiher b fiscal r mnear lic (Wdfrd (995, Canzneri e al. (998, Schmi-Grhe and Uribe (997, Cchrane (998 idenified ha in rder fr he mnear lic n affec rices i is necessar ha gvernmen exendiure and axes be exgenus rcesses. These and furher assumins are inrduced make he real ineres rae be deermined nl b he availabili f real resurces, bu n b mnear lic. In ur analsis we fllw Schmi-Grhe and Uribe (24, 26 and mdel nl gvernmen exendiure as a univiarae auregressive rcess, bu hwever, le us imlemen he siuain f acive fiscal lic. eal ineres rae is ressured b he iniial rice level which is adjusing be cnsisen wih a bunded ah f gvernmen liabiliies. Searching fr an imal lic rule, differen imali crieria can be alied. Maximizain f welfare funcin and chsing he feedback lic cefficiens under he exisence f rainal execains equilibrium is ne wa. In aricular, Schmid-Grhe and Uribe (24, 26 relied n ha searching fr a lic ha ields he highes level f lifeime uili given he cningen lans fr cnsumin and hurs f wrk. 2 Fr mre deails see als secin Facs 7

9 Wdfrd (22, ch.7 suggess a mre cmlicaed crieria f searching fr he imal rule in frward-lking mdels. A quadraic lss crierin is divided in w cmnens: he deerminisic cmnen f he equilibrium ahs f he arge variables and he sable ar ha deends nl n he equilibrium resnses unexeced shcks in erids afer. The imal feedback cefficiens shuld minimize he secnd ar. Bu he deerminisic cmnen des n have be minimized, bu a rule is chsen ha is cnsisen wih he lng-run average values ha ccur under he. Wdfrd (22 assers ha his crierin hels avid ime-incnsisenc f lic chice in frward-lking lic rules. Hwever, we rel n a simler crierin ha is cnsisen in he case f a cnemraneus lic rule. Oimal lic rule is deermined as minimizain f variables deviains frm heir sead-sae. I is direcl inercnneced wih widesread idea f minimizing lss funcins and hen deermining he imal lic cefficiens (see Tabellini (986, van Arle, Bvenberg and aih (995. This definiin f imali fr lic rules was used in, fr examle, Currie and Levine (99. The analsis in his aer is mainl based n Schmi-Grhe and Uribe (24. An indeh descriin f he aer cnce is rvided underneah. Benchmark aer In he research aer Oimal Simle And Imlemenable Mnear and Fiscal ules (24, Sehanie Schmi-Grhe and Marin Uribe aim cmue imal fiscal and mnear lic rules in a mdified real business ccle mdel. Secificall, heir mdel includes sick rices, a demand fr mne, disrinar axain and schasic gvernmen cnsumin. Furhermre, he accun fr caial accumulain and an acive fiscal lic, and d n rel n he resence f lum-sum subsidies und he disrins creaed b mnlisic cmeiin. These secificains make he ecnmic envirnmen mre realisic and disinguish he mdel frm man her wrks in he field. In rder find imal lic rules he auhrs rel n exlici welfare calculains. Fr his urse he cann wrk wih firs rder arximains, bu need arximae heir mdel u he secnd rder. The reasn is ha all he lic regimes under cnsiderain iml idenical nn-schasic sead saes, as a resul f which firs rder arximains wuld ield he same levels f welfare fr all ssible licies 3. 3 fr sme urses firs-rder accurac is n enugh. This is rue in aricular fr cmaring welfare acrss licies ha d n have firs-rder effecs n he mdel s deerminisic sead sae., Kim, Kim, Schamburg and Sims (23, see als Schmi-Grhe and Uribe (24b, Lmbard and Suherland (25 8

10 The auhrs ssemaicall calculae welfare levels fr a large number f lausible lic cefficiens find imal rules esseniall b rial and errr. As far as fiscal lic is cncerned he cnclude ha he welfare-imizing lic is assive, bu ha an acive lic des nl minr harm. Cncerning mnear lic he find ha while he inflain cefficien in he mnear rule is immaerial fr welfare, is i crucial ha mnear lic be insensiive uu. This ke resul is illusraed b imulse resnses f sme endgenus variables a echnlg shck. This ar f he auhrs aricle became he bench mark fr ur curren research. Briefl, aking General Equilibrium Mdel fr clsed ecnm, we included he exernal secr analze he exr-riened ecnm required in research. One f he crucial eculiariies f his fur-agen mdel lies in he inclusin f he sabilizain fund and il secr in he analsis. These and sme her dimensins wide he mdel and change sme f he equains suggesed b he benchmark aricle. Imulse resnses f sme endgenus variables n nl a echnlg shck, bu als a gvernmen urchases, il flw and il rices shcks are imlemened. Since his wrk analsis des n invlve he calculain f welfare levels, i culd and will rel n firs rder arximains f he sead sae. Mre cmrehensive descriin f he basic mdel and he innvains inrduced analze he exr-riened ecnm are described in he Secin Mdel. 9

11 3. Facs This chaer is deved a brief surve f macrecnmic lic in ussia, chiefl frm 2 he beginning f 27. The reasn f cnsidering jus his erid lies in hisrical evens ha haened in he ussian ecnm. Befre 99 here was n marke ecnm, bu he cmmand regime in USS erid. Afer 99 began a erid f marke frmain. The ecnm develed raidl and reached significan grwh raes, bu he crisis f 7 Augus 998 brke ff his rcess. The gvernmen culd n a ff is debs and undermined he ecnm b issuing mre and mre liabiliies. As a resul f his he ussian financial ssem was brken. Millins f ele ls heir jbs, hundreds f banks became bankru, share rices wen dzens f imes dwn, and s n. The ecnm was crushed. Bi b bi i sared recvering. This rcess k man ears and he curren ussian ecnm sill bears an imac f ha ime. If we analze he firs ears afer crisis, he wuld disr he aern f he curren ussian ecnm much. Tha is wh we sar ur analsis frm he firs ears f he rehabiliain erid. Saring wih he erid when he ecnm g ver his desrucive shck fr he ms ar and a las recnsrucin was under wa, he analsis can be carried u wihu a risk ge biased resuls. A he same ime he analsis wihin he erid f 2-26 gives us an adequae ime inerval cme sme clear cnclusins. The gal f his ar des n lie in irrefragable descriin f all ms imran macrecnmic asecs f ussian ecnm during he las ears. Als we dn make he emirical analsis f macrecnmic rcesses ineracins as ur aim. The bjec is frmulae slized facs regarding he dnamics f he macrecnmic variables resened in ur research. Slized facs f Fiscal and Mnear lic in ussia, 2-27 The macrecnmic siuain f mdern ussia frm 2 26 culd be characerized in he fllwing wa. During he las ears he inflain rai had been graduall declining. A he same ime he dnamics f mne sul grwh rae d n demnsrae he same rend. Currenc areciain akes lace because f favrable exernal marke cndiins. High exr revenues sur he grwh f real GDP. Daa is resened in Table 3..

12 Table 3.. Main macrecnmiс characerisics f he.f., Jan. Ma 27 The grwh f Cnsumer Price Index, % The grwh f Prducer Price Index, % The grwh f Mne sul (in he narrw sense, % The grwh f Mne sul, % The real areciain f exchange rae (rubles/u.s.dllar, % The change f real effecive exchange rae (rubles/freign currencies, % The grwh f real GDP, % Surce: Federal Sae Saisics Service Amng he main reasns f exr grwh is he increase in he ussian Federain s revenues frm il sales. Prices f energ carriers have grwn cnfidenl during he whle erid under review, demnsraing he ms significan grwh in The ussian Federain budge had a surlus ver he whle erid and grew dramaicall afer 25 as a resul f sae revenues increase frm il sales (Table 3.2. Budge surlus eners he sabilizain fund, he value f which has risen greal in ussia during he las ears. Table 3.2. Gvernmen budge f he.f., 2-27 Federal budge execuin Jan.-Ma 27 Tal evenues Bln.rub % GDP 7.6% 9.4% 8.5% 7.9% 23.7% 23.6% 2.8% evenues, less revenues enered a Bln.rub sabilizain fund accun % GDP 7.3% 6.8% 7.3% Tal Exendiure Surlus(/Defici(- Bln.rub % GDP 4.5% 7.8% 8.% 7.4% 6.3% 6.% 5.% Bln.rub % GDP 3.%.6%.6%.5% 7.5% 7.5% 6.7%

13 Surlus(/Defici(-, less revenues enered Bln.rub a sabilizain fund accun % GDP.%.7% 2.2% Surce: Federal Sae Saisics Service, Bank f ussia Le us cnsider imran fr ur analsis macrecnmic rcesses in greaer deail. Inflain and Mne sul Generall, inflain rae sabilizain is bserved in ussia. Wihin he erid under review inflain has had a emerae naure. Figure 3. illusraes he dnamics f annual Cnsumin Price Index, Prducer Price Index 4 and Mne sul. Figure 3. The dnamics f Price indices and Mne sul 6 The grwh f Price indices and Mne sul 5 4 % ears The grwh f Cnsumer Price Index, % The grwh f Prducer Price Index, % The grwh f Mne sul, % Daa surce: Bank f ussia, ur calculains Wihin he whle erid he rice index, defined b CPI, has declined cnfidenl. This was in sie f he fac ha mne sul grwh rae was bserved during sme erids. Mrever, we culd n bserve a sable decrease f mne sul grwh rae 5, unlike we did wih inflain. 4 As eviden frm figure 3. he inflain dnamics deend n hw we deermine i, eiher using Cnsumer Price Index r Prducer Price Index. Such a big difference culd be exlained b he fac f including il rices in he laer. 5 A mderae inflain jum culd be execed in he fuure, ha is due revius grwh f mne sul. Taking in cnsiderain ha he grwh f mne sul influences inflain indices wih sme ime lag and his influence lass lnger han ne erid, he revius increase f mne sul ells n rice index f 27 in full measure. This fac gives grunds n frecas inflain a a greal smaller rae han i was. 2

14 Slized fac : Inflain rae was siive and significanl large, bu decreased regardless f he high grwh rae f mne sul. educin f inflain was alms nwihsanding mnear lic f Bank f ussia in This surrising, a firs glance, fac culd be exlained b dnamics f mne velci. I means when mne sul was grwing u dramaicall, mne velci was cming dwn, hus, resraining he inflain grwh. Ineres rae as an insrumen f mnear lic fr inflain cnrl is fund as a n he ms subsanial ne. I culd be exlained b he exisence f high, even excess, liquidi in ussian ecnm during he analzable erid. The significan inflw f freign currenc was deermined b high il rices. Oen marke erains culd be admied as mre imran insrumen f inflain regulain, bu ineres rae rle is als graduall increasing. Budge Ever ear frm 2 26 he budge surlus has aken lace in ussian ecnm. Figures 3.2 and 3.3 deic federal budge balance in he abslue value and in ercen f annual GDP, resecivel. Figure 3.2. Federal Budge Balance Budge balance bln. rub ear Surlus(/ defici(- bln. rub. Daa surce: Bank f ussia 3

15 Figure 3.3. Federal Budge Balance in ercen f GDP Balance budge % 8,% 7,% 6,% 5,% 4,% 3,% 2,%,%,% ear Surlus(/ defici(- % GDP Daa surce: Bank f ussia, ur calculains Shar grwh f sae budge surlus in was caused b increase in exr duies which, in heir urn, had been rvked b high il rices. Since exr duies were a big ar f federal budge revenues during he las ears (eseciall, in 25-26, which is shwn in able 3.3, his imran fac is aken in cnsiderain in ur mdel. We sli exr duies as a searae ar f ax funcin. al axes. Slized fac 2: Due high il exr duies il axes cnsiue a huge fracin f he Table 3.3 Cnslidaed budge, , billins f rubles. 25, % GDP 26, billins f rubles 26, % GDP Tal revenues 525, 23,7% 6276,3 23,6% f which Exr duies 35,9 6,3% 895,8 7,% Tal exendiure 352,2 6,3% 428,3 6,% Surce: Ecnmic Exer Gru In 26 exr duies accuned fr abu 8 ercen (and abu 2 ercen in 25 f budge revenues, as eviden frm able 3.3. Ms ar f hese axes was enered a he.f. sabilizain fund accun 6. 6 The rder and cndiins fr sabilizain fund creain in he.f. are described in he.f. Budge Cde, asse 96-4

16 Slized fac 3: Budge balance f he ussian Federain had he surlus wihin he analzable erid ha was caused b high il rices. Sabilizain fund Sabilizain fund f he ussian Federain, esablished n he firs f Januar 24 and being a ar f he federal budge is amng he main bjecs f ur research. Per se, sabilizain fund is used fr srage f cash means ha have n been sen b he gvernmen wihin his erid, bu can be sen aferwards cver he deb. This is, in a sense, a sraegic asse ha culd be used in case f subsanial decrease f budge revenues r in case f an unexeced exendiure rise. Figure 3.4 illusraes he annual funds used, received and end erid value f he.f. sabilizain fund frm Figure 3.4. Sabilizain fund Sabilizain fund 5 4 bln. rub ear End erid value Annual received Annual used Daa surce: Bank f ussia The fficial size f sabilizain fund n he firs f June 27, declared b he Minisr f Finance f he ussian Federain, was billin rubles (ha is equivalen arximael billin. U.S. dllars. 7 I is wrh menin ha he main surces fr sabilizain fund are he il rducin ax and il exr duies ( u i mre recisel, he ar f exr duies frmed due he il rice in excess f is cu-ff value 8. Als, all f he unsen (unlanned budge surluses are ransferred a sabilizain fund accun. 7 A he exchange rae f Bank f ussia, The annual cu-ff il rice er barrel is seled legislaivel b he Gvernmen f he ussian Federain 5

17 Slized fac 4: Wihin he erid f large black ink f federal budge has rduced raid accumulain f funds in sabilizain fund. Figure 3.5 deics he dnamics f sabilizain fund in ercen f he.f. GDP. Figure 3.5. Sabilizain fund in ercen f GDP Sabilizain fund in ercen f GDP % ear Sabilizain fund/gdp, % Daa surce: Bank f ussia, ur calculains The relaive value f sabilizain fund was grwing inside f a erid, and is meaning, accrding frecass, wuld reach 9.2 ercen f GDP b he end f 27. Exchange rae The mnhl dnamics f exchange rae are resened n figure 3.6. Figure 3.6. Nminal exchange rae (rubles/u.s. dllars Exchange rae rub./u.s.$ f Jan Feb Mar Ar Ma Jun Jul Aug Se Oc Nv Dec mnh Daa surce: Bank f ussia 6

18 We culd bserve he increase in he value f he ruble wih resec U.S. dllar since 22. An ineresing fac is currenc areciain agains a backgrund f mne sul increase (see figure 3.7. Figure 3.7. The dnamics f nminal exchange rae and mne sul Nminal exchange rae, Mne sul rub./u.s.$ ,, 8, 6, 4, 2, mln.rub ear, Exchange rae, rub./$ Mne sul, mln. rub. Daa surce: Bank f ussia The increase f ruble exchange rae is clarified b exr grwh a grea exen, all he daa is rvided underneah. Exr increase effec was bigger hen mne exansin effec in erms f influencing n exchange rae. Exernal ecnmic acivi This aragrah surs he basis fr he fac ussia has an exr-riened ecnm a he resen ime. Figures 3.8 and 3.9 resen he annual exr and imr daa in abslue value and in ercen GDP frm Figure 3. illusraes he grwh rae f ussian exr and imr wihin he same erid. I is significan menin ha in sie f essenial grwh f rade balance variables, heir share in GDP did n change significanl. 7

19 Figure 3.8. The dnamics f Exr and Imr 35 Exr, Imr 3 mln. U.S. $ d ear Exr, mln. U.S. $ Imr, mln. U.S.$ Daa surce: Bank f ussia Figure 3.9. The dnamics f Exr and Imr in ercen GDP Exr, Imr, % GDP 35 3 % ear Daa surce: Bank f ussia, ur calculains Figure 3.. The grwh rae f Exr and Imr Exr/GDP, % Imr/GDP, % The grwh rae f Exr and Imr 4% 35% 3% 25% 2% % 5% % 5% % -5% ear Daa surce: Bank f ussia, ur calculains The rae f Exr grwh, % Тhe rae f Imr grwh, % 8

20 Slized fac 5: ussia has an exr-riened ecnm. Exr ermanenl equals abu ne hird f aggregae exendiure and has exceeded imr alms w imes wihin he whle erid under review. The verreresened figures shw ha exr s abslue value and is rae f grwh has risen annuall. Imr als has grwn annuall, bu fr all ha is grwh rae had slighl fallen dwn las ear. Since exr has had exremel high grwh raes fr he las w ears, le us cnsider his erid in mre deail. Table 3.4 includes he exr and imr daa f ussia in 26, and is value relaive 25. Table 3.4. Exr and Imr in (bln. U.S.$ Value relaive 25 Exr 34,5 25 Imr 63,9 3,8 Freign rade urnver 468,4 27 Trade balance 4,7 8,9 Surce: Bank f ussia Table 3.4 shws ha ussian exr exceeded imr in 26 dramaicall, hugh imr grwh was higher in relaive erms. As i has alread been menined, such a big exr culd be warraned b favrable siuain in energ marke. Imr grew because f ruble areciain. I is ineresing cmare he dnamics f ussian exr wih il rices. Figure 3.2 illusraes high siive crrelain beween hese w variables. Slized fac 6: Oil cnsiues a huge ar f ussian exr. 9

21 Figure 3.. The dnamics f Exr and Oil rices Exr, Oil rices mln. U.S.$ $ er n ear Exr, mln. U.S.$ Oil rice (er n, U.S.$ Dae surce: Bank f ussia, ur calculains 2

22 4. The Mdel The en ecnm general equilibrium mdel resened in ur wrk can be seen as BC mdel augmened wih sme addiinal feaures. Sme f hem, such as he exisence f nminal rigidiies, ime-varing disrinar axain, demand fr mne and mnlisic cmeiin n rduc markes were inrduced b Schmi-Grhe and Uribe (24 wh buil general equilibrium mdel fr he clsed-ecnm. We exand heir mdel b including he exernal secr, nn-rducing il secr and a fund fr accumulaing he huge revenues frm il exr ur analsis. B ding his we aler he mdel in rder make i alicable describing he curren rcesses in he ussian ecnm. There are fur ecnmic agens: Husehlds, Firms, he Gvernmen and he Exernal secr. Husehlds and firms slve heir imizain rblems and he Gvernmen, resened b Mnear and Fiscal auhriies, fllws is lic rules. The Exernal secr is mdeled in erms f addiinal resricins he mdel. Oil secr is inegraed in he mdel as an exra nn-rducing secr. The lic rule fr he sabilizain fund is inrduced. Husehlds There is a cninuum f idenical husehlds in he ecnm. The references f a ical husehld (ver cnsumin, c, and labr effr, h are given b he uili funcin E β γ [ c ( h ] σ σ, ( where σ is he ineremral elasici f cnsumin, and γ denes a reference arameer, β (, means a subjecive discun facr. Frm he echnical in f view, he uili funcin is sricl increasing in is firs argumen, sricl decreasing in he secnd, and sricl cncave. The cnsumin gd is rduced wih he varie f differeniaed gds, c i, i [,], c / ci di /(/, where > is he inraemral elasici f subsiuin acrss he range f differeniaed gds. 2

23 Then, he imal level f a gd f varie i is exressed b c imal level f c i P i i c P. This is he fr he minimizain rblem f al exendiure under he given level f cnsumin f he cmsie gd subjec is afremenined aggregain cnsrain. P i is he nminal rice f a gd f varie i a ime, and nminal rice index is secified as P ( Pi di. Since husehlds culd ariciae in all nminal cningen claims, heir erid-berid budge cnsrain is E r, x P c i τ L x P D ( τ [ w h ~ u k ] φ λ e ( τ, (2 where x is a nminal randm amen in erid s, denes a schasic discun s facr, P is he aggregae rice level, k is caial, i is invesmen, λ e ( τ is he aferax incme frm shares in il indusr 9, and he variable ~ φ denes afer-incme-ax rfis frm firm-wnershi L D. There is a lum-sum ax,, an incme ax rae,, and il ax rae,. The necessi disinguish he il ax as a searae ar f he ax funcin culd be exlained b he exr-rienain f he mdeled ecnm which ges huge exr duies, mainl frm il r, s exrain. The rices f labr and caial are w and u, resecivel. τ The caial accumulain equain (wih cnsan dereciain rae, δ is τ τ k ( δ k i. (3 The invesmen gd is a cmsie f cninuum f inermediae gds, i i, i [,], he demand fr which is given b i i P i i P. 9 Fr mre deails, see nex Subsecin Oil indusr. Assumin: Prfis are derived frm rducin firms. Fr mre deails, see nex subsecin Oil indusr. Abu 8% f ussian sae revenues (in 26 fell a riginae frm exr duies (2% in 25. The high rrin f revenues frm exr duies in he al revenues was exlained b high il rices. Fr mre deails, see secin Facs. 22

24 Maximizing he husehlds uili funcin subjec equains (2 and (3 and he n- Pnzi-game brrwing limi 2 ields he firs rder cndiins c ( λ, (4 δ γ (δ h P λ r, βλ, P cγ D w ( τ, (5 h λ D { λ τ u ]} βe [( δ, (6 where λ is he Lagrange mulilier. The il secr The il secr is mdeled under he assumin ha il is exraced b nn-rducing firms. I means ha here are w es f he firms: he firs gru cmunds f rducing firms, i rduces all he gds in he ecnm. And he secnd ne cmunds f il exracing cmanies. Under Firms in ur mdel we mean agens rducing all gds, exce il. Hence, il rducing cmanies are excluded frm his sense. I culd be jusified b he fac ha il flw is mainl deermined b he naural resurces f a cunr, bu n b caial r labur. Then, il is mdeled as an A(- exgenus rcess ρ ( ρ ε, where is a flw f il in erid, denes he sead-sae level f il flw. The il rice is deermined n he wrld marke, and hence, each cunr culd be cnsidered mainl as he rice-aker. The influence f he cunries n he il rice is negleced n make he analsis cmlicaed. A univariae auregressive rcess fr il rice ρ ρ ( ε, 2 The n-pnzi-game cndiin is inrduced guaranee he absence f Pnzi brrwing schemes. The culd ake lace if n brrwing limiain fr husehlds was inrduced. 23

25 where is wrld il rice, which is se in he freign currenc 3, n in he nainal ne, and where denes he sead-sae level f. Then, exraced wihin a cunr is exred. are al revenues frm il, in U.S. dllars. We assume ha all f il Since, in reali, il revenues (scks f il cmanies belng he Gvernmen as well as Husehlds, we include hem in ur mdel in accrdance wih his fac. Then, he al revenues frm il culd be deermined b he ideni ( λ τ λ τ λ (. Here λ and ( λ describe ars f il incme ha belng husehlds and he gvernmen, crresndingl, ha are received due heir share fracin in il rducing cmanies, and τ is an il revenue ax rae. The Gvernmen Gvernmen exendiure, g, is deermined exgenusl b he A(-rcess g ρ g g e, where g denes he sead-sae level f. This exendiure g ( ρ g g can be financed b cllecing axes, τ, rining mne, g, b issuing ne-erid risk-free deb, B, wih inernal, risk-free, nminal grss ineres rae,, and b sending ar f M sabilizain fund, div,. Sabilizain fund dividends are esimaed a a freign currenc and cnvered in rubles a a nminal exchange rae, E. Algeher, his ields he erid-berid cnslidaed gvernmen budge cnsrain (in nminal values M B B M P g P E τ div,. We build ur mdel under he unical assumin, suggesed b Schmi-Grhe and Uribe (24, ha he gvernmen minimizes he cs f rducing gvernmen gds. Then, he ublic demand fr an inermediae gd, gi, f each varie i, is g i P i g P. 3 Under freign currenc we mean U.S. dllar. 24

26 Using w furher definiins, his budge cnsrain can be cnvenienl rewrien. Firs, le he level f al gvernmen liabiliies in real erms a he beginning f erid in unis f erid gds be dened b l ( M B / P. Secndl, le m M / P be he al amun f real balances in circulain. Then he budge cnsrain can be ransfrmed l E div, ( / l ( g τ m (, (7 where e is he real exchange rae, P is he inflain rae. Als assuming P P, we cme simlificain f cinciding he inflain rae and rice index. The Euler equain, which cmbines husehlds firs rder cndiin, λ r βλ P P, and he n-arbirage cndiin, / E ( r, which shws he (, / inverse cnnecin beween erid, is given b, and erid rice f a rfli ha as ne dllar in λ E λ β. (8 Since axes in he mdel cnsis n nl f he sum f lum-sum axes, and (disrinar incme ax rae, s ha he clsed-ecnm axes, τ, are deermined b τ τ τ, (9 L D bu als include il ax rae, hen he whle ax revenue, T, fr an exr-riened ecnm is T τ τ λ. ( The gvernmen ses he ax rae based n a fiscal rule which is a funcin f he deviain f al liabiliies, l, frm heir arge level,l, and f he real secndar fiscal defici 4 4 l m We use his erm fr g inrduced b Schmi-Grhe and Uribe (24. 25

27 E' div l γ 2 g, m τ γ γ ( l l, ( where γ and γ 2 are cefficiens saing he resnsiveness f fiscal lic he resecive indicars, and γ is an aunmus ax cmnen. I is imran ne, hwever, ha Schmi-Grhe and Uribe never rel n bh arges simulaneusl, bu es liabili argeing ( γ 2 se zer and balanced budge argeing ( γ andγ se zer searael. In ur mdel we als imlemen eiher he case f balanced budge argeing r he sae f liabili argeing. I is shwn in Schmi-Grhe and Uribe (2 ha in rder make he fiscal lic fllwing a balanced-budge rule and cnsising f lum-sum axain, have n influence n rice level deerminain, he lng-run nminal ineres rae has be sricl siive. We will be cnsisen wih his resul in ur research. In he case f simulaneus liabili argeing and lum-sum axain he fiscal lic is called acive, accrding he erm suggesed b Leeer (99. In his siuain i influences n rice level deerminain. The resricins imlied n he cefficien γ cnsis f assuming i, frm he ne hand, be siive, and frm he her hand, be less han deerminisic real ineres rae. Algeher, his reresens a ver imran innvain cmaring her aricles ha assume fiscal lic be assive frm he ver use. This mdificain les he mnear lic la n nl an acive rle, bu sreading he varians f ssible equilibriums. Mnear lic is cnduced based n a Talr 5 -e rule ln( / α ln( / α E ln( / α E ln( / (2 where,, are he arge levels f he crresnding variables and α, α, α are he arameers f he crresnding variables weighs fr Mnear agen. In ur aer we imlemen he siuain f cnemraneus lic rule. Sabilizain fund One f he cenral feaures f ur mdel cnsiss f adding he sabilizain fund he analsis. The dnamics f sabilizain fund, F, in erid, is deermined b freign, risk-free, 5 Talr (993 26

28 nminal, grss ineres rae, F, abrad, fr examle, in U.S. reasuries., resuled frm he flaing sabilizain fund f revius erid, F F rev, div,. (3 Here, rev, denes gvernmen revenues frm il received frm is ssessin in il rducing cmanies, r frm axes imsed n husehlds il incme. rev, ( λ τ λ. (4 T simlif he analsis i is assumed ha il revenues are he nl surce fr he relenishmen f he sabilizain fund, since, in reali, i mainl cnsiss f il incme 6. Then, div, is a ar f sabilizain fund, sen wihin erid. Like he gvernmen revenues frm il, il dividends are als esimaed in freign currenc, U.S. dllars. Dividends are deermined accrding he sabilizain fund s lic rule div, F ξ ( F, (5 where F is a arge level f sabilizain fund. Inuiivel, his equain culd be exlained s ha in rder deermine he ar f sabilizain fund which shuld be sen, he deviain f is curren level frm is arge level is used. And his deviain is smhed wih sme seed, ξ. I is imran clear he siuain wih he exisence f w differen grss ne-erid, risk-free, nminal ineres-raes, and in ur mdel. denes he cnsan freign ineres-rae, a which nl he gvernmen can u u mne (accumulaed in he sabilizain fund. This fac requires he imsing f a new resricin n sabilizain fund: F >. And is an ineres rae ha is aid n inernal deb and a his rae n nl he gvernmen can inves asses, bu als her agens. 6 This fac is rved in Secin Facs 27

29 Firms Each firm in he mdel rduces a aricular gd 7 i [,], in a mnlisicall cmeiive envirnmen (i.e. he gds are imerfec subsiues. The idenical rducin echnlg used b all firms 8 is described b a Cbb-Duglas rducin funcin and b he echnlg shck,, which is driven b he auregressive rcess z where z is he sead-sae value f z z z z ( ρ z ε ρ z z, z F. θ θ ( k, h zk h The rducin funcin is hmgenus f degree ne, cncave, and has he siive firs derivaive f bh funcin argumens: caial services, k, and labr services, l. θ means i i he cs share f caial. The aggregae demand fr a dmesic gd i, dened b a i c i g im, is i i i i equal he aggregae absrin minus imr f his gd. Then, he aggregae demand fr all dmesics gds is given b: a ( P P a. i i Firms can hld mne and bnds s he al wealh f a firm includes he revenues frm ff-ake and frm hlding he financial asses. Each firm maximizes he resen discun value f rfis φ 9 i P i E [ ] r, s Ps φ is E r, s Ps ai uki w hi ( mi. s s P I is icall assumed (as well as in Schmi-Grhe and Uribe, 24, Chrisian e al., 23, Kllman, 23, emberg and Wdfrd, 992 ha caial culd be easil reallcaed acrss indusries. Each firm alwas saisfies he demand a is chsen rice ha gives he fllwing cnsrain he firm s rblem z F P i ( ki, hi a P. 7 eminding: in ur analsis we dn include il rducers in erm Firms 8 We make he aggregain f he firms frm he ver use, where i des n cause rblems wih undersanding he mdel. Technicall, i means ha we jus dr he subscri i f a aricular exressin. 9 T see he firms rfi derivain al Schmi-Grhe and Uribe, 24, aendix A 28

30 Als, firms have saisf a cash-in-advance cnsrain f he frm m vw h, which imlies ha a fracin ν f wages has be aid in cash. Parameer ν is charged wih exisence mne in he mdel, hen i is ν. In case f ν we cnsider cashless ecnm, herwise wih cash. Since hlding cash is csl (we resume sricl siive nminal ineres rae i is assumed ha firms hld nl he required amun s ha in equilibrium he cnsrain hlds wih equali m vw h. (6 The firs rder cndiins f he firms rblem (here, again, we made he aggregain f firms wih resec h and k, which reresen he firms demand equains fr labur and caial θ θ mc z ( θ k h w ν (7 mc z θk h u, (8 θ θ where mc denes marginal css. Bh f hese firs rder cndiins are idenical amng all he firms in he mdel. This is n s wih he hird cndiin which arises frm he fac f w-gru-f-firms ariining. Prices are assumed be sick, which is mdeled wih he Calv 2 mehd, which means ha in each erid a randml chsen fracin α f firms are frced mainain heir rices f he revius erid, while he remaining fracin f ( α firms can chse he rices imall wihin an erid. The rices ha are being rese are given b P ~. The firs rder cndiin f he firms rblem wih resec he rice P ~ is hen E s ~ s P, sα as mcs Ps r ~ P Ps, which can be rewrien, wih w auxiliar variables essenial fr calculain simlificains, as 2 See Calv (983 and Yun (996 29

31 2 x x, (9 where x 2 and are defined recursivel as 2 x,,,,, ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ s s s s s s s s s s s s s s s s s s x P P r E mc a P P mc a P P r E P P r E mc a P P mc a P P r E mc a P P mc a P P r E x α α α α α ~ ~ ~ x E mc a λ λ αβ (2 2 2 ~ ~ ~ x E a x λ λ αβ (2 The afremenined firs rder cndiin means ha firms are able chse he rice imall in he curren erid, chse he level in such a wa ha he weighed average f curren and fuure differences beween marginal css and marginal revenues are equal zer. Tha is cnsisen wih he sandard ecnmic cndiin f rfi maximizain. The aggregae rice level is he weighed average f he rices unchanged frm he revius erid,, and he rices rese in he curren erid P P ~. Divided hrugh b, he exressin fr he rice level becmes P α α ~ (, (22 where P P / ~ ~. 2 The cmuain f is cied frm Schmi-Grhe and Uribe (24,.2. Addiinall, we remind ha x P P and ~ ~ ~ ~ P P P P 3

32 In rder deermine he average mark-u, we al a laer versin f he aricle, Schmid-Grhe and Uribe (26. The average mark-u, am, is given as he quien f marginal css and he aggregae rice level. The relaive rice level is x P i P di, where P i are he rices f all he individual varieies, and P is he aggregae abslue rice level in erid. Based n his definiin he rice level can be cmued recursivel as x ~. (23 ( α α( x The inuiin f his cmuain is ha a fracin f ( α f all firms can adjus heir rices in ever erid, and se a relaive rice Pi, Pi, x erid which is given b di di P. P ~. The remaining firms kee heir rice frm he revius Then, he average mark-u is given b am x mc. (24 The exernal secr Our analsis exends he research aer b Schmi-Grhe and Uribe (24 als b including exernal secr he mdel. The necessi f including he furh agen is in he fac f cnsidering an exr-riened ecnm ha ges a large ar f is rfis frm inernainal rade, in aricular, frm il exr. Then, he balance f amens is CA KA, (25 where KA is caial accun 22, CA denes curren accun. Their sum is equal zer since he flaing exchange rae regime is cnsidered. Caial accun is creaed due he difference beween grss ne-erid, risk-free, nminal ineres-raes, and. We imlemen he siuain when inernal rae,, is smaller han exernal, in erid, hen caial accun 22 Als knwn as financial accun 3

33 defici frms. I crresnds he exr-rienain f ur ecnm, which imlies curren accun surlus. The sandard equain shwing he ineracin beween nminal and real exchange raes is E P e. (26 I is assumed ha unilaeral ransfers and ne facr amens are equal zer, hen curren accun equain is defined as exr, Ex, minus imr, e Im CA e Im. (27 We assume ha he cunr exrs nl il. We culd make his simlificain since he main ar f exr revenues cme frm il 23. Imr las a secndar ar in ur analsis i is mdeled as a univariae auregressive rcess Im ρ Im Im ( ρ Im Im ε Im, where I m denes he sead-sae level f imr. 23 See als Secin Facs in ur wrk 32

34 5. Mdel Analsis Frm a echnical in f view, we have imlemened he mdel in he Tlki rgram in he sandard wa b deermining he equilibrium, calibraing, lg-linearizing 33 equains, finding sead-saes, building marixes and deriving imulse-resnses a echnlg, gvernmen urchases, il flw and il rice shcks. Equilibrium The marke equilibrium cndiin, as usual, is fr demand and sul be equal, z k h θ θ s which is here reresened as where s mechanism. z θ θ k h, (28 s denes he css induced b he inefficien rice disersin brugh abu b he Calv s ( α α s ~ (29 Als, in equilibrium he ical resurce cnsrain mus hld c i g Ex Im. (3 A sainar cmeiive equilibrium is deermined b he equains f agens rblem imizain, lic rules, balance f amens and (8, (9, (3, (4, (, (27, (26 equains. D L I means ha fr a se f rcesses c, h, λ, w,, τ, τ, T, u, mc, k,, i,, s, ~, 2 ', l, m, x, x, F, res,, div,, KA, CA, E fr,... ha saisf he equains L D (3 (3 and eiher τ r. The iniial cndiins fr he sae endgenus variables τ are given as well as he exgenus schasic rcesses fr g, z,,, Im. τ 33

35 Lg-linearizain In his secin we rvide he lg-linearizain fr he equains ha deermine he equilibrium. We resen hem in grus fr he rblems f he varius agens and secrs, and schasic rcesses. Husehlds ( i i kk k k δ (3 ( h hh c σ γ σ λ (4 D D D w h hh c τ τ τ (5 δ τ τ τ τ λ λ u u uu u uu E D D (6 The Gvernmen ( ( ( ( (, div E div E mm m m g g l l ll τ τ (7 ( E λ λ (8 ( D D L L τ τ τ τ τ τ (9 ]( [ T T λ τ τ τ ( ( ( ( 2, m l m m l l gg ll div E div E γ γ ττ ( (2 α α α Sabilizain fund,, v di div rev rev F F F F (3 ]( [ ]( [(, rev ev r λ τ λ (4 34

36 ,, F F div iv d ξ (5 Firms (6 h w m v v w h k z mc ν θ θ (7 ( ( u h k z c m θ θ (8 2 x x (9 Since and Ex g i c Im g i c a Im,, we subsiue b (. e Ex a ' e [ ] ~ ( ( ~ ( ( ~ ( ( ~ x E x mc e e e mc e x x λ λ αβ (2 [ ] ~ ( ( ~ ( ~ ( ~ x E x e e e e x x λ λ αβ (2 ~ ( ~ ( ( α α (22 x x α α α α (23 c m x m a (24 (28 ( h k s z θ θ ( ~ ~ ( s s s s α α (29 Im Îm ( e e gg ii cc (3 Exernal secr A KAK ACA C (25 ' ' E ε (26 Im Îm ( e e ACA C (27 35

37 Schasic rcesses g z ρ ε g g ρ ε z z z g ρ ε ρ ε ρ ε Im Î m Im Îm Sead-sae In he fllwing we resen ur idenificain f he sead sae values f he mdel fr all he variables f he equilibrium. Slving his ssem f 33 equains was he challenging ar f ur wrk. This was achieved hrugh he islain f a submdel cnsising f he equains 3, 5, 6, 7, 7, 8, 9, 2, 2, 22, 28, 29 and 3, which was slved firs. We als made use f he cmmn racice f inrducing sme inermediae variables, in his case k h and h. In rder full idenif he sead saes we als had make use f he rais g, m, τ, /, Im/, ha are given in he calibrain ar f he mdel. (8 β u β ( δ D τ (6 ~ α (22 α ( α ~ s (29 α ( αβ m c ~ ( αβ (9 (2 (2 k h u mczθ θ (8 36

38 v h k mcz w ( θ θ (7 θ h k s z h (28 ( ( Im D g D w h s h s h s h k w h h τ γ δ τ γ (3 h h ( ( h w c D τ γ (5 h h k k kδ i (3 s g g ( ( δ γ δ λ h c (4 s D L ( τ τ τ D L τ τ τ (9 s m m τ e div m g l / ( (, (7 αβ ( ~ c m x (2 2 ( ~ αβ x (2, iv d (5 37

39 τ rev F s τ ( λ τ λ (4, rev, div, (3 T τ τ λ ( C A e Im (27 KA CA (25 E ' e' (26 Calibrain T find he imal mnear and fiscal lic rules we search ver he cefficiens f mnear lic rule, α, α and α, under eiher he balanced-budge r liabili argeing fiscal lic rule. These cefficiens are he funcins f mdel s arameers. Thus, we have give he numerical values he arameers achieve ur gal. Since he rsed mdel is buil fr an exr-riened ecnm, ha describes sme ical characerisics f he ussian ecnm, we calibrae i he ussian ecnm. The ime uni is equal a quarer. The main surces we alied calibrae he mdel, were saisical ussian ublicains, he rincial nes are rvided b Bank f ussia 24, Ecnmic Exer Gru 25, Federal Sae Saisics Service 26. The ar f calibrain ha des n deend n ecnmical eculiariies f he cunr, was aken frm sme aricles, Schmi-Grhe and Uribe (24, 26, Sbrdne (22, Gali and Gerler (999, Presc (986 and sme hers, under-menined. Cnsidering he husehlds rblem, we se he ineremral elasici f cnsumin, /σ, equal.5, and he imlied value f reference arameer, γ 3. 48, reling n Schmi-Grhe and Uribe (24 and Presc (986. The reference arameer ges is imlied value under sead-sae cndiins and under assumin ha ele deve abu 2 ercen f heir ime wrk. The value f quarerl subjecive discun rae is assigned a value f.4 ha is cmaible wih he annual real rae f ineres f 4 ercen (Presc, 986. Since his value was fund mainl fr U.S. ecnm, in ur analsis i wuld be his meaning fr freign ineres rae. 4, 24 Web-sie: 25 Web-sie: 26 Web-sie: h:// 38

40 We assign he value f ercen he annual dereciain, δ, a rae nrmall used in real business ccles mdels. Allwing fr Cbb-Duglas rducin funcin, he cs share f caial, ϑ, is se equal.6, which is much higher hen in U.S. r Eurean ecnm, bu crresnds he curren ussian siuain. I means ha nl abu 4 ercen f al firms css fall a wages. The rice elasici f demand,, is equal 5 (see Schmi-Grhe and Uribe, 24. The inflain rae is equal 9 ercen er ear in sead sae ha crresnds he fficial level, declared b Bank f ussia in he resul f 26. The share f gvernmens urchases in GDP in sead sae is equal 6 ercen, he rai f il revenues in GDP is se 2 ercen in sead sae, and he share f sead-sae imr has a value f 6.37 ercen in GDP. Sead-sae nn-il ax revenues GDP rai is equal 4 ercen. All f hese values were calculaed n he basis f saisical daa rvided b Bank f ussia, Ecnmic Exer Gru and Federal Sae Saisics Service ublished in ecnmic rers f 26. The rai f mne aggregae, M quarerl GDP is assumed be n he same level as Schmi-Grhe and Uribe (24 suggesed, s. 45 in sead sae. This level is ver clse m ussian siuain in 26. Then, i is cnsisen wih he ercen f cash ha firms reain as wage, ν. 82. The share f he firms ha cann change heir rice wihin an erid is assumed be equal 2/3 (see Schmi-Grhe and Uribe, 24, Sbrdne, 22, Gali and Gerler, 999. I means ha n average, firms change rices hree erids wihin a ear. Then, he remain ar f he firms, α, able change rices has value f /3. Calibraing il secr, we se is meanings in cnsisence wih fficial daa, rvided b he afremenined surces in ussia in 26. The il ax rae equals 54 ercen. Since il rducing cmanies belng husehlds as well as he gvernmen, heir shares are equal a value f.73 and.27, resecivel. In ur mdel here are five surces f uncerain: gvernmen urchases, echnlg shck, il flw, il rice and imr. Ever ne is mdeled in frm f a univariae auregressive rcess. The firs-rder crrelain f gvernmen urchases shck, echnlg shck, ρ z, is.82; f an il flw shck, ρ g, is equal.9; f ρ, is.75; f an il rice shck, ρ, is.85; f an imr shck, ρ Im, is.8. The sandard deviain is se.74 fr gvernmen urchases shck;.56 fr echnlg shck,.65 fr an il flw shck;.6 fr an il rice shck;.63 fr an imr shck. The firs w values f firs-rder crrelain 39

41 and sandard deviain were aken frm Schmi-Grhe and Uribe (24, and he res nes were decided b rial and errr, heir meanings d n influence n he resuls significanl. In able 5. we summarize he calibraed arameers. Table 5.. Calibraed Parameers σ / 2 Ineremral elasici f cnsumin θ.6 Cs share f caial 4 β.4 Quarerl subjecive discun rae 5 Price elasici f demand s.6 Sead sae share f gvernmen urchases g 4.9 Grss quarerl inflain rae 4 δ. Quarerl dereciain rae s.45 ai f M held b firms quarerl GDP m α 2 3 Share f firms ha can change heir rice each erid γ 3.48 Preference Parameer s.4 Sead sae nn-il ax revenue GDP rai τ ν.82 Cash requiremen (if ν cashless ecnm / 4.4 Quarerl freign ineres rae τ.54 Oil revenues ax rae λ.73 Share f husehlds in il secr s.2 Sead-sae share f il revenues s.637 Sead-sae share f Imr Im ρ.9 Firs rder serial crrelain f g g σ.74 Sandard Deviain f gvernmen urchases shck ε g ρ z.82 Firs rder serial crrelain f z σ.56 Sandard Deviain f echnlg shck ε z ρ.75 Firs rder serial crrelain f σ.65 Sandard Deviain f il flw shck ε ρ.85 Firs rder serial crrelain f σ.6 Sandard Deviain f il rice shck ε ρ.8 Im Firs rder serial crrelain f Im σ.63 ε Im Sandard Deviain f imr shck 4

42 Technical eculiariies f rgram imlemenain This ar briefl describes sme revisins we made imlemen ur rgram. T deermine imal lic feedback cefficiens and build imulse resnses we used Tlki rgram, ha is MATLAB rgram fr Analzing Nn-linear Dnamic Schasic Mdels (see Uhlig, 997. Frm he racical sandin, u a mdel in his rgram all f he lglinearized equains shuld be divided in hree grus accrding he fllwing ssem: CC DDz AAx BBx E [ FFx GGx HHx JJ KK LLz MMz ] NNz e z. In ur mdel equains (3, (4, (5, (7, (9 (9, (22 (3 belng he gru ha deermine sae endgenus variables; he equains wih her endgenus variables (6, (8, (2, (2 relae he secnd gru; five equains fr gvernmen urchases, echnlg, il flw, il rice and imr inrduce shcks he mdel. Variables have be allcaed he vecrs x, and z, cmrising endgenus saes, her endgenus variables, and exgenus schasic rcesses, resecivel. We idenif caial, liabiliies, mne demand, he nminal ineres rae, rice disersin, al rice level and sabilizain fund as endgenus saes, gvernmen exendiure, il rice, il flw, echnlg and imr as exgenus schasic rcesses and all he hers as endgenus variables. The indexing f he variables has be such ha nl indexes f, and execains f are used. The caial accumulain equain given in he mdel as k k i ( δ des n fulfil his cndiin. In rder make clear fr he Tlki rgram ha caial is a sae variable ha cann be changed when he shck ccurs, i is necessar lag all k b ne erid, s ha becmes and k becmes in all equains. Nw, k is he sck f k k k caial ha is being used fr rducin in erid bu i can nl be changed in erid. Marixes shuld be frmed in cmliance wih he abve ssem f equains. One f he eculiariies f Tlki imlemenain cnsiss in requiremen marix CC: is rank shuld be n less hen he number f endgenus variables included in i. Unfrunael, he classificain he vecrs x, and z, ha is described abve, rduces a CC marix ha 4

43 cnains 2 variables bu nl has a rank f 2, which can herefre n be rcessed b he Tlki. The reasn fr his rblem is ha he variables and x inrduced exress he x 2 firms rfi maximisain rblem in recursive frm are linearl deenden. We deal wih his rblem b mving he variable x in he vecr x f endgenus saes. 2 A rblem f he same class has been arisen when i was discvered ha he sead-sae level f gvernmen dividends (sen frm sabilizain fund was equal zer. T slve his rblem he dividends were se. -2 in sead sae, he minimum level given which rgram disinguishes hem frm zer. When all he arameers are idenified, he ssem f equains is full deermined and imlemened he Tlki rgram aking in cnsiderain he feaures described abve, he imulse resnses fr he variables f ineres culd be fund. Aendix 3 cnains he full versin f MATLAB cde ha allws geing hem. Hwever, his is n enugh find imal feedback cefficiens f lic rules, since his rgram rduces imulse resnses nl fr ne aricular se f cefficien values. We used he MATLAB cdes resened in Aendices 4A, 4B ha le us var w r hree cefficiens a he same ime. In his case i is ssible see he deviains f a aricular variable fr each cmbinain f hese cefficiens values Fr mre deails, see Chaer Mdel resuls 42

44 6. Mdel esuls In his chaer we inrduce he resuls we achieved. The mehd f analsis is mainl based n rial and errr. We buil a General Equilibrium Mdel fr he exr-riened ecnm and used a Tlki rgram fr MATLAB imlemenain find he se f imal lic rules. We cnsider an ecnm wihu incme axes; hence, we imlemen he mdel D frτ. A mnear ecnm is analsed, bu sme resuls have als been checked fr a nncash ecnm. Fiscal lic rules are cnsidered, firs budge balance, hen liabili argeing. Balanced budge lic rule The resuls are resened in accrdance wih he aim we se. Firs, we search fr he imal cefficiens f mnear lic rule in case f balanced budge argeing fiscal lic. Technicall, we use MATLAB cde frm Aendix 4a cnaining he rgram which le us see he deviains f an mdel variable ha ccur under ne f five % shcks a a aricular mmen. The resuls are resened in he frm f 3D marices ha shw he size f deviains given all values f ree-cefficien-cmbinains. T d his we remved he secific cefficien values frm he mdel imlemenain resened in Aendix 3. Fr α and α we search ver a grid frm -3 3, 28 hwever fr α we se a framewrk frm - exclude he nn-sable rs. The ses in value f α, α and α were.5,.5 and.2, resecivel, fr his erain. We chse hree variables esimae he deviains frm he sead sae: inflain, uu and sabilizain fund fllwed b shcks in gvernmen urchases, echnlg, il flw and il rice. T achieve he abvemenined gal we firs search fr he bes value f α find he imal range f values fr α and α. Table 6.. The resuls fr α in Variables Inflain Ouu Gvernmen urchases Shcks Technlg Oil flw Oil rice α α. 8 α. 2 α. 6 α. 2 Deviains frm sead-sae, abs. value e e e e-6 α α. 4 α. 4 α α. 2 Deviains frm sead-sae, abs. value.7825e e e e-7 28 We rel n values suggesed in Schmi-Grhe and Uribe (24 43

45 Sabilizain fund α α. 6 α. 2 α [; ] α [; ] Deviains frm sead-sae, abs. value e e The resuls resened in able 6., as well as he resuls fund fr her ime mmens afer he shck had ccurred, d n le us make a definie cnclusin abu he imal levels f α. Bu i resens he resuls f hw much he ineres rae shuld rel n is value in case f, fr examle, riri sabilizing f uu deviains given a aricular shck. Laer, we shw wha values he her w cefficiens shuld ake in his case. The value f ineres rae cefficien ha minimizes he abslue value f deviain frm sead sae differs dramaicall fr inflain, uu and he sabilizain fund given a aricular shck. This resul was als checked fr her ime mmens, and was cnfirmed. Hwever, he ineresing finding was ha under an value f α (given he meanings f her cefficiens he sabilizain fund has he same deviains frm sead sae in he case f il shcks. Bu i is rue fr he mmen f shck ccurrence. Bu if we lk behind, hen he value f α is significanl imran fr he sabilizain fund deviains. Under α. he deviain frm sead sae was significanl smaller han under her values f his cefficien, and n nl in he mmens befre he shck ccurred. This resul is imran fr us, since we imlemen he siuain f an exr-riened ecnm wih an emhasis n il secr. In aricular, il shcks were he cenral nes in exerience f mdern ussian ecnm. Furher, we imlemen he fllwing sraeg f searching imal lic cefficiens. We give a aricular value α 29 and ge he surface f deviains fr inflain, uu and he sabilizain fund under all values f he her w cefficiens wihin he inerval [-3; 3] wih se.2, given a aricular shck a a secified ime. Hence, we grah he surface f 3 2 ins. We cnsider α [.,.5,.3,.,,.3,.5,.9,. ]. Here, he values fund in he revius ar are aken in cnsiderain. Unfrunael, i is n ssible resen all figures fund in hese cases, s we will rvide nl sme f hem, in ur inin, he ms ineresing. We will resen he resuls nl fr he mmen when he shck ccurs. Firs, α is se equal. The ms fascinaing quesin here is wha haens wih inflain, uu and he sabilizain fund in case f an il rice shck. Acuall, hese resuls are highl crrelaed wih he nes fund under he il flw shck, bu he il rice shck is mre vial, s we cncenrae 29 This racice was als used in Schmi-Grhe and Uribe (24, 26 44

46 n is descriin. Here, figures 6.a, 6.b, 6.2a, 6.2b, 6.3a, 6.3b deic imulse resnses in. esuls are resened as a 3D-grah r/and as a 2.5D-grah. We believe his gives a beer rendiin. Figure 6.a. 3D - Imulse resnse f inflain a ercen il rice shck, α Figure 6.b. 2.5D - Imulse resnse f inflain a ercen il rice shck, α 45

47 Figure 6.2a. 3D - Imulse resnse f uu a ercen il rice shck, α Figure 6.2b. 2.5D - Imulse resnse f uu a ercen il rice shck, α Figure 6.3a. 3D-Imulse resnse f sabilizain fund a ercen il rice shck, α 46

48 Figure 6.3b. 2.5D-Imulse resnse f sabilizain fund a ercen il rice shck, α This grahs shw and he calculaed marices rve ha in case f α, ineres rae shuld feaure a sensiive resnse uu, fr ms f α values. In aricular, α shuld be se greaer han 2. Sabilizain fund imulse resnses are ver sensiive il shcks. This fac is adequae reali, since he sabilizain fund mainl cnsiss f il revenues. The reasn wh he deviains f uu and inflain are much bigger han fr sabilizain fund is in exisence f mulilicaive effec fr firs w variables. The 3D- and 2.5D- imulse resnses fr inflain and uu % gvernmen urchases shck are rvided in Aendix. In he case f he sabilizain fund here is n significan resnse uu r inflain shck, since i is deermined b il rices and il flw. Liabili argeing lic rule In his ar we resen he resuls fr he case f liabili argeing b fiscal lic. S far we have analzed a assive fiscal lic, i.e. he siuain when lic can n influence he rice index. The influences were creaed b mnear lic when he fiscal lic argeed a balanced budge. Hwever, in he case f liabili argeing fiscal lic culd be eiher assive r acive. 2 T imlemen he case f a assive fiscal rule we shuld se γ,, he acive 2 fiscal lic - γ,. The exlanain f hese inervals is rvided in Secin 7. 47

49 4 In ur analsis, he grss quarerl inflain rae is.9. Under he resricin f α we firs imlemen a assive fiscal rule. The ses in value f γ are equal.2, wihin he range frm..9. Fr α and we search ver a grid frm -3 3, as in he case f balanced budge argeing, wih a se f.5. We find u ha in ms cases he meaning f γ [.;.9 ] des n influence he resuls α significanl. I means ha given each value f γ here is he cmbinain f guaranees he same minimal deviain frm sead sae a he mmen α and α ha. The resuls are resened in able 6.2. This hhesis was als esed fr her mmens, and i was fund u ha i is ssible find he cmbinain f α and α values which des n lead significan differences in deviains frm sead-sae under an aricular γ f he assive fiscal lic. Table 6.2. The resuls fr γ in mmen Variables Inflain Ouu Sabilizain fund Gvernmen urchases Shcks Technlg Oil rice γ γ [.;.9 ] γ [.;.9 ] γ [.;.9 ] Deviains frm sead-sae, abs. value.49e e-4 γ γ [.;.9 ] γ [.;.8 ] γ [.;.9 ] Deviains frm sead-sae, abs. value.569e-4.3. γ γ. γ. 7 γ. Deviains frm sead-sae, abs. value.4653e e e-4 Frm able 6.2 i is eviden ha if he Gvernmen cares abu he sabilizain fund, hen in he case f each shck a aricular imal value fr γ exiss. Hwever, ur analsis shwed ha he deviains in his case are significanl less fr γ, ha is wh fr an γ he cmbinain f mnear feedback cefficiens ha rduces he deviain nl -2 bigger culd be fund. This analsis le us sulae ha in case f a assive fiscal lic wih liabili argeing he value f γ (given α des n cnfine mnear lic rule in is resnse uu and inflain. 48

50 Nw under he resricin f α we d n require fiscal lic be assive. We imlemen he case f il rice shck given α 3. As we have alread menined, he imal mnear lic rule shuld resnd uu significanl, ha is wh we ried sme values f is cefficien cnsisen wih his fac and resen here he exreme case. Fr α and γ we search ver a grid frm -3 3 wih he se f.5. The figures in Aendix 2 shw he imulse resnses f ur arge variables a ne ercen il rice shck. The ms remarkable resul is fr he sabilizain fund. Each value f γ culd eiher rduce n deviain frm sead sae given an value f α r cause he same deviain fr an value f α. 49

51 7. Discussin In ur numerical analsis we imlemened he mdel s varian wihu incme axes and mainl fcusing n mnear ecnm. We chse rial and errr mehd fr searching fr he imal lic rule cefficiens. We ried he mdel secificains under which Schmi-Grhe and Uribe (24 reached he ms significan resuls, bu in an exanded real business ccle mdel fr an exr-riened ecnm, and we mainl fcused n il rice shcks. Hwever, we did n reach such recise resuls as he did. We seleced inflain, uu and he sabilizain fund as he majr variables fr ur invesigain because inflain is icall he main gal fr sabilizain lic f he Cenral Bank, uu is he crucial variable fr bh licies and he sabilizain fund is he ke nvel variable f he mdel. The search f imal lic cefficiens was dne fr he budge balance and liabili argeing fiscal rules. Under his firs varian f a fiscal lic rule, we fund ha he value f ineres rae cefficien minimizing he abslue value f deviain frm sead sae differs dramaicall fr inflain, uu and he sabilizain fund given a aricular shck. Hwever, able 6. rvides he aricular values f feedback cefficiens fr his case. Bu he deviains frm he sead-sae are srngl insignifican in man cmbinains f hree cefficiens, and resening minimum f hem des n shw he real sae f affairs. T be sure abu his we als ried her ses fr feedback cefficiens (fr examle,.3,.3,.;.5,.2,.;.2,.2,.2;.2,.2,., bu he gave us he same icure. The 3-D marices fund in his analsis rve he fac f exisence f man cmbinains f cefficien values ha rvide insignifican deviains frm he sead sae. This sud s exerience alied cashless ecnm des n change he cnclusin. The inuiin f he resul we g in his ar is he fllwing: when mnear lic is free feaure an w f he ineres raes, inflain, uu feedback cefficiens, keeing ne f hem fixed, hen i culd find he imal cmbinain f hem which rduces he minimal deviain frm he sead-sae. Presened in figures a, b, 2a, 2b, 3a, 3b imulse resnses fr inflain, uu and he sabilizain fund fr il rice shck shw ha in case f α, he ineres rae shuld feaure a sensiive resnse uu, fr ms f he α values. In aricular, α shuld be se greaer han 2. The verificain f he mdel fr he cashless ecnm did n change ur cnclusin. 5

52 I is imran menin ha cmared he ms imran finding f Schmi-Grhe and Uribe (24, ha imal α equals zer in case f echnlg shck, hereb underlined ha ineres rae feaured a siive resnse uu reduce significan lsses. Our analsis f an exr-riened ecnm wih emhasis n he il indusr rduces he sie resul. E' div, Fr he case f liabili argeing he fiscal rule is τ γ γ ( l l, whileγ 2 is equal zer. As befre i is assumed ha incme axes are equal zer, s ha L τ τ. Then cmbining hese w cndiins wih he budge cnsrain (7, we ge l E', ( / ( γ l g γ γ l m ( div E div, If γ is less hen ne in abslue value, hen here is a sable r f gvernmen liabiliies. This means ha he grw a a rae less hen he real ineres rae, /. Then, fiscal lic indebedness grws wih he seed be cvered. Fiscal lic can n influence he rice level, i is assive. Bu if γ is higher han ne in abslue value, gvernmen liabiliies increase quicker han a he rae f he real ineres rae. In his case rvide slvenc f he gvernmen inflain shuld be adjused. This is he case f acive fiscal lic. Our analsis fund ha in he case f a assive fiscal lic wih liabili argeing, he value (wihin he inerval f balanced budge feedback cefficien in he fiscal lic rule (under he resricin ha ineres rae cefficien in mnear lic rule is equal zer des n cnfine mnear lic rule in is resnse uu and inflain. Schmi-Grhe and Uribe (24 als imlemened he liabili argeing fiscal lic, and fr he case f assive rule he rvide mre cncree resuls han we d. The fund ha given an value f balanced budge feedback cefficien he cmbinain f imal mnear cefficiens, fund in heir revius research, exiss and is he same fr all γ. Under he resricins f zer-, uu and ineres rae feedback cefficiens in he ineres-rae rule we searched fr he imal γ and α wihu a resricin n he naure f he fiscal lic. An ineresing resul was achieved fr he sabilizain fund. Each value f γ culd be eiher rducing n deviain frm he sead sae given an value f α r causing 5

53 he same deviain fr an value f α. This resul culd be inerreed in he wa ha here is he direc link beween gvernmen liabiliies, inflain and ar f sabilizain fund (is dividends. When he liabiliies grw he culd be eiher financed b he dividends frm il r b he inflain decrease raise he nminal value f dividends. 52

54 8. Summar and cncluding remarks In his aer we searched fr a se f eniall imal feedback cefficiens under il, echnlg and gvernmen urchases shcks in he ecnm. T address his issue we buil a general equilibrium mdel fr an ecnm wih huge il exr revenues n he benchmark f Schmi-Grhe and Uribe (24. The sabilizain fund was included in analsis. We k in accun sme imran eculiariies f he ussian ecnm ding he calibrain n he base f a Tlki rgram fr MATLAB imlemenain. Oimali was deermined as minimizain f variables deviains frm heir sead-sae. We did n give he irrefragable answer he quesin we cnsidered, bu we made rgress in deermining a se f cefficiens saisfing he requiremen f imal lic in an exr-riened ecnm. Our main findings are: under il rice shck imal mnear lic rule feaures a significan resnse uu; he cefficien f nminal ineres rae varies significanl fr differen shcks; cnsidering he sabilizain fund under assive fiscal lic wih liabili argeing each value f liabili argeing cefficien culd eiher rduce n deviain frm sead sae given an value f inflain feedback cefficien r cause exacl he same deviain. In ur fuure research we are ging deal wih he rblem mre hrughl. Firs f all, we will exand he cmuing ar f ur analsis b making shrer ses fr cefficiens s as make ur es-in grid mre recise. Secndl, we will make mre variains fr calculains, hus enhancing ur rial and errr analsis. The nex se will invlve exanding he mdel. Having buil a general equilibrium mdel fr an exr-riened ecnm wih emhasis n he il indusr and having searched fr he imal lic rules, we used he Talr rule describe mnear lic. In ur fuure research we will cmare he resuls we have achieved b using cnemraneus Talr rule wih he resuls under her classes f mnear lic rules like McCallum s. The aim is find he bes-describing mnear lic rule fr an exrriened ecnm wih a sabilizain fund wihu being cnfined simle rules. The assumin f a flaing exchange rae wuld be rejeced in analzing an ecnm where freign reserves are imran. This makes he analsis mre cmlicaed and increases he rle f currenc lic. Hwever, i culd describe sme imran eculiariies f he ussian ecnm which were negleced in his research due scarce ime recurses. Als, we are ging deermine he inercnnecin beween he sabilizain fund and mne sul. We are searching fr an equain ha bes describes he relainshi beween hese w variables. Since in general ur mdel is buil aking disrin axes in accun, we will search fr imal lic rules under an exanded varie f fiscal insrumens. 53

55 Having imlemened an emirical analsis f ussian ecnm, we fund u ha mne velci has decreased much in recen ears. This fac cmbined wih mne base grwh and an inflain decrease cnsiues a gd base fr hereical mdeling. T sum u, ur ririies fr fuure research lie in exending ur mdel f exr-riened ecnmies wih a sabilizain fund chiefl in he mnear shere make he resuls mre recise and alicable. 54

56 eferences Aarle B. van, Bvenberg L, aih M., Mnear and Fiscal Plic Ineracin and Gvernmen Deb Sabilizain, Jurnal f Ecnmics, 62(2, 995, -4. Bernanke S.B., Gerler M., Wasn M., Sims A.C., Friedman B.M., Ssemaic Mnear Plic and he Effecs f Oil Price Shcks, Brkings Paers n Ecnmic Acivi, N. 997, 9-57 Caldern, C., and Schmid-Hebbel K., Macrecnmic licies and erfrmance in Lain America, Jurnal f Inernainal Mne and Finance, 27(7, 23, Calv, G., Saggered rices in a uili-maximising framewrk, Jurnal f Mnear Ecnmics 2, 983, Canzneri, M., Crumb,. and Diba, B., Is he rice level deermined b he needs f fiscal slvenc?, Cenre fr Ecnmic Plic esearch Wrking Paer N. 772, 998 Chrisian, Lawrence J., Eichenbaum M., and Evans C., Nminal igidiies and he Dnamic Effecs f a Shck Mnear Plic, Nrhwesern Universi, Augus, 23 Clarida,., Gali J. and Gerler M., Mnear lic rules in racice: Sme inernainal evidence, Eurean Ecnmic eview 42(6, 998, 33-67, and NBE Wrking Paer 6254 Cchrane, J. H., Lng-erm deb and imal lic in he fiscal her f he rice level, NBE Wrking Paer 677, 998 Drbshevsk, S. and Kzlvska A., Inside asecs f ussian mnear lic, IET Wrking Paer 45, 23 Easwd., Macrecnmic Imacs f Energ Shcks, Oxfrd Ecnmic Paers, New Series, vl. 44, 992, Esanv A., Merkl C., Vinhas de Suza L., Mnear Plic ules fr ussia, BOFIT Discussin Paers, Nvember 24 Fr J. M.; Lilien M.D., Mnear Plic esnses Exgenus Shcks, The American Ecnmic eview, Vl. 76, N. 2, 986, Hall,., "Mnear Sraeg wih an Elasic Price Sandard in Price Sabili and Public Plic, Federal eserve Bank f Kansas Ci, 984, Kim J., Kim S., Schaumburg E., Sims A.S., Calculaing and using secnd rder accurae sluins f discree ime dnamic equilibrium mdels, Jurnal f Ecnmic Dnamics and Cnrl, 27, Kllmann,., Welfare Maximizing Fiscal and Mnear Plic ules, mime, Universi f Bnn, March 23 55

57 Leeer, E. M, Equilibria under Acive and Passive Mnear and Fiscal Plicies, Jurnal f Mnear Ecnmics 27, Februar 99, Lmbard, G. and Suherland, A., Cmuing secnd-rder-accurae sluins fr rainal execain mdels using linear sluin mehds, Jurnal f Ecnmic Dnamics and Cnrl, 25 McCallum B., Mnearis ules in he Ligh f ecen Exerience, NBE Wrking Paers 277, 984 Minella, A. Sringer de Freias P., Gldfajn I., Kfur Muinhs M., Inflain argeing in Brazil: Cnsrucing credibili under exchange rae vlaili, Jurnal f Inernainal Mne and Finance, 27(7, 23, 5 4 Mhan, M. and Klau M., Mnear lic rules in emerging marke ecnmies, Wrking Paer, Kiel Insiue fr Wrld Ecnmics, Seember 23. Presc E., Ther Ahead f Business Ccle Measuremen, Federal eserve Bank f Minnealis Quarerl eview, Fall 986, 9-22 emberg, J. J. and Wdfrd, M. D., Oliglisic Pricing and he Effecs f Aggregae Demand n Ecnmic Acivi, Jurnal f Pliical Ecnm, December 992, Schmi-Grhe, S. and Uribe, M., Price level deerminac and mnear lic under a balanced budge requiremen, Bard f Gvernrs f he Federal reserve Ssem, mime, 997, Jurnal f Mnear Ecnmics 45, Februar 2, Schmi-Grhe, S. and Uribe, M., Slving dnamic general equilibrium mdels using a secndrder arximain he lic funcin. 24b, Jurnal f Ecnmic Dnamics and Cnrl, 24, Schmi-Grhe, S. and Uribe, M., Oimal Simle And Imlemenable Mnear and Fiscal ules, mime, 24 Schmi-Grhe, S. and Uribe, M., Oimal Simle And Imlemenable Mnear and Fiscal ules: exanded versin, Nainal bureau f ecnmic research, Wrking aer 242, 26 Tabellini G., Mne, Deb and Deficis in a Dnamic Game, Jurnal f Ecnmic Dnamics and Cnrl,, 986, Talr, J., An Aeal fr ainali in he Plic Acivism Debae, in. W. Hafer, ed.. The Mnear versus Fiscal Plic Debae, New Jerse: wman and Allanheld, 986a, Talr, J. B., Discrein versus Plic ules in Pracice, Carnegie cheser Cnference Series n Public Plic 39, December 993,

58 Trres Garcia, A., Mnear lic and ineres raes: evidence frm Mexic, Wrking Paer, Kiel Insiue fr Wrld Ecnmics, 23, 2. Uhlig, H., A Tlki fr Analzing Nnlinear Dnamic Schasic Mdels Easil, mime Tilburg, 997 Vdvichenk A., Vrnina V., Mnear lic rules and heir alicain in ussia, EEC, 24, 47 Wdfrd, M., Price-level deerminac wihu cnrl f a mnear aggregae, Carnegie- cheser Cnference Series n Public Plic, Elsevier, vl. 43, 995, -46 Wdfrd M., Ineres and rices, 22 Yun, T., Nminal rice rigidiies, mne sul endgenei and business ccles, Jurnal f Mnear Ecnmics 37, 996,

59 Aendix Aendix. Imulse resnse f inflain and uu a ercen gvernmen urchases and echnlg shck, α Figure A.. 3D-Imulse resnse f inflain a ercen gvernmen urchases shck Figure A D-Imulse resnse f inflain a ercen gvernmen urchases shck 58

60 Figure A.2. 3D-Imulse resnse f uu a ercen gvernmen urchases shck Figure A D-Imulse resnse f uu a ercen gvernmen urchases shck 59

61 Aendix 2. Imulse resnse a ercen il rice shck, α, α 3 Figure A2.. 3D-Imulse resnse f sabilizain fund a ercen il rice shck Figure A D-Imulse resnse f sabilizain fund a ercen il rice shck 6

62 Figure A2.3. 3D-Imulse resnse f inflain a ercen il rice shck Figure A D-Imulse resnse f inflain a ercen il rice shck 6

63 Figure A2.5. 3D-Imulse resnse f uu a ercen il rice shck Figure A D-Imulse resnse f uu a ercen il rice shck 62

64 Aendix 3. MATLAB cde fr majr rgram % Maser_hesis_majr_rgram % Seing arameers: sigma 2; % Ineremral elasici f cnsumin hea.6; % Cs share f caial bea.4^(-/4; % Quarerl subjecive discun rae ea 5; % Price elasici f demand s_g.6; % Sead sae share f gvernmen urchases (g_bar/_bar i_bar.9^(/4; % Grss quarerl inflain rae dela.^(/4-; % Quarerl dereciain rae s_m.72/34; % ai f M held b firms quarerl GDP (m_bar/_bar alha 2/3; % Share f firms ha can change heir rice each erid gamma 3.48; % Preference Parameer s_au.4; % Sead sae ax revenue GDP rai (au_bar/_bar nu.82; % Cash requiremen (if nu, nn-mnear ecnm _fr.4^(/4; % Quarerl freign ineres rae au bar.54; % Oil ax lambda_.73; % Par f HH in il secr s_.2; % ai f Oil revenues GDP sigma_e_.65; % Sandard Deviain f il flw shck sigma_e_.6; % Sandard Deviain fil rice shck rh_.75; % Firs rder serial crrelain f ( rh_.85; % Firs rder serial crrelain f ( sigma_e_im.63; % Sandard Deviain f Imr shck rh_im.8; % Firs rder serial crrelain f Im( s_im.637; % ai f Imr GDP rh_g.9; % Firs rder serial crrelain f g( sigma_e_g.74; % Sandard Deviain f gvernmen urchases shck rh_z.82; % Firs rder serial crrelain f z( sigma_e_z.56; % Sandard Deviain f echnlg shck % Variables nrmalised in rder idenif he mdel au_d_bar ; % rae f disrinar (incme axes z_bar ; % sead sae f rduivi shck e_bar ; % real exchange rae % Cefficiens f fiscal lic rule gamma ; % cnsan erm in fiscal lic rule gamma ; % feedback cefficien fr deviain f las erid's liabiliies frm arge gamma2 ; % feedback cefficien fr secndar gvernmen budge defici % Cefficiens f mnear lic (Talr rule

65 alha_i 3; % feedback cefficien fr cnemrar inflain alha_ 2; % feedback cefficien fr uu ga alha_r ; % feedback cefficien fr ineres rae % Cefficiens f sabilizain fund lic rule ksi.7; % feedback cefficien f smhing he level f Sabilizain fund is arge level % Calculaing he sead sae: _bar i_bar/bea; % nminal ineres rae U_bar ((./bea-dela/(-au_d_bar; % renal rae f caial P_bar ((-alhai_bar^(-ea/(-alha^(./(-ea; % relaive rice f gds whse rice is adjused in erid S_bar ((-alhap_bar^(-ea/(-alhai_bar^ea; % measure f css induced b inefficien rice disersin MC_bar ((ea-/ea(-alhabeai_bar^ea/(-alhabeai_bar^(ea-p_bar; % marginal css f rducin K_H_bar (U_bar/(MC_barZ_barhea^(/(hea-; % rai f caial labur inu W_bar (MC_barZ_bar(-heaK_H_bar^hea/(nu(_bar-/_bar; % wages Y_H_bar (Z_bar/S_barK_H_bar^hea; % rai f GDP er labur H_bar (Y_H_barW_bar/gamma(-au_d_bar-delaK_H_bar-s_gY_H_bar-s_Y_H_bars_ImY_H_bar^(-W_bar/gamma(-au_d_bar; % labur inu Y_bar Y_H_barH_bar; % uu C_bar W_bar/gamma(-au_d_bar(-H_bar; % cnsumin K_bar K_H_barH_bar; % caial inu I_bar K_bardela; % invesmen sending G_bar s_gy_bar; % gvernmen sending Lamda_bar C_bar^(-sigma(-H_bar^(gamma(-sigma; % marginal uili f cnsumin (lagrange cefficien au_l_bar (s_au-au_d_bary_bar; % lum-sum axes au_bar au_l_bar au_d_bary_bar; % incme and lum-sum axes M_bar s_my_bar; % cash requiremen div bar.; % dividends, he ar f sabilizain fund ha gvernmen sends L_bar (_bar(g_bar-au_bar-m_bar(_bar--div bare_bar(-_bar/i_bar^(-; % gvernmen liabiliies P_bar bar s_y_bar; % al revenues frm il X bar (P_bar^(--ea(Y_bar-P_bar barmc_bar/(-alhabeai_bar^(ea; % auxiliar variable used fr rewriing firms' equilibrium cndiins X_2_bar (P_bar^(-ea(Y_bar-P_bar bar/(-alhabeai_bar^(ea-; % auxiliar variable used fr rewriing firms' equilibrium cndiins rev bar (-lambda_s_y_barau barlambda_s_y_bar; % gvernmen revenues frm il, ha exand sabilizain fund F_bar (rev bar-div bar/(-_fr; % sabilizain fund T_bar au_barau bars_y_barlambda_; % all axes, including il axes E_bar e_bari_bar; % nminal exchange rae Im_bar s_imy_bar; % Imr CA_bar e_barp_bar bar-im_bar; % curren accun KA_bar -CA_bar; % caial accun % Declaring he marices. VANAMES ['caial ' % 'liabiliies ' %2 'mne demand ' %3 64

66 'ineres ' %4 'css f rice disersin ' %5 'x2 ' %6 'rice level ' %7 'sabilizain fund ' %8 'lamda ' %9 'cnsumin ' % 'hurs ' % 'incme and lum-sum axes ' %2 'lum-sum axes ' %3 'renal rae ' %4 'invesmen ' %5 'inflain ' %6 'uu ' %7 'marginal css ' %8 'wage ' %9 'new rices ' %2 'x ' %2 'average marku ' %22 'gv revenues frm il ' %23 'dividends frm il ' %24 'all axes ' %25 'curren accun ' %26 'caial accun ' %27 'nminal exchange rae ' %28 'gvernmen urchases ' %29 'echnlg ' %3 'flw f il ' %3 'il rice ' %32 'imr ']; %33 % Translaing in cefficien marices. % Endgenus sae variables "x(": k(, l(, m(, (, S(, PL(, F( % Endgenus her variables "(": lamda(, C(, H(, au(, au_l(, u(, I(, Pi(, (, mc(, w(, (, x(, x2(, AM(, rev_il(, div_il(, Taxes(, CA(, KA(, E'( % Exgenus sae variables "z(": g(, z(, (, (, Im( % Swich ha nain. Find marices fr frma % AA x( BB x(- CC ( DD z( % E_ [ FF x( GG x( HH x(- JJ ( KK ( LL z( MM z(] % z( NN z( esiln( wih E_ [ esiln( ], 65

67 % fr k( l( m( ( S( x2( PL( F( AA [K_bar,,,,,,, %(3,,,,,,, %(4,,,,,,, %(5, L_bar, M_bar_bar-M_bar, -_barl_bar/i_bar-_barg_bar_barau_barm_bar_bar,,,, %(7,,,,,,, %(9,,,,,,, %(,,,,,,, %(2,,, -nu/(_bar_barnu-nu,,,, %(7,,,,,,, %(8,,,,,,, %(6,,,,,,, %(22,,,,, -,, %(9,,,,,,, %(28,,,,,,, %(3,,,, S_bar,,, %(29,,,,,, -, %(23,,,,,, -, %(24,,,,,,, F_bar %(3,,,,,,, -ksif_bar %(5,,,,,,, %(4,,,,,,, %(,,,,,,, %(25,,,,,,, %(27,,,,,,, ]; %(26 % fr k(- l(- m(- (- S(- x2(- PL(- F(- BB [-(-delak_bar,,,,,,, %(3,,,,,,, %(4,,,,,,, %(5, -(_barl_bar/i_bar,,,,,, %(7,,,,,,, %(9, -(gammal_bargamma2l_bar/(l_bar-m_bar, gamma2m_bar/(l_bar-m_bar, -gamma2/(_bar-,,,, %(,,, -alha_r,,,, %(2 hea,,,,,,, %(7 (hea-,,,,,,, %(8,,,,,,, %(6,,,,,,, %(22,,,,,,, %(9 -hea,,,,,,, %(28,,,,,,, %(3 66

68 ,,,, -alhai_bar^eas_bar,,, %(29,,,,,,, %(23,,,,,, alha/i_bar, %(24,,,,,,, -_frf_bar %(3,,,,,,, %(5,,,,,,, %(4,,,,,,, %(,,,,,,, %(25,,,,,,, %(27,,,,,,, ]; %(26 % fr lamda( C( H( au( au_l( u( I( CC [,,,,,, -I_bar %(3, sigma, gamma(-sigmah_bar/(-h_bar,,,, %(4,, H_bar/(-H_bar,,,, %(5,,, _barau_bar,,, %(7,,, au_bar, -au_l_bar,, %(9,,, au_bar,,, %(,,,,,, %(2,, -hea,,,, %(7,, -hea,,, -, %(8,, -,,,, %(6,,,,,, %(22,,,,,, %(9,, -(-hea,,,, %(28, -C_bar,,,,, -I_bar %(3,,,,,, %(29,,,,,, %(23,,,,,, %(24,,,,,, %(3,,,,,, %(5,,,,,, %(4,,, -au_bar,,, %(,,,,,, %(25,,,,,, %(27,,,,,, ]; %(26 % fr Pi( ( mc( w( ( x( AM( CC2 [,,,,,, %(3,,,,,, %(4,,, -,,, %(5 _barl_bar/i_bar-e_bardiv bar/i_bar,,,,,, %(7, -au_d_bary_bar,,,,, %(9 67

69 gamma2-e_bardiv bar/i_bar,,,,,, %( -alha_i, -alha_,,,,, %(2,,, -,,, %(7,,,,,, %(8,,, -,,, %(6 alha(i_bar^(-ea(-ea,,,, (-alha(p_bar^(-ea(-ea,, %(22,,,,,, %(9,,,,,, %(28, Y_bar,,,,, %(3 -alha(i_bar^eas_barea,,,, (-alha(p_bar^(-ea(ea,, %(29,,,,,, %(23 -(alha/i_bar-alhai_bar^(ea-/(-alhai_bar^(ea-,,,,,, %(24,,,,,, %(3,,,,,, %(5,,,,,, %(4,,,,,, %(,,,,,, %(25,,,,,, %(27 -,,,,,, ]; %(26 % fr rev_il( div_il ( Taxes(all( CA( KA( E'( CC3 [,,,,, %(3,,,,, %(4,,,,, %(5, E_bardiv bar/i_bar,,,, E_bardiv bar/i_bar %(7,,,,, %(9, E_bardiv bar/i_bar,,,, E_bardiv bar/i_bar %(,,,,, %(2,,,,, %(7,,,,, %(8,,,,, %(6,,,,, %(22,,,,, %(9,,,,, %(28,,,,, %(3,,,,, %(29,,,,, %(23,,,,, %(24 -rev bar, div bar,,,, %(3, div bar,,,, %(5 rev bar,,,,, %(4,, T_bar,,, %(,,, CA_bar, KA_bar, %(25,,, CA_bar,, %(27 68

70 ,,,,, ]; %(26 CC [CC, CC2, CC3]; % fr G( Z( ( ( Im( DD [,,,, %(3,,,, %(4,,,, %(5 -_barg_bar,,,, %(7,,,, %(9 -gamma2g_bar,,,, %(,,,, %(2,,,, %(7,,,, %(8,,,, %(6,,,, %(22,,,, %(9, -,,, %(28 -G_bar,, -P_bar bar, -P_bar bar, Im_bar %(3,,,, %(29,,,, %(23,,,, %(24,,,, %(3,,,, %(5,, -(-lambda_p_bar bar-au barlambda_p_bar bar, -(-lambda_p_bar bar-au barlambda_p_bar bar, %(4,, -au barlambda_p_bar bar, -au barlambda_p_bar bar, %(,,,, %(25,, -P_bar bar, -P_bar bar, Im_bar %(27,,,, ]; %(26 % fr k( l( m( ( S( x2( PL( F( FF [,,,,,,, %(6,,,,,,, %(8,,,,,,, %(2,,,,, -alhabeai_bar^(ea-x_2_bar,, ]; %(2 % fr k( l( m( ( S( x2( PL( F( GG [,,,,,,, %(6,,, -,,,, %(8,,,,,,, %(2 69

71 ,,,,, X_2_bar,, ]; %(2 % fr k(- l(- m(- (- S(- x2(- PL(- F(- HH [,,,,,,, %(6,,,,,,, %(8,,,,,,, %(2,,,,,,, ]; %(2 % fr lamda( c( h( au( au_l( u( i( JJ [-,,,,, -(-au_d_baru_bar/(u_bar-au_d_baru_bar-dela, %(6 -,,,,,, %(8 -alhabeai_bar^eax bar,,,,,, %(2 -alhabeai_bar^(ea-x_2_bar,,,,,, ]; %(2 % fr Pi( ( mc( w( ( x( AM( JJ2 [,,,,,, %(6,,,,,, %(8 -alhabeai_bar^eax barea,,,,-alhabeai_bar^eax bar(ea,-alhabeai_bar^eax bar, %(2 -alhabeai_bar^(ea-x_2_bar(ea-,,,, -alhabeai_bar^(ea-x_2_barea,, ]; %(2 % fr rev_il( div_il( Taxes( CA( KA( E'( JJ3 [,,,,, %(6,,,,, %(8,,,,, %(2,,,,, ]; %(2 JJ [JJ, JJ2, JJ3]; % fr lamda( C( H( au( au_l( u( I( KK [,,,,,, %(6,,,,,, %(8 alhabea(i_bar^eax bar,,,,,, %(2 alhabea(i_bar^(ea-x_2_bar,,,,,, ]; %(2 % fr Pi( ( mc( w( ( x( AM( KK2 [,,,,,, %(6,,,,,, %(8, -(P_bar^(--ea(Y_bar-P_bar barmc_bary_bar/(y_bar-p_bar bar, -(P_bar^(--ea(Y_bar-P_bar barmc_bar,, -(P_bar^(--ea(Y_bar-P_bar barmc_bar(-- eaalhabea(i_bar^eax bar(ea, X bar, %(2, -(P_bar^(-ea(Y_bar-P_bar bary_bar/(y_bar-p_bar bar,,, (P_bar^(-ea(Y_bar-P_bar bareaalhabea(i_bar^(ea-x_2_bar(ea,, ]; %(2 7

72 % fr rev_il( div_il( Taxes( CA( KA( E'( KK3 [,,,,, %(6,,,,, %(8,,,,, %(2,,,,, ]; %(2 KK[KK, KK2, KK3]; % fr G( Z( O( _O( Im( LL[,,,, %(6,,,, %(8,,,, %(2,,,, ]; %(2 % fr G( Z( O( _O( Im( MM[,,,, %(6,,,, %(8,, -(P_bar^(--ea(Y_bar-P_bar barmc_bar(-p_bar bar/(y_bar-p_bar bar, -(P_bar^(--ea(Y_bar-P_bar barmc_bar(-p_bar bar/(y_bar-p_bar bar, %(2,, -(P_bar^(-ea(Y_bar-P_bar bar(-p_bar bar/(y_bar-p_bar bar, -(P_bar^(-ea(Y_bar-P_bar bar(-p_bar bar/(y_bar-p_bar bar, ]; %(2 NN[rh_g,,,,, rh_z,,,,, rh_,,,,, rh_,,,,, rh_im]; Sigma [sigma_e_g,,,,, sigma_e_z,,,,, sigma_e_,,,,, sigma_e_,,,,, sigma_e_im]; % Seing he ins: [l_equ,m_saes] size(aa; [l_equ,n_endg ] size(cc; [l_equ,k_exg ] size(dd; PEIOD 4; % number f erids er ear, i.e. 2 fr mnhl, 4 fr quarerl GNP_INDEX 7; % Index f uu amng he variables seleced fr HP filer IMP_SELECT [8]; % a vecr cnaining he indices f he variables be led HOIZON 5; % number f quarers fr imulse resnses DO_SIMUL ; % Calculaes simulains 7

73 SIM_LENGTH 5; DO_MOMENTS ; % Calculaes mmens based n frequenc-dmain mehds HP_SELECT :(m_saesn_endgk_exg; % Selecing he variables fr he HP Filer calcs. DO_COLO_PINT ; % Saring he calculains: d_i; 72

74 Aendix 4a. MATLAB cde fr searching 3 feedback cefficiens shck3 shcknumber33shck8; alha_ ; alha_i ; alha_r ; alha_i_arr -3:.5:3; alha arr -3:.5:3; alha_r_arr -:.2:; len_i lengh(alha_i_arr; len_ lengh(alha arr; len_r lengh(alha_r_arr; resuls zers(len_i,len_,len_r; fr i_i : len_i; fr i_ : len_; fr i_r : len_r; alha_i alha_i_arr(i_i; alha_ alha arr(i_; alha_r alha_r_arr(i_r; Maser_hesis_majr_rgram resuls(i_i,i_,i_res_ma(shcknumber,5; end; end end; 73

75 Aendix 4b. MATLAB cde fr searching 2 feedback cefficiens shck3 shcknumber33shck8; alha_ ; alha_i ; alha_i_arr -3:.2:3; alha arr -3:.2:3; len_i lengh(alha_i_arr; len_ lengh(alha arr; resuls zers(len_,len_i; fr i_i : len_i; fr i_ : len_; alha_i alha_i_arr(i_i; alha_ alha arr(i_; Maser_hesis_majr_rgram resuls(i_,i_ies_ma(shcknumber,5; end; end surf(alha_i_arr,alha arr,resuls; xlabel('\alha_\i'; label('\alha_'; 74