Comparing sticky prices and sticky information in a New Keynesian model based on forecast accuracy

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1 Comparing sicky prices and sicky informaion in a New Keynesian model based on forecas accuracy Dr. Pere Caraiani Insiue for Economic Forecasing Romanian Academy We esimae hree differen versions of a sandard New Keynesian model ha ake ino accoun various specificaions of he Phillips curve, including sicky prices, sicky informaion and sicky prices and indexaion. We compare hese models based on heir forecasing accuracy relaive o oupu and inflaion. For he case of oupu, he resuls are mixed as no specificaion is clearly favored. Wih respec o inflaion, he sicky informaion and sicky prices wih indexaion models ouperform he baseline model. The model wih sicky prices and indexaion also ouperforms he sicky informaion model in he shor run. The sicky informaion framework appears as having a limied value in improving he forecasing accuracy. Keywords: Phillips Curve, Sicky Informaion, New Keynesian, moneary policy. JEL Classificaion: C11, E31, E Inroducion The sandard New Keynesian model (NK from here), see Clarida, Gali and Gerler (1999) for a presenaion of he canonical specificaion, alhough has addressed several issues, has some difficulies in replicaing boh he inflaion persisence as well as he impac of moneary policy shocks. A soluion o hese difficulies was proposed by Mankiw and Reis (2002) who inroduced he idea of sicky informaion and show ha i can replicae he above menioned puzzles. Since hen, numerous sudies have been carried on analyzing wheher sicky informaion improves he performance of he New Keynesian Phillips curve, eiher in he parial equilibrium framework, or in general equilibrium. In a parial equilibrium framework, Dopke e al. (2006) esimaed he sicky informaion Phillips curve for four European economies, France, Germany, Ialy and UK. 1

2 The general equilibrium approach is much older han he incorporaion of sicky informaion ino he Phillips curve, daing o he idea of Lucas (1972) who incorporaed imperfec informaion ino his model consising in islands. Collard and Dellas (2003) was among he firs sudies ha included he sicky informaion ino he sandard DSGE model. A few sudies compared he performance of DSGE models wih sicky prices and sicky informaion. Traband (2006) showed ha alhough he model wih sicky informaion can reproduce he above menioned feaures in daa, he same performance can be reached when a model includes boh sicky prices and indexaion. Pausian and Pylarczyk (2006) exended he previous research by considering a medium size model as proposed by Smes and Wouers (2003). Surprisingly, hey found ha, in erms of poserior odds raio, he sicky price version ouperforms he sicky informaion specificaion. Furher evidences were found by Arslan (2008), who compared he response of a sicky informaion model and of a ypical NK model wih sicky prices o a cos push shock. The simulaion shows ha he sicky informaion framework leads o more realisic resuls. Kiley (2007) performed a comparison beween he sicky informaion NK model and he sicky price specificaion based on heir abiliy o model inflaion. His resuls indicae ha when a hybrid componen is included, he resuls of a NK model are improved. The resuls in Mankiw and Reis (2002) were revisied by Keen (2007) who showed ha heir resuls are sensiive o he calibraion of heir model. The resuls depend on he degree of real rigidiy as well as he way he moneary policy is specified. Recenly, new evidences agains he sicky informaion framework were found by Carillo (2012) who, based on esimaed VAR models on US daa, showed ha such a model leads o worse response following a produciviy shock as compared wih a sandard NK model wih inflaion indexaion and habi. We can conclude ha here is no definie answer on he usefulness of he sicky informaion framework and alhough he iniial conribuions have shown some advanages vis-avis he sandard New Keynesian framework, laer conribuions have also indicaed ha when he New Keynesian model depars from he sandard specificaion and i includes furher feaures, hen i can have a beer performance han a NK model wih sicky informaion. 2

3 In his paper, we compare hree differen New Keynesian models, one wih sicky prices, one wih sicky informaion and one wih boh sicky prices and indexaion which we esimae on US daa using a Bayesian mehodology. This sudy conribues o exising lieraure on his opic in a few ways. In conras wih previous approaches, we compare he differen specificaions for NK models based on heir forecasing abiliy. Alhough here is a growing lieraure regarding he abiliy of DSGE models o forecas as compared o alernaive approaches, mosly VARs, see Rubaszek and Skrzypczyński (2008) or Guangling e al. (2009), or facor models, see Wang (2009) for a relevan example, here is a weak lieraure regarding wha drives he abiliy of DSGE models o forecas, especially wih respec o heir specificaion (microfoundaions). Among he approaches o address hese shorcomings, we can enumerae Mahes and Wang (2012). However, hey compare differen models wihou precisely looking a wha kind of micro foundaions drives he accuracy of he differen models. This paper is organized as follows. The nex secion describes he models used wihin he paper. In he hird secion we presen he daa used in he esimaion, he calibraion and esimaion of he hree models and we discuss he resuling esimaes. We compare he forecas accuracies for oupu and inflaion for each of he models in he fourh secion. In he las secion we conclude and ouline possible fuure developmens. 2. Alernaive New Keynesian Models We presen here he models used hroughou he paper. We build on a ypical sicky price New Keynesian model o which we consider wo alernaives, namely a sicky informaion NK model as well as he augmenaion of he baseline sicky price model wih price indexaion The New Keynesian Model wih Sicky Prices We use he model proposed by Rabanal and Rubio-Ramirez (2005) which was esimaed on US daa. Besides being known o work well, he baseline model ogeher wih is differen 3

4 versions has also been esimaed for he case of Euro Area, see Rabanal and Rubio-Ramirez (2003). The baseline model is an enhanced version of a ypical New Keynesian model wih sicky prices and hus is a reasonable saring poin for our comparison exercise. The model assumes a closed economy and is a reasonable hypohesis given he large economy saus of US economy. We presen he model in is log linear form in he following equaions: y E y 1 ( r Ep 1 Eg 1 g ) (1) y a ( 1 ) n (2) mc w p n y (3) mrs r 1 y n g p y y ms rr 1 (1 r ) (5) (4) w p w p w p 1 1 (6) a g a 1 (7) a g a g 1 (8) g ms (9) m (10) p E p 1 k mc (11) p w p mrs (12) The firs equaion is a ypical New Keynesian IS curve showing he drivers of oupu: expeced oupu y, he real ineres rae, r, minus inflaion, he rae of change of prices p. The preference shocks g also drive he dynamics of oupu. Equaion (2) shows he linearized producion funcion, where a sands for he echnological process while n represens he hours worked. The nex equaion, he hird one, presens he relaionship beween marginal cos and nominal wage w. The marginal rae of subsiuion, mrs, and he hours worked are relaed in he fourh equaion. The preference shocks have a role in his relaionship oo. 4

5 The moneary policy rule is described in equaion (5). We have slighly modified he specificaion in Rabanal and Rubio-Ramirez (2003) by considering ha here is smoohing process for he ineres rae, in line wih he findings in Clarida, Gali and Gerler (1999). The real and he nominal wages are relaed in he sixh equaion. Finally, dynamics for prices and wages are shown in equaions (11) - (12). The baseline model assumes Calvo ype sicky prices, see equaion (11) for he specificaion of he New Keynesian Phillips curve. The parameer k p is given by: where 1 1 p 1 p 1 1 k (13) p p is he seady sae of ε, he elasiciy of subsiuion for he differen ypes of 1 goods. The key parameer of he New Keynesian Phillips curve wih sicky prices is Θ p, which sands for he probabiliy ha prices remain he same in he curren period. Finally, he model is closed by specifying he shocks in equaions (7) - (10). For produciviy and preferences here is assumed ha hey follow AR(1) processes, while for moneary policy and supply shocks, we simply assume hey are no correlaed over ime The New Keynesian Model wih Sicky Prices and Indexaion We look firs a a very used modificaion of he NK Phillips curve which consiss in allowing for backward-lookingness. This exension has been proposed by Gali and Gerler (1999) who have shown ha i can improve he modeling of inflaion dynamics wih respec o inflaion ineria. A sandard specificaion for a NK Phillips curve wih backward-lookingness is given below: p p b ' 1 f Ep 1 k pmc (14) Where k ' p k p 1 b 1 5

6 f 1 The newly inroduced parameer ω measures he degree of price indexaion relaive o he las period The New Keynesian Model wih Sicky Informaion We also consider he inroducion of he sicky informaion hypohesis wihin he Phillips curve. By changing only he Phillips curve, we are able o compare he differen specificaion of he Phillips curve wihin he same New Keynesian model. In his case, he opimizaion decision by he firms is changed. The firms now maximize he expeced profi in a monopolisic environmen facing sicky informaion. We assume a raher sandard specificaion as presened below: (15) j mc 1 E mc 1 j0 1 j The parameer ha measures he degree of informaion sickiness is ψ. The higher he parameer, he larger he number of firms ha updae heir informaion. Firms updae heir informaion every 1/ψ period. 3. The Esimaion of he New Keynesian Models 3.1. Daa We use he daa se proposed in he original paper by Rabanal and Rubio - Ramirez (2005). In doing so, one hand we are able o compare our resuls wih heirs. A he same ime, since his is no a replicaion exercise, we did no aim a obaining perfecly similar resuls, which would have been hard given he sensiiviy of he Bayesian esimaion o he prior choices, see Del Negro and Schorfheide (2008). On he oher hand, we are able o compare he inroducion of sicky informaion wih sicky prices and sicky prices and indexaion wihin models which are well known and esed. No a las, we provide an addiional esing of he 6

7 proposed model (a leas for he cases of he sicky prices and sicky prices wih indexaion), by providing a comparison of forecas accuracies. The daase comprises also, besides he hree key variables in any New Keynesian model, namely inflaion, ineres rae and he real oupu, he real wage, reflecing he inclusion of a wage decision in he model. The daa sources are he Bureau of Labor Saisics for oupu, prices and wages and he FRED daa base (based on he Board of Governors of he Federal Reserve Sysem) for he ineres rae. The oupu is given by he oupu for he non-farm business secor, and he corresponding deflaor as a measure of prices. The nominal wage is given by he compensaion a hourly level for he nonfarm business secor. The ineres rae, as i is usually done, is given by he federal funds rae. The sample for he series lass from he firs quarer of 1960 o he las quarer of The sample size is reasonable long o perform boh Bayesian esimaions and forecasing. Before using he daa series, all he series are demeaned as well as derended based on a quadraic rend, as i was done in he original paper by Rabanal and Rubio-Ramirez (2005) The Esimaion of he New Keynesian models We discuss in his secion he procedure o esimae he models and he resuls. We esimae he model given by equaions (1)-(12), as well as he wo alernaive specificaions. The model is comprised from he following variables: y, a, r, Δp, Δw, n, mc, rw, mrs, g, λ şi ms represening he oupu, he oal facor produciviy, he ineres rae, he inflaion, he growh rae of nominal wage, he labor effor, he marginal cos, he real wage, he marginal rae of subsiuion, he preference shocks, he inflaionary shock as well as he ineres rae shocks. Before esimaing he models, some of he parameers were calibraed. We calibraed some of he parameers based on he resuls in he lieraure. For example, he discoun facor β was calibraed a 0.99, while he γ parameer was se a 1. The parameer ε is also calibraed since, as i is argued in he original paper by Rabanal and Rubio Ramirez (2005), his parameer canno be esimaed a he same ime wih he parameer θ ha characerizes he degree of rigidiy of prices, namely how ofen he producers updae he prices. 7

8 The esimaion paradigm is he Bayesian one, and i is argued in he lieraure ha his is an adequae approach in dealing wih srucural models. We used wo chains of Meropolis Hasing draws, each wih a lengh. The resuling esimaions for each case are checked wih respec o convergence resuls (based on Brooks-Gelman saisics), univariae and mulivariae, as well as he accepance raes ha are ensured o lie beween 20 and 40%, he opimal range. The resuls of he esimaions are presened in Annex 1, Table 1.1 for he sandard New Keynesian model, Table 1.2 for he New Keynesian model wih sicky informaion and Table 1.3 for he New Keynesian model wih boh sicky prices and indexaion. We have repored he esimaes for he full sample. The firs hing we remark is ha he esimaion is sable across he differen specificaions as he differences beween he poserior means are raher minor. There is also, generally, a reasonable variaion beween he prior disribuions and he poserior disribuions. The esimaes of he Taylor rule are wihin he expeced range and confirm he general resuls in he lieraure. The esimaed coefficien for inflaion is around 1.5, indicaing an acive moneary policy. The smoohing parameer for he ineres rae is moderae, indicaing a moderae moneary policy. The esimaes are slighly lower han he ones in Rabanal and Rubio- Ramirez (2005). There are some larger differences as compared o he esimaes in he original paper, when i comes o he oupu coefficien. The esimaion of θ p suggess a moderae degree of price sickiness. There is larger price sickiness in he NK model ha allows for price indexaion. The price indexaion is moderae o srong, he poserior mean being esimaed a The degree of sicky informaion is however prey large, he firms updaing heir informaion every 9 periods (he inverse of he esimaed value of he degree of sicky informaion ψ). 4. Comparing he forecasing accuracy of he esimaed models In his secion we furher analyze he resuls of he esimaions based on he accuracy of he forecass. We performed ou-of-sample forecass for each of he models. The forecass were done in a recursive manner wih an ou-of-sample of 20 observaions (he ou-of-sample 8

9 approach is he ypical one in he DSGE lieraure), ha is o five years, corresponding o a sample beween Q and Q In order o check for he effec of he forecas horizon, we ran he forecasing exercises for differen horizons, ha is of 1 quarer, of 4 quarers and of 8 quarers. A firs measure o compare he forecas accuracies was based on he sandard RMSE saisic as presened below. We denoe he model by j each model, by h he forecas horizon, by τ 0 he beginning of he sample for forecas, namely 1997 Q1, by τ he τ-h predicion of a model for oupu for h seps in he fuure, and by 0 yi, h he acual observaion, while i is he variable of ineres, hen we can wrie: RMSE( h, i, j) T h 0 y 0 i, h E y j i, h T 2 (16) T h Given ha he RMSE saisic is, generally, no sufficienly informaive, we compue he forecas accuracies based on he Diebold Marion es ha allows o discriminae beween he compued RMSE of differen models. Annex 2 presens he RMSEs for each model for every corresponding forecas horizon. We have included he forecass only for inflaion and oupu. For he case of inflaion, he choice is jusified since we assume differen specificaions for he Phillips curve and hus we would expec he differen specificaions of he Phillips curve o significanly influence he dynamics and forecass of inflaion. We are also ineresed in checking he impac of he differen specificaions on he forecasing accuracy for oupu. Table 1. Diebold Mariano es resuls for oupu Forecasing Horizon M2 vs. M1 M3 vs. M1 M3 vs. M2 1 sep ahead seps ahead seps ahead Source: Own Compuaions 9

10 Table 2. Diebold Mariano es resuls for inflaion Forecasing Horizon M2 vs. M1 M3 vs. M1 M3 vs. M2 1 sep ahead seps ahead seps ahead Source: Own Compuaions. The resuls of applying he Diebold-Mariano es are presened in Table 1 for inflaion and Table 2 for oupu. We have compared no only he model wih sicky informaion (named M3 in he wo ables) o he wo models wih sicky prices (M1 is he baseline model, while M2 is he model wih boh sicky prices and indexaion), bu we have also compared he model exended wih indexaion o he baseline model. When looking a he resuls for oupu, we ha he resuls are mixed across specificaions and forecasing horizons, alhough we can observe ha a lower forecas horizons, 1 and 4 seps ahead, he baseline model M1 is beer han he model wih indexaion M2, however a 8 seps he model augmened wih indexaion becomes beer. The resuls for inflaion are, as we would have expeced, much clearer. Boh he exended model wih indexaion M2 and he model wih sicky informaion M3 clearly ouperform he baseline model a all forecas horizons. When models M2 and M3 are compared, he model wih indexaion M2 ouperforms he model wih sicky informaion a leas for 1 and 4 sep ahead forecass, and also has a lower RMSE a 8 seps ahead forecass. The resuls poin o he fac ha here is some uiliy in adoping he informaion sickiness, a leas when comparing o he baseline model. However his advanage becomes less clear when richer specificaions of a New Keynesian model are used, in our case, he price indexaion, and generally confirm he laes findings on his issue. 10

11 5. Conclusion We esimaed hree New Keynesian models which differ wih respec o he specificaions of he Phillips curve. Besides he sandard sicky prices, we have also considered he inroducion of indexaion as well as sicky informaion. The resuls of he esimaions are generally in line wih hose from he lieraure, poin o moderae sicky informaion and moderae o srong sicky informaion. The models were furher compared based on he abiliy o accuraely forecas oupu and inflaion. For he case of oupu, we have raher mixed resuls, no specificaion being clearly beer han he oher ones, alhough he baseline model appears o produce beer forecass in he shor run compared o he model wih indexaion, while he model wih indexaion performs beer in he medium run. This lack of definie resuls may come from he fac ha he oupu dynamics are much more influenced by differen srucural parameers and rigidiies. There are clearer resuls when forecasing inflaion. Beer forecass resul when using sicky informaion as compared o he baseline model, bu he sicky informaion model is ouperformed iself when indexaion is inroduced. These resuls are in line wih he laes findings in he lieraure ha poin o he fac ha alhough here is some value of inroducing sicky informaion, beer resuls can be obained wih more complex specificaions for he New Keynesian models wih sicky prices. The paper conribues o he growing ineres on he role of imperfec informaion oo and can be a saring poin o fuure research on he role of imperfec informaion, learning and bounded raionaliy in obaining accurae forecass. References Arslan, M.M. (2008). Dynamics of sicky informaion and sicky price models in a New Keynesian DSGE framework, Economic Modelling 25: Calvo, G.A. (1983). Saggered Prices in a Uiliy-Maximizing Framework," Journal of Moneary Economics 12(3):

12 Carrillo, J.A. (2012). "How well does sicky informaion explain he dynamics of inflaion, oupu, and real wages?" Journal of Economic Dynamics & Conrol 36: Collard, F., and H. Dellas (2004). Sicky Prices versus Sicky Informaion. A Horse Race," mimeo. Clarida, R., J. Gali and M. Gerler. (1999). The Science of Moneary Policy: A New Keynesian Perspecive, Journal of Economic Lieraure 37(4): Del Negro, M., and F. Schorfheide (2008). "Forming Priors for DSGE models (and How I Affecs he Assessmen of Nominal Rigidiies)," Journal of Moneary Economics 55: Döpke, J., J. Dovern, U. Frische and J. Slacalek. (2008). "Sicky Informaion Phillips Curves: European Evidence," Journal of Money, Credi, and Banking 40(7): , Gali, J. and M. Gerler. (1999). Inflaion Dynamics: A Srucural Economeric Approach, Journal of Moneary Economics 44 (2): Guangling, L., R. Gupa and E. Schaling. (2009). "A New-Keynesian DSGE model for forecasing he Souh African economy," Journal of Forecasing 28(5): Keen, B. (2007). Sicky Price and Sicky Informaion Price Seing Models: Wha is he Difference? Economic Inquiry 45 (4): Kiley, M.T. (2007). A Quaniaive Comparison of Sicky-Price and Sicky-Informaion Models of Price Seing, Journal of Money, Credi and Banking 39: Lucas, R. (1972). Expecaions and he Neuraliy of Money, Journal of Economic Theory 4 (2): Mankiw, N. G. and R. Reis. (2002). Sicky informaion versus sicky prices: a proposal o replace he New Keynesian Phillips curve, Quarerly Journal of Economics 117 (4): Mahes, C. and M.-C. Wang. (2012). "The Real Predicive Abiliy of New Keynesian Models," mimeo. Pausian, M. and E. Pylarczyk. (2006). Sicky conracs or sicky informaion? Evidence from an esimaed Euro area DSGE model, mimeo. Rabanal, P. and J.F. Rubio-Ramírez. (2005). Comparing New Keynesian Models of he Business Cycle: A Bayesian Approach, Journal of Moneary Economics 52 (6):

13 Rabanal P. and Juan Francisco Rubio-Ramirez. (2008). Comparing New Keynesians Models in he Euro Area: A Bayesian Approach, Spanish Economic Review 10 (1): Rubaszek, M. and Skrzypczyński, P. (2008). "On he forecasing performance of a smallscale DSGE model" Inernaional Journal of Forecasing 24: Traband, M. (2006). Sicky Informaion vs. Sicky Prices: A Horse Race in a DSGE Framework, Working Paper, Humbold Universiy Berlin. Smes, F. and R. Wouers. (2003). An Esimaed Sochasic Dynamic General Equilibrium Model for he Euro Area, Journal of he European Economic Associaion 1 (5): Wang, M-C. (2009). "Comparing he DSGE model wih he facor model: an ou-ofsample forecasing experimen," Journal of Forecasing 28(2): Walsh, Carl. (2003). Moneary Theory and Policy. The MIT Press, Cambridge, Massachuses, London, England. ANNEX 1. Resuls of he esimaion Table 1.1.The resuls of he Bayesian Esimaion for Sicky Prices Model Parameers Mean Prior Mean Poserior Confidence Inerval Confidence Inerval Prior Disribuion Sandard Deviaion ρ r Bea 0.10 γ π Normal 0.10 γ y Normal 0.10 θp Bea 0.15 e_a Uniform 0.02 e_g Uniform 0.02 e_ms Uniform 0.02 e_lam Uniform 0.02 Source: Own Compuaions 13

14 Table 1.2. The resuls of he Bayesian Esimaion for Sicky Prices wih Indexaion Model Parameers Mean Prior Mean Poserior Confidence Inerval Confidence Inerval Prior Disribuion Sandard Deviaion ρ r Bea 0.10 γ π Normal 0.10 γ y Normal 0.10 θp Bea 0.15 ω Bea 0.15 e_a Uniform 0.02 e_g Uniform 0.02 e_ms Uniform 0.02 e_lam Uniform 0.02 Source: Own Compuaions. Table 1.3. The resuls of he Bayesian Esimaion for Sicky Informaion Parameers Mean Prior Mean Poserior Confidence Inerval Confidence Inerval Prior Disribuion Sandard Deviaion ρ r Bea 0.10 γ π Normal 0.10 γ y Normal 0.10 ψ Bea 0.15 e_a Uniform 0.02 e_g Uniform 0.02 e_ms Uniform 0.02 e_lam Uniform 0.02 Source: Own Compuaions. ANNEX 2. RMSEs of he forecass wih DSGE models Table 2.1. Resuls for oupu Forecasing Sicky Sicky prices & Sicky informaion Horizon prices indexaion 1 sep ahead seps ahead seps ahead Source: Own Compuaions 14

15 Table 2.2. Resuls for inflaion Forecasing Sicky Sicky prices & Sicky informaion Horizon prices indexaion 1 sep ahead seps ahead seps ahead Source: Own Compuaions. 15