The vector autoregressive approach for testing present value models is applied to a heterogeneous-agent asset pricing model using historical observations of the S&P 500 index. Besides fundamentalists, who value assets according to expected dividends, the model features rational and contrarian speculators. Agents choose their strategy based on evolutionary considerations. Supplementing the standard present value model with speculative agents dramatically improves the model's ability to replicate observed market dynamics. In particular, the existence of contrarians can explain some of the most volatile episodes including the 1990s bubble, suggesting this was not a rational bubble.
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