Labour terms of trade and real wages

Several commenters on the previous post on the apparent disconnect between productivity and wages in the US pointed out that the choice of the deflator used to calculate real compensation might be a partial explanation. The standard theory of the firm expresses the real wage in terms of the price of output - not the price of consumer goods. Unfortunately for me - and for Econbrowser's Menzie Chinn, who made the same mistake - the BLS series for real compensation is deflated by the CPI index, not by the GDP deflator. (Thanks to tom in the comments for pointing this out).

But using the correct deflator turns out to be only a small step towards explaining the puzzle.

Here is a graph of the logs of hourly labour productivity and of real compensation using both the CPI and the GDP deflator:

Using the GDP deflator accounts for only a small fraction of the original gap.

This is not the first time that economists have puzzled over an apparent divergence between labour productivity and wages: this Brookings Papers on Economic Activity article from 1994 covers much the same ground. It may be that a fuller explanation lies in a better cost of living index - a dark and dense subject, upon which I can shed little light.

Even though the divergence between the two price indices is at best a minor contributor to the current puzzle, it's still interesting to see how they have evolved over time. Here is a plot of the ratio of the GDP deflator to CPI - i.e., labour's terms of trade - in Canada and the US since 1961:

When the labour terms of trade are improving, producer prices are rising faster than consumer prices: even if labour productivity is constant, workers' real buying power will increase. This happy state of affairs is what we saw in Canada during the period before the oil shock: between 1961 and 1975, improving labour terms of trade increased workers' buying power by an extra 15% on top of the increase due to productivity gains. In the US, meanwhile, the terms of trade were fairly stable.

The next fifteen years were not pleasant in either country: declining terms of trade reduced buying power by 10%, countering (and possibly more than countering) whatever gains were generated by higher productivity. Although they stabilised in Canada sometime around 1990, the terms of trade continued to fall in the US. (Or did they stabilise in 2000?)

Although movements in the labour terms of trade may not explain what's going on this cycle, they do offer an interesting perspective on the economic and political issues that have dominated the last few decades.

Update: Well, the 'puzzle' has been downgraded to a curiosity, thanks to the kind intervention - and not inconsiderable patience - of tom's comments. Menzie Chinn at Econbrowser has added a graph for the entire sample; I've prepared this just for comparison purposes:

Although real compensation is still lagging productivity, deviations of this size have occurred before - hence the downgrade to 'curiosity' status.

So the good news is that we don't have to drastically revise our understanding of how wages are determined. But the policy implications for a steadily deteriorating terms of trade for labour are still with us:

Comments

[tom]

Stephen,

How about trying this to solve the puzzel.

Go to the St.Louise Fed website here:

http://research.stlouisfed.org/fred2/release?rid=47&soid=22

Then under Productivity and Costs try these data sets: For productivity use -> Business Sector: Output Per Hour of All Persons; for compensation use -> Business Sector: Compensation Per Hour; and for the price deflator use -> Business Sector: Implicit Price Deflator.

Deflate the Compensation Per Hour by the Implicit Price Deflator to get Real Compensation Per Hour. (Do not use the Real Compensation Per Hour series on the website since, as we talked about earlier, it is deflated by a consumption deflator - the CPI). You can then compare the two series (productivity and real compensation) from 1947 to 2006. As you will see, the puzzel disappears, and as economic theory says, compensation is linked to productivity.

[tom]

Stephen,

In my haste I made a mistake. Please use the NONFARM Business Sector for the above data sets.

[Stephen Gordon]

Ah. That does shrink the gap to an accumulated shortfall of only 4%, so that accounts for about half of the gap in the original graph that used CPI.

(Oops - missed your correction. It's getting late, so I'll look at it again tomorrow. Again, thanks very much.)

[Menzie Chinn]

It's not clear it's a mistake to deflate by the CPI-U. If one wants to measure the real compensation from the perspective of the worker rather than the firm, then one would want to do exactly what BLS does. If one wants to see whether firms are equating the marginal product of labor to the real product wage (i.e., the wage deflated by the price of the firm's output) then one should do what Lazear did in his presentation.

I've now appended a graph of the wage deflated by the nonfarm business sector deflator (CEA preferred), by the CPI-U (BLS reported), and by CPI-RS (the research version of the CPI), preferred by some commentators, all against output per hour in the nonfarm business sector. See here

[tom]

When comparing productivity and compensation, I think the choice of the deflator boils down to how one believes workers are compensated. If you believe as I do that workers are compensated by employers on the basis of what they are producing, then one should use the output price deflator. On the other hand, if you believe workers are compensated on the the basis of what they consume, then use the consumption deflator.

[tom]

Menzie makes a great point when he writes, "If one wants to see whether firms are equating the marginal product of labor to the real product wage (i.e., the wage deflated by the price of the firm's output) then one should do what Lazear did in his presentation."

When testing economic theory use the output deflator.