Politicians, Taxes and Debt

Transcription

1 Review of Economic Studie 00) 77, /0/0040$0.00 doi: 0./j X x Politician, Taxe and Debt PIERRE YARED Columbia Univerity Firt verion received January 008; final verion accepted April 009 Ed.) The tandard analyi of the efficient management of income taxe and debt aume a benevolent government and ignore potential ditortion ariing from rent-eeking politician. Thi paper depart from thi framework by auming that a rent-eeking politician chooe policie. If the politician chooe extractive policie, citizen throw him out of power. We analye the efficient utainable equilibrium. Unlike in the tandard economy, temporary economic hock generate volatile and peritent change in taxe along the equilibrium path. Thi erve to optimally limit rent-eeking by the politician and to optimally generate upport for the politician from the citizen. Taxe reembling thoe of the benevolent government are very cotly ince the government over-ave and reource are wated on rent. Political ditortion thu caue the complete debt market to behave a if it were incomplete. However, in contrat to an incomplete market economy, in the long run, taxe do not converge to zero, and under ome condition, they reemble taxe under a benevolent government.. INTRODUCTION Economit hould ceae proffering policy advice a if they were employed by a benevolent depot, and they hould look to the tructure within which political deciion are made. Buchanan, 987, p. 43) Economit have hitorically baed their fical policy recommendation on reearch that aume government pend wiely and efficiently to benefit ociety. In practice, however, government run inefficiently, policymaker are partly motivated by re-election propect and peronal ambition, and citizen cannot perfectly regulate policymaker. Thi paper characterize optimal tax and debt management in the preence of rent-eeking politician. What reult i an analyi that decribe the bet economic policie citizen can realitically expect from their government. We tudy the economic environment of Luca and Stokey 983), and intead of auming the exitence of a benevolent government, we introduce an electoral accountability model a originally developed in Barro 973) and Ferejohn 986). We characterize the tochatic time path of taxe and debt, and we highlight why conventional policy precription which do not account for the elf-interet of politician can induce exceive rent-eeking and be ocially cotly. We conider a cloed economy with no capital, with hock to the productivity of public pending, and with complete market. The economy i managed by a rent-eeking politician. For a dicuion of the elf-intereted behaviour of politician and the implication for corruption and public good proviion, ee Acemoglu 003), Acemoglu, Johnon and Robinon 004), Acemoglu and Verdier 000), Banerjee 997), Buchanan and Tullock 96), North 98), Peron and Tabellini 000) and Shleifer and Vihny 993).. Thi i the ame motivation a that of Acemoglu, Goloov and Tyvinki 008a,b). 806

2 YARED POLITICIANS, TAXES AND DEBT 807 whoe utility increae in rent, which we define a exceive public pending with no ocial value. While citizen dicipline the politician by threatening to remove him from office for mibehaviour, the policie of the benevolent government cannot be implemented becaue of limited commitment: a politician cannot commit to policie once in office and citizen cannot commit to keeping the incumbent in power in the future. In order to focu our attention on pure rent-eeking ditortion, we impoe no limit on financial intrument, we abtract from default, we aume perfect information, and we fix the tochatic) interet rate by auming quai-linear preference. 3 We conider an infinitely repeated game between citizen and politician with double-ided lack of commitment in which reputation utain equilibrium policie. We examine efficient utainable equilibria. In uch an equilibrium, a politician who purue extractive policie i thrown out of power, and a politician who purue the policie expected by citizen i rewarded with future power. Thu, the incumbent politician follow equilibrium policie a long a rent are ufficiently high, ince thi raie the value of cooperation, and a long a government debt i ufficiently high, ince thi limit what he can acquire through maximally extractive policie prior to removal from office. Moreover, citizen agree to reward a well-behaving incumbent by not replacing him a long a equilibrium taxe are ufficiently low and public pending i ufficiently high. Efficient utainable policie thu olve the tandard programme of the benevolent government ubject to an incentive compatibility contraint for the politician and an incentive compatibility contraint for a repreentative citizen at every hitory. In our environment, the optimal taxe under a benevolent government are contant, o that they exhibit no volatility and no peritence. Raiing revenue ditort labour allocation, and it i optimal for the benevolent government to mooth thee ditortion over time by raiing a contant revenue and accommodating public expenditure need by trading contingent claim with the private ector. For example, if the government expect a temporary tochatic war at a future date, it purchae war inurance from the private ector with revenue which it raie in all period. Therefore, the revenue raied under peace before, during if the war doe not occur), and after the tochatic war i ued to finance the tochatic war. Our firt reult i that efficient taxe in the preence of political economy contraint are not contant but volatile. Thi i becaue a contant revenue policy uch a the one decribed for the benevolent government i aociated with too much rent-eeking by politician. Conider the example of a temporary tochatic war. Imagine that taxe were contant and the government received inurance payment from the private ector in the event of war. Every ingle unit of inurance that the politician can appropriate during the war mut be matched by one unit of equilibrium rent during or after the war, ince the politician could otherwie purue extractive policie i.e. tax heavily and appropriate the inurance payment) and be thrown out. In other word, the inurance payment finance equilibrium rent a oppoed to the war. Matching every unit of inurance with one unit of rent i inefficient ince citizen can be made trictly better off if the government cut taxe under peace, and therefore cut both inurance payment and rent during the war. Thu, taxe are not contant, and they tochatically increae in the event of war. 3. A i well known, departure from the Luca and Stokey 983) equilibrium occur even under a benevolent government if contingent debt i unavailable a in Barro 979), if default i poible, if there i imperfect information about public pending hock, or if the government cannot commit to the interet rate. Example of paper that explore thee friction include though by no mean are limited to Aguiar, Amador and Gopinath 009), Angeleto 00), Aiyagari et al. 00), Bohn 988), Buera and Nicolini 004), Chari, Chritiano and Kehoe 994), Chari and Kehoe 993a,b), Kydland and Precott 977), Kruell, Martin and Rio-Rull 005), Shin 007), Sleet 004) and Sleet and Yeltekin 006).

3 808 REVIEW OF ECONOMIC STUDIES Our econd reult i that efficient taxe in the preence of political economy contraint repond peritently to hock. Conider again the example of a temporary tochatic war. Imagine that taxe returned to their initial level following the war. Houehold could be made better off if taxe did not rie by a much during the war, and if intead the government iued debt during the war which it repay with a peritent increae in taxe following the war. Thi erve two purpoe. Firt, it mooth revenue raiing ditortion into future period after the war end. Second, the increae in debt make it eaier for citizen to provide incentive for the politician into the future ince it leave him with le to potentially appropriate. Thu, even though future taxe are unchanged by the pat realization of war under a benevolent government, they are peritently higher after the war in the preence of rent-eeking politician. Note that, neverthele, there may be a limit to the extent to which the rie in taxe during the war can be made entirely peritent. More pecifically, though citizen will upport an incumbent who raie taxe during the war, they are le likely to upport high taxe afterward under peace ince they benefit le from public good and potentially gain by replacing the incumbent. Thu, taxe may revert downward though not to their original level) after the war in order to generate upport for the incumbent by the citizen. More generally, we how that efficient taxe accommodate the incentive of politician by peritently increaing into the future, and they accommodate the incentive of citizen by peritently decreaing into the future. Thu, the volatile and peritent time path of taxe in our economy i qualitatively imilar to that generated in the abence of contingent debt, o that the preence of political economy contraint introduce a form of endogenou market incompletene. Our lat reult i that even though the hort-run behaviour of taxe in our economy reemble that under exogenouly incomplete market, the long-run behaviour of taxe i very different. Specifically, Aiyagari et al. 00) how that in an economy without tate-contingent debt, the benevolent government accumulate aet along the equilibrium path, until it can finance the entire tream of public pending with zero taxe. In our environment, there i no economic motive for the accumulation of aet ince tate contingent claim are available, and furthermore, the accumulation of aet i not politically utainable ince it ignore the incentive of politician. 4 To illutrate the long-run behaviour of our economy, conider the bet utainable equilibrium for the citizen. Along the equilibrium path, the government goe into further debt and thepolitician extract morerent whenever he require incentive i.e. whenever hi incentive compatibility contraint bind). If citizen do not gain enough by replacing the incumbent i.e. their incentive compatibility contraint doe not bind), then they will tolerate the tax rate increae until taxe reach a maximum. In the long run, the tax rate i contant a under a benevolent government. In contrat, if citizen tand to gain by replacing the incumbent along the equilibrium path, then taxe cannot conitently increae toward a maximum and they will be volatile and potentially peritent even in the long run. Thi paper make three contribution. Firt, it characterize optimal policie in the preence of rent-eeking politician. Thee are alo tudied in Acemoglu, Goloov and Tyvinki 008a,b). The current paper i different from their work in two important repect. Firt, it focue on the dynamic of government debt, which i an eential element of macroeconomic fical policie and i ruled out in their model. Second, it introduce aggregate hock which are not preent in their work. The optimal fical policy repone to aggregate hock i tudied in the work decribed in footnote 3, and we depart from thi work by focuing on the role of pure 4. Our dicuion in Section 5.3 conider the implication of not allowing for tate-contingent claim within our framework and how that debt rie along the equilibrium path.

4 YARED POLITICIANS, TAXES AND DEBT 809 rent-eeking ditortion. Second, our paper complement the literature on the political economy of debt by highlighting how the incentive of politician affect optimal policy precription. Thi literature ha emphaized how certain critical force uch a political rik, polarization and demographic caue government to accumulate more debt than i ocially optimal. The current paper how that a imilar force toward debt accumulation arie in an electoral accountability framework, and moreover that the rie in debt i actually efficient ubject to political economy contraint. The cloet work to our i that of Battaglini and Coate 008) who tudy the dynamic of taxe and debt in a political economy model; but they focu on the Markov perfect equilibrium in an environment with incomplete market in which competing group tochatically take power. The ditinguihing feature of the current paper i the focu on efficient utainable policie in an environment with complete market and with electoral accountability. Thee difference enable u to obtain different prediction for the hort and long run. 5 Finally, thi paper etablihe a connection between our model of electoral accountability in general equilibrium under aggregate hock and related model of conumption rik-haring with double-ided lack of commitment ee Alvarez and Jermann, 00; Kocherlakota, 996). The method ued in thi related literature allow u to explicitly characterize the path of policie in our framework. 6 The paper i organized a follow. Section decribe a imple three-period example with a tochatic war to illutrate our main reult. Section 3 decribe the dynamic general equilibrium model. Section 4 define a utainable equilibrium. Section 5 characterize the efficient utainable equilibrium. Section 6 extend the model to incorporate default and exogenou political replacement. Section 7 conclude, and the Appendix contain all the proof and additional material.. A SIMPLE THREE-PERIOD MODEL We begin by decribing the intuition for our main reult in a very tylized three-period verion of our infinite horizon model. Thi allow u to eaily illutrate the contraint impoed by the incentive of politician and the contraint impoed by the incentive of citizen. We how that each one of thee contraint on it own generate volatility and peritence in optimal taxe... Environment Conider an economy with t = 0,,. At every date t, the government collect tax revenue r t [0,r max ], chooe ocially beneficial public pending g t 0, and ocially wateful rent x t 0. Houehold welfare i declining in revenue and increaing in public pending and i equal to E 0 β t u r t,g t,θ t ) = E 0 β t r t + θ t g t )) g t. ) t=0,, t=0,, β 0, ) i the ocial rate of dicounting and the invere gro interet rate. θ t 0 parameterize the exogenou ocial value of public pending. Let θ 0 = θ = 0, and let θ 5. For related work on the political economy of debt, ee Aghion and Bolton 990), Aleina and Perotti 994), Aleina and Tabellini 990), Lizzeri 999) and Peron and Svenon 989). Song, Storeletten and Zilibotti 009) alo conider a dynamic model of debt, though they abtract from economic hock and focu on the role of demographic conflict in a repreentative democracy. 6. See alo Dixit, Groman and Gul 000), Kehoe and Levine 993), Kletzer and Wright 000) and Thoma and Worrall 988).

5 80 REVIEW OF ECONOMIC STUDIES be tochatically revealed at date with Pr {θ = } = Pr {θ = 0} = 0.5. In normal time, there i no ocial value to public pending; however, with probability 0.5, the economy may experience a public pending hock uch a a war at date. Conditional on being in power, the rent-eeking politician receive flow utility x t from rent and no direct utility from ocial welfare. Therefore, the welfare of the rent-eeking politician conditional on remaining in power in all three period i β t x t. E 0 t=0,, The elf-intereted politician can be interpreted a an individual or a group of individual who chooe fical policy. Like the benevolent ruler, the elf-intereted politician ha the unique ability to improve houehold welfare by financing and providing public good, but unlike the benevolent ruler he derive no utility from thi endeavour. The government finance public pending, rent, and pat debt by raiing tax revenue and borrowing from the private ector. Since policie for t depend on the realization of the hock, let j = L, H parameterize the tate of the world with L correponding to θ = 0and H to θ =. The government dynamic budget contraint in period 0,, and, repectively, are: g 0 + x 0 + b 0 = r β b j, ) j=, g j + xj + bj = rj + βbj,and 3) g j + xj + bj = rj + βbj 3 4) for j = H,L. b j t 0 repreent tate-contingent government debt, which mean that the government can effectively purchae war inurance in order to mooth the ditortion from raiing revenue. We let b 0 = b j 3 = 0... Benevolent government benchmark Conider the optimal policie of the benevolent government that maximize ocial welfare ) ubject to ) 4). The benevolent government chooe xt b = 0 in every period ince it doe not care about the welfare of the politician. Since public pending i only ueful at date during the war, it will let g H,b > 0 and let public pending equal to zero otherwie. Moreover, the government equate the marginal deadweight lo of revenue generation in period to the marginal benefit of public pending in period o that r H,b = g H,b. Finally, the government ue tate-contingent debt to mooth the ditortion from raiing revenue by letting revenue be contant. Since the preent dicounted value of the government liabilitie i 0.5βg H,b, it chooe a contant revenue to finance the liabilitie, which equal r b = 0.5βg H,b / + β + β ). In order to achieve thi, the government let b H = rb + β) g H,b, b L = rb + β), andb H = bl = rb. The path of revenue i diplayed in Panel A of Figure. The dotted line repreent the path of revenue in the event of war and the olid line depict the path of revenue in the event of peace, and thee two line coincide in the cae of the benevolent government. There are three important feature of the optimal policy under the benevolent government. Firt, r H,b = r L,b, o that revenue exhibit no volatility in repone to the hock. Second, debt b j and revenue rj are independent of j, o that policie in period exhibit no hitory

6 YARED POLITICIANS, TAXES AND DEBT 8 Panel A: Benevolent Government r t 0 t Panel B: Role of Politician Incentive r t 0 t Panel C: Role of Politician and Citizen Incentive r t 0 Peace at t= War at t= Figure Path of revenue dependence ince they are not a function of the period hock. Finally, b H <bl, o that the government purchae war inurance in period 0. Therefore, the optimal government policy would not be poible in the abence of contingent debt if the government were contrained to etting b H = bl..3. Role of politician incentive Now let u conider the bet equilibrium from the perpective of citizen under a rent-eeking government, and let u begin by focuing on the incentive of politician. In every period t, the incumbent politician chooe policie and market open and clear. Though the politician i elf-intereted and cannot commit to policie, he know that citizen will remove him from office at the beginning of the following period if he mibehave. 7 A politician who i thrown out after period t receive period t rent and a punihment equal to χ p k=t βk t for χ p > 0 which parameterize the trength of political intitution. Therefore, the bet policie for the citizen have to atify the contraint that the politician doe not want to extract maximal rent and be thrown out. Note that to extract maximal rent, the politician would raie a much revenue a poible today, take out a much debt a poible today, deliver zero public good, and repay current debt or collect debt payment from the private ector). 8 We let b j rmax + β) and b j rmax o that the rent generated by taxing and borrowing maximally in a given period t are equal to r max k=t βk t b t. In order for a politician to not extract maximal rent and be thrown out, he mut receive a ufficiently 7. We are implicitly auming the exitence of a fourth period in which citizen would punih a mibehaving incumbent in the third period. 8. See Section 6. for an extenion to a etting with default.

7 8 REVIEW OF ECONOMIC STUDIES high level of rent in equilibrium. Thu, the three incentive compatibility contraint for the politician in period 0,, and, repectively, are: x 0 + j=l,h t=, t=, β t x j t r max χ p) + β + β ) b 0, 5) β t x j t r max χ p) + β) b j,and 6) x j r max χ p) b j 7) for j = L, H. Therefore, the politician i le likely to deviate from equilibrium policie if he i receiving a high level of equilibrium rent ince thi increae the value of cooperation or alternatively if government debt i high or government aet are low) ince thi reduce the value of deviation. Thee two form of incentive proviion are intimately linked. Specifically, ubtitution of equation ) 4) into equation 5) 7) yield r 0 g 0 r max χ p) + j=l,h t=, β t r j t g j t r max χ p)) 0, 8) β t r j t g j t r max χ p)) 0, and 9) t=, r j gj r max χ p) 0 0) for j = L, H. Therefore, the incentive compatibility contraint on the politician come in the form of lower bound on the ize of taxe and upper bound on the ize of public pending. Thi i becaue there i a limit on the ize of reource owed to the government in any given period, ince if thee reource are large, the politician will have a high incentive to deviate and appropriate them a rent. Since reource cannot be too high, the government ha to finance more of it obligation with current and future taxe, a oppoed to pat taxe. The bet policie from the perpective of citizen maximize equation ) ubject to equation ) 4) and 8) 0) ince politician mut agree to follow equilibrium policie. Note that if χ p i very high i.e. political intitution are very trong), then equation 8) 0) never bind and the bet policy correpond to that of a benevolent government. Now imagine χ p i ufficiently low o that the exact policy of the benevolent government doe not atify incentive contraint 8) 0). Specifically, let 0 <r max χ p <. Are policy precription of revenue moothing like thoe of a benevolent government till optimal for citizen? Imagine that thi were the cae. For a given level of public pending g H,p,thelowet level of revenue that atifie equation ) 4) and 8) 0) would be optimal ince citizen dilike taxe. Since public pending i only poitive in period under j = H ince it i otherwie uele), incentive contraint 9) under j = H would be the mot binding contraint under a contant revenue, which mean that the lowet contant incentive compatible level of revenue would equal r p = gh,p +β + rmax χ p, making equation 9) an equality. In thi circumtance, reource are being diverted toward rent at ome date, and from equation ) 4), the period 0 value of thee rent i r p + β + β ) βgh,p > 0. A contant revenue policy uch a the one decribed i ub-optimal from the perpective of citizen ince it i aociated with too much rent-eeking. To ee why uch a policy i uboptimal, note that contraint 8) i lack under a contant revenue policy. Since revenue in period 0 are ued in part to finance rent at ome date, it i poible for the government

8 YARED POLITICIANS, TAXES AND DEBT 83 to both reduce revenue in period 0 a well a rent-eeking at ome date and improve the welfare of houehold, and thi i acceptable to politician a long a equation 8) i atified. Analogou reaoning applie to contraint 9) and 0) under j = L, which are both lack under a contant revenue policy. In other word, the government i taxing too much during peace and the revenue are financing rent which are not neceary to enure good behaviour by politician. Citizen are better off if the government cut taxe and rent. Following thi logic, the bet policie for citizen can be achieved by reducing revenue until incentive contraint bind under peace, o that r p 0 = rl,p = r L,p = r max χ p. Once the war take place, then revenue permanently increae with r H,p = r H,p = gh,p +β + rmax χ p >r p 0, o that equation 9) bind. The path of revenue under war and under peace i diplayed in Panel B of Figure. Note that the three important feature of the economy under a benevolent government are overturned. Firt, r H,p >r L,p, o that revenue ceae to be contant and exhibit volatility. If they were contant, there would be too much rent-eeking. Second, r H,p >r L,p,othat policie in period ceae to be hitory independent. Thi occur becaue r H,p >r L,p and it i optimal to mooth revenue ditortion going forward. Thi i alo tied to the fact that x H,p + b H,p >x L,p + b L,p, o that debt plu rent in period are alo higher in the event of a war ince thi not only relaxe incentive contraint at date, but it alo relaxe incentive contraint at date. Finally, an efficient equilibrium doe not require the exitence of inurance market. From date onward, the government i effectively paying for the public pending hock of ize g H,p with reource which it raie after the hock occur of ize r H,p + βr H,p >g H,p. For example, imagine that the government were contrained to uing only non-contingent debt o that b H = bl. Then the government could eaily et b H = bl = rmax χ) + β), xt H = xt L = 0fort =,, and x 0 = r max χ) + β + β ) under the bet policy. In thi ene, the incentive of politician generate an endogenou form of market incompletene ince inurance market are no longer needed depite their availability..4. Role of citizen incentive In practice, citizen may have an incentive to replace an incumbent politician even under good behaviour o that they cannot commit to a plan to keep an incumbent in power. In uch a circumtance, the incumbent would have to provide a ufficiently low level of taxation or a ufficiently high level of the public good to guarantee being able to remain in power. For implicity, imagine that replacing an incumbent at the beginning of period t provide a benefit χ c k=t βk t to citizen, where χ c parameterize the lack of popularity of the incumbent. For citizen to upport a well-behaving incumbent, the following incentive compatibility contraint need to be atified in period 0,, and, repectively: u r 0,g 0,θ 0 ) χ c + j=l,h t=, β t u t=, ) β t u r j t,g j t,θ j t χ c) 0, ) ) r j t,g j t,θ j t χ c) 0, and ) ) u r j,gj,θj χ c 0 3) for j = L, H. Since citizen dilike taxe and like public pending, equation ) 3) impoe upper bound on revenue and lower bound on public pending.

9 84 REVIEW OF ECONOMIC STUDIES Note that the incentive contraint on citizen in equation ) 3) function in an analogou fahion to the incentive contraint on politician in equation 8) 0). For example, imagine that intead of the current et-up, we let θ 0 = θ = andθ be determined a before, o that there i a tochatic peace in period and war otherwie. In uch an environment, the benevolent government would alo chooe contant revenue for the reaon dicued in Section.. In the preence of equation ) 3), however, the incentive of citizen would begin to matter for ufficiently high χ c, and in particular, equation ) would bind during the period of peace ince it i more difficult for the government to generate upport when it i providing zero public good. Analogou argument a thoe of Section.3 would imply that under equation ) 3), revenue ceae to be contant ince they decline in a peritent fahion conditional on the realization of peace at date. 9 Therefore, contraint on citizen ) 3) alone can generate volatility and peritence in taxe. Now conider how the incentive of citizen and thoe of politician interact in the original et-up with a tochatic war and peace in normal time. Satifying the incentive of politician require ufficiently high revenue and ufficiently low level of public pending. In contrat, atifying the incentive of citizen require ufficiently low revenue and ufficiently high level of public pending. The bet policy taking both et of incentive into account maximize equation ) ubject to equation ) 4), 8) 0), and) 3). Ifχ p and χ c are low, then politician incentive need to be taken into account, and citizen incentive can be ignored. Thu, the decription of the equilibrium in Section.3 hold. Neverthele, an increae in χ c implie that both et of incentive need to be taken into account and equation ) 3) are not atified under the policy decribed in Section.3. More pecifically, equation 3) under j = H i the mot binding contraint out of equation ) 3) ince taxe are very high and the government i not providing public good. Therefore, equation 3) bind under j = H and r H,p = χ c o a to atify the incentive of the citizen once the war end. Moreover, equation 9) alo bind under j = H o a to atify the incentive of the politician once the war begin, which implie that r H,p = g H,p + r max χ p ) + β) β χ c >r H,p. 0 Finally, for analogou reaon a in Section.3, r p 0 = rl,p = r L,p = r max χ p. The path of revenue under war and under peace i diplayed in Panel C of Figure. In um, revenue increae during the war in order to atify the incentive compatibility contraint of the politician that limit the reource with which the government can enter period. The permanence of thi increae i limited, however, by the incentive of citizen who are unwilling to tolerate high taxe once the war end. Conequently, while the incentive of politician limit the extent to which the government can finance the war with pat revenue which put upward preure on future revenue), the incentive of citizen limit the extent to which the government can finance the war with future revenue which put downward preure on future revenue). Each contraint on it own generate volatility and peritence in revenue. 3. DYNAMIC GENERAL EQUILIBRIUM MODEL In thi ection, we develop a dynamic general equilibrium model in the pirit of the model of Section. While the inight of the impler model will be preerved, the more ophiticated model allow u to micro-found the economic environment and the trategic interaction between citizen and politician. More importantly, the preence of dynamic allow u to analye the 9. In other word, the path of revenue in Panel B of Figure would be inverted. 0. We are implicitly auming that χ c < / o that the olution admit an interior level of public pending.

10 YARED POLITICIANS, TAXES AND DEBT 85 long-run propertie of the equilibrium and to better undertand the relationhip between our endogenouly incomplete market economy and an exogenouly incomplete market economy. 3.. Economic environment The economic environment i identical to that of Luca and Stokey 983) under quai-linear preference and with a ingle modification: the government can finance rent that are beneficial to politician Time and uncertainty. There are dicrete time period t = {0,..., } and a tochatic tate t S {,...,N} which follow a firt-order Markov proce with full upport for N. 0 i given. Let t = { 0,..., t } S t repreent a hitory, and let π k t) repreent the probability of k conditional on t for k t Houehold. There i a continuum of ma of identical houehold that, with ome abue of notation, derive the following utility from economic activity: ) E 0 β t u c t,n t,g t, t ), β 0, ). 4) t=0 c t i conumption, n t i labour, and g t i government pending. Our model conider a pecial cae of thi preference: u c t,n t,g t, t ) = c t ηn γ t /γ + θ t ) gt α /α, for0<α< <γ and θ t ) > 0. θ t ) i high low) when public pending i more le) productive. Thi utility function allow u to abtract away from bond price manipulation by the government which can potentially caue additional ditortion even under a benevolent government and to explicitly characterize equilibrium dynamic Politician. There i a large number of potential and identical elf-intereted politician who derive the following utility from economic activity: ) E 0 β t v x t ) 5) t=0 for x t which repreent rent. v x t ) i increaing and weakly concave, and for implicity, let v x t ) = x t. A politician who i out of power receive zero rent Market. Houehold wage are normalized to and are taxed at a linear rate τ t. b h t t+ ) 0 repreent debt owned by the houehold at t, which i a promie to repay unit of conumption at t + conditional on the realization of t+,andq t t+ ) i it price at t. We ignore bond of longer maturity tructure only for notational implicity. At every t, the. An extenion in previou verion of thi paper confirm our reult in the preence of rik averion. Detail available upon requet.. The trict concavity of v ) affect only the timing of rent but not the timing of taxe or public pending in the olution to the problem.

11 86 REVIEW OF ECONOMIC STUDIES houehold allocation ω t = budget contraint { c t,n t, { bt h t+ ) } } mut atify the houehold dynamic t+ S c t + b h t t) = τ t ) n t + t+ S q t t+ ) b h t t+ ), 6) ubject to n t 0. b g t t+ ) 0 repreent debt owned by the government at t, defined analogouly to the houehold debt. At every t, government policie ρ t = {τ t, { b g t t+ ) } } t+ S,g t,x t mut atify the government dynamic budget contraint g t +x t + b g t t) = τ t n t + q t t+ ) b g t t+ ), 7) t+ S ubject to g t 0andx t 0. The only difference between thee budget contraint and thoe of the tandard economy i that the rent x t i included on the left-hand ide of equation 7). We dicu the implication of allowing for default in Section The economy i cloed, and bond are in zero net upply: b g t t+ ) + b h t t+ ) = 0, 8) which combined with equation 6) and 7) implie the aggregate reource contraint c t + g t + x t = n t. 9) For notational implicity, we let b g t t+ ) = b t t+ ) for the remainder of the dicuion. Initial debt b 0 ) i exogenou. The following debt limit rule out Ponzi cheme b t t+ ) [ b, b ]. 0) Let b to be ufficiently low and b to be ufficiently high o that 0) doe not bind. More pecifically, b i the natural debt limit o that b = r max / β) for r max which repreent the maximal tax revenue that can ever be collected by the government ee Section 4.3). 3.. Political environment A in the electoral accountability model of Barro 973) and Ferejohn 986), citizen control politician by potentially removing them from office. Let P t+ = {0, } repreent the deciion by citizen to remove the incumbent in period t with P t+ = 0 repreenting replacement. The interaction between citizen and politician i a game:. Nature chooe the tate t.. Citizen make the replacement deciion P t+. 3. The incumbent politician chooe policie ρ t. 4. Market open and clear. 5. If P t+ = 0, the incumbent politician i replaced. 3. A i well known, allowing for default create ditortion even under a benevolent ruler ee Kydland and Precott, 977).

12 YARED POLITICIANS, TAXES AND DEBT 87 The important feature of thi game i that even though citizen make their economic deciion independently, they make their political deciion regarding the replacement of the politician jointly. Since citizen are identical, there i no conflict of interet between them. Thee joint political deciion can be achieved by a variety of formal or informal procedure uch a election or protet. We implify the dicuion by auming that the deciion i taken by the ame ingle repreentative citizen in every period. 4 Politician and citizen derive payoff aociated with P t+.ifp t+ = 0, the incumbent endure an exogenou cot χ p β) /β > 0 from t onward. χ p capture intitutional contraint on politician, which vary acro ocietie and are empirically important determinant of economic activity around the world. 5 In addition, if P t+ = 0, citizen receive an exogenou benefit χ c β) 0att. χ c parameterize the ocial benefit of political turnover, which i related to the fact that, even though all candidate politician are identical, citizen may derive non-pecuniary benefit from replacement. Throughout the text, we will often conider the pecial cae in which χ c equal zero. Our timing of event implie that an incumbent can chooe policie prior to removal from power. If intead P t+ i choen after the choice of policie ρ t, none of our reult change with the exception that incentive for politician and citizen are no longer provided contemporaneouly after the realization of t, and thi affect the exact characterization of policie. We prefer thi timing ince it facilitate the expoition of our reult. 6 Conider the incentive of politician and citizen implied by thi game. If citizen keep the incumbent in power, they cannot control hi policie. If the incumbent limit rent and provide public good, he cannot control citizen future replacement deciion. In the following ection, we invetigate how reputational conideration can alleviate the double-ided commitment problem faced by citizen and politician. 4. SUSTAINABLE EQUILIBRIA A in Chari and Kehoe 993a,b) we conider a utainable equilibrium. Individual houehold are anonymou and non-trategic in their private market behaviour, though the repreentative citizen i trategic in hi replacement deciion. The politician in power i trategic in hi choice of policie, and he mut enure that the government dynamic budget contraint i atified given the anonymou market behaviour of houehold. Uing thi definition, we characterize the entire et of utainable equilibria uing the primal approach. Thi allow u to elect the efficient utainable equilibrium in Section Definition Define h 0 t = { t,p t,ρ t } a the hitory of hock, replacement deciion, and policie after the realization of t. 7 Define h t = { t,p t+,ρ t } and h t = { t,p t+,ρ t}. A repreentative citizen replacement trategy ϒ aign a replacement deciion for every h 0 t. The incumbent politician trategy σ aign policie for every h t. A repreentative houehold allocation 4. Thi i identical to the deciion being made via majoritarian election with incere voting. 5. An alternative interpretation i that χ p i negatively related to the non-pecuniary value of holding political power or poitively related to an exogenou limit on the debt that can be iued by a politician deviating from equilibrium policie. 6. See footnote 6 for an explanation of how the alternative timing affect our reult. 7. Without lo of generality, we let incumbent politician follow identical trategie conditional on holding power o that their identity need not enter the public hitory.

13 88 REVIEW OF ECONOMIC STUDIES equence f aign an allocation at every h t. A tate price equence ζ aign a vector of tate price at every h t.letϒ h 0 repreent the continuation trategy of the repreentative citizen at t h 0 t and define σ h, f t h,andζ t h analogouly. t The repreentative citizen replacement trategy ϒ olve the repreentative citizen problem if at every h 0 t, the continuation trategy ϒ h maximize houehold welfare given t {σ,f,ζ}. The incumbent politician trategy σ olve the incumbent politician problem if at every h t, the continuation trategy σ h maximize the incumbent politician welfare t given {ϒ,f,ζ} and given the government equential budget contraint. A repreentative houehold allocation equence f olve the repreentative houehold problem if at every h t, the continuation allocation f h maximize houehold welfare given {ϒ,σ,ζ} and given the t houehold equential budget contraint. Note that becaue houehold are anonymou, public deciion are not conditioned on their allocation. Finally, a tate price equence ζ clear the bond market if at every h t, the continuation equence ζ h implie a zero net upply of bond given t {ϒ,σ,f}. Note that thee condition mut hold for all hitorie including thoe that occur with probability zero. Additional formalim of our equilibrium concept i included in the Appendix. Definition. A utainable equilibrium i a 4-tuple {ϒ,σ,f,ζ} for which ϒ olve the repreentative citizen problem, σ olve the incumbent politician problem, f olve the houehold problem, and ζ clear the bond market. 4.. Competitive equilibria The equilibrium path of a given utainable equilibrium i characterized by: ξ = { c t),n t),g t),x t)} t=0 which i feaible if n t), g t), and x t) are non-negative t. In thi ection, we review the neceary and ufficient condition etablihed by Luca and Stokey 983) for a competitive equilibrium equence, and in the next ection we conider the additional condition required for utainability. In a competitive equilibrium, the houehold equilibrium allocation ω = { ω t)} t=0 maximize it utility a a function of the equilibrium tax rate τ = { τ t)} t=0 and tate price q = { q t+ t)} t=0,forq t+ t) which repreent the price of a bond traded at t with payment conditional on t+. The olution to the houehold problem lead to the following reult. All proof are in the Appendix. Propoition Competitive Equilibrium). ξ i a competitive equilibrium if and only if it i feaible and it atifie c t) + g t) + x t) = n t) t, and ) β t π t 0) r n t)) g t) x t)) = b 0 ), ) t=0 t S t for r n) = n ηn γ. Equation ) i the reource contraint of the economy. r n) i the revenue generated by labour n derived from the houehold intratemporal condition. It i independent of conumption becaue of rik neutrality in conumption. Equation ) i the preent value budget contraint

14 YARED POLITICIANS, TAXES AND DEBT 89 of the government. It tate that total public pending, rent, and initial government debt are erviced by total revenue. Preent value are calculated uing probabilitie becaue of rik neutrality in conumption. Together with equation ), equation ) implie the atifaction of the houehold preent value budget contraint. Becaue of the completene of financial market, the atifaction of equation ) and ) i ufficient to imply the atifaction of the government preent value budget contraint in the future: β k t π k t) r n k)) g k) x k)) = b t t ) t, 3) k=t k S k for b t t ) repreenting a bond traded at t with payment conditional on t Sutainable equilibria A competitive equence ξ and replacement rule P = { P t)} t=0 need not be utainable.8 For intance, in any given period, the incumbent politician can maximize hi rent by chooing the revenue-maximizing tax rate τ max aociated with revenue r max and labour allocation n max. 9 Furthermore, he can et public pending to zero, repay the current debt b t t ), and borrow the maximal amount of debt b = r max / β). Since the government i maximally indebted in the future, public pending and rent are zero forever. From equation 3), if the politician i thrown out of power in the next period, hi continuation welfare i today i V b t t )) = r max / β) b t t ) χ p. Analogouly, in any given period, the repreentative citizen can throw out the incumbent politician, and the exiting politician will maximize hi current rent uing the policie decribed above. Since public pending and rent are zero and taxe are maximal forever independently of replacement deciion, the repreentative citizen will throw out all future politician and receive χ c forever. From equation ) and 3), the repreentative citizen continuation welfare today i U b t t )) = U AUT + b t t ) + χ c for U AUT = n max ηn maxγ /γ r max) / β). Thee fact imply a lower bound on equilibrium continuation value for the politician and the repreentative citizen. Specifically, let V {ξ,p} t ) and U {ξ,p} t ) be the equilibrium continuation welfare to the incumbent politician and citizen, repectively, implied by {ξ,p} at a hitory t. Lemma Wort Punihment). If {ξ,p} i a utainable equilibrium, then V{ξ,P} t ) V b t t )) t and U {ξ,p} t ) U b t t )) t. Lemma implie that there cannot be a utainable equilibrium in which the incumbent politician receive a lower welfare than what he would receive from maximally extractive policie and replacement and in which the repreentative citizen expect a lower welfare than what he could receive from throwing out the current and all future government. 8. P t ) refer to the choice of P t+ at hitory t. 9. Formally, n max = arg max n r n), r max = r n max ),andτ max = ηn maxγ.

15 80 REVIEW OF ECONOMIC STUDIES Thee obervation allow u to provide neceary and ufficient condition for a utainable equilibrium uing the method developed by Abreu 988). Propoition Sutainable Equilibrium). {ξ,p} i a utainable equilibrium if and only if ξ i competitive and {ξ,p} atifie V {ξ,p} t ) V b t t )) t, and 4) U {ξ,p} t ) U b t t )) t 5) for b t t ) determined by equation 3). Propoition implie that the lower bound on continuation utilitie etablihed in Lemma are not only neceary for a utainable equilibrium, but when combined with equation ) and ), they are ufficient. More pecifically, equation 4) and 5) emerge from the following punihment trategy. Whenever the incumbent politician or the repreentative citizen deviate from precribed policie and replacement rule, the politician and the repreentative citizen revert to an equilibrium in which the incumbent i thrown out, taxe are maximal, public pending i zero, and debt i maximal forever. Condition 4) and 5) guarantee that every deviation by the politician or repreentative citizen i weakly dominated. 0 Note that equation 4) and 5) illutrate the endogenou debt limit generated by the preence of politician. Government debt cannot be too low ince thi tighten the incentive compatibility contraint of the incumbent politician by providing him with more reource to potentially appropriate. Government debt cannot be too high, ince thi tighten the incentive compatibility contraint of the repreentative citizen by reducing the cot of throwing out the incumbent politician. Let repreent the et of utainable equilibrium equence {ξ,p}. 5. EFFICIENT SUSTAINABLE EQUILIBRIA Having characterized the entire et of utainable equilibria, we elect the efficient one o a to compare our economy to that under a benevolent ruler. To do thi, we reduce the problem into one involving a ingle endogenou tate variable that allow for a imple recurive repreentation of the problem Section 5.). We characterize the olution to thi program, and we conider hort-run dynamic Section 5.3) and long run dynamic Section 5.4). We relate our reult to ome of the previou literature Section 5.5). Finally, we conider a numerical example Section 5.6). 5.. Definition Definition. {ξ,p} i an efficient equilibrium if { ξ,p }.t. U { ξ,p } 0) > ) U {ξ,p} 0) and V { ξ,p } 0) >) V {ξ,p} 0). Our definition ignore the welfare of candidate politician and conider only the welfare of the incumbent politician in period 0. An efficient equilibrium olve max U ) ) {ξ,p} 0.t. V {ξ,p} 0 V0 and {ξ,p}. 6) ξ,p 0. Note that while we focu on the wort punihment, our analyi hold under any punihment for which V b t t )) equal a contant minu b t t ) and U b t t )) equal a contant plu b t t ).

16 YARED POLITICIANS, TAXES AND DEBT 8 In comparion, the original problem of Luca and Stokey 983) et x t) = 0 t and ignore contraint 4) and 5). For thi reaon, we will often conider the pecial cae of V 0 = 0. Aumption. The olution to equation 6) require P t) = t. In the Appendix, we provide a condition under which Aumption i atified. A an example, Aumption i alway atified if χ c equal 0, ince there i little benefit to the repreentative citizen from throwing out a politician and ince it i optimal to keep the ame politician in power forever o a to minimize the amount of rent required to induce hi cooperation. If Aumption were not atified, then an incumbent politician facing replacement would chooe the extractive policie decribed in Section 4.3. Thu, we are effectively ignoring equilibria in which uch policie are choen. In practice, politician might be replaced for exogenou reaon uch a term limit, and we explore thi poibility in Section Recurive program We now how that equation 6) ha a recurive repreentation. Let z t t ) = b t t ) + β k t π k t) x k). 7) k=t k S k We refer to z t t ) a debt net of rent. A benevolent ruler et z t t ) = b t t ). Let n = { n t)} and define c, g, and x analogouly. t=0 Lemma. {n, g} olve 6).t. b 0 ) = b and V {ξ,p} 0) = V if and only if {n, g} olve 6).t. b 0 ) = b + V and V {ξ,p} 0) = 0. Lemma tate that the equence of taxe and public pending which are efficient ubject to initial debt b and promied utility V to the politician alo are efficient, ubject to initial debt b + V and promied utility 0 to the politician. Thi reult i ueful ince it implie that we can write the recurive program a a function of a ingle tate variable correponding to the value of debt plu the continuation value to the politician. To undertand Lemma more formally, ue equation ) and 7) to rewrite equation 3), 4), and5), repectively: β k t π k t) r n k)) g k)) = z t t ) t, 8) k=t k S k z t t ) rmax β χ p t, and 9) β k t π k t) u n k) g k),n k),g k) ), k z t t ) k=t k S k U AUT + χ c t. 30). Equilibria that alo conider the welfare of candidate politician might feature replacement.

17 8 REVIEW OF ECONOMIC STUDIES Rewrite the period 0 welfare of houehold a β t π t 0) u n t) g t),n t),g t) ), t z 0 ) + b 0 ). 3) t=0 t S t Lemma i a conequence of the fact that the optimal {n, g} that maximize equation 3).t. equation 8) 30) only depend on z 0 ). Note that given thi unique optimal equence {n, g}, any equence {c, x} that atifie the reource contraint and equation 7) in period 0 i optimal. The reaon for thi flexibility i that the politician i inveted in the aet ued to pay for hi rent, and houehold are inveted in the aet ued to pay for their conumption. Conequently, it i poible to relax equation 4) by increaing rent i.e. the value of cooperation) while holding debt contant or by increaing debt i.e. the punihment from deviation) while holding rent contant. Becaue of rik neutrality, both of thee method are equivalent from a welfare perpective and have the ame implication for the incentive compatible equence of labour, public pending, and debt net of rent. Analogou argument hold with repect to the relaxation of equation 5). 3 Note that with repect to the three-period economy of Section, equation 9) i analogou to equation 8) 0) and equation 30) i analogou to equation ) 3). An implication of Lemma i that equation 6) can be written recurively. 4 Given equation 8) 3), and letting π k = Pr { t+ = k t = }, we can write: J,z) = max n g η nγ n,g,{z k } k S γ gα + θ ) α + β π k J k,z k ) 3) k S.t. z = r n) g + β π k z k 33) k S z k r max / β) χ p k S and 34) J k,z k ) z k U AUT + χ c k S. 35) J, z) repreent the highet poible welfare to houehold net of the tream of rent that can be achieved conditional on the tate and on the value of debt net of rent being equal to z. 5 Equation 3) repreent thi program written in a recurive fahion. n and g repreent labour and public pending today, repectively. z k repreent the value of debt net of rent conditional on the realization of the tate k following tate. Equation 33) enure that the value of debt net of rent i z. Equation 34) and 35) repreent recurive verion of equation 9) and 30), repectively. We can characterize J, z). Lemma 3. J,z) i defined over a compact interval [ ] z, z, i trictly concave, and i continuouly differentiable in z ) z, z.. z 0 ) i choen to minimize V ) {ξ,p} 0 ubject to feaibility and V {ξ,p} 0) max { V 0,V b 0 ))}. 3. Thi i in contrat with the work of Ray 00) and Acemoglu, Goloov and Tyvinki 008a,b) who how that payment mut be backloaded to provide incentive. Thi i not the cae here becaue of rik neutrality and the exitence of financial market. 4. Thi implification i a conequence of the quai-linearity of preference. In the preence of concave preference, the relevant program would have three tate variable:, b, andv. 5. The welfare of houehold in period 0 i J 0,z 0 )) z 0 ) + b 0 ).

18 YARED POLITICIANS, TAXES AND DEBT 83 Remark. The Luca and Stokey 983) olution i a olution to equation 3) 33). Thi problem add two ditortion to the original problem of Luca and Stokey 983). Firt, the generation of rent can crowd out houehold conumption and increae taxe by raiing z 0 ) above b 0 ). Second, the contraint on z function like endogenou debt limit. Specifically, if z i interpreted a debt, then equation 3) 35) are iomorphic to an economy under a benevolent ruler facing ad hoc debt limit. Let λ, βπ k φ k,andβπ k ψ k repreent the Lagrange multiplier for equation 33), 34), and 35), repectively. Firt-order condition and the envelope condition yield: n : ηn γ = + λ + γλ 36) g : θ ) g α = + λ 37) z k : J z k,z k ) = λ + φ k ψ k + ψ k 38) z : J z, z) = λ. 39) Equation 36) and 37) pin down output and conequently the tax rate) and public pending, repectively, a a function of λ. By equation 39), higher z i aociated with higher λ, higher taxe, and lower public pending. Equation 38) and 39) how that the lope of equation J ) only change if an incentive compatibility contraint bind. For example, under a benevolent ruler, the lope of equation J ) never change. Define g t) = g t) θ t ) / α), the value of public pending normalized by it productivity. Remark. The Luca and Stokey 983) olution i τ t) = τ t ) and g t) = g t ) t. A benevolent government moothe the deadweight lo from revenue generation by chooing contant taxe and it fixe the marginal product of public pending over time. We now conider how political ditortion alter thi prediction Equilibrium dynamic In the imple three-period economy of Section, the incentive compatibility contraint on politician and citizen created volatility and peritence in taxe. Thi i true here in the dynamic economy a well ince policy dynamic are characterized by S, rule Note that our timing of event deliver an exact S, rule for taxe. If intead citizen make the replacement deciion P t+ after market open and clear, then the wort punihment remain the ame, though τ t ) i replaced by τ t, t ) in equation 40) and g t ) i replaced by g t, t ) in equation 4).

19 84 REVIEW OF ECONOMIC STUDIES Propoition 3 Optimal Policy Dynamic). equation 6) have the following property: τ t) τ t ) = τ t ) τ t ) g t) g t ) = g t ) g t ) The unique equence τ and g which olve if τ t ) > τ t ) if τ t ) [ τ t ), τ t ) ] if τ t ) <τ t ) if g t ) > g t ) if g t ) [ ] g t ), g t ). if g t ) < g t ) 40) 4) Equation 40) and 4) are dynamic equation which characterize the time path of the tax rate and public pending. The propoition tate that perfect moothing take place i.e. τ t) = τ t ) and g t) = g t ) ) only if τ t ) and g t ) are within utainable interval which depend on t.otherwie,τ t) τ t ) and g t) g t ),andτ t) and g t) jump to the tate-dependent upper bound or lower bound of the utainable policy range. For example, if τ t ) <τ t ) and g t ) > g t ),thenτ t) jump to τ t ) and g t) jump to g t ). More pecifically, the tax rate cannot be below a tate-dependent lower bound τ t ),and normalized public pending cannot be above a tate-dependent upper bound g t ). Thi enure that the incentive compatibility contraint of the politician i atified at t. The government cannot enter a given tate with too many aet ince the politician would divert thee aet toward rent. Thi create upward preure on current and future taxe and downward preure on current and future public pending. In other word, public pending mut be financed with future, not pat taxe. Furthermore, the tax rate cannot be above a tate-dependent upper bound τ t ) and normalized public pending cannot be below a tate-dependent lower bound g t ). Thi enure that the incentive compatibility contraint of the repreentative citizen i atified at t.more pecifically, taxe cannot be too high and public pending cannot be too low going forward, ince otherwie citizen will want to replace the incumbent. In other word, public pending mut be financed with pat, not future, taxe. The tate-dependent bound for taxe and public pending are not a function of initial condition but of the exogenou parameter in the environment. For intance, a reduction in χ p make it more difficult to atify the incentive compatibility contraint of politician and put upward preure on the lower bound for taxe and downward preure on the upper bound on normalized public pending. Moreover, an increae in χ c make it more difficult to atify the incentive compatibility contraint of citizen and put downward preure on the upper bound for taxe and upward preure on the lower bound for normalized public pending. While the bound for taxe and normalized public pending are independent of initial condition, the level of τ 0) and g 0) are determined by the initial condition z 0 ), which depend on b 0 ) and V 0. Given 40) and 4), we can decribe the relationhip between our environment and that of a benevolent ruler. Note that if χ p i ufficiently high, the cot to politician of being thrown out of power i high o that the lower bound on taxe and the upper bound on public pending never bind. Furthermore, if χ c i ufficiently low, the benefit of replacing incumbent i low, o that the upper bound on taxe and the lower bound on public pending alo never bind.

20 YARED POLITICIANS, TAXES AND DEBT 85 Corollary. If χ p = and χ c = 0, then the unique equence τ and g that olve equation 6) have the following property: τ t) = τ t ) and g t) = g t ) t. Therefore, if V 0 = 0, o that z 0 ) = b 0 ), then the olution will exactly coincide with that under a benevolent ruler of Luca and Stokey 983). In contrat, if χ p i low, then the incentive compatibility contraint on the politician occaionally bind, and if χ c i high, then the incentive compatibility contraint on the repreentative citizen occaionally bind. By the ame reaoning a in the example of Section, it i inefficient in uch circumtance to maintain a fixed tax rate. More generally, the tax rate reflect the lat binding incentive compatibility contraint, ince hock to the productivity of public pending create variation in the tightne of incentive contraint, and taxe repond peritently to thee hock. Theorem Short-Run Volatility and Peritence). Ifχ p <χ p or χ c >χ c, V 0, 0.t. the olution to equation 6) admit τ t) τ k) for t = k. Thi theorem etablihe that there are initial condition under which the tax rate experience peritent change after an incentive compatibility contraint bind. For example, imagine that χ c = 0, V 0 = 0, and χ p <r max / β) b 0 ), o that the politician incentive compatibility contraint bind at date 0 and τ 0) = τ 0 ). If the initial tate 0 choen i uch that τ 0 ) <τ ) for ome 0, then the tax rate will increae in a peritent fahion whenever the tate occur. A in the example of Section, taxe are volatile ince the government i limited in it ability to mooth revenue raiing ditortion. Moreover, taxe repond peritently to hock and are moothed into the future the extent allowed by future incentive compatibility contraint. Thi peritence not only moothe economic ditortion going forward, but it relaxe future incentive compatibility contraint through the implied change in debt net of rent. A way to ee thi i to note that debt net of rent i alway within tate-dependent bound aociated with the S, bound for taxe and public pending: z t t ) [ z t ), z t ) ]. 4) How are the bound on taxe related to the tate of the economy? In the three-period example of Section, the lower bound on taxe i higher when public pending i more productive the politician require incentive), and the upper bound on taxe i lower when public pending i le productive the repreentative citizen require incentive). In a dynamic economy, thi i generally true under independent identically ditributed i.i.d.) hock. 7 Propoition 4 i.i.d. Tax Interval). If π k = π k k, S,thenτ ) <τk) and τ ) < τ k) if θ ) <θk). Thi mean that under i.i.d. hock, the lower and upper bound for the utainable range of taxe will be increaing in the productivity of public pending θ. Intuitively, when θ increae, public pending increae, and thi tighten the incentive compatibility contraint 7. Thi reult tand in contrat to Battaglini and Coate 008) in which politician require le pork during high public expenditure hock.