Asian Economic and Financial Review ROBUST MONETARY POLICY IN AN UNCERTAIN ECONOMIC ENVIRONMENT: EVIDENCE FROM TUNISIAN ECONOMY.

Transcription

1 Asian Economic and Financial Review journal homepage: hp:// ROBUST MONETARY POLICY IN AN UNCERTAIN ECONOMIC ENVIRONMENT: EVIDENCE FROM TUNISIAN ECONOMY Ramzi Drissi Universiy of Carhage & Life Research Uni, Tunisia ABSTRACT This paper ries o sudy he robus moneary policy in an uncerain economic environmen. More precisely, our idea is o know how o conduc moneary policy in he case ha he cenral bank does no correcly perceive he rue model. Our approach is o esimae a dynamic macroeconomic model wih hree represenaions of dynamics inflaion, each wih microeconomic foundaions. The hree versions of model are esimaed on Tunisian economy daa wih he Bayesian echniques. Our resuls show ha he uncerainies of he srucural parameers affec he dynamic soluions for he economy, bu also on he objecive funcions of he cenral bank. His cauion increased wih he weighs carried by he ineres rae in he loss funcion. Thus, our resuls show he effeciveness of he simple robus rule of Levin and Williams. Keywords: Uncerainy, Nominal rigidiies, Robus conrol, Taylor Rules, opimal moneary policy, Bayesian conrol. JEL Classificaions: E31, E32, E52, E58, E INTRODUCTION In recen years, progress in macroeconomic modeling was done o give new perspecives on he impac of uncerainy on he evoluion of moneary policy. In order o make decisions, cenral banks use models for forecasing he implicaions of heir acions. Alhough here are many available models, economiss end o sudy principally issues abou moneary policy in a Neo- Keynesian framework. Curren research on moneary policy business cycles inroduces sicky prices and inefficien marke equilibrium as a source of moneary non-neuraliy. The main characerisics of Neo-Keynesian models, known as he Neo-Keynesian Phillips (NKP) curve, is he inroducion of opimizing behaviour, raional expecaions and as he resuling inflaion specificaion, he dependence of curren inflaion and a measure of oupu gap (Clarida e al., 1999). E y (1) 1 The Equaion (1) depends only on he fuure behaviour of he driving variable. However, he implicaions of he NKP curve are in conradicion wih empirical sudies, regarding he impac of 969

2 disurbances (Mankiw and Reis, 2002). The inconsisencies beween purely forward-looking models and he daa, led many researchers (Clarida e al., 1999) o use "Hybrid' NKP curve which includes boh backward- and forward-looking elemens. So he Equaion (1) can be rewrien as follows: (1 ) E y (2) 1 1 The moivaion for including ineria is largely empirical and jusified heoreically wih an assumpion ha a fixed proporion of firms has backward-looking price seing behaviour. Empirically, he adequacy of his model, which ness he pure forward-looking sicky price model and inheris he good properies of backward-looking models, o daa is very conroversial. Indeed, empirical work abou weighs on Backward-Looking (BL) behaviour, don' lead o a se of consensual values. In general, sudies based on maximum likelihood esimaion sugges ha he esimaed weigh on backward-looking behaviour is he highes, while works using full informaion maximum likelihood echniques show ha inflaion dynamics depend only on Forward-Looking (FL) behaviour. To be more precise, on he one hand, Clarida e al. (1999) argue ha purely forward-looking curve provides a good approximaion of he dynamics of inflaion, in paricular he assumpion, and find ha he degree of backward-looking behaviour is highly significan in he "hybrid' curve. On he oher hand, Fuhrer (1997), Robers (2005), find ha BL behaviour seems more imporan han FL behaviour, when using he full informaion mehod insead, respecively. Esimaes are no clear and flucuae significanly. In his siuaion, moneary auhoriies face inerial degree uncerainy. Moreover, we know ha his parameer affecs dramaically he effeciveness of moneary policy. We know also ha properies of opimal moneary policy depend on degree of inflaion persisence (Lansing and Trehan, 2003; McCallum and Nelson, 2004). Various models have been proposed in he lieraure bu none has ye provided an unconroversial descripion of he ransmission process. When moneary auhoriies examine he implicaions of uncerainy wih one model, hey underesimae largely he acual amoun of uncerainy, since each model in iself consiues a simplificaion which absracs from relevan aspecs of realiy. As a resul, hey can' afford o rely on a single reference model of he economy bu need o have a number of alernaive modeling ools available. In pracice, cenral banks avail hemselves of alernaive quaniaive models of he economy as opposed o relying on a single all-encompassing one and make 'average' choices (Blinder, 2000). So, i would seem wise o develop robus rules in order o face uncerainy adequaely. A number of sudies have herefore sared expressing model uncerainy in he form of a variey of alernaives models (Levin and Williams, 2003). As, uncerainy is dominan, i is imporan o undersand how alernaive policies can be seleced when he cenral bank canno accuraely observe he macroeconomic variables. Given he curren economic siuaion in Tunisia, he cenral banker is sill faced wih he problem in selecing he bes model or a class of models. Therefore, he cenral bank mus have a heir disposal he ools for modeling he mos accurae. For his reason, in his paper we ry o deermine he robus moneary policy in an uncerain economic environmen. Our approach is o esimae a dynamic 970

3 macroeconomic model wih hree represenaions of he dynamics of inflaion, each wih microeconomic foundaions for he daa of he Tunisia economy wih Bayesian echniques. The res of he paper is organized as follows: he second secion describes hree ypes of uncerainy: shocks, parameers and models suggesed in he lieraure. In secion hree, we sudy in paricular he las ype of uncerainy, using differen nominal rigidiies modeling sraegies. Then (secion four), afer having he empirical seup of he model, we propose o find a robus simple rule across he range of models seleced. A final secion concludes. 2. THE FORMS OF UNCERTAINTY In he lieraure (Issing, 2002), we can disinguish several ypes of uncerainy 1. In our paper we define hree ypes of uncerainy bu we are ineresed in wo ypes. The firs one consiss in sudying shocks robusness. The second one akes ino accoun uncerainy parameers wihin a model. The las one refers o model uncerainy. In nex secion, we describe succincly hese hree approaches Robusness o Alernaive Types of Disurbances Iniially, he lieraure has quesioned he way he moneary surprises could be incorporaed in expecaions o generae shor-erm increase in producion. A growing number of cenral banks have abandoned he sysem of inermediae arge variables such as exchange rae or money growh and lead o direc policies around he sabiliy of inflaion in a discreionary manner is ie, subjec o he influences of he economy. However, Kydland and Presco (1977) showed ha, besides being associaed wih an inflaion bias, discreionary policy suffers from a bias sabilizaion and is much lower han wih he poliical commimen in erms of Welfare. Woodford (2003) aemps o adop an inermediae posiion based on he principles of commimen while presening he advanages of discreionary framework. He advocaes he use of opimal argeing rules while offering he possibiliy o change in ways ha provide no incenive o deviae from he objecives declared by he cenral banker. In his conex, he ransparency of he policy pursued by he auhoriies deermines is credibiliy. The idea of a Timeless perspecive means i suffices ha he equilibrium be opimal subjec o cerain consrains on he economy's iniial evoluion o preven he policymaker from exploiing he exising expecaions a he ime ha he policy commimen is chosen. In choosing is commimen for he fuure, i akes ino accoun he consequences of is commimens for he privae-secor expecaions a earlier daes. The raional expecaion equilibrium expeced o prevail from ime = 0, given a commimen o he policy rule a ha dae, needn' minimize expeced losses from ha dae condiional upon he economy's sae a ha ime. Tha behavior allows he policymaker's behavior o be consisen over ime he advanages ha allows for he credibiliy o 1 Always he researchers refer o Alan Greenspan s quoe from he 2003 Jackon Hole meeing, which has gained widespread aenion: Uncerainy is no jus an imporan feaure of he moneary policy landscape; i is he defining characerisic of ha landscape. 971

4 he privae secor of he cenral bank's commimens and for he likelihood ha he privae secor can learn o predic fuure policy. The choice of a rule of conduc from such a perspecive eliminaes he problem of he ime inconsisency of opimal policy in he sense ha he same reasoning ha is used o suppor he choice of he opimal rule a one dae can be used o suppor for he same rule a any laer dae. Formally, (Giannoni and Woodford, 2003a, 2003b) define opimaliy of a rule from a imeless perspecive as follows: 1) The non-predeermined endogenous variables z can be expressed as a ime-invarian funcion of a vecor of predeermined variables z and a vecor of exogenous variables s represened by Equaion (3): Z f0 fzz fss, 0 2) The equilibrium evoluion of he endogenous variables y, for all daes 0, minimizes he discouned quadraic loss funcion subjec o he consrains implied by he economy's iniial sae z 0, he srucural equaions and a se of addiional consrains of he form: (3) E e E[ f f Z f S ] on he iniial behavior of he predeermined endogenous Z 0 0 z s 0 0 variables. The equilibrium dynamics resuling from commimen o a policy ha is opimal from a imeless perspecive involve he same responses o unanicipaed shocks in all periods 0. This commimen o an opimal rule dominaes boh he average inflaion bias and he sub-opimal dynamic responses o shocks, someimes wih discreionary policy. Woodford (2010) describe hese rules as robusly opimal. I s are opimal in ha he rule suppors he equilibrium consisen wih an opimal commimen policy when evaluaed from he imeless perspecive. And i s are robus in ha he coefficiens in he policy rule are independen of he parameers ha characerize he behavior of he exogenous, sochasic disurbances. Thus, he policymaker implemening such a rule does no need o know wheher disurbances are highly persisen or ransiory or wheher demand shocks are more volaile han cos shocks. This form of robusness is no exhausive. There is also considerable uncerainy abou he correc specificaion of he non-sochasic erms in he model equaions Uncerainy wihin a Model Robus Policy wih Parameers Uncerainy Sodersrom (2002) assume ha he policymaker wans o deermine he robus opimal rule faced wih parameers uncerainy ino he following model: y y ( i ) (4) y y (5)

5 Where y and are respecively he oupu gap and he inflaion (in log), i represens he y nominal ineres rae, 1 and 1 are iid (supply and demand) shocks i.i.d. wih mean zero. Equaion (4) represens he IS curve. Oupu gap depends posiively on is own pas value; negaively on he Δi. Equaion (5) represens he Phillips curve. The change in inflaion depends posiively on he lag of y, and a shock ( 1 ). A each ime, he main parameers are assumed independen and o be random variables wih means: E ( 1), E ( 1), E ( ), and variances 1 2, 2, 2, and 2. When he Cenral Bank ses is ineres rae a ime, i is assumed o know all realizaions of he parameers up o and including period bu i does no know heir fuure realizaions and hus canno be cerain abou he effecs of policy on he economy. The Cenral Bank's opimizaion problem consiss in minimizing a quadraic loss funcion subjec o he model equaions. To illusrae he effecs of including muliplicaive uncerainy ino he model, he rewries he problem as a conrol problem wih value funcion, using a sae-space formulaion. The resoluion becomes more complicaed han he cerain case. The opimal rule is in paricular a funcion of a marix given by ieraing on he Riccai equaion. When he parameers are non-sochasic, he variance-covariance marix of he sae vecor coincides wih he variance marix of he disurbance vecor. Thus i is independen of he insrumen rule. The opimal policy rule is independen of he degree of uncerainy, ha is o say, is cerainly equivalen. In conras, when he parameers are uncerain in a muliplicaive form, he variancecovariance marix depends on he sae of he economy, he insrumen and he variances of he parameers as well as hose of he addiive disurbances. Thus, cerainy equivalence no longer holds. Due o uncerainy's muliplicaive feaure, Sodersrom (2002) resoluion becomes ineresing Uncerainy a la Hansen and Sargen Hansen and Sargen (2003, 2007) inroduce anoher ype of uncerainy beween parameers uncerainy and model uncerainy. They sudy he robus opimal policy solving a robus Sackelberg (2011) 2 problem wihin he following forward looking model is given by Equaion (6): y 1 Ay BU (6) Where y a vecor of sae variables and jump variables is, U is a decision rule. The decision rule is chosen, as he previous secion, by minimizing a quadraic loss funcion y Qy U RU, subjec o he model represened by he Equaion (6). We should ake ino consideraion ha Hansen and Sargen (2003, 2007) assume ha all agens share he same approximaing model and 2 For more deails on he Sackelberg problem see for insance Marke Srucure and Equilibrium. 973

6 heir doubs are common knowledge. The saring poin consiss in considering he model represened by Equaion (6) as an approximaion of he following rue model is given by Equaion (7): y Ay BU CW (7) 1 1 Where W 1 represen a vecor of unknown specificaion errors finie, around he approximaing model used by he leader wherew 1 0. Is can feed back, possibly nonlinear on he hisory y (is are hisory dependen meaning ha W 1 depend on lags of z, he sae variables. Hansen and Sargen (2003, 2007) impose a consrain upon he variances of he misspecificaions wha simplifies he problem. They invesigae he deerminaion of he decision rules conducing worscases analyses. All he agen share he same approximaing model and heir errors are common knowledge. The policymaker considers he model as he reference model, which represens he mos likely descripion of he economic srucure. However, he knows his model could be subjec o a wide range of disorions. Under robus conrol, he resuling policy rule performs sufficienly well even if he underlying economic srucure does no coincide wih he policymaker's reference model. Hence, he equilibrium is he oucome of a wo-person game. The cenral Bank wans o minimize he maximum welfare loss due o model misspecificaions by specifying an approximae policy. The evil agen shares he same reference model ha he cenral bank and he same objecive funcion bu he wans o maximize raher han minimize he loss conrary o he policymaker. They use a hree sep algorihm for solving a muliplier version of he robus Sackelberg (2011) problem. The firs sep is similar o he previous secion (2.2.1). I uses Bellman equaion and yields o a Riccai equaion which deermines implicily he opimal rule. Seps 2 and 3 use he lagrangian problem and he firs order condiions in order o obain a relaion beween he lagrangian mulipliers and y. Then we can obain a robus opimal Uncerainy beween Models Levin and Williams (2003) show opimal rules for a given model have a represenaion ha is invarian o know changes in he shock process. Thus, hese rules are no robus o varying model. They wonder wheher any simple rule can provide robus performance across a range of alernaives represenaions of he economy. They show ha a robus oucome is possible only in cases where he objecive funcion places subsanial weigh on sabilizing boh oupu and inflaion. Each of hree models hey use, provide a plausible represenaion of he dynamic behaviour of he US economy and represen differen perspecives abou expecaions formaion and oher srucural characerisics of he economy, ha is o say, a New Keynesian Benchmark (NKB) model (forward looking model), he Rudebusch and Svensson (1999), (RS) model (VAR model) and he Fuhrer (2000) Habi Persisence (FHP) model in which he inflaion rae responds o a combinaion of forward looking and backward looking erms. 974

7 They assume ha he policymaker's loss funcion L has he form given by Equaion (8): L Var( ) Var ( y ) Var ( i ). (8) Where,, and denoe weighs aached o he sabilizaion of inflaion, oupu gap and ineres rae, respecively. Idenifying he source of he lack of robusness of each opimal rule is difficul because of heir complicaed formulaion in erms of leads and /or lags of he arge variables. Thus, Levin and Williams (2003) use he following class of simple hree parameers (,, ) rules are given by Equaion (9): i i 1 (1 ) y (9) When he model is no he one used o define he conrol parameers he auhors compare he value obained wih he opimal value. In fac, he Equaion (10) below inerpreed heir resuls using a faul olerance approach of each model wih respec o deviaions from opimal policy. For example, if he rue model is (RS) and he policymaker choose NKB or FHP so he consequences in erms of loss could generae indeerminaion or bad resuls. % L 100*( L L ) / L rule generaed opimal rule rule generaed (10) These rules can generae dynamic insabiliy. This mehod leads o robus resuls for a large range of macro-models. In general, he resuls naurally depend on he preferences of he policy. However, hey also find large differences depending on he chosen reference model. As Levin and Williams (2003), we sudy he robusness of he models by he Bayesian approach o obain a robus rule. This approach represened by Equaion (11) is o minimize he objecive funcion using he conrol variables (,, ) under consrains of he hree (RS, NKB, FHP) models. B L NKBL NKB FHPL FHP RSL (11) RS Where 1. For simpliciy we assume ha he coefficiens in Equaion (11) are equal. 3. PRICE RIGIDITY FORMATION AND INFLATION DYNAMICS In his robusness analysis, we consider hree non-nesed alernaives represenaions of he inflaion dynamics, each one having formal microeconomic foundaions. These 3 models have he same IS curve in common, in order o be focused on uncerainy abou he ype of nominal rigidiy, ie: Calvo Rigidiy: where in each period, each firm is able o revise is price wih probabiliy 1. Conversely, i mus keep is price unchanged from one period o he nex wih probabiliy. 975

8 Taylor Rigidiy: The Taylor model is based on he idea ha here are rigidiies conneced o he exisence of conracs in he economy. Taylor (1980) uses 2-period conracs. The idea is ha he firm can only choose is price every second period. Conrary o Calvo rigidiy, his modelizaion assumes ha firms know hey canno change heir price in he following period. However, hey can do i wih he probabiliy 1 wihin 2 periods. A ime, here are 2 ypes of conracs in he economy: hose which are defined a ime and hose are defined a ime -1. Sicky Informaion: Conrary o he wo previous models, firms adjuss heir prices a each ime bearing in mind ha he informaion se does no develop a he same ime. The arrival of informaion updae opporuniy is similar o Calvo model. Every period only a random fracion of firms receive new informaion abou he sae of he economy. Of course, he Phillips curves we obain are fundamenally differen Common Framework Consider an economy consiss of a coninuum of household (mass 1) and a coninuum of firms (mass 1). Indeed, a common framework is a mean o obain comparable New Keynesian Phillips curves and o explain he main differen responses observed across each specificaion essenially by he naure of nominal rigidiies Firms A each ime, each firm ( j ) produces one differeniaed good (j) using a linear echnology: y ( j) a l ( j), where y he oupu gap and a is he labor produciviy and l ( j ) is he labor demand wihin a monopolisic compeiion framework on he goods marke a la Dixi and Sigliz (1977). The Equaion (12) represens he price index and he inflaion are wrien respecively: 1 (12) 1 P p ( j) dj and ln( P / P 1) Households 1/1 0 The workers are assumed mobiles across secors and he labor supply l is assumed independen of he household. In equilibrium: 1 l l( j) dj) Each household maximizes he uiliy 3 funcion a ime : Wih he consumpion index: E 0 0 u( C, l) (13) (14) 3 We do no include real money balances (M/P) ino our uiliy funcion. Because DSGE models assume nominal shor-erm ineres rae as he moneary policy insrumen, so ha money supply is considered as endogenous; see for insance, Woodford, M., Opimal moneary policy ineria. Review of Economic Sudies, 70(4):

9 1 1 1 C c ( ) 0 j dj (15) Where c( j ) is he j firm's consumpion of good z, represens he elasiciy of subsiuion beween varieies of he consumpion good. Consider he following insananeous CES Uiliy funcion: C 1 11/ 1 11/ 1 l u( C, l ) 1 Where is he ineremporal labor supply elasiciy and, is he ineremporal consumpion elasiciy. Moreover, a each period, he represenaive household faces a budge consrain represened by Equaion (17) as follows: PC B R B wl (17) Where w is he real wage, 1 1 riskless asses holding by he household a ime. is he firms profi in ime and (16) B represens he amoun of Keynesian IS Curve The maximizaion of he uiliy 4 funcion subjec o consrain budge gives he firs order condiion of he problem. The log-linearizaion of he Euler condiion leads o he opimizing IS curve: (18) Considering ( ) xˆ ˆ ˆ n y y, and ˆ yˆ E ( yˆ ) E ( Rˆ ˆ ) 1 1 are flexible, we can rewrie he IS curve as follows: 3.2. Framework Price Seing Calvo-Pricing Model i he deviaion of he ineres rae from is level when he prices xˆ E ( xˆ ) ( iˆ E ( ˆ )) 1 1 As Tillmann (2009), Chrisiano e al. (2005), Ravenna and Walsh (2006), we adop a sandard forward-looking moneary model and draw on recen work of and ohers who inroduce he cos of working capial ino a general equilibrium Model. In fac, in each period, a fracion 1 of firms, drawn a random, are allowed o rese heir price opimally. The ohers are consrains o keep heir prevailing price and do no re-opimize. As a resul, he likelihood of any one firm o be able o change is price is independen from he pas and all firms who change heir price choose he same price. Soi * p le prix fixé par les firmes qui peuven ajuser leur prix. (19) 4 Call u he proporional deviaion of u around is seady sae value u : ( u log( u / u) ). 977

10 The dynamics of he price index is given by Equaion (20): 1 1 * 1 P P 1 (1 )( p ) (20) and he log-linearizaion of price index leads o Equaion (21): Pˆ Pˆ (1 ) pˆ * 1 An each ime, he firm mus se is price aking accoun of he risk ha i will no be allowed o (21) change is price in he fuure. Le * p be he opimal nominal price which maximize he escomped sum of expeced profis, muliplied by he probabiliy o no modify he price. The log-linearizaion gives: (22) Where w * s ˆ (1 ) ( ) ( ˆ ˆ p E s Ps ) s s s is he real marginal cos a ime s. I is a funcion of curren and fuure ap s s expeced nominal marginal coss. Combining Equaion (22) wih he one including P ˆ, Pˆ 1 and pˆ *, we obain Equaion (23): (1 )(1 ) (23) ˆ MC E ( ˆ ) 1 Opimal rese prices are given by marginal coss, as firms maximize profis in an imperfecly compeiive environmen. Moreover, he deerminaion of he labor supply and he price chosen by firms gives he Equaion (24): 1 (24) n ( )( yˆ yˆ ) ˆ Thus, noing xˆ yˆ yˆ n and he Equaions (23) and (24), he Phillips curve can be wrien by Equaion (25): ˆ ˆ ( ˆ x E 1) (25) Wih, (1 )(1 ) 1 ( ). We assume a each period, an exogenous shock ò ò x ò affecs he economy srucure. Finally, he IS and Phillips curve 5 can be wrien by Equaion (26) as follows: (26) ˆ ˆ ( ˆ x E 1) ò xˆ E ( xˆ ) ( iˆ E ( ˆ )) ò x See Equaions (16) and (22). 978

11 Taylor-Pricing Model Asian Economic and Financial Review, 2014, 4(7): Following Taylor (1980) firms are followed o rese heir conrac price every 2 periods. Firms are oherwise symmeric in every oher respec. A any period, 2 overlapping conracs are in force. A ime, consider p ( 1), he price defined by he firm which has updaed a period -1. The program of he firm which is allowed o rese is price conracs, a ime, is: p ( ) p ( ) max ( ) 1 i p () E C i i P i i0 P i P i And he firs order condiion gives he Equaion (29): E C P C P p () 1 E C P C 1P (28) (29) Moreover, he price index P is a funcion of he prices fixed a ime -1 and hose a ime. In a symmeric 2-period seup, he log of he aggregae price level is given by Equaion (30): ˆ pˆ ˆ 1( 1) p( ) (30) P 2 1 Combining Equaions (25) and (26), one obains around he seady sae:. Thus, C P C P E ( ) ( ) p () C P C P P C P C 1 P 1 E ( ) ( ) C P C P x Using a fis-order Taylor approximaion of he kind 1 xˆ x Equaion (32): However, as ˆ ˆ ˆ ( ˆ 1) ( ˆ 1) ˆ 1 1 x P E x E P P 21 xˆ ˆ ˆ ˆ 1 P 1 E 1( x ) E 1( P ) 1 ˆ x wih and ˆ Phillips Curve is given by Equaion (33): (31), o he Equaion (30), we find he x he oupu-gap, he inflaion ˆ 1 1 ( x x ( E ( x ) E ( x )) ( E ( 1) E 1( )) (32) Pˆ Pˆ. The Finally, adding demand and supply shocks, we obain he following sysem given by Equaion (34): (33) ˆ x xˆ ˆ ˆ E ( x 1) ( i E ( 1)) ò 1 ˆ ( xˆ xˆ ( E ( xˆ ) E ( xˆ ))) ( E ( ˆ ) E ( ˆ )) ò (34) 979

12 Sicky Informaion Framework Price Seing Mankiw and Reis (2002) assume ha informaion diffuses slowly hroughou price seers. Tha means ha when a firm ses is price, i has no full informaion abou he sae of he economy. Neverheless prices are flexible in he sense ha firms can change heir price every period, bu hey do no have necessarily he informaion abou he acual sae of he economy. The fracion of firms ha did no receive new informaion se prices according o heir older informaion se. Therefore prices fixed based on differen informaion ses coexis in he economy. Formally, a ime, a firm f ha up daed is informaion, j period ago, se is price x ( f ) such as: x f p f * ( ) E j ( ( )) (35) Where p * ( f ) is he f could choose if i receives informaion a ime. In ha case, he firm would choose p * ( f ) which maximizes is profi given by Equaion (36): * w p( f ) p ( f ) arg max p ( f ) C p ( f ) a P (36) Where P is he overall price level a ime. Finally, he Equaion (37) yields he expression of opimal price: * * p ( f ) P p 1 The log-linearizaion of he overall price level is given by Equaion (38): j * (1 ) ( ˆ E j p ) j0 Subracing price index given by Equaion (38) a ime 1 Pˆ given buy Equaion (37), he inflaion equaion can be wrien as follows: (1 ) j ˆ E ( ) 1 j 1 j0 Pˆ Pˆ Pˆ Pˆ (37) (38) and using he firs order condiion Rearranging he erms in he Equaion (39) above, adding in paricular he equaion relaive o he overall price level and supply and demand shocks, we obain he Equaion (40): (39) ˆ x x xˆ ( ˆ ˆ E x 1 1( i 1) ò ) ò (1 ) ˆ ˆ (1 ) ˆ ( ˆ ˆ ) j x Ej x x 1 ò j1 (40) 980

13 4. EMPIRICAL SETUP This secion briefly oulines he empirical seup by illusraing daa, choice of priors and esimaion mehodology: We adoped he empirical approach oulined in Haider and Drissi (2009) and Smes and Wouers (2005) and we esimae he DSGE 6 models wih employing Bayesian inference mehods Geweke (1999), DeJong e al. (2000). This involves obaining he poserior disribuion of he parameers of he model based on is log-linear sae-space represenaion and assessing is empirical performance in erms of is marginal likelihood. In he following we briefly skech he adoped approach and describe he daa and he prior disribuions used in is implemenaion Daa Descripion We consider hree key macro-economic quarerly ime series from 1990q1 o 2011q4: oupu gap, inflaion rae and ineres rae. Tunisian daa are aken from he Naional Insiue of Saisics and Cenral Bank of Tunisia. All he daa are derended before he esimaion. Since he model has implicaions for he log deviaions from he seady-sae of all hese variables, so we pre-process he daa before he esimaion sage. The differen versions of he model described are esimaed in log-linearized forms using Bayesian echniques. The simulaions were performed under Dynare Choice of Priors The reasons of he priors choice refer o Haider and Drissi (2009); Tillmann (2009); Rabanal and Rubio-Ramirez (2005) and Smes and Wouers (2005) who esimae a Calvo model wih sicky prices and wages using European ime daa; Ben Aissa and N. (2009) using Tunisia daa. All he variances of he shocks are assumed o be disribued as an invered Gamma disribuion which guaranees a posiive variance wih a raher large domain. Cerain parameers need he specificaion of a policy rule. Smes and Wouers (2005) have shown ha a Taylor (1993) rule would approximae he behavior of 'synheic' cenral bank conduc of policy quie well. We use he following Taylor rule given by he Equaion (38): i i 1 (1 )( y y ) (41) i Where y and are respecively he oupu gap and he inflaion (in log), i represens he nominal ineres rae. We se he mean of o 1.5 and ha of y o 0.5, which is Taylor's original guess. The ineres rae smoohing coefficien has a bea prior disribuion. The discoun facor is calibraed o be 0.99 (which is quie convenional in he lieraure). We imposed dogmaic priors over he parameers, and because of an idenificaion problem. Since we are ineresing in he sandard deviaion of wo main parameers considered as uncerain, we se o The inverse elasiciy of labor supply has a normal prior disribuion wih a mean of 2 and a 6 Dynamic Sochasic General Equilibrium (DSGE). 7 hp:// 981

14 sandard error of And he ineremporal elasiciy of subsiuion disribuion wih a mean of 1 and a sandard deviaion of has a normal prior Variable Table-1. Priors and poseriors for model parameers esimaed using Tunisian daa. Disribuion of prior Medium of prior Mode of poserior Inerval Confidence of mode Variance of prior 1 normal normal normal Sandard derviaion of schocks: Inverse gamma x Inverse gamma The Table 1 shows he resuls of he Bayesian esimaion of he Calvo model using Tunisia daa ( ). The oupu gap, he inflaion and he ineres rae have been cenered in order o mach wih variables used in he model. The resuls sugges ha is equal o wih an esimaor sandard deviaion of is esimaed o wih an error of These values give us an idea of parameers uncerainy even if he esimaion is no he only source of uncerainy (misspecificaion). These figures have been used in all numerical resoluions which followed (even if were no Calvo model) Robus Opimal Policy I is possible o obain a robus opimal policy a la Levin and Williams (2003) bu his one depends on several variables of each model (Walsh, 2005). However, once he model is solved, he opimal policy depends only on pas variables which can be known in a recursive way. Therefore i is possible bu no obvious and operaional o deermine he opimal rule. Tha is why we focused on he sudy of he simple rules during his second sep of robusness analysis, such as he following Taylor rule is represens by Equaion (42): i i (1 ) x (42) This ype of rule is of course sub-opimal in comparison wih opimal rule bu easier o elaborae. The Tables 2 and 3 have been obained wih he following loss funcion 8 given by Equaion (43): L Var( ) Var( y ) 0.5 Var( i ) (43) 8 The values shown in he following able are obained wih a weigh in he loss funcion equal o 1 on he variance of inflaion and he oupu gap and equal o 0.5 in he variance of ineres raes. 982

15 Table-2. Parameers of he simple rule based on he model chosen. Models Calvo Taylor Sicky All The line 'All' in Table 2 is refers o he case where he hree (Calvo, Taylor, Sicky) models are aken ino consideraion a he ime and wih he same probabiliy. Table 2 repors he resuls of each model according o he parameers of he simple rule represens by Equaion (14). We can see ha he Calvo and Taylor models are quie similar while he Sicky informaion model behaves differenly. This feaure shows o which exend i is imporan o esablish a robus opimal rule. The parameers obained wih he Bayesian loss funcion are idenical o hose from he Calvo and Taylor models for 1 and 3. Bu on he conrary, hey adap an inermediae posiion for 2. Table-3. Comparison of losses in he differen combinaions. Calvo Taylor Sicky All Calvo (0.0) (2.9) (196.4) (18.3) Taylor (5.8) (0.0) (229.6) (9.0) Sicky (41.3) (37.6) (0.0) (8.4) The column "All" in Table 3 is used when we consider he hree models a he same ime wih equal probabiliy. The values beween parenheses indicae he percenage of "faul Tolerance". We define he welfare loss crieria faul Tolerance as given by: Where L L anoher model L L rue model rue model L denoes welfare losses based on he cenral bank s Taylor Rule parameers being rue model (44) consisen wih hose of he rue model, and Lanoher model denoes welfare losses based on he cenral bank s Taylor-rule parameers being inconsisen wih hose of he rue model. Which means he relaive difference beween he loss when he opimal parameers are used for he rue model or ha obained wih anoher model. Table 3, jus like Table 2, shows he big difference beween he model wih rigidiies according o he sicky informaion and he wo ohers. Then, using he parameers Sicky, while he rue model is he one wih Calvo rigidiy or Taylor rigidiy, we obain losses abou 200% higher han he ones obained choosing he parameers associaed. On he conrary, using he Calvo or Taylor parameers leads o a "faul olerance" from around 30% o 983

16 40%. Using a robus opimal simple rule reduces his gap beween he Sicky informaion and he ohers. In fac, when we use All, we observe a loss close o ha one which he opimal parameers for he hree models. The "faul olerance" is herefore very weak in comparison wih he wors case and wih he mean of he possible "faul olerance". We should use such a robus opimal rule when we do no know which model represens he bes descripion of he economic srucure. Table 3 suggess ha he second parameer is more imporan for he Sicky informaion model while he wo ohers one are more imporan for he Calvo and Taylor models. In conclusion, a robus rule allows o minimize he mos common error and above all o avoid big misakes. The robus simple rule is quie he same excep for he weigh of inflaion which is slighly higher. Tha is no very surprising since we knew as we have seen in secion 2.2 ha he Sicky informaion model is differen because here is a real inerial of he pas inflaion on he curren inflaion. 5. CONCLUSION We sudied in his paper he robusness of moneary policy wih wo ypes of uncerainy: uncerainy abou he parameers and uncerainy beween models. The uncerainy abou parameers has been examined wihin a Calvo model. I has been inroduced ino he reduced form. We chose o focus on he srucural parameers of he model, saring from is reduced form. The solving of robus rule in presence of uncerain parameers policy was sudied according o he Lagrangian. Our resuls have shown ha he uncerainy in he srucural parameers of he model has an impac on he dynamic soluions of he economy, bu also on he objecives of he various agens funcions, especially ha of he cenral bank. Moreover, when uncerainy is ransmied hrough he srucural parameers, he recommendaions of moneary policy. Are srongly relaed o he parameer sudied. Thus, for cerain parameers, he Brainard (1967) principle is recommended for ohers, i is Thiel s cerainy equivalence principle. The uncerainy beween models was sudied based on he mehodology of Levin and Williams (2003). The models differ by he ype of rigidiies; we hus considered a model of Calvo ype, Taylor ype and model ype Sicky informaion. The resuls show he effeciveness of he robus rule Levin and Williams. Finally, i appears ha inappropriae choice of models and parameers can have serious consequences in erms of social welfare. Indeed, he consequences on his choice can be imporan and has an impac on differen economic agens. REFERENCES Ben Aissa, M.S. and N. Rebei, Moneary policy design when consumpion prices are subsidized: The case of Tunisia, African Economic Conference 2009, Addis Ababa, Ehiopia. Available from: hp://webcache.googleuserconen.com/search?q=cache:hp:// s/page_aachmens/aec2009monearypolicydesignwhenconsumpionpricessubsidized.pdf Blinder, A.S., Cenral-bank credibiliy: Why do we care? How do we build i? American Economic Review, 90(5): Brainard, W., Uncerainy and he effeciveness of policy. American Economic Review, 57(2):

17 Chrisiano, L., M. Eichenbaum and C.L. Evans, Nominal rigidiies and he dynamic effecs of a shock o moneary policy. Journal of Poliical Economy, 113(1): Clarida, R., J. Gali and M. Gerler, The science of moneary policy: A new keynesian perspecive. Journal of Economic Lieraure, 37(4): DeJong, D., B. Ingram and C. Whieman, A bayesian approach o dynamic macroeconomics. Journal of Economerics, 98(2): Dixi, A. and J. Sigliz, Monopolisic compeiion and opimal produc diversiy. American Economic Review, 67(3): Fuhrer, J.C., Towards a compac, empirically-verified raional expecaions model for moneary policy analysis. Carnegie-Rocheser Conference Series on Public Policy, Elsevier, 47(1): Fuhrer, J.C., Opimal moneary policy in a model wih habi formaion, Working Papers No Federal Reserve Bank of Boson. Geweke, J., Using simulaion mehods for bayesian economeric models: Inference, developmen and communicaion. Economeric Reviews, 18(1): Giannoni, M.P. and M. Woodford, 2003a. Opimal ineres-rae rules: I. General heory. NBER Working Papers No Naional Bureau of Economic Research, Inc. Giannoni, M.P. and M. Woodford, 2003b. Opimal ineres-rae rules: II. General heory. NBER Working Papers No Naional Bureau of Economic Research, Inc. Haider, A. and R. Drissi, Nominal fricions and opimal moneary policy. The Pakisan Developmen Review, 48(4): Hansen, L.P. and T.J. Sargen, Robus conrol of forward-looking models. Journal of Moneary Economics, Elsevier, 50(3): Hansen, L.P. and T.J. Sargen, Robusness, book manuscrip. Available from hp://homepages.nyu.edu/~s43/. Issing, O., Moneary policy in a world of uncerainy. Economie Inernaionale, 92(4): Kydland, F.E. and E.C. Presco, Rules raher han discreion: The inconsisency of opimal plans. Journal of Poliical Economy, Universiy of Chicago Press, 85(3): Lansing, K.J. and B. Trehan, Forward-looking behavior and opimal discreionary moneary policy. Economics Leers, Elsevier, 81(2): Levin, A. and J. Williams, Robus moneary policy wih compeing reference models. Journal of Moneary Economics, 50(1): Mankiw, G.N. and R. Reis, Sicky informaion versus sicky prices: A proposal o replace he new keynesian phillips curve. The Quarerly Journal of Economics, MIT Press, 117(4): McCallum, B. and E. Nelson, Targeing versus insrumen rules for moneary policy. Federal Reserve Bank of S. Louis Review, 87(5): Rabanal, P. and J.F. Rubio-Ramirez, Comparing new keynesian models of he business cycle: A bayesian approach. Journal of Moneary Economics, Elsevier, 52(6): Ravenna, F and C.E. Walsh, Opimal moneary policy wih he cos channel, Journal of Moneary Economics, 53(2): Robers, J.M., How well does he new keynesian sicky-price model fi he daa? The B.E. Journal of Macroeconomics, De Gruyer, 5(1):

18 Rudebusch, G. and L.E.O. Svensson, Policy rules for inflaion argeing, NBER chapers, in: Moneary Policy Rules: Naional Bureau of Economic Research, Inc. Sackelberg, H.V., Marke srucure and equilibrium: 1s Ediion Translaion ino English, Bazin, Urch & Hill, Springer 2011, XIV, 134 p. Smes, F. and R. Wouers, Comparing shocks and fricions in US and euro area business cycles: A bayesian DSGE approach. Journal of Applied Economerics, John Wiley & Sons, Ld, 20(2): Sodersrom, U., Moneary policy wih uncerainy parameers. Scandinavian Journal of Economics, 104(1): Taylor, J.B., Aggregae dynamics and saggered conracs. Journal of Poliical Economy, Universiy of Chicago Press, 88(1): Taylor, J.B., Discreion versus policy rules in pracice. Carnegie-Rocheser Conference Series on Public Policy, Elsevier, 39(1): Tillmann, P., Robus moneary policy wih he cos channel. Economica, London School of Economics and Poliical Science, 76(303): Walsh, C.E., Parameer misspecificaion and robus moneary policy rules. Working Paper Series No 0477, European Cenral Bank. Woodford, M., Robusly opimal moneary policy wih near-raional expecaions. American Economic Review, American Economic Associaion, 100(1): Woodford, M., Opimal moneary policy ineria. Review of Economic Sudies, 70(4):