Cross-Dynastic Intergenerational Altruism: Revisiting the Isolation - PowerPoint PPT Presentation

Cross-Dynastic Intergenerational Altruism: Revisiting the Isolation Paradox Frikk Nesje Department of Economics, University of Oslo 7th CREE Research Workshop Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Introduction Altruism for own descendants and for the next generation as such ... ... leads to a preference externality. Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Introduction Altruism for own descendants and for the next generation as such ... ... leads to a preference externality. Capital investments might lead to a technological externality. Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Introduction Altruism for own descendants and for the next generation as such ... ... leads to a preference externality. Capital investments might lead to a technological externality. Research questions: Implications of altruism for the future of other households? Implications altered if households bargain? Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Contribution/ relation to the literature The “isolation paradox” (Marglin; Newbery; Sen; Warr and Wright). Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Contribution/ relation to the literature The “isolation paradox” (Marglin; Newbery; Sen; Warr and Wright). Voluntary contribution to public goods (Bergstrom et al; Warr). Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Contribution/ relation to the literature The “isolation paradox” (Marglin; Newbery; Sen; Warr and Wright). Voluntary contribution to public goods (Bergstrom et al; Warr). Dynastic intergenerational altruism (Barro; Bernheim and Bagwell). Altruism in networks (Bourl` es et al; Millner). Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Contribution/ relation to the literature The “isolation paradox” (Marglin; Newbery; Sen; Warr and Wright). Voluntary contribution to public goods (Bergstrom et al; Warr). Dynastic intergenerational altruism (Barro; Bernheim and Bagwell). Altruism in networks (Bourl` es et al; Millner). Hyperbolic discount functions (Laibson; Phelps and Pollak; Strotz). Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Contribution/ relation to the literature The “isolation paradox” (Marglin; Newbery; Sen; Warr and Wright). Voluntary contribution to public goods (Bergstrom et al; Warr). Dynastic intergenerational altruism (Barro; Bernheim and Bagwell). Altruism in networks (Bourl` es et al; Millner). Hyperbolic discount functions (Laibson; Phelps and Pollak; Strotz). Preference satisfaction (Hausman, Milgrom). Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Model: AK with 2 households Well-being recursively defined: W 1 = (1 − α D − α CD ) ln( c 1 t ) + α D W 1 α CD W 2 t +1 + , t t +1 � �� � : New component with α D ≥ α CD ≥ 0. Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Model: AK with 2 households Well-being recursively defined: W 1 = (1 − α D − α CD ) ln( c 1 t ) + α D W 1 α CD W 2 t +1 + , t t +1 � �� � : New component with α D ≥ α CD ≥ 0. Per-period budget constraint: c 1 = A ( k 11 t − 1 + k 21 − k 11 − k 12 t − 1 ) t , t t � �� � = y 1 t with A > 1, k 11 t , k 12 ≥ 0. t Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Model: AK with 2 households Well-being recursively defined: W 1 = (1 − α D − α CD ) ln( c 1 t ) + α D W 1 α CD W 2 t +1 + , t t +1 � �� � : New component with α D ≥ α CD ≥ 0. Per-period budget constraint: c 1 = A ( k 11 t − 1 + k 21 − k 11 − k 12 t − 1 ) t , t t � �� � = y 1 t with A > 1, k 11 t , k 12 ≥ 0. t Consider Markov Perfect Equilibria. Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Model: Implications 1 1 1 𝑑 𝑢 𝑑 𝑢+1 𝑑 𝑢+2 --- 2 2 2 2 2 2 𝑑 𝑢 𝑑 𝑢 𝑑 𝑢+1 𝑑 𝑢+1 𝑑 𝑢+2 𝑑 𝑢+2 --- Case α D > 0 , α CD = 0 Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Model: Implications 1 1 1 𝑑 𝑢 𝑑 𝑢+1 𝑑 𝑢+2 --- 2 2 2 𝑑 𝑢 𝑑 𝑢+1 𝑑 𝑢+2 --- Case α D > 0 , α CD > 0 Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium Assume full symmetry: α D = α CD > 0 and y 1 t = y 2 t > 0. Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium Assume full symmetry: α D = α CD > 0 and y 1 t = y 2 t > 0. Define by k 11 = k 12 = 1 2 sy 1 t the household 1 transfer to the next t t generation of each household. Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium Assume full symmetry: α D = α CD > 0 and y 1 t = y 2 t > 0. Define by k 11 = k 12 = 1 2 sy 1 t the household 1 transfer to the next t t generation of each household. The residual is consumed: c 1 t = (1 − s ) y 1 t . Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium 1 1 1 𝑑 𝑢 𝑑 𝑢+1 𝑑 𝑢+2 --- 2 2 2 𝑑 𝑢 𝑑 𝑢+1 𝑑 𝑢+2 --- Case α D = α CD > 0 Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium 1 1 1 𝑑 𝑢 𝑑 𝑢+1 𝑑 𝑢+2 --- 2 2 2 𝑑 𝑢 𝑑 𝑢+1 𝑑 𝑢+2 --- Case α D = α CD > 0 Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium 1 1 1 𝑑 𝑢 𝑑 𝑢+1 𝑑 𝑢+2 --- 2 2 2 𝑑 𝑢 𝑑 𝑢+1 𝑑 𝑢+2 --- 𝛾𝜀 = 𝛽 𝐸 𝜀 = 2𝛽 𝐸 𝜀 = 2𝛽 𝐸 Case α D = α CD > 0 Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium Generalizing Laibson: Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium Generalizing Laibson: 1 � � A 1 = α D (1 − s ) + 2 α D s , c t c t +1 with MPC t +1 = 1 − s . Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium Generalizing Laibson: 1 � � A 1 = α D (1 − s ) + 2 α D s , c t c t +1 with MPC t +1 = 1 − s . Since c t = (1 − s ) y t and c t +1 = (1 − s ) Asy t : ���� = y t +1 1 � � 1 = α D (1 − s ) + 2 α D s A . (1 − s ) y t (1 − s ) Asy t Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium Simplifying: � � 1 1 = α D (1 − s ) + 2 α D s s , Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium Simplifying: � � 1 1 = α D (1 − s ) + 2 α D s s , This gives α D s = > α D , 1 − α D satisfying the one-stage deviation principle, provided 1 > 2 α D . Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium = ... = 1 For general N , with k 11 = k 12 N sy 1 t : t t � � 1 1 = α D (1 − s ) + N α D s s , which gives α D s = > α D . 1 − ( N − 1) α D Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium = ... = 1 For general N , with k 11 = k 12 N sy 1 t : t t � � 1 1 = α D (1 − s ) + N α D s s , which gives α D s = > α D . 1 − ( N − 1) α D For α D > α CD , with k 11 = sy 1 t and k 12 = ... = 0: t t � � 1 1 = α D (1 − s ) + ( α D + ( N − 1) α CD ) s s , which gives α D s = > α D . 1 − ( N − 1) α CD Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium Result 1: Sensitivity The transfers to the future are sensitive to increasing α CD . ⇒ Critique of the robustness of the dynastic concept of intergen. altruism (goes beyond Bernheim and Bagwell). Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop

Results: Equilibrium Result 1: Sensitivity The transfers to the future are sensitive to increasing α CD . ⇒ Critique of the robustness of the dynastic concept of intergen. altruism (goes beyond Bernheim and Bagwell). Result 2: Crowding out In equilibrium, household 1’s intergenerational transfer to household 2 crowds out household 2’s internal transfer. Frikk Nesje (University of Oslo) Cross-Dynastic Intergenerational Altruism 7th CREE Research Workshop