Uneasy Money

UPDATE:  See my correction of an error in the penultimate paragraph.

Last week I read an article Paul Krugman published several months ago for the New York Review of Books just before his book End This Depression Now came out. The article was aimed not aimed at an audience of professional economists, and consisted of arguments that Krugman has been making regularly since the onset of the crisis just over four years ago. However, the following passage towards the end of the article caught my eye.

[S]ince the crisis began there has been a boom in research into the effects of fiscal policy on output and employment. This body of research is growing fast, and much of it is too technical to be summarized in this article. But here are a few highlights.

First, Stanford’s Robert Hall has looked at the effects of large changes in US government purchases—which is all about wars, specifically World War II and the Korean War. Figure 2 on this page [see below] compares changes in US military spending with changes in real GDP—both measured as a percentage of the preceding year’s GDP—over the period from 1929 to 1962 (there’s not much action after that). Each dot represents one year; I’ve labeled the points corresponding to the big buildup during World War II and the big demobilization just afterward. Obviously, there were big moves in years when nothing much was happening to military spending, notably the slump from 1929 to 1933 and the recovery from 1933 to 1936. But every year in which there was a big spending increase was also a year of strong growth, and the reduction in military spending after World War II was a year of sharp output decline.

Krugman did not explain his chart in detail, so I consulted the study by Robert Hall cited by Krugman. Hall’s insight was to focus not on government spending, just military spending, because other components of government spending are themselves influenced by the state of the economy, making it difficult to disentangle the effects of spending on the economy from the effects of the economy on spending. However, military spending is largely driven, especially in wartime (World War II and Korea), by factors unrelated to how the economy is performing. This makes military spending an appropriate instrument by which to identify and estimate the effect of government spending on the economy.

The problem with Krugman’s discussion is that, although using military expenditures allowed him to avoid the identification problem associated with the interdependency of government spending and the level of economic activity, he left out any mention of the behavior of the price level, which, many of us (and perhaps even Krugman himself) believe, powerfully affects the overall level of economic activity. Krugman artfully avoids any discussion of this relationship with the seemingly innocent observation “there were big moves in years when nothing much was happening to military spending, notably the slump from 1929 to 1933 and the recovery from 1933 to 1936.” But even this implicit acknowledgment of the importance of the behavior of the price level overlooks the fact that the huge wartime increase in military spending took place against the backdrop of rapid inflation, so that attributing economic expansion during World War II solely to the increase in government spending does not seem to warranted, because at least some of the increase in output would have been been forthcoming, even without increased military spending, owing to the rise in the price level.

It is not hard to compare the effects of inflation and the effects of military spending on economic growth over the time period considered by Krugman. One can simply take annual inflation each year from 1930 to 1962 and plot the yearly rates of inflation and economic growth that Krugman plotted on his figure. Here is my version of Krugman’s chart substituting inflation for the change in military spending as a percentage of GDP.

It is difficult visually to compare the diagrams to see which one provides the more informative account of the fluctuations in economic growth over the 33 years in the sample. But it is not hard to identify the key difference between the two diagrams. In Krugman’s diagram, the variation in military spending provides no information about the variation in economic growth during the 1930s. There are is a cluster of points up and down the vertical axis corresponding to big positive and negative fluctuations in GDP with minimal changes in military spending. But large changes in GDP during the 1940s do correspond to changes in the same direction in military spending. Similarly, during the Korean War in the early 1950s, there was a positive correlation between changes in military spending. From the mid-1950s to the early 1960s, annual changes in GDP and in military spending were relatively small.

In my diagram plotting annual rates of inflation against annual changes in GDP, the large annual changes in GDP are closely related to positive or negative changes in the price level. In that respect, my diagram provides a more informative representation of the data than does Krugman’s. Even in World War II, the points representing the war years 1942 to 1945 are not far from a trend line drawn through the scatter of points. Where the diagram runs into serious trouble is that two points are way, way off to one side. Those are the years 1946 and 1947.

What was going on in those years? GDP was contracting, especially in 1946, and prices were rising rapidly, exactly contrary to the usual presumption that rising prices tend to generate increases in output. What was going on? It all goes back to 1942, when FDR imposed wartime price controls. This was partly a way of preventing suppliers from raising prices to the government, and also a general anti-inflation measure. However, the result was that there were widespread shortages, with rationing of a wide range of goods and services.  The officially measured rate of inflation from 1942 to 1945 was therefore clearly understated. In 1946 and 1947, controls were gradually relaxed and finally eliminated, with measured inflation rates actually increasing even though the economy was contracting.  Measured inflation in 1946 and 1947 therefore overstated actual inflation by an amount corresponding (more or less) to the cumulative understatement of inflation from 1942 to 1945. That the dots representing 1946 and 1947 are outliers is not because the hypothesized causal relationship between inflation and GDP was inoperative or reversed, but because of a mistaken measurement of what inflation actually was.

To get a better handle on the relative explanatory power of the government-spending and the inflation hypotheses in accounting for fluctuations in GDP than visual inspection of the data allows, one has to work with the underlying data. Unfortunately, when I tried to measure changes in military spending from 1929 to 1962, I could not reproduce the data underlying Krugman’s chart. That was not Krugman’s fault; I don’t doubt that he accurately calculated the relevant data from the appropriate sources. But when I searched for data on military spending since 1929, the only source that I found was this. So that is what I used. I assume that Krugman was using a different source from the one that I used, and he may also have defined his government spending variable in a different way from how I did. At any rate, when I did the calculation, I generated a chart that looked like the one below. It is generally similar to Krugman’s, but obviously not the same. If someone can explain why I did not come up with the same numbers for changes in government spending that Krugman did, I would be very much obliged and will redo my calculations. However, in the meantime, I am going to assume that my numbers are close enough to Krugman’s, so that my results would not be reversed if I used his numbers instead.

Taking my version of Krugman’s data, I ran a simple regression of the annual change in real GDP (dGDP) on the annual change in government (i.e., military spending) as a percentage of GDP (dG) from 1930 to 1962 (the data start in 1929, but the changes don’t start till 1930). The regression equation that I estimated was the following:

dGDP = 3.60 + .70dG, r-squared = .295.

This equation says that the percent increase in real GDP in any year is 3.6% plus seven-tenths of the percentage increase in government (i.e., military) spending for that year.

I then ran a corresponding regression of the annual change in real GDP on the annual change in the price level (dP, derived from my estimate of the GDP price deflator). The estimated regression was the following:

dGDP = 2.48 + .69dP, r-squared = .199.

The equation says that the percent increase in real GDP in any year is 2.48% plus .69 times that year’s rate of inflation.

Because the r-squared of the first equation is about 50% higher than that of the second, there would be good reason to prefer the first equation over the second were it not for the measurement problem that I mentioned above. I tried a number of ways of accounting for that measurement problem, but the simplest adjustment was simply to add two dummy variables, one for price controls during World War II and one for the lifting of price controls in 1946 and 1947. When I introduced both dummy variables into the equation, it turned out that the dummy variable for price controls during World War II was statistically insignificant, inasmuch as there was some measured inflation even during the World War II price controls. It was only the dummy variable controlling for the (mis)measured inflation associated with the lifting of price controls that was statistically significant. Here is the estimated regression:

dGDP = 2.76 + 1.28dP – 23.29PCON, r-squared = .621

I also tried attributing the inflation measured in 1946 and 1947 to the years 1942 to 1945, giving each of those years an inflation rate of about 9.7% and attributing zero inflation to the years 1946 and 1947. The regression equation that I estimated using that approach did not perform as well, based on a comparison of adjusted r-squares, as the simple equation with a single dummy variable. I also estimated equations using both the government spending variable and the inflation variable, and the two price-control dummies. That specification, despite two extra variables, had an r-squared less than the r-squared of the above equation. [Update 11/20/2012:  This was my mistake, because the best results were obtained using only a dummy variable for 1946 and 1947.  When the government spending and the inflation variables were estimated with a dummy for 1946-1947, the coefficients on both variables were positive and significant.]  So my tentative conclusion is that the best way to summarize the observed data pattern for the fluctuations of real GDP between 1929 and 1962 is with an equation with only an inflation variable and an added dummy variable accounting for the mismeasurement of inflation in 1946 and 1947.

Nevertheless, I would caution against reading too much into these results, even on the assumption that the provisional nature of the data that I have used has not introduced any distortions and that there are no other errors in my results. (Anyone who wants to check my results is welcome to email me at uneasymoney@hotmail.com, and I will send you the (Stata) data files that I have used.) Nor do I claim that government spending has no effect on real GDP. I am simply suggesting that for the time period between 1929 and 1962 in the US, there does not seem to be strong evidence that government spending significantly affected real GDP, once account is taken of the effects of changes in the price level. With only 33 observations, the effect of government spending, though theoretically present, may not be statistically detectable, at least not using a simple linear regression model. One might also argue that wartime increases in government spending contributed to the wartime inflation, so that the effect of government spending is masked by including a price-level variable. Be that as it may, Krugman’s (and Hall’s) argument that government spending was clearly effective in increasing real GDP in World War II and Korea, and would, therefore, be likely to be effective under other circumstances, is not as self-evidently true as Krugman makes it out to be. I don’t say that it is incorrect, but the evidence seems to be, at best, ambiguous.