Monday, September 27, 2010

Interpreting Declining Productivity Trends

A week or so ago, Stuart Staniford wrote a piece regarding declining productivity gains in the US economy.  I draw different conclusions.  Stuart's chart of the data is shown here, and he concludes that there is a long-term trend of decreasing productivity gains, which will have serious consequences in the not-too-distant future.

Before fitting a simple linear regression to this data, there may be adjustments that have to be made. In this case, the quarterly data is strongly autocorrelated; the growth rate in one quarter tends to reflect the growth rate of the previous quarter.  This type of data problem has been recognized for a long time: it was part of the time series course I took in graduate school in the 1970s.

With an adjustment for autocorrelation made, the decline in productivity growth looks much less drastic.  My version of the chart is shown here.  While the trend line ends up in about the same place, it starts from a much lower level in 1950 (my chart starts from the beginning of the data in 1947; Stuart discarded the first couple of years of data for innocuous reasons; including the earlier data does make a difference).  While the negative trend is not as steep as Stuart's graph suggests, it is still statistically significant.

But that's not the end of the story.  Suppose that you asked the same question -- is there a statistically significant long-term negative trend -- at different points in time.  In particular, suppose you asked that as each quarter's data was added over the last 30 years.  The next plot shows an answer to that.  Each bar represents the calculated linear trend, with adjustment for autocorrelation, using all data from 1947 to that point, but only if the t-value for the coefficient is significant at a reasonable level.  What this appears to show is that during and following most recessions1, the long-term trend looks like it has a negative non-zero coefficient; except for those periods, the linear trend coefficient is not significantly different from zero2.  In effect, what we see is a variation on Friedman's "plucking" model for business cycles and long-term growth, originally published in 1964.

While I may disagree with Stuart's statistics, I don't disagree with his concern about declining productivity growth.  There are a number of reasons to believe that productivity growth will slow in the future, and that such a slowing will have consequences (eg, see here).  It's a critically important topic, particularly in an era with declining energy availability.  But I don't believe that the data show that it's happening just yet.

1 The recession of 1991-2 was, according to most measures, a very modest one. The trend coefficient estimate was negative during that period, but was not significant.

2 There are a few quarters where the estimate for the coefficient is positive rather than negative. However, none of those estimates are statistically significant at the level used.

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