In his entry, "Consumer Price Indexes," in The Concise Encyclopedia of Economics, Michael Boskin concludes that the CPI overstates inflation by 0.8 to 0.9 percentage points annually. That doesn't add up over the years; it compounds up. Here's a key paragraph:
The CPI currently overstates inflation by 0.8-0.9 percentage points: 0.3-0.4 points are attributable to failing to account for substitution among goods; 0.1 for failing to account for substitution among retail outlets; and 0.4 for failing to account for new products. Thus, the first 0.8 or 0.9 percentage points of measured CPI inflation is not really inflation at all. This may seem small, but the bias, if left uncorrected for, say, twenty years, would cause the change in the cost of living to be overstated by 22 percent.
Now Peter Klenow of Stanford University and Huiyu Li of the Federal Reserve Bank of San Francisco have found a further source of upward bias in the CPI: failure to account correctly for new goods and services that replace inferior old goods and services. In "Missing Growth from Creative Destruction," they write:
Products such as electronics and apparel are particularly affected because their quality changes frequently. The BLS uses several methods to adjust for these changes. These methods, and the Boskin Commission's critique of them, focus on updates made by existing producers, or "incumbents," to their own products. But what happens when a producer is replaced by a different producer--for example, when a new restaurant forces a nearby restaurant out of business because customers prefer their menu?
When a product disappears without being replaced by a new version from the same producer in the same location, the BLS typically fills in or "imputes" the missing price and then starts tracking a new item. In particular, the BLS imputes inflation for the disappearing item to be the same as inflation for similar products that remain on the market. The BLS resorts to such imputation roughly twice as often as it directly estimates quality changes (Aghion et al. 2017).
By the way, they use the term "inflation" in the above quote in a way that is not normally used. Inflation typically refers to increases in the prices of goods and services in general, not an increase in the price of a particular good. But it doesn't undercut their point.
Here's the problem:
In doing such imputation, the BLS assumes the inflation rate is the same for changeovers from old to new producers as it is for all surviving items. This may not be an accurate assumption of the true values. Research since Schumpeter (1942) highlights growth driven by so-called creative destruction. Under creative destruction, new producers replace existing producers precisely because they introduce a product with a lower quality-adjusted price. The items that survive are those that do not experience creative destruction. Most of these surviving items have not been updated at all, according to the BLS. Hence, by using the inflation of surviving products to approximate the inflation rate of products that disappear, the BLS could be overstating the inflation rate of the disappearing products.
Read the whole thing, which is not long, for the rest of their reasoning.
Their bottom line:
Although the bias does not explain much of the sharp decline in productivity growth, its magnitude is economically significant--nearly 0.6% per year on average, or about one-fourth of true growth.
Moreover, they note one implication of their finding that undercuts a claim by Klenow's colleague Raj Chetty:
Measuring real growth properly is useful for addressing a host of questions. For example, existing studies use measured inflation to calculate the real income of children relative to their parents. Chetty et al. (2017) find that 50% of children born in 1984 achieved higher incomes than their parents at age 30. Adjusting for missing growth would raise the real income of children about 17% relative to their parents, increasing the fraction of those who do better than their parents by a meaningful amount. Thus, to the extent that inflation is overstated due to imputed values, a larger fraction of children appear to be better off economically than their parents. This improvement in economic welfare can shine a bit more positive light on current conditions, despite the gloom of slower productivity growth.