We analyze the substitution bias in Laspeyres type price indexes, such as CPI, using 1959-1985 NIPA consumption data for 101 commodities. We employ two methodological approaches to calculation of the bias. First, we construct the tightest theoretical bounds on the COL by applyiong nonparametric methods, using algorithms developed by Afriat and by Varian. Second, following Diewert, we construct superlative price index formulas, namely Tornqvist and Fisher's Ideal indexes, under a chain as well as a fixed-base specification. Homothetic preferences are found to be consistent with the data, and sensitivitytests indicate that this result is not vacuous. If the hypothesis of homotheticity is maintained, the COL bias has upper and lower limits of 0.22 and0.14 percent per year, respectively. Using the superlative indexes as the measure of the COL, the bias is about 0.18 percent per year for the period 1959-85. This estimate is somewhat larger than found in earlier studies. Our useof more disaggregated data is found to be responsible for part of the difference, with the size of the estimated bias directly related to the extent of the aggregation.