Fiscal Burden and Immigration Policy in the U.S.

Fiscal Burden and Immigration Policy in the U.S. Ben Suwankiri May 7, 2008 1 Introduction 2 The Model Consider an economy consisting of overlapping generations inhabiting in a discrete time environment. Each individual lives for two periods, working in the first period of their lives and retired when old. The working generation is divided into two groups according to their exogeneously given skills: skilled (s) and unskilled (u). The old generation does not work. There is one good for consumption, which is produced by using the two perfect-substitute inputs 1, the two-types of labor. Y t = A t (wt s L s t + wt u L u t ) where u and s denote unskilled and skilled labor, and A t denotes Hicksneutral productivity growth. I assume wt s >wt u. 1 We will relax the assumption of production function later. This simplification, nonetheless, will provide sufficient insights for understanding the problem at hand. 1

Preferences of each generation: young, grown-up, and old, are given respectively by U(c y t,l t,c o t+2) =c y t ε(l t) 1+ 1 ε 1+ε + βco t+1 (1) U(c o t )=c o t. (2) Here, y denotes young s, and o denotes old s consumption, ε denotes the elasticity of labor supply, and β (0, 1) is the discount factor. Agents in the economy maximize the above utility functions subject to individual s budget constraint. With this preference, interest rate equals r = 1 1 and β individuals have no incentive to save. There is a transfer to everyone in the economy at time t, T t, that is financed by a uniform tax across all working individuals, τ t. Since the old generation has no income, their only source of consumption comes from this transfer. Individual s labor supply is given by l s t =(A t w s t (1 τ)) ε and l u t =(A t w u t (1 τ)) ε. (3) This, along with zero saving for individuals, yields the following indirect utility functions V h At wt h (1 τ t ) 1+ε = + T t + βt t+1 1+ε V o = T t, for h {s, u}. Hence the relevant preference parameters are (ε, β) Ω [0, ) [0, 1]. We will use these parameters to help in defining the political equilibrium. 2.1 Demography, Heterogeneity, and Labor Immigrants are assumed to have identical preferences as natives, so that we can aggregate their labor supply with that of the natives. Apart from taxes 2

and transfer policy, political process also select the quota for immigration. This quota consists of two parts: one selecting the size of immigrants to be admitted, and two selecting the proportion of immigrants that is skilled. I assume that all immigrants come to work, therefore there will never be an entering retired immigrant. I denote with µ t as the number of entering immigrants relative to native population in period t and denote with σ t the proportion of skilled young immigrants entering the country at time t, adding to the fraction s t of existing native skilled labor. Both of these policy variables are resticted to be in a unit interval. I assume all immigrants are naturalized in one period after their entrance (for this model, it is equivalent to roughly 30 years). Hence they gain voting power a period after as a part of the old cohort. From this, the aggregate labor supply of the two labor forces is given by L s t =(s t + σ t µ t )N t lt s L u t =(1 s t +(1 σ t )µ t ) N t lt u. The dynamics of the economy are given by the population dynamics These can be devided into two sets of equations, one governing the aggregate population dynamics, while the other governs the skilled dynamics. Since the skills are not endogeneous within the model, we assume for simplicity that the offsprings replicate exactly the skills of their parents. That is, N t+1 =[1+n + µ t (1 + m)] N t (4) s t+1 N t+1 =[(1+n)s t +(1+m)σ t µ t ] N t, where n and m are growth rate of native and immigrants respectively. We restrict n, m [ 1, 1] and n<m. These parameters will be crucial in analyzing any demographic benefits of immigration in addition to their economic benefits. Combining the two equations together, the skilled dynamics can 3

re-wrintten in a compact form as follows s t+1 = (1 + n)s t +(1+m)σ t µ t. (5) 1+n + µ t (1 + m) With this setup, it is important to see that not only the immigration level matters, but also the composition of the entering immigrants. 2.2 Fiscal Institution We model the fiscal institution with a balanced-budget tax and transfer system. As noted earlier, all workers pay a uniform tax rate of τ t in period t. This is used to finance a flat transfer to all individuals of the amount T t. There are no other government spending in the economy. On the expenditure side, we have the spending, T t, going to all young individuals, including the immigrants. The size of working population is (1 + µ t )N t. In addition, the transfers also go to the retirees, whose cohort is of the size (1 + µ t 1 )N t 1. All of these transfers must be financed from taxes of the skilled workers, wt s (s t + σ t µ t )N t lt s, and the unskilled workers, wt u (1 s t +(1 σ t )µ t ) N t lt u, which forms the total revenue in period t. We can put all these together in an equation, utilizing population dynamics in equation (4). Balancedbudget requires that the aggregate spending (transfers) and the aggregate tax revenue must match, hence T t = τ t ((s t + σ t µ t )wt s lt s +(1 s t +(1 σ t )µ t ) wt u lt u ), (6) 1+µ t + 1+µ t 1 1+n+µ t 1 (1+m) where the individual s labor supply equations are given above in equation (3). We note here that, due to uniform taxing system and transfer to all, the fiscal system provides a mechanism of redistribution from the rich to poor and from the young to the old. So the redistribution could be both interand intra-generational. 4

3 Political Equilibria Before looking at political equilibria of the model, it is important to see who forms the majority in the economy and under what conditions. Skilled Young Forms Majority under two conditions. Firstly, its size must dominates the unskilled young, that is s t > 1 2. Secondly, it must also dominate the old cohort or algebraically s t > 1+µ t 1 1+n + µ t 1 (1 + m). It can be shown that, under parameter restrictions above, the second condition of old domination is sufficient. 2 Unskilled Young Forms Majority under two conditions: dominating the size of the skilled young and the old cohort. These conditions are given respectively by s t 1 2, 1 s t > 1+µ t 1 1+n + µ t 1 (1 + m). Again, with restrictions on parameters above, satisfying the second dominance ineqality is sufficient. 2 To see this, using n < m 1 and µ [0, 1], we can get the following string of inequalities: 1+µ 1+n + µ(1 + m) > 1+µ (1 + µ)(1 + m) > 1 2. So if the skilled could dominate the old cohort, it automatically dominates the unskilled cohort. 5

Old Forms Majority when its size is larger than both skilled and unskilled young. This means 1+µ t 1 1+n + µ t 1 (1 + m) max{s t, 1 s t }. With three groups of voters, it is important how we allow each group to interact with one another through voting, as this will influence the final policy outcome. We first consider the simplest case, where all voters vote sincerely. This means all voters vote for their favorite policy, regardless of the probability of its victory. We will relax this assumption to allow for strategic voting below. 3.1 Sincere Voting Equilibrium In this paper, we focus on subgame-perfect Markov equilibrium. In this subsection, we focus on "sincere voting." Sincere voting refers to a voting behavior that individuals vote according to their absolute preference. With a single ideal point in range, that will be the policy in which the voters cast their vote for. This is the usual assumption in many political economy models. Formally, we define a sincere political equilibrium as follows. Definition 1. The policy function Ξ t = hτ t,σ t,µ t i = hτ (Ξ t 1 ),σ(ξ t 1 ),µ(ξ t 1 )i constitutes a Subgame-perfect Markov Equlibrium with Sincere Voting if Ξ t = Ξ(Ξ t 1 )=argmax τ t,σ t,µ t V d (Ξ t 1, Ξ t, Ξ(Ξ t )) s.t. N t+1 =(1+n + µ(ξ t 1 )(1 + m))n t and s t+1 = (1 + n)s t +(1+m)σ t µ t, 1+n + µ t (1 + m) where d {s, u, o} is the identity of the majority voter in the economy. This equilibrium concept requires that the resulting equilibrium policy today takes into the account of the policy variable will be implemented in the 6

future, in particular the effect that today s policy will influence tomorrow s policy. In addition to Markovian restriction, we require stationarity of the policy profile. This implies that the strategy profile will be time independent in the equilibrium. Voters in this period will take into the account next period s policy profile that is identical to the strategy being played today. Our first proposition captures what happens if all individuals in this economy vote sincerely. Proposition 2 (Sincere-voting Markov Equilibrium). There is a nonempty subset of preference parameters such that the following strategy profile forms a Subgame-perfect Markov Equilibrium. 0, if skilled forms the majority τt 1 = 1 J, if unskilled forms the majority 1+ε 1 J σt = µ t = 1, if old forms majority 1+ε 1, if either young forms the majority and s t [0, 1 1+n ) bσ < 1 2, if the skilled forms the majority and s t 1 1+n 1, if old forms the majority. 1 (1+n)s t m, if either young forms the majority and s t [0, 1 1+n ) bµ, if the skilled forms the majority and s t 1 1+n 1, if old forms the majority. where J = J(µ t,σ t,s t,µ t 1 ), bσ, andbµ are given in the appendix. As expected, the skilled is the only main contributor to the welfare state, while the other two population groups are net beneficiaries. Preference for the old is easily analyzed. If the old forms the majority, it will want maximal social security benefits, meaning taxing to the Laffer point. This will also imply allowing the maximal number of skilled immigrants as they contribute the most to social security system. It is interesting to see that, although the unskilled young cohort is the net beneficiaries in this welfare state, they are 7

still paying taxes. Hence the preferred tax policy is smaller than the Laffer point, weighing down by a wedge 1. Wewillprovidemorediscussionon J this wedge below. Clearly, the unskilled will also prefer to let in more skilled immigrants due to their contribution to the welfare state. The skilled native prefers more skilled immigrants for a different reason than the earlier two cohorts. They prefer a maximal amount of skilled immigrants here because this will provide the maximal number of skilled native next period. Thus, if the skilled are forward looking, they too will prefer the skilled immigrants for the sake of theire retirement next period. Note that wages for both workers are constant here, given the production function. Therefore, the only incentive for more immigrants is to expand the tax base. In general, different labor groups may be complementary to one another. That channel is absent from this result thus far. However, if that is the case, then the skilled may prefer more unskilled immigrant, while the unskilled will continue prefer more skilled immigrants. The immigration policy of either young group reflects the fact that they will want to put themselves as the old majority in the next period. Thus, instead of letting in too many immigrants, who will give birth to a large new generation, they will want to let in as much as possible before the threshold of majority is crossed. This strategic motive on immigration quota reflects the results previously studied by Sand and Razin [8]. Letting s t =1gets the result of these authors. They show that the current young majority voter may have an incentive to choose a different immigration quota that is not their ideal, in order to put themselves in the majority next period and choose the higher level of social security. There are two differences between our result and the one presented in their paper. Firstly, the equilibrium here has a bite even if the population growth rate is positive, whichcannot simply be done when there are only young and old cohort. In Sand and Razin [8], this strategic motive of the young can only be in effect when the native 8

population is shrinking. Another fundamental difference in these results is that, notice that in order to have some social security in the economy, the majority group has a choice of placing the decisive power either in the hand of next period unskilled or next period old. So for this to be an equilibrium, we need to verify additional condition that it is better for the majority young this period to go with the old generation next period. In the appendix, we show that it is the case. When s t 1, we have an odd situation (which is only possible when 1+n n>0). In this range of values, the number of skilled is growing too fast to be curbed by reducing immigration policy alone. To ensure that the majority lands in the correct hand, this period majority must make the unskilled cohortgrowtoweighdowntheinfluence of the skilled. This is done by restricting the composition of skilled immigrants, and may be restriction in the immigration quota as well. Any increase in the share of unskilled population will be a net burden to the fiscal system. Therefore, if the majority must increase this burden, they will want to do it as minimally as possible. In theory, (bσ, bµ) are non-unique. Different set of parameters will give rise to a different pair of solutions. However, with the population growth rate of the major host countries for immigration like the U.S. and Europe going below 1%, it is unlikely that this case should ever be of much concern. The tax choice of the unskilled young deserves an independent discussion. In the work by Razin et. al. [7], the authors find that "fiscal leakage" to the immigrants may result in a lower tax. There are no immigration policy variable, and they assume that all immigrants possess lower skill than the natives. Since this increases the burden of the fiscal system, the median voter will have an incentive to reduce the welfare state, instead of increasing it. To see such a resemblance the our result to the authors, one must first take immigration quota, µ t, and immigration composition, σ t,asgiven,thatisdo not treat them as a choice. The preferred tax rate of the unskilled native 9

will be τt u = 1 1 J 1+ε 1, J where J = J(µ t,σ t,s t,µ t 1 )= ³ w s 1+ε (s t + σ t µ t ) t w +1 t u st +(1 σ t )µ t 1+µ 1+µ t + t 1. 1+n+µ t 1 (1+m) (7) One can easily verify from these two expressions that τu t σ t > 0, andthereexists σ such that, for any σ t < σ, wehave τu t µ t < 0. Thefirst inequality tells us that more skilled immigrants allows for more intra-generational redistribution. That is, the fiscal leakage creates more burden, such that the majority "unskilled" voters would rather have the welfare state shrinks. This is the channel that is also present in Razin et. al [7] analysis. In addition, for any σ t > σ, we would get an expansion of the welfare state, because τu t µ t < 0. 3 Many interesting implications can still be drawn from this equation. For example, an increase in fiscal burden, captured by a fall in the fraction of skilled labor, s t, and in the population growth, n, would prompt the unskilled majority to lower taxes and hence the welfare state. 3.2 Strategic Voting Equilibrium When there are multiple electorates choosing policies, sincere voting assumption seems unreasonable. Afterall, people do not always vote for their most preferred policy, but instead for the best policy for them that will mostly win the election. Such a motive is referred to as "strategic voting" in the 3 Our use of "shrink" and "expand" should be properly justified. Recall that the tax rate preferred by the unskilled young worker is less than the level that is preferred by the old retirees. The tax rate preferred by the old retirees, τt o = 1 1+ε is the maximal tax rate, and the maximum welfare size an economy could have, given immigration policies. 1 Thereforethesizeofthewelfarestatewillbemonotonicwiththetaxrateτ [0, 1+ε ]. 10

literature. Voting strategically requires not only that all voters act consistent to their ideal preference when voting, but to take into the account of the likelihood that such a policy will be implemented. Therefore, to allow for strategic voting, we need more appartuses. Firstly, we discuss some necessary assumptions to make the model tractable. Assumption 1. Voters of the identical preference vote identically. This assumption simply says that all skilled voter identically, all unskilled vote identically, and all old vote identically. This assumption is not surprising and is already a part of most voting models, including sincere voting. Therefore, we don t have to consider splitting tickets, and division within groups, for example, half of the skilled vote for the old while the other half vote for the unskilled. Therefore, to understand voting behaviour of a population group, we only need to study its representative. Assumption 2. Three candidates, one from each group (skilled, unskilled, and old), submit the proposal for votes. Unlike the work by Besley and Coate [1], we do not endogeneous the number candidates here. Hence, there are no direct cost of running for office. However, there is an "electorative cost" of putting two identical candidates from the same group up for election, as they will cause a split voting in the group. To deal with this, we assume that there is only one candidate from each population group running for votes. We can also think of the election as a choice of delegation to an individual in the economy to implement the policies. Since there are only three types of individuals in the economy, the delegation will go to one of the three types, in the fashion of a citizencandidates model. 4 4 For seminal works on citizen-candidates model, see Osborne and Slivinski [?]forsincere voting, and Besley and Coat [1] for strategic voting setup. 11

Assumption 3. No commitment mechanism for policy implementation. Under Assumption 2, the implementation power will be in the hands of one of the three types of individuals. Similar to Besley and Coate [1], we assume that there are no commitment mechanism in the economy. Such commitment can usually be sustained through reputation and reelection motives, providing a punishment channel for failing the promise. Thus candidates could change platform and commit to vie for more votes. We assume these are absent from the model. Therefore, the winning candidate cannot credibly commit to implement a policy other than his own ideal policy, representing the cohort he belongs to. Assumption 4. No abstention. Voting abstention is a subject of a large literature. We forbid abstention from the model because, under Assumption 1, this reduces the political game to a simple "restricted" median voter game. In addition, without abstention, we are guaranteed to have a policy outcome without a need for an exogeneously-defined default policy. Voting Decisions. Each individuals decide on who to cast their single vote for. With an abuse of notation, let the set of three candidates be {s, u, o}, denoting their identity. Then, the decision to vote of any individual must be optimal under the correctly anticipated probability of winning and policy stance of each candidate. Under Assumption 1, we can focus on the decision of a representative from each group. Let e i t {s, u, o} be the vote for a candidate of individual i. Voting decisions e t =(e s t,e u t,e o t ) is a voting equilibrium at time t if X e i t =argmax P j (e i t, e it)v i τ j t,σ j t,µ j t eit {s, u, o} (8) j {s,u,o} where P j (e i t, e it) denotes the probability that candidate j {s, u, o} will win given the voting decisions, and e it is the optimal voting decision of 12

other groups that is not i. 5 Thus we require that each vote casts by the representative of each group is a best-response to the votes by the other groups. In addition, since Assumption 1 mandates identical voting for individuals of the same characteristics, the representative voter of each group must take into the account the pivotal power of their vote. In words, it is not only just one vote being cast, but entire the size of the group will vote identically. This is captured in the probability of winning for each candidate. Assumption 5. Each voting decision is not a weakly dominated voting strategy. 6 Weakly dominated voting strategy typically invites massive indeterminacy into the model, so we try to avoid such trivial trap. One such equilibrium, for example, suppse all three groups have the same weight (think one vote per group, without loss of generality), then if all three cast votes for the worst possible option, this will still statisfy the definition of the voting equilibrium. Ruling out weakly dominated voting strategy rules out this undesireable equilibrium. Tallying the Votes. To win, the candidates must garner the highest number of votes. The votes are tallied by adding up the size of each group that have chosen to vote for the candidates. The candidate with the most votes get to implement his ideal set of policies. This ideal set of policies of thecandidatesarethepolicieswestudiedinthelastsubsection. Votersknow these and will take them into consideration when voting. 5 The setup for voting equilibrium borrows heavily from Besley and Coate [1]. 6 Following Besley and Coate [1], a voting decision e i t is weakly dominated for i if there existes be i {s, u, o} such that X P j (be i t, e i t )Vt i for all e i t j {s,u,o} ³ τ j t,σ j t,µ j t X j {s,u,o} with strict inequality holding for from e i t. P j (e i t, e i t )V i t ³ τ j t,σ j t,µ j t 13

For brevity of notations, we will denote with vj i = V i τ j t,σ j t,µ j t as the utility individual i receives if candidate j is elected and implements the policies. It can be shown that each individual i can rank these policies according to their indirect utility functions. These are summarize the the following lemma. Lemma 3. Utility each individual gets from policies implemented by the candidats can be ranked as followed: For the skilled young: vs s >vu s >vo s For the unskilled young: vu u >vo u >vs u For the old: vo o >vu o >vs. o Clearly, each individual prefers the ideal policies of their representative candidate. Thus sincere voting equilibrium above captures this, when everyone in the economy votes according to the most preferred policies. With all these in hands, we are ready to define the subgame-perfect Markov political equilibrium under strategic voting. Definition 4. The policy function Ξ t = hτ t,σ t,µ t i = hτ (Ξ t 1 ),σ(ξ t 1 ),µ(ξ t 1 )i constitutes a Subgame-perfect Markov Equlibrium with Strategic Voting if Ξ t = Ξ(Ξ t 1 )=argmax τ t,σ t,µ t V d (Ξ t 1, Ξ t, Ξ(Ξ t )) s.t. N t+1 =(1+n + µ(ξ t 1 )(1 + m))n t and s t+1 = (1 + n)s t +(1+m)σ t µ t, 1+n + µ t (1 + m) where d {s, u, o} is the identity of the the winning candidate, decided by the voting equilibrium e t that satisfies equation (8). Like all models of strategic voting, there are multiple equilibria, depending on how each individual chooses to vote. In terms of terminology, we will refer to any group that votes for its representative candidate as voting 14

sincerely, while any group that votes for any candidate other than its representative candidate as voting strategically. All in all, there are 27 total voting vector that could arise. This large number is limited some what by Assumption 1-5. In particular, Assumption 5 rules out many voting decision that would result in a strange equilibrium. For example, if all three groups vote for the skilled representative candidate, and no group has the absolute majority in the economy. 7 That is an equilibrium, but the voting strategy for the unskilled and the old is weakly dominated. We use the definition below to characterize different equilibrium depending on its voting characteristics. Definition 5. K-group Swing Voting Equilibrium in an economy consisting of L ( K) groupsisasubsetofthesetofsubgame-perfectmarkovequlibria with Strategic Voting such that i.) K groups vote strategically, while L K voting sincerely. ii.) Winning Candidate must receive votes from a strategic voting group. This definition will help us sort the political equilibrium into different classes, depending on the number of groups that vote strategically. Although the definition uses the word "group," it could be easily changed to citizens for any more micro-based model. We have a total of three groups in the economy: skilled, unskilled, and old. So according to above definition, we would consider Zero-group, Single-group, Two-group, and Three-group equilibria. The Zerio-group Swing Voter Equilibrium coincides with the sincere voting equilibrium we already have described. Embedded in the definition above is the requisite that no group has the absolute majority in the economy. Therefore, the candidate could win by receiving the votes from the strategic voting group(s). We first look at the Single-group Swing Voting Equilibrium. 7 A group is the absolute majority in the economy if its size is more than 1 2. 15

Proposition 6 (Single-group Swing Voting Equilibrium). There is a non-empty subset of preference parameters such that the following strategy profile forms a Subgame-perfect Markov Equilibrium with Strategic Voting 1 1 J,ifskilledoroldvotesstrategically τt 1+ε = 1 J 1, if unskilled votes strategically 1+ε n σt = 1,ifanygroupvotesstrategically µ t = ( 1 (1+n)st m, if skilled or old votes strategically 1, if unskilled votes strategically where J = J(µ t,σ t,s t,µ t 1 ) is given in the appendix for Proposition 2. We provide the proof in the appendix. Interesting enough, once we allow the voters to vote strategically, we always get a positive level of welfare state, high level of skilled composition in immigration, and some positive level of immigration. The interpretation of all these policy variables are exactly the same as above, under sincere voting equilibrium. Proposition 7 (Two-group Swing Voting Equilibrium). There is a non-empty subset of preference parameters such that the following strategy profile forms a Subgame-perfect Markov Equilibrium with Strategic Voting τt = 1 1 J 1+ε 1,σt =1,µ t = 1 (1 + n)s t, m J where J = J(µ t,σt,s t,µ t 1 ) is given in the appendix for Proposition 2. Proof is provided in the appendix. Once we allow two groups to vote strategically, the unskilled has no incentive to vote strategically! They will always vote for their representative candidate, while the other groups will also vote for the unskilled. Proposition 8 (Three-group Swing Voting Equilibrium). There is no equilibrium in which all three groups vote strategically. 16

The proposition follows immediately from the Two-group Swing Voting Equilibrium. The fact that the unskilled has no incentive to vote strategically makes it impossible to have an equilibrium that all three groups vote strategically. 17

References [1] Besley, Timothy, and Stephen Coate (1997). "An Economic Model of Representative Democracy." Quarterly Journal of Economics, 112(1), pp. 85-114. [2] Borjas, George (1999). "Economic Analysis of Immmigration." In Orley Ashenfelter and David Card, editors, Handbook of Labor Economics, Vol. 3A. Elsevier, Amsterdam, The Netherlands, pp.1697-1760. [3] Casarico, Alessandra, and Carlo Devillanova (2003). "Social Security and Migration with Endogeneous Skill Upgrading." Journal of Public Economics, 87,pp.773-797. [4] Lee, Ronald, and Timothy Miller (2000). "Immigration, Social Security, and Broader Fiscal Impacts." American Economic Review Papers & Proceedings, 90(2), pp. 350-354. [5] Osborne, Martin, J., and Al Slivinski (1996). "A Model of Political Competition with Citizen-Candidates." Quarterly Journal of Economics, 111, pp. 65-69. [6] Razin, Assaf, Efraim Sadka, and Phillip Swagel (2002). "Aging Population and Size of Welfare State." Journal of Political Economy, 110(4), pp. 900-918. [7] Razin, Assaf, Efraim Sadka, and Phillip Swagel (2002). "Tax Burden And Migration: A Political Economy Theory And Evidence," Journal of Public Economics, 85(2), pp. 167-190. [8] Sand, Edith, and Assaf Razin (2007). "The Political-Economy Positive Role of the Social Security System in Sustaining Immigration (But Not Vice Versa)." NBER Working Papers # 13598. 18

[9] Storesletten, Kjetil (2000). "Sustaining Fiscal Policy Through Immigration." Journal of Polical Economy, 108(2), pp. 300-323. 19

Appendix 20