Speculating on higher order beliefs

Higher order beliefs - beliefs about others' beliefs - may be important for trading behaviour and asset prices, but have received little systematic empirical examination. We study more than twenty years of evidence from the Robert Shiller Investor Confidence surveys, which directly elicit details on investors' higher order beliefs about the U.S. stock market. We find that investors' higher order beliefs provide substantial motivations for non-fundamental speculation, e.g., to buy into a stock market perceived to be overvalued. To explore the equilibrium implications, we construct a model of level k thinking that matches the evidence, where some speculative investors mistakenly believe that asset price movements are driven by other, less sophisticated investors. The model reveals that speculators' higher order beliefs amplify stock market overreaction and excess volatility; these phenomena persist in equilibrium due to investors' limited strategic reasoning.