A Dual-arge Moneary Policy Rule for Open Economies: An Applicaion o France ABSRAC his paper proposes a dual arges moneary policy rule for small open economies. In addiion o a domesic moneary arge, his rule arges he nominal exchange rae a a fixed level. he policy rule is derived from he soluion of a dynamic programming problem and evaluaed in he conex of an open-economy model. Using French quarerly daa from 977:4 o 998:3, counerfacual simulaions show ha he dual arges rule performs beer han boh he hisorical discreionary policy and he single money-argeing rule in reducing he inflaion raes. JEL classificaion: E52; F4. Keywords: Moneary policy rule; Exchange rae arge; Counerfacual simulaions.
. Inroducion Moneary aggregaes conrol is commonly used as an inermediae goal of moneary policy because moneary arges have long been considered as an approximae means o communicae longer run policy objecives o he general public. Anchoring exchange raes, on he oher hand, is also of umos imporance o he disinflaion process in open economies. By keeping exchange rae wihin given margins around a cenral pariy, an inflaion-prone counry could "borrow" he low inflaion repuaion of a foreign counry. Examples include France s argeing Deusche Mark before he incepion of he European Cenral Bank. France sared o paricipae in he European Exchange Rae Mechanism in 979. he decision o join an exchange rae arge zone was a powerful incenive o disinflaion. However, as illusraed in Neely (994), he arge zone of he Franc/Deusche Mark exchange raes was realigned six imes from 979 o 987. Such lack of credibiliy on arge values failed o build a repuaion for price sabiliy. During his period, French moneary auhoriy resored o devaluaion o boos growh. Businesses relied on he devaluaion and had lile incenive o increase heir compeiiveness. However, he growh obained hrough devaluaion was merely an illusion because of he depreciaion of domesic currency. Furhermore, he growh caused higher price level and required more devaluaion. his made he agens ge used o devaluaion, facor furher devaluaion, and renew inflaion ino heir expecaions. One way o solve his cycle of depreciaion, inflaion and hen more depreciaion is o announce an explici policy rule o arge he exchange rae. Recen lieraure on moneary policies has indicaed ha he key o lowering expeced inflaion is o build a repuaion for price sabiliy. he mechanism by which his can be achieved is o propose a formal rule ha eliminaes policymakers' discreion o inflae. his paper proposes a moneary policy rule in which exchange rae is used as an inermediae arge. By proposing an explici policy rule o an open economy like France, we wish o see wheher he French economy could have performed beer during he period 979-
998. his policy rule is differen from hose in previous sudies in ha, firs, his rule links a shor-erm moneary policy insrumen o wo inermediae arges, one exernal and he oher inernal, where he exernal arge is he exchange rae. Second, he rule is evaluaed in he conex of an open-economy model. Finally, he policy rule used is derived from he opimal soluion of a dynamic programming problem. he evaluaion of he rule is conduced by using saisical simulaions of he economy. he performance of he policy rule is gauged by comparing he inflaion raes and real GDP growh raes in he simulaed and he hisorical daa. 2. Model and Mehodology he objecive funcion is a quadraic loss funcion ha penalizes deviaions of he arge variables from heir arge values. Since he effec of moneary policy on prices or oupu occurs wih considerably more delay han ha on a financial variable, using a financial variable as an inermediae arge could provide an earlier signal ha policy has deviaed from he goals. herefore, he variables in he objecive funcion are inermediae arges and he auhoriy bases heir decisions on observaions of he inermediae arges insead of he goals. he resuling variaions of he goals are hen used o evaluae he rule. Specifically, he cenral bank's objecive is o minimize: E0 = {(-w) (m - m ) 2 +w (e - e ) 2 }, () where m is moneary aggregae, e is exchange rae, and w is he penaly he cenral bank places on deviaions of exchange raes from heir arge values. he economy is characerized by a small open-economy model ha includes: (I) he IS funcion saes ha real oupu depends on he expeced real ineres rae, real exchange rae, an index of fiscal policy, and a fiscal policy shock. 2
(II) he LM funcion equaes money demand and money supply. he open economy money demand depends no only on domesic real income and ineres raes, bu also on real exchange raes. (III) Open-economy Phillips curve relaes inflaion o he lagged change of oupu, lagged exchange rae, pas inflaion, and a supply disurbance. he expeced price is derived by aking expecaions of his equaion. (IV) Exchange rae deerminaion equaion links he ineres rae o he nominal exchange rae. (V) Governmen consumpion and foreign price level are assumed o be exogenous and can be specified as auoregressive processes. Denoe y (real GDP), r (nominal reasury bill raes), g (real governmen consumpion), p (GDP deflaor), e p (expeced price a condiional on informaion available a -), q = e p + p F (real exchange rae), e (nominal Franc/Deusche Mark rae), F p (German price level), and m (nominal M3). All he variables, excep ineres raes, are in logarihms. By using he French quarerly ime series daa for he period 977:4-998:3, he following model provides a good fi of he daa (he sandard errors are in parenheses): y = 2.569 -.5[r -(p e -p )] + 0.60 q + 0.849 g, (2) (0.272) (0.580) (0.035) (0.037) m p =0.02 + 0.055 y -0.00r +0.007q +.54(m - p )-0.574 (m 2 -p 2 ), (3) (0.0) (0.029) (0.30) (0.008) (0.079) (0.076) p - p = -0.009 + 0.63( y - y 2 ) + 0.0 q + 0.72 (p (0.007) (0.02) (0.007) (0.074) - 2 p ), (4) e =.264-6.222 r, (5) (0.045) (.854) p F = - 0.03 +.87 p F - 0.262 p F, (6) (0.008) (0.08) (0.05) 3
g = 0.090 + 0.759 g + 0.229p F, (7) (0.050) (0.07) (0.06) Equaions (2)-(7) are esimaed by 3SLS. he esimaed srucural coefficiens all have expeced signs. In addiion, mos of he esimaes are significanly differen from zero a he 0% level excep he ineres rae and exchange rae in equaion (3). Combining () wih (2)-(7), we express he cenral bank's conrol problem as: Minimize E0 = Z ' K Z, (8) subjec o Z = b + B Z - + C r + η, (9) where Z = (y, m - m, e - e, p, p F, g, r, m, y -, m - - m, e - - e, p -, p F, g -, r -, m ) ', b is a consan vecor, η is a linear combinaion of he residuals vecor, and B, C, and K are consan marices. he marix K is diagonal wih - w on he second diagonal elemen, w on he hird, and zeros elsewhere. he arge pah for he money sock, m, is assumed o be he smoohed money supply process represened by an fied AR(2) process: m = 0.084 +.570m - 0.579 m 2. he exchange rae is argeed a a fixed level e, which is se o he hisorical value in 979:. We choose his value because he objecive of he EMS was o sabilize exchange raes beween is members, and France paricipaed in all he mechanisms insiued by he EMS since is incepion in 979. he problem is o choose he domesic nominal ineres raes r,..., r o achieve (8), given he iniial condiion Z 0. By using Bellman's (957) mehod of dynamic programming he problem is solved backward [see Chow (975, ch. 8)]. ha is, he las period is solved firs, given he iniial condiion Z -. Having found he opimal r, we solve he wo-period problem for 4
he las wo periods by choosing he opimal r -, coningen on he iniial condiion Z -2, and so on. Leing, he opimal policy rule can be expressed as (a echnical Appendix deailing he derivaions is available from he auhors upon reques) r = GZ - + f, (0) wih G = - (C ' HC) - (C ' HB), f = - (C ' HC) - C ' (Hb - h), H = K + (B + CG) ' H(B + CG), and h = - [I - (B + CG) ' ] - (B + CG) ' Hb. he conrol variable (r ) depends only on he predeermined variables. Subsiuing he esimaed coefficiens in (2)-(7) ino (0) and simulaing over ime o ge seady sae values of he marices H and G in (0) yield he opimal policy rule. he economy is assumed o face he same se of shocks ha acually occurred in he hisorical period. herefore he reduced form soluions of he esimaed equaions, he opimal policy rule, and he hisorical shocks from he srucural model are used o generae he counerfacual daa. We focus on wo measures of economic performance ha should reflec he concerns of policymakers: he inflaion rae and real GDP growh rae. Given he convenional definiion of a recession as wo quarers of declining GDP, we focus on he wo-quarer growh raes of real GDP. herefore he means and sandard deviaions of he annual inflaion raes and he woquarer real GDP growh raes over he simulaion period are he saisics of paricular ineres. o assess he imporance of he exchange rae arge, we conduc he simulaions over various values of w, he penaly weigh on he exchange rae arge in he loss funcion (). By varying he value of w from zero o one, we wish o see how imporan he exernal arge is relaive o he inernal arge. In paricular, we compare he performances of a dual arges rule (w>0) o hose of a single moneary arge rule (w = 0). 5
3. Simulaion resuls and conclusions able repors he means and sandard deviaions of he annual inflaion raes, he sandard deviaions of he wo-quarer real GDP growh raes, and he mean absolue values of he quarerly changes in he ineres raes. Firs of all, when he exchange rae is argeed (w 0), he simulaion resuls are very similar across differen w s. On he oher hand, he single moneary argeing rule (w=0) produces very differen resuls from hose of he dual arges rules. his is due o he fac ha, compared o he oher variables, he exchange rae has much smaller effecs on oupu and inflaion [see equaions (2) and (4)]. However, since he ineres rae elasiciy of exchange raes is very high (-6.22), if he variaion in exchange rae is no penalized, he adjusmens of he ineres raes called by economic shocks will significanly affec he exchange raes. For example, a % increase in he ineres rae will cause a 6.22% drop in he exchange rae. If he exchange rae is no argeed, he effec will be fully ransmied o oupu and inflaion raes. Furhermore, flucuaions in hese variables will call for more adjusmens of he insrumen. his is why he variaion in he ineres raes is much higher when w = 0. Secondly, compared o he dual arges rule, argeing he money supply alone will cause higher inflaion raes. On he oher hand, he variance of inflaion raes is lower because degrading a domesic nominal anchor will cause price insabiliy. However, he sabilizaion of he inflaion raes requires more rapid adjusmens of he ineres rae insrumen, which resuls in flucuaions in oupu growh. hirdly, commimen o an explici policy rule could have sabilized French annual inflaion raes. he sandard deviaion from he single money-argeing rule is abou % lower han ha in he hisorical daa and abou 0.3% lower when he exchange rae is argeed. Finally, compared o he hisorical daa, he single moneary argeing rule causes higher inflaion raes. However, if he exchange rae is argeed, he mean annual inflaion rae is 6
significanly lowered. Furhermore, he dual arges rules no only produce lower inflaion raes han hose in he daa bu also reduce he flucuaions of he inflaion raes. In sum, simulaions of he simple macroeconomic model and he policy rules sugges ha, compared o he hisorical policy, he primary benefi of using a policy rule in France is o reduce he inflaion rae volailiies. However, shor-run real GDP growh raes would be more volaile han hey have been over he pas fifeen years. argeing he nominal exchange rae eliminaes inflaion expecaions resuling from foreign disurbances and srenghens domesic credibiliy of moneary policy. herefore he moneary auhoriies in small open economies should no ignore he influences of he exchange rae volailiy on domesic inflaion. he model and he mehods of deriving an opimal policy rule saed in his paper can be applied o oher argeing mechanisms such as nominal GDP argeing rules and real GDP/Price argeing rules. For example, in equaion (8), le Z = (y, p, A ) ',where y is real oupu, p is price level, and A is a vecor of non-arge variables. he cenral bank s objecive is equivalen o (/ ) E 0 = {(-w) (y - y ) 2 +w (p - p ) 2 }. hen equaion (8) becomes a GDP/Price argeing rule. Exensions for fuure research include evaluaing combinaions of exchange rae arge and oher arge variables in an open economy seing. 7
REFERENCES Bellman, Richard E. (957). Dynamic Programming Princeon, N.J.: Princeon Universiy Press. Chow, Gregory C. (975). Analysis and Conrol of Dynamic Economic Sysem: John Wiley & Sons Press. Neely, Chrisopher J. (994). "Realignmens of arge Zone Exchange Rae Sysem: Wha Do We Know?" Federal Reserve Bank of S. Louis Review Sepember/Ocober: 23-34. 8
able. Simulaion Resuls: 979:-997:4 Mean Annual Inflaion Rae(%) Sandard Deviaion of Annual Inflaion Rae(%) Sandard Deviaion of wo-quarer Real GDP Growh Rae (%) Mean Absolue value of Quarerly Change in Ineres Raes (Annual Rae %) Hisorical Daa: 4.98 3.95 0.958 0.629 Simulaed Daa w=0 5.669 2.972 2.866 2.264 w=0. 3.448 3.664.600 0.085 w=0.2 3.445 3.683.602 0.039 w =0.3 3.444 3.689.602 0.023 w =0.4 3.444 3.693.603 0.05 w =0.5 3.443 3.694.603 0.00 w =0.6 3.443 3.696.604 0.007 w =0.7 3.443 3.697.604 0.004 w =0.8 3.443 3.697.604 0.002 w =0.9 3.443 3.698.604 0.00 w = 3.443 3.698.604 0.000 w is he penaly weigh received by he exchange rae arge in he welfare funcion: (/) E 0 = {(-w) (m - m ) 2 +w (e - e ) 2 }. 9
echnical Appendix: (for referees review only and no inended for publicaion) Equaions (2) - (7) can be expressed as X = A 0 + A X + A 2 X - + A 3 X -2 + A 4 r + A 5 u, (A.) where X = (y, m - m, e - e, p, p F, g, r, Rewrie (A.) as X = A 6 + A 7 X - + A 8 X -2 + A 9 r + A 0 u, m ) '. he consan marices A's should be obvious. where A 6 = (I-A ) - A 0, A 7 = (I-A ) - A 2, A 8 = (I-A ) - A 3, A 9 = (I-A ) - A 4, and A 0 = (I-A ) - A 5. A firs-order sysem can be formed as: X X A6 A = + 0 I A X X A9 A + r + 0 7 8 0 0 2 0 which can be rewrien as: u, Z = b+b Z - + C r + η. (A.2) he cenral bank s objecive is o minimize E0 = Z ' K Z, subjec o (A.2). he marix K is diagonal wih -w on he second diagonal elemen, w on he hird, and zeros elsewhere. he problem is o choose r,..., r o achieve he objecive, given he iniial condiion Z 0. By using Bellman s (957) mehod of dynamic programming he problem is solved backward. he following derivaions follow hose in Chow (975, ch. 8). Consider he problem for he las period. I is o minimize V =E (Z ' K Z ) = (b+bz +Cr ) ' K (b+bz +Cr )+ E ( η ' Kη ). (A.3) Le H =K. Differeniaion of (A.3) wih respec o r yields V r =2 C ' H (b + B Z + C r ) =0. (A.4) 0
he soluion of (A.4) gives he opimal policy rule for he las period rˆ =G Z +f, where G = -(C ' H C) (C ' H B), f =-(C ' H C) C ' H b, and rˆ is he opimal choice of r. Now consider he problem for one more period -. By he principle of opimaliy in dynamic programming we minimize he following value funcion wih respec o r : V =E 2 [(Z ' K Z )+Vˆ ], (A.5) where Vˆ is he minimum value of V. he soluion of he firs-order condiion of (A.5) yields rˆ = G Z 2 + f, where G = -(C ' H C) (C ' H B), f = -(C ' H C) C ' (H b-h ), H =K+(B+CG ) ' H (B+CG ), and h = - (B+ CG ) ' H b. Having found he opimal r and r, we similarly solve he hree-period problem by choosing he opimal r 2, and so on. he opimal policy rule a ime, wih iniial condiions H =K and h = 0, can be expressed as: rˆ =G Z +f, where G = -(C ' H C) (C ' H B), (A.6) f = -(C ' H C) C ' (H b-h ), (A.7) H =K+(B+CG + ) ' H + (B+CG + ), and (A.8) h = - (B+CG + )(h + -H + b). (A.9)
If all he characerisic roos of he marix (B+CG) are smaller han one in absolue value, solving (A.5)-(A.9) recursively yields he opimal policy in he seady sae: r =GZ +f, where G = -(C ' HC) (C ' HB), f = -(C ' HC) C ' (Hb-h), H = K + (B+CG) ' H (B+CG), and h = - [I-(B+CG) ' ] (B+CG) ' Hb. 2