J.W. Mason has an interesting series of posts over at slack-wire on the relationship between productivity growth, changes in the unemployment rate and changes in labor force participation. Productivity is a huge determinant of living standards and of GDP growth projections moving forwards. Mason's posts led me to ask the following question. Given the importance of labor productivity growth in determining the standard of living of the average American, how confident are we that it has actually fallen? And how confident are we that labor productivity growth has fallen permanently.

Figure 1 is a plot of US labor productivity from 1948Q1 through 2016Q2. The mean (plotted as the red line) is 1.42 and the standard deviation is 1.53. The data, from FRED II, is quarterly GDP measured in 2009 dollars divided by total non-farm payrolls and expressed as an annual percentage four quarter rate of change. A few features stand out from Figure 1. First, productivity growth is highly volatile. Second, it is less volatile in the second half of the sample, and third, the mean appears lower after 1980. But I wouldn’t bet the farm on the fact that the mean of productivity has fallen permanently.

One way to test this is to split the data into two subsamples and compare the means. This is what I do in Figure 2. The top sample is the data from 1948Q1 to 1982Q1. The second is from 1982Q2 to 2016Q2. The red line in each case is the common mean.

** ****Mean Std Dev.**

**Common Sample 1.42 1.53**

**First Subsample 1.46 1.82**

**Second Subsample 1.38 1.18**

In each case, the mean of the second subsample lies well within one standard deviation of the mean of the second sample. Given reasonable assumptions about the distribution of these random variables, a formal hypothesis test would not reject the assumption that the means of the productivity distributions for the two subsamples are the same.

Figure 3 plots smoothed density estimates for the two subsamples from Figure 2. These estimates help gain a visual impression of the likelihood of observing a given value for productivity growth, before and after 1982Q1.

In each of these two graphs, the blue curve represents data from 1948Q1 through 1982Q1 and the red line represents data from 1982Q2 through 2016Q2.

The graph in the top panel smooths the data using a smoothing window that is chosen on the assumption that each sample comes from a normal distribution. The graph in the lower panel uses a wider window to average adjacent points. This wider window takes account of the fact that the distributions may not be normal and may instead have fat tails.

What do I learn from Figures 1 through 3? There is evidence for a reduction in the volatility of labor productivity growth after 1982. This is what is sometimes referred to as the 'Great Moderation'. There is weaker evidence for a reduction in the mean of labor productivity growth. Even during the 1950s and 1960s there were many years when labor productivity growth was negative, sometimes by as much as 2% per year. In the post 1980 period there are fewer years with large positive increases in labor productivity, but also fewer years with large drops.

Has productivity growth fallen permanently? The jury is still out.