I think I made a similar objection to the colleague in question and we had an argument about exactly what we meant by "mean reversion" which was terminated by me resigning for unrelated reasons. Basically technically yes, but unless the cycles are really big Kondratieff things, over an economically meaningful horizon, your forecast is going to be dominated by whether they're cycles around a fixed number or cycles around a trend.
I take your remark to imply that your colleague considered cyclostationarity to be a type of mean reversion. That's interesting because I should have thought the obvious objection is that it is a type of *stationarity* - it's right there in the name! The "trend" isn't a straight line, but it is still a deterministic function. You could go farther and interpret stationarity obtained by differencing (e.g. exponential growth) to be "stationary with respect to a deterministic non-linear function".
I can see the case for saying that there is only one type of forecast, although that is unsatisfyingly tautological ("predictions are made about predictable processes"). And I can see the case for distinguishing between different types of predictable feature. But I am not persuaded by the hybrid argument that two of these three are "really" the same and the other is "really" different.
Well, at the very least, we can all agree that mean reversion can be distinguished from other types of regularity, and that therefore it must be possible to devise a criterion that puts reversion in one category and everything else in another. For one thing, trends and reversion can be combined - as "pixie theory" itself does.
The same question arises in relation to output growth and recessions. The standard view is (3), return to long run trend, but the evidence is more supportive of (2). For example, in looking at the divergence between Australia and New Zealand since 1980, the best explanation is that New Zealand has had more and deeper recessions. For those who aren't aware, NZ invented inflation targeting around 1990
back in the days when the unit root debate was causing beer and blood to be spilled, I used to say that the Fall of the Roman Empire really did happen, it wasn't just a particularly large and sustained deviation from trend.
There's a lot of potential digression points here, notably the slightly fantastical status of aggregate productivity figures in the first place - but concentrating on the thing that worries those of us stuck with this Chancellor on this island:
What worries me is that the most coherent story of the mechanics for "catch up" (either to the old level, or beyond) in productivity is that we've had a decade of really stupid decisions and failures to invest. So, the theory might go, stop making stupid decisions and do some investing and things will (one might guess) at least catch up. Trouble is, so far the government seems quite keen to continue with past stupid decisions and also not invest...
The point at the end about the new Chancellor is spot on. She knows too much to think that growth will come from austerity plus dull competence, but that’s the theory of growth she seems to be pitching. That suggests that she has an *actual* theory of growth she doesn’t want to talk about and ‘ah, mate, it’ll sort itself out, we’re bound to catch up a bit’ (combined with some nice ‘global productivity frontiers’ graphs) is a very, very obvious candidate.
I’m planning on writing a piece on this at some point, but I am about 80% certain that the UK’s apparent comparative weakness in productivity is heavily influenced by how successful the ONS is at recording hours compared to everyone else (and also incentives around hour reporting and the difficulty of capturing services activity in GDP). The ONS has far better standards for reporting than comparative countries, and it essentially results in the UK being penalised on measures such as productivity, homelessness and COVID fatalities as we actually bother to record failures. Other countries like Canada and Peru that also have well renowned statistics agencies have a similar problem - the biggest loser in this is Peru, which according to stats had the worst COVID death rate. This is clearly nonsense - what happened is you had a mediocre healthcare system coupled with a highly effective statistics agency, and so meant that you were both failing to save people and doing an excellent job of keeping track of who you didn’t save.
I can believe that as an explanation of levels, but does the ONS get better every year? - this is a trend over time. although I suppose one implication would be that the change in trend productivity is really just a reflection of how much better the ONS got at measuring hours after they moved to Newport
Factor in a few potential changes like restrictions on overtime (meaning people just stop reporting it), and the productivity issues aren’t a UK thing, they’re a worldwide thing (or in my opinion, a ‘the EU is totally useless’ thing).
It feels like someone has cause-and-effect reversed... The data doesn't "revert to the mean"; the mean BY DEFINITION follows the data. It's an *assumption* that there's something stable to "revert" to ..
yes that's true, but when you see it reverting over and over again, and you have at least a semi-plausible theory of why that might be, I think your confidence grows that the assumption corresponds to something (not necessarily directly observable) in reality
Every time you turn around, your shadow is right there. Do you "revert to your shadow", or does the shadow follow you? Unless the trend is definitely accelerating, any move will "move towards" the updated mean. More rigo(u)r is required to show there is even a "thing" to move toward, rather than a simple mathematical definitiin.
I think it's land and housing in the Georgist sense and I think Rachel reeves does too. I just don't think it's only land and housing and I fear she's put all her eggs in one basket
if I were you I would also be worrying that there's many a slip between cup and lip on the journey between "land and housing" and "sure, all previous tweaks to the planning system have been pretty ineffective but this one is gonna be the charm"
That productivity graph is for the UK but I believe it would apply about as well in Canada? I'm not quite sure because I haven't seen Canadian productivity figures in the same graphical form.
However, one place it definitely doesn't apply is the US. America is only one country, true, but it is a very large and important one. So it seems possible that pixies are conserved; they may have left the UK but only for greener pastures abroad. Perhaps they could be lured back to the old country? Immigration policy might be key after all!
Coincidentally I have just read the excellent guest post by Brian Potter on Noah Smith's substack about the state of ship-building in America. I was shocked to learn that America hasn't been good at building ships since the age of sail! So it seems that ship-building is in the remit of an entirely different class of pixie - selkies, perhaps.
the fact that I am alive and speak only rudimentary German is testament to the ability of the USA to build ships that are adequate to the task when they set their minds to it, so I won't comment on that!
yes, hedgehog charts like that can be drawn for lots and lots of places, which makes me v suspicious of purely British explanations for our productivity malaise, and slightly more inclined to believe in pixies.
Potter dealt with American ship-building efforts during both world wars, as well as the 1970 Act leading to “the largest peacetime shipbuilding program in U.S. history.” He isn't saying that America *can't* build ships, just that it can't build them at less than twice the price of competitors. That, it seems, has been steadily true since the transition to steam (despite America having innovated steam-powered river boats.)
I think there's also a third kind of forecast, leaving us with:
- things will stay the same as they are now
- things will keep changing the way they've been going
- things will go back to how they were
I was thinking the same thing - cyclostationary processes are forecastable in a third, different way from the other two.
I think I made a similar objection to the colleague in question and we had an argument about exactly what we meant by "mean reversion" which was terminated by me resigning for unrelated reasons. Basically technically yes, but unless the cycles are really big Kondratieff things, over an economically meaningful horizon, your forecast is going to be dominated by whether they're cycles around a fixed number or cycles around a trend.
Saved by the resignation!
I take your remark to imply that your colleague considered cyclostationarity to be a type of mean reversion. That's interesting because I should have thought the obvious objection is that it is a type of *stationarity* - it's right there in the name! The "trend" isn't a straight line, but it is still a deterministic function. You could go farther and interpret stationarity obtained by differencing (e.g. exponential growth) to be "stationary with respect to a deterministic non-linear function".
I can see the case for saying that there is only one type of forecast, although that is unsatisfyingly tautological ("predictions are made about predictable processes"). And I can see the case for distinguishing between different types of predictable feature. But I am not persuaded by the hybrid argument that two of these three are "really" the same and the other is "really" different.
My interpretation ends up agreeing with both you and with Dan's colleague:
1. stationary, cyclostationary, etc., are all extrapolation of trends. Meaning, "current data agrees with the model, future data will too."
2. mean reversion is "look, it deviates from the model right now, but it will come back to agree with the model eventually."
The two predictions differ because of your assessment of the present, not of the future.
Well, at the very least, we can all agree that mean reversion can be distinguished from other types of regularity, and that therefore it must be possible to devise a criterion that puts reversion in one category and everything else in another. For one thing, trends and reversion can be combined - as "pixie theory" itself does.
The same question arises in relation to output growth and recessions. The standard view is (3), return to long run trend, but the evidence is more supportive of (2). For example, in looking at the divergence between Australia and New Zealand since 1980, the best explanation is that New Zealand has had more and deeper recessions. For those who aren't aware, NZ invented inflation targeting around 1990
back in the days when the unit root debate was causing beer and blood to be spilled, I used to say that the Fall of the Roman Empire really did happen, it wasn't just a particularly large and sustained deviation from trend.
There's a lot of potential digression points here, notably the slightly fantastical status of aggregate productivity figures in the first place - but concentrating on the thing that worries those of us stuck with this Chancellor on this island:
What worries me is that the most coherent story of the mechanics for "catch up" (either to the old level, or beyond) in productivity is that we've had a decade of really stupid decisions and failures to invest. So, the theory might go, stop making stupid decisions and do some investing and things will (one might guess) at least catch up. Trouble is, so far the government seems quite keen to continue with past stupid decisions and also not invest...
The point at the end about the new Chancellor is spot on. She knows too much to think that growth will come from austerity plus dull competence, but that’s the theory of growth she seems to be pitching. That suggests that she has an *actual* theory of growth she doesn’t want to talk about and ‘ah, mate, it’ll sort itself out, we’re bound to catch up a bit’ (combined with some nice ‘global productivity frontiers’ graphs) is a very, very obvious candidate.
"there are really only two methods of forecasting – extrapolation of a trend, or mean reversion."
I might need to get this as a tattoo.
I’m planning on writing a piece on this at some point, but I am about 80% certain that the UK’s apparent comparative weakness in productivity is heavily influenced by how successful the ONS is at recording hours compared to everyone else (and also incentives around hour reporting and the difficulty of capturing services activity in GDP). The ONS has far better standards for reporting than comparative countries, and it essentially results in the UK being penalised on measures such as productivity, homelessness and COVID fatalities as we actually bother to record failures. Other countries like Canada and Peru that also have well renowned statistics agencies have a similar problem - the biggest loser in this is Peru, which according to stats had the worst COVID death rate. This is clearly nonsense - what happened is you had a mediocre healthcare system coupled with a highly effective statistics agency, and so meant that you were both failing to save people and doing an excellent job of keeping track of who you didn’t save.
I can believe that as an explanation of levels, but does the ONS get better every year? - this is a trend over time. although I suppose one implication would be that the change in trend productivity is really just a reflection of how much better the ONS got at measuring hours after they moved to Newport
Productivity levels have largely been static in most advanced economies since 2008 (apart from the US with its reaping of low interest rates). https://ourworldindata.org/grapher/labor-productivity-per-hour-pennworldtable?tab=chart&country=USA~JPN~DEU~GBR~FRA~CAN~NLD~ESP~SWE~CHE~ITA
Factor in a few potential changes like restrictions on overtime (meaning people just stop reporting it), and the productivity issues aren’t a UK thing, they’re a worldwide thing (or in my opinion, a ‘the EU is totally useless’ thing).
It feels like someone has cause-and-effect reversed... The data doesn't "revert to the mean"; the mean BY DEFINITION follows the data. It's an *assumption* that there's something stable to "revert" to ..
yes that's true, but when you see it reverting over and over again, and you have at least a semi-plausible theory of why that might be, I think your confidence grows that the assumption corresponds to something (not necessarily directly observable) in reality
Every time you turn around, your shadow is right there. Do you "revert to your shadow", or does the shadow follow you? Unless the trend is definitely accelerating, any move will "move towards" the updated mean. More rigo(u)r is required to show there is even a "thing" to move toward, rather than a simple mathematical definitiin.
I think it's land and housing in the Georgist sense and I think Rachel reeves does too. I just don't think it's only land and housing and I fear she's put all her eggs in one basket
if I were you I would also be worrying that there's many a slip between cup and lip on the journey between "land and housing" and "sure, all previous tweaks to the planning system have been pretty ineffective but this one is gonna be the charm"
That productivity graph is for the UK but I believe it would apply about as well in Canada? I'm not quite sure because I haven't seen Canadian productivity figures in the same graphical form.
However, one place it definitely doesn't apply is the US. America is only one country, true, but it is a very large and important one. So it seems possible that pixies are conserved; they may have left the UK but only for greener pastures abroad. Perhaps they could be lured back to the old country? Immigration policy might be key after all!
Coincidentally I have just read the excellent guest post by Brian Potter on Noah Smith's substack about the state of ship-building in America. I was shocked to learn that America hasn't been good at building ships since the age of sail! So it seems that ship-building is in the remit of an entirely different class of pixie - selkies, perhaps.
the fact that I am alive and speak only rudimentary German is testament to the ability of the USA to build ships that are adequate to the task when they set their minds to it, so I won't comment on that!
yes, hedgehog charts like that can be drawn for lots and lots of places, which makes me v suspicious of purely British explanations for our productivity malaise, and slightly more inclined to believe in pixies.
Potter dealt with American ship-building efforts during both world wars, as well as the 1970 Act leading to “the largest peacetime shipbuilding program in U.S. history.” He isn't saying that America *can't* build ships, just that it can't build them at less than twice the price of competitors. That, it seems, has been steadily true since the transition to steam (despite America having innovated steam-powered river boats.)