Emergence of Housing Bubbles with Phase Transitions: The Role of Demand-Side Factors

We analyze how equilibrium housing prices are determined along with economic development in an overlapping generations model with perfect housing and rental markets, in which housing prices and rents are both endogenous. We focus on demand-side factors: home buyers income and the elasticity of substitution between consumption and housing. We characterize the long-run rent growth rate in all equilibria and show that, when this elasticity exceeds one (the empirically relevant case), rents grow more slowly than income. The economy then exhibits a two-stage phase transition in the income ratio of home buyers relative to home sellers. When this ratio is low, only fundamental equilibria exist. Above a first threshold, fundamental and bubbly equilibria coexist and the outcome is selected by self-fulfilling expectations. Above a second threshold, fundamental equilibria cease to exist and housing bubbles are necessary for equilibrium. We further prove that the fundamental equilibrium is always unique and the bubbly equilibrium is unique whenever the elasticity of intertemporal substitution is not far below 1/2. Uniqueness lets us study expectation-driven booms: if agents anticipate future income growth, housing prices rise and contain a bubble today even when current incomes lie in the fundamental region, with the price-income and price-rent ratios rising together. Finally, contrary to the common understanding that land eliminates dynamic inefficiency in overlapping generations models, we show that inefficient equilibria arise robustly, and only for intermediate income ratios.