Stability of Money Demand in an Emerging Market Economy: An Error Correction and ARDL Model for Indonesia

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1 Stability of Moey Demad i a Emergig Market Ecoomy: A Error Correctio ad ARDL Model for Idoesia Noer Azam Achsai Departmet of Ecoomics ad Graduate School of Maagemet ad Busiess Bogor Agricultural Uiversity, Idoesia achsai@yahoo.com (preferred) or achsai@mb.ipb.ac.id Tel: ; Fax: Abstract Predictig a stable moey demad fuctio is oe of the key elemets of moetary policy sice moetary aggregates has theoretically importat iflueces o output, iterest rate ad ultimate price level. By employig the vector error correctio model (VECM) ad autoregressive distributed lag (ARDL) approach, this paper ivestigates the M2 moey demad for Idoesia i the period of 1990:1-2008:3. The results idicate that the demad for real M2 moey aggregate is coitegrated with real icome ad iterest rate. The real icome has positive relatioship with real moey demad, both i the log-ru ad short-ru. O the other had, iterest rate has a egative ifluece o M2 i the short-ru, but has o statistically sigificat relatioship i the log-ru. Furthermore, we fid that the ARDL model is more appropriate i predictig stable moey demad fuctio of Idoesia i compare to VECM. Keywords: Moey demad, coitegratio, ARDL model, stability test JEL Classificatio Codes: E41, E44, G2 1. Itroductio A stable moey demad fuctio forms the core i the coduct of moetary policy as it eables a policy-drive chage i moetary aggregates to have predictable iflueces o output, iterest rate ad ultimate price. Because of its importace, therefore, may studies have bee carried out worldwide i the last several decades (Sriram, 1999). Majority of the study cocered with the data from the idustrial coutries. Examples are Hafer ad Jase (1991), Miller (1991), McNow ad Wallace (1992) ad Mehra (1993) for the USA; Arize ad Schwiff (1993), Miyao (1996) ad Bahmai-Oskooee (2001) for Japa; Drake ad Chrystal (1994) for the UK; Haug ad Lucas (1996) for Caada; Lim (1993) for Australia ad Orde ad Fisher (1993) for New Zealad. Relatively few studies were coducted o developig coutries. However, it has bee icreasig i recet years, primarily triggered by the cocer amog cetral baks ad researchers aroud the world o the impact of movig toward flexible exchage rates regimes, globalizatio of capital markets, ogoig fiacial liberalizatio ad iovatio i domestic markets, ad the coutry-specific evets o the demad for moey (Sriram, 1999). As far as Idoesia is cocered, couples of studies have bee coducted by employig Johase s error correctio model. The results, however, seem to be cotradictive. Price ad Isukido (1994) used quarterly data over 1969:1 1987:4 period. The results were based o three differet methods of testig for coitegratio. Eagle Grager method showed that there was weak evidece of coitegratig relatioship. Furthermore Johase s coitegratio techique foud up to two coitegratig vectors, but the error correctio model (ECM) did t fid a sigificat relatioship. Research Joural of Iteratıoal Studıes - Issue 13 (March, 2010) 54

2 Dekle ad Pradha (1997) who re-examied the relatio usig aual data over , did ot fid ay coitegratig relatioship for ay defiitios of moey demad. I this paper, agai we explore the M2 moey demad fuctio i Idoesia, usig Johase s stadard coitegratio model. As Bahmai-Oskooee ad Bohl (2000) ad Bahmai-Oskooee (2001), however, stadard coitegratio model may ot imply stable relatio-ships amog set of variables. I this paper, therefore, we also employ the autoregressive distributed lag (ARDL) methods itroduced by Pesara ad Shi (1995) ad Pesara, Shi ad Smith (1996). Usig the ARDL approach, we shed light ot oly the coitegratig properties of M2, icome ad iterest rate, but also the stability of M2 moey demad fuctios itself. The rest of the paper is orgaized as follows. I sectio 2 we explai the data ad also itroduce the moey demad fuctio, the vector error correctio model ad the ARDL approach to coitegratio. Sectio 3 gives the empirical results ad discuss about the stability of the moey demad fuctio. Sectio 4 summarized the research fidigs ad gives cocludig remarks. 2. Data ad Methodology I this research we use secodary data of Idoesia, cosistig of real M2 moey demad, real output (GDP) ad Iterest rates (call moey rates). All the data are take from the Iteratioal Fiacial Statistics Database. Usig quarterly data over 1990:1 2008:3 period, we try to test the ull hypothesis of o coitegratio agaist the alterative usig two methods, amely the VECM (Johase (1988) ad Johase ad Juselius (1990)) ad the ARDL model (Pesara ad Shi (1995) ad Pesara, Shi ad Smith (1996)). All calculatios are carried out usig Microfit The M2 Moey Demad, ECM ad ARDL Approach of Coitegratio As is commo i the literature that the basic model of moey demad begis with the followig fuctioal relatioships: M/P = f (S,OC) where the demad for real balaces M/P is a fuctio of the chose scale variable (S) to represet the ecoomic activity ad the opportuity cost of holdig moey (OC). M stads for the selected moetary aggregates i omial term ad P for the price. I empirical researches, we geerally specify the moey demad as a fuctio of real balaces. Usig the real moey balace as depedet variable will also mea that price homogeeity is explicitly imposed ito the model. Additioally, there are less severe ecoometric problems associated with usig real rather tha omial moey balaces as the depedet variable (Sriram, 1999). I this paper, followig Miyao (1996) ad Basmai-Oskooee (2001) we cosider the followig M2 demad for moey i Idoesia: l M2 t = a + b ly t + c r t + e t (1) where M2 is the M2 moetary aggregate i real term, Y the real icome, r the iterest rate ad e a error term. I the first step, we employ the vector error correctio model (VECM) of Johase (1988) ad Johase ad Juselius (1990). The VECM pertaiig to the variables i Eq (1) ca be writte as follows: Δl M 2 t bjδl M 2t j + c jδ Yt j + = a0 + l j = 1 j = 1 j = 1 ( β l M 2t + β2 lyt + β3r εt d Δr + α 1 ) + (2) I this step, the ull hypothesis of o coitegratio defied by H 1 : α = 0 is tested agaist the alterative H 1 : α < 0. The β j represets the log-ru relatio betwee the variables, while b j, c j ad d j j t j Research Joural of Iteratıoal Studıes - Issue 13 (March, 2010) 55

3 represet short-ru coefficiets of moey, icome ad iterest rate from the previous quarters (see Johase (1988) ad Johase ad Juselius (1990) for details). Depedig o the power of uit root test, however, differet tests may yield differet results. Due to this ucertaity, Pesara ad Shi (1995) ad Pesara, Shi ad Smith (1996) itroduced the so-called ARDL of testig for coitegratio. This approach has the advatage of avoidig the classificatio of variables ito I(1) or I(0) ad ulike stadard coitegratio tests, there is o eed for uit root pre-testig (Basmai-Oskooee, 2001). The error correctio versio of the ARDL model pertaiig to the variables i Eq. (1) is as follows: Δl M 2 t bjδl M 2t j + c jδ Yt j + = a0 + l j = 1 j = 1 j = 1 + δ 1 M 2t 1 + δ 2 lyt 1 + δ 3rt 1 + εt d Δr j t j l (3) I this model, the ull hypothesis of o coitegratio defied by H 0 : δ 1 = δ 2 = δ 3 =0 is tested agaist the alterative of H 1 : δ 1 0, δ 2 0, δ 3 0 by meas of familiar F-test (see Pesara ad Shi (1995) ad Pesara, Shi ad Smith (1996) for details). 3. Empirical Results ad Discussio I this sectio, we will preset the results ad their scietific explaatio. Moreover, we also compare the VECM agaist ARDL models i order to fid the best ad more stable moey demad fuctio Vector Error Correctio Model I the first step of VECM, we test the preset of uit root usig DF ad ADF tests, ad the results are preseted i Table 1. We lear from the table that the series are ot statioary i level ad statioary i the first differece. Therefore the cocept of coitegratio is relevat. Table 1: Uit root test of Dickey-Fuller (DF) ad Augmeted Dickey Fuller (ADF) Variable DF ADF lm ΔlM * * ly ΔlY * * r Δr * * *) statioary at 5% level. Further aalysis usig λ max ad Trace tests show that there are at least two coitegratig vectors betwee M2, Y ad r. Here we simulated the model up to time-lag = 8 ad the results are robust for all choice of lag order. It is, however, ot easy to fid a sigificat log-ru relatioships amog the variables. We fid a sigificat relatioships at 5% level oly i the VECM(5) as see i Table 2. Research Joural of Iteratıoal Studıes - Issue 13 (March, 2010) 56

4 Table 2: Coefficiets of VECM(5) for Moey demad fuctio of Idoesia: 1990:1-2008:3. A. Short-ru coefficiets Regressor Coefficiet Stadard Error T-Ratio[Prob] Itercept [.000] lm2(-1) [.029] lm2(-2) [.006] lm2(-3) [.001] lm2(-4) [.131] ly(-1) [.004] ly(-2) [.303] ly(-3) [.047] ly(-4) [.346] r(-1) [.063] r(-2) e [.068] r(-3) e [.067] r(-4) E E [.609] ecm1(-1) [.000] DUMMY [.000] B. Log-ru coefficiets ly ( )* r (.57109) Itercept ( ) *) Numbers i parethesis are the coefficiets ormalized to lm2. Based o the results from Table 2, we try to examie three issues. The first issue is to establish coitegratio amog M2, Y ad r. Our result shows that the coefficiet of lagged error-correctiomodel term is statistically sigificat at 5% level. That meas M2, Y ad r i Idoesia i the period of study are coitegrated. Ufortuately, this result is ot robust to the choice of the lag-order. We could ot fid ay other sigificat coefficiet for ECM terms at 5% level for the model with lag-order 6, 7 or 8. All the coefficiets of the lagged-ecm terms i the three models are isigificat. The secod issue is the stability of the moey demad fuctio. Here we employ the CUSUM ad CUSUMSQ tests proposed by Brow, Durbi ad Evas (1975). The tests are applied to the residuals of the model. The CUSUM test is based o the cumulative sum of residuals based o first set of observatios. It is updated recursively ad is plotted agaist the break poits. If the plot of CUSUM stays withi 5% sigificace level (portrayed by two straight lies whose equatios are give i Brow et. al (1975), the the coefficiet estimates are said to be stable. Similar procedure is used to carry out the CUSUMSQ which is based o the squares recursive residuals. Graphical represetatios of these two tests for the above model are provided i Figure 1 Research Joural of Iteratıoal Studıes - Issue 13 (March, 2010) 57

5 Figure 1: Plot of CUSUM (above) ad CUSUMSQ (below) statistics for the model VECM(5). Plot of Cumulative Sum of Recursive Residuals Q2 1993Q4 1996Q2 1998Q4 2001Q2 2003Q4 2006Q2 1.5 Plot of Cumulative Sum of Squares of Recursive Residuals Q2 1993Q4 1996Q2 1998Q4 2001Q2 2003Q4 2006Q2 From the figures, we lear that both CUSUM ad CUSUMSQ statistics are ot stay i the critical itervals. It suggests that there is stability problem durig the period of 2001:3 2004:1. We, therefore, coclude that the Idoesia M2 moey demad fuctio based o VECM(5) is istable over the period of study. The third issue from the Table 1 is a iferece about the short-ru ad log-ru coefficiet estimates of M2 moey demad fuctio. As expected, the icome has a sigificat impact o the moey demad, both i the short-ru ad log-ru. Its positive relatio suggests that the icrease of output will be followed by the icrease i moey demad. O the other had, the iterest rate has o sigificat impact, both i the short ru ad the log-ru as well. Therefore, we coclude that icome seems to have stroger ifluece comparig to the iterest rate Autoregressive Distributed lag (ARDL) I the secod stage, we employ the ARDL approach to the same data. We impose up to maximum eight lags o each first differeced term i the ARDL model. We estimate the model based o R-Bar- Square, Akaike Iformatio Criterio (AIC) ad Schwarz Bayesia (SB) ad Haa-Qui (HQ). As Bahmai-Oskooee (2001) oted, oly a appropriate lag selectio will be able to idetify the true dyamic of the model. Geerally, all selectio criteria give similar results. The AIC, SB ad HQ suggest that the most appropriate model is ARDL(5,2,7), whereas the R-Bar-Square choose the ARDL(5,6,7) model. Our further aalysis usig R-Square ad Adjusted-R-Square shows that the ARDL(5,6,7) model is the most appropriate oe. The full iformatio estimates of the ARDL(5,6,7) is preseted i Table 3, whereas the estimates of the ARDL(5,2,7) is preseted i Appedix 1. Research Joural of Iteratıoal Studıes - Issue 13 (March, 2010) 58

6 Table 3: Full iformatio estimate of ARDL(5,6,7) model ( lm2 t as depedet variable) based o R-Bar- Square. A. Short-ru coefficiets Regressor Coefficiet Stadard Error T-Ratio[Prob] Itercept [.165] lm2(-1) [.005] lm2(-2) [.161] lm2(-3) [.000] lm2(-4) [.042] ly [.409] ly(-1) [.002] ly(-2) [.595] ly(-3) [.123] ly(-4) [.285] ly(-5) [.310] r [.044] r(-1) [.010] r(-2).9546e [.421] r(-3) [.005] r(-4).1533e e [.988] r(-5) E [.370] r(-6) e [.009] DUMMY [.235] ecm(-1) [.210] B. Log-ru coefficiets ly (3.0640)* r (1.2720) Itercept ( )* Note: Numbers i parethesis are the coefficiets ormalized to lm2. *) statistically sigificat at 5% level. From the Table 3, we lear that there is sigificat coitegratio amog M2, Y ad r. We also fid the similar relatios betwee the three variables i compare to those of VECM. The coefficiet estimates of icome are positive ad statistically sigificat, both short-ru ad log-ru. Furthermore, i Figure 2 we preset the graphical represetatio of CUSUM ad CUSUMSQ test for the ARDL(5,6,7) based o R-Bar-Square. The similar results are also foud from the ARDL(5,2,7) model based o AIC, SB ad HQ. Thus, o matter which criteria we used, the M2 moey demad fuctios based o ARDL approach are stable. Research Joural of Iteratıoal Studıes - Issue 13 (March, 2010) 59

7 Figure 2: Plot of CUSUM (above) ad CUSUMSQ (below) statistics for the model ARDL (based o R-Bar- Square). Plot of Cumulative Sum of Recursive Residuals Q1 1994Q3 1997Q1 1999Q3 2002Q1 2004Q3 2007Q1 1.5 Plot of Cumulative Sum of Squares of Recursive Residuals Q1 1994Q3 1997Q1 1999Q3 2002Q1 2004Q3 2007Q1 Comparig the results of VECM ad ARDL models, we geerally fid similar results. However, the ARDL model is better that those of the VECM. The moey demad model based o ARDL is stable, while the ARDL model is ot stable. Moreover, the ARDL also resulted i better idicators i term of R-Square ad Adjusted R-Square. They are 0.78 ad 0.68 respectively, i compare to 0.71 ad 0.58 for the VECM model. Therefore the ARDL model ca explai more variability of moey demad i compare to the VECM model. 4. Cocludig Remarks The objective of this research was to estimate the Idoesia M2 moey demad usig vector error correctio (VECM) ad autoregressive distributed lag (ARDL) model. The results suggested that there was coitegratig relatioship amog real moey aggregate, real icome ad iterest rate i Idoesia durig the period of study. The real icome had sigificat ifluece o the real moey balace. The impact was also stroger i compare to those of the iterest rates. The results also showed that the ARDL model was better tha VECM. Furthermore, the result also showed that the ARDL model was stable, while the VECM model was ot stable. Therefore, we should fid ad iterpret the model carefully whe we use the VECM. The wrog choice of the lagorder may lead us to a misleadig coclusio. Research Joural of Iteratıoal Studıes - Issue 13 (March, 2010) 60

8 Refereces [1] Achsai, N.A., O. Holtemöller ad H. Sofya (2005). Ecoometric ad Fuzzy Modelig of Idoesia Moey Demad. I Cizek, P., W. Härdle ad R. Wero (Eds). Statistical Tools i Fiace ad Isurace. Spriger. Berli, Germay [2] Arize, A.C. ad S.S. Shwiff (1993). Coitegratio, Real Exchage Rate ad Modellig the Demad for Broad Moey i Japa. Applied Ecoomics 25(6): [3] Arize, A.C. (1994). A Re-examiatio of the Demad for Moey i Small Developig Ecoomies. Applied Ecoomics 26(3): [4] Bahmai-Oskooee, M. (2001). How stable is M2 moey demad fuctio i Japa?. Japa ad the World Ecoomy 13: [5] Brow, R.L., J. Durbi ad J.M. Evas (1975). Techiques for testig the costacy of regressio relatios over time. Joural of the Royal Statistical Society B, 37: [6] Deckle, P ad M. Pradha (1997). Fiacial Liberalizatio ad Moey Demad i ASEAN Coutries: Implicatios for Moetary Policy. IMF Workig Paper WP/97/36. [7] Drake, L ad K.A. Chrystal. (1994). Compay-Sector Moey Demad: New Evidece o the Existece of a Stable Log-u Relatioship for the UK. Joural of Moey, Credit ad Bakig 26(3): [8] Hafer, R.W. ad D.W. Jase (1991). The Demad for Moey i the Uited States: Evidece from Coitegratio Test. Joural of Moey, Credit ad Bakig 23(2): [9] Haug, A.A. ad R.F. Lucas. (1996). Log-Term Moey Demad i Caada: I Search of Stability. Review of Ecoomic ad Statistics 78(2): [10] Johase, S (1988). Statistical Aalysis of Coitegratig Vactors. Joural of Ecoomic Dyamics ad Cotrol 12: [11] Johase, S ad K. Juselius (1990). Maximum Likelihood Estimatio ad Iferece o Coitegratio with applicatios to the demad for moey. Oxford Bulleti of Ecoomics ad Statistics 52: [12] Lim, G.C. (1993). The Demad for the Compoets of Broad Moey: Error Correctio ad Geeralized Asset Adjustmet System. Applied Ecoomics 25(8): [13] McNow, R ad M.S. Wallace (1992). Coitegratio Test of a Log-Ru Relatio betwee Moey Demad ad Effective Exchage Rate. Joural of Iteratioal Moey ad Fiace 11(1): [14] Mehra, Y.P. (1993). The Stability of the M2 Moey Demad Fuctio: Evidece from a Error-Correctio Model. Joural of Moey, Credit ad Bakig 25(3): [15] Miller, S.M (1991). Moetary Dyamics: A Applicatio of Coitegratio ad Error- Correctio Modellig. Joural of Moey, Credit ad Bakig 23(2): [16] Miyao, R (1996). Does a Coitegratig M2 Demad Relatio Really Exist i Japa? Joural of the Japaese ad Iteratioal Ecoomics, 10: [17] Moosa, I.A. (1992). The Demad for Moey i Idia: A Coitegratio Approach. The Idia Ecoomic Joural 40(1): [18] Orde, D. ad L.A. Fisher (1993). Fiacial Deregulatio ad the Dyamics of Moey, Prices ad Output i New Zealad ad Australia. Joural of Moey, Credit ad Bakig 25(2): [19] Pesara, M.H. ad Y. Shi (1995). A Autoregressive Distributed Lag Modellig Approach to Coitegratio Aalysis. I: Strom, S. et. al. (Eds). Ceteial Volume of Ragar Frisch. Cambridge Uiversity Press. [20] Pesara, M.H., Y. Shi, ad R.J. Smith (1996). Testig for the exixtece of a log-ru relatioship. DAE Workig Paper No Departmet of Applied Ecoomics, Uiversity of Cambridge. [21] Sriram, S.S. (1999). Demad for M2 i a Emergig-Market Ecoomy: A Error- Correctio Model for Malaysia. IMF Workig paper WP/99/173 Research Joural of Iteratıoal Studıes - Issue 13 (March, 2010) 61

9 [22] Sriram, S.S. (1999). Survey Literature o Demad for Moey: Theoretical ad Empirical Work with Special Referece to Error-Correctio Models. IMF Workig paper WP/99/64. Appedix 1 Full iformatio estimate of ARDL(5,2,7) model ( lm2 t as depedet variable) based o Schwarz- Bayes, Akaike Iformatio Criterio ad Haa-Qui. A. Short-ru coefficiets Regressor Coefficiet Stadard Error T-Ratio[Prob] Itercept [.004] lm2(-1) [.001] lm2(-2) [.162] lm2(-3) [.000] lm2(-4) [.001] ly [.643] ly(-1) [.003] r e [.010] r(-1) E [.001] r(-2) E E [.838] r(-3) e [.007] r(-4) E E [.495] r(-5) E [.007] r(-6) e [.041] DUMMY [.104] ecm(-1) [.054] B. Log-ru coefficiets ly (4.2268)* r.0661 (1.8790) Itercept ( )* Note: Numbers i parethesis are the coefficiets ormalized to lm2. *) statistically sigificat at 5% level. Research Joural of Iteratıoal Studıes - Issue 13 (March, 2010) 62