“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.