Debunking Disagreement Over Cost-Of-Living Adjustment

I’ve spent much of the 2010s trying to make the case that American living standards are better, and have improved more than the conventional wisdom would suggest. The flood of overly pessimistic analyses and claims could occupy my entire workweek if I had nothing else to do and were to focus daily on pushing back against it. Unfortunately, making the case that the conventional wisdom is wrong involves some moderately technical arguments about how we measure income and prices and about the proper demographic context for understanding income trends. That means that my attempts to show that the conventional wisdom is wrong have required a lot of methodological throat clearing, repeated each time, before I can get to showing more accurate results.

No more. I’m intending to write one or more reference documents to which I’ll simply link when writing about living standards in the future. In this one, I focus on how to adjust income growth for the rise in the cost of living. There is disagreement about the best way to do so.

Let me be clear: there should not be. Read on and you will understand why, and you will hear my thoughts on why most analysts are still “doing it wrong.”

So-called “price indices” attempt to measure the price of consuming goods and services that yield a constant level of “utility” (satisfaction) over time. If prices go up but the things we buy get better, then we may get more satisfaction from what we buy despite the price increases. If the things we buy don’t get any better but prices drop, that too is a gain in utility and a fall in the cost of living. In contrast, if prices go up and the things we buy don’t get better at the same rate, then the cost of living will rise.

Adjusting incomes for increases in the cost of living is an undisputed prerequisite for assessing income trends. If median income doubles over several decades but the cost of living doubles correspondingly, then there has been no increase in “real” income. In this scenario, $80,000 would buy the same level of satisfaction that $40,000 bought years earlier.

There are any number of technical issues that make price measurement imprecise, and the issues are bigger the longer the period between income comparisons. We must accept that we cannot know the “true” increase in the cost of living. But many commentators, in my experience, jump from this uncontroversial fact to a sort of nihilism that denies entirely the usefulness of attempting to assess income trends. Well, OK, but then we can justify any policy affecting the income distribution by saying “who knows?” Another camp, oddly, uses the measurement issues associated with estimating the cost of living to justify using the conventional indices used by the Census Bureau and a majority of researchers, without bothering to argue the merits of those and alternative indices.

However, within the limits of our ability to measure prices accurately, some indices capture changes in the cost of living better than others. And quite simply, the most-used indices are inferior to an index created by the Bureau of Economic Analysis in the Commerce Department—the “Personal Consumption Expenditures (PCE) deflator.” Again, there should be no controversy about this, as I will proceed to demonstrate.

For a long time, analysts of income trends relied on the “Consumer Price Index for All Urban Consumers (CPI-U)” to account for the rising cost of living. But this was a relatively crude measure. It had a number of methodological and computational problems. In particular, its treatment of the cost of homeownership was flawed prior to 1983. This problem was severe enough that in mid-1989 the Bureau of Labor Statistics—the agency in charge of producing the CPI-U—recommended that researchers conducting trend analyses use an alternative index, the “CPI-U-X1.” This alternative attempted to correct the homeownership flaw all the way back to 1967, and it showed less inflation over time than the CPI-U did. By the time of the BLS statement, the Congressional Budget Office had already abandoned the CPI-U for the CPI-U-X1. The Census Bureau began using the CPI-U-X1 for income trend analyses in 1993.

It is worth emphasizing: the major federal agencies analyzing income trends stopped using the CPI-U for that purpose two decades ago. But even prominent researchers have relied on it in recent years. Thomas Piketty and Emmanuel Saez used it in their original income concentration analyses and continued to do so through the mid-2000s. A year and a half ago, Arindrajit Dube used it to claim (wrongly) that the minimum wage would be $10.60 if it were at its 1968 level of purchasing power. And Michael Greenstone and Adam Looney used it four years ago to argue (incorrectly) that men’s earnings had fallen by 28 percent between 1969 and 2009.

This is not an ideological point. A number of liberal and pessimistic analysts have long used price indices other than the CPI-U, including the researchers at the Economic Policy Institute and the Center on Budget and Policy Priorities. And Piketty, Saez, and Dube changed to better price indices when the flaws of the CPI-U were pointed out to them. None of these researchers use what I will argue is clearly the best inflation measure, but they all have accepted that the CPI-U should not be used to look at long-term income trends.

The CPI-U-X1 corrected the housing-cost problem, but other shortcomings remained. Over the last twenty years, a number of improvements have been made to the CPI-U and CPI-U-X1 (which indicate the same inflation from 1983 forward). Perhaps most importantly, twenty years ago, neither the CPI-U nor the CPI-U-X1 accounted for consumer “substitution,” a failure that strongly overstated the rise in the cost of living. Consumers are not helpless when the price of something we enjoy goes up. While we are generally unambiguously worse off for the price increase, we can partially mitigate the loss in utility by buying more of other things that aren’t growing more expensive. I will say it again, because past experience tells me that many people will misunderstand the importance of substitution bias: when the price of something that is valued by people goes up without the quality improving, people are worse off. But they are less worse off than they would otherwise be because they can substitute cheaper items for those that have become more expensive. They are not indifferent between having what they used to have before prices went up and what they have after substituting.

The CPI-U did not account for such substitution until 1999, and to this day it does not fully account for the ability of consumers to respond to relative price changes. Since 1999, the CPI-U recognizes that consumers can buy more red delicious apples when gala apples become more expensive, but it does not recognize that consumers can buy more oranges when apples become pricier.

The Bureau of Labor Statistics created, in 1999, another price index—the “CPI research series using current methods,” or “CPI-U-RS”—to try to extend backward in time to late 1978 the better treatment of substitution and other improvements made to the CPI-U over the years. To be clear, the CPI-U, today, does not include retroactive improvements for earlier years. Using the CPI-U means ignoring the existence of a measure—the CPI-U-RS—that tries to take today’s much improved CPI-U and to update the past CPI-U estimates to address acknowledged problems that have since been corrected.

Because it is clearly superior to the CPI-U, the CPI-U-RS is, today, the most widely used price index by analysts of income trends. Analysts largely followed the lead of the Census Bureau, which began using the CPI-U-RS in 2001. Today, income analysts generally use a price index series that relies on the CPI-U-RS going back to December 1978 (it shows the same inflation as the CPI-U from 1999 forward), and the CPI-U-X1 going back to 1967. (Prior to 1967, researchers committed to the CPI series must return to the demonstrably flawed CPI-U.)

The CPI-U-RS is a major improvement on the CPI-U and CPI-U-X1, but it has significant shortcomings that also overstate the increase in the cost of living over time. For one, the CPI-U-RS also fails to account for “upper-level substitution”—the ability of consumers to switch from apples to oranges (or from coffee to tea or from beef to pork) when the relative prices of the two change. Second, prior to December of 1978, the CPI-U-RS is like the CPI-U and CPI-U-X1 in not taking any account at all of substitution. Since many income analyses consider trends since 1969, that means that the 1969 to 1978 inflation trend is more biased upwards than the post-1978 trend (which is also biased upwards).

The Bureau of Labor Statistics has put out, since 2002, yet another price index—the “Chained Consumer Price Index,” or “C-CPI-U”—that does attempt to fully account for substitution bias. It is not difficult to see that the Bureau prefers the C-CPI-U to the CPI-U and CPI-U-RS, and any serious scholar of consumer theory would. Substitution bias is a universally acknowledged problem, and the C-CPI-U is the only index the Bureau has that might adequately address it. There are two problems with the C-CPI-U, though. The less important one is that it is produced with a lag. While preliminary estimates are released relatively quickly, the most recent year for which a final index value is available is currently 2012. Far more problematic is the fact that the C-CPI-U is available only back to 2000. That means it cannot be used for income analyses that examine trends beginning before 2000.

Fortunately, there is an alternative index that estimates trends in prices for consumer goods, fully addresses substitution, and that goes all the way back to 1929. We have arrived at the PCE deflator, which is the measure of inflation the Federal Reserve Board prefers to consult and the measure used by the Congressional Budget Office today in its income analyses.

Setting aside the issue of substitution, there are arguments about the extent to which the PCE deflator is or is not conceptually or methodologically more appropriate than the family of CPI measures. The PCE, for instance, is based on purchases made not only by households but by nonprofit organizations. It takes into account third-party payments for health care, and it differs from the CPI indices in other ways. (Although it is partly derived from CPI indices for various categories of goods and services.)

These objections are irrelevant. The PCE and the C-CPI-U are very consistent with each other in showing less inflation than the other CPI measures. This is true over the years for which the measures are all available:

And it is true if we estimate C-CPI-U values further back in time. In the following chart, I extend the published final C-CPI-U as follows. For both the C-CPI-U and the CPI-U-RS, for the years 2000-2012, I compute the annual change in each index. In each year, I compute the ratio of the change in the C-CPI-U to the change in the CPI-U-RS. I average this ratio across the years 2000-12 to create an adjustment factor. Finally, I use this adjustment factor, with the annual change in the CPI-U-RS for the years 1969-2000, to extend the C-CPI-U back to 1969. As the chart shows, this extended C-CPI-U series tracks the PCE very closely:

The chart shows that from 1969 to 2012, the PCE and my extended C-CPI-U series indicate that prices rose by a factor of 5, while the CPI-U-RS gives the ratio as 5.5 and the CPI-U as 6.3. These distinctions are important. If nominal income—income prior to taking the rising cost of living into account—rose by a factor of 7.2 over this period (as my own estimates suggest), using the CPI-U to adjust for inflation would give the conclusion that “real” income rose by 16 percent. Using the PCE or C-CPI-U, we would conclude that real income rose by 45 percent—nearly three times as much. For comparison, the CPI-U-RS would indicate a 31 percent increase—substantially lower than the estimate from indices that fully take substitution into account.

And even this is not the end of the story, because even the PCE deflator is likely to overstate the rise in the cost of living. A thorny problem is the way in which new goods and services are introduced to the “consumption bundle” that is priced out every year. In practice, it can be many years before a new product—such as the cell phone—is included in the consumption bundle. By then its price has often dropped significantly, meaning that the decline in its cost has been largely missed as its adoption has become more widespread. Another problem is the increasing difficulty of adjusting for “quality” improvements. Think about how much more value we get from a mobile phone or a personal computer with internet connection today than we did twenty years ago. So much of what is available over the internet is free or very low cost. How much would someone have had to pay in 1995 for what the iPhone provides today?

A prominent commission in 1996 estimated that the CPI-U overstated inflation between 1995 and 1996 by 1.1 percent, with a potentially larger bias in earlier years. A retrospective in 2006 by economist and former commission member Robert Gordon concluded that the bias was probably a bit higher than the commission guessed—1.2 to 1.3 percent—because it underestimated the importance of substitution bias, subsequently revealed by the C-CPI-U. And he estimated the overall bias to the CPI-U still amounted to at least 1.0 percent even after the improvements to the index over the subsequent decade.

The chart below repeats the last one but adds a new inflation trend line. The “Corrected CPI-U” line adjusts the annual change in the CPI-U downward by 1.0 percent point per year, a conservative adjustment given the Gordon conclusions. Prices rise by a factor of 4.2 according to this index—much less than the PCE and C-CPI-U would suggest.

With this rate of inflation, a 7.2-fold increase in nominal income would result in a 75 percent increase in real income rather than the 16 percent suggested by the official CPI-U. Using the PCE looks like a very conservative choice for cost-of-living adjustment in this context. Lowering the annual change in the CPI-U by half a percentage point instead of a full point yields basically the same increase in real income as does using the PCE.

The case for using the PCE deflator to adjust incomes for increases in the cost of living that eat into purchasing power is strong. The case for using the CPI-U-RS, the conventional choice, is fairly weak. The case for using the CPI-U is nonexistent. Why, then, is the CPI-U-RS rather than the PCE deflator the most popular price index?

In large measure, the reason is that analysts have tended to take their cues from the Census Bureau, which uses the CPI-U-RS for its income trend figures (but, inexplicably, still uses the CPI-U to adjust the poverty thresholds each year for trend analyses). Very few researchers—even within academia—have expertise in the methodologies of price adjustment (I do not either), so they trust in the decisions of the Census Bureau. I suspect that the Census Bureau uses the CPI-U-RS rather than the PCE deflator partly out of inertia and wanting to stay somewhat consistent with past publications and practices. There may also be internal political considerations, as the Census Bureau and Bureau of Labor Statistics often collaborate, and the latter has been in charge of developing the CPI family of indices.

But the Census Bureau still could use the CPI-U-RS for its historical poverty analyses, rather than the CPI-U, and it could use the C-CPI-U for analyses of more recent income and poverty trends or as a substitute for the CPI-U-RS from 2000 through the present. It already accepts disjunctures in its CPI-U-RS/CPI-U-X1/CPI-U series extending from before 1967 to the present. Or the Bureau of Labor Statistics could build a C-CPI-U-RS research series to attempt to extend the C-CPI-U back in time. More simply, it could just issue a statement that the PCE is the best price deflator available for long-term trend analyses of income.

There is also the reality that many parties in Washington and many outside parties interested in influencing Washington have biases in favor of analyses that convey gloomier news. Advocates and politicians on the left want to promote agendas that involve redistribution and more government intervention into markets. Politicians on the right, meanwhile, must tend to middle class anxieties (and most of these policymakers mistakenly believe, along with other Americans, that our problems are worse than they appear). Policymakers from both parties have an interest in painting a dour picture of the economy when their opponents are in power.

Meanwhile, academic and policy researchers on the left often believe that economic problems are relatively great, and so results that reinforce the view that we have calamitous problems help generate support for their preferred policies. Researchers across the ideological spectrum—and their institutions and funders—want to attract attention, which creates a bias in favor of more dramatic results. And journalists are largely left-leaning*, making them predisposed to believe gloomy economic news, eager to help people in need through their writing, and disproportionately likely to have relationships with left-leaning researchers producing work that corresponds with their priors. Even moderate and conservative journalists face pressures to find and report on dramatic results; if it bleeds it leads. Finally, the spread of overly gloomy results to policymakers, consumers of news, and citizens tend to give people the impression that things are worse than they are, reinforcing many of the dynamics that incentivize gloomy news in the first place. People are generally more pessimistic and negative in polling that asks about the economic problems of others than they are when asked about their own economic situation.

These are powerful forces working against knowledge of the state of our living standards. If you’ve read this far, the challenge is yours to accept: produce a reason to disbelieve the case I have made or change your priors about how well we are doing and hold others accountable in producing, disseminating, and publicizing economic research that conveys the truth as best it can.

* Among both social science faculty and journalists, self-identified liberals outnumber conservatives by roughly four to one. The Pew Research Center for the People and the Press found in 1995, 2004, and 2007 surveys of both national and local journalists that self-identified liberals strongly outnumbered conservatives (p. 55). In 2007, among national journalists, 32 percent declared themselves “very liberal” or “liberal” compared with 8 percent who declared themselves “very conservative” or “conservative”. In 1995, the figures were 22 percent and 5 percent. In contrast, nationally representative surveys of American adults and voters consistently find self-identified conservatives out-numbering liberals by a factor of two to one. For instance, averaging across all of the surveys in which it asked about ideology in 2012 in its daily tracking poll, Gallup found that 38 percent of Americans identify as conservative compared with 23 percent identifying as liberal.