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The Federal Reserve, an institution I respect greatly as an information source, just came out with an analysis of America’s real manufacturing output, and though I hate to say it, it looks like the central bank has blown it.

According to the Fed’s release yesterday on June industrial production, “For the second quarter as a whole, manufacturing production rose at an annual rate of 6.7 percent….” That sounds great, of course, but it’s not what’s shown by the Fed’s data tables if I’m reading them correctly.

Second quarter manufacturing production covers the period from April through June, right? So we’re looking at the change from March to April, April to May, and May to June. The Fed’s data tables for manufacturing, using the North American Industry Classification System, show that manufacturing output expanded from the index number of 100.4178 in March to 101.3206 in June. (These figures aren’t actual production amounts, whether in value or volume terms, but production expressed using an index with the 2007 level representing 100.)

The way I was taught, to get the annualized growth rate for the quarter, you take the actual growth in percentage terms and multiply it by four. So 101.3206 minus 100.4178 equals 0.9028. You divide that by the 100.4178 March number and you get a (solid) 0.0899 percent quarterly growth rate. You then multiply that by four to get the quarter’s annualized growth rate (since there are four quarters in a year). The product: a shade under 3.60 percent. Again, that’s a nice number, but it’s not 6.70 percent. So “Washington, we seem to have a problem.”