In the United States, a large fraction of transaction among banks takes place over Fedwire, which is an electronic payments system operated by the Federal Reserve System. During 2008, on an average day, 521,000 payments were made over Fedwire, with a total value of $2.7 trillion. The median value of such transactions was $24,000, and the average value was $5.8 million. To put this in context, annual GDP in 2008 was $14.3 trillion, so average total daily transactions over Fedwire were about 19% of total annual GDP. Do these statistics indicate that there might be some large measurement error in the official U.S. national income accounts, or is this entirely consistent with official GDP numbers being accurate measures of aggregate economic activity

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Do these statistics indicate that there might be some large measurement error in the official U.S. national income accounts, or is this entirely consistent with official GDP numbers being accurate measures of aggregate economic activity?

The statistics about transactions among bank has nothing to do with a country's GDP. The GDP measures the market value of all the final and legal goods and services produced within a country during a given period. Money being transferred form one bank to another has nothing to do with the production of goods and services.

E.g. I have money on banks A, B and C. Today I decided that I would transfer $10,000 from my account on bank A to my account on bank B because I am interested in cash deposit. After looking at the interest rates paid by a CD, i decided it is not worth it. So I transfer my $10,000 out of bank B, but this time I'm sending it to my account on bank C. During the past 2 days I transferred $20,000 between banks but actually didn't add 1¢ to the country's GDP.