Last week I did a post based on a chart that I saw in an article in the New York Review of Books by Paul Krugman. Relying on an earlier paper by Robert Hall on the empirical evidence about the effectiveness of fiscal stimulus, Krugman used the chart to illustrate the efficacy of government spending as a stimulus to economic recovery. While Krugman evidently thought his chart was a pretty compelling visual aid in showing that fiscal stimulus really works, I didn’t find his chart that impressive, because there were relatively few years in which changes in government spending were clearly associated with large changes in growth, and a lot of years with large changes in growth, but little or no change in government spending.
In particular, the years in which government spending seemed to make a big difference were during and immediately after World War II. The 1930s, however, were associated with huge swings in GDP, but with comparatively minimal changes in government spending. Instead, changes in GDP in the 1930s were associated with big changes in the price level. The big increases in GDP in the early 1940s were also associated with big increases in the price level, the rapid rise in the price level slowing down only in 1943 after price controls were imposed in 1942. When controls were gradually lifted in 1946 and 1947, inflation increased sharply notwithstanding a sharp economic contraction, creating a spurious (in my view) negative correlation between (measured) inflation and the change in GDP. From 1943 to mid-1945, properly measured inflation was increasing much faster than official indices that made no adjustment for the shortages and quality degradation caused by the price controls. Similarly, the measured inflation from late 1945 through 1947, when price controls were being gradually relaxed and dismantled, overstated actual inflation, because increases in official prices were associated with the elimination of shortages and improving quality.
So in my previous post, I tried to do a quantitative analysis of the data underlying Krugman’s chart. Unfortunately, I only came up with a very rough approximation of his data. Using my rough approximation (constructing a chart resembling, but clearly different from, Krugman’s), I ran a regression estimating the statistical relationship between yearly changes in military spending (Krugman’s statistical instrument for fiscal stimulus) as a percentage of GDP and yearly changes in real GDP from 1929 to 1962. I then compared that statistical relationship to the one between annual changes in the price level and annual changes in real GDP over the same time period. After controlling for the mismeasurement of inflation in 1946 and 1947, I found that changes in the rate of inflation were more closely correlated to changes in real GDP over the 1929-1962 time period than were changes in military spending and changes in real GDP. Unfortunately, I also claimed (mistakenly) that that regressing changes in real GDP on both changes in military spending and inflation (again controlling for mismeasurement of inflation in 1946-47) did not improve the statistical fit of the regression, and did not show a statistically significant coefficient for the military-spending term. That claim was based on looking at the wrong regression estimates. Sorry, I blew that one.
Over the weekend, Mark Sadowski kindly explained to me how Krugman did the calculations underlying his chart, even generating the data for me, thereby allowing me to reconstruct Krugman’s chart and to redo my earlier regressions using the exact data. Here are the old and the new results.
OLD: dGDP = 3.60 + .70dG, r-squared = .295
NEW: dGDP = 3.26 + .51dG, r-squared = .433
So, according to the correct data set, the relationship between changes in government spending and changes in GDP is closer than the approximated data set that I used previously. However, the newly estimated coefficient on the government spending term is almost 30% smaller than the coefficient previously estimated using the approximated data set. In other words a one dollar increase in government spending generates an increase in GDP of only 50 cents. Increasing government spending reduces private spending by about half.
The estimated regression for changes in real GDP on inflation changed only slightly:
OLD: dGDP = 2.48 + .69dP, r-squared = .199
NEW: dGDP = 2.46 + .70dP, r-squared = .193
The estimated regression for changes in real GDP on inflation (controlled for mismeasurement of inflation in 1946 and 1947) also showed only a slight change:
OLD: dGDP = 2.76 + 1.28dP – 23.29PCON, r-squared = .621
NEW: dGDP = 3.02 + 1.25dP – 23.13PCON, r-squared = .613
Here are my old and new regressions for changes in real GDP on government spending as well as on inflation (controlled for mismeasurement of inflation in 1946-47). As you can see, the statistical fit of the regression improves by including both inflation and the change in government spending as variables (the adjusted r-squared is .648) and the coefficient on the government-spending term is positive and significant (t = 2.37). When I re-estimated the regression on Krugman’s data set, the statistical fit improved, and the coefficient on the government-spending variable remained positive and statistically significant (t = 3.45), but was about a third smaller than the coefficient estimated from the approximated data set.
OLD: dGDP = 2.27 + .49dG + 1.15dP – 13.36PCON, r-squared = .681
NEW: dGDP = 2.56 + .33dG + 1.00dP – 13.14PCON, r-squared = .728
So even if we allow for the effect of inflation on changes in output, and contrary to what I suggested in my previous post, changes in government spending were indeed positively and significantly correlated with changes in real GDP, implying that government spending may have some stimulative effect even apart from the effect of monetary policy on inflation. Moreover, insofar as government spending affects inflation, attributing price-level changes exclusively to monetary policy may underestimate the stimulative effect of government spending. However, if one wants to administer stimulus to the private sector rather than increase the size of the public sector at the expense of the private sector (the implication of a coefficient less than one on the government-spending term in the regression), there is reason to prefer monetary policy as a method of providing stimulus.
The above, aside from the acknowledment of Mark Sadowski’s assistance and the mea culpa for negligence in reporting my earlier results, is all by way of introduction to a comment on a recent post by my internet buddy Lars Christensen on his Market Moneterist blog in which he welcomes the looming fiscal cliff. Here’s how Lars puts it:
The point is that the US government is running clearly excessive public deficits and the public debt has grown far too large so isn’t fiscal tightening exactly what you need? I think it and the fiscal cliff ensures that. Yes, I agree tax hikes are unfortunate from a supply side perspective, but cool down a bit – it is going to have only a marginally negative impact on long-term US growth perspective that the Bush tax cuts experiences. But more importantly the fiscal cliff would mean cuts in US defense spending. The US is spending more on military hardware than any other country in the world. It seems to me like US policy makers have not realized that the Cold War is over. You don’t need to spend 5% of GDP on bombs. In fact I believe that if the entire 4-5% fiscal consolidation was done as cuts to US defence spending the world would probably be a better place. But that is not my choice – and it is the peace loving libertarian rather than the economist speaking (here is a humorous take on the sad story of war). What I am saying is that the world is not coming to an end if the US defense budget is cut marginally. Paradoxically the US conservatives this time around are against budget consolidation. Sad, but true.
I am not going to take the bait and argue with Lars about the size of the US defense budget. The only issue that I want to consider is what would happen as a result of the combination of a large cut in defense (and in other categories of) spending and an increase in taxes? It might not be catastrophic, but there seems to me to be a non-negligible risk that such an outcome would have a significant contractionary effect on aggregate demand at a time when the recovery is still anemic and requires as much stimulus as it can get. Lars argues that any contractionary effect caused by reduced government spending and increased taxes could be offset by sufficient monetary easing. I agree in theory, but in practice there are just too many uncertainties associated with how massive fiscal tightening would be received by public and private decision makers to rely on the theoretical ability of monetary policy in one direction to counteract fiscal policy in the opposite direction. This would be the case even if we knew that Bernanke and the FOMC would do the right thing. But, despite encouraging statements by Bernanke and other Fed officials since September, it seems more than a bit risky at this time and this place to just assume that the Fed will become the stimulator of last resort.
So, Lars, my advice to you is: be careful what you wish for.
PS Noah Smith has an excellent post about inflation today.