We survey the variance-bounds tests of asset-price volatility, stressing the econometric aspects of these tests. The first variance-bounds tests of the present-value relation reported apparently striking evidence of excess volatility of asset prices. The statistical significance of the results, however, was either marginal or, in the case of model-free tests, impossible to assess. Moreover, the tests were soon criticized for a number of biases. Various other tests of the present-value relations were later developed, avoiding in different degrees the econometric problems attending the first-generation tests also found excess volatility, though sometimes of borderline statistical significance. This finding of excess volatility is robust and is difficult to explain within the representative-consumer, frictionless-market model. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.
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