IS-LM model with a general consumption tax

Transcription

1 Edith Cwan Univesity Reseach Online ECU Publicatins Pe S-LM mdel with a geneal cnsumptin tax. H. Cheung Cheung,. (2003). S-LM mdel with a geneal cnsumptin tax. Jndalup, Austalia: Edith Cwan Univesity. This Othe is psted at Reseach Online.

2 S-LM Mdel with a Geneal Cnsumptin Tax By.H. Cheung Edith Cwan Univesity Schl f Accunting, Finance and Ecnmics Wking Pape Seies Edith Cwan Univesity Septembe 2003 Wking Pape 0305 Cespndence addess: D.H. Cheung Schl f Accunting, Finance and Ecnmics Faculty f Business and Public Management Edith Cwan Univesity 100 Jndalup Dive Jndalup WA 6027 Austalia Phne: 61+ (8) Fax: 61+ (8) y.cheung@ecu.edu.au

3 Abstact OECD tax evenue statistics shw that n aveage the shae f cnsumptin tax is almst equal t that f incme tax. Hweve, cnsumptin tax hadly attacts any attentin fm intemediate macecnmic textbks, nt t mentin its inclusin in S-LM mdel. This pape cmpaes the S cuves unde an incme tax egime and a geneal cnsumptin tax egime. t als examines the tade ff between the incme tax ate and the cnsumptin tax ate in a dual tax egime. Key wds: Geneal cnsumptin tax; S-LM mdel; fiscal plicy; tax ate tade ff; intemediate macecnmics JEL cde: A22, E21, E62, H20

4 1. ntductin An examinatin f the OECD gvenment evenue statistics eveal that in the last decade, thee is a spead in the use f geneal cnsumptin taxes, especially the VAT type, t eplace specific cnsumptin taxes. 1 Geneal cnsumptin taxes ae nw in place in 29 f the 3O OECD cunties (with the exceptin f the USA, which nly has state and lcal sales taxes). As a matte f fact, a cmpaisn f the 1985 data (Kusell et al., 1996) and the 1998 data (OECD, 2001b, p.13) n shaes f tax evenue shws that the pecentage f cnsumptin taxes has slightly inceased ve the 13 yeas by abut ne pe cent fm 31 t 32 pe cent while the pecentage f incme taxes has slightly deceased fm abut 36 t 35 pe cent. 2 Table 1: Pecentage shaes f tax evenues, OECD cunties, Unweighted OECD aveage ncme (Pesnal and Cpate) 1000 Tax type and OECD cde Scial Secuity 2000 Gds and Sevices 5000 Othes (incl. 3000, 4000, and 6000) * Changes * Based n the 23 membe cunties in They wee Austalia, Austia, Belgium, Canada, Denmak, Finland, Fance, Gemany, Geece, eland, taly, Japan, Luxembug, Nethelands, New Zealand, Nway, Ptugal, Spain, Sweden, Switzeland, Tukey, UK, and USA. Suces: OECD (2001b, p.11), OECD (2003), and Kusell et al. (1996) Thee ae vaius aguments f a geneal cnsumptin tax but what am cncened hee is its incpatin int the S-LM mdel in intemediate macecnmic textbks. 3,4 sample a list f intemediate macecnmic textbks Blanchad (2000), DeLng (2002), Fame (1999), Hall and Tayl (1999), Mankiw (2003), Miles and Sctt (2002), Pentecst (2000), and Tayl and Msa (2000) and as fa as am awae, geneal cnsumptin tax hadly attacts any attentin in the S-LM mdel, which is still an imptant analytical tl at that level f instuctin. Nevetheless, Tayl and Msa (2000, pp ) did examine the ne-ff pice effect f the impsitin f a geneal cnsumptin tax in an ecnmic fluctuatins mdel epesented by an inflatin-ate-eal-gdp diagam. 5

5 2 n my intemediate macecnmic unit, incpate a geneal cnsumptin tax cmpnent int the S-LM assignment. 6,7 The students feedback wee psitive and they appeciated the me ealistic appach. An S-LM mdel with a cnsumptin tax cmpnent gives them a tl t analyze (a) the impact f an impsitin f a geneal cnsumptin tax, (b) the effect f a change in cnsumptin tax ate, and (c) the tade ff between cnsumptin and incme tax ates t maintain tax evenue neutality. deem that the inclusin f a geneal cnsumptin tax has eniched my students leaning expeience. The aims f this pape ae (a) t cmpae the S cuves unde a cnsumptin tax egime with that unde an incme tax egime, and (b) t exple the tade-ff between incme and cnsumptin tax ates. n the next sectin, eview a typical thee-sect S-LM mdel with a pptinal incme tax. n sectin tw, set ut the altenative S-LM mdel with a cnsumptin tax egime. als biefly discuss the pssible questins abut switching fm an incme tax t a cnsumptin tax egime. n sectin thee, examine the S-LM mdel with bth kinds f taxes. fcus n the tade ff between the tw kinds f taxes given tax-evenue neutality. als include a numeical example t illustate the tade-ff. Sectin fu is the summay. 2. The S-LM Mdel with an ncme Tax This sectin pesents a typical S-LM mdel f a clsed ecnmy pesented in intemediate macecnmic textbks, f example, Mankiw (2003, pp ). The mdel is encapsulated in fllwing fu equatins The ttal demand functin: The mney demand functin: ( M P) D E = C ( ) + ( ) + d = m d G = L(, ) The equilibium cnditin in the pduct maket: = E The equilibium cnditin in the financial maket: m d = m s = m 0 whee E is ttal demand f gds and sevices, C is cnsumptin, incme, is investment, is eal inteest ate, geneal pice level, ( M / P) d is dispsal (eal) is gvenment spending, M is mney, P is is demand f eal balances, L is liquidity, is eal incme eal s GDP, m is the supply f eal balances, and m is eal mney balances. 0 G D

6 3 T facilitate the discussin, specify the linea fm f the cnsumptin functin, investment functin, tax functin, and mney demand functin as C + D = C C (1) = T = t (2) m d = L L whee C is baseline cnsumptin, C is maginal ppensity t cnsume, is baseline investment, is inteest sensitivity f investment, T is tax evenue, t is pptinal incme tax ate, L is incme sensitivity f demand f mney, and L is inteest sensitivity f demand f mney. Withut futhe ad, the equatins f the S and the LM cuve ae C + + G 1 C (1 t) = (3) and m = L 0 L + L espectively. And the equilibium values ae C + + G + αm0 * = 1 C (1 t) + αl and ( C * = + + G ) L L [1 C [1 C (1 t)] + (1 t)] m L 0 with α = L. Fm equatin (3), we knw that a change in the incme tax ate tates the S cuve anticlckwise f t > 0 and clckwise f t < 0 with the vetical intecept as the pivt pint. F the cmpaative statics f the S-LM mdel with an incme tax egime, they ae well cveed in any f the intemediate macecnmic textbks. 3. The S-LM Mdel with a Cnsumptin Tax With a geneal cnsumptin tax and n incme tax, we need t ewite the tax equatin (2) t becme equatin (2 ) T = v C (2 ) whee v is the pptinal cnsumptin tax ate. With a geneal cnsumptin tax, the cncept f dispsable incme D and the deteminatin f cnsumptin level ae nt as cleacut as thse descibed in textbks. Husehld cnsumptin C depends n the level f D

7 4 but the latte als depends n hw much the husehlds cnsume. This feedback lp makes the deivatin f the S equatin me cmplicated f students. When substitute the cnsumptin, the investment, and the tax equatins int the equilibium cnditin f the pduct maket, the substitutin ges n feve with the fllwing equatin emeging: 2 2 n n n = ( C + C ) (1 C v + C v + L + ( 1) C v ) + + With the sum f the gemetic seies equals 1 /( 1 + C, the abve equatin can be eaanged t give the equatin f the cnsumptin-tax S cuve: G C = + (1 + C ( (1 + C + G ) 1 C (1 (1 + C (4) This equatin is fa me cmplex than the incme-tax S equatin, descibed by equatin (3); the cnsumptin tax ate v appeas in the numeat and the denminat f bth the intecept and the slpe. Cnsequently, a change in v nt nly tates the S cuve but als shifts the S cuve at the same time. This cntasts t the pue tatin effect f a change in the incme tax ate. Patial deivatives f the intecept and the slpe with espect t v shw that a change in the cnsumptin tax ate shifts the S cuve (t the left f v > 0 and t the ight f v < 0) and tates it (anticlckwise f v > 0 and clckwise f v < 0) with the vetical intecept as the pivt pint. With the LM cuve emains the same, the equilibium values f is *= C + ( 1 C + G ) (1 + C (1 + αl + αm (1 + C 0 (1 + C. 3.1 Sme questins abut switching tax egime Thee ae sme inteesting questins abut switching tax egime. Fistly, des the switch fm ne tax egime t anthe invlve same tax evenue? And is tax evenue neutal equivalent t eal GDP neutal? Secndly, what is the psitin (indicated by the intecept and the slpe) f the cnsumptin-tax S cuve as cmpaed t that f the incme-tax S cuve? Thidly, what is the value f the tax evenue neutal cnsumptin tax ate? t is easnable t ague that a new tax egime is at least tax evenue neutal tax evenue enhancing in its inceptive yea f the gvenment t fulfill its financial cmmitments. t is me likely t be tax evenue neutal t avid the accusatin f evenue gabbing. And as lng as tax evenue des nt change, eal GDP emains at the same level. 8

8 5 T see this assetin, efe t the the definitin f eal GDP whee is the sum f C, saving S and T. Since bth C and S ae functins f, which in tun depends n T given, a stable tax liability means stable cnsumptin and saving, ceteis paibus. That is, tax evenue neutality implies eal GDP neutality. The numeical example in the next sectin attests t the validity f this assetin. Anthe easn that the gvenment may pefe t maintain neutality is that a depletin enhancement ceates an ecnmic shck that the gvenment has t handle n tp f the administative pblems f changing the tax system. D Hw des the psitin f a cnsumptin-tax S cuve cmpae t its incme tax cuntepat? Since have adpted the same set f equatins except the tax equatin, can cmpae equatins (3) and (4) t discen thei diffeences. Appaently, the cnsumptin-tax S cuve has a lwe intecept than that f the incme-tax S cuve because C ( 1 + C < C. t is hweve me difficult t ascetain the elative values f the slpes f the tw S cuves. With tax-evenue and eal-gdp neutality (at least in the sht un and n change in mnetay plicy) the equilibia f the ecnmy with the tw tax egimes must be the same. A lwe intecept f the cnsumptin-tax S cuve implies it has t have a elatively flatte slpe as depicted in Figue 1. Suppse the ecnmy stats with an initial equilibium pint A, the elatively steepe and slid S is the incme-tax S cuve and the elatively flatte and bken S C is the cnsumptin-tax S cuve. LM * B A B H S C S C S S * * C * Figue 1: Effectiveness f fiscal plicy unde diffeent tax egime

9 6 A elatively flatte S C als implies that fiscal plicy is elatively less effective in an ecnmy with a cnsumptin tax than ne with an incme tax. Again efe t Figue 1. An equal incease in gvenment expenditue G causes bth S cuves t shift t the ight by the same amunt t pint H. The new equilibium f an incme tax egime is pint B and f a cnsumptin tax egime is pint B. t is appaent that fiscal plicy is less effective unde a cnsumptin tax egime. This bsevatin can be safely extended t a tax egime with a cnsumptin tax cmpnent. As f the thid questin, it is best handled in a dual-tax egime, which will be discussed in the next sectin. 4. The S-LM Cuve with Bth Taxes Replace the tax equatin (2) by ne with bth incme and cnsumptin taxes: T = t + v C (2 ) Withut epeating the deivatin pcess, the equatin f the dual-tax S cuve is = C + G 1 C (1 t) + C v + 1 (5) ( + C ( 1 + C The intductin f a cnsumptin tax int an ecnmy with nly incme tax again lwes the intecept and flattens the slpe f the S cuve. The bsevatins petain t a cnsumptin tax egime again apply hee. The highe the cnsumptin tax ate, the flatte the S cuve and the lwe its vetical intecept. Figue 2 depicts the S cuves f the thee tax LM * A S S C S +C * Figue 2: The S cuves unde the thee tax egimes

10 7 egimes unde tax-evenue neutality and S +C is ne f the many pssible S cuves (depends n the cmbinatin f t and f a dual-tax egime. Nte that the value f v in equatin (5) is less than that in equatin (4) due t the pesence f incme tax and tax-evenue neutality. The inclusin f bth taxes facilitates the study f tade ff between the tw tax ates unde the cnditin f tax-evenue and eal-gdp neutality. T calculate the tade-ff ati between the tw tax ates, substitute epeatedly the cnsumptin equatin (1) int tax equatin (2 ) yields 2 T = t + v ( C + C tc ) (1 C v + C v + L + ( 1) Again apply the sum f the gemetic seies, have C v 2 n n n ) T = t C + v + C 1+ C (1 t) Ttal diffeentiate equatin (6) and set dt v = d = dc = dc (6) = 0, and using the equilibium value * C = + ( 1 C v = t C + G )(1 + C + α m0 (1 + C, get (1 + α L (1 + C + C t C whee B = + G + ( 1+ α L ) + B(1 + C < 0 + B C (1 t) α m 0. Thee is a negative tade ff between the tw tax ates, indicated by the negative sign f the patial deivative v t, t maintain tax-evenue neutality. That is, t < 0 ( t > 0) implies v > 0 ( v < 0 ) t keep T = 0. call this patial deivative the tade-ff ati and its value is detemined by all the paametes in the system f equatins. The tade-ff ati is less than ze because cnsumptin tax has a nawe tax base than incme tax. Let say thee is a cut in the incme tax by t < 0, the fist und incease in (7) dispsable incme is D = t > 0. The incease in dispsable incme is allcated t cnsumptin and saving. Theefe, fm the gvenment viewpint, t > C v f t = v. T maintain evenue neutality, the gvenment has t have t < v. A numeical example is given belw t illustate my pint. Equatin (8) summaies the effect f a change in each paamete n the value f tadeff ati:

11 8 v = f ( t, v, C,, G, M 0, P0, C t +, +, L t is imptant t nte that the + ( ) sign n tp f a paamete in the abve equatin indicates smalle (lage) tade ff between the tw tax ates. t is als imptant t pint ut that the tade-ff ati vaies with the stuctue f the ecnmy, epesented by all the paametes. That is, a diffeent stating pint (e.g., a diffeent cmbinatin f the initial v and t) entails a diffeent value f tade-ff ati., L ) (8) 4.1 A numeical example Suppse C = $10b,C = 0. 75, = $ 400b, = $ 800b, L = 0. 9, L = $ 900b, M = $400b, P = 4 (epesents an index f 400),G = $200b With t = 20%, the D equilibium values f the ecnmy ae: * = $582.41b, T* = $116.48b, * =$465.93b, C* = $359.44b, public saving T* - G* = -$83.52b, shae f gvenment = 34.34%, * = 0.47%, * = $22.96b, pivate saving = $106.48%, and natinal saving ate = 3.94%. The tade ff between incme and cnsumptin tax ates can be btained by applying the values f the paametes t equatin (7). The esult is v t = , which means a ne pe cent eductin in incme tax ate equies a pe cent incease in cnsumptin tax ate t maintain the tax evenue. T ascetain the validity f the cncept, calculate the equilibium set f values f the fllwing thee cases with t = 20% and v = 0% as the baseline: (a) dual tax egime with t = 15% and v = 8.10%, (b) dual tax egime with t = 13.83% and v = 10%, and (c) single tax egime with v = L and behld, thei equilibium sets f values ae the same (allwing f unding e). 9 The equatins f the fu S cuves ae tabulated in Table 2 and the esults agee with the patten shwn in Figue 2. Table 2: S equatins unde diffeent tax egimes Tax egime Equatin f S cuve ncme tax egime with t = 20% = Dual tax egime with t = 15% and v =8.1015% = Dual tax egime with t = % and v = 10% = Cnsumptin tax egime with v = % =

12 9 5. Summay cnside that the incpatin f a geneal cnsumptin tax in the S-LM mdel bings it me in line with the eality that students expeience. Even thugh the mathematics invlved is me cmplicated, the inclusin f a geneal cnsumptin tax allws students t appeciate (a) the effect f a change in the cnsumptin tax ate, and (b) the tade ff between incme and cnsumptin tax ates. t is als fund that fiscal plicy is less effective with a cnsumptin tax cmpnent than withut.

13 10 NOTES 1. The mst ecent example is Austalia. n July 2000, the Austalian Cmmnwealth Gvenment intduced the Gds and Sevices tax (GST) a VAT-type geneal cnsumptin tax t eplace its whlesale sale taxes (six diffeent ates), financial institutin duties, debit tax, cnveyancing duties n business ppety and five the stamp duties. 2. Quite a few ecnmists, e.g. Kusell et al. (1996), egad scial secuity tax as incme tax because it is incme based. f we take this psitin, then the shae f incme taxes has deceased fm 61 pe cent t 60 pe cent ve the 13-yea peid. 3. Nmally, the base f a geneal cnsumptin tax shuld lgically include all gds and sevices, which may nt be plitically acceptable. n fact, the Austalian GST has exemptin (i.e., ze ating) n seveal kinds f gds and sevices (fd, health, educatin, childcae sevices, hspitals and nusing hmes, lcal gvenment ates, wate and seweage chages, and chaitable activities) t incease the pgessivity f the tax. 4. Cnsumptin is egaded as a geene and equitable tax than incme tax in the sense that ecnmic agents ae taxed accding t the esuces they use up (i.e., actual cnsumptin) athe than thei ptential cnsumptin. F a suvey, see Atkinsn and Stiglitz (1987, pp ). 5. When Austalia intduced its GST in July 2000, the impact was a ne-ff incease in quately inflatin ate by 2.3%. Simila pattens wee bseved in bth New Zealand (1987) and Canada (1991). 6. DeLng (2002) is the adpted textbk f my intemediate macecnmic unit. 7. t is an analytical execise based n a case study using a fu-sect S-LM speadsheet mdel. 8. This is nly valid in a vey sht-un mdel such as the S-LM whee pices ae assumed t be igid. nflatin statistics shw that the intductin f a geneal cnsumptin tax ceates a ne-ff diect effect n pices paid by cnsumes, which in tun lwes eal GDP, ceteis paibus. Als see end nte did the calculatin by an S-LM speadsheet mdel.

14 11 REFERENCES Atkinsn, A.B., and J.E. Stiglitz Lectues n Public Ecnmics. Lndn: McGaw Hill. Blanchad, O Macecnmics. 2 nd ed. Uppe Saddle Rive, N.J.: Pentice Hall. DeLng, J. B Macecnmics. Bstn: McGaw-Hill. Fame, R. E. A Macecnmics. Cincinnati: Suth-Westen Cllege Publishing. Hall, R. E., and J.B. Tayl Macecnmics. 6 th ed. New k: W.W. Ntn & C. Kusell, P., V. Quadini, and J.-V. Rís-Rull Ae cnsumptin taxes eally bette than incme taxes? Junal f Mnetay Ecnmics 37, Mankiw, N. G Macecnmics. 5 th ed. New k: Wth Publishes. Miles, D., and A. Sctt Macecnmics: Undestanding the wealth f natins. New k: Jhn Wiley & Sns. OECD. 2001a. Cnsumptin tax tends: VAT/GST, excise and envinmental taxes. Pais. OECD. 2001b. Tax and the ecnmy: A cmpaative assessment f OECD cunties, OECD Tax Plicy Studies N. 6, Pais. OECD Tends in tax budens and tax stuctues. Available: Pentecst, E Macecnmics: An pen ecnmy appach. Hundmills: Macmillan. Tayl, J.B., and. Msa Macecnmics. Austalian ed. Miltn, QLD: Jhn Wiley & Sns.