Tag Archives: statistics

The Problem with Musical Chairs

Scott Sumner has a recent paper with the Adam Smith institute outlining the basic tenets of Market Monetarism. In this paper he discusses why the central banks should abandon inflation targeting and instead target the expected value of future nominal GDP (NGDP).

I have no disagreement on the policy advice. But I do have an issue with the way that Scott justifies his “musical chairs” model of employment. In particular, the key stylized fact — the countercyclicality ratio of wages divided by nominal GDP — is not unique to his model. As such, it does not provide any smoking gun for the market monetarist claim that fluctuations in nominal GDP are key to understanding the business cycle.

In the “musical chairs” model, we have a bunch of workers working for certain nominal wages. Along comes a nominal GDP shock. Then because wages and hours worked per person are sticky in the short run, there are fewer employment opportunities. “Musical chairs” refers to how everybody can be in a job (and dance around) so long as nominal GDP growth is humming along. But when the music stops, some are left without a chair and we are left with unemployment.

There is no arguing with this set of relations. The events I have described above are nothing more than a consequence of various accounting identities. The problem arises when Scott tries to ascribe a causal interpretation to this story. In his story, a monetary policy maker allows nominal GDP to fall because of a monetary policy error. Causality then flows through the wages and hours relationship, and as a result contractions in nominal GDP result in unemployment. Statistically, this means that we should see the ratio of total wages to nominal GDP ratio rise during recessions. Indeed, we see this relation.

Here is our disagreement. I cannot think of models of the macroeconomy in which we don’t see this relationship! Those who live by accounting identities are also doomed to die by them. I can rewrite the wages/NGDP relationship as:

Employment = NGDP/(nominal wages)

And so of course any increase in the wage/(nominal GDP) ratio is associated with a negative change in employment! This is true even in an RBC world in which recessions are caused by technology shocks. In that world, a negative technology shock pushes marginal workers out of the labor force, employment falls, and as such the ratio of nominal income to wages will increase.

Now, I still believe that a model of nominal GDP + sticky wages is a powerful framework. Wages are indeed sticky, as evidenced by a spike in the wage change distribution at 0. And if wages are sticky, monetary tightness and declining nominal GDP mean that people are paid high real wages and as such there are fewer jobs. Alternatively, you can view it as a liquidity issue as companies just don’t have enough nominal cash flows to pay those persistently elevated wages. So I don’t think there are too many issues with the underlying framework. I would just advise more caution on the way that statistical evidence is used.