International Parity Relations between Poland and Germany: A Cointegrated VAR Approach

Transcription

1 Research Seminar a he Deparmen of Economics, Warsaw Universiy Warsaw, 15 January 2008 Inernaional Pariy Relaions beween Poland and Germany: A Coinegraed VAR Approach Agnieszka Sążka Naional Bank of Poland & Warsaw School of Economics

2 0 Plan of presenaion 1 Inroducion 2 Some definiions 3 Inernaional pariy condiions 4 A visual inspecion of he pariies 5 The coinegraed VAR model 6 The empirical analysis 7 Summary and conclusions Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 1

3 1 Inroducion On 1 s May 2004 Poland joined EU and is obliged o join EMU afer having fulfilled he Maasrich crieria. Is Poland ripe for he euro (has i achieved a sufficien degree of convergence owards he euro area)? Usual perspecive: opimum currency area heory, comparing coss and benefis of moneary inegraion. This paper: inernaional pariy relaions, modelled joinly wihin he coinegraed VAR framework as in Juselius and MacDonald (2000, 2004). Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 2

4 1 Inroducion Specific quesions: Do he inernaional pariy relaions posulaed by economic heory hold for Poland relaive o he euro area (represened by Germany)? Wha are he common sochasic rends driving inflaion, ineres raes and he real exchange rae? Do he developmens in Poland significanly affec hose in he common currency area, or can he laer be reaed as exogenously given? Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 3

5 2 Some definiions 1) A sochasic process is (weakly) saionary if: ( ) μ x E x = is expeced value is consan for all (mean saionariy) ( ) 2 Var x = σ is variance is consan for all (variance saionariy) ( ) ( ) s = τ x τ s = γ τ Cov x, x Cov x, is auocovariance depends only on, bu no on (covariance saionariy) τ Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 4

6 2 Some definiions 2) A sochasic process is inegraed of order d, I (d), if i becomes saionary afer being differenced d imes. Saionary processes are inegraed of order 0, I (0). Uni roo processes are inegraed of order 1, I (1). If is I (d), hen Δx is I (d 1). x x Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 5

7 2 Some definiions x 3) Two (or more) sochasic processes are coinegraed of order d, b (wih b <d), CI (d, b), if hey are inegraed of order d and here exiss heir linear combinaion which is inegraed of order b. E.g. wo uni roo processes are coinegraed of order (1, 0) if here exiss heir linear combinaion which is saionary. Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 6

8 3 Inernaional pariy condiions 1) Purchasing power pariy (PPP): ppp = p p s p p s domesic price level foreign price level spo exchange rae (in price noaion) ppp deviaion from PPP (real exchange rae imes -1) Empirical es: esing wheher ppp is saionary. Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 7

9 3 Inernaional pariy condiions 2) Uncovered ineres pariy (UIP): s i s i ( ) s s s = i i Δ + s domesic nominal bond yield wih mauriy s foreign nominal bond yield wih mauriy s E Under raional expecaions: ε whie noise disurbance Combining he above equaions: Δ Δ ( Δs ) + s ε s s + s = E + + ( s s i ) i ε s s + s = + Empirical es: esing wheher is saionary. ε Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 8

10 3 Inernaional pariy condiions 3) Real ineres pariy (RIP, Fisher pariy): s r s r domesic real bond yield wih mauriy s foreign real bond yield wih mauriy s Fisher decomposiion: Under raional expecaions: ν whie noise disurbance Combining he above: r = Empirical es: esing wheher is saionary. Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 9 ν s r s ( ) Δp s ( Δp ) s + s s i = r + E + Δ p+ s = E + ( s s ) ( i ) i Δp s Δp s = + + ν ν

11 4 A visual inspecion of he pariies 1) Prices and exchange raes: PPP fails o hold Price differenial Poland - Germany and he spo exchange rae PDIFF S INFLDIFF Inflaion differenial and he deviaion from PPP PPP Inflaion differenial and he deviaion from PPP, derended INFLDIFFDETRENDE PPPDETRENDED Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 10

12 4 A visual inspecion of he pariies 2) Depreciaion rae and home vs. foreign ineres rae spread: UIP fails o hold Depreciaion rae and he ineres rae spread Poland - Germany BONDDIFF SCHANGE Depreciaion rae and he ineres rae spread, derended BONDDIFFDETRENDE SCHANGE Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 11

13 4 A visual inspecion of he pariies 3a) Real ineres raes: RIP fails o hold Real ineres raes POLAND GERMANY Real ineres raes, 12-monh moving averages MAPOLAND MAGERMANY Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 12

14 4 A visual inspecion of he pariies 3b) Home vs. foreign ineres rae and inflaion differenial: some evidence supporing RIP Ineres spread and he inflaion differenial Ineres spread and he inflaion differenial, 12-monh moving averages BONDDIFF INFLDIFF MABONDDIFF MAINFLDIFF Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 13

15 5 The coinegraed VAR model The coinegraed vecor auoregression (VAR) model in he vecor equilibrium correcion (VEC) form: x x x Δ = Π 1 + Γ1 Δ Γk 1Δ k+ 1 x + ΦD + ε x D ε Π, Γi, j 1 vecor of endogenous I (1) variables vecor of deerminisic componens vecor of i.i.d. Gaussian error erms Φ coefficien marices Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 14

16 5 The coinegraed VAR model x x x Δ = Π 1 + Γ1 Δ Γk 1Δ k+ 1 x + ΦD + ε The coinegraion hypohesis can be expressed as a reduced rank resricion on he marix Π: Π = α β α, β j r coefficien marices wih rank r, r j β x 1 α coinegraion relaions (seady sae or equilibrium relaions); pulling forces adjusmen coefficiens marix; pushing forces Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 15

17 5 The coinegraed VAR model The moving average (MA) represenaion of he model: x ~ = s + s= 1 ~ β α ε + C ( L) ε A, β = β ( α β ) 1 common sochasic rends heir loadings α, β C ( L) orhogonal complemens o α, β : ( α, α ) rank( β, β ) = j, α α = 0, β β 0 rank = = lag polynomial; A depends on iniial values Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 16

18 5 The coinegraed VAR model Relevan variables: The I (2)-ness problem: Transformed vecor: x x p [ p p i i s ] = ~ I = ( 2) [ ] Δp Δp i i ppp ~ I() 1 Sylised scenario: Neoclassical world: j r = 2 common sochasic rends (CT) and r = 3 coinegraion relaions (CR) Nominal rigidiies, rade barriers, facor immobiliy, informaion asymmery ec.: j r = 3 CT, r = 2 CR Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 17

19 6 The empirical analysis 1) Daa descripion Poland = home counry, Germany = foreign counry Sample covering 1994:M1 o 2006:M1 Time series: monhly daa, no seasonally adjused Prices: CPI (source: IMF IFS) Ineres raes: Treasury bill raes (source: IMF IFS) Exchange rae: end-of-monh DM/PLN spo rae as announced by he Naional Bank of Poland Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 18

20 6 The empirical analysis 2) VAR specificaion and esimaion, specificaion ess VAR specificaion: unresriced consan, cenred seasonal dummies, oher dummies; lag lengh: 2 Residual ess: no auocorrelaion; normaliy rejeced due o excess kurosis, bu no skewness problems; residuals from equaion 3 exhibi ARCH effecs Assumpions ha are crucial for valid saisical inference (no auocorrelaion, no skewness) are saisfied. Parameer consancy confirmed by recursive ess Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 19

21 6 The empirical analysis 3) Deerminaion of he coinegraion rank Trace (Johansen) es r = 2 ; problem: low power Graphs of coinegraion relaions r = 2 Roos of he companion marix j r = 3, i.e. r = 2 The unresriced esimae of he marix α r = 2 Recursively calculaed race es saisics The sysem variables are pulled by 2 CR (equilibrium relaions, seady saes) and pushed by 3 CT. r = 2 Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 20

22 6 The empirical analysis 4) Tesing resricions on he parameers of he marix α a) Tess of a zero row in, i.e. of a uni vecor in = esing he long-run weak exogeneiy of a variable A variable is weakly exogenous if i influences he oher variables, bu is iself no influenced by hem. α b) Tess of a uni vecor in, i.e. of a zero row in = esing wheher a variable is exclusively adjusing A variable is exclusively adjusing if shocks o i have only emporary effecs on he oher variables. α α α Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 21

23 6 The empirical analysis Tesing resricions on he marix resuls: i) i and ppp are individually weakly exogenous. ii) and ppp are also joinly weakly exogenous. i Cumulaed shocks o he German bond rae and he deviaion from PPP (he real exchange rae) define wo of he hree common rends pushing he sysem. iii) No variable is exclusively adjusing. α Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 22

24 6 The empirical analysis 5) Tesing resricions on he parameers of he marix Tess of saionariy of he model variables and heir linear combinaions = looking for meaningful CR Aim: finding ou wheher he linear combinaions of he model variables defined by inernaional pariies: a a ( ) ( i ) i b Δp Δp c ppp ( ) ( i ) Δp b i Δp c ppp or, alernaively: are saionary. If his is he case, he pariies are said o joinly hold and consiue he pulling forces of he sysem. Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 23 β

25 6 The empirical analysis Saionariy ess resuls: i) Δp is he only variable ha seems saionary by iself ii) None of he simple pariies is saionary: PPP: UIP: i is I (1) RIP: ppp ( Δp Δ ) ( ) i ( i Δ ) is I (1) and no coinegraed wih p ( p ) ( i ) ( p ) i p and i Δ are boh I (1) and no CI; and Δp Δ are boh I (1) and no CI Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 24

26 6 The empirical analysis Saionariy ess resuls (coninued): iii) None of he linear combinaions of he pariies: a a ( ) ( i ) i b Δp Δp c ppp ( ) ( i ) Δp b i Δp c ppp or is saionary. b) Tess of he long-run exclusion of a variable from he coinegraion space = ess of a zero row in i Resul: can be excluded from he coinegraion space. β Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 25

27 6 The empirical analysis The coinegraion relaions evenually adoped: CR1 imposes a long-run homogeneiy resricion on domesic and foreign inflaion and domesic ineres rae: CR 1 The domesic inflaion is parly impored, parly he resul of inflaion expecaions (refleced in he domesic bond rae), and parly affeced by he real exchange rae. CR2 = Δp aδp ( 1 a) i b ppp relaes domesic real ineres rae o foreign inflaion: CR ( ) i Δp aδp 2 = Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 26

28 Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 27 6 The empirical analysis The esimaed resriced model (long-run srucure): ppp i p p CR Δ = Δ ( ) p p i CR Δ Δ = = Δ Δ Δ Δ Δ CR CR ppp i i p p

29 7 Summary and conclusions The sysem is pushed by hree common rends. The German bond rae and he real exchange rae are boh individually and joinly weakly exogenous. The cumulaed shocks o hese wo variables define wo of he hree sochasic common rends. The sysem is pulled by wo seady saes: one imposing a homogeneiy resricion on boh inflaion raes and he domesic ineres rae, and one relaing he domesic real ineres rae o foreign inflaion. Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 28

30 7 Summary and conclusions The simple inernaional pariy relaions (PPP, UIP, RIP) are inconsisen wih he Polish-German daa. The analysis failed o idenify coinegraion relaions ha would be linear combinaions of he pariies. Possible explanaion: shor sample, covering a period of Poland s ransiion from cenrally planned o marke economy. Given ha, he esimaed model and he coinegraion relaions are surprisingly sable. Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 29

31 7 Summary and conclusions Specific research quesions: Do he inernaional pariies hold for Poland relaive o he euro area (represened by Germany)? No. Wha are he common sochasic rends driving inflaion, ineres raes and he real exchange rae? See previous pages. Do he developmens in Poland significanly affec hose in he common currency area? No, he laer be reaed as exogenously given. Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 30

32 An earlier and more echnical version of his paper can be found a: hp:// Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 31

33 Thank you for your aenion! Agnieszka Sążka Inernaional Pariy Relaions beween Poland and Germany 32