## The Future Isn’t What It Used to be But I will Alway Comment on Krugman

I try to avoid forcasting, but I confidently forecast that, in the future, I will continue to try and try to find cases on which I disagree with Paul Krugman.

In The Economic Future Isnâ€™t What It Used to Be (Wonkish) Krugman notes that forecasts of potential output of the US and the EU are now far below what they were in 2008. He argues that this probably shows a genuine long run damaging effect of the great recession (following Ball,Fatas, & Summers (listed in alphabetical order)). Following Blanchard and Summers, he calls this hysteresis (introducing the word to economic was brilliant) . Finally he argues that this is immensely important, because if demand shortfalls cause permanent damage it it is much more important to fight them compared to say, inflation.

I agree, but I want to stress a point of partial disagreement.

Krugman notes the reported decline in estimates of potential output for given years (so the 2018 estimate of 2018 potential output is far below the estimate of 2018 potential output in 2008). He considers 3 cleverly named explanations of the pattern happenstance, hypochondria and hysteresis. The third is his favored hypothesis that most of the change is a true change in potential output due to slack demand.

Happenstance would be a coincidental exogenous decline in the rate of growth of potential output which happened, by pure coincidence, to occur at roughly the same time as the great recession. Krugman dismisses this (following others) by noting that the decline in estimated potential output is greater in countries who experienced more severe recessions. The happentance argument requires not one coincidence but dozens across countrie.

The hypochondria hypothesis is that potential output is what was forecast and actual output is far below potential output. Krugman argues against this by considering the simplest model of potential output which is output plus a constant times the unemployment rate (maybe minus that constant times a constant guess of the natural unemployment rate). This model is called an Okun’s law model. Like all sensible people, he assumes that official etimates of the natural unemployment rate are nonsense, but he notes that the actual unemployment rate in the Euro-zone is now 8.2%, shockingly high by US standard but lower than the average from 1990 through 2008. If one assumes that the Eurozone natural rate is actually 4%, then one concludes that potential output is higher than current output, and that potential output in the 90s was higher than then current output. This means that the change in potential output is not misseatimated and has, in fact, been extraordinarily small, and that forecasts of potential made in 2008 were too pessamistic to exactly the same degree as current forecast, so the change in the forecasts reflects a true change.

This would be convincing except for the facts that actual estimates of potential output are based on much fancier models, which are less robust that the super simple Okun’s law model, and that forecasts of potential output are based on a third model (that it it is standard to not evaluate the model used to estimate potential output by comparing out of sample forecasts to outcomes — the result of this standard exercise would be too humiliating).

ultra wonkery (which may be totally wrong) after the jump

This post is getting too long. I am going to put a simple discussion here before discussing how potential output is actually estimated and forecast.

Krugman’s argument is that the output gap is, in fact, roughly a constant times cyclical unemployment (unemployment minus the natural rate of unemployment). But consider a slightly fancier model in which it is assumed that potential output is a random walk with drift (so there is an expected rate of change and deviations from that expected change last forever). Then, to be extreme, assume that the output gap has zero persistence, so it is a white noise. If one goes all the way and assume that the two disturbance terms are iid normal, then there is a very simple formula for potential output — it is a geometrically weighted average of current and lagged output. Now assume that there were several periods with output below potential and that currently output is equal to true potential output (so the correctly estimate output gap is zero). Estimated potential output would not, however, be current output. Rather it would be a weighted average of current and lagged output. So the estimate would suggest that output is higher than potential output and the economy is in an unsustainable boom. The insistance on smoothing means that past errors in estimating cyclical unemployment still matter.

Actual official estimates are much more problematic.

I am going to dicuss the European Commission DG EcoFin estimates and forecasts ,because they are binding on Eurozone treasuries in theory (but not in Italy where everything is allowed especially that which is specifically forbidden — at least the current government refuses to obey Brussels). Also because I have looked at them a lot. krugman looks at IMF estimates which are similar.

OK the standard approach to potential output is first to assume GDP is produced with capital, labor, and technology. Potential labor input is labor supply times one minus the natural rate of unemployment (which must be estimated). Potential capital in use is just the estimated capital stock estimated using data on investment and assumptions abut depreciation. One component of the output gap (actual output minus potential output) is due to capital which is not being used, so one component is based on partial capacity utilization. This is not observed and is estimated based surveys of managers and especially on output minus what one would expect given employment and the capital stock. Finally technological progress is estimated based on output minus what one would expect given employment and the capital stock. It should be clear that there is a serious problem separate from the estimation of the natural rate of unemployment.

So one question is whether official estimates of technological progress from 2008 to 2018 are correct or if it was underestimated because of an incorrect model of the effect of slack demand on capacity utilization. The other is whether official estimates of the natural rate of unemployment are markedly worse than the guesses made in the 60s based on almost no data.

OK so first decomposing Solow’s residual, that is, the growth of output not explained by the growth of the capital stock or employment. Some official estimates are implauible. I live in Italy where they estimate a negative rate of technological progress (not just backward and behind in the race, but running toward the starting line not the finish line). How could this be a mistake ?

Well first the decomposition is Bayesian which means it relies a lot on assumptions and not on data (it means that a simpler approach gave crazy results). Second it relies on assumptions about the time series properties of technology and capacity utilization. One assumption (which Krugman stresses) is that it is assumed that fluctuations in capacity utilization are temporary and capacity utilization return to normal in a year or two. But another is that, when estimating technology, it is assumed that the rate of technological progress fluctuates. Technically technology is assumed to be a second order random walk, so the expected change (drift) is itself a random walk.

This means that a temporary downturn causes a dramatic decline in estimated potential output. The disappointing output is divided between estimated technological progress and capacity utilization. The disappointing estimate of technological progress causes a reduction in estimated drift and reduced estimates of future technological progress. This implies absurd estimates of the expected value of GDP in the very long run (I think that for Italy it implies an estimate that Italian GDP will be almost exactly zero in 3000).

In fact, the model is not used to forecast the future (making predictions is always difficult especially about the future). Now consider what happens if there is a downturn due to slack demand which is not recognized as such and which lasts a mere 10 years. The early disappointments cause low estimates of the rate of technological progress and low estimated technology. The later positive surprises as the output gap shrinks do not completely cancel the effect on estimates of the current level of technology. They do imply a high estimated rate of technological progress — which is ignored when forecasting future technology. The pattern of etimates and forecasts shows slow growth followed by normal growth, basically because it is assumed that future technological progress must be normal.

Before going on, I have to admit that the DG EcFin decomposition of Solow’s residual is not based entirely on assumptions. They also use survey’s. But only for manufacturing are manager asked about capacity utilization. For most of the economy a standard confidence question is used. This is a question about perceive and forecast changes. Basically it is just assumed that “it’s getting better” means “it’s better than average”. If there is low demand followed by normal demand, the calculation implies extraordinarily high capacity utilization. In fact, it is exactly this which caused the estimate of negative technological progress for Italy, the demand that Italy have a deficit of 1.6% of GDP, much current conflict in which I do not want to agree with the current Italian government and quite possibly their electoral victory. I am about to rant so I will change topics.

Similarly, the fact that unemployment is now normal (for the Eurozone) does not mean that estimates of cyclical unemployment and its contribution to the output gap are normal. The reason is that, again, it is assumed when estimating the current natural rate of unemployment that it is a second order random walk (that is the drift is itself a random walk). Again this model implies insane long run forecasts — in particular that negative unemployment rates are not unlikely. Again it is used to smooth and not to forecast. In fact, they assume that the natural rate of unemployment quickly converges to a function of a few slowly changing labor market intitutions. This means that although the current unemployment rate for the Eurozone is less than 2% greater than it was in 2008, the estimated natural rate (NAWRU) is very high, so it is asserted that Eurozone labor markets are, on average, about to overheat (I just read that in an DG EcFin publication).

Basically in both cases, the assumptions that potential output could easily have changed a lot in the recent past and will grow normally in the future imply estimated hysteresis no matter what is true of the real world.

The ultra simple 1960s era model considered by Krugman does not have this defect. A consistent application of the model used to filter and smooth would imply crazy forecasts which don’t correspond to anyone’s hypothesis. The actual set of inconsistent assumptions favors the hysteresis hypothesis.

Finally, in conclusion, I believe that there is hysteresis do to the effects of demand on technological progress and the (balanced) effects on the accumulation of human and physical capital. This basically just means I believe in endogenous growth. But official estimates of potential output have almost no effect on my belief.

“Krugman dismisses this (following others) by noting that the decline in estimated potential output is greater in countries who experienced more severe recessions. ”

In this I think Krugman fails to allow for the tendency of forecasters to extrapolate even those things which clearly cannot keep going on forever. A 2008 forecast still reflects people who don’t think home prices can fall. Does not the decline in potential output also correlate with larger bubbles? Is not the more severe recession follow as a consequence? The biggest drop in potential output is an indicator of those who made the largest error in forecasting.

The drop in the rate of increase in potential output comes because the growth cannot go on forever. For 40 years after WW2 growth increased as households added workers. Then the portion of women in the workforce reached a peak. Our economy does not usually allow people to create demand unless they can pay for it. So growth slowed.

Then in 1997 irrational exuberance cranked up our ability to spend, which cranked up investment, which changed our forecasts. It took a decade for people to realize that it was just another thing that could not go on forever.

I don’t argue that hysteresis does not exist, but I think bad forecasting is too large a part to slide over.