Suppose for the sake of argument that the output of these intermediate suppliers had increased in unmeasured ways.

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So long as you can count final goods, unmeasured improvements in the supply of intermediate services will succeed in raising measured productivity.

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If unemployment is to be curbed, South Africans have to become more enterprising and the unmeasured numbers who somehow scrape a living encouraged into the formal sector.

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In fact, using this technique, we can move beyond the limitations of traditional approaches by running additional analysis to discover new, previously unmeasured categories based on recurring themes within the data.

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In late 2011, President Obama had EPA back off trillion-dollar ozone regulations (well, at least until 2013) in an outright, however reluctant, acknowledgement of the job impacts that otherwise go unmeasured.

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As a result, the ratio of output to input for those final-goods producers, which is to say their productivity, would be higher: it would reflect the unmeasured improvement in service-supplier productivity after all.

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Some are encouraged that the official jobless rate has stayed as low as 4.5% though there are reasons to think this number is artificially low because adjustments made to reflect unmeasured jobs in new start-ups may now be too big.

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Clinical results from any specialized cancer center are typically very difficult to reproduce in broader multicenter trials, in part because there may be differences, whether measured or unmeasured, between those presenting at renowned centers of excellence and those who remain close to home.

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