Two Essays in Business Cycle Theory

Transcription

1 Universiy of New Orleans Universiy of New Orleans Theses and Disseraions Disseraions and Theses Two Essays in Business Cycle Theory Nazneen Ahmad Universiy of New Orleans Follow his and addiional works a: hps://scholarworks.uno.edu/d Recommended Ciaion Ahmad, Nazneen, "Two Essays in Business Cycle Theory" (2005). Universiy of New Orleans Theses and Disseraions hps://scholarworks.uno.edu/d/297 This Thesis is brough o you for free and open access by he Disseraions and Theses a ScholarWorks@UNO. I has been acceped for inclusion in Universiy of New Orleans Theses and Disseraions by an auhorized adminisraor of ScholarWorks@UNO. The auhor is solely responsible for ensuring compliance wih copyrigh. For more informaion, please conac scholarworks@uno.edu.

2 TWO ESSAYS IN BUSINESS CYCLE THEORY A Disseraion Submied o he Graduae Faculy of he Universiy of New Orleans in parial fulfillmen of he requiremens for he degree of Docor of Philosophy in Financial Economics by Nazneen Ahmad M.S., Universiy of New Orleans, 2005 M.A., York Universiy, 2000 Augus 2005

3 2005, Nazneen Ahmad ii

4 Acknowledgmen I wan o express my deepes appreciaion o he Chairman of my disseraion commiee, Dr. Wei Xiao, who no only provided excellen guidance bu also served as a menor and role model. He earned my special graiude for his coninuous suppor, paience and persisen opimism. He was always here o lisen, o give advice and help me hink hrough boh analyical and compuaional problems. I would like o hank my disseraion commiee members Drs. Michael Morris, Asuyuki Naka, Arja Turunen-Red and Gerald Whiney for heir valuable commens and encouragemens. I am grealy indebed o my parens Drs. Mesbahuddin Ahmad and Farida Akhar for heir uncondiional love and suppor. They have been a never-ending fund of srengh, wisdom and inspiraion hroughou my life. I dedicae his disseraion o hem. I would like o hank my brohers Tanveer Ahmad and Waquar Ahmad and my siser-in-law Shahanara Ali for heir encouragemens o pursue my disseraion. My sincere graiude goes o my husband and bes friend, Dr. Imiaz Ahmed Mazumder for his love, undersanding and sacrifices hroughou he docoral program a he Universiy of New Orleans. iii

5 Table of Conens Lis of Tables...v Lis of Figures... vi Absrac... vii Essay 1 End of Double Taxaion and Economic Recovery 1. Inroducion The Model The Economy Calibraion and Sysem Dynamics Quaniaive Resuls Economic Recovery from Permanen Reforms Economic Recovery from Temporary Reforms The Growh Effecs Sensiiviy Analysis Conclusion...23 Essay 2 Prospec Theory and he Welfare Cos of Business Cycles 1. Inroducion The Prospec Theory and Consumer Preferences The Framework Consumer Preferences Measuring Gains and Losses Uiliy from Gains and Losses Welfare Cos Esimaion Compuaion and Quaniaive Resuls Sensiiviy Analysis Conclusion...39 References...41 Via...43 iv

6 Lis of Tables Table 1. Parameer Values of he Benchmark Model...7 Table 2. Long Run Changes in he Levels...9 Table 3. Sensiiviy Analysis...21 Table 4. Welfare Coss of Flucuaions in Asse Reurns...35 Table 5. Welfare Coss wih CRRA Prospecive Uiliy Funcion...38 Table 6. Sensiiviy Tes...39 v

7 Lis of Figures Figure 1A. Transiional Dynamics of Oupu...9 Figure 1B. Transiional Dynamics of Oupu...10 Figure 2A. Transiional Dynamics of Invesmen...11 Figure 2B. Transiional Dynamics of Invesmen...12 Figure 3A. Transiional Dynamics of Employmen...13 Figure 3B. Transiional Dynamics of Employmen...13 Figure 4. Transiional Dynamics of Governmen Expendiure...14 Figure 5. Transiional Dynamics of Oupu...15 Figure 6. Transiional Dynamics of Invesmen...16 Figure 7. Transiional Dynamics of Employmen...17 Figure 8. Transiional Dynamics of Governmen Expendiure...18 Figure 9. Growh Rae of Oupu...19 Figure 10. Growh Rae of Oupu...19 Figure 11. Real GDP and S & P 500 Composie Index...26 Figure 12. Uiliy Funcion Suppored by he Prospec Theory...28 Figure 13. Uiliy of Gains and Losses...37 vi

8 Absrac This disseraion sudies wo ineresing business cycle issues. The firs issue concerns he effeciveness of ax policies in simulaing an economic recovery. The second issue concerns he coss of business cycle flucuaions o an invesor who chooses o inves in risky asses. The firs essay evaluaes he effeciveness of he end of double ax policy in simulaing an economic recovery by analyzing he ransiional dynamics of he economy s aggregaes oward he seady saes. The effeciveness of his policy is compared wih wo alernaive policies ha reduce corporae income or personal income axes. Alhough all of hese ax policies are found o simulae he economy s levels of oupu and invesmen, he end of double axaion appears o exer he mos significan impac on he aggregae levels of hese variables in he shor run. Based on his finding, we claim ha he end of double axaion is an effecive policy for simulaing an economic recovery in he shor-run. In a hough-provoking exercise Lucas (1987 and 2003) argues ha he welfare coss of business cycles is negligible. The second essay follows up on his argumen by incorporaing prospec heory ino he formulaion of individual preferences. Prospec heory proposes ha agens care abou changes in heir wealh level raher han he level of heir final wealh, and individuals are also aken o be more sensiive o losses han gains in heir financial wealh. According o he prospec heory, herefore, he agens ake flucuaions in he asse reurns seriously. Resuls from empirical ess find ha an individual invesor, on average, would give up vii

9 % of he average reurns, she receives from invesing in he risky asse, in order o eliminae all he flucuaions associaed wih her asse reurns. This resul is inerpreed as an indicaion of much larger welfare coss han Lucas s esimaes. viii

10 Essay 1: End of Double Taxaion and Economic Recovery 1. Inroducion The long-run impac of capial income axaion on he economy has been exensively sudied in he lieraure. In Chamley (1986) s seminal work, for example, he opimal rae of capial income ax is shown o be zero in he seady sae of a general equilibrium model wihou uncerainy. Zhu (1992) and Chari e al. (1994) show ha a similar conclusion holds for a sochasic version of he economy. Lucas (1990), on he oher hand, shows ha if he capial income ax is eliminaed and all he governmen revenues are raised from he labor income ax, he long-run growh rae of capial sock and oupu will increase significanly. Devereux and Love (1994) and & ( Imrohoroglu (1998) presen similar resuls for economies wih human capial and wih over-lapping generaions. Few researchers, however, have paid much aenion o he shor-run dynamics associaed wih he changes in he capial income ax rae. In paricular, when he economy emporarily deviaes from is long-run growh pah and falls ino a recession, can he capial income ax rae be used as an effecive ool o speed up he economic recovery? How does i compare wih oher policy measures such as labor income axes? This issue has become paricularly ineresing wihin he conex of a recen policy change. In May 2003, he congress passed he Jobs and Growh Tax Relief Reconciliaion Ac, in which i promised o eliminae he ax on dividend income of he invesors reroacive o January 1, 2003 hrough December 31, The declared goal of he ac was o speed up an economic recovery by encouraging consumer spending and promoing privae secor invesmen. Clearly, he law was very much focused on achieving shor-erm economic objecives. In he U.S. ax sysem, corporae capial income is axed a boh he corporae and individual levels. In he firs sage, a company is axed on is profis, ypically a a marginal rae of 35%. In he second sage, when he company passes along is profis o he invesors in he form of dividends, he invesors are axed on he dividends, a a marginal rae of 38.6%. This is called double axaion. The marginal federal ax rae on capial income sums up o as high as 60%. In oher words, for every dollar of profi a company could pay ou in dividends, as lile as 40 cens acually reaches he invesors. If he firms reain he afer-ax earnings, he shareholders are axed on he appreciaion in he sock value due o he afer-ax earnings ha are reained and 1

11 reinvesed in he firm. This cumulaive ax on reained earnings is up o 48%. If he double axaion on capial income is eliminaed, a company would pay ax on is profi a he sauory corporae ax rae, bu here will be no ax on he invesors dividends. Policy-makers expec ha he end of double axaion on capial income would promoe capial formaion by encouraging he privae secor o inves and in urn generae a fas economic expansion. In his paper, we evaluae he effeciveness of he end of double axaion policy as a ool for simulaing economic recoveries. Specifically, we sudy a real business cycle model in which firms are subjec o he double axaion sysem similar o he one we jus described. In period one, a negaive and persisen shock drags he economy ino a emporary recession. Then, in an aemp o end he recession, he governmen eliminaes he double axaion on capial income. We evaluae he impac of his policy by analyzing he ransiional dynamics of he aggregae variables owards he seady saes. We consider boh a emporary policy ha eliminaes dividend axes for only 3 years and a permanen policy ha eliminaes dividend axes forever. We also compare he effeciveness of his policy wih wo alernaive policies ha reduce labor income and business income axes. A policy is desirable if i leads o a fas ransiion back o he seady sae and causes he leas loss of oupu in a given period of ime. Lucas (1990), Devereux and Love (1994) and & ( Imrohoroglu (1998) also sudy he quaniaive effec of capial income axes in general equilibrium models. Using endogenous growh models, hey are able o idenify he impac of his policy on he long-run growh rae of he economy. Therefore, heir focus is on he growh effec of capial income axes. The model environmen we consider is a neo-classical economy where he growh rae of he economy is deerminisic. Eliminaing dividend axes has no growh effec in his environmen. Insead, here will be a level effec which is refleced by changes in seady sae oupu and oher aggregae variables. The ransiion dynamics from one seady sae level o anoher is he focus of his sudy, since such dynamics shed ligh on how he economy recovers from a recession wih he help of alernaive ax policies. The resuls of our sudy are summarized as follows. The end of double ax policy has considerable shor-run effec on he economy. For emporary reforms, over he periods of no double axaion, he economy exhibis greaer increase in he oupu level han hose over he periods of reduced corporae income or reduced personal income ax rae. For permanen reforms, he end of double axaion exers sronger seady-sae oupu and invesmen effecs 2

12 compared o hose for wo oher policy reforms. However, he economy s long run employmen is simulaed only when he personal income ax rae is reduced permanenly. The res of he paper is organized as follows. The model is presened in secion 2. Secion 3 presens he parameer values of our benchmark economy and he mechanism ha generaes he ransiional dynamics of he economy. Quaniaive resuls are provided in secion 4. Secion 5 ess he robusness of our resuls. Secion 6 concludes he paper. 2. The Model We consider a decenralized neoclassical economy. The economy consiss of hreesecors: households, firms and he governmen. The households own he firms and receive profi from he firms in he form of dividends. The firms produce a unique good, which can be eiher consumed in he curren period or ransformed o physical capial in he nex period. The governmen axes he privae secor on heir earnings from labor as well as capial services o finance is spending. 2.1 The Economy There are a large number of infiniely lived idenical individuals in he economy. The preferences of he represenaive household are of he following form: max β (ln c + θln l ), (1) = 0 where 0<β<1 is he discoun facor, θ represens preference for leisure, and c and l are consumpion and leisure per capia. The uiliy funcion is sricly increasing, concave, and wice coninuously differeniable. The household splis oal ime beween work and leisure aciviies. Normalizing he oal ime endowmen o one, he ime consrain akes he following form: n l = 1 (2) + The household receives wages a a rae w for each uni of labor supplied and ren a a rae r for each uni of physical capial (k ) supplied o he firm. In addiion, as he owner of he firm, he receives dividend from he firm. The household pays axes on all hese incomes a hree differen raes. Thus he budge consrain of he household is c + i = w n + r k, (3) 3

13 and he ax bill paid by he household a each period of ime is as follows: Where τ p >0, τ d axed. The index, η [ 0,1] = τpw n + ητd[(1 τb )(rk φki )] + τb (rk φki ), (4) >0 and τ b >0 respecively are he raes a which wages, dividends and profis are, indicaes wheher or no capial income is axed wice. The parameer ϕ k represens he fracion of invesmen ha is deduced from he firm s axable income. This fracion of deducion from he business axable income represens an elemen of he U.S. ax code ha provides incenive o he privae secor o inves. The firm combines physical capial and labor, o produce he final good, using he following producion echnology: y = α n 1 α A k, (5) Where α represens he share of capial in oal oupu. A represens he random produciviy shock variable, which follows AR(1) process, given by: A +1 = ρ A + ε, (6) Where 0< ρ <1 is he persisence parameer and ε~ N(0, σ ). The capial accumulaion of he economy occurs hrough he following dynamic consrain: i = k+ 1 (1 δ)k, (7) where δ is he rae of capial depreciaion. In equilibrium, profi maximizaion by he firm implies ha boh facors are paid heir marginal producs. Thus we have he following: r y = α, (8) k y w ( 1 α) = (9) n Given he associaed consrains he household chooses consumpion, leisure, and capial o maximize her lifeime uiliy, which yields he following necessary condiions for equilibrium: 1 = λ, (10) c 2 ε 4

14 θ 1 n y = λ (1 α) n (1 τ ), (11) p y αβλ [1 ( τpη(1 τb ) + τb )] = [1 φk ( τpη(1 τb ) + τb )][ β(1 δ) λ + 1 k + 1 λ ], (12) Where λ is he Lagrange muliplier associaed wih he household s budge consrain. Equaion (10) equaes he marginal uiliy of consumpion o is opporuniy cos ( λ ). Equaion (11) equaes he marginal disuiliy of supplying labor o he afer-ax real wage. Equaion (12) equalizes he pos-ax marginal coss and benefis of invesing in fuure capial. The governmen ses he ax code parameersτ p, τ d, τ b,η and ϕ k o raise a specific level of per capia governmen revenue each period. Governmen revenue, g, does no conribue o eiher producion or individual uiliy. For simpliciy, we assume ha he governmen budge is balanced each period. The budge consrain of he governmen is defined as follows: g = τpw n + ητd (1 τb )(rk φki ) + τb (rk φki ). (13) c,n,k+ 1, y,g ha saisfies he following: i) given wage and he raes of reurn on invesmen, he household chooses consumpion, leisure and capial accumulaion o maximize uiliy, ii) firms maximize profis given he facor prices, iii) governmen s budge is balanced and vi) all markes clear. The household s budge consrain (3) and he governmen s budge consrain (13) yield he following marke clearing condiion for he economy: A dynamic equilibrium of he economy consiss of he sequences { } y = c + i + g. (14) 3. Calibraion and Sysem Dynamics Mos parameers are calibraed o be consisen wih exising findings in he lieraure. Someimes we vary some parameers around our iniial benchmark seings for robusness check purposes. King and Rebelo (2000)[henceforh KR] se he value of labor s share parameer as 2/3, which is a sandard value for he long-run labor income share in he U.S. GNP. Following KR we se he value of capial s share in oal oupu, α equal o The convenional annual depreciaion rae used in neoclassical growh lieraure is 10% (King & Plosser, 1982, KR, 1990). As we are ineresed in quarerly analysis, we use δ= KR derives he value of he 5

15 discoun facor by seing he seady sae ineres equal o 6.5%, which is he average annual reurn o capial in he U.S. 1 For our quarerly model we se β so ha he quarerly ineres rae is (0.065/4)%. In he neoclassical lieraure, he value of persisen parameer ranges beween.9 and.979. We se ρ equal o.95. Following KR (1999) he sandard deviaion of innovaion, σ ε is se KR chose he value of leisure preference parameer θ o mach he seady sae work hours, which is Following hem we se θ o be Personal income ax rae, τ p, is se o 0.253, on he basis of he 1994 U.S. ax schedule for married axpayers wih no children who file IRS form 1040 joinly. Corporae income ax rae, τ b, is se o 0.35, o mach he sauory corporae ax rae. In he U.S. ax sysem, dividends received by a shareholder generally are axed a he same rae ha applies o he personal income ax; he capial gains, however, are axed a a lower rae. The Job and Growh Tax Relief Reconciliaion Ac of 2003, reduces he 10- and 20-percen long-erm capial gain axes respecively o 5 and 15%. In our model, we do no specify he proporion of afer-ax profi ha is reained by he firm and ha is disribued as dividends o he shareholders. As he dividend ax is generally higher han he ax on capial gains, if all he afer-ax profi of he firm of our benchmark economy is axed a he dividend ax rae, eliminaion of double axaion would generae an upward bias in our resuls. To avoid he bias, he afer-ax profi of he firm is axed a a rae equal o he weighed average of ax raes on reained earnings (capial gain) and ax raes on dividends. The average dividend pay ou for all COMPUSTAT acive firms for was 17.62% and for was 28.55%. The average reained earnings in hese wo periods respecively were 82.38% and 71.45%. Therefore, on average, in hose 20 years he proporion of dividend paid ou was 23% and he firms reained 77% of heir afer-ax profi. Based on hese esimaes, he ax rae on dividend (afer-ax profi) for our benchmark model is calculaed as follows: [average dividend pay ou (23%)*ax rae on dividend (25%)+ average reained earning (77%)*capial gain ax rae (15%)]=17.3%. To capure he double axaion of capial income he index η is se o 1. ϕ k is se o o mach he effecive marginal capial ax rae, which is The annual average reurn on he Sandard and Poor 500 index over is 6.5%. 6

16 Table 1: Parameer Values of Benchmark Model Parameer Value Empirical fac o mach τ p τ b τ d φ k η β α θ δ γ ρ σ ε Personal income ax Business income ax Dividend ax Fracion of unaxed invesmen Index Discoun rae Share of capial in GDP Preference for leisure Rae of capial depreciaion Long-run growh rae Persisence Sandard deviaion of innovaion Fied value from 1994 U.S. ax schedule Sauory corporae ax rae Average dividend pay ou=23% Effecive marginal capial ax rae=0.16 Double axaion on business income Average reurns o capial=6.5%, per annum Average share of labor income in GNP = 2/3 Average pos-world War II supply of labor hour=.20 Share of gross invesmen= 0.295, per annum Average per capia oupu growh rae=1.6% Errors in Solow residual Sandard deviaion of he errors in Solow residual The long run growh rae of a neoclassical economy is deermined by he exogenous rae of echnological progress, γ. This long run rae remains unchanged in all he alernaive ax policy regimes. Thus in he long run, k y γ = c + 1 = + 1 = + 1, c k y Which is se o in our model. To analyze he shor-run dynamics of he benchmark economy during differen ax policy regimes, we linearize he firs order condiions around he seady sae as in King and Rebello (1988). The se of linearized equaion yields he following law of moion for he sae variables of our model: s ε. + 1 = ms + +1 The following equaion specifies, given he iniial capial sock and level of produciviy, how consumpion, work effor, invesmen, governmen expendiure, oupu and shadow prices are deermined by he sae variables, in response o a 1% negaive produciviy shock o he economy. z =, s Where z is he vecor of all he conrol variables of he model. 7

17 4. Quaniaive Resuls We calculae he seady sae value of oupu for our benchmark economy where individuals are axed on heir personal as well as corporae income and he firms are axed on heir profi. In period one, a negaive and persisen shock his he economy and drags oupu below is long run level emporarily. We solve he ransiional dynamics of oupu, of he benchmark economy, owards he seady sae. In he nex sep, we assume a policy change in he economy ha eliminaes ax on dividend. The dynamics of oupu caused by his policy are solved and compared o he oupu dynamics in he benchmark economy. The difference beween hese wo dynamics explains he effeciveness of he end of double axaion in simulaing he economy s oupu level. We also evaluae he effeciveness of wo oher policies in reviving he economy from recession in he similar fashion. The firs policy reduces he corporae income ax and he second policy reduces he ax on individual s personal income. The impacs of he policies on he oher variables of he economy, e.g. invesmen, employmen, governmen spending and welfare are also examined. Figures 1 hrough 10 plo he ransiion dynamics of he variables in alernaive ax policy regimes. The quaniaive resuls are presened in hree subsecions. Firs, he impacs of permanen reforms in he ax policies are examined. Second, we solve he dynamics of he economy s variables generaed by emporary reforms in he policies. Third, he growh effecs of boh emporary and permanen policy reforms are briefly discussed Economic Recovery from he Permanen Reforms The permanen ax policy reforms yield new seady sae levels for he economy s aggregaes. The ransiional dynamics from he original seady sae levels o he new levels describes how he economy recovers from he recession wih he help of alernaive ax policies. The changes in he long run levels of he economy s aggregaes produced by he ax policies are repored in Table 2. The immediae response o a permanen end of double axaion is a 0.78% increase in he level of oupu compared o ha in he benchmark economy wih double axaion. Figure 1A compares he dynamics of oupu in he double axaion economy wih ha in he end of double axaion economy. 8

18 Table 2: Long Run Changes in he Levels Tax Policy η=0 τ b =0.27 τ p =0.238 Changes in Seady Sae Levels (in percenage) Oupu Invesmen Governmen Employmen Welfare Spending Noe: Row 1, 2 and 3 repor he percenage changes in he seady sae levels of he economy s variables respecively generaed by a permanen end double axaion, a permanen 8% reducion in he corporae income and a permanen 1.50% reducion in he personal income ax rae, compared o heir seady sae values in he benchmark economy wih no reform. The percenage change in he seady sae level of oupu generaed by a permanen end of double axaion is calculaed using he following equaion: y 1 y, y where y is he seady sae level of oupu in he benchmark economy wih double axaion and y1is he seady sae level of oupu yielded by a permanen end of double ax policy. As is clear, he level of oupu immediaely shifs up following he end of double axaion and coninues o move upward unil i converges o is higher long run level. We calculae ha he new seady sae oupu produced by a permanen end of double ax policy is 0.21% higher compared o ha in he benchmark economy. Noe: The doed pah describes he oupu dynamics in he economy wih double axaion. The pah describes he oupu dynamics caused by a permanen end double axaion. 9

19 In he nex sep, we examine wheher he corporae or he personal income ax policy reforms can generae an equivalen increase in he long run oupu. Saring from he benchmark economy in which here is double axaion and he ax raes on personal and corporae incomes respecively are 25.3% and 35%, he ax on corporae income is varied. We find ha a permanen 8% reducion in he corporae income ax yields a 0.21% increase in he long run oupu. From a similar exercise, we find ha an equivalen increase in he long run oupu is produced when he personal income ax rae is permanenly reduced o 23.8%. This rae is 1.2% lower han ha in he benchmark economy. However, as dividend ax rae is calibraed as he weighed average of ax raes on dividend and capial gains and dividends are axed a he same rae as he personal income, when he ax on personal income is reduced permanenly, he ax on dividend is essenially reduced permanenly. This dividend ax rae is 17%, which is 0.3% lower han ha in he benchmark economy. Noe: The doed pah describes he oupu dynamics in he benchmark economy. The pah describes he oupu dynamics caused by a permanen end double axaion ; he pah describes he dynamics generaed by a permanen reform in he corporae ax and he pah describes he dynamics generaed by a permanen reform in he personal income ax policy. Figure 1B compares dynamics of oupu produced by he alernaive ax policy reforms. An imporan feaure of hese dynamics is ha he iniial response of oupu o he end of double axaion is much greaer han hose caused by reducions in he corporae or in he personal 10

20 income ax rae. In addiion, he oupu rajecory in he end of double ax economy lies above hose in he oher economies for abou 20 quarers. A permanen end of double axaion also simulaes he economy s long run invesmen level significanly. Figure 2A shows ha his policy causes an immediae jump in he economy s invesmen level; invesmen increases hrough ime oward is new saionary level. Noe: The doed pah describes he oupu dynamics in he economy wih double axaion. The pah describes he oupu dynamics caused by a permanen end double axaion. Invesmen dynamics produced by he alernaive policy reforms are compared in Figure 2B. Alhough he corporae income ax policy reform iniially exhibis an invesmen advanage over he end of double ax policy, he invesmen rajecory driven by he end of double axaion overakes ha driven by corporae ax policy reform approximaely in one year and i evenually converges o a higher long run level. In he long run, reducions in he corporae income or in he personal income ax ha yield an equivalen oupu effec generae a relaively weak impac on he economy s invesmen level. Table 2 repors ha he permanen end of double ax policy raises he seady sae invesmen by 4.85%, while a permanen 8% reducion in he corporae income ax yields a 3.10% and a permanen 1.5% reducion in he personal income ax yields a 0.30% increase in he long run level of invesmen. 11

21 Noe: The doed pah describes he invesmen dynamics in he benchmark economy. The pah describes he invesmen dynamics caused by a permanen end double axaion ; he pah describes he dynamics generaed by a permanen reform in he corporae ax and he pah describes he dynamics generaed by a permanen reform in he personal income ax policy. The end of double ax policy produces a negaive impac on he economy s long run employmen level. Figure 3A shows ha he employmen level drops immediaely afer imposiion of his policy; i evenually converges o a new seady sae level which is 2.03% lower han is benchmark level. I is o be noed ha unemploymen does no exis in our heoreical model. A reducion in he long run employmen herefore, does no have any adverse impac on he economy. This is revealed in our long run welfare benefi esimaion. Table 2 repors ha in he long run he end of double axaion generaes posiive welfare benefi. From Equaion (1), i follows ha in he long run he eliminaion of dividend ax generaes higher levels of consumpion and leisure for he individuals compared o hose in he benchmark economy. Thus reducion in he long run employmen caused by he end of double axaion is compensaed by an increase in he long run leisure, which in urn increases he long run welfare of he individuals. We also find ha his welfare benefi is higher han hose caused by he alernaive policy reforms. 12

22 Noe: The doed pah describes he employmen dynamics in he economy wih double axaion. The pah describes he employmen dynamics caused by a permanen end double axaion. Noe: The doed pah describes he employmen dynamics in he benchmark economy. The pah describes he employmen dynamics caused by a permanen end double axaion ; he pah describes he dynamics generaed by a permanen reform in he corporae ax and he pah describes he dynamics generaed by a permanen reform in he personal income ax policy. 13

23 A comparison of he employmen dynamics produced by he alernaive ax policy reforms are porrayed in Figure 3B. I appears ha he economy s long run employmen is simulaed only when personal income ax is reduced. One possible explanaion of his resul hinges on he conflicing income and subsiuion effecs of a change in he real wage. I follows from Equaion (4) ha a reducion in he personal income ax raises he real wage in he economy. This encourages he individuals o work hard and produces a larger income effec. On he oher hand, he end of double ax policy and a reducion in he corporae income ax induce he individuals o enjoy more leisure and produce larger subsiuion effecs. Noe: The doed pah describes he governmen spending dynamics in he benchmark economy. The pah describes he spending dynamics caused by a permanen end double axaion ; he pah describes he dynamics generaed by a permanen reform in he corporae ax and he pah describes he dynamics generaed by a permanen reform in he personal income ax policy. All he ax policies yield a negaive impac on he long run governmen spending. The inuiion of his is clear from Equaions (4) and (13). Adopion of all he ax policies immediaely drags spending below ha in he benchmark economy and he spending dynamics caused by he policy reforms remain below ha in he benchmark economy hrough ime oward he lower saionary levels. However, Table 2 repors ha he long run 14

24 governmen spending is significanly lower in he end of double ax regime compared o hose in oher policy regimes Economic Recovery from he Temporary Reforms In his secion, we assume ha in he period immediaely afer he negaive shock he governmen eliminaes dividend axes only for 12 quarers. In our se up, emporary reform in a ax policy is expeced o have ransiory impacs on he economy s aggregaes as he aggregaes evenually converge o heir original long run levels. Figures 5 hrough 8 plo he dynamics of he economy s aggregaes generaed by emporary reforms in he ax policies. The impacs of a emporary end of double axaion hroughou he reform period are he same as hose caused by he permanen end of double ax policy during he same span of ime. For example, as Figure 5 shows, a emporary end of double axaion causes an immediae jump in oupu and he oupu rajecory lies above ha in he benchmark economy hroughou he reform period. We calculae ha over hese 12 quarers, he economy, on average, enjoys 0.38% higher level of oupu compared o he benchmark economy. Bu, immediaely afer he reimposiion of dividend ax, oupu drops by -1.81% relaive o is benchmark level. Afer his massive decline, he oupu level increases slowly o cach up wih is long run level. Noe: The doed pah describes he oupu dynamics in he benchmark economy. The pah describes he oupu dynamics caused by a emporary end double axaion ; he pah describes he dynamics generaed by a emporary reform in he corporae ax and he pah describes he dynamics generaed by a emporary reform in he personal income ax policy. 15

25 While emporary reforms in he corporae ax and in he personal income ax policies simulae he oupu level over he reform period, he impacs are much weaker han ha generaed by a emporary eliminaion of dividend ax. We find ha over he reform period, on average, emporary reducion in he corporae ax or in he personal income ax, respecively yield a 0.056% and a 0.055% increase in he oupu level relaive o ha in he benchmark economy. While oupu exhibis a sharp drop immediaely afer he corporae or he personal income ax raes are raised back o heir original raes, he magniude of hese drops are considerably lower han ha caused by he re-imposiion of dividend ax. In addiion, emporary reforms in he corporae or in he personal income ax policies cause a faser ransiion back o he seady sae and also cause less loss of oupu relaive o ha caused by a emporary end of double ax policy during he ransiion owards he seady sae. Noe: The doed pah describes he invesmen dynamics in he benchmark economy. The pah describes he invesmen dynamics caused by a emporary end double axaion ; he pah describes he dynamics generaed by a emporary reform in he corporae ax and he pah describes he dynamics generaed by a emporary reform in he personal income ax policy. The emporary reforms in he ax policies produce similar impac on he economy s invesmen level. Over he periods of end of double axaion reduced corporae or personal income ax raes, on average, he economy experiences respecively 0.25%, 0.28% and 0.01% increase in he invesmen level compared o he benchmark economy. Figure 6 compares he 16

26 ransiional dynamics of invesmen generaed by he emporary reforms in he ax policies. Terminaion of all he policy reforms afer 12 quarers cause immediae decline in he economy s invesmen level. However he magniude of his downfall is greaer for he re-imposiion of dividend ax compared o hose caused by he erminaion of oher policy reforms. In addiion, he invesmen rajecory generaed by re-imposiion of dividend ax lies below hose generaed by erminaion of he oher policy reforms unil i reaches he seady sae. This implies ha hroughou he ransiion process, a emporary end of double ax policy causes greaer loss of invesmen relaive o ha caused by he emporary reforms in he oher ax policies. Noe: The doed pah describes he employmen dynamics in he benchmark economy. The pah describes he employmen dynamics caused by a emporary end double axaion ; he pah describes he dynamics generaed by a emporary reform in he corporae ax and he pah describes he dynamics generaed by a emporary reform in he personal income ax policy. Figure 7 shows ha even during he reform periods a emporary end of double axaion or a emporary reducion in he corporae ax do no simulae he economy s employmen level, which is consisen wih he resuls for permanen policy reforms. As in each period, he governmen budge is balanced, immediaely afer he ax policy reforms are erminaed, he economy s governmen spending increases and converges o is long run level quickly. 17

27 Noe: The doed pah describes he spending dynamics in he benchmark economy. The pah describes he spending dynamics caused by a emporary end double axaion ; he pah describes he dynamics generaed by a emporary reform in he corporae ax and he pah describes he dynamics generaed by a emporary reform in he personal income ax policy The Growh Effecs As he long run growh rae of our benchmark economy is deermined exogenously, he ax policy reforms are expeced o have only ransiory effecs on he economy s growh rae. In his secion, we analyze he effecs of boh permanen and emporary reforms in he ax policies on he shor-run growh. The resuls are summarized in Figure 9 and 10. Figure 9 shows ha a permanen end double axaion generaes a ransiory increase in he oupu growh rae compared o is long-run rae. As expeced, he lengh of he ransiional dynamics is shor and he economy reaches is seady sae growh rae quickly. An imporan feaure of he dynamics is ha he increase in growh rae generaed by a permanen end of double ax policy is higher han hose caused by permanen reducions in he corporae or in he personal income ax rae. We calculae ha in he period immediaely afer he dividend ax is eliminaed, oupu grows a a rae 2.14% higher han ha in he benchmark economy. The growh raes yielded by he reforms in corporae or personal income ax policy in his period respecively are 0.49% and 0.38% higher han ha in he benchmark economy. 18

28 Noe: The doed pah describes he growh dynamics in he benchmark economy. The pah describes he growh dynamics caused by he emporary end double axaion ; he pah describes he dynamics generaed by reform in he corporae ax and he pah describes he dynamics generaed by reform in he personal income ax policy. Figure 10 shows ha, similar o ha for he permanen reforms, a emporary end of double ax policy produces sronger shor-run growh effecs han hose produced by he wo oher policy reforms. Immediaely afer he reforms are erminaed, oupu exhibis a negaive growh effec for a shor period. However, as before, he lengh of he ransiion dynamics is shor and he economy s growh rae caches up wih is long run rae quickly. 19

29 The above resuls provide a few imporan messages regarding he impacs of he alernaive ax policies on he economy. For a quick economic recovery a emporary as well as a permanen reform in he policies appear o be useful. While he permanen reforms generae long run oupu advanages, he emporary reforms generae only emporary advanages. Therefore, he permanen reforms in he policies are preferable compared o he emporary reforms. While a permanen reducion in he corporae or in he personal income ax rae may yield he same oupu effec as ha yielded by a permanen end of double axaion, iniially he end of double ax policy exers much sronger impac on oupu ha lass for a considerably long period (abou 20 quarers). The permanen end of double ax policy also causes a faser ransiion back o he seady sae oupu. The invesmen effec as well as he welfare effec of a permanen end of double ax policy appear o be sronger han hose produced by he wo oher policy reforms. Thus as a ool for achieving quick economic recovery a permanen end of double axaion urns ou o be more desirable han he wo oher policy reforms. On he oher hand, when he reforms are adoped only for a shor period, he ransiion period of oupu o is seady sae is he longes for end of double axaion. In addiion, he re-imposiion of dividend ax causes greaer oupu as well as invesmen losses compared o hose caused by he erminaion of wo oher policy reforms. 5. Sensiiviy Analysis We perform some compuaional experimens wih differen choices for some parameer values o deermine he robusness of he main quaniaive resuls derived in he previous secion. Table 3 repors he resuls of hese experimens. Firs wo rows of Panel A in Table 3 repors he seady sae impacs of a permanen end of double ax policy in an economy ha depars from he benchmark economy only wih respec o he firm s decision regarding dividend pay ou. In he pervious secion, we used a ax rae of 17.3% on dividend based on he hisoric average of 77% earning reenion rae of he firms. In his secion, we re-calculae he impacs of he ax policies by changing he proporion of aferax profi reained by he firms. Firs, we assume ha he firms do no reain any earnings afer paying ax on is profi. Hence, given ha he double axaion prevails in he economy, he shareholders pay ax on heir dividends a he rae ha applies o personal income. 20

30 Table 3: Sensiiviy Analysis Tax Policy Aggregae Changes in he Levels (in percenage) Oupu Invesmen Governmen Spending Panel A: End of Double Taxaion, η = 0 Employmen Welfare Reained earning= Reained earning=. 9,τ d = α = α = ϕ k = ϕ k = δ = δ = Panel B: Reducion in Corporae Income Tax, τ b = Reained earning= Reained earning=. 9,τ d = α = α = ϕ k = ϕ k = δ = δ = Panel C: Reducion in Personal Income Tax, p = Reained earning= Reained earning=. 9,τ d = α = α = ϕ k = ϕ k = δ = δ = Noe: In our benchmark economy, he share of capial in oupu, α=0.33, he fracion of deducible business axable income, ϕ k = 0.844, he capial depreciaion rae, δ= 0.025, he double axaion index, η=1, he corporae income ax rae, τ b =0.35 and he personal income ax rae, τ p = The ax funcion akes he following form: = τ [w n + η(1 τ )(r k φ i )] + τ (r k φ i ) (15) p b k We find ha when he firms disribue he enire afer-ax profi as dividends, a permanen end of double ax policy exers much sronger long run impacs on oupu as well as on b k 21

31 invesmen han hose in our original exercise. These long run impacs are also significanly greaer han hose produced by he oher policy reforms. On he oher hand, when he earning reenion rae is high (90%), he impac of end of double ax policy on he long run oupu is a lile weaker han hose caused by he oher policy reforms. The inuiion of hese resuls can be undersood by comparing Equaion (4) wih Equaion (15). I follows from Equaion (4) ha when he firms reain a proporion of afer-ax earning, he shareholders pay ax on he dividends a a rae of τ d, which is calibraed as 17.3%. On he oher hand, Equaion (15) shows ha when he firms disribue he enire afer-ax profis as dividends and double axaion prevails, dividends are axed a a higher rae (25.3%). Therefore when he dividend pay ou raio is high and he ax on dividend is eliminaed, he shareholders receive higher reurns on heir invesmen compared o ha when he dividend pay ou is less. This encourages he shareholders o inves more. We es he sensiiviy of our resuls o capial s share in oal oupu by considering an increase in capial s share (se α=.35) and also a decrease in capial s share (se α=.30) in oupu relaive o ha in he benchmark economy. For a higher value of α, he impac of end of double axaion is sronger han ha for is benchmark value; for a lower value, is impac appears o be considerable. In addiion, for boh values of α, he impac of his policy on he long run invesmen is significan. These resuls prove he robusness of our previous findings. We examine he sensiiviy of our resuls o changes in he fracion of deducible business axable income from is benchmark value ( ϕ =0.844). For a lower value of ϕ ( ϕ =0.5), all he k ax policies exer significan impacs on he seady sae oupu and invesmen, he impacs of end of double ax policy however appears o be he sronges. An ineresing finding is, for a near complee deducion of business axable income ( ϕ =0.99), he impacs of end of double axaion on he long run oupu as well as invesmen are negaive. The inuiion of his resul follows from equaion (4). When ϕ k =0.99, he shareholder s oal amoun of axable corporae income is significanly reduced. Therefore eliminaing dividend ax does no increase he reurns on invesmen significanly. On he oher hand, when amoun of axable corporae income is large, he end of double axaion encourages he household o inves more as i implies ha she receives higher reurns on a larger amoun of corporae income. k k k 22

32 6. Conclusion The paper evaluaes he effeciveness of end of double ax policy in simulaing a quick economic recovery. We compare he impacs of his policy wih hose of wo oher policy reforms ha reduce personal income and business income axes. We consider boh permanen and emporary reforms in hese policies. A simple neoclassical model wih exogenous growh is used as a benchmark economy. We find ha he ax policy reforms have considerable influence on he economy and ha he ransiional effecs of differen policy reforms on he economy s variables play a useful role in evaluaing he overall impac of he policies. Given ha he emporary reforms only offer emporary benefis, he permanen reforms in he axaion policies are more useful for he long run economic well-being. While all he ax policy reforms considered in his sudy simulae he long-run levels of oupu as well as invesmen of he economy, we find a significan quaniaive difference. A permanen end of double axaion yields higher level of oupu compared o hose yielded by permanen reforms in he oher policies for a considerably long period; his policy also causes a faser ransiion back o he seady sae oupu. The reforms in he corporae income or he personal income ax policies ha yield an equivalen seady sae oupu effec generae a relaively weak impac on he economy s long run invesmen level. A sensiiviy analysis performed in secion 6 proves he robusness of our analysis and also gives us some addiional insighs regarding he effeciveness of he end of double ax. We find ha eliminaing dividend ax can acually reduce he seady sae oupu if he firm s invesmen expendiure is almos enirely deduced from heir axable income. On he oher hand, when he firms are axed on a significan proporion of heir invesmen spending, eliminaing dividend ax exers significan oupu benefi. We also find ha he higher is he dividend pay ou, he greaer is he impac of end of double ax policy on he long run oupu of he economy. Based on our findings we claim ha a permanen end of double axaion is an effecive fiscal ool for simulaing an economic recovery. 23

33 Essay 2: Prospec Theory and he Welfare Cos of Business Cycles 1. Inroducion According o Lucas (1987), he welfare cos of business cycles is small and negligible. Using a simple represenaive agen model where preferences of he agens are logarihmic, he esimaes he welfare cos as he percenage of consumpion he consumers would be willing o pay o swich from a flucuaing consumpion pah o a perfecly smooh consumpion pah. He finds ha o have all he volailiies in consumpion eliminaed, he consumer would only give up less han one-enh of one percen of consumpion (abou $8.5 per person per quarer). Lucas s provocaive claim naurally sirs up a series of new aemps o re-examine he issue. Many of hese effors involve he relaxaion of Lucas assumpions on consumer preferences and he consumpion processes. In a laer survey paper, however, Lucas (2003) poins ou ha hese exensions mosly give rise o similar conclusions. For example, Orok (2001) incorporaes ime-non-separabiliies in consumer preferences in his welfare cos calculaion, and finds ha he welfare cos is of he same magniude as ha esimaed by Lucas. Dolmas (1998) esimaes he poenial welfare gains from eliminaing consumpion volailiy using non-expeced uiliy and finds ha depending on parameer choices, he gains range from one o weny percen of consumpion. However, he concludes ha for reasonable parameer choices he welfare cos of consumpion volailiy is always significanly below he welfare benefi of an addiional percenage poin of consumpion growh in perpeuiy. Campbell and Cochrane (1999) calculae he welfare cos by incorporaing habi formaion ino he formulaion of consumer preferences. They find ha he cos of consumpion volailiy is significanly large. However, Lucas poins ou ha he resul largely hinges on he relaxaion of he size of an exra parameer ha does no exis in sandard uiliy funcions. In his paper we also calculae he welfare cos of business cycle flucuaions. Our angle is o incorporae a new behavioral heory abou consumers he prospec heory ino he formulaion of consumer preferences. The prospec heory was firs proposed by Kahneman and Tversky (1979). They conduced psychological ess o invesigae how he agens behave and make decisions when hey face differen kinds of gambles. Their experimen revealed wo imporan aspecs of invesors psychology. Firs, he invesmen decisions of he agens are 24

34 affeced by he gains and losses in heir wealh and no by he final sae of heir wealh. Second, when he agens experience an equal amoun of gain and loss in heir wealh, hey are hur significanly more by he loss han ge pleasure from he gain. This aiude of he agens is ermed as loss aversion. We believe hese behavioral rules may urn ou o be crucial in erms of measuring he cos of business cycles. For one hing, we concern abou business cycles mainly because of he possible losses eiher losses of consumpion during a recession, or losses of wealh during inflaion. For anoher, mos would no deny ha hese losses concern us more han he gains during good imes. The prospec heory has been quie popular in economics and behavioral finance. In paricular, i has been used o offer a soluion for he equiy premium puzzle in financial marke sudies. The equiy premium puzzle refers o he abnormally high difference in he reurns beween a risky asse such as equiy and a risk-free asse ha canno be explained by heories. Benarzi and Thaler (1995) argue ha if an invesor is loss averse and has he endency o monior changes in he value of his porfolio frequenly, a high equiy premium is required o compensae him for he volailiies in sock reurns. Barberis, Huang, and Sanos (2001) offer an explanaion of he equiy premium puzzle using he prospec heory preferences in a general equilibrium framework. They show ha if he loss aversion aiude of an invesor is combined wih he endency o become more risk-seeking afer gains have occurred and more risk-averse afer a sequence of losses, highly volaile sock reurns and high equiy premium migh be generaed in equilibrium. The abiliy of he prospec heory o explain he invesor s behavior and psychology under uncerainy inspires us o incorporae his heory in our sudy. We proceed as follows. To be consisen wih he prospec heory, we assume ha he agen derives direc uiliy from he reurns on his financial invesmens as well as from consumpion. The reurns flucuae during he course of business cycles, resuling in gains from invesmen in some periods and losses in he ohers. The agen prefers o have smooh reurns and is willing o pay a fracion of he reurns she receives o eliminae all he volailiies in he reurns on her invesmens. In his way she can enjoy he uiliy from he smooh reurns and does no have o worry abou any loss in her asse. We follow Lucas mehod o calculae he percenage of he reurns he agen would pay o have all he flucuaions in he reurns on her invesmens eliminaed. We find ha for reasonable values of our parameers, he agen would give up % of he average reurns on her 25

35 invesmens o swich from he world wih reurn flucuaions o he world of zero flucuaions. We believe ha his indicaes a welfare cos ha is much larger han Lucas s esimaes. Our sudy herefore relies heavily on he premises of he prospec heory ha losses in financial reurns are criical o consumers, and such losses occur during he course of business cycles and can be used o measure he cos of hese cycles. A naural quesion, hen, is how closely flucuaions in invesmen reurns are relaed o business cycle flucuaions. Researchers have documened subsanial linkages beween an economy s performance and he performance of financial markes, including he procyclical movemens of sock prices. In fac, he posiive correlaion of sock price index and real economic aciviy over he course of many business cycles is one of he major empirical facs abou he US economy. If he macroeconomic growh rises, demand for a ypical company s produc rises and he revenue of he company should also increase. This leads o an appreciaion of he company s share price. Likewise, during a marcoeconomic downfall he demand for a company s produc declines and his evenually resuls in a share price decline. Figure 11: Real GDP and S & P 500 Composie Index Noe: The - - line represens derended real GDP and he line represens derended S & P 500 sock index reurns. 26