THE TWO-PERIOD FRAMEWORK (CONTINUED)

Transcription

1 GOVERNMENT AND FISCAL POLICY IN THE TWO-PERIOD FRAMEWORK (CONTINUED) SEPTEMBER 30, 2014 Govenment in the Two-Peiod Model ADYNAMIC MODEL OF THE GOVERNMENT So fa only consumes in ou two-peiod famewok Intoduce govenment in vey simple fom Exists fo both peiods Has spending in each peiod it needs to finance can be financed via Taxes Issuing govenment debt/assets Stat of economic planning hoizon End of economic planning hoizon Notation g 1 : eal govenment spending in peiod 1 g 2 : eal govenment spending in peiod 2 b 0 : govenment asset position at beginning of peiod 1/end of peiod 0 b 1 : govenment asset position at beginning of peiod 2/end of peiod 1 b 2 : govenment asset position at beginning of peiod 3/end of peiod 2 : eal inteest ate between peiods Septembe 30,

2 Model Stuctue GOVERNMENT BUDGET CONSTRAINT(S) Adopt a lifetime view of the budget constaint(s) All analysis conducted fom pespective of beginning of peiod 1 Peiod-1 govenment budget constaint Peiod-2 govenment budget constaint g b t (1 ) b g b t (1 ) b Asset position at end of peiod 1/beginning of peiod 2 the key link Assume = 0 (no defaults + stictly inceasing utility ) Combine into lifetime budget constaint (LBC) Solve peiod-2 budget constaint fo b 1 and substitute into peiod-1 budget constaint g t g t (1 ) b IMPORTANT: Govenment must balance its budget ove its lifetime, not necessaily in each peiod Pesent discounted value (PDV) of all lifetime govenment expenditue Pesent discounted value (PDV) of all lifetime govenment income Fo gaphical simplicity, will often assume b 0 = 0 (i.e., govenment begins life with zeo net wealth). Note this is a diffeent assumption than b 2 = 0. Septembe 30, Model Stuctue CONSUMER BUDGET CONSTRAINT(S) Intoduce tax payments into consume side of famewok All in eal tems fo simplicity can cast in nominal tems by multiplying by P Peiod-1 budget constaint c1 t1a1a0 y1a0 Peiod-2 budget constaint c2 t2 a2 a1 y2 a1 Combine into lifetime budget constaint (LBC) Solve peiod-2 budget constaint fo a 1 and substitute into peiod-1 budget constaint c y t c y t (1 ) a Pesent discounted value (PDV) of all lifetime expenditue Pesent discounted value (PDV) of all lifetime disposable income (i.e., afte-tax income) Septembe 30,

3 Model Stuctue CONSUMER BUDGET CONSTRAINT(S) consume savings in peiod 1 consume savings in peiod 2 c1t1a1a0 y1a0 c2 t2 a2 a1 y2 a1 a a y a t c a2 a1 y2 a1t2 c2 Septembe 30, Maco Fundamentals ECONOMY-WIDE RESOURCE FRONTIER Consume lifetime budget constaint c2 y2 t2 c1 y1t1 (1 ) a0 1 1 Govenment lifetime budget constaint g2 t2 g1 t1 (1 ) b0 1 1 Summing the two yields economy-wide esouce fontie c2 y2 g2 c1 y1g1 (1 )( a0 b0) 1 1 aka poduction possibilities fontie (PPF) The GDP accounting equation in two-peiod fom Suppose = 0 fo gaphical simplicity c 2 y 2 - g 2 IMPORTANT: taxes do not diectly appea in the esouce fontie slope = -(1+) THEOREM (intemediate mico): If taxes ae lumpsum, then consume optimal choices can be obtained by analyzing eithe the consume LBC o the economy-wide esouce fontie (supeimpose indiffeence map), and eithe appoach will yield the same pedictions. y 1 - g 1 c 1 Resouce Fontie An impotant theoetical esult fo the analysis of tax policy. Septembe 30,

4 Fiscal Policy and National Savings EFFECTS OF TAX POLICY National savings = savings by consumes + savings by govenment + savings by fims fim No fims in ou model (yet..), so s1 0 piv s1 y1t1c Analyzing effects of changes in 1 tax policy on optimal govt s1 t1g consumption choices is the key 1 nat piv govt s s s y t c t g y c g Policy Expeiment: Is national savings affected by a decease in t 1? Suppose g 1 and g 2 do not change Question 1: Effect on t 2? t 2 must ise (examine govenment lifetime budget constaint) Question 2: Effect of tax changes on consumes optimal choice of peiod-1 consumption? Using intemediate mico theoem, NO EFFECT ON optimal c 1 Taxes ae lump sum Cucial logic Economy-wide esouce constaint does not depend diectly on taxes optimal choice of c 1 unaffected by the change in tax policy Question 3: Effect of tax changes on peiod-1 national savings? NONE because neithe g 1 no c 1 changed Septembe 30, Fiscal Policy and National Savings RICARDIAN EQUIVALENCE Ricadian Equivalence Theoem: Fo a given PDV of govenment spending, neithe consumption no national savings is affected by the pecise timing of lump-sum taxes A benchmak esult/concept in the theoy of macoeconomic policy Septembe 30,

5 Fiscal Policy and National Savings RICARDIAN EQUIVALENCE Ricadian Equivalence Theoem: Fo a given PDV of govenment spending, neithe consumption no national savings is affected by the pecise timing of lump-sum taxes A benchmak esult/concept in the theoy of macoeconomic policy Economic Intepetation: Rational consumes undestand that a tax cut in shot un means a tax incease in the futue (because PDV of govenment spending is unchanged) Thus entie tax cut is saved by consumes in ode to pay highe taxes in the futue Pivate savings and govenment savings move in exactly offsetting ways s 1 piv y 1 a 0 t 1 c 1 Rises when t 1 deceases, GIVEN that we have CONCLUDED that c 1 does not change s 1 gov t 1 b 0 g 1 Deceases when t 1 deceases Septembe 30, Fiscal Policy and National Savings RICARDIAN EQUIVALENCE Ricadian Equivalence Theoem: Fo a given PDV of govenment spending, neithe consumption no national savings is affected by the pecise timing of lump-sum taxes A benchmak esult/concept in the theoy of macoeconomic policy Economic Intepetation: Rational consumes undestand that a tax cut in shot un means a tax incease in the futue (because PDV of govenment spending is unchanged) Thus entie tax cut is saved by consumes in ode to pay highe taxes in the futue Pivate savings and govenment savings move in exactly offsetting ways Ricadian Equivalence is to tax theoy as pefect competition is to basic economic theoy Pediction elies cucially on lump-sum taxes Septembe 30,

6 Maco Fundamentals NATURE OF TAXATION Lump-Sum Tax A tax whose total incidence (i.e., total amount paid) does not depend in any way on any decisions/choices an individual makes Real-wold examples:? Septembe 30, Maco Fundamentals NATURE OF TAXATION Lump-Sum Tax A tax whose total incidence (i.e., total amount paid) does not depend in any way on any decisions/choices an individual makes Real-wold examples:? Taxes in ou two-peiod famewok so fa Lump-sum! Total amounts t 1 and t 2 paid by consume ae independent of any of thei decisions/choices Peiod-1 budget constaint Peiod-2 budget constaint c1t1a1a0 y1a0 c2 t2 a2 a1 y2 a1 Popotional (aka distotionay) Tax A tax whose total incidence depends on decisions/choices an individual makes In simple two-peiod famewok: consumes only make consumption choices c 1 and c 2 τ is consumption tax ate (aka sales tax ate) Peiod-1 budget constaint Peiod-2 budget constaint (1 2)c2 a2 a1 y2 a1 (1 )c a a y a Septembe 30,

7 Fiscal Policy and National Savings PROPORTIONAL TAXATION τ is consumption tax ate (aka sales tax ate) Peiod-1 budget constaint Peiod-2 budget constaint (1 2)c2 a2 a1 y2 a1 (1 )c a a y a Combine into consume LBC (1 2) c2 y2 (1 1) c y (1 ) a Septembe 30, Fiscal Policy and National Savings PROPORTIONAL TAXATION τ is consumption tax ate (aka sales tax ate) Peiod-1 budget constaint Peiod-2 budget constaint (1 2)c2 a2 a1 y2 a1 (1 )c a a y a Combine into consume LBC (1 2) c2 y2 (1 1) c y (1 ) a Slope is (1 ) Non-lump-sum taxes: optimal consumption choices must be detemined using consume LBC, not economy s esouce fontie (i.e., intemediate mico theoem does not apply) Changes in tax ates do affect optimal consumption choices because they change slope of consume LBC Ricadian Equivalence Theoem does not apply Changes in tax ates do affect national savings Septembe 30,

8 Maco Fundamentals RICARDIAN EQUIVALENCE? So why the fascination with Ricadian Equivalence? A benchmak esult/concept in the theoy of macoeconomic policy Effects of actual policy poposals can be compaed to the Ricadian Equivalence benchmak In pactice, does seem like tax ebates ae sometimes saved Septembe 30, Maco Fundamentals RICARDIAN EQUIVALENCE? So why the fascination with Ricadian Equivalence? A benchmak esult/concept in the theoy of macoeconomic policy Effects of actual policy poposals can be compaed to the Ricadian Equivalence benchmak In pactice, does seem like tax ebates ae sometimes saved At aggegate level, total tax collections sometime seem lumpsum (i.e., independent of aggegate macoeconomic activity) GDP (o any aggegate measue of eal activity ie, consumption) moves up and down ove time but total tax evenue of the govenment fluctuates vey little time Septembe 30,

9 Maco Fundamentals RICARDIAN EQUIVALENCE? So why the fascination with Ricadian Equivalence? A benchmak esult/concept in the theoy of macoeconomic policy Effects of actual policy poposals can be compaed to the Ricadian Equivalence benchmak In pactice, does seem like tax ebates ae sometimes saved At aggegate level, total tax collections sometime seem lumpsum (i.e., independent of aggegate macoeconomic activity) GDP (o any aggegate measue of eal activity ie, consumption) moves up and down ove time but total tax evenue of the govenment fluctuates vey little Ricadian Equivalence Is a theoetical benchmak Is an empiical benchmak time Ricadian Equivalence is about the (lack of) effects of changes in tax policy, holding total govenment liabilities fixed. If g 1 and/o g 2 change, Ric. Equiv. does not apply. Septembe 30, INFINITE-PERIOD FRAMEWORK SEPTEMBER 30,

10 Intoduction BASICS Moden wokhose macoeconomic famewoks featue an infinite numbe of peiods A moe ealistic (?) view of time Especially useful fo thinking about asset accumulation and asset picing The intesection of moden maco theoy and moden finance theoy Hee, suppose just one eal asset Call it a stock i.e., a shae in the S&P 500 (In Chapte 14, two nominal assets: bonds and money) Index time peiods by abitay indexes t, t+1, t+2, etc. Impotant: all analysis conducted fom the pespective of the vey beginning of peiod t so an infinite futue (peiod t+1, peiod, t+2, peiod t+3, ) fo which to save Septembe 30, Intoduction BASICS Timeline of events Notation c t : consumption in peiod t P t : nominal pice of consumption in peiod t Y t : nominal income in peiod t ( falls fom the sky ) a t-1 : eal wealth (stock) holdings at beginning of peiod t/end of peiod t-1 Septembe 30,

11 Intoduction BASICS Timeline of events The definining featues of stock Notation c t : consumption in peiod t P t : nominal pice of consumption in peiod t Y t : nominal income in peiod t ( falls fom the sky ) a t-1 : eal wealth (stock) holdings at beginning of peiod t/end of peiod t-1 S t : nominal pice of a unit of stock in peiod t D t : nominal dividend paid in peiod t by each unit of stock held at the stat of t Septembe 30, Intoduction BASICS Timeline of events The definining featues of stock Notation c t : consumption in peiod t P t : nominal pice of consumption in peiod t Y t : nominal income in peiod t ( falls fom the sky ) a t-1 : eal wealth (stock) holdings at beginning of peiod t/end of peiod t-1 S t : nominal pice of a unit of stock in peiod t D t : nominal dividend paid in peiod t by each unit of stock held at the stat of t π t+1 : net inflation ate between peiod t and peiod t+1 P P P t 1 t t 1 t1 1 Pt Pt y t : eal income in peiod t ( = Y t /P t ) Septembe 30,

12 Intoduction BASICS Timeline of events The definining featues of stock Notation c t+1 : consumption in peiod t+1 P t+1 : nominal pice of consumption in peiod t+1 Y t+1 : nominal income in peiod t+1 ( falls fom the sky ) a t : eal wealth (stock) holdings at beginning of peiod t+1/end of peiod t S t+1 : nominal pice of a unit of stock in peiod t+1 D t+1 : nominal dividend paid in peiod t by each unit of stock held at the stat of t+1 π t+2 : net inflation ate between peiod t+1 and peiod t+2 Pt 2 P t 1 P t 2 t2 1 Pt 1 Pt 1 y t+1 : eal income in peiod t+1 ( = Y t+1 /P t+1) Septembe 30, Intoduction BASICS Timeline of events Notation And so on fo peiod t+2, t+3, etc Septembe 30,

13 Maco Fundamentals SUBJECTIVE DISCOUNT FACTOR Infinite numbe of peiods a moe seious view of time Impatience potentially an issue when taking a seious view of time Individuals (i.e., consumes) ae impatient All else equal, would athe have X utils today than identical X utils at some futue date An intospective statement about the wold An empiical statement about the wold Septembe 30, Maco Fundamentals SUBJECTIVE DISCOUNT FACTOR Infinite numbe of peiods a moe seious view of time Impatience potentially an issue when taking a seious view of time Individuals (i.e., consumes) ae impatient All else equal, would athe have X utils today than identical X utils at some futue date An intospective statement about the wold An empiical statement about the wold Subjective discount facto A simple model of consume impatience β (a numbe between zeo and one) measues impatience The lowe is β, the less does individual value futue utility Septembe 30,

14 Maco Fundamentals SUBJECTIVE DISCOUNT FACTOR Infinite numbe of peiods a moe seious view of time Impatience potentially an issue when taking a seious view of time Individuals (i.e., consumes) ae impatient All else equal, would athe have X utils today than identical X utils at some futue date An intospective statement about the wold An empiical statement about the wold Subjective discount facto A simple model of consume impatience β (a numbe between zeo and one) measues impatience The lowe is β, the less does individual value futue utility Simple assumption about how impatience builds up ove time Multiplicatively: i.e., discount one peiod ahead by β, discount two peiods ahead by β 2, discount thee peiods ahead by β 3, etc. Do individuals impatience eally build up ove time in this way?...limited empiical evidence so eally don t know Septembe 30, Model Stuctue UTILITY Pefeences v(c t, c t+1, c t+2, ) with all the usual popeties Lifetime utility function Stictly inceasing in c t, c t+1, c t+2, c t+3, Diminishing maginal utility in c t, c t+1, c t+2, c t+3, v(c t,c t+1,c t+2,c t+3, ) v(c t,c t+1,c t+2,c t+3, ) etc. c t c t+1 Septembe 30,

15 Model Stuctue UTILITY Pefeences v(c t, c t+1, c t+2, ) with all the usual popeties Lifetime utility function Stictly inceasing in c t, c t+1, c t+2, c t+3, Diminishing maginal utility in c t, c t+1, c t+2, c t+3, v(c t,c t+1,c t+2,c t+3, ) v(c t,c t+1,c t+2,c t+3, ) etc. c t c t+1 Lifetime utility function additively-sepaable acoss time (a simplifying assumption), stating at time t vc (, c, c, c,...) uc ( ) uc ( ) uc ( ) uc ( ) t t1 t2 t3 t t1 t2 t3 Septembe 30, Model Stuctue UTILITY Pefeences v(c t, c t+1, c t+2, ) with all the usual popeties Lifetime utility function Stictly inceasing in c t, c t+1, c t+2, c t+3, Diminishing maginal utility in c t, c t+1, c t+2, c t+3, v(c t,c t+1,c t+2,c t+3, ) v(c t,c t+1,c t+2,c t+3, ) etc. c t c t+1 Lifetime utility function additively-sepaable acoss time (a simplifying assumption), stating at time t vc (, c, c, c,...) uc ( ) uc ( ) uc ( ) uc ( ) t t1 t2 t3 t t1 t2 t3 Utility side of infinite-peiod famewok no diffeent than Chapte 1 model except no longe possible to epesent gaphically Septembe 30,