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Economists object to using the CPI to adjust for inflation in contracts for several reasons in addition to the substitution bias. Two of the main problems concern the choice of weights and adjustments for quality improvements or new goods, but there are other, additional drawbacks.
First, the CPI is an inaccurate measure of the inflation you face if you buy a bundle of goods that's very different from that of the average urban consumer. Thus, the CPI tends to be an inaccurate measure of inflation for people who live in a rural area (where both prices and goods consumed differ from those in urban areas) or who have unusual tastes. Large increases in oil prices during the 1970s and early 1980s, for example, caused the CPI to rise rapidly because urban consumers use a great deal of gasoline and oil. Someone who didn't drive as much or who used wood or coal as a home heating fuel did not see relevant prices rise as fast as the CPI suggested.
William Noel Blisard and James R. Blaylock ("Construction of True Cost of Food Indexes from Estimated Engel Curves," American Journal of Agricultural Economics, 73(3), August 1991:775-83.1991) calculate cost-of-food indexes (using 16 goods) and show that biases differ across demographic groups for 1980-1985. They find, for example, that the true cost-of-food index rose 21.8% for a nonwhite, single-person household in the Northeast, whereas the inflation rate for a comparable white household was 0.7% higher in 1983. Inflation rates also vary with family size: The inflation rate for a single-person household was 1.8% higher in 1985 than the inflation rate for a five-person family that bought a different bundle of goods.
Second, the failure of the government to adjust adequately for quality improvements in goods and for new goods leads to an upward bias. For example, the power of computers has increased substantially every year for many decades. Failing to account for this improvement biases the change in the price of computers upward. The quality-adjusted price of computers has fallen much more than the unadjusted measure that the government used in the past.
Third, the CPI does not include prices for pollution or goods and services that are produced in the home. Fourth, the government does not measure the prices of many durable goods accurately. In earlier versions of the CPI, a bad decision concerning housing prices led to very large upward biases in the CPI. Even after some improvements in the methodology, measuring changes in housing prices remains one of the major problems with the CPI.
Fifth, tax bracket creep has been a major problem. Michael R. Baye and Dan A. Black ("Income Taxation, Labor Supply and the Theory of Income-Based Cost-of-Living Indices," European Economic Review, 36(1), January 1992:83-100) note that, in the past, the United States had tax bracket creep: Over time, inflation increased workers' nominal incomes, pushing them into higher tax brackets. To keep their utilities constant over the period 1972-1982, their incomes would have had to rise 0.7% per year more rapidly than prices. Thus, tax bracket creep more than offset the substitution bias. Recent changes in tax laws have apparently reduced or eliminated bracket creep.