In my previous post, I discussed Arthur Laffer’s op-ed in Monday’s *Wall Street Journal*, in which he argued that a comparison across 34 countries belonging to the OECD showed that the adoption of greater fiscal stimulus in the 2007-09 time period was bigger declines in the rate of economic growth. Laffer argued that this correlation provides conclusive empirical refutation of the Keynesian doctrine that additional government spending can stimulate economic recovery.

In my earlier post, I complained that Laffer had not explained the meaning of one of the variables — the change in government spending as a percentage of GDP — that he used to make his comparison, and did not provide an adequate source for where his numbers came from, noting that when I tried to calculate the same number using the data on the St. Louis Fed website, I arrived at a substantially smaller value for the US change in government spending as a fraction of GDP than Laffer’s reported. I also observed that the change in government spending as a percentage of GDP can rise not just because of an increase in government spending, but can also rise because of a contraction in total GDP, making the comparison Laffer was purporting to perform invalid, the comparison amounting to no more than a restatement of the truism that countries with bigger contractions in GDP would experience bigger reductions in their rates of growth than countries with smaller reductions in GDP.

JR, a diligent commenter to my post, kindly provided me with the source for Laffer’s numbers on the IMF website, confirming that the numbers Laffer used for the change in government spending as a percentage of GDP did indeed reflect the underlying data reported by the IMF. JR was unable to reproduce Laffer’s numbers for the change in real GDP growth, and neither could I. But when I calculated the changes and replaced them in Laffer’s table, I found a similar negative relationship and a better fit (higher r-squared) than shown in Laffer’s table. In either case, the main reason for the negative correlation is that a decrease in real GDP growth is, by definition, correlated with an increase in government spending as a percentage of GDP. So Laffer’s result is pre-ordained by his choice of variables.

To show what is going on, I provide below two scatter diagrams of Laffer’s table with his numbers and my corrections of the numbers. You can see that the downward slope of the regression line is steeper using his original numbers, but there is less variation around the regression line with the corrected numbers.

To see what happens when you eliminate the inherent negative correlation between the change in government spending as a percentage of GDP and the rate of growth of GDP, I recalculated the government spending variable as the real percentage change in GDP between 2007 and 2009. Substituting that redefined variable which is definitionally independent of changes in GDP gives me the following scatter diagram. The slope is still negative, but it is an order of magnitude less than the slope of the regression line implied by Laffer’s numbers.

I then tried on further variation which was to replace the change in the growth rate of real GDP between 2007 and 2009 with the change in real GDP between 2007 and 2009. Here is the scatter diagram for corresponding to that change in variables.

As you can see, the regression line now has a positive slope, though it is probably statistically insignificant given the very low value of the r-squared. But in view of the simultaneity issues, I mentioned in my previous post, that is hardly surprising.

Some readers are probably wondering why I bothered posting all this. I am asking myself the same question, but I just couldn’t help trying to figure out what Professor Laffer was up to. Perhaps this makes it all a bit clearer.

I put together a little piece on my view on the Lesser Depression:

http://socialmacro.blogspot.com/2012/08/the-balance-sheet-recession-hypothesis.html

Alright! I influenced a post. Except it’s “RJ”, not “JR” ;)

Totally facebooking this.

The last graph you produce has been used by Krugman many times now and I think is actually a step backwards from Laffer.

I say this for precisely your same criticism: there is an automatic correlation between change in government spending and change in GDP.

Start with Y = C + G, then dY = dC + dG.

So if the largest change is from government spending in a time period then change in GDP (dY) should, by definition, be directly related to the change in government spending (dG).

Further if the change in government spending was planned then by subtracting this amount from gdp (the x-axis value from the y-axis value at each data point) would reveal no multiplier effect.

Laffer at least attempts to relate the second order change in GDP to a first order change (d^2Y to dG), which to me is not so clearly a flaw from a definitional standpoint (like that which exists in Krugman’s graph). However it makes absolutely no sense to me why that would be a good intuitive relationship to establish either way.

Of course these charts by Laffer and Krugman make no sense at all from a statistical standpoint as you have said because of the simultaneity issues….

My analysis of Romney’s choice of Paul Ryan:

http://socialmacro.blogspot.com/2012/08/something-i-didnt-expect.html

I was able to reproduce Laffer’s numbers and posted an analysis of this numbers at http://usbudget.blogspot.com/2012/08/laffer-on-ineffectiveness-of-stimulus.html . As I mentioned at the end of the analysis, I believe that all publications should mandate that precise sources be given and, if possible, links be provided to background material that explains the author’s calculations. Anyhow, thanks for your analysis as it and other critiques helped prompt me to look more closely at Laffer’s numbers.

RJ, Sorry about getting your initials backwards. I guess that I am vulnerable to random attacks of dyslexia. In the future, I will try to catch them before going into print.

LAL, The definition Y = C + G, does not in and of itself impose a relationship between Y and G, a change in G could leave Y unchanged and simply be offset by an opposite change in C. Whether that is true or not depends on what the data show. But G/Y and Y are necessarily related, because a reduction in Y must increase G/Y unless G is reduced at least proportionately with Y.

R. Davis, Nice job. Glad that you found what I wrote helpful.