Testing Fiscal Reaction Function in Iran: An Application of Nonlinear Dickey-Fuller (NDF) Test

Transcription

1 Iran. Econ. Rev. Vol. 1, No. 3, 17. pp Tesing Fiscal Reacion Funcion in Iran: An Applicaion of Nonlinear Dickey-Fuller (NDF) Tes Ahmad Jafari Samimi* 1, Saeed Karimi Peanlar, Jalal Monazeri Shoorekchali 3 Received: 16, Ocober 17 Acceped: 16, December 18 Absrac T his paper is o convince he usage of he nonlinear uni roo ess when dealing wih a nonlinear model. To do so, he saionary es for variables in a model iles Fiscal Reacion Funcion in Iran has been applied according o boh he ordinary and he Nonlinear Dickey- Fuller (NDF) ess. Resuls show ha while variables under invesigaion are saionary in a nonlinear form, augmened Dickey- Fuller es indicaes endency o fail and rejec he null hypohesis of a uni roo in he presence of nonlinear dynamics. Therefore based on he resuls of Nonlinear Dickey-Fuller (NDF), he paper esimaes he fiscal reacion funcion (FRF) in Iran. The esimaed nonlinear regression suppors a hreshold behavior of wo regimes in applying he fiscal reacion. Finally, findings confirm ha fiscal policy in Iran is counercyclical hough no sensiive in order o reac o accumulaion of he governmen deb. Keywords: Uni Roo Tes, Nonlinear Dickey-Fuller (NDF) Tes, STR Model, Fiscal Reacion Funcion, Iran. JEL classificaion: C, E3, H6, H Inroducion Granger-Newbold (1974) firsly showed ha when ime series variables are non-saionary, he classical regression resuls may be misleading. Therefore, i is absoluely necessary, before esimaing he regression equaion, ha saionary of he variables be examined using 1. Deparmen of Economics, Universiy of Mazandaran, Mazandaran, Iran (Corresponding Auhor: jafarisa@umz.ac.ir).. Deparmen of Economics, Universiy of Mazandaran, Mazandaran, Iran (s.karimi@umz.ac.ir). 3. Deparmen of Economics, Universiy of Mazandaran, Mazandaran, Iran (jalalmonazeri@gmail.com).

2 568/ Tesing Fiscal Reacion Funcion in Iran:... he uni roo ess. Accordingly, a number of uni roo ess go presened by several economiss, o check saionary of ime series variables. However, a few of hese ess are used in mos experimenal sudies. Lyocsa e al. (11) in reviewing 155 papers from 17 journals, showed abou 96.6% of hese papers for saionary es used Augmened Dickey Fuller or Dickey Fuller (ADF and DF respecively), DF-GLS, Phillips-Perron, Ng-Perron and KPSS es. Whereas many of hese papers used nonlinear models in heir sudies, hese radiional uni roo ess show endency o fail rejecing he null hypohesis of a uni roo in he presence of asymmeric dynamics; so resuls of hese ess may be misleading. Hence, esing lineariy agains nonlineariy is necessary when researchers wish o consider a nonlinear modeling. Accordingly o he low power of radiional uni roo ess o rejec he null hypohesis of a uni roo in he presence of asymmeric dynamics, nonlinear saionary ess such as hreshold auoregressive [TAR] models (Tong, 199) or smooh ransiion auoregressive [STAR] models (Teräsvira, 1994) have become quie popular in applied new ime series economerics (Demerescu and Kruse, 13: 4). Examining he resuls of sudies by Saranis (1999), Taylor e al. (1), Sarno e al. (4), He and Sandberg (5), Li (7), McMillan (7) and Nobay e al. (1) showed ha smooh ransiion models are paricularly successful in his respec. These sudies indicaed ha ime series variables such as real effecive exchange raes of 1 major indusrial counries [he G-1] (Saranis, 1999), real exchange raes of he US, he UK, Germany, France, and Japan (Taylor e al., 1), real money balances of he US (Sarno e al., 3), France s unemploymen rae (Li, 7), price-dividend raios of several counries (McMillan, 7), and inflaion of US (Nobay e al., 1) had nonlinear behavior and when he performance of he nonlinear uni roo ess which accommodae a smooh nonlinear shif in he level, he dynamic srucure, and he rend are compared o he classical uni roo ess, i is found ha hese nonlinear ess are superior in erms of power. Following he previous sudies and according o he consideraions menioned, his paper examines variables saionary of Fiscal Reacion Funcion in Iran using a uni roo es in he smooh

3 Iran. Econ. Rev. Vol. 1, No.3, 17 /569 ransiion auoregressive (STAR) framework. In oher words, we ry o invesigae he necessiy of using he nonlinear uni roo ess when considering a nonlinear modeling. I should be menioned ha here already exiss several uni roo ess in he smooh ransiion auoregressive (STAR) framework, such as Enders and Granger (1998), Bec, Salem, and Carrasco (), Eklund (3a), Eklund (3b), Kapeanios, Shin, and Snell (3), He and Sandberg (5), and Li (7). However, we use a Nonlinear Dickey-Fuller (NDF) es in a firs order Logisic Smooh Transiion Auoregressive model (LSTAR (1)) by Li (7). Finally, according o he resuls of uni roo ess, his paper examines "fiscal susainabiliy of governmen Policies" in he form of a nonlinear fiscal reacion funcion. For his purpose, a fiscal reacion funcion was esimaed using a Smooh Transiion Regression (STR) model in Iran for he period The res of he paper is organized as follows. In Secion he models are presened. This secion includes wo pars: -1- Nonlinear Dickey-Fuller (NDF) F es in he form of a LSTAR (1); -- The basics of fiscal reacion funcions. Esimaes of uni roo ess and fiscal reacion funcion in Iran are presened in Secion 3. Finally, concluding remarks are given in Secion 4.. The Model This secion includes wo pars. In he firs par, he Nonlinear Dickey- Fuller (NDF) es in he form of a LSTAR (1) 1 is inroduced, where we believe in using nonlinear models, esing lineariy agains nonlineariy in he uni roo es is a necessary. In he second par, he fiscal reacion funcion in he nonlinear form is inroduced..1 Nonlinear Dickey-Fuller (NDF) Tes Consider he following wo STAR models; he firs equaion does no have a consan erm, whereas he second one does: Case 1: y u u y y F( ;, c ) ; iid (, ) (1) 1. See Li and He, 7. See Burger e al., 11

4 57/ Tesing Fiscal Reacion Funcion in Iran:... u u Case: y y ( y )F(;,c) ; iid(, ) () The ransiion funcion F( ;, c) in (1) and () is defined as follows: 1 1 F( ;, c ) (3) (1 exp ( c ) ) The resulan smooh ransiion regression [STR] model is discussed a lengh in Terasvira (1998). The ransiion funcion F( ;, c) is a coninuous funcion ha is bounded beween o1. The ransiion funcion depends on he ransiion variable (), he slope parameer ( ) and he vecor of locaion parameers (c). The ransiion variable is a linear ime rend (), which gives rise o a model smoohly changing parameers. Our goal is o es he null hypohesis of a random walk wihou drif agains he sable nonlinear LSTAR (1) model. The null hypohesis can be expressed as he following parameer resricion: Case1: Case : H H * :, :, , 11 1 (4) As implies ha he ransiion funcion F( ;, c), hen represens ha he model is linear, ; 1 represen a 1 11 random walk wihou drif. However, will lead o an idenificaion problem under he null hypoheses o remedy he problem, we follow he approach which Li and He (7) use, and we apply Taylor expansion of around in F( ;, c). The firs and hird order Taylor expansion is as follows: ( c) F ( ;, c) r1 ( ) 4 3 ( c) ( c) F3 ( ;, c) r ( ) Subsiuing he above equaions ino, afer merging he erms, we ge he following auxiliary regressions: 3 (5)

5 Where he parameers are defined as follows: Iran. Econ. Rev. Vol. 1, No.3, 17 /571 s 1 (1, ) ; (, ), (, ) (,,, ) , (, ,,, ) 3 33 s 3 (1,,, 3 ), (6) Then he corresponding auxiliary null hypoheses are: H H * m m : : m mi 1, mj, i;, j 1; m 1,3 m 1, mj, j 1; m 1,3 (7) To invesigae he null hypoheses of uni roo es, we use he Nonlinear Dickey-Fuller (NDF) F es. We derive wo heorems ha are used o deduc he D-F F ess saisic disribuions: I) Nonlinear Dickey-Fuller (NDF) F ha does no conain * inercep: Consider models y y s u hold, and assume ha ( * m) 1 ( 1 m) m m u fulfills assumpion u (, ) wih E u ), hen for m=1, 3, such ha: ψ m ψ p, Υ m m (ψ m ψ m ) d (Ψ m ) 1 Π m, (8) (s m ) Υ m ( x m (x m )) 1 Υ L m σ (Ψ m ) 1 Where he parameer resricions are as follows: Υ 1 = diag{t 1 }, T 1 = [T T ], (r 1 ) = [1 ] Υ 3 = diag{t 3 }, T 3 = [T T T 3 T 4 ], (r 3 ) = [1 ] ψ m (φ m ), ψ m = (φ ḿ ), x m = [y 1 s m ] Ψ m = σ u C m Π m = E m ( 4 C m = [c ij ] (m+1) (m+1), E m = [e i ] (m+1) 1 1 c ij = r i+j W(r) dr, e i = (W1 1 (i 1) r i W(r) dr 1 i) Accordingly, we have Nonlinear D-F F es saisics as follows: F m = (ψ m ψ m )(R m ) {(s m ) R m [ x m (x m )] 1 (R m )} 1 R m (ψ m ψ m ) (9)

6 57/ Tesing Fiscal Reacion Funcion in Iran:... = (ψ m ψ m )(R 1 m )Υ m L {s m Υ m R m [ x m [(Ψ m ) 1 Π m ][σ u (Ψ m ) 1 ] 1 [(Ψ m ) 1 Π m ] (x 1 1 m )] (R m ) Υ m } Υ m R m (ψ m ψ m ) = (Π m )(Ψ m )Π m σ u II) Nonlinear Dickey-Fuller (NDF) F ha conains boh in inercep and dynamics: Consider models * y s y s u hold, and assume ha u * ) fulfills m m ( 1 m ) m m ( m 1 assumpion u (, ) wih E u ), hen for m=1, 3, such ha: ( 4 Υ m (ψ m ψ m ) d Ψ m 1, ψ m ψ m p, s m Υ m ( x m x m) 1 Υ m L σu Ψ m 1 Where he parameers are defined as follows: Υ 1 = diag{t 1 }, T 1 = [T 1 T 3 T T ], r 1 = [ 1 ] Υ 3 = diag{t 3 }, T 3 = [T 1 T 3 T 5 T 7 T T T 3 T 4], r 3 = [ 1 ] s m ψ m = (λ m, φ m), ψ m = (λ m, φ m), x m = [ y 1 s ] m Ψ m = [ A m u m B m σ u B m σ ] Π u C m = [ σ ud m m σ ] u E m A m = [a ij ] (m+1) (m+1), B m = [b ij ] (m+1) (m+1), C m = [c ij ] (m+1) (m+1) D m = [d i ] (m+1) 1, E m = [e i ] (m+1) 1 a ij = T (i+j 1) T =1 d = W(1) (i 1) r i W(r)dr, 1 1 i+j, b ij = r i+j W(r)dr, c ij = r i+j W(r) dr 1 e i = (W(1) (i 1) r i W(r) dr 1 i) Accordingly, we have Nonlinear D-F es saisics as follows: F m = (ψ m ψ m )Ŕ m {s m R m ( x m x m) 1 Ŕ m } 1 R m (ψ m ψ m ) (1) F m = (ψ m ψ m ) Ŕ m Υ m {s 1 1 m Υ m R m ( x m x m) Ŕ m Υ m } Υ m R m (ψ m ψ m ) L (ψ m Π m ) {σ u Ψ 1 m } 1 (Ψ 1 m )/ = Π mψ 1 m Π m /σ u 1

7 Iran. Econ. Rev. Vol. 1, No.3, 17 /573. Fiscal Reacion Funcion (FRF) The issue of fiscal susainabiliy has aken on special imporance in he afermah of he global financial crisis. Alhough for fiscal susainabiliy is provided several definiions, almos all of hese definiions are associaed wih fiscal policy. In a comprehensive definiion, fiscal susainabiliy can be considered as a measure of fiscal dependence on he governmen's recen behaviors, compared o he las fiscal developmens and changes in he macro-economic level. To empirically assess fiscal susainabiliy, he concep of fiscal reacion funcion can be used. Fiscal reacion funcions usually specify, for annual daa, he reacion of he primary balance/gdp raio o changes in he one-period lagged public deb/gdp raio, conrolling for oher influences. In oher words, if he public deb/gdp raio increases, governmen should respond by improving he primary balance, o arres and even reverse he rise in he public deb/gdp raio (Bohn, 1995, 7). According o Burger e al. (11), he basic fiscal reacion funcion is in he following form: ( B / Y) 1 ( B / Y) 1 3( D / Y) 1 4( y) (11) Where: B/Y= Primary Balance/GDP D/Y= Governmen Deb/GDP ŷ =Oupu Gap According o Terasvira (1994) and wih he aim of considering he asymmeric effecs of deb level and macroeconomic flucuaions over governmen decisions, for equaion (11) is considered a non-linear srucure based on he smooh ransiion regression (STR) model: (B / Y) ( ).G(,c,s ) u (1) K G, c, s 1 exp s ck, k 1 Where: = vecor of explanaory variables ( ( B / Y ) ;( D / Y ) and( yˆ 1 1 ) )., 1,..., p The parameer vecors of he linear and he 1 ˆ

8 574/ Tesing Fiscal Reacion Funcion in Iran:... nonlinear par., 1,..., p = The parameer vecors of he linear and he nonlinear par. G, c, s ) = Transiion Funcion. ( s = Transiion variable. = Slope parameer. c Vecor of locaion parameers. Governmen Deb/GDP is hree ypes 1 : Deb o he cenral bank/gdp (DCY) Deb o domesic banks and non-bank financial insiuions/gdp (DOY) Foreign deb/gdp (DXY) 3. Empirical Resuls This secion is o convince he usage of he nonlinear uni roo ess when dealing wih a nonlinear model. To do so, he saionary properies for he variables in a model iles Fiscal Reacion Funcion in Iran has been esed using boh he ordinary as well as he Nonlinear Dickey-Fuller (NDF) ess for he period In he firs sep, he saionary of variables has been esed, using he ordinary Augmened Dickey-Fuller es. The resuls are presened in Table 1. According o Table 1, he oupu gap (GAP) is only saionary in level [I ()] and oher variables are inegraed of order 1 [I (1)]. Based on Augmened Dickey-Fuller es resuls, non-saionary variables should be differenced before being used in esimaing equaion (1). However, i should be noed ha he differencing processes lead o loss of valuable informaion regarding he variable level. 1. I should be noed as menioned by a disinguished referee ha he official governmen debs are no a good and real represenaion of he acual governmen debs due o he socalled hidden governmen debs. In anoher words, he acual governmen debs are much higher han he official ones. However, due o he fac ha one of he objecive of he presen paper was o deal wih he impacs of differen governmen debs and also due o lack of viable daa regarding hidden debs for he esimaion purpose during he period under consideraion, he presen research concenraed on he above 3 kinds of governmen debs.

9 Iran. Econ. Rev. Vol. 1, No.3, 17 /575 Table 1: Augmened Dickey-Fuller F Tes Variable Inercep Inercep and Trend -Sa Prob BY D(BY) DCY D(DCY) DOY D(DOY) DXY D(DXY) -4.. GAP *Criical Values: 1% level: -3.6; 5% level: -.93 and 1% level: -.6 This secion deals wih ess he saionary properies of he variables using Nonlinear Dickey-Fuller (NDF) approach in he form of a LSTAR (1). To do so, he following seps should be done: 1. Tesing Lineariy agains STR Model and Model Specificaion Towards building up he LSTAR model, he firs sep is o carry ou a Lagrange Muliplier (LM)-ype es o es lineariy agains STAR models alernaives. Based on he probabiliy values of F es saisics repored in able, i can be concluded ha lineariy of he model has been rejeced. Therefore, he nex sep is o find a suiable nonlinear model for ransiion variable (rend). As seen from able, he resuls regarding differen nonlineariy ess shown by F, F3 and F4 probabiliies he esimae STR model is LSTR1 for he ransiion variables. Table : Tesing Lineariy agains STR Model and Model Specificaion Variable p- Transiion p- p-value p-value Suggesed Under value Variable value F F F3 Model Tes F4 BY Trend LSTR1 DCY Trend LSTR1 DOY Trend LSTR1 DXY Trend LSTR1 GAP Trend LSTR1 *Noe: Teräsvira (1998) advises choosing he LSTR or he ESTR model if he rejecion of he null hypohesis of F3 es is he sronges. In case of he sronges rejecion of he null hypoheses of F or F4, LSTR1 is chosen as he appropriae model.

10 576/ Tesing Fiscal Reacion Funcion in Iran:.... Esimaion of Nonlinear Dickey-Fuller (NDF) F Tes Saisic Value In his secion, we esimae equaion () and Nonlinear Dickey-Fuller (NDF) F in he form of a LSTAR (1) ha conains boh inercep and dynamics [equaion (1)]. The resuls of hese esimaes are presened in Table 3. According o he Nonlinear Dickey-Fuller (NDF) F saisic repored in Table 3, he null hypohesis of a random walk wihou drif is rejeced agains he sable nonlinear LSTAR (1) model. So, variables under invesigaion are saionary in a non-linear form. According o Nonlinear Dickey-Fuller (NDF) es resuls and unlike he Augmened Dickey-Fuller es resuls, he value of variables level can be used o esimae he equaion (1). The resuls of Augmened Dickey-Fuller es and Nonlinear Dickey-Fuller (NDF) es showed ha esing lineariy agains nonlineariy is necessary when researchers wish o consider a nonlinear modeling; because radiional uni roo ess such as he Augmened Dickey-Fuller es show a endency o fail rejecing he null hypohesis of a uni roo in he presence of asymmeric dynamics. Table 3: Nonlinear Dickey-Fuller (NDF) F Variable Under Tes Nonlinear Regression (NDF) F BY ** BY 1 (3..36BY 1) (1 exp ( DCY *** DCY 1 (.3BY 1 ) (1 exp 15.9( DOY *** DOY 1 (.1DOY 1) (1 exp 7.3( 9.89 DXY *** 1.59DXY 1 ( DXY 1) (1 exp 44.7(.76 GAP *.71GAP 1 (.76.71GAP 1) (1 exp 44.5( 4.94 *Criical Values: 1% level: 16.9; 5% level: and 1% level: Noe: * Significan a 1%; ** Significan a 5% and *** Significan a 1% According o he resuls of uni roo ess, he value of variables level is used o esimae fiscal reacion funcion (FRF) in Iran. The firs sep is specificaion in he esimaion of a STR model.

11 Iran. Econ. Rev. Vol. 1, No.3, 17 /577 Specificaion involves esing for nonlineariy, choosing s and deciding wheher LSTR1 or LSTR should be used. Those resuls of he esimaions are presened in Table 4. According o probabiliy values of F es saisics repored in able 4, he null hypohesis of his es, based on he lineariy of he model, is rejeced for ransiion variables ( DX / Y) 1 and ( DC / Y) 1. For selecing he opimal ransiion variable, he variable ha he null hypohesis is rejeced sronger is seleced. According o probabiliy values of F repored in Table 4, ( DX / Y) 1 is seleced as an opimal ransiion variable. Selecion of a suiable model for variable ransiion (( DX / Y) 1 ) based on he ess saisic F, F3 and F4, is he nex sep a STR model specificaion. Consisen wih he resuls repored in Table 4, he suiable proposed model is LSTR1 for variable ransiion. Table 4: Tesing Lineariy agains STR Model Transiion Variable p-value F p-value F p-value F3 p-value F4 Suggesed Model B/Y(-1) Linear GAP() Linear DC/Y(-1) LSTR1 DO/Y(-1) Linear DX/Y(-1)* LSTR1 *see noaion in able 1 Table 5: STR Esimaion and Tess for Misspecificaion esimae -sa p-value Linear Par CONST GAP() DC/Y(-1) DO/Y(-1) DX/Y(-1) Nonlinear Par B/Y(-1) DC/Y(-1)..4.3 DO/Y(-1) DX/Y(-1) R:.7 AIC:.8 SC:.54 HQ:.5 Tess for Misspecificaion The second and hird seps in he esimaion of an STR model involve finding appropriae saring values for he nonlinear esimaion

12 578/ Tesing Fiscal Reacion Funcion in Iran:... and esimaing he model, and evaluaion of he model usually includes various ess for misspecificaion such as error auocorrelaion, parameer non-consancy, remaining nonlineariy, ARCH and non-normaliy. Esimaion resuls of his sep are presened in Table 5. According o ess of misspecificaion, he esimaed nonlinear model is evaluaed as accepable in erms of qualiy. In he model secion, he ransiion funcion G, c, s ) said o be a ( coninuous funcion ha is bounded beween o1. The ransiion funcion depends on he ransiion variable (s), he slope parameer ( ) and he locaion parameer (c). The esimaed final amouns for slope parameer and locaion parameer are equal o 1.3 and 3.9. Therefore, he ransiion funcion is as following: 1 G 1.3,3.9,(DX / Y) 1 exp 1.3 (DX / Y) 3.9 (13) 1 1 Since ransiion funcion is (G=) in he firs regime, he firs regime equaion is as follows: ( B / Y).83( DX / Y).83.51GAP 1.18( DC / Y) 1.53( DO / Y) 1 (14) And ransiion funcion is 1 (G=1) in he second regime; so, we have for he second regime: ( B / Y).11( DO / Y).83 59( B / Y) 1 1.7( DX / Y).51GAP.4( DC / Y) 1 1 (15) The esimaed nonlinear regression suppor a hreshold behavior of wo regimes in he fiscal reacion funcions. The posiive coefficien of he variable DX/Y and he negaive coefficien of he variables DC/Y and DO/Y, in he firs regime (when he raio of governmen foreign deb o GDP is below 3.9%), indicaes ha governmen reacion o foreign deb is susainable, while governmen reacion o deb o he cenral bank and domesic banks and non-bank financial insiuions are no susainable. In addiion, he posiive coefficien of he variables DX/Y, DC/Y and DO/Y in he second regime (when he raio of governmen foreign deb o GDP is above 3.9%) shows governmen reacion o all hree ype of deb (deb o he cenral bank,

13 Iran. Econ. Rev. Vol. 1, No.3, 17 /579 domesic banks and non-bank financial insiuions and foreign deb) is susainable. However, he small regression coefficiens indicae a weak susainabiliy. In oher words, fiscal policy was no sensiive o reac o accumulaion of he governmen deb. Finally, he posiive coefficien of he variable GAP in boh regimes confirms he hypohesis "couner-cyclical response of he governmen fiscal policies" in Iran. 4. Concluding Remarks In his paper, i was invesigaed he necessiy of using nonlinear uni roo ess, when i was considered a nonlinear modeling. Accordingly, variables saionary of Fiscal Reacion Funcion in Iran were examined using he Augmened Dickey-Fuller and Nonlinear Dickey- Fuller (NDF) es. Resuls showed ha radiional uni roo ess such as he Augmened Dickey-Fuller es have endency o fail, rejecing he null hypohesis of a uni roo in he presence of asymmeric dynamics. Therefore, esing lineariy agains nonlineariy is necessary when a nonlinear modeling is considered. In he second par and according o he resuls of Nonlinear Dickey-Fuller (NDF), he value of a variable level was used o esimae fiscal reacion funcion (FRF) in Iran. The esimaed nonlinear regression suppor a hreshold behavior of wo regimes in he fiscal reacion funcion. Findings confirmed ha fiscal policy was no sensiive o reac o he accumulaion of he governmen deb. Therefore, due o he impac of public deb on long-run economic growh hrough various channels, i is necessary ha "deb susainabiliy" be considered as a main variable in he objecive funcion of fiscal policies in Iran. Finally, he resuls showed ha fiscal policy in Iran is counercyclical. References Bohn, H. (1995). The Susainabiliy of Budge Deficis in a Sochasic Economy. Journal of Money, Credi and Banking, 7(1),

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