The power of choice of transformation, part 3

 

The last part in this series is dedicated to the Covid recession, which  by the fact that it was lead to hugely anomalous data points makes life of macroeconomic analysts much harder. Here I will discuss how especially the usual transformation used in economic print, the year-over-year growth rate, end up not communicating almost anything to the user. In other words, this piece is really not about demonstrating power of transformation, but rather the lack of power.

Background: Basic transformations

Bit of background. Economists are mostly interested in how are things changing, rather than how things are. For stable macroeconomic time series like unemployment rate this poses no problem: graphing level will show you both where we are, and whether we are going up or down. But of trending time series this is not the case – if you take long enough sample then the increasing level screws up with the scale so that all you see you are now higher than in beginning, but not whether you have recently increased or decreased.[1]

The obvious solution is to use growth rate. But which one? We have simple growth rate, annualized growth rate, year-over-year growth rate… and recently even things like year-over-two-years growth rate! All of them have their place in the macroeconomists’ toolkit, and it is up to the economist to choose which one to use, giving us the power of choice of transformation. That is why they pay us the big bucks. Just kidding.

The most popular transformation in economic press is the year-over-year. This is probably for two reasons for this choice. First, year-over-year gives you comparable numbers like annual growth rate.[2] This is also true for annualized growth rate, which explains its use. However, year-over-year growth rate also has the advantage of not being too volatile, which is not the case for simple growth rate and especially not for annualized growth rate. This for example explains why year-over-year is THE statistic used for reporting GDP growth rates for emerging markets, which have more volatile quarterly series than developed countries, which either use simple growth rate (in case of euro zone) or annualized growth rate (in case of US).[3]

YoY growth rate and pandemic

This then explains why people usually use it. But here comes the catch: year-over-year growth rate is sometimes a horrible statistic for telling you the story. To see why, consider the case of euro zone GDP. Everybody roughly knows the story: GDP decline in 2020q1, then collapsed in 2020q2, before partially rebounding next quarter. Afterword it was mostly flat for next two quarters, before rebounding during the second and third quarters of 2021.

Now consider looking on the year-over-year growth rate of euro zone GDP during the pandemic:

 

Can you immediately tell the story from it? Well, for starters, there was a huge collapse in 2020q2. So far so good. But what about the  development in following quarters? Well, year-over-year growth rate was still very negative in 2020q3-2021q1, albeit less. This tells you that GDP was still lower than year before. Finally, in 2021q2 there is a spike, followed by a drop.

Looking at this you would hardly conclude that by far the biggest rebound was in 2020q3, unless of course you spend quite some time thinking it through. Instead, you would conclude that it was 2021q2 which was the best quarter. Of course, this was not the case and the strong year-over-year growth rate was really about the low comparison base from year ago – that is 2020q2.[4] Similarly, you would conclude that 2021q3 was much worse than 2021q2, which is not true. Simply, in periods of abnormal movements, such as the pandemic, year-over-year growth rate will often tell you more about what happened during this quarter last year, rather than the current quarter.

The lost power of transformation

But this drawback of year-over-year growth rate is not the main point of this post. Rather, the point is that this chart fails completely in it the main goal expected from charts: telling a story to the reader. Or even worse, it tells a misleading story. And yet, this is a chart which was common during the pandemic, and is still common. Simple, the authors are throwing away their power to tell a story with a chart by choosing the wrong transformation.

P.S.: What is the solution? Of course, simple growth rate would be the best growth rate here. But personally, I became a huge fan of indexed charts. Why? For starters, they tell you the same story like level of the series, which is really the story to tell here – down a lot, then partially up but not all the way.

 

 

Simple growth rate will struggle to communicate this – and might be even misleading due to its non-linearity. Second, unlike levels, index tells you also relative magnitudes. In the original level graph you could see that GDP went from 2,600,000 to roughly 2,300,000. But this is a completely useless information in that if it would be instead 5,200,00 and 4,600,000 it would tell you the same story. Simply, most readers have no idea about current level of GDP and such information is not valuable to them. Worse, what is really relevant to them is by how much are we lower, e.g. by 10% or 20%? To figure this out they would need to do calculation in their head.

And here comes in the power of index charts. From index chart you can see that you went to 85, and hence 15% below the index  quarter. Moreover, you can also easily read off the magnitudes of quarterly movements to get growth rate: for example, going from 85 to 96 tells you that you increased by 11% of the pre-crash value.[5] Hence index chart tells you the level story, while also containing basic information about the story of quarter-to-quarter changes.

P.P.S.: Lately I also started using index values for analyzing sequence of monthly data. Namely, I index all data to the same month of last year. Like that I can see the year-over-year growth rate, if I want to, but also have the story of levels, undisturbed by the base effects, which would be the case if I would be showing year-over-year growth rates.

 

 

 

 

 

 

 

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[1] Unless of course you are looking at Italian GDP. 😉

[2] By annual growth rate I just mean the simple growth rate for data in annual frequency.

[3] Fun story: back during the depth of pandemic Czech business daily had article comparing the performance of US, euro zone and China. The problem? It was comparing the numbers are reported by statistical offices, and hence comparing simple growth rate with annualized growth rate with year-over-year growth rate. Yes, that is sometimes the quality of Czech business journalists.

[4] While it was a good quarter, that was just a coincidence which is almost irrelevant to the shape of the curve: Year-over-year growth rate would be huge even if 2021q2 would show moderate decline.

[5] Note that this is not the same as growth rate, which was more like 14%. That said, I would argue that it is more valuable information than growth rate: you don’t really care that you increased by 14% from 2020q2 level; it is more valuable to know that you have increased by 11% of the pre-crash value.

The power of choice of transformation, part 2

The second piece in this series is dedicated to modelling and to monetary policy. It has been motivated by this nice chart from the Goldman Sachs:

 

This chart is highlighting that we should not think that recession is coming just because of the tightening we have seen already, because lot of the effect of tightening has already been felt simply because tightening has started almost a year ago. Which I think is important point to make and the chart is very useful in putting numbers to this idea.

That said, after thinking about this chart I started wondering whether it does not overstate its case. The odd thing that stroked me was the fact that the effect of the tightening is tending to zero over time. At first glance it does sound reasonable that after tightening ends the effect it has should gradually become zero. And in-so-far as focusing on the process of tightening (that is raising rates), this is just logical conclusion.

However, that is not how this graph is being used and interpreted. The chart was being used to argue that the impact of monetary policy as such is going to wane in coming quarters, which is a different point from the impact of just the tightening process. The point to realize is that the end point of tightening is relevant; in other words, if we end up with high interest rates[1], then that should have negative effect on growth irrespective of whether the rates are being raised further or not. In the parlance of Fed, they want to raise rates to rates to restrictive level and keep them there. The use of word “restrictive” implies that that high level will have continuously negative effect on aggregate demand as long as rates are at that level. In other words, the effect of tightening will be non-zero even after the end of the tightening process; as higher rates stay, the effect will stay as well.

How is this all related to power of transformation? Well, in the report where the chart was used the authors come clean and say that the model links the effect on growth to changes in the financial conditions index. This then leads to the conclusion that when changes in monetary policy go to zero, the effect goes to zero. However, the choice of changes in financial conditions as the driver of growth is not as self-evident as it might seem. I can as plausibly argue that it is the level of financial conditions that is relevant for growth, with high level implying lower growth. Indeed, this is what one would take away from standard macroeconomics models.

Ultimately, the point is not that either changes or level is the correct choice.[2] I think it is fair to say that both matter: level is important, but rapid changes in level can carry much bigger punch than the change in level alone would imply, and hence changes are important too. The point is different: The story the chart (and underlying model) say is really a function of the choice of transformation; if different transformation would be used, the story would be completely different. Hence the power of choice of transformation.

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[1] High of course needs a benchmark, as in high relative to what. Here I mean high relative to (long-term) neutral rates.

[2] I would view this view irrespective of econometric arguments. For example, I am pretty sure the authors chose changes in financial conditions index either because they  concluded that the series has a unit root, or because they concluded that it fits better. Neither of these would persuade me that this is the only correct perspective.

The power of choice of transformation, part I

 

Two example recently reminded me about a thought I have been having for a while: Sometimes it feels that most of macro analysis is really about choosing the right transformation. I will illustrate it in three posts. First, a post about euro zone energy inflation.

For most of the 2022 there was a discussion about whether the spike in euro zone inflation is driven solely by surge in energy prices, or whether it is more broad-based. (Of course, the truth is somewhere in between those two…). One side was pointing out that half of the inflation was accounted for by energy component directly:

Of course the other side countered that also the other non-energy components are elevated and that inflation is very broad-based:

To which the first side countered that it is because of energy – i.e. pass through. And here comes the power of choice of transformation. How do you make the case that energy drives the rest of the basket, or that it does not? Enter a chart from Riccardo Trezzi (tweet has been deleted since):

Looks like energy CPI goes up and down all the time without causing any large spike in overall CPI, right? Implying that the current spike in energy should not be the cause for spike in overall inflation, given that it is not that abnormal, right? Well, look again, this time using the level of both series rather than the y/y growth rate:

This paints completely different picture: while there were surges in energy prices before, the current surge is simple in a league of its own (and there even isn’t another professional league…). Energy prices have surged by almost 100% in period of 1,5 year, with previous largest surge in similar period was more like 25%.

My point is not to settle the debate. My point is to show how the simple act of choice of transformation wields immense power in macroeconomic analysis. As I always say, good statistician./macroeconomist can show anything with any dataset…

The future perspective on current monetary policy

 

Ever since the Fed and the ECB have embarked on their journey of rapid tightening, there was a heated debate about the appropriateness of this policy. Ultimately, this question rests on the persistence of current inflation, which pits against each other the by-now-infamous team transitory against their opponents of team persistent. At this point it is fair to say that we really don’t know which side was correct, or maybe more precisely, which side was more correct, as neither of the extreme perspectives were likely correct. But what about in future, will we know? I don’t think so. I think both sides will claim forever that they were correct, and ultimately, the actions of the central banks will prove both of them correct.

What do I mean? Imagine that in a 1-2 years  from now inflation is back to around target. What does that mean for team transitory and team persistent? Team transitory will be able to point out to inflation back to target and say “See, the inflation spike was after all not persistent, given that we went back to target. Of course, the team persistent will say that the only reason why inflation went back to target was because of the action by central banks, which broke down the persistent inflation, and that without such action the inflation would be persistent. And as for central banks themselves, clearly, if inflation comes back to target, they will feel vindicated, claiming that their policy was correct all along. Hence, inflation going back to target settles nothing.

Arguably, if inflation only goes back to 2% and not below, I would conclude that team transitory was not correct: the rapid tightening clearly will have impact  on inflation rate, and hence if even with it we do not undershoot, then in absence of it we would have overshot the target.

Now imagine that in 1-2 years from now, inflation is actually well below target, likely in combination with recession between now and then. Does this change the debate? Does it vindicate team transitory? I don’t think that team persistent will accept defeat in this situation. They will claim that the inflation was persistent, and that central bank had no choice but to tighten rapidly, even if it meant recession and below-target inflation rate. They will point out that in absence of such action the sky-high inflation rate would lead to de-anchoring of expectations and inflation persistently above target. In other words, the argument was that breaking down the high inflation and landing exactly on target simply was not in cards.

Arguably, in such situation I would conclude that team persistent was not correct: while I can see a case to be made about inflation expectations de-anchoring, like this kind of Jedi Mind Economics is not really persuasive for me: we have very little understanding of how expectations get formed, what can cause inflation expectations to de-anchor, and whether that would actually meaningfully influence inflation. So if the argument rests solely on theocratizing about evolution of inflation expectations, count me out. (I am not saying that inflation expectations are irrelevant, just that given our current empirical understanding, I would not make them central to my explanations of empirics).

Only if inflation even after 2 years is still clearly above target is there a chance that the discussion will be concluded. It will be hard for team transitory to argue that 4 years of high inflation is really a transitory phenomenon. That is, unless there is further shock along the way, but again, that to me will start to feel tenuous.

 

“Markets are now firmly signaling recession in euro zone”, aka continuing in the folly of more inversions, more recessions

 

Following the ECB December meeting, which brought strong hawkish surprise, we woke up to headlines of markets now more firmly signaling recession for euro zone, given that German yield curve has inverted. These articles we accompanied by graph showing inversion between 2yr and 10yr yield curve reaching levels not seen in decades.  Among other places, here is FT from Dec 16^th:

 

Of course, the movements in the yields after the ECB meeting were not in any way driven by expectations of coming recession. The 2yr yield jumped by 25bps (a 6-sigma event, apparently) on the day of the meeting, and surged by further 20 bps since then. The 10yr yield also increased, albeit by smaller 14bps on the day, and since then by further 30 bps. This is hardly the stuff preceding recessions. Aren’t yields supposed to go down in recessions?

The story is the same as in U.S.. The ECB made it clear it will go further above neutral then previously thought, with markets now pricing further 125bps hikes or so in coming months. This will take the overnight rates to around 3.25%, way above any reasonable estimate of long-run neutral rate. By simple arithmetic in the form of expectations hypothesis, this means much higher 2yr yield than 10yr yield, since policy rates will be above neutral only temporarily.

So no, markets are not suddenly signaling recession in euro zone. They are just signaling that the central bank will take rates further above neutral and stay there longer. Of course, this makes recession more likely – my subjective recession odds have increased on the day – but that is not what is behind the market moves.

 

 

The folly of more inversions, more recessions

 

With the whole yield curve now inverted (see below), and 2s-10s yield curve most inverted since 1980s,  the talk of inversions signaling recessions is growing louder and louder. This, to me, is simply baffling.

 

The case for linking inversions to recessions was always simple. Indeed, it is more of an observation connected with somewhat sound logic: Inversions occurred before all the recessions[1], and there is reason why inversions could be reflection of collective wisdom about coming decrease in interest rates below neutral due to coming recession (and hence signal of coming recessions).

That is all fine. Where I get lost is how does this apply to current inversions. For example, the 2s-10s inversion deepened significantly following the lower than expected US CPI report two weeks ago. This report led markets to (a) reprice the future path of federal funds, (b) correspondingly lower the 2-year yield, and also (c) lower the 10yr yield. Since (c) happened to a larger extent than (b), we ended up with deeper inversion.  On face of it, this might seem to somebody like bad news causing deeper inversion, right?

Do not count me in that camp. To see why, notice that the decrease in 10yr yield was different from the decrease in 2yr yield in that it mostly was not about lower expected path for fed funds rate.[2] Moreover, in so far as it was it was about expectations about future policy, it did not reflect expectations that policy rates will move eventually below neutral level, which is at the core of the signaling theory of yield curve inversion. Rather it reflected expectations that policy rates will rise less above neutral than was expected before. And if it was not about below neutral expected future rates, it is hard to argue that it was in some reflection of markets increasing their odds of recession, even though the inversion deepened significantly. If anything, it is hard to find anybody who thought the news were not good, as indicated by a positive stock market reaction. I am therefore struggling to follow the people who say that this development to them suggests risk of recession has increased.

Or take the most extreme example, the policy rate yield curve, which inverted only now. Is this in any way further strengthening of a signal of coming recession? Again, I struggle to see the argument. There are two reasons why the policy yield curve inverted now: the drop in 10yr yield, which I already argued was not a portend of coming recession; and increase in fed funds rates by the Fed during the November meeting. Of course, the increase in fed funds rate on its own can cause recession, but that is not the argument of yield curve believers. Rather, they argument is “Hey, it inverted, it must be a bad signal.” But if the inversion is caused by the central bank that increased fed funds rate, as expected, how can anybody interpret it as a signal of anything? Will it recession suddenly become much more likely on December 14, when policy yield curve will invert even more following the next hike, compared with December 13? I did not think so.[3]

So why are we having inversions if it is not because markets are pricing lower future rates because of recession? In other words, what do I say to somebody who might argue that long-term rates are always above short-term rates, unless markets expect policy rates to decrease, which is typically due to recession? Well, as you might guess, it is the typically, which is the problem. This inversion is not typical in that it is caused by the central bank itself. In other words, the central bank’s plan is for policy rates to follow an inverted “roof-shaped” path – rising significantly and temporarily above neutral before declining back to neutral.

This on its own should mean inversion, if bond yields are expected average future short-term interest rates (aka the expectations hypothesis). Therefore, the current inversions do not need to signal anything about the financial markets’ recessionary beliefs, just that they believe Fed’s intentions to go above neutral.[4] And this is what makes current inversion different from previous experiences: Back then, central bank was not hell-bent on going above neutral in fight against inflation, rather, it was trying to find neutral. And this, I think is an appropriate end to blog that has “folly” in its title: ending it with variation on the biggest folly of all, “this time is different”.

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[1] Of course, the statistician in me wants to scream something about N<10, but that is not the point for today.

[2] This is of course unsurprising, because changes in expectations about future rates rarely shift enough to move the 10yr yield, which is presumably the average expected value of fed funds rate over the whole 10yr horizon. Rather, the CPI report was catalyst for more broad repricing, which showed up as much lower real 10yr yield. Personally, I think it was in the spirit of coordination games a signal that this is finally the time when everybody will stop worrying that 10yr yield will rise further, and hence signal for everybody to buy 10yr yield, but that is purely speculation on my part.

[3] Similar argumentation applies to the 3m-10yr yield curve, even though there things are of course continuous.

[4] Note that the standard rules of logic apply – I am not saying markets are not expecting recession, or that recession will not happen, just that current inversions do not imply that markets are expecting one (even if they might be).  

The Swiss option for renumeration of excess reserves, reconsidered

 

When the Swiss central bank announced change to its renumeration of excess reserves held by commercial banks, I voiced skepticism that this would work. Specifically, I wrote that “when the system has large amount of excess reserves then this renumeration scheme should negate the increase in policy rates” and later that “one could address this by increasing the threshold [b]ut this would negate the desired goal of this policy which is decreasing the sums paid to commercial banks”.  Few months later, we know that the Swiss central bank did exactly what I said in the second part of the quote: it set the threshold above which excess reserves earn 0% interest to very high number – 28 times the required reserves. So while marginal excess reserves do pay 0% interest rate, the point where this marginal rate starts to apply is very high, so high that most (or no?) banks actually reach it.

In terms of the overnight market this means that there are banks that will borrow excess reserves at rates close but below the deposit rate, since they will be able to earn the deposit rate. In aggregate, the overnight (SARON) rate will stay close to the deposit rate, something we have indeed observed since the change (see picture below). The only difference is that the overnight rate is slightly below the deposit rate, rather than slightly above deposit rate, as was the case before the change. This reflects the fact that the banks lending reserves out now earn rate below deposit rate (0%), while borrowers earn deposit rate, so that the price of the transaction has to be in between those two. (Before lenders earned deposit rate, so the lower bound was the deposit rate; borrowers presumably would have to borrow at equivalent of marginal refinancing rate).

What about the effect on the payments from central bank to the commercial banks, which is presumably the main motivation? Of course, the policy means that for the 28-multiples of required reserves it is the deposit rate that applies, which means that the central bank is still paying large sums of money to commercial banks, despite the change it did. So, this policy should achieve very little in the direction of the desired outcome of lowering payments to commercial banks and corresponding losses for the central bank. That said, it does not achieve zero effect: as long as some banks are above the 28-multiple threshold, which is presumably the case, they are being paid less than what they would be paid otherwise.

So why did the Swiss central bank do it? It is hard to say. Partly, it might be simple theater for the public: setting the marginal rate for excess reserves to 0% means that the central bank can claim it did something. Equally, it might be issue of redistribution of excess reserves and profits: the change pushes excess reserves towards banks that are below the threshold and punishes banks with largest amount of excess reserves. What else? I think the evolution of ESTR, which stayed close to deposit rate despite it rising above 0%, makes it clear that the change can hardly be motivated by desire to impact the market interest rates, as the bank claimed; if anything, the move leads to slightly lower market interest rates.[1]

What does all this imply for the future behavior of the ECB? The fact that this is a lot about playing politics, rather than macroeconomic or financial policy, it is hard to know what the ECB will do. There are arguments for it not to do anything. First, it would avoid the whole messy business, including possible unintended consequences, perspective that might win given the limited effect on what it is supposed to achieve. Second, since it leads to lower overnight rate, and the magnitude of the effect might be hard to calibrate – especially in euro zone money market with much larger number of commercial banks and much bigger heterogeneity of excess reserves (see below).

 

 

 

That said, the ECB might still go for it despite the limitations. Apart from doing something for the sake of doing anything, even if the savings for the central bank would be small, the main motivation I could see is the positive effect on the redistribution of excess reserves: with potentially large costs of missed opportunity for banks above the threshold, there would be strong incentive for them to lend their reserves to banks below threshold. In environment of much higher overall interest rates this could have desirable financial stability effects. That said, since German banks would be hurt the most in terms of lost profits, the redistribution effects could also be a reason why this does not pass – the German central banker might not be too happy about this.

On balance, I now think that the ECB will stay clear of any change. It feels like that if they would do anything, they would have done it already when the changed the LTRO terms. The fact that back then they went for lowering the interest rate on required reserves – from main refinancing rate to deposit rate – but not for tiering suggests that they might have decided that going down this road offers too little benefit and too much risk. But of course, the ECB could easily surprise me once again.

 

 

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[1] Specifically, the bank said that it “ensures that the secured short-term Swiss franc money market rates remain close to the SNB policy rate”. True, they mention secured rates, which in euro zone are disconnected from the deposit rate, but that is mostly down to collateral shortage, and I don’t see how renumeration change affects that.