Just because economics relies on numbers doesn't make it a mathematical science. For example, gross domestic income — the costs incurred and income earned in the production of the nation's output — should equal gross domestic product (GDP).

It doesn't. Ever. The Bureau of Economic Analysis (BEA) adds up the two columns, draws a line and reconciles them with the notation, "statistical discrepancy."

Sometimes there are anomalies within GDP. BEA's third guess at first-quarter GDP was a lot weaker than growth implied by labor inputs (employment and hours worked). Real GDP growth was revised from 2.4 percent to 1.8 percent — one-fourth of last quarter's output gone in a flash!

The major source of the adjustment was to real consumer spending on services, which was slashed to 1.7 percent from 3.1 percent, based on new data from the Census Bureau's Quarterly Services Survey (QSS). The QSS, which gathers revenue from the sales of a wide range of services, is a relatively new addition to the BEA's statistical library.

Joe Carson, head of global economic research at AllianceBernstein LP, was quick to point out (to BEA, too) the inconsistency between reported GDP and output implied by an alternative method of calculation: using the sum of aggregate hours worked (the number of employees times the number of hours) and productivity.

"Hours worked in the private service sector is growing faster than output, which would imply a decline in productivity," Carson says. "If that were true, firms would be shedding workers rather than hiring."

Neil Dutta, head of economics at Renaissance Macro Research, has trouble with the math as well. Private hours worked for the overall economy rose 3.6 percent and productivity increased 0.5 percent in the first quarter, implying a 4.1 percent increase in GDP.

Could the Labor Department have overestimated employment and hours? "It's hard to see why," given solid growth in individual withholding and corporate taxes reported by the Treasury, he says. Tax data tend to be reliable because people don't withhold taxes, and corporations don't pay taxes on income they didn't earn. (Sometimes they don't pay it on earned income either.)

That leaves productivity growth, which is a derived number: output divided by hours worked. Mathematically, it has to be revised down with GDP. "Whether that's an accurate reflection, given strong tax receipts and hours, is the question," Carson says.

And one that may not be resolved anytime soon. This is a problem for Federal Reserve policymakers, who seem to be relying on high-frequency data to make decisions about the size of their monthly asset purchases, and financial markets, which are focused — for good reason — on the Fed's intentions.

Given the erratic nature of the data, taking a longer-term view would probably produce better results and might even allow markets to do the same. Heck, next month the BEA will release a comprehensive revision of the National Income and Product Accounts dating back to 1929. It's too soon to expect a reconciliation of the first-quarter's anomalies, but the Great Depression might undergo a tweak.

Caroline Baum is a Bloomberg View columnist.