In the comments thread to a recent post, Brad de Long argues against my claim that it’s appropriate to focus on multifactor productivity, pointing out
falling prices of IT have led to an *enormous* increase in the rate of capital deepening. Stagnant capital productivity and slow growth in multifactor productivity are not inconsistent with rapid growth in labor productivity if capital goods become really cheap really fast…
On reflection, I think Brad is correct at least in principle. The point he makes reflects the distinction between “embodied” productivity growth, which arises from better and cheaper machines, and “disembodied” productivity growth, which is the residual captured in multifactor productivity calculations. The remaining issue is how the numbers work out
The BLS estimates that the rental price for capital services has been fell by about 2 per cent per year from 1995 to 2000, so if the GDP deflator was rising by around 1 per cent, that makes a real price decline of 3 per cent. This seems plausible – Sichel estimates that the real cost of computing services is declining by about 8 per cent a year (17 per cent for hardware, 8 per cent for software, 0 per cent for computing services labor), computing services are still well under half of all capital services, and the real decline for other capital services is modest.
Now for a back of the envelope exercise which I think works out OK for a simple Cobb-Douglas technology with coefficients of two-thirds for labor and one-third for capital. To keep the capital share of national income constant at one third, you would want real capital stock per hour worked to grow at 4.5 per cent annually yielding growth in output per hour of 1.5 per cent per year. If you add in MFP and trend labor composition growth of 1 per cent, you get labor productivity growth of 2.5 per cent per year, which fits the late 90s almost exactly, as does the implied decline in output per unit of capital of 1.0 per cent per year. Add in trend labor force growth of 1 per cent per year, assume constant hours per worker, and the growth rate required to maintain a stable unemployment rate is 3.5 per cent.
All this is exactly in agreement with Brad’s own analysis of the historical average performance from 1960 to 2001, and the assumption that the period 1995-2000 was about average, not as good as the 1960s, but a lot better than the 1980s. The main difference from the average is that the relationship between embodied and disembodied productivity growth has switched. For the entire period, embodied growth is about 1 per cent and disembodied (TFP + composition) about 1.5 per cent.
The big question is how to interpret the experience from 2001 onwards with the unprecedently rapid decline in hours, and the corresponding rise in measured productivity, reaching a growth rate of 4 per cent per hour. In a previous post, I argued that labor composition effects such as the declining employment of teenagers could account for as much as 1 percentage point. Taking account of the fact that labor composition changes were already having a modest positive effect, I’d prefer a net additional impact of around 0.75 per cent. Now if we assume that growth in the capital stock did not decline by as much as growth in hours worked, yielding, say an extra 2.25 percentage points of capital deepening, we can get an extra 0.75 per cent productivity growth from this source. The total extra productivity growth induced by declining hours, then gives extra annual growth of 1.5 percentage points. Added to the ‘underlying’ growth rate of 2.5 per cent, this gives 4 per cent, which matches Brad’s graph exactly.
On the basis of this preliminary analysis, I don’t see any need to suppose that there has been an upward shift in underlying productivity growth since 2000. What remains puzzling is the macroeconomic behavior of the US economy during the bubble and bust.