## Working Papers

General Equilibrium and Dynamic Inconsistency

(with Kirill Borissov and Ronald Wendner), CESifo Working Paper No. 9846.

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.

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

Dissonance Minimization and Conversation in Social Networks

(with Kirill Borissov and Mikhail Anufriev), CESifo Working Paper No. 9433. R&R in the Journal of Economic Behavior and Organization.

Abstract: We study a model of social learning in networks where the dynamics of beliefs are driven by conversations of dissonance-minimizing agents. Given their current beliefs, agents make statements, tune them to the statements of their associates, and then revise their beliefs. We characterize the long-run beliefs in a society, provide the necessary and sufficient conditions for a society to reach a consensus, and show that agents' social influences (weights on the consensus belief) are decreasing in their dissonance sensitivities. Comparing the outcomes of two models, with and without conversation, we show that conversation leads to a redistribution of social influences in favor of agents with higher self-confidence. Finally, we provide analytical insights for the model where agents minimize dissonance by revising both beliefs and network, and show that an endogenous change of network may prevent a society from reaching a consensus.

Network in the DeGroot model (left) and in the model with conversations (right)

## Publications

Economic Growth Models with Heterogeneous Discounting (with Kirill Borissov), Computational Mathematics and Mathematical Physics, 63 (3), pp. 337–359, 2023.

Abstract: A survey of theoretical economic growth models with agents having different subjective discount factors is proposed. The structure of equilibrium paths in such models, their dynamics and convergence to stationary equilibria, and the relationship with Pareto optimal paths are described. Models with socially determined discount factors in which time preferences are formed endogenously are discussed, and the basic difficulties associated with social choice in the case of heterogeneous discount factors are examined. The models presented in the paper shed light on internal mechanisms of a market economy that lead to the division of society into the rich and the poor.

Collective Choice with Heterogeneous Time Preferences, Journal of Economic Surveys, pp. 1–32, 2022.

Abstract: This paper reviews recent research on the aggregation of heterogeneous time preferences. Main results are illustrated in a simple Ramsey model with many agents with additively time-separable utility functions who differ in their discount factors. We employ an intertemporal view on this model and argue that preferences of a decision maker should be represented by a sequence of utility functions. This allows us to clarify the issue of dynamic inconsistency and relate it to simple properties of discounting. We distinguish between private and common consumption cases. In the private consumption case, we discuss the properties of sequences of additively time-separable social welfare functions and explain why the notion of Pareto optimality under heterogeneous time preferences becomes problematic. In the common consumption case, we focus on the problem of collective choice under heterogeneous time preferences, discuss the difficulties with dynamic voting procedures and review some ways to overcome them. We conclude by highlighting the implications of our discussion for the problem of choosing an appropriate social discount rate.

Economic Growth and Property Rights on Natural Resources (with Kirill Borissov), Economic Theory, 65 (2), pp. 423–482, 2018.

Abstract: We consider two models of economic growth with exhaustible natural resources and agents heterogeneous in their time preferences. In the first model, we assume private ownership of natural resources and show that every competitive equilibrium converges to a balanced-growth equilibrium with the long-run rate of growth being determined by the discount factor of the most patient agents. In the second model, natural resources are public property and the resource extraction rate is determined by majority voting. For this model we define an intertemporal voting equilibrium and prove that it also converges to a balanced-growth equilibrium. In this scenario the long-run rate of growth is determined by the median discount factor. Our results suggest that if the most patient agents do not constitute a majority of the population, private ownership of natural resources results in a higher rate of growth than public ownership. At the same time, private ownership leads to higher inequality than public ownership, and if inequality impedes growth, then the public property regime is likely to result in a higher long-run rate of growth. However, an appropriate redistributive policy can eliminate the negative impact of inequality on growth.

On Discounting and Voting in a Simple Growth Model (with Kirill Borissov and Clemens Puppe), European Economic Review, 94, pp. 185–204, 2017.

Abstract: In dynamic resource allocation models, the non-existence of voting equilibria is a generic phenomenon due to the multi-dimensionality of the choice space even if agents are heterogeneous only in their discount factors. Nevertheless, at each point in time there may exist a ``median voter'' whose preferred instantaneous consumption rate is supported by a majority of agents. Based on this observation, we propose an institutional setup («intertemporal majority voting») in a Ramsey-type growth model with common consumption and heterogeneous agents, and show that it provides a microfoundation of the choice of the optimal consumption stream of the «median» agent. While the corresponding intertemporal consumption stream is in general not a Condorcet winner among all feasible paths, its induced instantaneous consumption rates receive a majority at each point in time in the proposed intertemporal majority voting procedure. We also provide a characterization of stationary voting equilibria in the case where agents may differ not only in their time preferences, but also in their felicity functions.