The first is that I thought a little bit more research and data analysis on this topic on my part would be appropriate, given the huge amount of response this post received, Krugman included but not only.

What I did, therefore, was derive from my model what I call the "output-gap elasticity of the deficit." In a graph of the output gap on the horizontal axis and the deficit on the vertical axis, this is the slope of the relationship, aggregating the output-gap elasticities of all the constituent pieces.

In other words, an elasticity of +1 means that, for every 1 percentage point drop in the output gap, the deficit can be expected to rise by 1 percentage point as the result of solely cyclical factors. An elasticity of +4 implies a 4 percentage point increase in the cyclical deficit for every 1 percent drop in the output gap. (Note: A "drop" in the output gap means it becomes more negative, i.e. the economy is further below potential, whereas an "increase" in the gap means it becomes more positive, i.e. the economy is further above potential.)

Although you get a more accurate estimate of the structural deficit from breaking down to components, once you've estimated the elasticity, you can use this on the aggregates and get a very close estimate of the structural deficit. For example, if we had a structural deficit of 8 percent of GDP, an output gap of 6 percent of GDP and an elasticity of 1, as we do now, roughly speaking, then it follows our structural deficit is approximately 2 percent of GDP.

Here's what the output-gap elasticity of the deficit looks like, graphed, from 1953 to 2012:

So this should be pretty amazing, even if expected. My model indicates that there was very weak cyclicality in the deficit until the mid-1990s. Suddenly, deficit cyclicality emerges and becomes incredibly strong.

Although spending cyclicality has increased, further breakdowns of this data show that the increase in deficit cyclicality is almost entirely due to an increase in revenue cyclicality. The increase in revenue cyclicality, in turn, comes almost entirely from an increase in individual and corporate income tax revenue cyclicality.

Why is that?

First, spending side: cyclicality increases under Clinton and Obama. Clinton, because of his reductions in spending during the 1990s boom; Obama, because of a more aggressive response to the recession in income-support transfer payments. Second, revenue side: cyclicality increases under Clinton, Bush, and Obama. Clinton, because of the 1990s boom and the significant increase in income tax revenues amid that boom; Bush and Obama, because of significant drops in income tax revenues when their two recessions hit.

I have written, in the original Bloomberg post, that increasing income tax revenue cyclicality appears to be caused by an increasing amount of that tax burden being borne by the highest incomes (who have very volatile incomes.) Note I am not saying that the highest incomes are paying more as a percentage of their income; indeed, that is not true. I am saying that, as a share of total tax revenue, more of it is coming from the highest reaches of the income distribution. That is true.

And it is so because of increasing income inequality. As income inequality has increased, and a larger share of income goes to the top, the share of income tax revenues which come from the "volatile top" has also increased. The graph of the share of income taxes borne by the highest incomes has increased just in the same way that their share of income has increased.

[Reihan Salam of the

*National Review*also has comments on my post about revenue cyclicality.]

The second thing is that looking directly at the primary balance and the output gap is suggestive of cyclical deficits, but it's not sufficient proof -- this is why I broke down revenue tax-by-tax, and spending program-by-program. My process, for sure, is not proof of causation, but it narrows the amount of assumptions needed to draw a causational mechanism.

What I mean by that is, suppose in the last recession, instead of spending on federal income-security programs (like unemployment insurance) rising and revenues on individual and corporate income taxes falling, we saw payments to veterans and to seniors soar amid the recession.

Just looking at the aggregate level deficit, or even aggregate expenditure and revenue, will give a "false positive" for cyclicality.

Similarly, if spending in a structural category were to fall and spending in a cyclical category were to rise amid a recession, looking at the aggregates will give us a "false negative" for cyclicality.

So you do have to dig to the more detailed level in order to make a rigorous argument for cyclical causation of deficits. It's not airtight -- suppose there was a sudden structural increase in spending in a heavily cyclical program -- but it's much more convincing, especially when we might think there are structural changes which correlate with cyclical changes.

I'll post my data on the output gap elasticity of the deficit on the "Data" tab.

**Update: It seems I made a calculation error in my Excel spreadsheet. I have updated the graph, though the findings of this article do not change.**

What do the standard errors on this look like?

ReplyDeleteSo I just did an error analysis on this -- it took forever. The standard error of the slope obviously varies over time, but to give you some idea of what it is, the median value is 0.175, and the mean value is 0.237. (The skewness comes from the earliest values in the dataset and the 2007 recession.) So it's pretty good on an RSE basis.

Delete'As income inequality has increased, and a larger share of income goes to the top, the share of income tax revenues which come from the "volatile top" has also increased. The graph of the share of income taxes borne by the highest incomes has increased just in the same way that their share of income has increased.'

ReplyDeleteMore or less what Art Laffer promised, btw. Does Krugman actually realize the implications of this?

Evan, this is very interesting, but the graph doesn't seem to track the rise in inequality. Income inequality has steadily increased over 40 years, whereas this chart seems to show a one-time bump in cyclical responsiveness. Any thoughts?

ReplyDelete