“Pretium iustum mathematicum, licet soli, Deo notum”
Sometimes we get accused of being hard on central bankers. It is, however, not central bankers per se, nor any given particular practitioners, that ruffle our feathers. Rather, central planning and economic forecasting in general is where our criticism falls. Central bankers just happen to be the best examples of where the worst practices reside. According to their own website, the Federal Reserve employs in excess of 400 PHD economists. Hard to fathom what great schemes they are formulating.
We fall rather squarely into the Hayek and Taleb camps on this topic. Call it “the pointlessness of forecasting”, a topic that obviously aligns with our oft discussed “challenge of measurement” (see our September 2021 Risk Update https://convex-strategies.com/2021/10/19/risk-update-september-2021/).
Hayek titled his Nobel Prize acceptance speech “The Pretence of Knowledge”. We have quoted and linked this speech many times and implore readers, if you have not yet done so, to give it a thorough reading. In seven short pages his speech gives as clear a summary as you can find of what Taleb, Mandelbrot and Bak wrote in their many masterful books.
One could be forgiven for thinking Hayek’s speech was a contemporary text. He states in the first paragraph “the economists are at this moment called upon to say how to extricate the free world from the serious threat of accelerating inflation which, it must be admitted, has been brought about by policies which the majority of economists recommended and even urged governments to pursue.” We might argue that our theme for this month’s Update has been triggered by a burst of research papers very much along the lines of the sentiment expressed by this Hayek quote.
In “The Black Swan”, Nassim Taleb’s epic tome, he titles Part 2 as “We Just Can’t Predict”. As with any of Nassim’s works, this section is chock full of absolutely world-class quotes and jibes. As Nassim puts it: “Our predictors may be good at predicting the ordinary, but not the irregular, and this is where they ultimately fail”. Whether it involves economic forecasting or optimized portfolio investment strategies, it comes down to the same issue: “What matters is not how often you are right, but how large your cumulative errors are”. It is the impact (scale), not the frequency (probability), that matters.
In an obvious nod to Shannon’s Information Theory, Nassim notes: “I have also studied this effect using the mathematics of information: the more detailed knowledge one gets of empirical reality, the more one will see the noise (i.e., the anecdote) and mistake it for actual information.”
We can’t resist throwing in our favourite visualization of this point, the football pitch with the overlays of the Guassian Normal Distribution curve and the Shannon Entropy Curve. The former measures the frequency of outcomes, while the latter measures their impact. Scoring and saving goals define the outcome of the match.
Figure 1: Normal Distribution vs Shannon’s Entropy Curve
Source: Convex Strategies
We need search no further than our old friends at the ECB, Philip Lane and his team of crack PHD economists, to show the ongoing pointlessness of their efforts to forecast the future outcomes of their own price stability measures, the HICP Index. We can update in figure 2 for the July HICP numbers against their history of forecasts, most recently updated in June. Their error versus their forecasts of just one year ago is several orders of magnitude larger than the absolute underlying forecast.
Figure 2: Eurozone HICP yoy% change (blue) to July 2022 vs ECB quarterly forecasts through June 2022
Source: Convex Strategies, Bloomberg
Having proceeded down the pointless path of forecasting, they then commit the mortal sins of both using their forecasts in satisfaction of their “targeting” of this measure (note, Goodhart’s Law: “When a measure becomes a target, it ceases to be a good measure”) and calibrating policy decisions accordingly. We have said it over and over again but will hand it over to Nassim this time; “Anyone who causes harm by forecasting should be treated as either a fool or a liar.”
To their credit, the ECB finally jumped on the wagon and announced their first rate hike in over a decade. They even powered-up and raised rates by a full 50bp, bringing their Deposit Facility Rate all the way up to 0%. This, of course, on the back of HICP hitting an all-time high of 8.9% and Eurozone Unemployment hitting an all-time low of 6.6%. As we like to say, “that ought to do it”.
Figure 3: ECB Deposit Rate (white). Eurozone HICP yoy% (orange). Eurozone Unemployment Rate (blue – inverted)
Despite the historic nature of the rate increase, the bigger fanfare around their announcement related to the unveiling of the new Transmission Protection Instrument (TPI). This, as widely anticipated, is the new tool to combat the risk of what they’ve dubbed “fragmentation”. The TPI was the active topic of discussion on the subsequent press conference.
We described it thusly at the time:
“The ECB’s official comments are off-the-charts quality! This TPI thing is a wannabe bureaucrat’s dream come true. Unlimited (“there is no ex-ante limit to that program”), absolute discretion (“the Governing Council decides in sovereignty in respect to eligibility to the TPI”), and no transparency (“there are certain components that are best kept unpublished, undisclosed, uncommented upon”).”
We promise that we are not making any of that up. The quotes inside the parenthesis can all be found in the above linked transcript of the press conference. Christine Lagarde actually said those things. And the market loved it.
We weren’t the only ones to notice the unprecedented self-granted power absolutes by the unelected leaders of the ECB. Renowned British journalist, Ambrose Evans-Pritchard phrased it this way in his note in the Telegraph:
“The anti-fragmentation tool gives the ECB sweeping powers to decide when to rescue a country and stave off default, and when to leave it defenceless. By this mechanism, it can dictate budget policies, or enforce pension reforms, or order changes to labour law, without a democratic mandate. It can keep obedient pro-EU governments in power, and topple those with a different ideology à la Grecque.”
The next ECB policy meeting is in early September. Like all the rest, they have given up on their “Forward Guidance” (it worked better, in their minds, when rates were being kept low) so we will just have to wait and see what comes at that time. We will also get the revised quarterly projections that will undoubtedly continue to lend support to our premise of “the pointlessness of forecasting”.
In a very similar vein to the ECB’s meeting, the Bank of England also powered forth with a 50bp rate hike, raising the Bank Rate to 1.75% (figure 4). As ever, they stressed their commitment to fulfilling their price stability mandate with the step-up in aggressiveness to a larger scale rate hike. Before anybody could question if they sincerely thought a 1.75% policy rate was indeed a sign of stern commitment to restoring CPI back below the 3% upper bound of their target band, having just raised their year-end forecast of it to 13.1%, they immediately and vigorously tried to restore calm by laying out their vision of a deep and long recession to commence by early next year.
Figure 4: BOE Bank Rate (blue). GBP 2yr swap (white). UK CPI yoy% (orange) and year end BOE projection (dashed)
We poked some fun at BOE’s forecasting prowess way back in our October 2021 Update (https://convex-strategies.com/2021/11/19/risk-update-october-2021/). At that time, they were hilariously forecasting “peak inflation” of 5% in April. As Nassim might observe, a fool or a liar?
Figure 5: UK CPI yoy% change and forecast as of September 2021
Source: Bank of England, Office for National Statistics, BBC
In their latest announcement they have reconstructed their picture as below.
Figure 6: UK CPI yoy% change and forecast as of August 2022
Obviously, we are all meant to believe that their leap to a 1.75% policy rate will, in very short order and presumably through the near-term instigation of a long and deep recession, be the correct path to bringing inflation back from a now forecast level of 13.1% to below their target. It might be worth pointing out that in recent periods their forecasts, just like those of the ECB, have had a bias towards massively undershooting the eventual true outcomes. We have no way of knowing if the increasingly negative real policy rates over these recent periods have had anything to do with these outcomes.
Well respected UK based economist, Ricardo Reis, released a recent paper that has some great charts that highlight our point about forecasting. https://personal.lse.ac.uk/reisr/papers/22-whypi.pdf
As we have mentioned in the past, the best thing about the UK and the Bank of England is that they have historical data! Check out this wonderful picture with 800 years of UK inflation. Each dot represents the given 20yr average of inflation (horizontal axis) and the volatility of inflation (vertical access). The most telling dot is the most recent documented 20yr period, 1997-2016. To many a central planner they would leap in the joy of victory to proclaim that dot as proof that they had solved “it”!
Figure 7: Eight Hundred Years of Inflation in the United Kingdom, 1217 to 2016
Source: https://personal.lse.ac.uk/reisr/papers/22-whypi.pdf /Millennium dataset of the Bank of England
We will avoid the dramatization of drawing a bright red arrow to where we are heading for the current dot, but it is not difficult to surmise that it is high and to the right. A lot. This year being currently projected at 13.1% by an institution that undershot their projection over the last 9 months by circa 8%. If you had based your forecasts around the normal probability distribution generated by the 1997-2016 mean and variance, today’s current numbers would be so many standard deviations away from expectations that the simplistic math would say it was nigh on impossible, aka fat tailed. Interestingly, if you used the entire 800yr dataset, the biggest outlier would be the 1997-2016 period. Where is the anomaly?
A couple of other worthwhile charts from the Reis paper have to do with the market pricing for options in the interest rate and inflation markets. Reis has pulled out of these option prices the implied probability distributions for longer dated forward inflation expectations. The first chart shows the shifting probability distributions by quarters from December 2020 till March 2022 in the US. The distribution, that might have previously been confused for being Normal, is shown to be significantly skewed to the higher side. The second chart shows the increase in the probabilities, as implied by the respective option markets, of significantly higher inflation levels 5yrs into the future for the US and the Eurozone.
Figure 8: Option Implied Probability Distributions for US Inflation
Source: https://personal.lse.ac.uk/reisr/papers/22-whypi.pdf /Millennium dataset of the Bank of England
Figure 9: Option Implied Probabilities for Higher Inflation for US and Eurozone
Source: https://personal.lse.ac.uk/reisr/papers/22-whypi.pdf /Millennium dataset of the Bank of England.
Reis, who throughout the note comes at things through a fairly narrow neo-Keynesian lens, does rather hit the nail on the head in his analysis of these two charts. “If central bankers are risk managers, they should care more about these disasters than about the average outcomes that was so often cited in 2021”. We could not agree more! Classic ‘x’ vs ‘f(x)’ mindset, and to our way of thinking exactly how risk managers should behave.
In a somewhat similar line of thinking, acclaimed financial author Andrew Smithers has a new book out titled “The Economics of the Stock Market”. In a recent note, “The Stock Market Model: A New Foundation for Economic and Monetary Policy”, Andrew outlined his premise from the book of a two equilibria model: “One is the balance between savings and investment, and the other is the ratio between companies’ net worth and their market value, or q ratio.” We might paraphrase the essence of the “q ratio” as a measure of fragility, or asset bubbles.
The note lays out a fundamental flaw with the existing consensus economic model, which revolves around the core belief of a single equilibrium, in that it is not supported by empirical evidence. Using a model that doesn’t align with empirical ex-poste circumstance, to then forecast and target for the purpose of policy setting, is clearly toying with some pretty obvious unexpected outcomes.
“The problem with these single equilibrium models is that this conclusion is not only wrong but dangerous, as it results in monetary policy decisions which destabilize the economy while seeking to stabilize it.”
Andrew quotes a chap by the name of Doyne Farmer, a physicist that is part of a crowd working on what he terms “Complexity Economics”. Think of it as the application of Chaos Theory to economics. You can check out the opening chapter of Doyne’s upcoming book here: https://static1.squarespace.com/static/54afc2eae4b0fb47dcb12dd5/t/61b371adc50ab0289c4a1751/1639149998258/DRAFT+Chapter+1+-+Making+randomness+predictable.pdf.
This is a fantastic read and, for those familiar, will bring you back to Nassim’s discussions of Lorenz and Poincare. Those not familiar with these names, are likely familiar with the chaos theory allegory attributed to them known as the “butterfly effect”.
[Butterfly Effect: “In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.” Lorenz/Poincare.]
As Farmer puts it “Chaos combines two essential properties. The first is called ‘sensitive dependence on initial conditions’, which means that, on average, nearby trajectories separate from each other at an exponential rate. The second is endogenous motion, meaning that even though there are no external shocks – the dynamical system is deterministic – it never settles down to rest.” If we were to summarize broadly, when it comes to forecasting the future, you first need to know from whence you are starting. From there, if future variables interact dynamically, you really have no chance. Doyne’s path to complexity and randomness came, to an extent, via casino games, thus there is an amount of what Nassim refers to as the Ludic fallacy in his path through randomness. (https://en.wikipedia.org/wiki/Ludic_fallacy#:~:text=The%20ludic%20fallacy%2C%20proposed%20by,world%20of%20games%20and%20dice%22.)
We love reading and playing with concepts such as those presented by Farmer and his colleagues, think of it as searching for Mandelbrot’s illusive Fractal Geometry solution. In the end, however, we once again come down on the side of Taleb, i.e. in reality it just isn’t predictable so manage your pay-out function. Again from The Black Swan: “He (Poincare) introduced nonlinearities, small effects that can lead to severe consequences, an idea that later became popular, perhaps a bit too popular, as chaos theory….. (his) entire point is about the limits that nonlinearities put on forecasting; they are not an invitation to use mathematical techniques to make extended forecasts”.
Following along this theme, Graeme Wheeler (former RBNZ Governor) and Bryce Wilkinson published a whitepaper entitled “How Central Bank Mistakes after 2019 Led to Inflation”. As an added bonus, the incomparable William White provided a Foreword for the paper. In his customary style, Mr. White cuts right to the chase of the matter: “Central bankers have fundamentally misread the nature of the system they are trying to control”.
Wheeler and Wilkinson come right out and say it: “Central bank policies are the main cause of high inflation….Central banks overdid interest rate cuts and the scale of their quantitative easing, and many continued large asset purchase programs when it was clear from the tightness of the labour market and rise in bond yields from late 2020 that their economies were stronger than forecast and that inflation pressures were starting to build”.
They show average inflation across advanced economies as below.
Figure 10: Annual Average CPI across Advanced Economies 2000-2022
Source: The New Zealand Initiative. World Economic Outlook database
We thought this was a nice adaptation to their chart, adding in average policy rates for the respective years as well.
Figure 11: G7 (Advanced Economies) Average CPI and Average Policy Rate 2000-2022
Source: World Economic Outlook database. Bloomberg. Convex Strategies
The authors, Wheeler and Wilkinson, lay out six areas worthy of review/criticism:
- Central banks became over-confident in their inflation targeting framework.
- Central banks were over-confident in the models they use to base monetary policy decisions.
- Central banks were excessively optimistic that they could successfully ‘fine tune’ economic activity.
- Central banks took their eye off their core responsibilities and focused on issues that were much less central to their roles.
- Dual mandates for monetary policy create conflicts.
- Did some central banks try too hard to support government political objectives in making judgements about monetary policy?
We wouldn’t argue with any of it. Again, if central banks are to behave as risk managers, the point is for them to implement policies that recognize the shortcomings of their efforts, not policies that concentrate around the inevitably flawed expected outcomes. As is commonly the case, some of the best commentary on the unintended consequences of pointless forecasting, nonsensical targeting and ruinous policy comes from the BIS. Section II of their most recent Annual Economic Report is titled “Inflation: a look under the hood”.
This is a fantastic piece of research. The key conclusion, at least from our perspective and it really shouldn’t come as much of a surprise to folks, is that inflation has what we would call in the volatility trading world positive spot-vol correlation. High inflation correlates with high volatility of inflation. High inflation has higher correlation across economies. The pass through of wages to inflation is higher in high-inflation regimes. And so on, and so on. Put simply, “risk” is high inflation. As our friend Hari Krishnan said it in his excellent book, “Market Tremors”, “risk is about vulnerability, not predictability”. The BIS note echoes our views on risk management with a simple observation that the “key challenge for the central bank is to avoid transitions from low-to-high-inflation regimes in the first place”. Amen. Figure 12 highlights the obvious nature of the current pickle.
Figure 12: US CPI Index (blue) vs US Real Weekly Wages Index (white). Normalized
Source: Bloomberg, Convex Strategies
One last link for you (though with a couple of extra links embedded inside of it).
This is an interview with Edward (Eddie) Chancellor on his new book which is due for release in August, “The Price of Time: The Real Story of Interest”. We cannot wait to get our hands on this beauty and will undoubtedly work it into future Updates once we have had a chance to be educated yet further.
The killer quote in the interview – “There is a running joke that the economists of the BIS are widely read and widely ignored among the central banking community. Claudio Borio and Bill White are the heroes in this story. In the end, they will have the last laugh. Their economics is much richer, much more intellectually diverse, and draws more on history. It just was not popular among central bankers. Just read the two papers by Bill White, «Is Price Stability Enough?» from 2006, and his 2012 paper, «Ultra Easy Monetary Policy and the Law of Unintended Consequences». It was always there, for everyone to see”.
Eddie, you had us at hello!
Central bankers, just like investment managers, need to manage their risk by focusing on what they don’t know, not what their models expect.
We led off this Update with a Latin quote. Hayek introduced us to the term in his aforementioned speech. He attributes it to “the Spanish schoolmen of the 16th century”; “pretium mathematicum, the mathematical price, depended on so many particular circumstances that it could never be known by man but was known only to God.”
Had Hayek, who passed away in 1992, lived long enough to see Men in Black 3 (2012) he may have amended it to “known only to God and the last surviving Archanan”.
Griffin the Archanan
Even for Griffin, about the only forecaster we would put any stock in, it is no easy task. How many of your run-of-the-mill central bank economists are even going to get round to asking that one critical question?
“Did you have chocolate milk this morning?”
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