Saturday, 5 March 2016

Uncovering the Bad Math and Logic (and the Bias) at the New York Times

"The point of studying economics is so as not to be fooled by economists."
- Joan Robinson

Just as I was finishing my long post on the controversy over Gerald Friedman's analysis of Bernie Sanders' policy program, the debate entered a new stage. Christina and David Romer stepped up to the challenge that was issued by defenders of Friedman's work, and released a critique which at least took that work seriously, while still disagreeing with its methods and conclusions in the strongest possible terms.

The Romers' paper was then featured in an installment of the NYT's The Upshot written by Justin Wolfers - a professor of public policy at the University of Michigan - titled "Uncovering the Bad Math (or Logic) Behind Bernie Sanders' Economic Plan".

Because The Upshot has a wide readership, and is likely to be taken by many people as a source for accurate and informed discussion, I'm going to go through Wolfers' piece first, and then I'll go on to say something about the points in the Romers' actual paper which it doesn't cover.

1. Government Spending and the Output Level

There are two takeaways:

(1) This may be the most ironically named piece the Times has ever published, since it contains a mathematical error which is both elementary and significant to the discussion.

(2) Wolfers reproduces the theoretical biases of the Romers, failing to subject them to any scrutiny - and as we'll see, they deserve quite a lot.

First, the mathematical error. Let's look at the following quote from the piece:

The issue here is all about levels versus changes. In the usual telling, changes in government spending lead to changes in output. In Mr. Friedman’s spreadsheets, changes in government spending permanently raise the level of output. Mr. Friedman confirmed to me that this was how he had made his calculations.

The same levels-versus-changes confusion leads Mr. Friedman’s calculations to show that a permanent increase in the level of government spending — like that proposed by Senator Sanders — will yield a permanent rise in the rate of change of output. This is the reason he finds that the Sanders plan has such enormous effects on economic growth...

The multiplier he uses is on average 0.89. In the Congressional Budget Office models that he’s drawing from, this means that if the government spends $100 more today, output will rise by $89 this year, but when that stimulus is withdrawn next year, output will then fall back to its earlier level.

From start to finish, that $100 extra government spending yields $89 worth of more stuff. By contrast, in Mr. Friedman’s figures, output stays $89 higher each year, forever. Over a 10-year period, this means that $100 of government spending yields a total of $890 worth of more stuff, implying a 10-year multiplier of 8.9.

This is not a conservative estimate; it’s so high that I know of no study that suggests such large effects, nor of any economist who would defend this view.

Friedman includes estimates of the fiscal multiplier for government spending for the years 2015-2026, inclusive - that is, for twelve years. Wolfers averages those 12 numbers, to arrive at the 0.89 figure. But Friedman is doing a 10-year estimate of the impact of Sanders' policies starting from the beginning of 2017 - i.e. from when Sanders would become President.

The average for 2017-2026 is 0.84. 

Now, taking this correction into consideration, one might think Wolfers made a small error, and Friedman actually applies a 10-year multiplier of 8.4 to Sanders' permanent spending increase.

One would be wrong.

Friedman attributes a 9% increase in GDP as of 2026 due to Sanders' increase in non-healthcare federal spending. But that increase isn't 1% of GDP - as it would have to be for Wolfers' analysis to make sense, given his (incorrectly calculated) 10-year multiplier. The permanent portion of the non-healthcare spending increase in Sanders' plan is 1.4% of GDP. So even if, following the Romers, Wolfers were to insist that that growth derive solely from the permanent portion of that spending increase, he should, by his own lights, have inferred that Friedman was applying a 10-year multiplier of 6.4 - which is about what the Romers think his 10-year multipliier is - not 8.9 (or 8.4).

That's still a huge multiplier. But here we come to point (2). To put it bluntly:

This isn't what Friedman is doing.

Wolfers thinks this is what Friedman is doing because the Romers think this is what Friedman is doing. But the Romers think this is what Friedman is doing because it's the only way to make sense of Friedman's results, from the perspective of the model they use to estimate future effects of economic policy. Friedman, however, is using a very different sort of model.

Ron Baiman, in his comment on the Romers' paper, gives a clear and succinct statement of what Friedman is actually doing. He is assuming that Sanders' policies are going to change the current CBO baseline for GDP growth; and when he applies a yearly multiplier, he is applying it to the new, changed baseline, rather than to the old CBO baseline, because the old baseline will no longer reflect the potential of the economy, once Sanders' policies are in place.

This point brings us to the heart of a deep theoretical disagreement.

The Romers, as Friedman observes in his response to them, belong to a school of thought according to which it makes no sense to talk about economic policies like Sanders' budget proposals changing the economy's potential productive capacity or potential for growth. That potential is not something we can exercise control over. And if adverse events cause the economy to fall below its potential capacity, it will eventually return to it all by itself.

To be a "liberal" economist of this school - like not only the Romers, but also Krugman and DeLong - is to believe that policy interventions can return the economy to capacity a little more quickly. To be conservative is to believe that policy interventions will only lengthen this process.

This - believe it or not - is what separates liberals and conservatives on the power of public policy, within the confines of mainstream macroeconomics.

Friedman, on the other hand, doesn't accept any of this (and he's not alone). We'll come to the question of why in a bit. But first, back to Wolfers and the Times.

We've discussed permanent spending changes, but what about short term ones - specifically, Sanders $1 trillion infrastructure program? Let's look at another quote:

Most economists believe that temporary increases in government spending will yield temporary increases in output. To see why the effect of stimulus is temporary, realize that if raising government spending raises output, then because the end of a stimulus program means cutting government spending, the same forces are later set in motion, but in reverse. And so in the standard story, a temporary stimulus improves the economy, but only temporarily.

Here’s the problem: Mr. Friedman’s calculations assume that removing a stimulus has no effect. The result is that temporary stimulus has a permanent effect.

It hardly needs pointing out that Wolfers' argument as stated is question-begging. (There's the bad logic. Wolfers' piece, despite its title, fails to identify a single logical error in Friedman's work.) A fair statement of the relevant question would be: Can temporary government spending programs ever shift the economy's baseline - and even potential - growth trends, such that they cause the economy to reach higher output levels long after they've ended?

We know Friedman's answer. As he confirmed in his discussion with Wolfers, he is using a model according to which temporary changes in government spending can permanently change the level of output - they do this by causing structural changes in the economy which push the actual and potential growth trends up. That second point is the one Wolfers doesn't seem to grasp, and that's why his simple arithmetic example doesn't match up with Friedman's results.

Once we understand Friedman's answer, we have to ask whether we agree with it.

If the temporary spending in question is (a) a large investment in (b) core infrastructure (like transportation and telecommunications) which is (c) currently in terrible shape, then there is good reason to think the answer is Yes. In other words, what "most economists realize" (if they do) is wrong.

One quick aside before we look at some of that evidence - The two points of Wolfers' which I've quoted are a bizarre combination. I've made a guess about how he arrives at his estimate of Friedman's 10-year multiplier, but that guess assumed he was only working from the average value of the yearly multipliers (which he calculated incorrectly), and Sanders' proposal for permanently increased spending (which he also got wrong). But now we see that he believes Friedman is treating the effects of the 2017-2021 infrastructure spending (totaling $1 trillion, or 5% of a single year's GDP) on the GDP level as permanent. So based on his assumptions about what Friedman is doing, and the fact that Friedman estimates that all non-healthcare spending increases are responsible for that 9% of extra GDP as of 2026, Wolfers shouldn't even have attributed to Friedman a 10-year multiplier of 6.4. It should have been in the neighborhood of 4.6 - still very high (the hard upper limit on fiscal multipliers is around 3), but considerably less than 8.9. Since his assumptions about what Friedman is doing are wrong, though, this point needn't detain us.

On to the evidence.

The research of David Anschauer, of the Chicago Fed, has shown that the stock of nonmilitary public capital, and in particular of core infrastructure, is one of the major determinants of the productivity of private capital.

In plain English, business owners get more out of the stuff they use to do business - like trucks, say - when the places they do business in have a lot of high quality core infrastructure - like roads and bridges.

Military capital, on the other hand, is of very little importance to productivity growth. Anschauer's findings on this point can be supplemented by Mike Kimel's conclusion that changes in federal non-military spending explain over 94% of the change in the real GDP growth rate during the New Deal - a conclusion which is especially relevant if the US is currently stuck in a low-employment equilibrium (more on that below).

Alice Munell, of the Boston Fed, then extended Anschauer's research, and applied it to the question of falling multifactor productivity (of private capital and labor) over the period 1969-1987 as compared with the rising productivity of 1948-1969:

[M]uch of what had been attributed to multifactor productivity growth in the first half of the period really reflected increased output that was due to the buildup of public infrastructure. And much of the decline in multifactor productivity growth after 1969 has reflected the near cessation of public investment. In other words, much of the drop in published multifactor productivity numbers may reflect the omission of public capital from the calculation of inputs rather than a decline in technological innovation.

That last point is important. As Friedman observes in his response to the Romers, they belong to the school of thought that must - in the absence of large-scale destruction of land or capital, population decline, or shifts in individual preferences (none of which have been observed) - attribute declining productivity to a decline in technological innovation. They cannot attribute it to something like a decline in public investment.

Anschauer's original conclusion, that investment in core infrastructure has a robust and long-term positive impact on productivity (and thus, output) has held up well in contexts - like the contemporary United States - in which large infrastructure systems have fallen into disrepair and have urgently needed investment for some time.

He has recently also argued that public capital investment pushes up the national investment rate by encouraging private investment in the capital stock - which also increases productivity (and thus, output).

Alan Harvey applies the point about public capital investment encouraging private investment (leading to higher productivity, leading to higher levels of output) to the present debate:

Romer appears to suggest in the Wolfers piece that multipliers act only during the period of stimulus spending, and she faults Friedman for misunderstanding stocks and flows. It should be obvious, however, that a measure which provokes additional private investment can claim credit for economic activity induced by that additional investment. If Prof. Romer is suggesting otherwise, she is wrong. Investment in equipment and facilities by government contractors and investment in housing by newly employed workers would be among the most likely sources of induced stimulus.

Before moving on to discuss some other aspects of the Romers' paper, let's finish with Wolfers' piece:

When I pointed Mr. Friedman to this critique of his analysis, he simultaneously accepted and rejected it.

He accepted it, telling me that “I may have made a mistake.”

But he also rejected this critique, arguing that his figures are based on an alternative view of the world, stating: “To me, when the government spends money, stimulates the economy, hires people who spend, that stimulates more private investment. That remains, and at the next year, you’re starting at the higher level.” He admits that this “is not standard macro,” and described it as the understanding of an earlier generation of economists — a sub-tribe of Keynesians he called “Joan Robinson Keynesians.” (Joan Robinson was a contemporary of John Maynard Keynes at Cambridge.)

When I pressed Mr. Friedman on whether he was right to conclude that standard assumptions suggest that Mr. Sanders’s economic program will have such large effects, he said, “I have to stop saying ‘standard.’ ” It became apparent in our conversation that he simply hadn’t realized that he had mischaracterized mainstream economics, leading him to describe his disagreement with Ms. and Mr. Romer as “a measure of my ignorance of modern macro, and my disagreements with modern macro.”

Yes, Friedman may have made a mistake - in what he was actually trying to do; namely, estimating the changes to actual and potential output levels which would result from the structural changes in the US economy caused by the full implementation of Sanders' policies, and applying estimated yearly multipliers to the changed baseline for GDP growth. Perhaps he did and perhaps he didn't - the details of his work are as open to scrutiny as anyone else's, and no one with an appreciation of the complexity of these issues would fail to countenance the possibility of error. But we know that he did not make the mistake Wolfers thinks he made, because it is Wolfers' sums which don't add up.

Once we understand what Friedman is doing, the next sentence becomes clear. His is a view of the economy according to which government spending can encourage private investment, which can increase productivity, which increases output levels. The increase in output levels which results from higher productivity (from higher private investment) remains after the temporary government spending which encouraged that investment - substantial spending on badly neglected core infrastructure - ends. And the evidence for that view of the economy is good.

All Wolfers manages to achieve then, is a retraction by Friedman of his claim that his assumptions were all "standard". I endorsed this claim myself in my first post on this debate, because I - like Friedman, I presume - had a broader understanding of what counted as standard than those in the very middle of the mainstream apparently do.

Well, so be it. Thus far, it is Friedman's "non-standard" view that should be winning adherents. And the case for it is about to get even stronger.

As far as the Times' coverage of Sanders' proposals and Friedman's analysis thus far, all I can say is: Gentlemen, you have got to do better than this.

2. Labor: Productivity and Employment

The attentive reader will have noticed that although we've spent some time examining the claim that public investment in core infrastructure can push up actual and potential long-term growth trends, we haven't yet talked about the influence of Sanders' specific permanent measures.

As Ron Baiman explains, Sanders' permanent measures - increased healthcare and non-healthcare spending; more progressive taxation; and regulatory reforms such as a higher minimum wage, tougher rules on overtime pay, and the pro-labor Workplace Democracy Act - would dramatically reduce inequality in America.

Lower inequality reduces the national savings rate, because the wealthy have a much lower marginal propensity to consume. This translates into higher demand, and higher private investment and employment to meet that demand. From there, via Verdoorn's Law, comes higher labor productivity and thus higher output. (See the discussion of Verdoorn's law at the end of my previous post on the debate over Sanders' policies.)

This growth in employment - as Friedman points out - would itself contribute to raising the employment-population ratio, as those who had given up on looking for work are encouraged to try again. Sanders' policies - particularly funding youth job training and creation, closing the gender pay gap, instituting guaranteed paid maternity leave, and funding affordable childcare - would also contribute to increasing labor force participation. Increasing demand and productivity translate into further increased employment from those re-entering the labor market, and increased real wages (and there's plenty of room for those to increase, as I also discussed in my previous post). This would likewise boost demand, private investment, productivity, and output, even further.

Essentially, this entire debate over Friedman's projections comes down to two questions:

The first, emphasized by Lars Syll, is whether Verdoorn's Law applies to the modern US economy - and the evidence says that it does, however much the Romers insist that it doesn't.

The second, emphasized by Friedman, is whether the US economy is stuck well below its potential capacity in a low-employment equilibrium.

If it is - and that sure as hell is what it looks like - then the Keynes-Verdoorn story told above - Friedman calls this "the Keynesian-Kaldor case with equilibrium unemployment and growth dependent on the level of the output gap" (Verdoorn's Law is often called the Verdoorn-Kaldor Law, after the Post-Keynesian economist Nicholas Kaldor whose research led to similar conclusions) - is the right one. Policy can push the economy toward higher employment, higher capacity utilization, higher growth, and even higher potential capacity and growth, in the long-term.

The Romers, of course, reject this as a description of the state of the US economy. But their reasons for doing so boil down to (1) a theory-based rejection of the claims that (a) the economy can get stuck at a low-employment equilibrium, and that (b) productivity can be determined by forces other than endowments, preferences, and technological innovation; and (2) a belief that the Fed's estimate of the NAIRU, which puts it at the current rate of U3 unemployment, is reasonable, and that being at the NAIRU is the right way to understand what it means for the economy to be at capacity.

I addressed (2) at length in my previous post - the belief doesn't hold up. We've covered (1)(b) in this post. So let's deal with (1)(a).

I can't do it any better than James Galbraith. Here is a quote from Ch. 10 of his 2014 book "The End of Normal", which he made publicly available as part of his own response to the Romers' paper:

[Christina] Romer and [Jared] Bernstein, senior economists with the incoming Obama team and in Bernstein’s case the progressive economists’ lone representative on the team, predicted that with no stimulus package unemployment would peak at about 9 percent in early 2010.

With stimulus, they held that the peak would be around 8 percent in early 2009, a mis-forecast for which they were criticized somewhat unfairly. The more important point is that with or without stimulus, Romer-Bernstein projected that unemployment would return to near five percent by 2014. And they projected that a return to unemployment below 6 percent, expected in 2012, would be delayed only by six months if there were no stimulus...

Of course forecasting failures became apparent quite quickly when the economy did not remain on the growth track anticipated in early 2009. 2010 was a disappointment, as were 2011 and 2012; from the trough of the slump economic growth never exceeded 2.5 percent. The ratio of employment to population never improved, and unemployment declined largely because in increasing numbers people ceased looking for work. Residential investment in 2012 was half its 2005 levels; total investment remained more than ten percent below its previous peak.

And what happened when the economy did not cooperate with the forecasts? Did this bring on a review of the models? Again, one might hope so. Again, one would be disappointed. The simple response of the forecasters to the failures was to run the models again, with a new starting point. Thus the five-year window for the start of a full recovery kept receding into the future, year by year, like a desert mirage. In 2009, full recovery was expected by 2014; in 2010, the date became 2015, and so forth. Each year, the forecasters told us, the world would be “back to normal” – with full employment, recovered output, and high investment – five years hence.

It’s plainly unsatisfactory, to forecast in this way. But what’s the alternative? To develop a different point of view, one needs a model capable of generating a picture of the future that does not necessarily yield a mirror of the past. To do that, one needs a structured grip on the underlying mechanics. One needs a vision of how the economy works, and one needs to have the courage to assert that vision – ironically – in spite of the fact that it cannot be derived from the past statistical record. This is the hard part. But only in this way can one see that the baseline is baseless, that equilibrium is vacuous, that the past growth path is not the single best forecast. There is no way to build such a model for use by functionaries, and hence no easy escape from the mental traps of statistical prediction.

One final point, to put things in perspective: Friedman's analysis predicts a net 32% increase in GDP as of 2026 if Sanders' full policy program is implemented. We've only been exploring his claim that part of that increase, 9%, would result from non-healthcare spending measures. That's quite a bit less than the estimated impact of the switch to single-payer healthcare, and less even than what's estimated for the regulatory reform. Even if the Romers were right about the impact of Sanders' non-healthcare spending proposal, that would hardly be, to quote Wolfers, "the whole shebang".


  1. Wonderful and comprehensive post!

  2. Great article, good to get some perspective on that NYT article.