Inflation and Price Measurement: A Primer

“When the official statistics on economic growth understate real economic growth, it reduces public faith in the political and economic system.” Martin Feldstein, Journal of Economic Perspectives, Spring 2017.

People use a variety of statistics to gauge how the economy is doing. And policymakers need data to guide their actions and evaluate their performance. How fast is the economy growing? Are prices rising quickly or slowly? The answers to these questions are based on measures like real gross domestic product (GDP) and the consumer price index (CPI). As it turns out, it is fairly straightforward to measure nominal GDP, so the challenge of estimating real growth arises from the need for accurate measures of prices.

Price measurement also is key for inflation-targeting central bankers, who need a number as a guide and for public accountability. To be credible, that number must be based on an index constructed using established scientific methods. The properties of the number―how well it reflects what it is we are trying to measure―affects both how the target is set and how policy is used to achieve its goal.

Reflecting a set of well-known (and nearly insurmountable) difficulties, measured inflation has an upward bias. That is, the inflation numbers that statistical agencies report are consistently higher than the theoretical construct we would like to compute. As a direct consequence of this upward bias in inflation measurement, our estimates of growth in real output and real incomes are systematically too low.

The big question today is whether the bias in inflation measurement, and hence the bias in the measurement of growth, has increased in recent years. As Martin Feldstein describes in detail, the answer to this question is important, as it affects how we collectively view long-run progress. If published statistics show sluggish real growth, as well as slow growth in real wages and incomes, then people may be unduly pessimistic, with younger generations expected to fair no better than their parents. A worsening bias would add to that pessimism.

In practice, however, careful recent analysis suggests that inflation measurement bias has not changed much since the early 2000s. For the CPI, the best estimate is that inflation currently is overstated by roughly 0.85 percentage points per year, while the price index of personal consumption expenditures (PCE) overstates inflation by roughly 0.5 percent points annually.

Before getting to the details, we start with a general discussion of how economy-wide prices are measured and the sources of upward bias. The most prominent price measure is the CPI computed by the Bureau of Labor Statistics (BLS). The CPI is designed to answer the following question: “How much more would it cost today to purchase the same basket of goods and services that was bought at some fixed date in the past?” Importantly, in answering this question, the CPI focuses on out-of-pocket expenditure. In contrast, the PCE price index includes expenditures that are not paid for directly. These include medical care paid for by employer-provided insurance, as well as government-supplied Medicare and Medicaid. (For a detailed comparison of the CPI and the PCE price index, see here and here.)

Stepping back, a typical consumer price index is intended to measure the inflation experience of a “representative” consumer or household. To construct the index, the government statisticians use expenditure surveys to figure out what consumers buy and where they buy it. In the process, four types of mistakes give rise to bias: substitution of one good for another in consumption, variation in shopping patterns, changes in the quality of goods, and the introduction of new goods.

The first difficulty is that consumer-purchasing patterns change all the time, while surveys are infrequent. As the relative prices of goods change, consumers will tend to shift their expenditure patterns away from the goods that have become more expensive and towards those that have become less expensive. The willingness to make such substitutions lessens the impact of relative price changes on consumers’ standards of living. However, to the extent that statisticians fail to take such substitution possibilities into account, overall measures of consumer price inflation will be subject to substitution bias.

Moulton’s up-to-date estimates indicate that substitution bias alone leads the published CPI to overstate inflation by 0.40 percentage points per year. Because of differences in the weighting formulas―the CPI has fixed weights that are adjusted every two years, while the PCE price index is chain-weighted, so the weights change every quarter―the substitution bias in the PCE price index is much smaller: just 0.05 percent points per year. Put differently, by re-setting the basket weights each quarter, the PCE price index reflects the changes in consumer-purchasing habits more rapidly than the CPI.

As an aside, we should note that there is a version of the CPI—called the Chained CPI—that uses a scheme in which weights change frequently like those of the PCE index. On average, from 1999 to 2017, when the CPI rose by 2.14 percent per year, the Chained CPI rose by 1.87 percent and the PCE price index by 1.84 percent. That is, the long-run trend in the PCE price index is 0.30 percent per year lower than that of the CPI, and very close to that of the Chained CPI.

Returning to the sources of overstatement, failing to account for changes in where consumers shop gives rise to outlet-substitution bias. If consumers shift to stores that charge lower prices—think Walmart or Costco—statisticians need to shift where they gather their price data. If they don’t, it imparts an upward bias to the CPI. In practice, Moulton estimates outlet-substitution bias at only 0.08 percentage points per year.

The greatest challenges for constructing an accurate price index arise from changes in the quality of the goods and services, as well as the inclusion of new goods. Failure to take into account all the improvements in the quality of a good or service—known as quality-change bias—leads to yet another source of inflation overstatement. Suppose, for example, that all cinemas raise ticket prices when they introduce elaborate new sound systems that enhance the overall movie-going experience. If consumers willingly pay the higher ticket prices because they value the greater sound and picture quality, but statisticians simply record the higher ticket prices without account for the changed quality, then reported inflation will exaggerate the true, quality-adjusted increase of prices.

Finally, new goods bias arises when the statisticians fail to recognize the introduction of new goods or services on which consumers spend a significant fraction of their income. The distinction between genuinely new goods and new varieties of existing goods is not always clear cut, although few would dispute that smart phones or fully self-driving cars are genuinely new goods, while more durable shoes or clothing, say, are simply better varieties of existing goods. Delays in recognizing the introduction of new goods that are subsequently purchased by most consumers may impart an upward bias to a consumer price index because such goods typically experience rapid price declines following their introduction that would be omitted from the index.

These last two sources of bias—changes in quality and the introduction of new goods—are conceptually very similar: when the quality of a good improves, we could just treat it as an entirely new good. Consequently, they are frequently lumped together in computing their impact. Combining these effects, Moulton estimates that the CPI and the PCE price index are subject to an upward bias of 0.37 and 0.45 percentage points per year, respectively. (For a list of papers that examine price measurement bias, see the reference section of Moulton’s recent report.)

The following chart brings together the estimates for these various sources of bias. Importantly, these numbers are smaller than those from the well-known 1996 Boskin Commission report, which concluded that the CPI overstated inflation by 1.1 percentage points per year. But they are roughly the same as those in a 2003 study by Lebow and Rudd. That is, there were large statistical improvements immediately following the Boskin Commission’s report―the BLS implemented a broad array of methodological changes to reduce the bias―but there has been virtually no change in the estimated bias over the past 15 years. (For a list of major changes in CPI methodology over the past 20 years, see Moulton’s Appendix B.)

Estimated Bias in the CPI and PCE Price Index (Percentage Points Per Year)

Source: Table 5,  Moulton (2018) .

Source: Table 5, Moulton (2018).

To be sure, many people are skeptical of the idea that things like measurement bias from the introduction of new goods are no bigger today than a generation ago. It sure feels as if technology has been advancing faster—especially when you are watching how frequently your smart phone is downloading updates. And what about all that “free” digital content like Google and Facebook? As we argued in an earlier post, because information technology goods and services account for less than one percent of what people buy, mismeasurement of their prices has only a very small impact on inflation. Health care, with a weight of 8 percent of the CPI and 17 percent of the PCE price index, is a completely different story. (It is also important to keep in mind that food, energy and shelter―items where technological change plays a fairly modest role―combined account for over half of the CPI.)

As for all the free stuff, Google and Facebook provide services in the same way as newspapers, radio and television did in the 20th century. They make a deal with us: services in exchange for advertising. As Nakamura, Samuels, and Soloveichik show, to a large extent, Internet services supported by advertising have substituted for advertising supported media of other types.

Returning to where we started, we need to understand what is happening to real growth and inflation both in the short run and over the long run. Calculating these requires accurate measures of prices. But price indices suffer from well-known upward biases. That is, statistical measures of inflation overstate true inflation. This overstatement has important implications.

In the case of monetary policy, the fact that standard price indices like the CPI and the PCE price index have an upward bias means a central bank that wants to achieve true price stability has to aim at a numerical target that is greater than zero. But, as we have discussed before, since monetary policymakers don’t want properly measured prices to fall on average over long periods of time, they will target true numbers that are above zero. This asymmetry means that the actual number will equal the bias plus some buffer against the risk of deflation. The fact that their conventional policy tool—nominal interest rates—can’t go much below zero only makes this asymmetry worse. Taken together, these considerations provide the rationale for targets like 2 percent—the number chosen by the FOMC for its PCE price index target.

Finally, there is the issue of the impression people have about their own welfare. To fully appreciate the consequence of overstating inflation, take the simple case of real median household income in the United States. Using the conventional CPI, the Bureau of the Census reports average annual growth of 0.65 percent per year over the past two decades. That means incomes are doubling every 108 years. However, if the CPI overstates inflation by 0.8 percentage points per year, correctly measured real incomes are doubling once every 47 years—or more than twice as fast. We agree with Feldstein that reporting persistent stagnation of real income, as opposed to modest growth, can significantly diminish public support for our market-based economic system.