GOVERNMENT AND FISCAL POLICY IN THE CONSUMPTION-SAVINGS MODEL SEPTEMBER
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1 GOVERNMENT AND FISCAL POLICY IN THE CONSUMPTION-SAVINGS MODEL SEPTEMBER 26, 2013 A 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 oth peiods Has spending in each peiod it needs to finance can e financed via Taxes Issuing govenment det/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 0 : govenment asset position at eginning of peiod 1/end of peiod 0 1 : govenment asset position at eginning of peiod 2/end of peiod 1 2 : govenment asset position at eginning of peiod 3/end of peiod 2 : eal inteest ate etween peiods Septeme 26,
2 Model Stuctue ADYNAMIC MODEL OF THE GOVERNMENT Economic activities/actions descied y peiod udget constaints Peiod-1 govenment udget constaint g (1 ) t Total expenditue in peiod 1: peiod-1 spending + wealth to cay into peiod 2 Total income in peiod 1: peiod-1 tax collections + income fom wealth caied into peiod 1 (inclusive of inteest) Peiod-2 govenment udget constaint g (1 ) t Total expenditue in peiod 2: peiod-2 spending + wealth to cay into peiod 3 Total income in peiod 2: peiod-2 tax collections + income fom wealth caied into peiod 2 (inclusive of inteest) Septeme 26, Model Stuctue ADYNAMIC MODEL OF THE GOVERNMENT Economic activities/actions descied y peiod udget constaints Peiod-1 govenment udget constaint g (1 ) t can ewite as g1 10 t10 Total expenditue in peiod 1: peiod-1 spending + wealth to cay into peiod 2 Total income in peiod 1: peiod-1 tax collections + income fom wealth caied into peiod 1 (inclusive of inteest) Peiod-2 govenment udget constaint g (1 ) t can ewite as Savings duing Asset income peiod 1 (a flow) duing peiod 1 (a flow) g2 2 1 t2 1 Total expenditue in peiod 2: peiod-2 spending + wealth to cay into peiod 3 Total income in peiod 2: peiod-2 tax collections + income fom wealth caied into peiod 2 (inclusive of inteest) Savings duing Asset income peiod 2 (a flow) duing peiod 2 (a flow) Definition: A govenment s savings duing a given peiod is the change in its wealth duing that peiod Fiscal suplus if govenment savings is positive Suplus/deficit is Fiscal deficit if govenment savings is negative a flow measue Septeme 26,
3 Model Stuctue GOVERNMENT BUDGET CONSTRAINT(S) Adopt a lifetime view of the udget constaint(s) All analysis conducted fom pespective of eginning of peiod 1 Peiod-1 govenment udget constaint Peiod-2 govenment udget constaint g t (1 ) g t (1 ) Asset position at end of peiod 1/eginning of peiod 2 the key link Assume = 0 (no defaults + stictly inceasing utility ) Septeme 26, Model Stuctue GOVERNMENT BUDGET CONSTRAINT(S) Adopt a lifetime view of the udget constaint(s) All analysis conducted fom pespective of eginning of peiod 1 Peiod-1 govenment udget constaint Peiod-2 govenment udget constaint g t (1 ) g t (1 ) Asset position at end of peiod 1/eginning of peiod 2 the key link Assume = 0 (no defaults + stictly inceasing utility ) Comine into lifetime udget constaint (LBC) Solve peiod-2 udget constaint fo 1 and sustitute into peiod-1 udget constaint g t g t (1 ) IMPORTANT: Govenment must alance udget 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 0 = 0 (i.e., govenment egins life with zeo net wealth). Note this is a diffeent assumption than 2 = 0. Septeme 26,
4 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 y multiplying y P Peiod-1 udget constaint c1 t1a1a0 y1a0 Peiod-2 udget constaint c2 t2 a2 a1 y2 a1 Comine into lifetime udget constaint (LBC) Solve peiod-2 udget constaint fo a 1 and sustitute into peiod-1 udget constaint c y t c y t (1 ) a Pesent discounted value (PDV) of all lifetime expenditue Pesent discounted value (PDV) of all lifetime disposale income (i.e., afte-tax income) Septeme 26, Maco Fundamentals ECONOMY-WIDE RESOURCE FRONTIER Consume lifetime udget constaint c2 y2 t2 c1 y1t1 (1 ) a0 1 1 Govenment lifetime udget constaint g2 t2 g1 t1 (1 ) Summing the two yields economy-wide esouce fontie c2 y2 g2 c1 y1g1 (1 )( a0 0) 1 1 aka poduction possiilities fontie (PPF) The GDP accounting equation in two-peiod fom Septeme 26,
5 Maco Fundamentals ECONOMY-WIDE RESOURCE FRONTIER Consume lifetime udget constaint c2 y2 t2 c1 y1t1 (1 ) a0 1 1 Govenment lifetime udget constaint g2 t2 g1 t1 (1 ) Summing the two yields economy-wide esouce fontie c2 y2 g2 c1 y1g1 (1 )( a0 0) 1 1 aka poduction possiilities 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 e analyzed using 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. Septeme 26, Maco Fundamentals NATIONAL SAVINGS National savings = savings y consumes + savings y govenment + savings y fims fim No fims in ou model (yet..), so s1 0 piv s1 y1t1c1 s1 t1g1 nat piv s s s y t c t g y c g Septeme 26,
6 Fiscal Policy and National Savings EFFECTS OF TAX POLICY National savings = savings y consumes + savings y govenment + savings y fims fim No fims in ou model (yet..), so s1 0 piv s1 y1t1c1 s1 t1g1 nat piv s s s y t c t g y c g Policy Expeiment: Is national savings affected y 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 udget 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 Cucial logic Taxes ae lump sum (will define/discuss next time ) Economy-wide esouce constaint does not depend on taxes optimal choice of c 1 unaffected y the change in tax policy Septeme 26, Fiscal Policy and National Savings EFFECTS OF TAX POLICY National savings = savings y consumes + savings y govenment + savings y fims fim No fims in ou model (yet..), so s1 0 piv s1 y1t1c Analyzing effects of changes in 1 tax policy on optimal s1 t1g consumption choices is the key 1 nat piv s s s y t c t g y c g Policy Expeiment: Is national savings affected y 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 udget 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 Cucial logic Taxes ae lump sum (will define/discuss next time ) Economy-wide esouce constaint does not depend on taxes optimal choice of c 1 unaffected y the change in tax policy Question 3: Effect of tax changes on peiod-1 national savings? NONE ecause neithe g 1 no c 1 changed Septeme 26,
7 Fiscal Policy and National Savings RICARDIAN EQUIVALENCE Ricadian Equivalence Theoem: Fo a given PDV of govenment spending, neithe consumption no national savings is affected y the pecise timing of lump-sum taxes A enchmak esult/concept in the theoy of macoeconomic policy Economic Intepetation: Rational consumes undestand that a tax cut today means a tax incease in the futue (ecause total govenment spending is unchanged) Thus entie tax cut is saved y consumes in ode to pay highe taxes in the futue Pivate savings and govenment savings move in exactly offsetting ways s y t c piv Rises when t 1 deceases, GIVEN that we have CONCLUDED that c 1 does not change s t g Deceases when t 1 deceases Septeme 26, Fiscal Policy and National Savings RICARDIAN EQUIVALENCE Ricadian Equivalence Theoem: Fo a given PDV of govenment spending, neithe consumption no national savings is affected y the pecise timing of lump-sum taxes A enchmak esult/concept in the theoy of macoeconomic policy Economic Intepetation: Rational consumes undestand that a tax cut today means a tax incease in the futue (ecause total govenment spending is unchanged) Thus entie tax cut is saved y 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 what pefect competition is to standad economic theoy Pediction elies cucially on lump-sum taxes Septeme 26,
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