THE THEORY OF THE FISCAL WINDFALL FROM IMMIGRATION INTRODUCTION In earlier analysis of the costs and benefits of immigrants to natives by way of the public coffers (see e.g. Simon, 1989, chapter 4), I asserted that the old-age expenditures for youthful immigrants in their retirement years should be excluded from the analysis because their children pay for these expenditures (and also because fiscal events that occur long after immigrants' arrival are relatively unimportant because of discounting, but that argument will be seen to no longer be relevant). And I characterized the result of there being no (actually, only a few) older persons among immigrants as a one-time windfall benefit to natives by way of immigration and the Social Security and Medi- care system. No theoretical basis was then given for this proposition because I thought it to be intuitively obvious. In fact, the proposition is both imprecise and not exactly correct. The purpose of this brief paper is to lay a theoretical foundation under the general idea so that the magnitude of the effect can be calculated both in an idealized situation and with actual data when they are available. The nub of the explanation is that any average group of natives - including all, from the youngest to the oldest - may be considered to be in a dynamic equilibrium with respect to taxes and government expenditures; the in-payments from workers equal all the out-payments, including those for the non-working elderly and for children. But because a cohort of immigrants arrives without an accompanying group of non-working elderly (the few who come are not eligible for Social Security, though they do receive other forms of government transfers), an arrival cohort of immi- grants is not in a dynamic equilibrium as are natives; instead, immigrants gradually move toward the same dynamic equilibrium as natives during the period that the working-age persons in the immigrant cohort age. The difference each year between the dynamic-equilibrium taxes and transfers of natives and the immi- grant' taxes and transfers (putting aside public goods for now) constitutes the benefit to natives through the public coffers. The windfall does not go on forever; the amount of windfall per year declines from the time of the arrival cohort's entry until the working-age persons in the first generation reach retirement (which in practice happens gradually, of course), at which time the dynamic equilibrium is reached and there is neither windfall nor deficit. This implies that the receipt of old-age benefits nowadays by immigrants who have been in the U. S. for many years since their twenties or thirties should properly be considered part of an equilibrium system that includes their own children's genera- tion. The children of retired immigrants support their parents with their taxes, just as the children of natives do for their parents. Hence the retired immigrants are no special burden upon natives. None of this can be understood or estimated when one looks only at current flows of taxes and expenditures, which is why studies that examine only current flows, undifferentiated by the arrival cohort of immigrants, do not reveal the crucial role of expenditures on the elderly. THE ANALYSIS Assume for both natives and immigrants a) stationarity over time of per-person output and income, b) equality of output of persons within the working ages 20-60, c) a birth rate equal to replacement, d) no deaths until 80 at which point all die; hence there is a rectangular age distribution. Consider the period under discussion to be four years, to make the accompanying graph easier to read. All sums may be considered to refer to the overall effects of (say) 1000 natives comprising the age distri- bution at a particular moment, and to a cohort of immigrants that upon arrival has the same numbers of persons in the youth and worker categories but no retired persons. For natives the human movements into the youth (Yn), worker (Wn) and retired (Rn) brackets each period equal the movements out of those brackets, and therefore the numbers remain constant in each category. The natives (N) diagram shows that if in period I taxes (Tn) equal government expenditures on individuals (En) plus relevant public goods expenditures (P) (which are not cap- tured by the survey data), then the same equality will hold in period II and in each subsequent period. If En equals Sn (Social Security plus Medicare plus other expenditures on the aged) plus Qn (other, including public schooling, welfare, medicaid, etc.), then Tn = Sn + Qn + P. (1) The relevant expenditures on public goods will be assumed to be the same in this analysis for natives and immigrants, with no economies of scale. A more accurate treatment of public goods is possible, but would only be a distraction here. Now consider the immigrants (M) diagram, and a single cohort of immigrants (so we have neither the complexity nor the simpli- fication of considering flows). This cohort is assumed to arrive with zero Rm (retired persons) and therefore equals (Yn + Wn), or M = N - Rn. (2) There is no requirement for immigrants that taxes equal expenditures, as there is for natives in the long run (i. e. a balanced budget). In any period the excess of taxes over public expenditures on individual immigrants (Tm - Em - Pm) may be called Xt. Given that Tm = Tn and using (1), Xi = (Sn + Qn + P) - (Qm + P + Sm), and since Qm = Qn, (3) Xi = Sn - Sn. (4) Given that in the first period SmI = 0, XI = Sn. In the first period XI equals the amount Sn that would be paid to retired persons if the cohort were in dynamic equilibrium and there were as many immigrant as native retired persons (per arrival cohort of immigrants). The diagram then shows that the age distribution of M is the same in period II as in I except that Rm will not be zero but instead will contain persons age 60-65 (who have aged from period I), equal in number to 1/5 of RN in a given period. Hence (TmII - EmII - P) = 4/5 Sn. (5) In the following periods the fractions are 3/5, 2/5, 1/5, and XVI is zero. So if we put aside the matter of discounting, the total effect is (15/5 = ) 3Sn. Hence the "contribution" of a cohort of new immigrants to the public coffers is the discounted sum of the (Tm - Em - P) amounts (where & is a summation sign): &~Xt = (Sn + 4/5Snd + 3/5Snd2 + 2/5Snd3 + 1/5Snd4. THE MAGNITUDE OF THE EFFECT The idealized model provides an intuitive basis for the importance of the effect analyzed here. Remembering that each period is four years in length, the undiscounted 15/5 of Sn is equal to 12 years' contributions to (or use of) transfers to the elderly. If one year's contribution is 15 percent of income, the total undiscounted effect is 180 percent of an average worker's earnings. In other terms, an immigrant who arrives in the middle of the labor-force years transfers to natives something less than two years' income, as a windfall to natives, discounting aside. Because most of the windfall occurs in the early years (9/15 within the first eight of the 40 years), a rough discounted estimate might be more than one year's income, depending on the discount factor. Realistic calculations would be more demanding because age distributions are not uniform, people enter and leave the work force at various ages, death does not occur to all persons at the same age, and so on. But such a realistic calculation would probably show a larger effect than the idealized calculation because the mid-point of the actual age distribution of working- age immigrants is younger than the mid-point of the working-age years. THE ANALYSIS IN CONTINUOUS TERMS [to come] THE EFFECT ON COUNTRIES OF EMIGRATION At first thought it would seem that the effect on a country of emigration would be the mirror image of the effect on the country of immigration, even if not in the same quantities. But this is not so, for several reasons. First, poor countries have much smaller support systems for the aged, especially for the rural aged. Second, their tax-collection systems are less developed. Third, the total volume of taxes collected is much smaller, mainly because incomes are lower. Therefore, it is quite possible that the flow of remittances from the emigrant would be a more important gain to the country of emigration than the tax-and-elderly-support loss might be. EFFECTS OF PARTICULAR AGE CATEGORIES It might seem intuitively plausible that over its lifetime a newly-born immigrant would be in zero net balance with the rest of the society with respect to public-coffers outgoes and in- comes. But upon further inspection this becomes less obvious. A newly-born immigrant arriving without parents - say, an adoptee - has exactly the same economic status as does a newly- born native. So the issue is no longer part of the special economics of immigration. If we now proceed to ask the same question about a native new-born, the answer to the question still is not obvious. And the issue no longer has policy relevance, as long as parents are free to have children. Therefore there is no need for the sort of idealized analysis used above to guide an empirical examina- tion. And if one were to proceed to a more realistic inquiry, many new sorts of issues arise. Technological change and produc- tivity increase that occur over the course of the baby's lifetime become very important, more important than with respect to immi- grants who arrive ready to go to work with contemporary technolo- gy. Hence output cannot be so reasonably assumed constant, even in an idealized model. But even more important, a single infant bears no resemblance to a complete system in dynamic equilibrium, and henceforth the model used above does not apply at all; an entirely different sort of enquiry is required. Friedman (1972) provided such an analysis. REFERENCES Friedman, David, "Laissez-faire in population: the least bad solution", Population Council Occasional Paper, 1972. Simon, Julian L., The Economic Consequences of Immigration to the U. S. (Oxford: Basil Blackwell, 1989). page 1 article5 immwndfl November 24, 1995 