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Using a compilation of measurements of the stellar mass density as a functionof redshift we can infer the cosmic star formation history. For z < 0.7 thereis good agreement between the two star formation histories. At higher redshiftsthe instantaneous indicators suggest star formation rates larger than thatimplied by the evolution of the stellar mass density. This discrepancy peaks atz = 3 where instantaneous indicators suggest a star formation rate around 0.6dex higher than those of the best fit to the stellar mass history. We discuss avariety of explanations for this inconsistency, such as inaccurate dustextinction corrections, incorrect measurements of stellar masses and a possibleevolution of the stellar initial mass function.

The Evolution of Stellar Mass Density and its Implied Star Formation History