Lags from Money to Inflation in a Monetary Integrated Economy: Evidence from the Extreme Case of Puerto Rico. Abstract

Transcription

1 Lag from oney o Inflaon n a oneary Inegraed Economy: Evdence from he Exreme Cae of Puero Rco Carlo A. Rodríguez * Abrac Th paper ude he me lengh of he long and hor run effec of money growh over nflaon n an economy wh a hgh degree of moneary negraon: he cae of Puero Rco. The gnfcan nfluence of polcy nervenon and own pa and whch have greaer nfluence over he nflaon wll be alo analyzed. oney growh meaured a he rae of growh of oal bankng depo and nflaon wh he rae of growh of he Conumer Prce Index. Accordng o he reul, a dynamc expanon of money refleced on prce mmedaely, bu he unary effec occur approxmaely n en quarer. Alo, local nflaon gnfcanly nfluenced by polcy nervenon and own pa hory, bu polcy nervenon have a greaer nfluence. Undad de Invegacone Económca Deparameno de Economía Unverdad de Puero Rco Recno de Río Pedra Enayo y onografía Número 139 epembre 28 * Caedráco Aocado de Economía, Unverdad de Puero Rco, Recno de Río Pedra.

2 1 Facore que ncden obre la pobldad de una deaceleracón económca en Puero Rco I. Inroducon Accordng o monear hough, nflaon, n eence, a moneary phenomenon n he ene ha a dynamc ncreae n he general level of prce mu be due o he rae expanon of he moneary upply whch exceed he growh n amoun of money demanded by economc un. In he evene and n he begnnng of he eghe auhor lke Shapro, (1973), Selden (1975), Rogalky and Vno (1977), Alogokouf and Parde (1983) and Barh and Benne (1975), ndcaed ha h bond beween nflaon and change n he money upply no nananeou. A ha me, moneary aggregae (1 o 2) were condered he be moneary polcy ndcaor n he Uned Sae. In ha cae, moneary auhore focued on long run nflaonary dynamc accordng o he followng objecve funcon: mn T [, m( ), m& ( ) ]d (1) Subjec o: m ( ) = m and m( T ) = mt (2) Where: he nflaon rae, he me, m( ) he money upply, m& () he money growh and m ( ) = m, m( T ) = mt are he endpon condon. Snce he 1982, he Federal Reerve Syem of he Uned Sae ue he fed fund nere rae a a moneary polcy nermedae objec, o conrol nflaon, growh and unemploymen. In h cae, he moneary polcy proce urn ou o be endogenou. However, n h fr repor o he Congre he new Charman of he Federal Reerve, Ben Bernanke, pon ou he followng: Wh he economy expandng a a old pace, reource ulzaon rng, co preure ncreang, and hor-erm nere rae ll relavely low, he Federal Open arke Commee (FOC) over he coure of 25 connued he proce of removng moneary polcy accommodaon, rang he federal fund rae 2 percenage pon n egh ncremen of 25 ba pon each. A meeng on January 31 of h year, he FOC raed he federal fund rae anoher 1/4 percenage pon, brngng level o 4-1/2 percen. Alhough he oulook conan gnfcan uncerane, clear ha ubanal progre ha been made n removng moneary polcy accommodaon. A a conequence, n comng quarer he FOC wll have o make ongong, provonal judgmen abou he rk o boh nflaon and growh, and moneary polcy acon wll be ncreangly dependen on ncomng daa. (Semannual oneary Polcy Repor o he Congre, Before he Commee on Fnancal Servce, U.S. Houe of Repreenave, February 15, 26). Thee rae n he nere rae, due o a more exogenou polcy, wll have drec effec n frm ha are enble o h varable. In h cae, econome wh a greaer number of frm ha depend on bankng loan o fnance her nvemen wll be more enve o he moneary polcy. On he oher hand, f he unary effec of money growh over he nflaon are no

3 Carlo A. Rodríguez 2 nananeou, her effec over he economy wll la for ome perod. For example, he nomnal nere rae, ha he real nere rae plu he nflaon, wll have a uanable growh due o he prce ncreae. Th paper eek o conrbue o h opc, reakng he approach of money growh nflaonary effec n econome wh a hgh degree of moneary negraon. Th work wll parcularly addre he followng ue: 1. he me lengh of he unary effec of money growh on nflaon; 2. he hor run effec of moneary growh on nflaon; 3. f polcy nervenon or pa nflaon exer gnfcan nfluence on he nflaonary proce; 4. f nervenon nfluence he evoluon of he nflaon more han nflaon own pa. In h paper, he economy of Puero Rco wll be uded a an exreme cae becaue: 1. a commonwealh errory of he Uned Sae; 2. he dollar he offcal currency; 3. ubjec o he U.S. bankng regulaon; 4. here free rade beween boh econome; 5. here a hgh concenraon of U.S. frm parcularly n he manufacure and commerce ecor. To develop h work, he econd par preen he heorecal foundaon and ome economerc conderaon ha wll be very ueful n aeng he emprcal evdence. The la par preen he general concluon. II. Theorecal and economerc conderaon Th econ preen a general cheme of he andard heorecal expoon ha ugge he relaon of he varable ued n he emprcal analy. Th cheme are from he analy of he quany equaon of money, arng from he followng defnon of exce demand n he money marke: (Z m ): Z m d ( ) = (3) Where d and repreen he money demand and upply, repecvely. To analyze nflaon dynamc, equaon (1) hould be expreed n quany form: Z = kpy (4) m ( ) In whch k he money velocy recprocal (whch aumed conan), P he prce level, Y he real producon level and PY he nomnal producon level. In equlbrum: kpy = (5) ( ) Th o ay: kpy =. (6)

4 3 Facore que ncden obre la pobldad de una deaceleracón económca en Puero Rco Dfferenang h equaon obaned: dv + V d = Y dp + P dy. (7) Where he money velocy V. Combnng (7) wh he quany equaon of money yeld: dv V V d V Y dp P dy = + PY PY +. (8) dv V dy Y, By he conan velocy aumpon: =, and by he money neuraly poulae = equaon (8) may be wren a: d dp P = (9) When udyng h relaon n a moneary yem negraed no anoher, mu be borne n mnd ha he capacy of local auhore o generae a local moneary polcy and moneze deb wh own currency praccally null. In h cae, h yem canno ue moneary polcy o ablze economy. Th mple ha he local money upply depend on he moneary condon of he moneary yem o whch negraed. In addon, becaue of he common currency, he local moneary upply a proporon of ha of he counry o whch he local yem negraed. The equaly expreed n (9) can be adaped o he followng ochac funconal form, whch f he daa be: P β µ ( ι & ) e & = (1) Where ι he money upply proporon ha correpond o he negraed counry; d = & for perod, β repreen he nflaon elacy repec o he money upply and u he error erm, wh zero mean and conan varance. In logarhm: p & = β ( ι m& ) + µ (11) In whch he mall cae leer repreen he logarhm of he varable. Snce he proporonal change of nflaon n repone o he money upply n h ype of economy ake everal perod, equaon (11) can be preened a a general form of a drbued lag model: p & = β ι m& + µ (12) = ( ) Aumng ha money grow more or le a he ame rae, he [ ] p ~ = ~ = = β ~ ( ι m& ) ~ ( ι m& ) = β P& = dp P E & equlbrum value wll be: Where he permanen value of local nflaon and money growh n he negraed counry are p and m ~ & o. Therefore, for (13) o be fne mu fulfll: (13) and ~ &

5 Carlo A. Rodríguez 4 = β < (14) Accordng o he unary effec: lm = β = 1. (15) The hor run effec wll be approxmaely: = β ( ) β = = = B β ι m&, whch known a he equlbrum mulpler. Equaon (12) may be wren n erm of drbuve lag a: ( ι m& ) ( L)( ι m& ) + µ and he long run effec wll be: = β L + µ = (16) Where L repreen he lag operaor and B(L) he polynomal n L B( L) Th model can be rewren (16), a: = ( λ L) ( ι m& ) p & = β + µ (17) 2 ( = + β L + β +K) β. 1 2 L Where λ known a he movng average form or he drbuve lag. Th equaon can be rewren a: β ( ι m& ) p & = + µ (18) ( 1 λl) ulplyng by (1- λl) and groupng: p & = β ( ι m& ) + λ 1 + v (19) Where, v = µ λµ 1. In h cae, he maller λ he greaer wll be he relave effec of moneary polcy nervenon from he counry o whch he local yem negraed. In h ype of model, bede analyzng he long run mulpler, he medan lag mean lag λ 1 λ log 2 log λ wll be ued a a ummary meaure of he peed wh whch nflaon repond o money growh. Alo one may analyze he proporon of he long run effec n perod : β β * = (2) β Snce, n h ype of model, he unary value drbued hrough me wh wegh declnng down o zero. In he long run, he ne effec of he dynamc ncreae n he general level of prce mu be proporonal o money upply growh and h rae of expanon wll be: T [, ι m( ), ι m& ( ) ] d = 1 (21) and

6 5 Facore que ncden obre la pobldad de una deaceleracón económca en Puero Rco The hor run repone of local nflaon wll depend a much on moneary polcy nervenon a on own pa. Accordng o (19), β > λ f he local nflaon depend le on pa han on money growh. On he conrary f β < λ he pa of he varable wll have more nfluence. Thu, he value of h parameer deermne wheher a feedback rule ued by he Federal Reerve or local upply and demand facor wll be more effecve n reranng he local nflaonary proce. Under h regme, hgh rae of nflaon n he pa could caue a polcy o ncreae nere rae o conrol he nflaonary phenomenon. If he polcy were effecve hen he nflaon rae n he fuure would be reduced, hereby affecng h varable n negraed yem mlar o Puero Rco. On he oher hand, maller hor run elacy and maller λ coeffcen mean ha ake more me o fulfll he unary effec n prce, and vce vera. III. Emprcal Evdence A. Daa conderaon One of he more mporan apec n h paper he ype of varable o ue. Alhough monear heory expoe clearly he varable o nclude, he conformaon of he moneary ecor and he acal yem n Puero Rco ugge he elecon of proxy. Fr of all, he mplc deflaor n Puero Rco calculaed annually. However, he daa reflec a hgh correlaon beween h varable and he conumer prce ndex (CPI), whch calculaed quarerly. For h reaon, he CPI wll be ued a a proxy. v Graph 1: Scaer Plo beween he Gro Produc Deflaor v and Conumer Prce Index (CPI) Gro Produc Deflaor On he oher hand, he only mode of money creaon n Puero Rco hrough bankng depo. In addon, bank n Puero Rco are ed o he Federal Reerve Syem of he Uned Sae and he dollar, a he local currency. In h cae, U.S. polcy acon wll have drec effec n he Puero Rcan yem (Toledo, 22; Rodrguez and Toledo, 26). CPI Th work aume ha oal bankng depo are a good approach of money upply 1 ι m& wll be repreened by he growh of (Toledo, 1996; Rodrguez, 25). Tha mean ha ( )

7 Carlo A. Rodríguez 6 oal bankng depo. The ue of h varable doe no elmnae U.S. polcy effec on he economy of Puero Rco (Toledo, 1996). B. Lag Beween oney Growh and Inflaon From he emaon of (19), he reul are: Table 1 oney - Inflaon Equaon Lnear Regreon - Emaon by Inrumenal Varable Dependen Varable GLP Quarerly Daa From 1996:1 To 25:4 Uable Obervaon 4 Degree of Freedom 38 Cenered R** R Bar ** Uncenered R** T x R** ean of Dependen Varable Sd Error of Dependen Varable Sandard Error of Emae Sum of Squared Redual Durbn-Waon Sac Durbn-h Varable Coeff. T-Sa Sgnf. ******************************************************* β λ Table 2 Shor and Long Run Impac ulpler Varable Coeffcen β λ β 1 = β λ β 2 = β λ β 3 = β λ β 4 = β λ β 5 = β λ β 6 = β λ β 7 = β λ β 8 = β λ.55

8 7 Facore que ncden obre la pobldad de una deaceleracón económca en Puero Rco 9 β 9 = β λ.22 1 β 1 = β λ.9 β Lag medan Lag mean The parameer are gnfcan a a 5 percen gnfcance level and he model doe no preen auocorrelaon problem, accordng o he Durbn-h e. Accordng o Table 2, he maxmum effec occur n a perod of en quarer, wh he long run elacy beng equal o The greaer effec occur n he hor run wh: = ( ). Th mean ha, n he ι m& hor run, a one percen ncreae n nde money generae an ncreae of approxmaely.67 percen n nflaon. Accordng o he reul of he medan lag and he mean lag, nflaon repond rapdly o money growh change. Neverhele, 1 quarer are requred for he unary effec on nflaon. IV. Concluon Th work nvegae he emporary lengh of he unary change beween nflaon and money growh n a moneary negraed economy. The cae of Puero Rco wa uded hrough he drbued lag analy baed on he quany equaon. Accordng o he emprcal evdence a dynamc expanon of money n h ype of economy refleced on prce mmedaely, bu he long run effec occur approxmaely n en quarer. Local nflaon receve gnfcan nfluence of he polcy nervenon and own pa. However, polcy nervenon have a greaer nfluence becaue β > λ. For he cae of Puero Rco, h mean ha he nvemen projec ha are enble o bankng loan wll alo be enve o he Uned Sae moneary acon. The mayor effec wll la wo quarer. An exogenou moneary polcy n he Uned Sae wll have a rapd ncreae over he nflaon of Puero Rco and wll have a greaer effec n he hor run local nvemen. Tha mean ha he prce of he local commode ha are enve o hee acon wll be affeced mmedaely. However, he fnal reul wll depend on he ype of polcy conduced by he FED.

9 Carlo A. Rodríguez 8 V. Reference Barh, J. R. and Benne, J. T. (1975) Co-puh veru Demand-pull Inflaon: Some Emprcal Evdence: Commen, Journal of oney, Cred and Bankng, 7, Rodríguez, C. (25). La eabldad de la demanda de dnero en Puero Rco, Reva de Economía y Negoco, 1, and W. Toledo (26). Lo efeco de la aa de lo fondo federale de lo Eado Undo en una economía pequeña, abera y dolarzada: el cao de Puero Rco, unpublhed paper. Rogalky, R. R. and J.D. Vno (1977) Sock Reurn, oney Supply and he Drecon of Caualy, The Journal of Fnance, 32, Selden, R. T. (1975) oney Growh and he Long-Rae of Inflaon, The Amercan Economc Revew, 65, Shapro, A. A. (1973) Inflaon, Lag, and he Demand of oney, Inernaonal Economc Revew, 14, Toledo, W. (1996) La neuraldad del dnero: Una dcuón de la leraura y un anál empírco para Puero Rco, Sere de Enayo y onografía de la Undad de Invegacone Económca, 78, Y Snce, f P he Gro Domec Produc Deflaor he expreon PY : N * Y, where Y N he Nomnal Gro Y Domec Produc. dy The poulae ha = re on he noon ha change n real producon depend on producvy, Y echnologcal progre and knowledge, and no on moneary varable. Th are accordng o he followng lag operaor polynomal (Ender, 24; Paeron, 2): 2 ( λl) + ( λl) = A( L) = 1+ λl + K. If, < 1 = λ, h polynomal : A( L) 1 =. 1 λl v However, hould be noed ha Puero Rco bake of good and ervce dae back o Therefore, recen flucuaon n he prce of mporan good are no condered. v Unlke many counre, n Puero Rco he Gro Naonal Produc ued nead of he Gro Domec Produc (GDP) becaue he producon relaed o exernal nvemen gnfcanly hgh. In h cae, he Gro Naonal Produc a beer meaure of nernal acvy.