Monetary Finance in the Age of Corona Virus: MMT and the Green New Deal

The world is going through a remarkable transformation in the aftermath of an unprecedented shut down of economies all over the globe. Before the crisis there was already significant debate about how to pay for the costs associated with the transition to a low carbon environment. That debate has intensified as treasuries and central banks are scrambling to find ways to pay, not just for climate change policies, but also for social insurance to compensate the millions of workers who have been asked to sacrifice their livelihoods for the social good.

Rebuilding Macroeconomics will host a Webinar on Wednesday May 20th, 2020 from 16:00 to 19:30 BST (UCT+1). to discuss these issues. The conference is organized and co-hosted by Professor Roger Farmer from the Management Team and Megan Greene of the Advisory Board.  We have an exciting line up of prestigious speakers. If you would like to join us for the discussion please contact Richard Arnold of Rebuilding Macroeconomics.

The Peters Paradox

This is a post I wrote in advance of an upcoming online conference on May 18th on ergodicity. The programme is available here. To participate, please send an email to Richard Arnold saying you would like to register for the Ergodicity day on 18th May.

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Since I’m working on non-ergodic behaviour in economic models, I was intrigued by recent claims from Ole Peters.[1] In a series of articles, blogs and notably in a TED talk (here), Ole has made some rather strong assertions about the way economists model choice under uncertainty. According to Peters, economists do not understand the concept of ergodicity. As a consequence, we have apparently made some rather bad blunders.

What, you may ask, is ergodicity and why does it matter? Imagine you are repeatedly confronted with an uncertain world. A good example is the one that Ole gives us. You start with $100 and a casino offers you a gamble in which the house flips a fair coin. If it comes up heads you win $50. If it comes up tails, you lose $40. The first question you might reasonably ask is; should you trust the casino? Is the coin really fair? Does it really have a 50% chance of heads and a 50% chance of tails or is the house shading the odds? To answer that question, you consult a friend who has a Ph.D. in statistics, and she advises you to observe someone else playing the game for a while.

If each flip takes 30 seconds then after watching for roughly eight and a half hours you will have acquired a list of 1,000 observations and, if the coin is fair, roughly 500 of the times you should have seen a head and the other 500 observations should be tails. I say roughly because the chance of 500 heads in 1,000 flips is itself a random variable so you might for example, see 503 heads and 497 tails. But you are very unlikely to see 200 heads and 800 tails unless the casino has been cheating. The exact statement is that if the process is ergodic then the proportion of heads in n tosses will converge to p where p=0.5 for a fair coin.

Notice I slipped in the word ergodic to this definition. That’s a very important idea in problems like the one I just described, where we are trying to estimate an unknown quantity. In this case, we are estimating the probability, p, that a single toss of a coin will come up heads. If the coin is fair, p is equal to 0.5. If the casino is cheating by weighting the coin, p might be different from 0.5. That’s what we hope to find out by observing repeated flips of the same coin.

So far so good. But how do we know the casino doesn’t cheat occasionally. Suppose that the house has a whole boatload of different coins. Some of them are fair and some of them are not. Now your statistician friend advises you that the experiment she proposed of counting the frequency of heads in a series of flips will tell you nothing about the next flip. Averaging a sequence of flips only works if each flip has the same value of p. For the estimation of p using sample averages to make sense, the process must be ergodic.

Now we know a little bit about ergodicity, let’s look at Ole’s experiment. You watch Ole’s TED talk video and explain it to your friend. The one with the Ph.D. She listens carefully but seems a bit puzzled. The first thing she points out is that Ole is certainly not assuming non-ergodicity of the coin flip since he explicitly assumes that the coin that is flipped is fair. Peters is not asking about the distribution of wins or losses in repetitions of a game: no, he is instead asking about the distribution of your wealth if you play the game n times. Let’s call this random variable W(n). The assumption that you start with $100 means that W(0)=100. What Peters studies are sequences {W(i)}_(i=1)^N where you play this game N times and you reinvest all of your wealth at every stage.

You explain this to your friend and she now understands a little better. The random variable W(i) is not ergodic. In fact for i≠j, W(i) and W(j) do not even have the same probability distribution. If you play the game once you will have $150 with probability 0.5, or $60 with probability 0.5. There are only two possible outcomes. If, on the other hand, you play the game twice by reinvesting your wealth after stage 1 you will have $36 with probability 0.25, $90 with probability 0.5 and $225 with probability 0.25. If you win twice, you win a lot, but the most likely outcome (statisticians call this the mode) is that you will be $10 poorer if you play the game twice.

In Figure 1 I have graphed the probability distribution of the logarithm of your wealth in Peters’ game after playing it for N times. It is clear from this picture, that a person whose utility is equal to the logarithm of his wealth might think twice about participating in a game where he is required to invest all of his winnings on every play. Although, using this strategy, there is a small probability of making a spectacular gain, the probability mass of the gambler’s utility is shifting to the left the longer he plays the game.

On Figure 2, I’ve plotted the number of times you play the game on the horizontal axis against the logarithm of your expected wealth after playing the game n times on the vertical axis. This is the population analogue of what Ole calls the ‘ensemble average’ and it is clear from this picture that the log of the ensemble average is growing over time.

How can it be that a gambler is almost always losing, but on average he is winning? That’s because the largest possible gain grows so fast that it outweighs all of the more likely losses. But people don’t just care about the average gain from an investment. They also care about the risk. It’s for that reason that economists posit the existence of a utility function. We assume that utility has the property that the average utility of a change in wealth is less than the utility of the average change. Functions that have that property are called ‘concave’ and the assumption that people maximize the expected value of the logarithm of wealth is the most commonly used example of a function with this property.

As long as people care about the utility of wealth, rather than wealth itself, they will try to avoid taking risky bets. And the sequence of bets that Peters offers us is one that would not be taken by a person with logarithmic utility. If you have logarithmic utility, after playing Peters’ game n times, using the strategy of reinvesting your wealth every period, the average of the logarithm of your wealth will be smaller than when you started and it will keep falling, the longer you keep playing the game. But even though the average utility of your wealth will fall over time, the logarithm of your average winnings will keep getting bigger.

Ole Peters plays the game for a thousand periods to generate a sequence of random variables. He repeats this exercise many times on a computer, and he averages each of the many sequences to arrive at what he calls an ensemble average. He plots this average on a logarithmic scale and shows that is it is increasing linearly over time. By plotting the average of a large number of sequences on a logarithmic scale Ole is showing you the sample analogue of Figure 2. He is showing you the logarithm of the averages of sequences of binomial random variables.

Next, he takes a very long single sequence of random variables and he plots that sequence on a logarithmic scale and shows that it is falling over time. What Ole is doing in that second picture is showing you a sequence of random variables drawn from the probability distributions I have drawn in Figure 1. The fact that one of his pictures is increasing over time and the other is falling has nothing to do with ergodicity. It is a consequence of the fact that the expectation of the log of a random variable is always less than the log of the expectation, a result that is known in the statistics literature as Jensen’s inequality.

How should you behave when faced with a sequence of gambles in which you win $50 with probability 0.5 and you lose $40 with probability 0.5? That question was answered in 1956 by John Kelly, a researcher at Bell Labs. Kelly showed that the gambler should reinvest a fixed amount of his wealth at every stage of the game and that this strategy is equivalent to maximizing the expected geometric growth rate of wealth. When the odds are so strongly in his favour as they are in the Peter’s example, a gambler who follows the Kelly criterion will become spectacularly rich in a relatively short period of time.

Ole does us all a favour by drawing attention to the importance of ergodicity in problems of uncertainty. But I do not agree with Ole’s conclusion, that economists should jettison the idea that people maximize expected utility. [2] In my own research, J.P. Bouchaud and I are exploiting the properties of non-ergodic random variables to understand how people behave when the future cannot be easily predicted using averages of past behaviour. I do not think that our research agenda needs to jettison more than two hundred years of progress in decision science in order to achieve that goal.

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[1] I am grateful to Jean-Philippe Bouchaud, Doyne Farmer, Robert MacKay, Ian Melbourne and Ole Peter for comments on an earlier version of this blog. Any remaining errors are mine alone.

[2] Modern finance theory uses a version of expected utility that originates with the work of Kreps and Porteus. In this version, the utility functions in each period obey the axioms of expected utility. These ‘period utility functions’ are knitted together through time by a sequence of non-linear aggregators. The people who hold these preferences are not expected utility maximizers overconsumption sequences.

Jack Hirshleifer: A Memory

I was approached last month by Junyao Ying, a UCLA alum who is now working in China. Junyao and his wife Weiyi Qiu have recently translated Jack’s book, Investment Interest and Capital into Chinese. Junyao asked me to write a few words about Jack for the translation. This is what I wrote.

The economics department at UCLA was a very exciting place in the 1980s, not least because of Jack Hirshleifer.  Many of us ate lunch every day in the Faculty Center, and being in Southern California, most days we ate outdoors in the sunshine.  Jack would arrive at 12.00 sharp with an economic question for the day that he would pose to the table. Jack’s questions would be from the news of the day and the analysis he expected would be in the UCLA style. 

The department had a unique approach to economics and Jack, along with Harold Demsetz, Armen Alchian, Ben Klein and later, Al Harberger, were a huge part of that. Their economics was intuitive, often verbal, but always incisive.  One story, relayed to me by another UCLA  giant of the era, Axel Leijonhufvud, expresses well the Socratic teaching style that permeated the UCLA curriculum. As Axel relays it, he was sitting in on Armen’s first graduate micro class when the master appeared, paced back and forth for a few minutes, and then boomed loudly: “So why don’t we sell babies anyway?”

Jack had the same approach. Many of our discussions would end up around one of his favorite topics: the economics of disasters. Earthquakes were never far from our minds and Jack was an expert on what today we might call black swan events. LA earthquakes are relatively frequent but they typically register less than 5.0 on the Richter Scale, enough to shake the floor, but usually not to do much damage. Sometimes we see larger quakes and every century or so, an 8.0 magnitude quake brings significant loss of life. Jack pointed out that, if you go far enough back in the fossil record, there have been earthquakes large enough to cause a slippage in the earth’s crust large enough to move two points that were previously next to each other five miles apart!

Jack was an economic imperialist. He believed passionately that the economic method can and should be applied to all of the social sciences. While we may not all share that opinion, in this time of crisis, we can nevertheless benefit from Jack’s insights. He may not be here in person to opine on how to deal with black swan events,  but we can still learn from Jack by reading his written words.

Roger Farmer April 2020

For my Chinese readers, here is the translation

Contagion

Central banks throughout the world are charged not only with price stability, but also with maintaining financial stability. For example, the Federal Reserve is charged with maintaining maximum employment and stable prices and the Bank of England now has an entire new building packed with financial regulators. 

 Historically, the Fed has achieved its employment mandate by raising the interest rate when output is growing at what the Fed deems to be an unsustainable rate and lowering the interest rate when the economy is, in the judgement of Fed policy makers, about to enter a recession. In recent years, a chorus of economists has fretted that the Fed Funds rate, currently at 1.58%, is too low for a cut to have a substantial impact if the economy were to head into a major recession. Those fears are now being realized in a major way. 

The current expansion that began in June of 2009 is the longest in post-war US history. The effect of Coronavirus on economic activity will mark the end of that expansion and we are now seeing the fears of market participants reflected in a stock-market crash with major market indices that dropped by more than 10% last week, wiping out all of the gains from the previous year. The Fed response of a fifty-basis point cut has not calmed fears. To the extent that the market reflects fundamentals, a fall in values caused by expected future supply disruptions is to be expected and is not necessarily a bad thing. But there is a real danger that Coronavirus will spread not only though biological contagion, but through financial contagion.

The supply chain disruptions emanating from China will mean that there are fewer goods available for consumption in the US and Europe. A market response to that disruption should result in a temporary increase in prices as markets allocate a reduced physical supply to a constant nominal demand. But movements in the five-year forward inflation expectation rate suggest that market participants expect the opposite. Inflation expectations by this measure have fallen by a half a percentage point in five days and they are currently in free fall. Markets are concerned that the supply disruption will trigger further demand cuts that lead to a doom loop of self-fulling expectations.

The stock market is driven not just by fundamentals. It is driven by fear. Market values are, to paraphrase Keynes, like a beauty contest in which the judges are not evaluating the natural beauty of the contestants, they are evaluating the opinions of the other judges of the competition. For every Warren Buffet, investing for the long run, there are ninety-nine investors looking to make a quick profit. 

Day to day market fluctuations do not show up in the employment statistics. Persistent market fluctuations do. My published research documents that a 30% persistent drop in the stock market, if not contained, will lead to a 13.5% increase in the unemployment rate. Stock market crashes do not just reflect fundamentals arising from supply side shocks. They amplify those effects and can, sometimes, be independent causal factors that create recessions or deepen recessions arising from what would otherwise be relatively minor supply disruptions.

There are two ways in which stock-price movements feed back to the real economy. The first is through wealth effects on aggregate demand. When 401k stock portfolios fall by 30% and remain down for three months, households respond by cutting back on spending. The second is through wealth effects on aggregate supply. Many small and medium size businesses rely on the net wealth of their owners to guarantee business loans. When the asset positions of entrepreneurs fall substantially there is a chain reaction through networks of overlapping contracts that generates waves of bankruptcies and layoffs of workers.  

For some time, the Fed has aimed to hit an inflation target of 2%. To achieve that target they lower the interest rate when inflation falls and raise it when inflation increases. There has been a chorus of views, to which I subscribe, urging the members of the Federal Open Market Committee to aim not for an inflation target, but for a nominal GDP target. The Fed should act, not to keep inflation at 2%, but to keep nominal GDP growing at a steady rate. 

If central banks do not act in a more decisive manner soon, the supply disruption from Coronavirus will lead to a precipitous fall not just in employment and real GDP, but in nominal GDP. The supply side disruption shouldlead to a fall in real GDP. It should not be permitted to lead to a fall in nominal GDP. When short-term interest rates are at or close to zero, as they are now, cutting the interest rate is not sufficient to prevent financial collapse. As I have argued for more than a decade central banks and national treasuries should intervene directly by buying stocks. 

Direct market intervention of a central bank is not unprecedented. During the Asian Financial Crisis the Hong Kong Monetary Authority invested in the stock market and their intervention is widely credited with preventing Hong Kong from experiencing the worst effects of the contagion that affected other countries in the region.  The Federal Reserve is currently constrained by the Federal Reserve Act from directly purchasing stocks. The US Treasury is not and an emergency intervention to create a US wealth fund, backed by Treasury Debt that was subsequently purchased by the Federal Reserve Open Market Committee is one possible way that a policy of this kind could be quickly enacted.  

Whatever happens in the next two months, the longest post-war expansion is about to come to an end. The depth of the ensuing recession will depend in no small part on the speed and effectiveness of the policy response.   

Taxing Billionaires

I just read a fascinating twitter exchange between @Noahpinion and @gabriel_zucman. My scoring so far:

Noah: 10: Gabriel: 0

Gabriel argues for taxing billionaires immediately based on the principle of “ability to pay”. Noah asks if his reasoning is based on some unarticulated moral principle; or is it on practical grounds. The State needs the revenue today, for example, and the intertemporal capital markets are imperfect. Gabriel avoids the question and scores three parrots (out of three) on my newly invented epigone scoring system for repeating himself without answering the question.

I suspect that Gabriel’s answer to Noah, which he resists articulating, is that he believes the argument for taxing immediately to be moral.

There is a better answer.

The ownership of wealth, whether or not the income from that wealth is converted into a taxable income flow, may be converted into influence over social and political institutions. The primary way this happens is through the creation of non taxable foundations with charitable status. There are many such institutions that support a diverse range of activities. And the goals of the institutions are not goals that we would all support. The charitable aims of foundations funded by the Koch brothers, for example, are not the same as the charitable aims of those funded by George Soros.

My views on whether this is a good thing have shifted. I wrote a piece in the Guardian in 2014 which predicted the current fervor to tax the wealth of the billionaire class. I argued in 2017 in favor of a modest wealth tax, an idea picked up by Martin Sandbu in the FT. But the calls for expropriation, coming from the self-immolating wing of the Democrats, will inevitably be self defeating.

I do not subscribe to the attempt to impose equality of outcomes. Human beings are diverse creatures with an amazing range of talents and abilities. Market economies operate within institutional frameworks that are constantly evolving. In the past, we designed ways of moderating markets to ensure that the inequality that is inherent in capitalism is not so extreme that the institution destroys itself. Those moderating mechanisms are in need of reform as wealth inequality is again approaching levels deemed unacceptable by the average citizen.

Part of the problem, is that the growth of social media companies is generating wealth in the form of capital gains rather than dividends. The solution is to tax capital gains at the same rate as ordinary income as I argued here in Project Syndicate. It is not to appropriate the wealth created by these companies. And I do not myself, see a moral argument for leveling the wealth of every member of society to the point where we are all homogenized.

There is no indication from the observation of Mao’s China or the former Soviet Union that wealth redistribution on a massive scale by the State leads to equality of outcome for the citizens of those societies.

Government is not a benevolent institution. It is an alternative form of power hierarchy in which the power of billionaires to influence our lives is replaced by the power of politicians. Whatever their rhetoric, and however superficially accountable they are through an imperfect electoral process, politicians are ultimately acting in their own interests.