American workers lose their jobs when carburetors they once made are imported instead. The federal data notices the decline in employment but fails to revalue the carburetors or even pinpoint that they are foreign-made. Because it seems as if $100 carburetors are being produced but fewer workers are needed to do so, productivity falsely rises — in the national statistics.

“We don’t have the data collection structure to capture what is happening in a real time way, or what is being traded and how it is affecting workers,” said Susan Houseman, a senior economist at the W.E. Upjohn Institute for Employment Research in Kalamazoo, Mich., who has done pioneering research in the field. “We have no idea how to measure the occupations being offshored or what is being inshored.”

The statistical distortions can be significant. At worst, the gross domestic product would have risen at only a 3.3 percent annual rate in the third quarter instead of the 3.5 percent actually reported, according to some experts at the conference. The same gap applies to productivity. And the spread is growing as imports do.

That may help to explain why the recovery from the 2001 recession was a jobless one for many months and why the recovery from this recession is likely to generate few jobs for many months.

In addition, more detailed import data would help to explain wage inequality, by linking some low wages more accurately to particular industries exposed to import competition.

On another front, many argue that labor productivity is rising faster than the pay of workers who made the greater productivity possible. That argument would be watered down if more accurate data showed that productivity had been overstated.

“What we are measuring as productivity gains may in fact be changes in trade,” said William Alterman, assistant commissioner for international prices at the Bureau of Labor Statistics.

The federal agencies that compile the nation’s statistics increasingly acknowledge that they lack the detailed data needed to calculate the impact of imported goods and services as imports rise from an insignificant 5 percent of all economic activity 35 years ago to more than 12 percent today, not counting petroleum. As a result, many imports are valued as if they were made in the United States and therefore higher in price than their imported counterparts.

The problem is particularly acute in manufacturing. Imported components constitute an ever greater share of the computers, autos, appliances and other finished merchandise that roll off assembly lines in the United States — and an ever greater share of all of the nation’s imports.

But the statistical system is not yet up to the task of sorting out which components are made here, which are made overseas and the resulting impact on employment. As Lori G. Kletzer, an economist at the University of California, Santa Cruz, put it, “We don’t know what jobs have been offshored.”

The same holds for services. An accounting firm in New York with 50 employees outsources some of its functions to less expensive accountants in India: the paperwork on an income tax return, for example. That work comes back to New York by computer transmission and is billed at New York rates, as if it were value added in this country.

Grappling with these blind spots, nearly all of the 80 experts at the conference, which was sponsored by the Upjohn Institute and the National Academy of Public Administration, agreed that the statistics now published tend to overstate the strength of the economy. That view was shared by those who attended from the Bureau of Economic Analysis, the Bureau of Labor Statistics and the Federal Reserve, all big players in measuring economic performance.

The stated goal, among those at the conference, is to repair the statistics, but that requires several years, lots of money (from Congress) to gather more information about what companies are doing, and whole new procedures for measuring imports. Much of the conference was devoted to an analysis of the gap between existing data and reality, and ways to close that gap.

Imports and exports are recorded, of course, as they enter and leave the country. The American trade deficit speaks volumes. But when it comes to who gets what import — particularly which manufacturer gets what component or what metal or what machine — these details are not gathered.

Instead, the federal agencies use an import price index, much of it imputed from small samples, that fails to capture just when an auto company switches from a domestically made carburetor to a less expensive Chinese model, and whether that shift is in all of the company’s plants or just those in Michigan.

“We can’t pick up the price shift,” Mr. Alterman said. “We are not designed to do that.”