Another month, another suspenseful buildup to inflation statistics and anticipation of the Federal Reserve’s response to them. Because inflation and the Fed’s response are so important for both the economy and politics, it’s worth understanding precisely what the various measures of inflation are.

It’s not so simple. One market-based measure is the dollar’s value against gold. By that measure the dollar has declined over decades so that, as of this writing, one needs about 1,955 of them to purchase an ounce of gold.

Most Americans buy a lot of things other than gold, though. In an effort to track the prices of all those other things, the federal government has developed two different measures: the Consumer Price Index, or CPI, and the Personal Consumption Expenditure Price Index, or PCE. The CPI comes from the Department of Labor’s Bureau of Labor Statistics, while the PCE comes from the Department of Commerce’s Bureau of Economic Analysis.

The government inflation numbers are imperfect. Even the government admits that. The key problem is that while the government can track prices pretty well, it’s much less good at tracking how people dynamically adjust to price increases by changing their behavior.

The best index, the Bureau of Labor Statistics acknowledged in a 2011 analysis, would reflect “consumer substitution” as “relative prices change.” Alas, “in practice,” such indexes “are difficult to implement in real time because such indexes require expenditure data for the period that is current, and such data are not available.”

This may seem arcane, but it has huge implications for policy and politics. If, say, the price of beef goes up but the price of chicken goes down, a family may be able to keep its dinner price constant by eating more chicken and less beef. What matters to most families is the price of dinner, not the price of beef.

An inflation statistic that measures only beef prices without also capturing the fact that families are buying less steak and more chicken gives a misleading picture of what’s happening in the real economy.

The fight over measuring inflation dates back more than 100 years to two German economists, Ernst Louis Etienne Laspeyres and Hermann Paasche. Laspeyres, who died in 1913, developed an inflation index that is the model for the Consumer Price Index. It measures prices but ignores whether people buy more or less of an item because of the substitution effect. The index developed by Paasche, who died in 1925, measures the prices but also captures the changes in quantities of items consumed.

The Personal Consumption Expenditure Price Index is a “Fisher-Ideal” formula, named after the American economist Irving Fisher. It is the geometric average of a Laspeyres index and a Paasche index. If you want a pure Paasche index from the government, you are out of luck, so far as I can tell. The government doesn’t release it, even though doing so might calm some of the concern about the effects of rising prices.

A few concrete examples will help illustrate the point about the inadequacy of the government inflation numbers. A chairman of the Council of Economic Advisers during the Obama administration, Jason Furman, who now teaches at Harvard, observes that one component of the PCE index is the “price” of “Portfolio management and investment advice services.”

These asset management fees, typically a fixed percentage of assets under management, “effectively automatically go up/down when the stock market goes up/down.” If your retirement account goes up ten percent and your asset manager charges you a flat annual fee of 1 percent, or 0.1 percent, of your account value, the government counts those now-increased fees as “inflation.” 

Transportation is another one that is hard to get a fix on. A lot of white-collar workers still are not commuting to work five days a week. What happens to parking costs or gasoline prices is less relevant if your commute several days a week consists of rolling out of bed and turning on the computer.

Even the all-in cost of a “vehicle mile traveled” matters less if an employee or freelancer is staying home. Relatedly, if the price of a restaurant dessert for a business lunch has soared, that’s less painful when it’s infrequent and one is, as a “remote” employee,  more often eating a dessert baked at home.

George Gilder’s new book “Life After Capitalism” offers the example of a hammer and a nail gun. A government accounting of the price of a hammer isn’t so helpful; what contributes to the construction costs is the time and price of sinking a nail into a two-by-four. 

Even comparing apartment rents in a single place from year to year may be a distorted measure. People move: “Leaving New York for Miami Can Save Nearly $200,000,” a Bloomberg News headline advises. The CPI and the PCE don’t really capture that dynamism.

Republicans don’t want to hear this; they’d rather run for election blaming Biden’s spending for runaway inflation.  The public-employee unions and retirees who are core Democratic constituents don’t want to hear this, either; high inflation numbers are key to negotiating higher wages and pension cost-of-living adjustments. 

Even the Fed chairman, Jerome Powell, might not want word to spread that without heroic central bankers riding to the rescue with precisely calibrated monetary policy, markets and families have a way of adjusting to price changes with their own quiet power.