  Using a compilation of measurements of the stellar mass density as a function
of redshift we can infer the cosmic star formation history. For z < 0.7 there
is good agreement between the two star formation histories. At higher redshifts
the instantaneous indicators suggest star formation rates larger than that
implied by the evolution of the stellar mass density. This discrepancy peaks at
z = 3 where instantaneous indicators suggest a star formation rate around 0.6
dex higher than those of the best fit to the stellar mass history. We discuss a
variety of explanations for this inconsistency, such as inaccurate dust
extinction corrections, incorrect measurements of stellar masses and a possible
evolution of the stellar initial mass function.
