Velocity of Money Functions in Pakistan and Lessons for Monetary Policy

Transcription

1 SBP Research Bulletn Volume 6, Number 2, 2010 Velocty of Money Functons n Pakstan and Lessons for Monetary Polcy Muhammad Omer * Abstract: Ths paper s an attempt to contrbute to the ongong debate: should central bank of Pakstan adopt the nflaton targetng or contnue wth the monetary targetng as a monetary polcy strategy? A pre-requste for monetary targetng strategy s a stable money demand functon, whch n turn requres stablty n velocty. Instablty n velocty on the other hand s beleved to stem from the volatlty of the nterest rate. The paper estmates velocty of money functons and explores ther stablty n Pakstan. The results show that base and broad money veloctes are ndependent of the nterest rate fluctuatons. It s also found that veloctes of all the three monetary aggregates (.e., M0, M1, and M2) have stable relatonshp wth ther determnants. These fndngs support the use of monetary aggregates as nomnal anchor. JEL Classfcaton: E12, E5 Keywords: monetary targetng, ncome velocty of money, money demand functon 1. Introducton The State Bank of Pakstan s among the few central banks whch have been usng monetary targetng strategy for the conduct of ther monetary polcy. 1 In such a strategy, monetary aggregates are used as a nomnal anchor whch ndrectly serves the basc objectve of prce stablty. The achevement of targeted nflaton remans less bndng wth ths regme; however, the devaton of realzed nflaton from the targeted one could stll be used as a measure of performance of a central bank. Based on such measure adopted by Omer and Saqb (2009), the SBP s performance n achevng prce stablty remans weak, specfcally n the post fnancal lberalzaton perod. * Analyst, State Bank of Pakstan; muhammad.omer@sbp.org.pk The author s thankful to Sajd Choudhry and Julo Carrllo for ther helpful comments. 1 For a last couple of years, however, the SBP monetary polcy statements have been focusng more on movements n nterest rates than on monetary aggregates.

2 38 SBP Research Bulletn, Vol. 6, No. 2, 2010 Recent surge n nflaton n Pakstan snce FY08 and stores of successes wth nflaton targetng n varous countres, renewed the debate on the monetary targetng strategy followed by the SBP. Number of authors have argued for and aganst the adopton of nflaton targetng strategy lke Monuddn (2009), Felpe, (2009), Akbar and Rankaduwa (2006), Khald (2006), Khan and Schmmelpfennng (2006), and Chaudhry and Choudhary (2006). Also, a great number of authors has assessed f quantty theory of money, the bass of monetary targetng, holds for Pakstan lke Omer and Saqb (2009), Qayyum (2006), Kemal (2006) and Abbas and Husan (2006). Besdes the above two drectons, a few authors have revsted the assumptons of quantty theory of money (QTM) that forms the buldng block of the monetary targetng strategy. Of these assumptons, two are crtcal, frst ncome velocty of money or ts growth rate s constant, and second snce monetary shock does not has a long run real effect, a stable velocty mples a stable money demand functon over the long run. A stable money demand functon, on the other hand, makes monetary aggregates a favorable canddate for the ntermedate target; otherwse, nterest rate should be adopted as nomnal anchor as argued by Mshkn (2004). In case of Pakstan, Omer and Saqb (2009), whle testng the QTM explore the constant velocty assumpton. They test the statonarty of the veloctes related wth all the three defntons of monetary aggregate (.e., M0, M1, and M3) and report that veloctes are not mean revertng and hence unstable. They conclude that the SBP has very lmted ablty to control the monetary aggregates or money supply; however, t has sgnfcant control over the nterest rates due to money endogenety. Therefore, the SBP should adopt nterest rate as ts nomnal anchor. A smlar concluson has been drawn by Monuddn (2009) who fnds money demand functon n Pakstan as unstable. However, both papers have been crtczed on the bass of ether specfcaton or methodology adopted For money demand functon, nterest rate s beleved to be the major source of nstablty. Volatlty n the nterest rate makes the velocty of money volatle and hence the money demand. Alternatvely, as ndcated by the Bordo and Junong (2004) the changng defnton of money and/or development of fnancal nsttutons could be a stronger source of nstablty. The objectve of ths paper s therefore frst to check f the nterest rate s a sgnfcant determnant of velocty of money n Pakstan, as generally perceved; and second, f ths relatonshp of velocty wth ts determnants s stable n the long run. Ether an nsgnfcant nterest rate n the velocty functon or a stable relatonshp of velocty wth ts determnants and/or both wll lend necessary support to the monetary aggregates for ther use as nomnal anchor. An unstable

3 Muhammad Omer 39 velocty on the other hand, not only sets the premse of the unstable money demand functon but may also support the vew of Omer and Saqb (2009) that the SBP should revst ts monetary targetng strategy and consder nflaton targetng. The rest of the paper s structured as follows. The next secton presents a revew of the exstng lterature on the subject and secton 3 syntheszes the money demand functon usng velocty of money and explans the methodology and the data sources. Secton 4 dscusses the result of the velocty functon and the last secton conssts of concludng remarks. 2. Revew of lterature In the lterature money demand functon has been studed usng both velocty and conventonal formulaton. Ths secton presents the detaled revew of the lterature on money demand functon usng both the formulatons separately, to account for overall progress on ths area. Before the collapse of the Bretton Woods System, M1 money was consdered stable n the ndustralzed economes. However, snce 1974 the conventonal M1 money demand functon began to over predct the demand for money, whch Goldfeld (1976) termed as the case of mssng money. The woes of conventonal money demand functon ncreased n the 1980s as t under-predcted the velocty of money, whch rose faster than expected. Economsts have snce been concerned that the velocty of Ml and several other monetary aggregates from 1981 to at least 1986, declned to an unpredcted extent. They have questoned the contnued pursut by central banks of monetary targets. Unpredctablty of velocty s the key reason polcymakers n the Unted States and elsewhere have gven for abandonng monetary targetng. Inherent role of velocty n the stablty of money demand prompted researchers to conduct a detaled study of money demand functon usng velocty. In fact velocty s another way n whch money demand functon can be expressed (Sklos, 1993). Bordo and Junong (1981, 1987, 1990, and 2004) usng long term data study the behavor of velocty among a number of developed economes, and fnd that velocty declned n these economes n phase of monetzaton and then recovered wth the fnancal nnovatons and deregulatons. As a tool for emprcal analyss, the authors used ordnary least square n most of ther studes. Later on, Bordo et al. (1997) provde necessary methodologcal support to ther nsttutonal hypothess usng co-ntegraton and the error correcton technques. In comparson to the relatvely lmted lterature on the velocty, conventonal

4 40 SBP Research Bulletn, Vol. 6, No. 2, 2010 money demand attracted a large number of researchers, prmarly because of ts easy to understand formulaton. Even f one starts wth the post Bretton Woods perod, Goldfeld (1973), Boughton (1981), Arango and Nadr (1981), Butter and Fase (1981), Rose (1985), Hendry and Ercsson (1991), Mehra (1991), and Leventaks (1993), are a few among the vast pool of the authors who made a sgnfcant contrbuton on the conventonal models of money demand. A bref summary of the recent lterature has been gven n the annexure that dscusses conventonal money demand functon n terms of stablty. Among selected developed countres, except Germany, UK and Swtzerland, the money was found to have a stable and long run relatonshp wth ts determnants. Smlarly, among the selected group of the developng countres, except Chna and Nepal, the money demand was found to be stable. The nstablty n the Chnese money demand stems from the rapd fnancal developments started snce 1980s. Lee and Chen (2008) fnd the structural breaks n 1980 and n 1993, whch they lnked wth the crtcal fnancal and economc developments. As mentoned above, Monuddn (2009) fnds an unstable money functon for Pakstan. Hs results show a large negatve ntercept for the estmated broad money demand model. Surprsngly, no satsfactory explanaton s provded for the relatvely large negatve ntercept, whch leads to suspcon of specfcaton bas. For example, Bordo and Junong (1990) suggest that n an economy where nterest rate s not free to respond to the market forces (regulated economy) the expected nflaton should be ncluded n the demand functon. However, Monuddn (2009) study gnores expected nflaton despte ncludng the perod of fnancal represson ( ) n the sample. On the other hand, the samples used by other studes lke Brahman-Oskooee and Rehman (2005) and Qayyum (2006) do not go beyond the year Therefore, ther results should be vewed wth cauton as ther samples do not fully encompass the effect of second generaton of fnancal reforms ntated n 2000s. The result of another study on Pakstan by Abbas and Husan (2006) should also be vewed wth cauton as they do not explctly undertake any stablty test and rely on the sgnfcance of regresson as ndcaton of the long run and stable M2 demand functon. Whle there are number of studes that test stablty of conventonal money demand functon for Pakstan, there s hardly one that examnes the stablty of velocty of money except some bref revews by Blquees and Shehnaz (1994) and Omer and Saqb (2009). Blquees and Shehnaz (1994) document a slowdown n velocty between and They used the number of bank branches as proxy for the fnancal development and conclude that fnancal development n Pakstan has sgnfcantly affected the velocty of money. Nether they attempted

5 Muhammad Omer 41 to nvestgate the long run relatonshp nor dd they conduct any stablty test of ther fndngs. Omer and Saqb (2009), on the other hand used nstablty n the money velocty as one of the reasons for dsapprovng the monetary targetng strategy adopted by the SBP. They argued that quantty theory of money assumes a constant or statonary velocty whle ncome veloctes of M0, M1, and M2 are not mean revertng or statonary n Pakstan. On the bass of ther fndngs, they conclude that all three veloctes are unstable. Ther result of non-statonary veloctes has been crtczed also, of beng non robust. The above revew of exstng lterature clearly shows that conventonal formulaton of money demand s more popular among the researchers precsely due to smple analytcal formulaton and nterpretaton. However, ths study focuses on velocty formulaton of money demand functon. As ndcated earler, the objectve of ths study s to nvestgate the stablty of velocty, whch s not possble usng conventonal money demand functon. Moreover, the velocty formulaton s strongly based on economc theory of permanent ncome hypothess propounded by Mlton Fredman. On contrary, those who worked wth conventonal money demand functon, a large number of them have followed Arango and Nadr (1981) approach whch has been severely crtczed for beng ad hoc and lackng theoretcal foundaton. 3. Data and methodology A combnaton of conventonal equaton of exchange and Fredman (1956) demand functon of real money balances gves us the followng functon for velocty of money through a smple algebrac manpulaton: log V ( m) = β + β log Y + β r + β log Y + β π + ε (1) p t e Where V(m) s ncome velocty of money measured as a rato of nomnal GDP to some monetary aggregate and m = 0, 1, 2 for the respectve monetary aggregate,.e., M0, M1 and M2; Y p s the real permanent ncome per capta; r s real nterest rate; Y t represents the transtory ncome measured as the rato of the per capta overall ncome and permanent ncome; and π e s expected nflaton.. We expect a postve sgn for permanent ncome n the above equaton as any ncrease n t wll ncrease the number of transactons n the economy thereby affectng the velocty postvely. Transtory ncome, on the other hand should have a unty coeffcent n the regresson. A coeffcent that s postve but less than one would ndcate that the velocty moves pro-cyclcally and would be consstent wth the Fredman s permanent ncome hypothess. Over the cycle, the transtory

6 42 SBP Research Bulletn, Vol. 6, No. 2, 2010 ncome would ncrease the demand for money, because cash balances serve as a buffer stock. In the long run these transtory balances would then be worked off, returnng to the coeffcent to unty (Bordo and Junong, 1990). The real nterest rate s also expected to have a postve sgn as an ncrease n t would decrease the demand of real money balances and thus a rse n the velocty wth a gven level of ncome. The mpact of the nflaton on velocty s ambguous and the coeffcent could take ether postve or negatve sgn dependng upon ts relatve nfluence on money balances and ncome growth. In order to estmate the relatonshp between the velocty of money and ts determnants as mentoned above, we have used autoregressve dstrbuted lag (ARDL) model suggested by Pesaran and Shn (1999) and Pesaran et al (2001). The advantages of usng ARDL are (a) t can be appled on a tme seres data rrespectve of whether the varables are ntegrated of order zero or one, (b) t can take suffcent numbers of lags to capture the data generatng process n a generalto-specfc modelng framework (Laurenceson and Cha, 2003); and (c) a dynamc error correcton model (ECM) can be derved from ARDL through a smple lnear transformaton (Banerjee et al., 1993). The ECM ntegrates the short-run dynamcs wth the long run equlbrum wthout losng long-run nformaton. Although the am s to estmate the long-run relatonshp and examne ther stablty, the ARDL approach also ncorporates the short run dynamcs as only relyng upon long run estmates wll not be suffcent. Indeed, Ladler (1993) argues that only relyng on long-run money demand functon s napproprate, as some of the problems of nstablty n the money demand functon could stem from nadequate modelng of the short-run dynamcs characterzng departures from the long-run relatonshp. We estmate the followng ARDL model for examnng the stablty of velocty of money functon. l m n o p Δ log V ( m) = γ 0 + γ1 Δ log V ( m) 2 log t + γ Δ Y + γ 3 Δ r + γ 4 Δ π + (2) p γ Δ Y + γ log V ( m) + γ log Y + γ r + γ π + γ Y + ζ t p t 5 6 t 1 7 t 1 8 t 1 9 t 1 10 t 1 t Whereγ 6, γ 7, γ 8, γ 9, γ 10 are the long run coeffcents whle γ 1, γ 2, γ 3, γ 4, γ 5 and ζ represents the short run dynamcs and random dsturbance term respectvely. t The null hypothess that the long run relatonshp does not exst,.e.,

7 Muhammad Omer 43 γ = γ = γ = γ = γ 0 s tested aganst the alternatve hypothess γ = 6 γ 7 γ 8 γ 9 γ10 0 by means of famlar F-test. However, the asymptotc dstrbuton of ths F-statstc s non-standard rrespectve of whether the varables are I(0) or I(1). Pesaran et al. (2001) have tabulated two sets of approprate crtcal values. One set assumes all varables are I(1) and another assumes that they are all I(0). Ths provdes a band coverng all possble classfcatons of the varables nto I(1) and I(0) or even fractonally ntegrated. If the calculated F-statstc les above the upper level of the band, the null s rejected ndcatng contegraton. Next step n ARDL estmaton, as outlned by the Pesaran and Pesaran (1997), s estmaton of the long run relatonshp based on the approprate lag selecton crteron such as Adjusted R 2, Akake Informaton Crteron (AIC), or Schwarz Bayesan Crteron (SBC). The choce of lag selecton crtera s mportant and only an approprate lag selecton crteron wll help n dentfyng the true dynamcs of the model. Once determned, the ARDL model gves the long run contegratng coeffcents of the model. Based on these long run coeffcents, the estmaton of dynamc error correcton s carred out usng formulaton of equaton (3). The coeffcents δ 1, δ 2, δ 3, δ 4 and δ 5 show the short run dynamcs of the model and δ 6 ndcates the dvergence/convergence towards the long run equlbrum. A postve coeffcent ndcates a dvergence, whle a negatve coeffcent ndcates convergence. l m n o p Δ log V ( m) = δ 0 + δ 1 Δ log V ( m) 2 log t + δ Δ Y + δ 3 Δ r + δ 4 Δ π + (3) p 0 δ Δ Y + δ ECM + ϑ t 5 6 t t The stablty of the estmated model has been examned by usng CUSUM and CUSUMSQ tests, proposed by the Brown et al. (1975). Also some other dagnostc tests were appled on resduals such as Lagrange Multpler (LM) test for seral correlaton, Ramsey Reset test for functonal form msspecfcaton, and Jarque-Berra Test for normalty. The LM test assumes null hypothess that resduals are serally uncorrelated whle Ramsey Reset assumes that the specfed model has lnear functonal form. Smlarly, Jarque-Berra test hypotheszes that the resduals are normally dstrbuted. All of the above hypotheses are tested at 95 percent level of confdence. For all estmaton purposes annual data startng from 1975 to 2006 has been used; t s the perod for whch a consstent set of data of all the requred varables s avalable. The startng year corresponds to the offcal dvson of all fnancal and

8 44 SBP Research Bulletn, Vol. 6, No. 2, 2010 economc statstcs between East and West Pakstan (Blquees and Shahnaz, 1994) and the termnal year (2006) s the last year for whch offcal estmates of a consstent M1 data s avalable. The data s obtaned from Handbook of Statstcs on Pakstan Economy (2005) and dfferent ssues of monthly statstcal bulletn both publshed by the State Bank of Pakstan, Karach. Before estmaton, logarthmc transformaton appled to all varables except real nterest rate (call money rate) and nflaton (percent change n CPI). The varable per capta real permanent ncome has been constructed usng the long-run trend n the log of per capta real GDP. For ths purpose HP flter (λ= 100) has been appled on per capta real GDP snce 1950 followng Bordo and Junong (1990) Results Before estmatng the ARDL model, we have tested all the varables for statonarty by usng Augmented Dckey Fuller (ADF) test and found per capta permanent ncome and three veloctes as dfferenced statonary and transtory ncome, nflaton and real nterest rate as level statonary. 3 The results of ARDL bound test are reported n Table 1 for three specfcatons of the model wth lags rangng from 1 to 3 as the co-ntegraton s senstve to the choce of lag length. Lmtng maxmum lag to 3 s normal practce n lterature dealng wth the annual data. The choce of ths procedure s to explore the possble contegraton relatonshps that mght be emergng at varous lag levels. It s found that per capta permanent ncome, real nterest rate, transtory ncome and nflaton are found to have long-run relatonshp wth veloctes V(1) and V(2) 4 as the computed F-statstcs s hgher than the upper lmt of the bound wth lags hgher than one. However, n case of V(0), no such evdence of contegraton. s found. However as dscussed earler, Bahman-Oskooee and Bohl (2000) consder these results as prelmnary due to arbtrary choce of lag selecton, and argue that the contegraton evdence based on error correcton s more effcent. 2 Although the study s confned to 1975 and 2006, the use of longer tme seres s more approprate for extractng a trend from the seres. 3 ADF test results can be obtaned from the author. 4 For Model of V(1), bound test for contegraton ntally conducted wth ntercept, and result thus obtaned ndcated V(1) s fractonally contegrated (Bahman-Oskooee, 2005). Later, trend was ntroduced n estmaton whch remarkably mproved the result of the bound test. Therefore, test results for V(1) ncludes trend.

9 Muhammad Omer 45 Tables 1. F-Test for Contegraton Lag 1 Lag 2 Lag3 V(0) V(1)ⁿ V(2) At 95% level Crtcal Values of bound s ⁿ Estmated usng trend In the next stage, we choose the optmal lag length for a gven model and estmate long run dynamcs of the ARDL model. Accordng to Pesaran (1997), AIC and SBC perform relatvely well n small samples. However, the SBC s slghtly superor to the AIC (Pesaran and Shn, 1999) and t s parsmonous n the sense t uses mnmum acceptable lag whle selectng the lag length and avods unnecessary loss of degrees of freedom. Therefore, usng SBC crtera optmal lag lengths (1,0,0,0,0) for M0 velocty, (0,0,3,3,2) for M1 velocty, and (3,3,0,0,0) for M2 veloctes selected whch respectvely corresponds to the varables velocty of money, permanent ncome, nterest rate, nflaton and transtory ncome. Table 2. Full Informaton Long Run Coeffcent Estmaton Varables (optmal Lags) Models 1(V(0)) ( ) Model 2(V(1)) ( ) Model 3(V(2)) ( ) Y p * ** * (3.1888) ( ) (2.589) r * (0.8364) (7.2307) ( ) π * ** (0.799) (7.9165) (1.6767) Y t * * ( ) (3.5878) (3.0711) Intercept * * * (17.655) (4.6035) ( ) Trend * ( ) * ndcates 5% level of sgnfcance; ** 10% level of sgnfcance; fgures n parenthess are t- statstcs The results of the long run co-ntegratng relatonshp of three forms of veloctes wth ts varables are reported n Table 2. Coeffcents of all the three models of

10 46 SBP Research Bulletn, Vol. 6, No. 2, 2010 veloctes are generally n conformty wth our theoretcal foundaton. Per capta permanent ncome bears a postve sgn n both V(0) and V(2) velocty functon, as envsaged earler. In quantum, one percent ncrease n the per capta permanent ncome wll ncrease the V(2) velocty by 1.54 percent n the long run. For V(1), however, the relatonshp was found to be negatve but nsgnfcant. The mpact of transtory ncome s also postve and sgnfcant but very small for V(1) and V(2). Ths mples frst, both V(1) and V(2) are pro-cyclcal whch lnks the underlyng behavor of velocty wth the per capta permanent ncome. Second, the mpact of the busness cycle fluctuatons on velocty of money and thus on the money demand s although very trval but sgnfcant. Whle a sgnfcant and postve relatonshp between the nterest rate and V(1) has been found, both the V(0) and V(2) are found to be nsenstve to the changes n the real nterest rate. Ths ndcates that economc agents respond to nterest rate ncrease by swtchng ther deposts away from demand deposts that effectvely bear zero rate of return to nterest-bearng tme deposts. On the other hand, nflaton has been found havng a sgnfcant relatonshp wth V(1) and V(2) n the long-run and nsgnfcant wth V(0). The short run dynamcs of the veloctes of money have been gven n Table 3 for three defntons,.e., V(0), V(1) and V(2). Not much nterpretaton could be attached to the short-run coeffcents. All they show s the dynamc adjustment of these varables. However, the negatve coeffcent of the error correcton term wth sgnfcant t-statstc confrms the contegraton among the varables n all three veloctes. As argued by Bahman-Oskooee and Bohl (2000), ths evdence of contegraton s more effcent than the bound test. These contegratng relatonshps are due to the nterest rate, nflaton, and transtory ncome n case of V(1) velocty, and due to per capta permanent ncome and the transtory ncome n case of the V(0) and the V(2) veloctes. Besdes, the results show that all three estmated models cannot reject the null hypotheses of LM tests, Ramsay- reset test and the Jarque-Berra test. In other words resduals are serally uncorrelated, normally dstrbuted, and the specfed models are functonally lnear. These test results show that the estmated error correcton models are statstcally adequate. The graphcal presentaton of CUSUM and CUSUMSQ tests s provded n Fgure 1. All the graphs of CUSUM and CUSUMSQ statstcs stay comfortably well wthn the 5 percent band ndcatng that the estmated relatonshps of all three veloctes are stable.

11 Muhammad Omer 47 Table 3. Full Informaton Short run Estmate wth ECM Model 1 V(0) Model 2 V(1) Model 3 V(2) ΔV(m) * 0.463* (4.20) (2.56) ΔY p 0.837* * * * (3.15) (-1.15) (2.09) (-4.55) (-2.44) Δr * * (0.41) (1.68) (-4.39) (-3.86) (0.52) Δπ * * 0.010** (0.41) (1.10) (-4.89) (-4.08) (1.96) ΔY t 1.0E-5-3.0E-6-4.0E-5* 3.0E-5* (2.44) (-0.47) (4.12) (3.91) ΔTrend 0.016* e(-1) -0.33* * (-2.44) (-6.80) (-4.04) Adjusted R^ LM Stats Ramsey's Reset Normalty * ndcates 5% level of sgnfcance; ** 10% level of sgnfcance 5. Concludng remarks The paper explores the factors that determne the long run behavor of ncome velocty of money. The estmated result shows that n long run the M0 and M2 veloctes depend on the ncome and the busness cycle fluctuatons and are ndependent of the nterest rate fluctuatons - a beleved root cause for velocty nstablty. On the other hand, we have found M1 velocty depends on the nterest rate and nflaton besdes ncome. In terms of the polcy perspectve, ndependence of both M0 and M2 veloctes from nterest rate fluctuatons strengthens ther role as nomnal anchors for monetary polcy. Interestngly ths s the case n practce n Pakstan: the monetary authorty of Pakstan uses M0 and M2 as nomnal anchors for operatonal and ntermedate targets respectvely whle t had never used M1 offcally for polcy purposes. Instead, offcal reportng of M1 by the authorty has been abandoned snce 2006.

12 48 SBP Research Bulletn, Vol. 6, No. 2, 2010 We also fnd stable relatonshps between ncome veloctes of money and ther determnants on the bass of CUSUM and CUSUSMQ tests. These results are contrary to both Omer and Saqb (2009) and Monuddn (2009). However, our results are n lne wth Narayan et al. (2009) who use panel contegraton to estmate the money demand functon n South Asan countres of Inda, Pakstan, Bangladesh, Sr Lanka and Nepal. Based on ther fndng of stable money demand functon for the above countres (except Nepal), they suggested that the monetary targetng s a vable opton for conduct of monetary polcy for the central banks of these countres ncludng Pakstan. The caveat of ths study, however, s small sample sze, whch may rase questons on the robustness of estmaton results. A bootstrap smulaton technque has also been used to check the devaton of the varance, and the result shows that the bootstrap standard error remans close to the estmated standard error. However, ths result s not suffcent to complement the robustness tests recommended n lterature, whch could not be taken due to small sample sze. Even f the recent annual nformaton s ncorporated n the exstng sample, the sample sze remans nsuffcent for the conduct of the robustness tests. A natural way out s to use the quarterly data. Therefore, workng wth the quarterly data that provdes substantal data sze to conduct the robustness tests on the estmated parameter, could be a potental for future research.

13 Muhammad Omer 49 Fgure 1. CUSUM and CUSUMSQ of Recursve Resduals of Velocty Models Model of V(0): CUSUM CUSUMSQ Model V(1) CUSUM Model V(2): CUSUM CUSUMSQ CUSUMSQ

14 50 SBP Research Bulletn, Vol. 6, No. 2, 2010 References Abbas, K. and F. Husan (2006). Money, Income and Prces n Pakstan: A Bvarate and Tr-varate Causalty. South Asa Economc Journal, 7(1): Akbar, A. and W. Rankaduwa (2006). Inflaton Targetng n a Small Emergng Market Economy: The Case of Pakstan. SBP Research Bulletn, 2: Aknlo, A.E. (2006). The Stablty of Money Demand n Ngera: An Autoregressve Dstrbuted Lag Approach. Journal of Polcy Modelng, 28: Arango, S. and M.I. Nadr (1981). Demand for Money n Open Economes. Journal of Monetary Economcs, 7 (January): Asano, H. (1999). Fnancal Deregulaton and Stablty of Money Demand: The Australan case. Australan Economc Papers, 38(4): Bahman-Oskooee, M. (2001). How Stable s M2 Money Demand Functon n Japan?. Japan and the World Economy, 13: Bahman-Oskooee, M. and M.T. Bohl (2000). German Monetary Unfcaton and the Stablty of Long-run German Money Demand Functon. Economcs Letters, 66: Bahman-Oskooee, M. and Chomssengphet (2002). Stablty of M2 Money Demand Functon n Industral Countres. Appled Economcs, 34: Bahman-Oskooee, M. and G. Shabsgh (1996). The demand for money n Japan: Evdence from Contegraton Analyss. Japan and the World Economy, 8: Bahman-Oskooee, M. and H. Rehman (2005). Stablty of Money Demand Functon n Asan Developng Countres. Appled Economcs, 37: Banerjee, A., J. Dolado, J.W. Galbrath and D.F. Hendry (1993). Co-ntegraton, Error Correcton and the Econometrc Analyss of Non-statonary Data. Oxford: OUP. Blquees, F. and R. Shehnaz (1994). Income Velocty and Per Capta Income n Pakstan: to The Pakstan Development Revew, 33:4(2): Bordo, M.D., L. Junong, and P. Sklos (1997). Insttutonal Change and Velocty of Money: A Century of Evdence. Economc Inqury, 35 (Oct), Bordo, M.D. and L. Jonung (1981). The Long-Run Behavor of the Income Velocty of Money n Fve Advanced Countres, : An Insttutonal Approach. Economc Inqury, (January): Bordo, M. D. and L. Jonung (1987). The Long-Run Behavor of the Velocty of Crculaton: The Internatonal Evdence. Cambrdge Unversty Press. Bordo, M. D. and L. Jonung (1990). The Long Run Behavor of Velocty: The Insttutonal Approach Revsted. Journal of Polcy Modelng, 12:

15 Muhammad Omer 51 Bordo, M. D. and L. Jonung (2004). Demand for Money: An Analyss of the Long Run Behavor of the Velocty of Crculaton. Cambrdge: Cambrdge Unversty Press. Boughton, J.M. (1981). Recent Instablty of the Demand for Money: An Internatonal Perspectve. Southern Economc Journal, 47(January): Brown, R., J. Durbn, and J. Evans (1975). Technques for Testng the Constancy of Regresson Relatons Over Tme. Journal of the Royal Statstcal Socety, Seres B, 37: Butter, F.A.G. Den, and M.M.G. Fase (1981). The Demand for Money n EEC Countres. Journal of Monetary Economcs, 8 (September): Chaudhry, M. A., and M. A. S. Choudhary (2006). Why the State Bank of Pakstan Should not Adopt Inflaton Targetng? SBP Research Bulletn, 2: Darrat, A. F., and A. Al-Mutawa (1996). Modelng Money Demand n the Unted Arab Emrates. The Quarterly Revew of Economcs and Fnance, 36(1): Engle, R. F. and C.W. J. Granger (1987). Contegraton and Error Correcton: Representaton, Estmaton and Testng. Econometrca, 55: Felpe, J. (2009). Does Pakstan Need To Adopt Inflaton Targetng? Some Questons. SBP Research Bulletn, 5(1): Frankel, J. A. and M. P. Taylor (1993). Money Demand and Inflaton n Yugoslava, Journal of Macroeconomcs, 15: Fredman, M. (1956). The Quantty Theory of Money A Restatement. In M. Fredman (Eds.). Studes n the Quantty Theory of Money, Chcago: Unversty of Chcago Press: Goldfeld, S.M. (1973). The Demand for Money Revsted. Brookngs Papers on Economc Actvty, 3: Goldfeld, S.M. (1976). The Case of Mssng Money. Brookngs Papers on Economc Actvty, 3: Hafer, R.W. and D.W. Jansen(1991). The Demand for Money n the Unted States: Evdence from Contegraton Tests. Journal of Money, Credt, and Bankng, 23: Hafer, R.W. and A.M. Kutan (1994). Économc Reforms and Long Run Money Demand n Chna: Implcaton for Monetary Polcy. Southern Economcs Journal, 60, Haug, A. A. and R. F. Lucas (1996). Long Run Money Demand n Canada: In Search of Stablty. The Revew of Economcs and Statstcs, 78(2): Hendry, D. F., and N. R. Ercsson (1991). An Econometrc Analyss of U.K. Money Demand [ed] In Monetary Trends n the Unted States and the Unted Kngdom, by Mlton Fredman and Anna J. Schwartz. Amercan Economc Revew, 8I (March): 8-38.

16 52 SBP Research Bulletn, Vol. 6, No. 2, 2010 Hamor, N., and S. Hamor (1999). Stablty of Money Demand Functon n Germany. Appled Economcs Letters, 6: Hoffman, D. L. and R. H. Rasche (1991). Long-run Income and Interest Elastctes of Money Demand n the Unted States. The Revew of Economcs and Statstcs, 73: Johansen, S. (1988). Statstcal Analyss of Contegraton Vectors. Journal of Economc Dynamcs and Control, 12: Johansen, S. (1991). Estmaton and Hypothess Testng of Contegraton Vectors n Gaussan Vector Autoregressve Models. Econometrca, 59: Johansen, S. and K. Juselus, (1990). Maxmum Lkelhood Estmaton and Inference on Contegraton wth Applcatons to the Demand for Money. Oxford Bulletn of Economcs and Statstcs, 52: Kemal, A. (2006). Is Inflaton n Pakstan a Monetary Phenomenon? Pakstan Development Revew, 45: Khald, A. M. (2006) Is Inflaton Targetng the Best Polcy Choce for Emergng Economes? A Survey of Emergng Market Experences and Lessons for Pakstan. SBP Research Bulletn, 2 (1): Khan, M. and A. Schmmelpfenng (2006). Inflaton n Pakstan. Pakstan Development Revew, 45: Kremers, J. J., N. R. Ercson, and J. J. Dolado (1992). The Power of Contegraton Tests. Oxford Bulletn of Economcs and Statstcs, 54: Ladler, E. W. D. (1993). The Demand for Money: Theores, Evdence and Problems. 4 th edton, Harper Collns College Publshers, London. Laurenceson, J. and J. C. H. Cha (2003). Fnancal Reform and Economc Development n Chna. Cheltenham: Edward Elgar. Lee, C. and M. Chen (2008). Stablty of Money Demand Functon Revsted n Chna. Appled Economcs, 40: Leventaks, J. A. (1993). Modellng Money Demand n Open Economes over the Modern Floatng Rate Perod. Appled Economcs, 25(August): McNown, R. and M. S. Wallace (1992). Contegraton Tests of a Long run Relatatonshp between Money Demand and Effectve Exchange Rate. Journal of Internatonal Money and Fnance, 11: Mehra, Y. P. (1991). An Error-Correcton Model of U.S. M2 Demand. Federal Reserve Bank of Rchmond, Economc Revew, 77(May/June): Mshkn, F. S. (2004). Economcs of Money Bankng and Fnancal Markets. 7 th ed. Addson Wesley Seres n Economcs. USA. Monuddn (2009). Choce of Monetary Polcy Regme: Should SBP Adopt Inflaton Targetng? SBP Research Bulletn, 5(1): Narayan, P. K. (2008). Revstng the US Money Demand Functon: An Applcaton of the Langranges Multpler Structural Break Unt Root Test and the Bound Test for a Long- run Relatonshp. Appled Economcs, 40: 897-

17 Muhammad Omer Narayan, P. K, S. Narayan, and V. Mshra (2009). Estmatng Demand Functon for South Asan Countres. Emprcal Economcs, 36(3): Omer, M. and O. F. Saqb (2009). Monetary Targetng n Pakstan: A Skeptcal Note. SBP Research Bulletn, 5(1): Pesaran, H. M., Y. Shn, and R. J. Smth (2001). Bounds Testng Approaches to the Analyss of Level Relatonshps. Journal of Appled Econometrcs, 16: Pesaran, M. H., and B. Pesaran (1997). Workng wth Mcroft 4.0: Interactve Econometrc Analyss. Oxford Unversty Press. Pesaran, M. H. (1997). The Role of Economc Theory n Modelng the Long Run. The Economc Journal, 107(1): Pesaran, M. H. and Y. Shn (1999). An Autoregressve Dstrbuted Lag Modelng Approach to Contegraton Analyss. n S. Strom (ed.), Econometrcs and Economc Theory n the 20 th Century. The Ragnar Frsch Centennal Symposum, 1998, Cambrdge Unversty press, Cambrdge. Qayyum, A. (2006). Money, Inflaton and Growth n Pakstan. Pakstan Development Revew, 45: Ramchandran, M. (2004). Do Broad Money, Output, and Prces Stand for a Stable Relatonshp n Inda? Journal of Polcy Modelng, 26: Rose, A. K. (1985). An Alternatve Approach to the Amercan Demand for Money. Journal of Money, Credt and Bankng, 17(4): Sklos, P. L. (1993). Income Velocty and Insttutonal Change: Some New Tme Seres Evdence, Journal of Money, Credt and Bankng, (Aug):

18 54 SBP Research Bulletn, Vol. 6, No. 2, 2010 Annexure 2. Recent studes on the stablty of money demand functon Study Country Sample Method* Varables Results Asano. H(1999) Australa JJ, VECM Yr, M, P, Money demand functon s stable Haug. A and R. Lucas (1996) Canada 53:1-90:4 EG, JJ, PO, M1, Yr (short) Stable contegraton relatonshp Hamor N. and S. Hamor (1999) Germany 69:1-94:4 JJ, Chow Yr, M1, M2, M3 (call) Unstable Bahman-Oskooee M(2001) Japan 64:1-96:3 ARDL, CUSUM, CUSUMQ M2, Yr Stable relatonshp Narayan P K (2008) Bahman-Oskooee M and Chomssengphet (2002) USA 59:1-04:2 LM, structural break unt root, bound test OECD: Australa, Austra, Canada, France, Italy, Japan, Netherlands, Norway, Sweden, Swtzerland, UK, USA 79:1-98:3, 67:1-98:3, 57:1-98:4, 77:1-98:3, 74:1-98:3, 66:1-98:4, 66:1-98:3, 69:1-98:4, 75:4-98:4, 57:1-98:2, 57:1-98:2, 57:1-98:4 JJ, CUSUM, CUSUMQ M1, M2, Yr, (3-m tb) M2 (real), Yr (long) NEER M2 demand s stable Money demand s stable n most of the countres except Swtzerland and UK Narayan P.K, Narayan S, and V. Mshra (2009). Lee C C. and Me- Se C(2008) Inda, Pakstan, Bangladesh, Sr Lanka, Nepal Panel M2 (real), Yr (short) NEER Chna ADF, ZA unt root test for structural break, JJ M1, M2, Yr, (1-yr depost) Contegrated and stable money demand for all countres except Nepal Unstable

19 Muhammad Omer 55 Ramchandran N(2004) Darrat A F and Ahmed A M(1996) Inda CUSUM, CUSUMQ JJ UAE 74:1-92:2 JJ Chow, FH test Aknlo A E (2006) Ngera 70:1-02:4 ARDL, JJ, CUSUM, CUSUMQ Bahman-Oskooee M and Hafez R(2005) Inda, Indonesa, Malaysa, Pakstan, Phlppnes, Sngapore, Thaland 72:1-00:4 ARDL, JJ, CUSUM, CUSUMQ M3, Yr, P M1 (real) Def, Pe (d) (f) NER M2, Yr, NER, M1 (real) M2 (real) Yr P, E Monuddn (2009) Pakstan M2, Y Husan et al (2006) Pakstan M2, Y P, INV, Stable relatonshp The explanatory varables exert sgnfcant effect on M1 money holdng. Addtonally the relatonshp s stable. Contegraton and stable relatonshp exsts between the varables M1 money demand s stable n Inda, Indonesa, and Sngapore. For remanng countres M2 s stable. M2 s unstable M2 demand s stable Qayyum (2006) Pakstan M2, GDP, nflaton, nterest rate, government bond rate M2 demand s stable Note: (1) EG s Engle and Granger; PO s Phllps and Oulars; ;JJ s Johnsons and Julus; VECM s Vector Error Correcton Method; ARDL s Auto Regressve Dstrbuted Lag; ZA s Zvot and Andrew; ADF sr Augmented Dckey Fuller; CUSUM s Cumulatve Sum of Recursve Resduals; CUSUMQ s Cumulatve Sum of Squares of Recursve Resduals; FH s Farley- Hnch Test; (2) Yr, M, P,, (d), (f), Def, Pe, NEER, and INV represent real GDP, money supply, prces, nterest rate, nterest rate domestc, nterest rate foregn, non-ol GDP deflator, non-ol expected nflaton, nomnal effectve exchange rate.