[Paper Review] Housing Bubbles with Phase Transitions

Tomohiro Hirano, Alexis Akira Toda|arXiv (Cornell University)|Mar 20, 2023

Economic theories and models4 citations

TL;DR

This paper develops a rational bubble theory in an overlapping generations model with endogenous housing prices and rents, showing that housing bubbles emerge via a two-stage phase transition as homebuyers' income rises: first, bubbly and fundamental equilibria coexist; then, fundamental equilibria vanish entirely, making bubbles inevitable. The key result is that even with productive, non-reproducible housing, fundamental equilibria are inefficient in the coexistence region due to suboptimal intertemporal substitution and wealth concentration.

ABSTRACT

We analyze how equilibrium housing prices are determined in the process of economic development within an overlapping generations model with perfect housing and rental markets. We characterize the rent growth rate in all equilibria. The economy exhibits a two-stage phase transition: as incomes of home buyers rise, the equilibrium regime changes from fundamental to bubble possibility, where fundamental and bubbly equilibria coexist. With even higher incomes, fundamental equilibria disappear and housing bubbles become a necessity. We also discuss extensions and refinements such as equilibrium uniqueness, multiple savings vehicles, welfare implications, credit- and expectation-driven bubbles, and testable implications of our theory.

Motivation & Objective

• To resolve the theoretical puzzle of how rational housing bubbles can exist despite the Bubble Impossibility Theorem in dividend-paying assets.
• To analyze how income levels, credit access, and expectations about future income affect the emergence of housing bubbles in a dynamic general equilibrium setting.
• To investigate the welfare properties of equilibria with housing, particularly whether fundamental equilibria are efficient when bubbles coexist.
• To establish conditions under which housing bubbles are not just possible but inevitable due to structural phase transitions in the economy.

Proposed method

• Formulates a two-period overlapping generations model with endogenous housing demand, rent, and ownership prices.
• Introduces a competitive, frictionless market structure with rational expectations and separable preferences over consumption and housing services.
• Derives equilibrium conditions using the marginal utility pricing condition and characterizes the long-run growth path of housing prices and rents.
• Applies phase transition theory to show that the economy undergoes two critical thresholds as the young-to-old income ratio increases.
• Uses the Arrow-Debreu welfare criterion to assess efficiency, relying on the convergence of the sum of discounted Arrow-Debreu prices.
• Employs a detrended economy framework to analyze long-run efficiency and derive conditions for Pareto efficiency based on the growth rate of the risk-free rate relative to the economy’s growth rate.

Experimental results

Research questions

• RQ1 Under what conditions can rational housing bubbles exist in a dynamic general equilibrium model with endogenous rent and housing prices?
• RQ2 How do changes in homebuyers' income or access to credit influence the emergence and persistence of housing bubbles?
• RQ3 Why do fundamental equilibria become inefficient even though housing is a productive, non-reproducible asset?
• RQ4 What determines the transition from fundamental-only to coexistence of fundamental and bubbly equilibria, and when do fundamental equilibria cease to exist?
• RQ5 What are the welfare implications of housing bubbles, and when is a bubbly equilibrium Pareto efficient?

Key findings

• The economy undergoes a two-stage phase transition: as the young-to-old income ratio increases, it first transitions from fundamental-only to coexistence of fundamental and bubbly equilibria, then to a regime where only bubbly equilibria exist.
• When the income ratio exceeds the second critical threshold, fundamental equilibria disappear entirely, making housing bubbles inevitable for equilibrium existence.
• Even with low current income, housing bubbles can emerge if homebuyers have access to credit or hold high expectations of future income growth.
• In the coexistence region, fundamental equilibria are inefficient despite housing being a productive, non-reproducible asset, due to suboptimal intertemporal substitution and wealth concentration.
• Bubbly equilibria are efficient if the long-run risk-free rate grows faster than the economy’s growth rate; otherwise, they are inefficient.
• The fundamental equilibrium is always unique, and the bubbly equilibrium is unique if the elasticity of intertemporal substitution is not too far below 1/2.