Ready for euro? Empirical study of the actual monetary policy independence in Poland VECM modelling

Transcription

1 Macroeconomerics Handou 2 Ready for euro? Empirical sudy of he acual moneary policy independence in Poland VECM modelling 1. Inroducion This classes are based on: Łukasz Goczek & Dagmara Mycielska, "Ready for euro? Empirical sudy of he acual moneary policy independence in Poland," Working Papers , Faculy of Economic Sciences, Universiy of Warsaw. You can find link o his aricle here: hps://ideas.repec.org/p/war/wpaper/ hml You should copy raes.wf1 and vec_anoruo.wf1 ino he chosen folder. 2. Moneary Independence Hypohesis Inerbank ineres raes are he mos appropriae measures of he moneary policy sance in wo currency areas (Bernanke and Blinder, 1992). If domesic inerbank ineres raes reac o changes in he domesic moneary policy sance according o expecaions, his means ha his counry enjoys a large degree of moneary policy independence. If, however, inerbank ineres raes reac mosly o foreign ineres rae changes or if he wo economies are inricaely linked, as dicaed by close movemens of heir hreemonh inerbank ineres raes, i is unlikely ha domesic moneary policy exers much independence. An alernaive o his approach would be he use of he reference raes of he relevan cenral banks. These variables, however, change very infrequenly and show low variance. Moreover, i could be argued ha hese do no ake ino accoun marke expecaions; however, mos imporanly, i could be ha he cenral bank does no have any policy effeciveness despie seing is reference ineres raes relaively far from he ineres rae pariy. Hence, inerbank ineres raes provide an effecive means for invesigaing moneary policy independence and, based on he above lised reasons, i could be argued ha he measures of ineres raes chosen for he empirical model esimaed in he aricle are indeed appropriae. Le us consider he following Uncovered Ineres Pariy condiion: i i * E ( e e ) (1) 1 where is he difference operaor, i is he domesic nominal ineres rae, i* is he foreign nominal ineres rae, E is he expecaion operaor, e is he nominal exchange rae, is he risk premium and is he ime index. Moving (1) ino firs differences we obain: i i * E ( e e ) (2) 1 In a fixed exchange rae regime, he exchange rae is consan, and he depreciaion erm becomes zero. Assuming ha he risk premium does no affec he change in ineres raes and he expeced fuure exchange rae remain he same, he domesic ineres rae moves one on one wih he foreign rae change, ha is, here is a full ransmission of foreign ineres raes: i i * (3) According o he arge zone models he ineres raes may diverge persisenly under a flexible exchange rae regime only if he domesic policies are credible and he moneary auhoriy primarily arges Łukasz Goczek 2014/2015 1

2 Macroeconomerics Handou 2 domesic economic variables such as inflaion and oupu. Therefore, he size and he lengh of he deviaion can be used o measure he degree of moneary policy independence. 3. VECM in EViews Vecor Error Correcion (VEC) model is mulivariae generalizaion of ECM model known from he previous classes. You can see i also as VAR model designed for use wih nonsaionary ime series ha are known o be coinegraed. The specificaion of VEC models conains he coinegraion relaions, so i assumes ha he economy converges o he long-run relaionships. On he oher hand, i allows also for he shor-run adjusmen dynamics. Le us consider wo ime series for domesic and inernaional ineres raes ha form a bivariae daa vecor X given by: X i i* (4) The domesic inerbank ineres rae (Wibor_3M) is denoed by i, and he inernaional inerbank ineres rae (Euribor_3M) is denoed by i*. The wo variables are used o form a Vecor Auoregressive (VAR) model described by he following equaion: 0 1 i1 i i K X X u (5) 2 where he error erm u N(0, ) is uncorrelaed over, he daa vecor he number of lags, and X is p T dimension, K is i is he deerminisic coefficien marix (consan and rend) of a dimension p p. If he daa generaion process is non-saionary in levels and saionary in firs differences, hen equaion (5) can be rearranged o form a vecor error correcion mechanism: where K 1 * * 1 i i i1 X X X u (6) X ( X,1, )', * 1 1 * K, i1 i I (, 0, 1) K and 1 i j i j. For he ease of exposiion he coefficiens for he lagged regressors and he deerminisic erms were grouped ogeher, which is similar o he aking of his problem in mos economeric packages. Under he assumpion ha u, he marix is of reduced rank for he equaion (3) o be balanced. If X ~ I(1) and ~I(0) is of reduced rank, hen here exiss p r marices and such ha ' and equaion (3) can be ransformed o a form aking ino accoun he decomposiion of long -run coefficiens: K 1 * ' 1 i i i1 X X X u. (7) The erm ' X is he coinegraing vecor 1 showing he seady sae relaionship beween he * 1 ineres raes. In he conex of ineres raes hose are linear combinaions, which hemselves are nonsaionary, bu he relaionship beween hem is saionary wih a seady sae coinegraing vecor forming uncovered ineres rae pariy. 1 Under he condiion ha is of a reduced rank. Łukasz Goczek 2014/2015 2

3 Macroeconomerics Handou 2 If he marix is of rank one, i means ha a single coinegraing vecor exiss, and ' is 1 p +2 (consan and rend in he coinegraing relaionship). The coinegraing vecor can hen be rewrien as follows: 1 ' (,,, ) i i X (8) * * i * r If i is found during he empirical analysis of he wo ineres raes ha he rank is indeed one, his means ha here exiss a single coinegraion vecor - a single seady sae relaionship. This is an indicaion of moneary policy dependence in he currency areas. 4. VECM in EViews Remember, he coinegraion es is only valid if you have non-saionary series. Task: Find ou if he series: Wibor, Euribor are non-saionary. Check he inegraion order. Can hey be coinegraed? The purpose of he coinegraion es is o deermine wheher several non-saionary ime series are coinegraed or no. The presence of a coinegraing relaion forms he basis of he VEC specificaion. EViews implemens VAR-based Johansen ess. Le us open he series as a VAR: Esimae an unresriced VAR: Łukasz Goczek 2014/2015 3

4 Macroeconomerics Handou 2 Deermine lag lengh using informaional crieria: and hen selec View/Coinegraion Tes... Łukasz Goczek 2014/2015 4

5 Macroeconomerics Handou 2 Deerminisic componens assumpions of he Johansen es - Pracical guide: use case 1 only if you know ha all series have zero mean (unusual in empirical sudies); case 5 may provide a good fi in-sample bu will produce implausible forecass ou-of-sample.; use case 2 if none of he series appear o have a rend; use case 3 if series are rending and you believe all rends are sochasic; use case 4 if series are rending and you believe some of hem are rend saionary; use case 6 if you are no cerain which rend assumpion o use (Eviews will help you deermine he choice of he rend assumpion Łukasz Goczek 2014/2015 5

6 Macroeconomerics Handou 2 Here is he oupu: Unresriced Coinegraion Rank Tes (Trace) Hypohesized Trace 0.05 No. of CE(s) Eigenvalue Saisic Criical Value Prob.** None * A mos Trace es indicaes 1 coinegraing eqn(s) a he 0.05 level * denoes rejecion of he hypohesis a he 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Unresriced Coinegraion Rank Tes (Maximum Eigenvalue) Hypohesized Max-Eigen 0.05 No. of CE(s) Eigenvalue Saisic Criical Value Prob.** None * A mos Max-eigenvalue es indicaes 1 coinegraing eqn(s) a he 0.05 level * denoes rejecion of he hypohesis a he 0.05 level **MacKinnon-Haug-Michelis (1999) p-values The firs wo ables repor resuls for esing he number of coinegraing relaions. Two ypes of es saisics are repored: race saisics and he maximum eigenvalue saisics. For each able, he firs column is he number of coinegraing relaions under he null hypohesis, he second column is he ordered eigenvalues of he marix Π, he hird column is he es saisic, and he las wo columns are he 5% criical values. And he resuls overwhelmingly indicae one coinegraing equaion. Le us esimae he VECM. In he VAR oolbar click on Esimae and choose Vecor Error Correcion from he VAR Type ab. Remember ha now, lag inerval refers o firs differences of he variables in he VEC. Do no include consan and rend in he Exogenous Variables ab, hey should be specified in he Coinegraion ab. In ha ab you decide on he number of coinegraing equaions (less han he number of endogenous variables!) and he rend specificaion. If you wan o impose resricions on he coinegraing relaions and/or he adjusmen coefficiens, use he Resricions ab. Then click OK o esimae he VEC. Esimaion of a VEC model is carried ou in wo seps. Firs, using he Johansen procedure, he coinegraing relaions are esimaed. Then he error correcion erms is consruced from he esimaed coinegraing relaions and a VAR in firs differences including he error correcion erms as regressors is esimaed. Łukasz Goczek 2014/2015 6

7 Macroeconomerics Handou 2 The resuls: Coinegraing Eq: CoinEq1 WIBOR(-1) EURIBOR(-1) ( ) [ ] C ( ) [ ] Error Correcion: D(WIBOR) D(EURIBOR) CoinEq ( ) (9.6E-05) [ ] [ ] In he firs able you see resuls from he firs sep Johansen procedure (esimaes of coinegraing relaions). If you did no impose resricions, EViews will use a defaul normalizaion ha idenifies all coinegraing relaions. These resuls allow o alk abou no moneary independence in Poland. Diagnosic Views Task: Check for sabiliy of he model. Noe ha VECM imposes he roos of he equal number o he coinegraing equaions. Now le us view he errors: Łukasz Goczek 2014/2015 7

8 Macroeconomerics Handou 2 View/Coinegraion Graph... Graph of he residuals from he esimaed coinegraing relaions. Łukasz Goczek 2014/2015 8