The U.S. social security system faces funding pressure due to the aging of the population. This dissertation examines the welfare cost of social security reform and social security policy uncertainty under rational expectations and under learning. I provide an overview of the U.S. social security system in Chapter I. In Chapter II, I construct an analytically tractable two-period OLG model with capital, social security, and endogenous government debt. I demonstrate the existence of steady states depends on social security parameters. I demonstrate a saddle-node bifurcation of steady states numerically, and demonstrate a transcritical bifurcation analytically. I show that if a proposed social security reform is large enough, or if the probability of reform is high enough, the economy will converge to a steady state. In Chapter III, I develop a three-period lifecycle model. The model is inherently forward looking, which allows for more interesting policy analysis. With three periods, the young worker's saving-consumption decision depends on her expectation of future capital. This forward looking allows analysis of multi-period uncertainty. Analysis in the three-period model suggests that policy uncertainty may have lasting consequences, even after reform is enacted. In Chapter IV, I develop two theories of bounded rationality called life-cycle horizon learning and finite horizon life-cycle learning. In both models, agents use adaptive expectations to forecast future aggregates, such as wages and interest rates. This adaptive learning feature introduces cyclical dynamics along a transition path, which magnify the welfare cost of changes in policy and policy uncertainty. I model policy uncertainty as a stochastic process in which reform takes place in one of two periods as either a benefit cut or a tax increase. I find the welfare cost of this policy uncertainty is less than 0.25% of period consumption in a standard, rational expectations framework. The welfare cost of policy uncertainty is larger in the learning models; the worst-off cohort in the life-cycle horizon learning model would be willing to give up 1.98% of period consumption to avoid policy uncertainty.

The aim of this study is to analyse the impacts of the social security system reform performed in Turkey within the

Après une introduction générale et un survol de littérature, l’apport de cette thèse est que chaque gouvernement choisit pour son pays le flux de migrants qui maximise le bien-être social. Il s’ensuit naturellement l’introduction du concept de double frontière optimale. Dans un modèle OLG simple à la Galor (1986) avec 2 périodes, 2 pays et offre de travail exogène, le chapitre 2 étudie le rôle des différences d’épargne entre les pays sur l’équilibre stationnaire. Le planificateur social choisit le taux de migration qui conduit l’économie à la Règle d’Or (que les frontières soient coûteuses ou non). Si un pays laisse entrer alors l’autre laisse sortir, mais les taux de migration diffèrent à l’optimum social. Un planificateur mondial choisirait comme les individus. Le chapitre 3 développe un modèle OLG à 3 périodes et 2 pays. En 1ere période les jeunes s’éduquent avec des taux de rendement différent selon le pays, en seconde et troisième période ils offrent du travail endogène. Le taux de migration conduit chaque pays à l’optimum social et est tel qu’un des deux pays souhaite fermer ses frontières avant l’autre. Ces asymétries génèrent des incitations à la migration illégale, et par conséquent les salaires et taux d’intérêt ne s’égalisent pas à l’équilibre post-migratoire.Le chapitre 4 étend le précédent au cas où seuls les adultes sont autorisés à migrer et ajoute un système de retraite. Les pays receveurs souhaiteraient accueillir plus de migrants que les pays d’envois ne souhaiteraient en laisser partir. Le choix individuel de migration repose davantage sur un choix d’éducation des enfants que sur le choix de bénéficier d’une retraite. Ce résultat contredit la littérature sur ce point. / After a general introduction and a literature review, in a 2-country OLG model, this thesis considers a non yet studied case where each government chooses for his country theflow of migrants that maximizes the post-migration social welfare. Since decision flows are unilateral, it naturally follows the introduction of the concept of optimal two-sided-borders. In a simple OLG model à la Galor (1986) with 2 periods, 2 countries and an exogenous labor supply, Chapter 2 examines the differences in optimal migration flows when countrydiffers in time preferences. With or without costly borders, optimal flows that lead the economy to the Golden Rule differ, so that one country closes its borders before the otherone. A world social planner would make an opposite migration policy compared with the country-specific social planner. Chapter 3 develops an OLG model where young train and get the return to education next period, adult and old endogenously work. The optimal migration rates leading to the social optimum of each country differ. These asymmetries generate incentives for illegal migration, hence wages and interest rates do not equalize in the post-migration equilibrium. Chapter 4 extends the previous by introducing a pension system. If by the law, only adults are allowed to migrate, then the receiving country want to attract more migrants than the departure country would let go. The individual choice of migration depends more on the children education than on the retirement benefit choice. This result is not in line with the existing literature. The Welfare State is not the first reason for which migrants leave their country.