There is no sticky wage puzzle By Scott Sumner

Most people find the NGDP shock/sticky wage theory of the business cycle to be at least slightly plausible. However I’m often asked why wages have not adjusted yet. Surely it doesn’t take 7 years for full adjustment to a negative demand shock?

A Bentley student named Daniel Reeves sent me a very interesting San Francisco Fed study of downward wage inflexibility and the business cycle, by Mary Daly and Bart Hobijn. Daniel immediately saw many places in the paper where the NGDP targeting approach would fit beautifully. (Ironically I don’t recall the study mentioning NGDP.) I think he’s right, but first I’d like to discuss why this is such a great study.

The authors create a mathematical model of the labor market, where they assume a given fraction of workers each year are resistant to wage cuts. The theoretical model predicts this sort of wage increase distribution:

There are several things to note here. The distribution is asymmetric, as far fewer workers get pay cuts than you’d expect if there were bell-shaped distribution. Many of the workers that would normally get pay cuts are bunched together at the zero wage change level, due to the assumed downward wage inflexibility. Second, the light grey line shows the wage distribution in the steady state (normal times) and the darker line shows the wage distribution 12 quarters after a severe negative demand shock. Notice that the negative shock compresses more wage gains close to zero.

The next graph shows the actual distribution of wage gains in 2006 (assumed to represent the steady state) and 2011 (a few years after a major negative demand shock:

It’s pretty clear that there is downward wage stickiness at zero. Indeed after this study (and earlier ones that reached similar conclusions) there really can’t be any doubt. There is no theoretical explanation for the spike at zero other than money illusion, and there is no explanation for the increase in the spike after a negative demand shock that doesn’t imply short-run non-neutrality of money.

The model also predicts that the frequency of zero wage changes will be highly correlated with the unemployment rate, peaking slightly after the unemployment rate peaks. See what you think:

But can it explain the slow recovery from the 2008-09 demand shock? Yes it can, indeed that’s exactly what the model predicts:

That’s because after a negative demand shock there are many years of “pent-up wage deflation.” It takes many years for the labor market to adjust and the economy to heal. On the preceding graph 30 quarters corresponds to 7 1/2 years. I should add that the model is calibrated for the current level of wage stickiness (indeed it assumes a bit less that the current level.) But in other periods wages may have been more or less downward sticky than today. For example, wages had soared during and immediately after WWI, and it was fairly widely understood that under a gold standard they might have to return to normalcy at some point. Thus wage cuts in 1921 were quite common.

To some extent this paper repeats work done by others, but they also go well beyond previous research. For instance, they have a very nice explanation for why the Phillips Curve bends at low inflation rates. I should add that although they use inflation as their nominal scale variable, Daniel’s probably right that it fits the NGDP story even better. Consider the following:

Note that productivity growth has the same “greasing effect” on the labor market as inflation. When productivity growth is high wages have the tendency to rise anyway, which makes downward nominal wage rigidities less binding.

Consider China, which has extremely rapid productivity growth, and hence very rapid nominal wage growth, despite an inflation rate that’s fairly similar to the US. Because the trend growth in nominal wages is so high in China, you’d expect downward wage inflexibility to be much less of a problem in China than in the US. I frequently argue that NGDP growth is often the best proxy for the welfare costs and benefits of inflation, better than inflation itself. This is one more such example, as NGDP growth is strongly correlated with productivity growth plus inflation.

Just as rapid NGDP growth can keep a country above the zero interest rate bound, even if they have low inflation, rapid nominal wage growth can keep a country away from the zero lower bound of wage increases, even if they have low inflation. But the good news is that NGDP growth need not be all that rapid; moving from 2% inflation to 10% inflation has little addition benefit in their model (which assumes 2.7% productivity growth.) They also point out that a combination of a negative productivity shock and negative demand shock is especially harmful in their model. Which pretty much explains the past 7 years.

To summarize, their model nicely fits the stylized facts of nominal wage stickiness, especially at the zero rate change level, and it explains all the key attributes of the severe recessions that hit the US and Europe in 2008, which were accompanied by a slowdown in productivity growth. I’ve often been critical of modern macro research, but this paper is a near perfect example of how to creatively combine theory and empirical work, in a fashion that actually explains the world we live in. Highly recommended.