In response to one of the problems described in Reinsdorf (1994), the Bureau of Labor Statistics (BLS) has recently implemented a method to reduce 'formula bias'. This bias occurs when the BLS estimates a Laspeyres price index in which the quantity weights are measured in a past 'base period'. Current estimates of its magnitude rely upon either educated guesswork or strong parametric assumptions about the distribution of prices. In this paper I examine the bias of several different indexes without making the strong parametric assumptions of previous researchers by using Monte Carlo simulations. I do this by treating the price quotes collected by the BLS as a representative population from which price quotes can be sampled. The estimate of the bias using the old imputation method is lower than previous estimates, being about 0.20 points per annum for the commodities and services component of the CPI. The recently implemented seasoning method reduces the estimated bias to about -0.02. Although the bias of an index is sensitive to the base period of the Laspeyres, the simulations suggest that an index using seasoning is close to the Laspeyres index for reasonable definitions of the base period.