Bubble Necessity Theorem
Tomohiro Hirano, Alexis Akira Toda
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Asset price bubbles are situations where asset prices exceed the fundamental values defined by the present value of dividends. This paper presents a conceptually new perspective: the necessity of bubbles. We establish the Bubble Necessity Theorem in a plausible general class of economic models: with faster long-run economic growth (G) than dividend growth (G_d) and counterfactual long-run autarky interest rate (R) below dividend growth, all equilibria are bubbly with non-negligible bubble sizes relative to the economy. This bubble necessity condition naturally arises in economies with sufficiently strong savings motives and multiple factors or sectors with uneven productivity growth.