INFLATION PERSISTENCE AND DSGE MODELS. AN APPLICATION ON ROMANIAN ECONOMY

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1 Pere CARAIANI, PhD Insiue for Economic Forecasing Romanian Academy INFLATION PERSISTENCE AND DSGE MODELS. AN APPLICATION ON ROMANIAN ECONOMY Absrac. In his paper I sudy he inflaion persisence in Romanian economy using he DSGE approach. I esimae wo moneary DSGE models, a sandard CIA model and CIA model wih endogenous money. The resuls show ha he sandard CIA model ouperforms he augmened model in erms of predicions on inflaion persisence. A he same ime, while he sandard model can reproduce inflaion ineria for shor periods of ime, is performance is poor for higher lags. This suggess ha a more complex model migh beer predic he inflaion persisence phenomenon in Romanian economy. Keywords: inflaion persisence, DSGE models, moneary models, Bayesian echniques, Romania. JEL Classificaion: E31, E32, E Inroducion For Romania, which has as a long erm objecive he adopion of Euro, one of he policy objecives is he nominal convergence. One of he crieria of nominal convergence is he convergence of inflaion. The recen experience of CEE counries wih respec o inflaion shows ha he disinflaion process is much harder o manage han hough. Since unexpeced shock in inflaion seem o lead o long responses of inflaion, i is imporan o have an analysis of inflaion in erms of persisence. Inflaion persisence was no oo much sudied for he case of Romania, much less from a dynamic sochasic general equilibrium (DSGE, hereafer) perspecive. Mos of he sudies on he inflaion dynamics in Romania were realized under he sandard economeric framework, using eiher VAR models, like in Pelinescu and łurlea (24), or Pelinescu and Dospinescu (25) or a nonlinear approach, as in Albu (21). In his paper I use he DSGE framework o sudy inflaion dynamics. Recenly, several auhors discussed dynamic general equilibrium models for Romania, like Caraiani (27b), or Sancu and Ungureanu (27), bu inflaion dynamics were no discussed in deph. I sudy he inflaion persisence phenomenon in Romania using a moneary DSGE approach. I also invesigae if exensions of a sandard moneary DSGE model, can replicae beer he nominal feaures of real daa. The economeric

2 Pere Caraiani approach is a Bayesian one, which allows no only for esimaes of he parameers, bu also for model comparison in erms of poserior odds raio. I compare he models in erms of heir capaciy o replicae he second order momens in he real daa, namely he inflaion persisence, which is approximaed hrough he auocorrelaion funcion. I also draw some possible implicaions for moneary policy in Romania. The paper is organized as follows. In secion wo I presen he sandard moneary model and he augmened version feauring endogenous money. In he hird secion I esimae he wo models using Bayesian echniques. I also compare he model in erms of log marginal densiies and discuss he predicions of he model in erms of inflaion persisence. In he fourh secion I conclude and draw some possible policy implicaions. I also discuss fuure exensions of his paper. 2. The Models The real business cycles (RBC) models appeared as successful in modeling he real side of he economy. However, his approach proved unable o accoun for he moneary feaures of he business cycles, Chrisiano (1991). Two differen approaches emerged as an alernaive o he real business cycle models augmened wih money, namely he sicky price New Keynesian models and he limied paricipaion model. Unforunaely hey also appeared as having only a mild success in replicaing feaures of he real daa like inflaion persisence, oupuinflaion correlaions, or he liquidiy effec. Several recen papers, like Ireland (23) or Dimar, Gavin and Kydland (25), showed ha acually he real business cycles augmened wih money can replicae feaures in he daa like inflaion persisence, or inflaion-oupu relaion, if such models feaure Taylor rules, or endogenous money. These resuls favor he choice of a moneary DSGE model, namely he sandard CIA model, o sudy inflaion persisence in Romania. In his secion I presen he model I use in he subsequen analysis. I skech he building blocks of he model, he final linearized model o be esimaed and he main differences beween he alernaive models The CIA Model The model is a sandard cash-in-advance (CIA, hereafer) model which is aken from Walsh (23). There is a closed economy where here is a finie number of infiniely lived idenical agens. The households maximize he uiliy under a ypical budge consrain and a cash-in-advance consrain. The economy echnology is a Cobb Douglas producion funcion wih consan reurns o scale. The economy is hi by wo ypes of shocks, a produciviy shock affecing he producion funcion hrough he TFP and a moneary shock. The equaions below presen he log-linearized version of he model. Each variable is measured in percenage deviaions from he seady sae. y = αk 1 + ( 1 α) h + z (1)

3 Inflaion Persisence and DSGE Models. An applicaion on Romanian Economy This equaion is he linearized producion funcion. There are wo facors of producion, he capial and he hours worked. The producion of funcion is of consan reurns o scale ype, α sanding for he capial share. y c = y m δx (2) k k y c y m + k δ k (3) ( 1 ) 1 = k k The second equaion is he linearized resource consrain relaion. I implies ha he oupu is eiher consumed or invesed. Equaion (3) below shows he dynamic of he invesmens. y ( E y k ) r = α k +1 (4) The marginal produc of capial is expressed in equaion (4). λ E λ + r (5) = +1 hs y + λ = 1+ ψ h (6) 1 hs λ i Eπ Eλ (7) = = ( + E φm+ 1 π +1) λ (8) Equaions (5) o (8) are derived from he firs order condiions of he opimizaion problem of he household. Thus equaion (5) sands for he ypical Euler equaion which resuls from he opimal choice of consumpion. The nex equaion shows he inra-emporal opimal choice wih respec o labor-leisure. Equaion (7) is he Fisher equaion, while equaion (8) is he marginal uiliy of consumpion. m = m π + em 1 (9) Equaion (9) expresses he dynamic of he money supply which is a random walk processes and is influenced by inflaion and he money supply shocks. c = m (1) Equaion (1) is he linearized cash-in-advance consrain. em ρ em + u (11) = m 1 = z z 1 e z ρ + (13) Finally, equaions (11) and (13) express he wo shocks, on he money supply and on he PTF, as AR(1) processes.

4 Pere Caraiani 2.2. The CIA Model wih endogenous money I inroduce here a sligh variaion on he sandard CIA model. The change implies he inroducion of a Taylor rule wihin he model. Similar research was done by Dimar e al. (23), Chen (23), or Suh (24). Here I follow he approach of Suh (24) who exended he sandard CIA model wih a Taylor rule. Suh (24) shows ha one of he proper ways o inroduce he Taylor rule in he CIA model is o keep he Fisher equaion and combine i wih he Taylor rule. Thus, equaion (7) becomes: ω1 1 ω2 = i + y + Eλ λ ω +1 (14) 1 ω1 3. The Esimaion of he Models In his secion I esimae he models I presened in he las secion. The esimaion was done using Bayesian echniques. Several parameers were calibraed for each of he model according o he resuls in he lieraure The Esimaion of he CIA Model The se of parameers o be esimaed is given by { α, β, δ, φ, ψ, hs, ρ a, ρ u, yk, ck, σ u, σ a }. Following Caraiani (27a), I can calibrae α, β and δ. α, he share of capial, is calibraed o.4. The discoun facor β is calibraed o.98. The quarerly depreciaion rae of capial δ was compued a.24. As for he ime allocaed o work, he daa in Romanian economy sugges ha an is equal o.28 is a reasonable choice. The parameers yk and ck, corresponding o he seady sae raio beween oupu and capial, and consumpion and capial, are compued from he values of he oher parameers. The remaining parameers, namely{ φ, ψ, ρ a, ρ u, σ a, σ u }, are esimaed using Bayesian echniques. The daa series which are used are he GDP and he inflaion. The daa series are beween 2 quarer one and 27 quarer four. The GDP series is he quarerly GDP in 1995 consan prices. The inflaion rae is proxied by he GDP deflaor. All he iniial series were logged, de-seasonalized and hen filered wih he Hodrick Presco filer. The Bayesian esimaion was done hrough wo chains of 1. Meropolis Hasings draws. The final accepance raio for he firs block was of 81.1%, while for he second block i was of 81.7%. The mulivariae saisics indicaed ha he convergence was achieved, Annex A.

5 Inflaion Persisence and DSGE Models. An applicaion on Romanian Economy Table 1 The resuls of he Bayesian Esimaion for he sandard CIA model Parameers Media Prior Media Poserior Confidence Inerval Confidence Inerval Prior Disribuion Sandard Deviaion φ Normal.5 ψ Normal.5 ρ u Bea.25 ρ a Bea.25 e_a Invered Inf. Gamma e_u Invered Gamma Inf. Source: Own Compuaions Table 1 shows ha he esimaion produced high auocorrelaion coefficien for boh he echnological and moneary AR processes. The esimaed values for φ and ψ are much higher han in Walsh (23). For example, he coefficien of he relaive risk aversion is esimaed a 2.63, while Walsh (23) calibraed he coefficien a The Esimaion of he CIA Model wih endogenous money The same subse of parameers namely{ α, β, δ, hs} is calibraed as in he previous secion.the remaining parameers, namely{ φ, ψ, ρ a, ρu, σ a, σ u, ω1, ω2}, are esimaed using Bayesian echniques. The Bayesian esimaion was done hrough wo chains of 1. Meropolis Hasings draws. The final accepance raio for he firs block was of 6.6%, while for he second block i was of 7.78%. The mulivariae saisics indicaed ha he convergence was achieved, Annex B Table 2 The resuls of he Bayesian Esimaion for he augmened CIA model Parameers Media Prior Media Poserior Confidence Inerval Confidence Inerval Prior Disribuion Sandard Deviaion ω Normal.25 ω Normal.25 φ Normal.5 ψ Normal.5 ρ u Bea.25 ρ a Bea.25 e_a Invered Inf. Gamma e_u Invered Gamma Inf. Source: Own Compuaions

6 Pere Caraiani The esimaion of he inflaion parameer in he Taylor rule, Table 2, confirms he fac ha he Naional Bank of Romania followed firs of all he price sabilizaion. While officially adoped in 24, Romania prepared he adopion of he new regime a few years before. The esimaion confirms his behavior. I also appears ha, for he considered period, less imporance was given o he oupu gap flucuaions. The second esimaion shows close values for he common parameers wih he firs model, confirming hus he firs esimaion A Bayesian Comparison of he Models I is also ineresing he compare he wo esimaions in erms of poserior odds raio. I presen he log-marginal likelihoods in he able below. The logmarginal likelihoods are he resul of he Bayesian esimaions. Table 3 presens he resuls from he wo esimaions. Table 3 Bayesian Comparison Model Log Marginal Likelihood Log Bayes Facor Sandard CIA Model CIA Model wih Endogenous Money Source: Own Compuaions. We can use Jeffreys (1961) humb rule o discriminae beween he models. According o his rule, a log-bayes facor higher han wo is decisive agains he alernaive model. We can see ha he wo models have approximaely equal qualiies of fi. Thus i appears ha he inroducion of he endogenous money does no improve he qualiy of fi. Since in economics we follow he parsimonious principle, i follows ha we should favor he simpler model, namely he sandard CIA model Inflaion Persisence I urn now o he analysis of he implicaions of he esimaed models on he inflaion persisence. I analyze he inflaion persisence by using he auocorrelaion funcion in he real daa and he heoreical auocorrelaion funcions prediced by he models.

7 Inflaion Persisence and DSGE Models. An applicaion on Romanian Economy Table 4 Auocorrelaion Funcion of Inflaion Model Auocorrelaion Funcion ρ(2) ρ(2) ρ(3) ρ(4) ρ(5) Real Daa Sandard CIA Model CIA Model wih Endogenous Money Source: Own Compuaions. In able 4, I presen he auocorrelaion funcion from he real daa, from he sandard CIA model and from he CIA model wih endogenous model. I compued he auocorrelaion funcion for five periods corresponding o five quarers, which is a reasonable span for analyzing he ineria of inflaion. In figure 1, we can see he same auocorrelaions funcion as a graphic. The figure gives us a beer image of how well he models can reproduce he real daa paer. We can noice ha he real daa is characerized a srong persisence in he firs periods. Aferwards, he auocorrelaion in inflaion decreases in an accelerae way. Thus, we can see he persisence of auocorrelaion in Romania is characerized by an unusual paern in he medium run. The sandard CIA model leads o very good predicion of he inflaion persisence for he firs hree lags. Bu for higher lags, i canno reproduce he acceleraed decrease of auocorrelaion in he real daa. The CIA model wih endogenous model leads o a lower persisence for all he five lags considered. We can noice ha he auocorrelaion coefficiens are sensibly lower han hose in he real daa or hose prediced by he sandard CIA. However a lag five, he model succeeds o produce a good fi, bu his appears more as a resul of a coincidence.

8 Pere Caraiani The auocorrelaion funcion in real daa and he alernaive CIA models DATA CIA CIA_ENDOGENOUS Source: Own Compuaions. Figure 1 Again, he sandard CIA model is favored over he CIA model wih endogenous money. Here he resuls are much clearer, as he sandard CIA model succeeds o reproduce he persisence in real daa for he firs hree momens. However, he auocorrelaion funcion in real daa is also characerized by unusual decrease in he medium run (lags 4 and 5) which is harder o reproduce wih he CIA model in boh forms. 4. Conclusions The purpose of his paper was o invesigae he inflaion persisence in Romanian economy using a moneary DSGE model. While simpler in is srucure, he sandard CIA model can accoun for inflaion persisence in Romanian economy, for shorer spans of ime. Inroducing endogenous money, while shown in he lieraure o improve he predicions of he model, does no lead o beer predicions for he case of Romania. In erms of Bayesian comparison, he sandard CIA model performance is relaively he same as he CIA model augmened wih endogenous money. However, based on he principle of parsimony, he sandard CIA model should be preferred for analyzing he inflaion persisence in Romania.

9 Inflaion Persisence and DSGE Models. An applicaion on Romanian Economy REFERENCES [1]Albu, L. L. (21), Evoluion of Inflaion-Unemploymen Relaionship in he Perspecive of Romania s Accession o EU, Romanian Journal of Economic Forecasing 2 (3-4): 5-23; [2]Brooks, S.P., and A. Gelman (1998), General Mehods for Monioring Convergence of Ieraive Simulaions, Journal of Compuaional and Graphical Saisics 7 (4): ; [3]Caraiani, P. (27a), An Analysis of Economic Flucuaions in Romanian Economy Using he Real Business Cycle Approach. Romanian Journal of Economic Forecasing 8 (2): 76-86; [4]Caraiani, P. (27b), An Esimaed New Keynesian Model for Romania, Romanian Journal of Economic Forecasing, 8 (4): ; [5]Chen, S. (23), Macroeconomic Policy and Taylor Rule in an Equilibrium Business Cycles Mode, unpublished manuscrip, Universiy of Wisconsin, Madison, Deparmen of Economics; [6]Chrisiano, L. (1991), Modeling he Liquidiy Effec of Money Shock, Federal Reserve Bank of Minneapolis Quarerly Review 15(1): 3-34; [7]Dimar R.D. & W. Gavin & F. Kydland (25), Inflaion Persisence and Flexible Prices, Inernaional Economic Review 46(1): ; [8]Ireland, P. (23), Endogenous Money or Sicky Prices, Journal of Moneary Economics 5 (8): ; [9]Kydland, F. and E. Presco (1982), Time o Build and Aggregae Flucuaions. Economerica 5 (6): ; [1]Jeffreys, H. (1961), Theory of Probabiliy. Oxford Universiy Press. [11]Pelinescu, E. and G. łurlea (24), Modelling Inflaion in Romania, Romanian Journal of Economic Forecasing 5(4): 68-86; [12]Pelinescu E. and A. Dospinescu (25), Impulse Analyses of he Romanian Inflaion, Romanian Journal of Economic Forecasing no. 4; [13]Sancu S. and A. Ungureanu (27), Model of General Dynamic Equilibrium, Calculable a he Real Secor Level of he Romanian Economy, Economic Compuaions and Economic Cyberneics Sudies and Research, 1-2; [14]Suh, J. E. (24), Two Essays on Moneary Policy under he Taylor Rule. Ph.D. diss., Texas A&M Universiy; [15]Walsh, C.E. (23), Moneary Theory and Policy, 2 nd Ed., Cambridge, MA: MIT Press.

10 Pere Caraiani ANNEX A. Mulivariae convergence diagnosics for CIA Model 1 5 Inerval 1 m2 5 4 m3 2 ANNEX B. Mulivariae convergence diagnosics for CIA Model wih Endogenous Money 2 1 Inerval 4 m2 2 2 m3 1