Working Papers

Present-Biased Envy, Inequality, and Growth
(with Kirill Borissov and Ronald Wendner), CESifo Working Paper No. 11090, 2024.

Abstract: We take into account that envy (relative consumption concerns) is more pronounced in the present than in the future. We consider a Ramsey-type model in which agents differ only in their initial capital endowments but are identical in their exogenous parameters. Agents' preferences exhibit present-biased envy: agents are naive and care about how their consumption levels compare to that of others in the current period. Our results suggest that present-biased envy affects both the level of inequality and the income level in an economy. First, present-biased envy generates the Matthew effect (the relatively rich get richer while the relatively poor get poorer), leading to a highly unequal long-run distribution of wealth. After some finite time, only those agents who were the wealthiest from the outset own the entire capital stock. All other agents are in the maximum borrowing state and spend their wages to repay the debt. Second, present-biased envy makes agents effectively more impatient, lowering the long-run capital stock and the aggregate income level compared to those in an economy without envy. 

Agents who are the wealthiest from the outset have positive consumption levels in all periods and eventually own the entire capital stock, while all other agents drive their consumption level to zero after some finite time and reach the maximum borrowing state

Heterogeneous Bequests and Social Inequalities
(with Kirill Borissov, Stefano Bosi and Thai Ha-Huy), HAL Working Paper hal-04236588, 2023.

Abstract: We study a growth model with two types of agents who are heterogeneous in their degree of family altruism. We prove that every equilibrium path converges to a unique steady state, and study the effect of altruism on the properties of steady-state equilibrium. We show that aggregate income is positively related to both level of altruism and altruism heterogeneity. When altruism heterogeneity is low, income inequality follows an inverse U-shaped pattern relative to the level of altruism, which is consistent with the crosscountry Kuznets curve. When altruism heterogeneity is high, income inequality monotonically decreases with the level of altruism. Our results suggest that heterogeneous altruism is an important mechanism linking economic growth and income inequality.

Steady-state Gini index and the level of altruism: moderate heterogeneity

General Equilibrium and Dynamic Inconsistency
(with Kirill Borissov and Ronald Wendner), CESifo Working Paper No. 9846, 2022.

Abstract: We study the role of expectations of naive agents in a general equilibrium version of the Ramsey model with quasi-hyperbolic discounting. When agents recognize others' naivete, as strongly suggested by empirical evidence, they revise consumption paths, correctly anticipating prices in a resulting sliding equilibrium (perfect foresight). When agents are unaware of others' naivete, as is typically assumed in the literature, they revise both consumption paths and price expectations (quasi-perfect foresight). We prove the existence of sliding equilibrium under perfect foresight for the class of isoelastic utility functions. We show that generically quasi-hyperbolic discounting matters for saving behavior: sliding equilibrium under perfect foresight is observationally equivalent to some optimal path in the standard Ramsey model if and only if utility is logarithmic. We compare sliding equilibria under different types of foresight and show that perfect foresight implies a higher saving rate, long-run capital stock, and consumption level than quasi-perfect foresight.

Structure of a sliding equilibrium under perfect foresight

Kantian Optimization with Quasi-Hyperbolic Discounting
(with Kirill Borissov and Ronald Wendner), CESifo Working Paper No. 9790, 2022.

Abstract: We consider a neoclassical growth model with quasi-hyperbolic discounting under Kantian optimization: each temporal self acts in a way that they would like every future self to act. We introduce the notion of a Kantian policy as an outcome of Kantian optimization in a given class of policies. We derive and characterize a Kantian policy in the class of policies with a constant saving rate for an economy with log-utility and Cobb–Douglas production technology and an economy with isoelastic utility and linear production technology. In all cases, the Kantian saving rate is higher than the saving rate of sophisticated agents, and a Kantian path Pareto dominates a sophisticated path.

We use Kant's categorical imperative as a as a principle of rationality in intrapersonal context

Work in Progress