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NOMINAL RIGIDITIES AND WAGE-PRICE DYNAMICS IN ESTIMATED DSGE MODEL: APPLICATION FOR THE CZECH ECONOMY

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WORKING AER 8/8 NOMINAL RIGIDITIES AND WAGE-RICE DYNAMICS IN ESTIMATED DSGE MODEL: ALICATION FOR THE CECH ECONOMY Miroslav Hloušek December, 8 Řada sudií Working apers Cenra výzkumu konkurenční scopnosi
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WORKING AER 8/8 NOMINAL RIGIDITIES AND WAGE-RICE DYNAMICS IN ESTIMATED DSGE MODEL: ALICATION FOR THE CECH ECONOMY Miroslav Hloušek December, 8 Řada sudií Working apers Cenra výzkumu konkurenční scopnosi české ekonomiky je vydávána s podporou projeku MŠMT výzkumná cenra MO54. Vedoucí pro. Ing. Anonín Slaný, CSc., Lipová 4a, 6 el.: Brno, NOMINAL RIGIDITIES AND WAGE-RICE DYNAMICS IN ESTIMATED DSGE MODEL: ALICATION FOR THE CECH ECONOMY Absrac: Te goal o is paper is o examine imporance o nominal rigidiies especially o wages and prices in e Czec economy. As a ool, DSGE model o open economy wi nominal rigidiies is used. Te model is esimaed on daa o e Czec economy using Bayesian ecniques. Te model is evaluaed in erms ow i is e daa and e dynamical properies o e model are sudied. Te empasis is pu on wage-price dynamics. Nex, e relaive imporance o nominal rigidiies is examined using sensiiviy analysis. Te conclusion is a wages are more rigid an prices and us wage rigidiy and price rigidiy are inercangeable. Tis oucome sould be aken ino consideraion or orming o moneary policy by e cenral bank and modelling o beaviour o e Czec economy. Absrak: Cílem éo práce je prozkouma význam nominálníc rigidi obzvlášě mezd a cen v české ekonomice. Jako násroj je použi DSGE model oevřené ekonomiky s nominálními rigidiami. Model je odadnu na daec české ekonomiky pomocí Bayesovskýc ecnik. oé je model zodnocen podle oo, jak vysiuje daa, a jsou sudovány jeo dynamické vlasnosi. Důraz je kladen na dynamiku mezd a cen. omocí analýzy cilivosi je zkoumán relaivní význam nominálníc rigidi. výsledků vyplývá, že mzdy jsou rigidnější než ceny a edy, že mzdová a cenová rigidia nejsou vzájemně zaměnielné. Tyo závěry by měl bý zoledněny při uskuečňování moneární poliiky cenrální bankou a pro modelování cování české ekonomiky. Recenzoval: Ing. er Harasimovič, M.A. . INTRODUCTION.. Moivaion Te primary objecive o moneary auoriy is o mainain price sabiliy. Te cenral banks usually use model ramework or analysis o e economy and governing is policy. Teir model approac is based on New Keynesian paradigm o wic main eaures are various ypes o nominal rigidiies. Tese rigidiies can sem rom wages or prices. Erceg e. al ( sow or e baseline New Keynesian model wi sicky prices a e opimal moneary policy compleely sabilizes e price level and e oupu gap in reacion o socks. Tus e cenral bank is able o replicae lexible price equilibrium allocaion wiou welare losses. Wen only wages are sicky, e naural allocaion is also aainable, bu requires ull sabilizaion o nominal wages. Wen bo prices and wages are sicky e naural equilibrium can no longer be aained. More imporanly, moneary policy a ocuses exclusively on sabilizing price inlaion, as mos cenral banks do, is subopimal. Te policy sould be aimed a appropriae weiged average o price and wage inlaion o miigae welare losses relaive o e opimal policy. Tese weigs are uncions o srucural model parameers a describe preerences and ecnologies. Some o ese parameers express degree o price or wage sickiness. Tus e imporance o nominal rigidiies, especially o wages and prices, as signiican impac or pursuance o moneary policy and is sabilizaion eecs... Background Nominal rigidiies are e cornersone o models wi label New Keynesian economics. Meodologically, ey build on e Real Business Cycle (RBC eory a as origins in e seminal papers o Kydland and resco (98 and resco (986. Bo eories are based on opimizing beaviour o agens (irms and ouseolds, bo include raional expecaions and clearing markes. As a ool, Dynamic Socasic General Equilibrium (DSGE models are exensively used or macroeconomic analysis. Tey are calibraed or esimaed and used or simulaion and evaluaion o model economies. However, New Keynesian approac inroduces several new aspecs suc as monopolisic compeiion and nominal rigidiies wic give rise o sor run nonneuraliy o moneary policy. Conrary o RBC eory were moneary acors do no play signiican role, cenral bank in New Keynesian world can inluence e real ineres rae (roug conrolling nominal ineres rae and subsequenly oer real variables. Bu in e long run, all prices and wages adjus and economy reurns o is naural equilibrium. New Keynesian models are no only in e cener o academic researc, bu ey are also widely used in cenral banks and oer insiuions or orming and evaluaing o economic policy. Today's economies are open economies and ey sould be modelled in a way. DSGE models wi marke imperecions and nominal rigidiies a are exended o open economy are reerred o as New Open Economy Macroeconomics (NOEM. Tis new class o models originaes rom Obseld and Rogo (995. Bu eir 'Excange Rae Dynamics Redux' model assumes sickiness in prices a lass only or one period. Recen DSGE models in NOEM radiion are more realisic. Tey assume a rigidiy lass or more an one period and allow sickiness in bo Nice inroducion and overview o New Keynesian models provides Gali (8. 4 prices and wages. Te quesion weer wages are more rigid an prices or oer way around remains a maer o empirical esing and can be counry speciic. Tere is number o empirical sudies on relaive imporance o price and wage sickiness, or various counries using various esimaion ecniques. Te resuls sow quie mixed picure. Bergin (3 uses maximum likeliood or esimaion o e model wi price and wage rigidiies a are inroduced in e orm o adjusmen cos. He ess resriced models wi lexible wages and/or prices relaively o e bencmark model wi bo ypes o rigidies or Ausralia, Canada and e UK. He concludes a nominal rigidiies are key elemens o e NOEM models in all ree counries. Regarding relaive imporance, price rigidiy is more imporan an wage rigidiy. Te version o model a assumes lexible prices is rejeced or all ree counries, wile e version wi lexible wages is rejeced only or Ausralia. Conrary o Bergin, oer auors inroduce nominal sickiness in e orm o Calvo conracs implying a bo rigidiies are presen rom e beginning. Ten e relevan quesion is wic o e conracs lass longer and accouns bes or model i. Ambler e al. (3 combine GMM and SMM or esimaion o DSGE model or Canada. Teir model assumes Calvo pricing mecanism or domesic prices, impor prices and wages and e esimaion resuls indicae a wage conracs las longer an price conracs. Smes and Wouers (3 esimae DSGE model or Euro area using Bayesian ecniques. Relaive imporance o nominal rigidiies says in avour o price sickiness. Adolson e al. (5 use ricer model wi more nominal (and real rigidiies and esimae i also on Euro daa using Bayesian meods. Teir resuls conirm indings o Smes and Wouers. Rabanal and Rubio-Ramirez (5 also repor a sicky wages models or e Euro area are rejeced by e daa. Crisiano e al. (5 esimae DSGE model or US economy by minimizing a measure o e disance beween e model and empirical impulse response uncion. Te leng o Calvo conracs were quie similar bu subsequen quaniaive analysis sows a sicky wages play a crucial role in e model's perormance wile sicky prices play only limied role or good i o e model. Del Negro and Scoreide (8 argue a some degree o price rigidiy is needed o describe US daa bu e wole issue is muc more complex and e resuls may be inluenced by e coice o priors or parameers and daa ses. Finally, Mai (5 ound ou or Norwegian economy a wage conracs las longer an price conracs bu adjusmen o socasic socks is aser or wages an or prices... Czec daa evidence Cyclical beaviour o e real wage is crucial in elping o discriminae beween eories o business cycle. I can also elp o deermine e source o nominal rigidiy. Cyclical beaviour o e real wage in e Czec economy is no ypical. Te business cycle and e correlaion uncion o labor produciviy and e real wage is depiced in Figure (le and side. 3 Bo ime series are obained by Crisiano and Fizgerald (3 band pass iler. 4 Te values o cross-correlaion coeicien indicae a e real wage is raer acyclical. Correlaion coeicien is no saisically signiican excep o e lead o ive periods. Tis negaive value o Generalized meod o momens (GMM and Simulaed meod o momens (SMM. 3 Labor produciviy is calculaed as raio o GD and number o workers, e real wage is nominal wage divided by CI. 4 Te business cycle lucuaions are deined as ose beween six and iry wo quarers, same as in Agresi and Mojon (5. 5 correlaion coeicien can be explained by looking on e cyclical beaviour over ime. Tere is eviden procyclical beaviour a e beginning o e sample period, bu rom e real wage beaves counercyclicaly. Rig and side o Figure sows e same caracerisics or sorened sample. Te correlaion coeicien conirm srong counercyclical beaviour o e real wage lagging e cycle o oupu (per worker by ree periods. Te real wage is usually ound o be procyclical or acyclical in oer counries. 5 Turning o e eories o business cycle lucuaions, sylized ac o counercyclical real wage is in avour o Keynesian model wi sicky wages raer an sicky prices, as i is illusraed in e.g. Romer (6. However, Romer uses only simple saic model. Te lagging beaviour o e real wage suggess a saggered wage conracs embedded ino dynamic model sould be appropriae eaure o model o e Czec economy. Nex, ere are many oer acors a play, e.g. various ypes o socks, ransmission mecanisms, openness o e economy and also muual relaionsip beween wages and prices (wage-price spiral. Tis is quie complex issue wic also says in avour o using model approac wi dynamics... Te goal o e paper Te researc quesion o is paper is weer wages are more sicky an prices or more broadly wic ype o nominal rigidiies is e mos imporan or modelling o e Czec economy. Te objecive is no only o esimae parameers a capures degree o nominal rigidiy bu also o invesigae wage and price dynamics. To provide answer o is quesion, e DSGE model o open economy wi nominal rigidiies on various markes is used. Te model is esimaed on Czec daa using Bayesian ecniques. Te beaviour o model is sudied along several dimensions including impulse responses, variance decomposiion or sensiiviy analysis, wi empasis pu on relaive imporance o wage and price sickiness and eir join dynamics. Te reminder o e paper is organized as ollows. Secion describes e DSGE model used or e analysis, is derivaion rom opimizaion problems o agens, and symmeric equilibrium o e model. Nex seps beore esimaion are loglinearizaion around e seady-sae and soluion o e sysem using sae-space orm. Secion 3 deals wi daa, eir ransormaion and esimaion meodology. Secion 4 presens and discusses resuls o e esimaion. Te model is evaluaed in erms ow i is e daa beore e dynamical properies o e model are sudied. Some oer model implicaions regarding excange rae pass-roug and wage-price dynamics are covered in is secion as well. Secion 5 ocuses on sensiiviy analysis. Te relaive imporance o nominal rigidiies is esed via marginal likeliood and vecor auocorrelaion uncions. Finally, e issue weer wage rigidiy and price rigidiy are inercangeable is examined. Secion 6 concludes wi prospecs or urer researc.. THE MODEL Te model is borrowed rom Mai (5, exended (especially by expor marke rigidiies and adjused or Czec economy condiion. Te inspiraion or exension 5 See e.g. Romer (6, Kydland and resco (99 or Sock and Wason (998 6 was ound in Adolson e al. (5. Similar models are used in papers o Ambler e al. (3 or Smes and Wouers (3. Te model diers rom Mai (5 in several aspecs. Te money are assumed endogenous and are no explicily modeled wiin e (money-in-e-uiliy ramework. Second, e prices o expor inermediae goods are assumed sicky and are modeled in Calvo syle. Resuling illips curve inroduces new cannel o slow price adjusmen. and can improve i o e model. Some addiional amendmens relaes o speciic eaures o e Czec economy or esimaion procedure. Te ineres rae rule is modiied; besides ineres rae smooing includes only deviaion o inlaion rom arge and oupu gap. Tis speciicaion is more in accordance wi regime o moneary policy o e Czec Naional Bank. Nex, elasiciy o subsiuion across diereniaed oreign (impored inermediae goods is ime-varying and is subjec o sock. Inroducion o markup sock o impor prices allows o use addiional ime series or esimaion and us o draw more inormaion rom daa. Te derivaion o e model is similar o Mai's work, bu or readers convenience and several modiicaions, I presen i in is secion... Houseolds Te model consis o coninuum o ouseolds indexed on inerval i (,. Houseolds is endowed wi a diereniaed labor skill. Tey are coosing a consumpion plan and also cooses wage rae plan or all =,,, 3, K o maximize an expeced discouned ininie sream o uiliy o e orm were ρ E β c, ( C ( i abc = ρ ν E is e condiional expecaions operaor, 6 (, ls, ( i ν β is e discoun acor, C (i is consumpion, (i denoes ours worked by e ouseold, c, is consumpion preerence sier (or aggregae preerence sock a is common o all ouseolds and, is labor supply sock. ρ is e consan relaive risk ls aversion coeicien or e inverse o e elasiciy o ineremporal subsiuion, ν is e inverse o e (Frisc elasiciy o labor supply wi respec o e real wage and ab [, is exernal abi persisence in e previous period's aggregae consumpion. 7 Te ouseold's budge consrain is given by C ( i B ( i SB ( i T ( i B ( i S B ( i W ( i ( i D ( i ( R R rp E x Ω E x denoes expecaion o variable x made under inormaion se 6 = ( Ω available in ime. 7 Tis orm o abi ormaion is called cacing up wi Joneses . I is moivaed by explaining empirical ac o ump-saped gradual response o consumpion and inlaion o socks. For more deails see e.g. Furer ( or Ljungqvis and Ulig (. 7 Te rig and side o equaion ( expresses sources, e le and side is usage o e sources. is price level in e economy and ence C (i denoes nominal consumpion o e ouseold. B (i and B ( i are domesic-currency and oreigncurrency bonds respecively purcased a ime, S is nominal excange rae quoed as domesic currency per uni o oreign currency. R and R denoe e gross nominal domesic and oreign ineres raes beween and, respecively. rp measures risk premium a relecs deparures rom uncovered ineres pariy condiion. T (i are axes paid o governmen (or ransers wen T is negaive. W (i is nominal wage rae and us W ( i ( i is wage income rom supplying (i unis o labor (ours worked o e various inermediae goods-producing irms. Houseolds own all irms us ey receive D (i unis o consumpion good as dividends rom equiies o inermediae goods-producing irms. Te ouseolds can carry weal beween periods using domesic and oreign bonds. Domesic bonds are denominaed in e domesic currency and oreign bonds are denominaed in e oreign currency. A e beginning o e period e bonds maure and provide B and S B ( i addiional unis o consumpion. Te ouseold decide o buy B new unis o domesic bonds a e cos / R and new unis o oreign bonds a e cos /( R. Te endogenous (gross risk rp B premium rp capures a inernaional inancial markes are incomplee. I is negaive uncion a depends on e raio o oreign bond o domesic oupu. 8 were oldings and S B rp = exp ψ log( rp, ( Y Y is e aggregae level o oupu, B is e aggregae oreign bonds, is a sock o e risk premium. Tis uncion as ollowing rp properies, rp and rp ( =. I B , domesic ouseolds are carged a premium o e oreign ineres rae, i B ey receive a lower ineres reurn on eir inernaional savings. I ere are no bonds, e risk premium is equal o one. Eac ouseold cooses consumpion (i B C, and porolio a consis o domesic and oreign bonds, B (i and ( i. Te irs order condiions or ese opimizaion problems are: ( i ρ c, [ C ( i abc ] = Λ (3 8 Tis raio ensures saionary dynamic pa or domesic consumpion and weal and us a unique seady sae. 8 Λ ( i = β R E [ Λ ( i ] (4 were R SE[ Λ ( i] = R rp E[ Λ ( i S ] (5 Λ is Lagrange muliplier conneced wi budge consrain in ime. Equaion (4 is sandard Euler equaion. I saes a ouseolds wan o equalize expeced marginal uiliies across ime periods aking ino accoun relaionsip beween (subjecive ime preerence acor and marke rae o reurn on savings. Equaion (5 is risk-adjused uncovered ineres pariy condiion. Is meaning is e same, e ouseold only adds ino consideraion possibiliy o invesing ino oreign asses. Te ouseold is endowed wi diereniaed labor skill a oers in monopolisically compeiive labor markes. Labor services o ouseolds are imperec subsiues and us e ouseolds can coose eir nominal wage subjec o demand imposed by e irms. Te ouseolds se eir nominal wage rae and sand ready o supply e quaniy o labor demanded or a wage by irms. However, no all ouseolds are able o selec eir wage rae eac period. Resul o is wage seing implies exisence o nominal rigidiies a are modeled in e orm o Calvo (983 conracs. In eac period, ere is a consan probabiliy a a worker is no able o re-adjus er wage. I e workers do no ave opporuniy o rese eir wages, ese wages are adjused by wage inlaion rom previous period as a resul o indexaion were W ( i = w, W W w, = (6 W Similarly, ere is a probabiliy δ a e ouseold will be able o cange er w wage. Ten e worker akes ino accoun a se may no re-opimize er wage in e nex periods. Tus, se indexes er wage o (price inlaion and ecnology grow so a er wage periods aer e wage is se as new W ( i = k zy, kw ( i k = were W new (i is e wage se in ime a remains ixed unil e nex opporuniy or wage seing, and were = (7 δ w zy, = y (8 y, 9 were y is e level o ecnology in e economy in ime. As e markup or workers a revise eir wages sould be posiive in e seady sae, we mus impose resricion a e ime-varying elasiciy o subsiuion across dieren ypes o labor, is greaer an uniy. Te worker wo ses new wage solves opimizaion problem max W new ( i E w = ls, ( βδ w ( i ν =,, K, subjec o budge consrain ( or and labor demand rom aggregaor 9 ( i = W ( i ( i, j dj = W w, ν ( j Tis opimizaion resuls in e ollowing irs order condiion E ν w, c, s, ( βδ w Λ, ( new k zy k w, W ( i k = =. (9 = Te negaive erm in equaion (9 is e marginal disuiliy o labor eor (addiional ours worked and e posiive erm is e marginal revenue rom slig increase o e wage rae. In e opimum, e expeced sums o ose expressions sould be equal. A e resuling wage rae, e workers are ready o supply any amoun o labor demanded rom irms. In equilibrium, ere is a racion δ w o workers a canges eir wages a ime. Te expeced ime beween wage adjusmens, or equivalenly, e number o periods or a e wage reamains ixed is en e wages are no canged or one year. δ w. For example, i δ =.75 Tis srucure o labor marke implies a ouseolds are eerogeneous and eir labor income and us consumpion and asses oldings may dier. To ensure idenical consumpion in equilibrium, we assume a ouseolds ave access o sae coningen securiy markes wic provides em ull insurance agains idiosyncraic socks in labor income. Consumpion will be same or all ouseolds in equilibrium and only e wage rae and labor supply will dier... roducion side o e economy Te producion srucure o e economy is depiced in Figure. Monopolisically compeiive markes are depiced by dased lines. Tere are ree ypes o irms in e model economy: coninuum o inermediae goods producing irms, coninuum o exporing irms a give brand names o inermediae goods and various aggregaors. Domesic inermediae irms uses labor and capial as acors o w 9 Labor demand uncion is soluion o aggregaor's labor packing problem and is deined laer. Te ime beween wage adjusmens ollows a geomeric disribuion. producion. ar o domesic inermediae goods is expored and e oer par ogeer wi impored inermediae goods is used or producion o inal goods. Final goods is eier consumed by ouseolds and governmen or used as capial inpu in producion o inermediae goods. Opimizaion problem o ese irms is described in ollowing subsecions.... Domesic inermediae goods Tere is coninuum o domesic inermediae goods irms indexed on inerval j (,. Te irm producing good Y H, ( j as ollowing producion uncion: were ψ ψ ψ H ( j = y ( j K y is a produciviy sock, K Y C G Y ( = is par o inal goods a is no consumed (capial and ψ is labor inensiy o producion uncion. Domesic irm cooses level o labor and capial (or given prices o minimize is cos o producion min W ( j K ( j, K subjec o producion uncion (. Te irs order con
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