A more cheerful picture of productivity growth than the official statistics give us emerges from new research into what has been happening at the level of individual firms.

Economists at the Wellington think tank Motu, David Maré and Dean Hyslop, together with independent researcher Richard Fabling, have figured out how to quality-adjust the labour input that goes into the calculation of productivity.

It turns out that in the period they looked at, from 2001 to 2012, average skill levels fell by some 1.8 per cent.

Adjusting for that means growth in labour input was weaker and (as output growth remains the same) productivity growth was stronger than would otherwise appear.

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The official productivity series from Statistics NZ says output in the measured sector (which excludes areas such as health and education, where productivity is much harder to measure) rose 2.9 per cent over the 11 years to March 2012. That is not much to show for 11 years, but the period straddled a nasty recession followed by a feeble recovery.

About two-fifths of the increase in output can be explained by a rise in hours worked; the rest is an improvement in labour productivity.

Labour productivity growth can be broken down, in turn, into a contribution from "capital deepening" - more capital plant per worker - and "multi-factor productivity", which is that remaining part of the growth in output which cannot be explained by increases in inputs of labour and capital.

It captures more intangible things like technological change and efficiency gains in the way firms do things, but also changes in skill levels.

One weakness of the traditional statistical approach is that it measures labour inputs in purely quantitative terms - headcount or hours worked.

"Such analyses implicitly assume there is no change in the quality of labour over time which, in the context of increasing levels of training and qualifications in New Zealand over the past decades, is open to question," say Maré and the other researchers.

But in fact, over the period they looked at, the average skill level of the workforce in New Zealand firms declined by 1.8 per cent.

That reflected strong growth in employment in the years preceding the recession. The labour market was tight, with unemployment rates wobbling around the 4 per cent mark. Skill shortages were a constant complaint in business surveys.

The surge in new, lower-skilled workers offset the effects of rising skills among the existing workforce, diluting the overall level.

Combined with the effects of the recession itself, when employment dropped less than output as firms hoarded labour, the upshot was pretty feeble multi-factor productivity growth - just 1.5 per cent altogether over the 11 years, or an average 0.14 per cent per annum.

Happily, this was combined with a 34.5 per cent increase in the capital input, delivering a 19.5 per cent rise in the ratio of capital to labour over the same period.

Capital deepening has been the bigger contributor to labour productivity growth since at least 2000 and especially since the 2008 recession.

On Statistics NZ's numbers, labour productivity has grown by an average 1 per cent a year between 2008 and 2014, with nine-tenths of that coming from more capital per worker and only one tenth from gains in multifactor productivity.

Capital deepening has been the bigger contributor to labour productivity growth since at least 2000.

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However when Maré and his co-researchers adjust the labour input for changes in skill levels, a less dismal picture emerges. On that basis, the labour input grew 13.3 per cent over the 11 years rather than 15 per cent on a (full-time equivalent) headcount basis.

The mathematical consequence is that multifactor productivity grew 2.7 per cent over that period, or 0.24 per cent a year on average - twice as good, or only half as bad, as the unadjusted measure.

Their proxy measure for skills is based on pay, a more realistic metric than formal qualifications.

The researchers had access to an extraordinarily rich set of data, affording a much more high-resolution picture of changing productivity performance and skills at the level of individual firms.

The data allowed them to track through time the performance of individual firms, which accounted for the vast majority of employment, while anonymised tax information told them who was employed by whom and when and how much they were paid.

When the researchers control for factors like age and gender, the pay rates give an indication of the person's relative value to his or her employer - a reasonable proxy for skill.

The dilution of skills occurred mainly in the years before the global financial crisis and in larger enterprises, which are better able to absorb less-skilled workers.

Employment growth has been strong again over the past couple of years. Should we expect a similar effect?

Not necessarily.

The period of skill dilution was one when labour force participation (the proportion of the working age population either working or actively seeking work) was trending higher and the unemployment rate was low. Over the past couple of years the participation rate has stabilised, at a high level, and unemployment is running about 2 percentage points higher than it was then.

Hiring intentions in ANZ's monthly survey of business sentiment, which had been sagging, rebounded last month to the highest level since June. But the labour market is nothing like as tight as it was in the mid-2000s.