Empirical Estimation of Is-Lm Model for the US Economy by Applying Jmulti

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1 Empirical Esimaion of Is-Lm Model for he US Economy by Applying Jmuli ISSN : (73) Dushko Josheski 1, Darko Lazarov 2 1 FTBL, UGD, Krse Misirkov bb, Sip, Macedonia, dushkojosheski@gmail.com 2 FE, UGD, Krse Misirkov bb, Sip, Macedonia, darko.lazarov@ugd.edu.mk Absrac The main goal of he paper is o examine how well he dynamics properies of he esimaed model of he US economy mach o he heoreical predicion o he IS-LM model or wih oher words o es he heoreical IS-LM model for he US by applying ime series esimaions (sandard VAR and VECM ime series models). The ineres variables in he models are: real GDP, hree monh inerbank ineres rae, and real moneary base. Several pre esimaion ess have been made: 1) he Jarque - Bera es of normaliy shows ha he normaliy of he ime series is no problem in hese models, bu he ARCH LM es of heeroscedasiciy indicaes ha he moneary base and inerbank ineres rae are heerosedasic; 2) The ADF es for uni roo and Johansen es for co inegraion have been made o idenify he opimal number of lags of he variables in he models. The applied pos esimaion Chow es for VAR model indicaed ha he model is no sable and herefore we use VECM model. The esimaed resuls based on applying VECM model show ha if he sysem is in disequilibrium aleraion in he change of inerbank inerchange ineres rae, log of real GDP, and moneary base will be downward 5.5%, 4.6% and 0.4% respecively. The chow es indicaes ha he VECM model is sable. Keywords IS-LM model, Vecor Auo Regression, VECM, JMULTI 1. Inroducion The IS-LM model inroduced by John Hicks has played a vial role in explaining a major par of Keynesian macroeconomics since This model has buil a framework for researchers and policy makers o discuss abou he effecs of economic policy (fiscal and moneary) and he implicaions of real policy issues. The iniial IS-LM model concludes ha he governmen can influence he economy via inflaion and unemploymen, hrough a righward shif of he IS curve by he fiscal policy or by a shif of he LM curve by he moneary policy. The IS-LM model inheris Keynesian beliefs wih regard o efficiency of governmenal policies on he economy. Neverheless, here exiss a sligh conradicion relaed o he influence of defici spending on he economy beween he Keynesian and he IS/LM model. Keynes uses defici spending as a ool o simulae he aggregae demand, resuling in an increase of he naional income. This defici spending leads o a lower savings rae or o an increase in privae fixed invesmens, which finally causes an increase in fixed invesmens (Friedman 1978). Keynes hypohesizes ha he defici spending may acually "crowd in," or encourage, he privae fixed invesmen hrough he acceleraor effec, which helps long-erm growh (Friedman 1978). Furhermore, Keynesians argue ha, provided governmen deficis 1

2 are spen on producive public invesmens (e.g., infrasrucure), he resul is a direc increase in he poenial oupu (Friedman 1978). On he oher hand, he IS/LM explains ha defici spending leads o an increase in he ineres rae and produces he so-called "crowding ou phenomenon," which is he discouragemen of privae fixed invesmens ha in urn decrease he long-erm growh of he supply side, or poenial oupu. In his paper, we empirically analyze his conroversial argumen of he influence of he governmen defici on he economy. While he iniial IS/LM coninues o play an imporan role as a policy ool, i has been criicized as an obsolee insrumen in he academic communiy. The main criicism is ha his model canno explain simulaneous occurrences of high inflaion and high unemploymen raes in he economy. Moreover, he shif in cenral banks from argeing he money supply o following an ineresrae rule also undermines he imporance of his model as a policy ool. Neverheless, he model has been vigorously revived by he inroducion of new "expecaion" conceps, while keeping is original simpliciy and clearness. The new IS/LM model is a powerful macroeconomic ool, suppored no only in academic and governmen environmens, bu also in business and oher non-academic environmens. The main purpose of his sudy is o examine how well he dynamics properies of he esimaed model of he US economy mach o he heoreical predicion o he IS-LM model or wih oher words o es he heoreical IS-LM model for he US by applying ime series esimaions. The paper is organized in inroducion, hree main secions, and general conclusion. 2. Empirical esimaion of he IS-LM model 2.1 Daa descripion The variables ha we use in he empirical esimaions are U.S. ime series daa: logarihm of real GDP, q, hree monh inerbank ineres rae, i (hree monh bankers' accepance rae), and real moneary base, m (log of S. Louis adjused moneary base/gdp implici price deflaor). The observaions for he ineres rae and he moneary base are convered o quarerly frequency by averaging he monhly values. 1 The daa are quarerly US daa from he ime period from he firs quarile of 1970 o he las quarile of he As we can see from he plo he equilibrium beween money marke and goods marke is achieved in he period. By presening he descripive saisics we repor he mean minimum and maximum and sandard deviaion of he ineresed variables in our models. Table 1 Descripive saisics of he variables. sample range: [1970 Q1, 1997 Q4], T = 112 DESCRIPTIVE STATISTICS: variable mean min max sd. dev. m q i e e e e e e e e e e e e-02 1 Original ime series are from he Federal Reserve Economic Daa (FRED) daabase. 2

3 For he beer presenaion of he daa in is dynamics in he analyzed period we plo he daa on he following graph: Figure 1 Plo of Time Series 1970Q1 1997Q4 2.2 Time series ess The Jarque - Bera es of normaliy and ARCH LM- es of heeroscedasiciy wih 2 lags Tes of normaliy and es of heeroscedasiciy are being conduced: JARQUE-BERA TEST variable essa p-value(chi^2) skewness kurosis m q i ARCH-LM TEST wih 2 lags variable essa p-value(chi^2) F sa p-value(f) m q i Normaliy is no a problem in his model, bu heeroscedasiciy is presen. This is because series have unequal variances. Ineres raes are volaile, same as moneary base. 3

4 ADF es We Augmen: Y = Y -1 + u 1. Consan or drif erm ( 0) random walk wih drif 2. Time rend (T) es H O: uni roo condiional on a deerminisic ime rend and agains H A: deerminisic ime rend 3. Lagged values of he dependen variable sufficien for residuals free of auocorrelaion ADF: Y = 0 + T + Y Y Y Y -n + u The main problems wih uni roo ess are as follows: 1) low power in shor ime series (rend o under-rejec H 0: uni roo agains H A: saionary and endemic problem); 2) Criical values for UR ess depend on wha he es is condiioned on; 3) Criical values differ wih specificaion of he esing equaion (Inclusion/exclusion of drif erm, deerminisic ime rend, lags of he differenced variable and he number of lags); and anoher problem (erms o conrol for srucural breaks also change he criical values) Here is a sample of ime series modeling bu wih ime break: y ˆ y ˆ ˆ DU k ˆ ˆ DT cˆ y 1 i 1 i i eˆ Same as in any ADF es μ : consan or esimaed drif erm β : (deerminisic) ime rend y -1: 1 s lag Δy -i: lagged differences To implemen empirically subrac y -1 from boh sides β 1 = ([ά-ha] 1) dd ˆ ( TB) We use JMULTI sofware ha adds seasonal dummy variables in he models and adds Trend break dummies. Definiion: T B Time of he break is a period in which a one-ime break in srucure occurs i.e., a change in he parameers of he rend funcion.how o idenify T B? (Perron, 1990, p.161) Usually visual inspecion is sufficien, Relae T B o major evens (Grea Sock or Oil crash) Terms added o he ADF es D(TB) Models a one-ime change in he inercep, i.e., in he level of he series a crash, = 1 if = T B+1; oherwise 0, DV=1 for he single period immediaely afer he break. ADF es for moneary base (log of "S. Louis Adjused Moneary Base"/"GDP Implici Price Deflaor") Table 2 ADF es for money base. ADF Tes for series: m sample range: [1970 Q4, 1997 Q4], T = 109 lagged differences: 2 inercep, ime rend, seasonal dummies asympoic criical values 4

5 reference: Davidson, R. and MacKinnon, J. (1993), "Esimaion and Inference in Economerics" p 708, able 20.1, Oxford Universiy Press, London 1% 5% 10% value of es saisic: regression resuls: variable coefficien -saisic x(-1) dx(-1) dx(-2) consan rend sdummy(2) sdummy(3) sdummy(4) RSS OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA sample range: [1972 Q4, 1997 Q4], T = 101 opimal number of lags (searched up o 10 lags of 1. differences) Akaike Info Crierion 3 Hannan-Quinn Crierion 3 Final Predicion Error 3 Schwarz Crierion 1 From he above ables abou he moneary base, his variable is uni roo wih a drif variable. Coefficien on he rend variable is small bu significan above sas. From he opimal endogenous lags info crieria opimal number of lags for his variable is hree lags. Table 3 ADF es for ineres rae. ADF Tes for series: i sample range: [1970 Q4, 1997 Q4], T = 109 lagged differences: 2 inercep, ime rend, seasonal dummies asympoic criical values reference: Davidson, R. and MacKinnon, J. (1993), "Esimaion and Inference in Economerics" p 708, able 20.1, Oxford Universiy Press, London 1% 5% 10% value of es saisic: regression resuls: variable coefficien -saisic x(-1) dx(-1) dx(-2) consan rend sdummy(2)

6 sdummy(3) sdummy(4) RSS OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA sample range: [1972 Q4, 1997 Q4], T = 101 opimal number of lags (searched up o 10 lags of 1. differences): Akaike Info Crierion 5 Final Predicion Error 5 Schwarz Crierion 0 Hannan-Quinn Crierion 0 The variable, ineres raes in US economy has uni roo and opimal number of endogenous lags by he info crieria is up o 5 lags. Table 4 ADF es for log of real GDP. ADF Tes for series: q sample range: [1970 Q4, 1997 Q4], T = 109 lagged differences: 2 inercep, ime rend, seasonal dummies asympoic criical values reference: Davidson, R. and MacKinnon, J. (1993), "Esimaion and Inference in Economerics" p 708, able 20.1, Oxford Universiy Press, London 1% 5% 10% value of es saisic: regression resuls: variable coefficien -saisic x(-1) dx(-1) dx(-2) consan rend sdummy(2) sdummy(3) sdummy(4) RSS OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA sample range: [1972 Q4, 1997 Q4], T = 101 opimal number of lags (searched up o 10 lags of 1. differences): Akaike Info Crierion 2 Final Predicion Error 2 Schwarz Crierion 1 Hannan-Quinn Crierion 1 This variable has uni roo wih a drif erm since he coefficien on he rend erm is significan, and opimal number of lags are maximum up o 2. Tesing for coinegraion 6

7 The equilibrium marix in he error-correcion model. Procedure is as follows: calculae he rank of, i.e., number of independen rows or columns here exis 3 possibiliies 1. Rank() = 0 VECM reduces o a VAR in 1 s differences 1 s differences are I(0) no coinegraion 2. Rank() = 2 This Occurs only when boh variables saionary and wha follows no common rend independen variables over-differenced and correc model is in levels, no 1 s differences 1. Rank() = 1 One independen row deerminan of = 0 (Produc of Diagonal 1) (Produc of Diagonal 2) = 0 One co-inegraing vecor (r), each erm in is assumed non-zero and long-run or equilibrium coefficien on Y or Z. Procedure is as follows : Decompose ino 2 qr marices where = marix of shorrun adjusmen coefficiens in he EC Model = each row is one of he r. Table 5 Johansen Trace es for money base and log of real GDP. Johansen Trace Tes for: m i q unresriced dummies: D[1982 Q1] D[1982 Q2] resriced dummies: S[1982 Q1] sample range: [1970 Q3, 1997 Q4], T = 110 included lags (levels): 2 dimension of he process: 3 inercep included seasonal dummies included response surface compued: r0 LR pval 90% 95% 99% OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA sample range: [1972 Q4, 1997 Q4], T = 101 opimal number of lags (searched up o 10 lags of 1. differences): Akaike Info Crierion 6 Final Predicion Error 2 Schwarz Crierion 2 Hannan-Quinn Crierion 2 Since here is uni roo beween hese variables, hey are coinegraed of order 1 I(1) as Johansen es shows. Opimal number of endogenous lags by info crieria is 2. ARIMA for hree monhs ineres rae (i) variable Three monhs inerbank ineres rae is being esed for opimal lags by Hannan and Rissanen es. And he opimal number of lags is (1,0). Table 5 Hannan-Risaanen Model Selecion for ineres rae. OPTIMAL LAGS FROM HANNAN-RISSANEN MODEL SELECTION (Hannan & Rissanen, 1982, Biomerika 69) 7

8 original variable: i order of differencing (d): 0 adjused sample range: [1972 Q4, 1997 Q4], T = 101 opimal lags p, q (searched all combinaions where max(p,q) <= 3) Akaike Info Crierion: p=1, q=0 Hannan-Quinn Crierion: p=1, q=0 Schwarz Crierion: p=1, q=0 For 1 s difference of he variable opimal number of lags is zero (0,0). Table 6 Hannan-Risaanen Model Selecion for firs difference ineres rae. OPTIMAL LAGS FROM HANNAN-RISSANEN MODEL SELECTION (Hannan & Rissanen, 1982, Biomerika 69) original variable: i order of differencing (d): 1 adjused sample range: [1973 Q1, 1997 Q4], T = 100 opimal lags p, q (searched all combinaions where max(p,q) <= 3) Akaike Info Crierion: p=0, q=0 Hannan-Quinn Crierion: p=0, q=0 Schwarz Crierion: p=0, q=0 ARIMA for moneary base variable m (log of "S. Louis Adjused Moneary Base"/"GDP Implici Price Deflaor") The resul indicaes ha his variable is firs difference variable. And he opimal number of lags is (1, 1). Table 7 Hannan-Risaanen Model Selecion for money base. OPTIMAL LAGS FROM HANNAN-RISSANEN MODEL SELECTION (Hannan & Rissanen, 1982, Biomerika 69) original variable: m order of differencing (d): 1 adjused sample range: [1973 Q1, 1997 Q4], T = 100 opimal lags p, q (searched all combinaions where max(p,q) <= 3) Akaike Info Crierion: p=1, q=1 Hannan-Quinn Crierion: p=1, q=1 Schwarz Crierion: p=1, q=1 Model: ARIMA(0,1,0) Final Resuls: Ieraions Unil Convergence: 1 Log Likelihood: Number of Residuals: 111 AIC : Error Variance : SBC : Sandard Error : DF: 106 Adj. SSE: SSE: Dependen Variable: m Coefficiens Sd. Errors T-Raio Approx. Prob. CONST S S S TREND

9 The above able presens ARIMA (1, 0) model for S. Louis moneary base adjused for CPI deflaor. Trend is only variable ha is significan while ohers including seasonal dummies and consan are no significan. This is uni roo wih a drif variable. ARIMA for real GDP variable (log of real US GDP) The resul indicaes ha his variable is 1 s difference variable opimal lags (1, 0). In he ARIMA model for log of real US GDP only consan erm is significan. Table 8 Hannan-Risaanen Model Selecion for log of real GDP OPTIMAL LAGS FROM HANNAN-RISSANEN MODEL SELECTION (Hannan & Rissanen, 1982, Biomerika 69) original variable: q order of differencing (d): 1 adjused sample range: [1973 Q1, 1997 Q4], T = 100 opimal lags p, q (searched all combinaions where max(p,q) <= 3) Akaike Info Crierion: p=1, q=0 Hannan-Quinn Crierion: p=1, q=0 Schwarz Crierion: p=1, q=0 Model: ARIMA(0,1,0) Final Resuls: Ieraions Unil Convergence: 1 Log Likelihood: Number of Residuals: 111 AIC : Error Variance : SBC : Sandard Error : DF: 106 Adj. SSE: SSE: Dependen Variable: q Coefficiens Sd. Errors T-Raio Approx. Prob. CONST S S S TREND VAR ime series model VAR is model he analyzed he relaionship beween wo or more variables modelled as a VAR.Vecor Auo - Regression where each variable regressed on lags of iself and he oher variables, X = vecor of q variables of ineres, boh endogenous and exogenous variables, disincion deermined by he analysis = marix of coefficiens k = maximum lag = an error erm ( whie noise ) X 1X 1 2 X 2... k X k 9

10 m( m( 1) m( 2) ) ) ) ) m( 3) m( 4) ) ) ) ) m( 5) m( 6) ) ) ) ) CONST S1( u1( S2( u2( S3( u3( TREND( This VAR model conains daa form 1971 Q3 o 1997Q4. The CUSUM es below shows ha m, q and i equaions do no leave he margins of normal disribuion. Figure 2 CUSUM es for normal disribuion for ineres rae, money base and real ineres rae CHOW es for VAR 10

11 Chow es for VAR shows srucural sabiliy of he model and if he model is no sable we should coninue esing. Table 9 Chow es for srucural break in VAR. CHOW TEST FOR STRUCTURAL BREAK On he reliabiliy of Chow-ype ess..., B. Candelon, H. Lükepohl, Economic Leers 73 (2001), sample range: [1971 Q3, 1997 Q4], T = 106 esed break dae: 1978 Q1 (26 observaions before break) break poin Chow es: boosrapped p-value: asympoic chi^2 p-value: degrees of freedom: 75 sample spli Chow es: boosrapped p-value: asympoic chi^2 p-value: degrees of freedom: 69 Chow forecas es: boosrapped p-value: asympoic F p-value: degrees of freedom: 240, 3 From he above able for Chow es, break poin chow es showed ha he model is no sable, also sample spli es showed ha, while chow forecas es is only significan a 10%, his means we have o coninue wih VECM model. VECM model 2.4 VECM ime series model The VECM ime series model ha we use o es he heoreical IS-LM model in he paper is presened by he following equaions: Y Z (1 (1 1 ( 1 Y In marices ) Y Y (1 Z 21 1 ( ) Y 11 2 (1 11 ( 21 23) ) Y ) 2 Z ( 22 ) Z (1 1 ( ( (1 ) Z Y ) Z ) Z ) 24 Y ) Z 2 2 Differences Levels (1' ) Differences Levels (2' ) Differences Levels 11

12 dm( m( 1) d ) d ) CONST S1( u1( S2( u2( S3( u3( TREND( The esimaed resuls of he VECM model indicae ha if he sysem is in disequilibrium aleraion of he inerbank inerchange ineres rae, log of real US GDP, and moneary base will be downward 5.5%, 4.6% and 0.4%, respecively. Chow es for VECM These resuls below show ha CHOW es implies sabiliy here which means ha VECM models are sable. Table 10 Chow es for srucural break in VECM. CHOW TEST FOR STRUCTURAL BREAK On he reliabiliy of Chow-ype ess..., B. Candelon, H. Lükepohl, Economic Leers 73 (2001), sample range: [1970 Q2, 1997 Q4], T = 111 esed break dae: 1973 Q2 (12 observaions before break) break poin Chow es: boosrapped p-value: asympoic chi^2 p-value: degrees of freedom: 9 sample spli Chow es: boosrapped p-value: asympoic chi^2 p-value: degrees of freedom: 3 Chow forecas es: boosrapped p-value: asympoic F p-value: degrees of freedom: 297, 6 3. Conclusions The main purpose of his paper has been o examine how well he dynamics properies of he esimaed models of he US economy mach o he heoreical predicion o he IS-LM model or wih oher words o es he heoreical IS-LM model for he US by applying ime series esimaions (sandard VAR and VECM ime series models). The ineres variables in he models are: real GDP, hree monh inerbank ineres rae, and real moneary base. Several pre esimaion ess have been made: 1) he Jarque - Bera es of normaliy shows ha he normaliy of he ime series is no problem in hese models, bu he ARCH LM es of heeroscedasiciy indicaes ha he moneary base and inerbank ineres rae are heerosedasic; 2) The ADF es for uni roo and Johansen es for co inegraion have been made o idenify he opimal number of lags of he variables in he models. The applied pos esimaion Chow es for VAR model indicaed ha he model is no sable and herefore we 12

13 use VECM model. The esimaed resuls based on applying VECM model show ha if he macroeconomic sysem is in disequilibrium (when he economy is ou of is balanced pah) aleraion of he inerbank inerchange ineres rae, log of real GDP, and moneary base will be downward 5.5%, 4.6% and 0.4% respecively. The chow es indicaes ha he VECM model is sable. References 1. L ukepohl, H. & Poski, D. S. (1996). Tesing for causaion using infinie order vecor auoregressive processes, Economeric Theory 12: L ukepohl, H. & Poski, D. S. (1998). Consisen esimaion of he number of coinegraion relaions in a vecor auoregressive model, in R. Galaa & H. K uchenhoff 3. L ukepohl, H. & Reimers, H.-E. (1992a). Granger-causaliy in coinegraed VAR processes: The case of he erm srucure, Economics Leers 40: L ukepohl, H. & Reimers, H.-E. (1992b). Impulse response analysis of coinegraed sysems, Journal of Economic Dynamics and Conrol 16: L ukepohl, H. & Saikkonen, P. (1999a). A lag augmenaion es for he coinegraing rank of a VAR process, Economics Leers 63: L ukepohl, H. & Saikkonen, P. (1999b). Order selecion in esing for he coinegraing rank of a VAR process, in R. F. Engle & H. Whie (eds), Coinegraion, 7. Causaliy, and Forecasing. A Fesschrif in Honour of Clive W.J. Granger, Oxford Universiy Press, Oxford, pp L ukepohl, H. & Saikkonen, P. (2000). Tesing for he coinegraing rank of a VAR process wih a ime rend, Journal of Economerics 95: L ukepohl, H., Saikkonen, P. & Trenkler, C. (2001). Maximum eigenvalue versus race ess for he coinegraing rank of a VAR process, Economerics Journal4: L ukepohl, H., Saikkonen, P. & Trenkler, C. (2004). Tesing for he coinegraing rank of a VAR process wih level shif a unknown ime, Economerica 72: L ukepohl, H. & Schneider, W. (1989). Tesing for nonnormaliy of auoregressive ime series, Compuaional Saisics Quarerly 5: MacKinnon, J. G., Haug, A. A. & Michelis, L. (1999). Numerical disribuion funcionsof likelihood raio ess for coinegraion, Journal of Applied Economerics 14: Magnus, J. R. (1988). Linear Srucures, Charles Griffin, London. 14. Magnus, J. R. & Neudecker, H. (1988). Marix Differenial Calculus wih Applicaions in Saisics and Economerics, John Wiley, Chicheser. 15. Mann, H. B. & Wald, A. (1943). On he saisical reamen of linear sochasic difference equaions, Economerica 11: Mardia, K. V. (1980). Tess for univariae and mulivariae normaliy, in P. R. 17. Krishnaiah (ed.), Handbook of Saisics, Vol. 1, Norh-Holland, Amserdam, pp

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