Estimating market power is often complicated by a lack of reliable marginal cost data. A number of empirical studies identify industry competition and marginal cost levels by estimating the firms' first order condition within a conjectural variations framework. Few studies, however, have analyzed the accuracy of this technique. In this paper, we use direct measures of marginal cost for the California electricity market to measure the extent to which estimated mark-ups and marginal costs are biased. Our results suggest that the technique poorly estimates mark-ups and the sensitivity of marginal cost to cost shifters.