THE ROLE OF UNCERTAIN GOVERNMENT PREFERENCES FOR FISCAL AND MONETARY POLICY INTERACTION 3

Transcription

1 Olga S. Kuznetsova, Sergey. Merzlyakov THE ROLE OF UNCERTIN OVERNMENT PREFERENCES FOR FISCL ND MONETRY POLICY INTERCTION Ths paper explores the role of uncertan government preferences for fscal and monetary polcy nteracton. Our analyss shows that the uncertanty aout government preferences does not affect the macroeconomc equlrum f the fscal multpler s known. In the case of multplcatve uncertanty, uncertan government preferences make fscal polcy more contractonary, whle monetary polcy ecomes more expansonary. Ths leads to hgher expected nflaton and lower expected output, whch means a stronger nflaton as. JEL Classfcaton: E5, E58, E6, E6. Key words: fscal and monetary polcy nteracton, multplcatve uncertanty, uncertan preferences. Natonal Research Unversty Hgher School of Economcs. Laoratory for Macroeconomc nalyss. Research Fellow. E-mal: okuznetsova@hse.ru Natonal Research Unversty Hgher School of Economcs. Laoratory for Macroeconomc nalyss. Deputy Head. E-mal: smerzlyakov@hse.ru The study was mplemented n the framework of the asc Research Program at the Natonal Research Unversty Hgher School of Economcs n 05.

2 . Introducton Uncertanty s an nherent feature of any economc system. Therefore, macroeconomc agents, such as governments and central anks, should take uncertanty nto account. Ths s emphaszed n the economc lterature (Estrella, Mshkn (999, Soderstrom (00, Lane (00, De rauwe, Senegas (006. In ths paper we explore the role of uncertan government preferences for fscal and monetary polcy nteracton. The economc mpact of uncertanty depends on ts orgns. s Tnergen (95 and Thel (958 show n the case of addtve uncertanty, certanty equvalence holds. Ths means that ths type of uncertanty does not change agent ehavour. However, f uncertanty affects the loss functon of the agent or the channels of polcy transmsson, an agent s optmal ehavour s not certanty equvalent. For example, for multplcatve uncertanty, agents do not have complete nformaton aout the magntude of macroeconomc polcy effects. s ranard (967 shows, n ths stuaton the polcymaker ecomes less actve n reactng to macroeconomc shocks. Ths phenomenon was called the ranard conservatsm prncple y lnder (998. There s no consensus n the economc lterature aout the welfare effect of multplcatve uncertanty. Swank (99 and Pearce, Soue (997 fnd that multplcatve uncertanty reduces nflaton as and, therefore ncreases socal welfare. Koayash (00 shows that even n the asence of nflaton as, multplcatve uncertanty leads to an ncrease n socal welfare. Cccarone, Marchett (009 emphasze that the fndngs of Koayash (00 are correct only f the preferences of socety and the central ank concde. Wthout dout, multplcatve uncertanty should affect the nteracton of the government and the central ank. consderale part of the economc lterature s devoted to fscal and monetary polcy nteractons. Startng from Sargent, Wallace (98 ths topc has ecome especally popular. Taelln (986, and lesna, Taelln (987 developed a formal descrpton of the strategc nteracton of fscal and monetary polcy. eetsma, ovenerg (999 consder a conflct of nterest etween the government and the central ank, namely the regulaton of pulc det and nflaton. They show that all macroeconomc polcy targets are achevale rrespectve of whether the central ank s ndependent or not. nother ssue concerns the dea that oth fscal and monetary authortes can use ther nstruments to nfluence aggregate demand fndng a compromse etween output and nflaton. For example, ndersen, Schneder (986 note that two ndependent authortes do not automatcally guarantee the achevement of the target level of output. lnder (98 questons

3 the dea that macroeconomc targets can e acheved under fscal and monetary polcy coordnaton. Dxt, Lamertn (00a also show that n equlrum wth the coordnaton of fscal and monetary authortes, output s lower than the target level, whle nflaton s hgher. Dxt, Lamertn (00, however, show that fscal and monetary polcy can acheve macroeconomc targets f the government and the central ank share output and nflaton targets. Ths result holds even f the weght coeffcents n the loss functons of the fscal and monetary authortes are dfferent. Whle research on fscal and monetary polcy nteracton s well-estalshed, at present the role of uncertanty n ths lterature s lmted. s a rare excepton, D artolomeo, ul, Manzo (009 ncorporate the uncertanty aout the fscal multpler nto the model y Dxt, Lamertn (00. They show that even f the government and the central ank share output and nflaton target levels, multplcatve uncertanty does not allow them to acheve these targets. In equlrum output s too low and nflaton s too hgh. In other words, nflaton as s present. D artolomeo, ul (0 analyse the uncertanty aout the monetary polcy multpler and come to the same concluson: n equlrum multplcatve uncertanty causes neffectve levels of output and nflaton. To our knowledge, there are no other studes aout polcy nteractons under uncertanty. The lterature neglects the role of uncertan preferences n polcy nteractons. lthough several studes focus on uncertan preferences under dfferent economc frameworks, they do not rase the queston of polcy nteractons. For example, Sert (00 analyses the desgn of optmal monetary polcy n a multperod model, when socety does not know the central ank preferences. Sert (00 shows that due to the reputaton motve of central ankers, average nflaton decreases. Hefeker, Zmmer (0 pont out that under uncertan monetary authorty preferences, central ank ndependence s no longer a suffcent condton for achevng macroeconomc targets. Hefeker, Zmmer (0 nstead emphasze the prmary role of the central ank s conservatsm. In turn, Sorge (0 also questons the effcency of delegatng monetary polcy to an ndependent and conservatve central ank n the case of severe model uncertanty. He shows that n some cases t could e optmal to delegate monetary polcy to the central ank, whch s less conservatve than socety. The economc lterature descres a numer of mplcatons for the uncertanty aout polcymaker preferences. Nevertheless, none of these studes consders the strategc nteracton etween fscal and monetary polcy. Further, the exstng research does not deal wth uncertan government preferences. In developed countres the prolem of uncertan central ank preferences s less sgnfcant than uncertan government preferences. For example, the targets of

4 the European Central ank are clearly defned: nflaton less than %. Moreover, lnder et al. (008 confrm that n recent years the transparency of monetary polcy has consderaly ncreased all over the world. Ths means that the assumpton of certan central ank preferences s relevant. t the same tme, the transparency of fscal polces has not sgnfcantly changed, although government preferences are exposed to consderale changes n electon perods. Our paper flls ths gap. We modfy the model of D artolomeo, ul, Manzo (009 y addng the uncertanty aout government preferences. s a result, we show that uncertan government preferences do not change the characterstcs of macroeconomc polcy f the fscal multpler s certan. In the case of multplcatve uncertanty, uncertan government preferences lead to a more expansonary monetary polcy and a more contractonary fscal polcy. The paper s organzed as follows. In Secton we descre the model of fscal and monetary polcy nteracton. In Secton we analyse the mpact of uncertan government preferences on macroeconomc equlrum. Secton dscusses the man fndngs and future drectons for research.. Model.. Model framework We modfy the model of D artolomeo, ul, Manzo (009 y ntroducng uncertan government preferences. The economy s descred y the standard aggregate demand and aggregate supply functons: e ( π y y π a, ( π m c, a,, c > 0, ( e where π s the rate of nflaton, π s the expected rate of nflaton, y s the level of real output, y s the natural level of real output, s the nstrument of fscal polcy (for example, transfers, m s the monetary polcy nstrument (for example, the growth rate of the money supply. Followng the tradtonal macroeconomc approach (see Kydland, Prescott (977, the target level of output exceeds the natural level of output: y * > y. Followng D artolomeo, ul, Manzo (009, we assume that fscal multpler s a random varale wth mean and varance σ. Thus, σ characterzes the degree of multplcatve uncertanty. The losses of the government and the central ank are gven y the followng functons:

5 L E ( π π * ( y y *, ( C,, E s the expectaton operator. where { } The loss functons of the central ank ( L C and the government ( L depend on the devatons of nflaton (π and output ( y from ther target levels π * and y *. Parameter C s the central ank preference regardng the stalzaton of output and nflaton, whle s the correspondng characterstc of the government. Contrary to D artolomeo, ul, Manzo (009, we assume that s a random varale. It has a unmodal and symmetrc dstruton over the nterval [ ; ] wth a cumulatve dstruton functon F(. Followng Rogoff (985 we assume that the central ank s more conservatve than the government,. ecause of the symmetry of the dstruton of, the expected government type equals to C for all F(. The varance of vares for dfferent dstruton functons. Consequently, the varance of measures the uncertanty aout government preferences. We assume that the government and the central ank smultaneously and ndependently choose ther polces after the expectatons have een formed. Mnmzng the government loss functon under constrant ( and (, we otan the optmal acton for the government of type :, ( where c( m, ( a c( y y e * π m, c ( σ 0 π * ( a 0 σ. c c >, > Thus, ( represents the functon of the government response to central ank acton. From ( t follows that m ( a c c < 0. Ths means that the government responds to an The specal case wth unformly dstruted s presented n Kuznetsova, Merzlyakov (05. 5

6 ncrease of m wth a contractonary polcy (for example, y reducng transfers. It should e noted that ths effect weakens wth a rse of multplcatve uncertanty ( > 0. m Usng the government response functon ( we otan the average government acton ( df( : where Φ, (5 ( df Φ concavty of functon s the mplct characterstc of the dstruton of. Due to the, ts expected value depends postvely on the varance of. Note that for two dfferent cumulatve dstruton functons F ( and F ( ( E df < ( E df (, we have Φ F ( < Φ( F ( ( σ (, such that. Thus, for the dstruton of wth hgher varance Φ s hgher. In other words, Φ characterzes the uncertanty aout government preferences. Mnmzng the central ank losses, we otan the central ank response functon: m π * π ( y * y ( c ( a c e. (6 The optmal monetary acton m decreases wth an ncrease n. fter fndng the ntersecton of the response functons (5 and (6 we defne the level of nflaton expectatons: e π m c. (7 Next, we susttute the nflaton expectatons at the ntersecton pont and defne the parameters of equlrum... Equlrum The equlrum values of monetary acton m ~, government acton ~ and the average government acton ~ depend on all the parameters of our model ncludng the characterstc of uncertanty Φ : ~ Φ m π * c, (8 ( y * y Φ 6

7 ~ Φ ( y * y, (9 Φ ~ X X Φ ( y * y, (0 Φ where cσ ( a c, c( ( a c ( ( a c c 0 σ, c( a c 0, ( ( ( ac c a c σ, ( a c c 0 ( a c ( a c ( c ( c ( σ 0 c ( a c 0 X c.,, X a c 0, We start the analyss of equlrum (8 0 y characterzng the functon of government acton ~. For all possle dstrutons of, Proposton s true. Proposton. For all dstrutons of ; and for any < the equlrum transfers ~ ~ are postve for any government type. Moreover, > 0 and ~ ( < 0. Proof. See ppendx. over nterval [ ] In other words, Proposton states that n any equlrum fscal polcy s expansonary. Furthermore, the stronger the government preference wth respect to the stalzaton of output, the more expansonary fscal polcy. t the same tme due to concavty of functon ~ ( the average government acton ( ~ s less than the acton of the average government type ~ ( y * y Φ. Φ Usng (8 0 we can derve the equlrum expected output and nflaton: ~ e ( a c Φ ( π π * c y * y σ c, ( Φ ~ y e y * σ a( a c Φ. ( ( y * y Φ c 7

8 Wth the use of ( and ( we arrve at Proposton. Proposton. For all dstrutons of over nterval [ ] ; and for any <, equlrum s characterzed y nflaton as: the expected rate of nflaton exceeds ts target level π *, whle the expected level of output s elow ts target level y *. Proof. See ppendx. Ths result s n lne wth D artolomeo, ul, Manzo (009, who show that for multplcatve uncertanty the government and the central ank cannot acheve ther targets even f they share them. Thus, we demonstrate that preference uncertanty aggravates the nflaton as prolem. We analyse n detal the orgns of ths effect n Secton.. Uncertan government preferences s stated earler, the varance of characterzes the uncertanty aout government preferences. Comparng equlra for dfferent dstrutons we come to the followng results. Proposton. Let ( m ~ ( F ; ~ ( F ; ( F unmodal dstruton of over nterval [ ] and for any F ( and ( ~ ~ F ~ denote the equlrum under the symmetrc ; wth CDF F. Then for any σ > 0 ( ( F, such that ( E df < ( E df ( m ( F < m( and ~ ( ~ F ( F ~ e( ~ e π F < π ( F and ~ e( ~ e y F y ( F Proof. See ppendx. > for all, >. : The frst part of Proposton states that the uncertanty aout government preferences forces the central ank to e more expansonary, whle the polcy of the government wth any ecomes more contractonary. The explanaton s straghtforward. Due to Proposton, n equlrum government acton ~ ( s an ncreasng concave functon. So f the varance of rses, the average government acton ~ decreases. decrease n ~ leads to an ncrease n 8

9 central ank acton m ~. Ths n turn forces the government to decrease ts acton ~ n accordance wth the response functon (. s a result, the average government acton ~ goes down. The process contnues untl a new equlrum s acheved. The second part of Proposton states that for a dstruton wth hgher varance the expected level of nflaton s hgher, whle the expected level of output s smaller. In other words, the uncertanty aout government preferences aggravates the prolem of nflaton as, descred n Proposton. Ths result complements the man fndng of D artolomeo, ul, Manzo (009, who show that multplcatve uncertanty also causes ths prolem. Moreover, n our model multplcatve uncertanty s a necessary condton for nflaton as. It can e easly shown that f σ 0, Proposton s correct. Proposton. If 0 σ, for any cumulatve dstruton functon ( c m ~ π * ( y * y ( y y and ~ ~ * ~ π * * π ( F and ( F Proof. See ppendx. a ~ y y., a F : Proposton ( ndcates that n the asence of multplcatve uncertanty the preference uncertanty does not affect equlrum. For any dstruton functon F( the governments of ( y * y all types choose the same amount of transfers ~ ~, so the average government a acton does not depend on the dstruton of. Consequently, monetary acton s also constant. s a result, the uncertanty aout government preferences s no longer relevant. Thus, the man fndngs of Dxt, Lamertn (00 hold, and the government and the central ank are ale to acheve oth nflaton and output targets, as shown n Proposton (. In other words, wthout multplcatve uncertanty, nflaton as dsappears despte uncertan government preferences.. Concluson Ths paper contrutes to the exstng lterature on macroeconomc polcy under uncertanty. lthough varous mplcatons of uncertanty have een well studed, consderale 9

10 gaps n ths area stll reman. For nstance, the prolem of uncertan government preferences deserves more attenton and requres further analyss. In ths paper we consder the mpact of uncertan government preferences on the man characterstcs of macroeconomc polcy. Our analyss shows that f the fscal multpler s known, uncertan government preferences do not affect macroeconomc equlrum. In the case of multplcatve uncertanty, uncertan government preferences make fscal polcy more contractonary, whle monetary polcy ecomes more expansonary. s a result, expected nflaton rses and expected output drops. Thus, the nflaton as prolem worsens. The prolem of dfferent forms of strategc nteracton s eyond the scope of our paper: we consder that the government and the central ank conduct ther polces smultaneously and ndependently. The analyss of the nfluence of uncertan government preferences on macroeconomc polcy for varous forms of strategc nteracton s a promsng avenue for further research. 0

11 ppendx Proof of Propostons and. From ( we can see that the nfluence of on government acton depends on the sgn of expresson ( : (, (. ( (. (. Susttutng the equlrum values (8 0 nto expresson ( s ( * y ( m m( F ~ ~ ( F σ с we otan: ( y * y( c a c. (. Φ( F y s postve, the sgn of (. concdes wth the sgn of denomnator ( Φ( F. Φ ( F and are always postve. If 0, ( Φ F 0 < ( < some further dervatons are needed. y assumpton <, thus ; [ ] automatcally. For 0 < > for all. Consequently, for any cumulatve dstruton functon F the followng holds: ( df ( ( df Φ( F <. (. The rght-hand sde of (. can e further rewrtten as: df ( where we use ( ( df df, as we assume that (. and (.5, we conclude that, (.5, s dstruted over nterval [ ; ]. So, usng Φ ( F <. (.6

12 Thus, for 0 >, 0 ( < < Φ с F σ. s a result: ( ( ( 0 ~ ~ < F F m m. (.7 Usng (., (. and (.7, we get that 0 ~ > and ( 0 <. Moreover, as 0 ( < Φ F, we conclude that ( * ( * * ~ π σ π π > Φ Φ c a c y y c e, (.8 ( * ( * * ~ y c a a c y y y y e < Φ Φ σ. (.9 Q.E.D.

13 ppendx Proof of Propostons and. s we have seen, the dstruton of hgher varance s characterzed y a hgher value of Φ : ( ( E df < ( E df ( Φ( F ( < Φ( F (. (. Wth (. and defntons (8 from the man text, Proposton follows drectly. If 0 σ, from (. ( m m( F ~ ~ ( F 0. Takng nto account (. we can conclude that n ths case 0. Ths means that governments of any type choose the same level of transfers ~ σ ( y * y a. If all government types choose the same acton, the average acton also equals ths level. Susttutng the average government acton nto (6, ( and (, we mmedately arrve at Proposton. Q.E.D.

14 References. lesna., Taelln. (987 Rules and dscreton wth noncoordnated monetary and fscal polces, Economc Inqury, vol., pp ndersen T., Schneder F. (986 Coordnaton of fscal and monetary polcy under dfferent nsttutonal arrangements, European Journal of Poltcal Economy, vol. (, pp eetsma R., ovenerg L. (999 Does monetary unfcaton lead to excessve det accumulaton?, Journal of Pulc Economcs, vol. 7, pp lnder. (98 Issues n the coordnaton of monetary and fscal polcy, NER Workng Paper No lnder. (998 Central ankng n theory and practce, Camrdge, Mass.: MIT Press. 6. lnder., Ehrmann M., Fratzscher M., de Haan J., Jansen D.-J. (008 Central ank Communcaton and Monetary Polcy: Survey of Theory and Evdence, Journal of Economc Lterature, vol. 6 (, pp ranard W. (967 Uncertanty and the effectveness of polcy, mercan Economc Revew, vol. 57 (, pp Cccarone M., Marchett E. (009 Revstng the role of multplcatve uncertanty n a model wthout nflatonary as, Economcs Letters, vol. 0, pp De rauwe P., Senegas M. (006 Monetary polcy desgn and transmsson asymmetry n EMU: Does uncertanty matter?, European Journal of Poltcal Economy, vol., pp D artolomeo., ul F., Manzo M. (009 Polcy uncertanty, symoss, and the optmal fscal and monetary conservatveness, Emprca, vol. 6, pp D artolomeo., ul F. (0 Fscal and monetary nteracton under monetary polcy uncertanty, European Journal of Poltcal Economy, vol. 7, pp Dxt., Lamertn L. (00a Interactons of commtment and dscreton n monetary and fscal polces, mercan Economc Revew, vol. 9, pp Dxt., Lamertn L. (00 Symoss of monetary and fscal polces n a monetary unon, Journal of Internatonal Economcs, vol. 60, pp Estrella., Mshkn F. (999 Rethnkng the role of NIRU n monetary polcy: mplcatons of model formulaton and uncertanty, n: Taylor J. (ed Monetary polcy rules, Unversty of Chcago Press, Chcago, pp

15 5. Hefeker C., Zmmer. (0 The optmal choce of central ank ndependence and conservatsm under uncertanty, Journal of Macroeconomcs, vol., pp Koayash T. (00 Multplcatve uncertanty n a model wthout nflatonary as, Economcs Letters, vol. 80, pp Kuznetsova O., Merzlyakov S. (05 Macroeconomc polcy under uncertan fscal polcy preferences, Russan Journal of Economc Theory, vol., pp. 9-0, (n Russan. 8. Kydland F., Prescott E. (977 Rules rather than dscreton: the nconsstency of optmal plans, Journal of Poltcal Economy, vol. 87 (June, pp Lane P. (00 Monetary-fscal nteractons n an uncertan world: lessons for European polcymakers, n: ut M. (ed Monetary and fscal polces under EMU: nteracton and coordnaton, Camrdge Unversty Press, pp Pearce D., Soue M. (997 Uncertanty and the nflaton as of monetary polcy, Economcs Letters, vol. 57, pp Rogoff K. (985 The optmal degree of commtment to an ntermedate monetary target, The Quarterly Journal of Economcs, vol. 00 (, pp Sargent T., Wallace N. (98 Some unpleasant monetarst arthmetc, Federal Reserve ank of Mnneapols Quarterly Revew, Fall, pp Sert. (00 Monetary polcy wth uncertan central ank preferences, European Economc Revew, vol. 6, pp Soderstrom U. (00 Monetary polcy wth uncertan parameters, Scandnavan Journal of Economcs, vol. 0, pp Sorge M. (0 Roust delegaton wth uncertan monetary polcy preferences, Economc Modellng, vol. 0, pp Swank O. (99 etter monetary control may ncrease the nflatonary as of polcy, The Scandnavan Journal of Economcs, vol. 96 (, pp Taelln. (986 Money, det and defcts n a dynamc game, Journal of Economc Dynamcs and Control, vol. 0, pp Thel H. (958 Economc forecasts and polcy, North Holland: msterdam. 9. Tnergen J. (95 On the theory of economc polcy, North Holland: msterdam. 5