Wordle

If you have been on Twitter, you have probably seen pictures like this:

This is Wordle, an addictive little game where the goal is to work out the five letter word in six guesses or less. There is one Wordle a day.

Guesses tell you something about the solution:

  • Green means the solution has that letter is in that position.
  • Yellow means that letter is in the solution, but not in that position.
  • Black usually means that letter is not in the solution at all. (More correctly, black means that letter is in the answer fewer times than you guessed. Look at the first guess ‘TREES’ in the image above. The first ‘E’ is coloured yellow but the second is black. That tells you the answer has exactly one E.)

There is one other rule. Guesses have to be a word (in English). You cannot guess ‘AEIOU’.

I’ve played Wordle for about two weeks, I have settled on the same first word each time. It seems to work pretty well, but I got to wondering whether I could do better. I wanted to know two things:

  1. What is the best word to use as the first guess?
  2. What is the best strategy for making the second guess? I’ll explain the choices in a moment.

Yesterday, I decided to find the answer. I downloaded a dictionary and extracted the five-letter words. There were 4,622 of them in all, a number small enough to make brute force viable. I would get my answers by trying every possible combination of answer/first guess/second guess. Or so I thought.

What does ‘best’ mean? For this analysis, I defined ‘best’ as the guess words or strategy which leaves the smallest number of possible answers after each guess, on average.

This post is the story of a day’s effort to find an optimal strategy for Wordle. And I think I found it, a clear but surprising strategy. Skip straight to the conclusion to find it if the details don’t interest you. I’m not absolutely certain this is the optimal answer. If it is not, it is probably close. YMMV.

If this sounds like a great way to take all the fun out of a game, well for me it’s was opposite. This was all great fun.

Getting started

To work out the best word combinations or strategy for Wordle, I need to calculate the number of possible words from any combination of answer and guesses.

The first thing to do, after downloading a list of words, was to write a Wordle colouring function. The function takes a guess and answer as input and returns the Wordle letter colours as a string, for example “12213” with 1 = green, 2 = yellow and 3 = black.

Next, I wrote a function takes a guess (e.g. “HELLO”) and Wordle colours as inputs and then turns that into useable information about the solution. That information is a set of constraints, for example “the second letter of the answer must be E” and “the fifth letter cannot be Y,” etc.

These constraints can then be applied to the list of 4,622 five-letter words. Any word which does not satisfy all of the constraints is excluded. The list of remaining words at the end of that process is the number of possible answers for that guess/Wordle colour combination.

So, for example, if my guess/Wordle combination tells me the four letter of the answer is ‘A’, I can exclude all words in the list of 4,622 which do not have ‘A’ as their second letter.

The guess/Wordle combination tells us about the position of letters in the answer and the how many times a letter appears in the answer:

Position:

Green letters mean that letter is in that position in the answer.

Yellow letters mean that letter is not in that position in the answer.

Number:

A black letter tells you the exact number of times that letter is in the answer. It is equal to the number of times that letter appears in your guess as yellow or green. In most cases, this is zero, so a black letter is not in the answer. However, guesses which include a letter more than once can reveal more. If the guess is “TREES” and one E is yellow and one is black, then we know E appears exactly once in the answer. If both ‘E’s were black then we know there are zero ‘E’s in the answer. If both were any combination of yellow or green then the answer would have exactly two ‘E’s.

Any green or yellow letters which have no equivalents coloured in black gives us the minimum number of times that letter appears in the answer.

With these functions working and tested, it was on to trying out combinations of answer/guesses to find the first guess word that on average produces the smallest number of possible answers.

Question 1: What is the best first word?

Every Wordle starts blank and we have (almost) no priors about the answer. The game is not strategic in any sense, at least in the first round. So in principle the optimal strategy is probably going to use the same first word each time since we start each game without about the same information. But which word?

I can think of three reasons why this same-first-word-strategy might not be quite true. We start with at least some information about the answer because (probably) the game is designed not to re-use answers. We may also learn something about the distribution of answers (i.e. how Wordle is choosing answers), or the set of possible answers. Does Wordle choose common five-letter words more often? If it does, that is going to affect the optimal first guess.

Another possibility is that the game uses the optimal first word as its answer in a puzzle. If that ever happens, then that word will probably (though not certainly) cease to be the best first guess (assuming the system does not re-use past solutions).

To find the best first guess word, I wanted to try every possible guess against every possible answer, both drawn from my list of 4,622 words. For each guess/answer combination, I would do the following:

1. Calculate the Wordle colours, then

2. Use the combination of guess/Wordle colours to calculate the constraints (position and letter number), and finally

3. Apply those constraints to eliminate words from the list of 4,622.

This gives me the number I am interested in: the number of possible solutions left after I have made my first guess. The best word is the one which leaves me with the smallest number of possible answers after the first guess, on average.

Given a set of 4,622 words, there are about 18 million combinations of guesses and answers. To go through every one would take my ageing laptop 33 hours.

But I don’t need to try every possible first guess. Some first guesses are going to be better a priori candidates than others.

I suspect that the optimal first guess probably has no repeated letters. Wordle requires figuring out which letters are in the answer word, and then finding their position. There are 26 letters but only five positions, so the bigger problem is finding the letters. It is probably optimal to cast the widest possible net early on with words that have no repeated letter.

The first guess should also probably have the most common letters in it. I get the distribution of letters in the list of 4,622 five-letter words (not the whole dictionary), then assign a score to each word based on the frequency of the letters it uses. I exclude any words with repeated letters, then sort the list according to its letter score with the highest score first.

Here are the top ten words in that list (by the way, the best first guess word is not in this top 10):

I should say something about distribution. My analysis assumes Wordle picks its answers uniformly from the set of possible words. At the start of my analysis yesterday morning, I worried that Wordle might favour more common five-letter words. That would skew things, possibly a lot. But then I found the solution to yesterday’s puzzle was ‘REBUS’ which makes me think common words do not get special treatment from Wordle. But who knows.

I checked my assumptions about no duplicated letters and common letters by running tests over a sample of possible answers. I tested all possible guesses (all 4,622 of them) but only against random samples of answers. These tests confirmed that words with repeated letters are bad first guesses. One duplicated letter produces about double the number of possible answers compared to words without repeated letters. Words with two repeated letters produced four times more possible answers.

This test also suggested the worst possible word to use as a first guess is ‘MUMMY’.

Out of these tests I pulled the top 98 guess words from my list, sorted by letter distribution, to run against the comprehensive set of possible answers (I don’t know why 98, I think 99 was the first word on my list with duplicated letters, so I stopped there).

And here is the result. The best word to use as a first guess in Wordle is: TARES

As a first guess, TARES produces on average 83.4 possible words. Here is the top ten:

What strikes me about this result is the lack of vowels. Until now, I have been using “ADIEU” as a first guess (how much French is in Wordle?). Most of the top ten words only have two vowels. Go figure.

This result is based on a sample of the best 98 candidate first guesses. That number is too small to give me total confidence that I have not excluded a better answer. I have a bit more work to do yet.

Question 2: What is the best strategy for the second guess?

So we have our first guess. The question now is whether and how to use the information which is revealed by the first guess.

This choice is less obvious than it may first appear. The first guess is going to tell us about some of the letters in the solution and it will say something about their positions. It seems obvious that we should use that information to refine our second guess.

But using that information comes at a cost of re-using letters we already know about, rather than discovering new letters we did find with the first guess.

There is a trade-off between discovering new letters versus finding the position of letters we know are somewhere in the answer, or limiting our choices to the smaller set of possible solutions.

The question is whether it is better to ignore what we learn from the first guess and try a completely new word, knowing it is wrong; or is it better to use the information from the first guess to improve our second guess?

To test this, I ran two second-guess scenarios:

  • The ‘naïve’ scenario ignores the information returned from the first guess and makes a second guess with five new letters.
  • The ‘strategic’ scenario (I couldn’t think of a better name) incorporates information from the first guess by limiting second guesses to the set of possible answers implied by the first guess. So, if the first guess revealed the second letter is ‘A’ then the in this scenario the second guess will always have ‘A’ as its second letter.

For both of these scenarios, second guesses always follow the optimal first guess, which is TARES.

As in the analysis of first guesses, the goal is to find the strategy which produces the smallest number of possible answers after the second guess, on average.

Naïve scenario

To test the naïve scenario, I pulled from of the list of 4,622 words all the words which have no letters in common with TARES. There are only 267 of these words. This makes up the possible set of second guesses in the naïve scenario. Because the naive scenario ignores the information from the first guess, our task in this scenario is to find the single word which best follows TARES each and every time.

Here is what I did to find this word:

1. For every possible answer (all 4,622 of them), I make a first guess of TARES and calculate the Wordle.

2. From the list of possible second guesses (words which have no letters in common with TARES), and regardless of the first guess result, I choose a word, then calculate the Wordle for this second guess.

3. I then work out the number of possible answers by calculating and applying the constraints from the first guess/first Wordle combination to the list of 4,622, then to that shortened list I apply the constraints from the second guess/second Wordle combination.

This gives me the information I need, the number of remaining possibilities for that first guess/second guess combination.

Here is what I found. The best second guess word to use is: BLOND

So, under a naïve approach which ignores information from the first guess, the best-performing combination of first and second guesses is TARES/BLOND. On average, this combination leaves 7.5 possible words after the second guess. Here are the top ten second guesses following a first guess of TARES.

Having found this TARES/BLOND combination yesterday, I was keen to try it out on today’s Wordle. It worked about as well as it possible: after the second guess, TARES/BLOND left only one possible answer as solution for today’s Wordle: BOOST.

Awesome.

Strategic Scenario

The challenge has been set. The question is whether and in what circumstances is it better to use the information from the first guess in the second guess. The mark to beat is 7.5 average possible answers after the second guess.

The second guess in this scenario is conditioned on the information we glean the first guess. As a result, we are not looking for a single word as a second guess. Instead, we are looking at the average performance of using first guess information to inform the second guess compared to TARES/BLOND no-matter-what.

I suspect this strategy in this strategic scenario is going to perform better the more yellow and green letters turn up in the first guess. I also suspect a mixed strategy might be best: if there is a lot of green and yellow in the first guess, don’t ignore it. Otherwise, go BLOND.

Given this hunch, I decide to keep separate results according to the number of yellow and green letters revealed by the first guess, rather than just report an overall average.

Here are the steps in this second scenario:

1. For every possible answer (again, all 4,622), I make a first guess of TARES and calculate the Wordle.

2. Given the result of the first guess, I make a list of all possible answers and choose my second guess from this list. This means that if the first guess reveals ‘A’ as the second letter of the solution, my second guess is only going to use words which have ‘A’ as their second letter.

3. For each result of the second guess, I calculate the number of possible answers, then add that number to the green/yellow combination from the first Wordle (this will make more sense in a moment). I also keep a count of the number of times each green/yellow combination appears.

At the end of this calculation, having gone through every possible answer/second guess combination (with TARES always as the first guess) I calculate the average number of possibilities for each second guess for each green/yellow combination from the first guess. These results can be compared with the results to the performance of the naïve strategy using TARES/BLOND.

Here is the result:

At first, I did not believe this result. While it confirmed the intuitive finding that the more green and yellow letters there are in the first guess, the better it is to use that information.

But is it really that bad to get three green letters and no yellows on the first guess? Does that combination really deliver 29 possible words on average after the second guess? And are three greens on the first guess really worse than no greens or yellows at all?

Digging a little deeper, it turns out the three greens performance is being largely driven by words ending in ‘es’. There are a lot of five letter words which have a vowel as the second letter ending in ‘es’. To check this, I re-ran the strategic scenario but excluded any results from words ending in ‘es’ and which produced zero yellow letters in the first guess. Sure enough, three greens are much more useful when the solution happens not to be word ending in ES.

As if to confirm how strangely unhelpful three greens on the first guess is, I stumbled across this on Twitter this morning:

I feel his pain. But perhaps this result is more likely than it seems – that is, if you get three greens in the first place. That probably does not happen very often, I reckon about 1.2% of the time (again, subject to on how Wordle chooses its solutions and also how people choose their guesses).

Some caveats

I’m not sure it’s really necessary to have caveats. This was a day long project and a heap of fun to do. It’s the holidays. I haven’t had a chance to really look at this properly, or to really test the code. The winners only won narrowly and further analysis could change things. I have not checked for similar work, who knows what others have found. The big caveat, though, is distribution. If Wordle is choosing common or obvious five-letter words more often than others, then some or all of this goes out the window. I don’t know if they do.

Apart from that, if these results are wrong, my instinct after all of two weeks playing this game is that it is not by too much. That three greens result bothers me, though.

Conclusion: Optimal Wordle strategy

Based on this analysis and all the assumptions in it, here is the optimal Wordle strategy:

First guess: TARES

Second guess: unless your first guess has four or five green and/or yellow letters, your second guess should always be BLOND.

If Wordle ever uses TARES as an answer, then change your first guess word. Try another word from the top ten above.

Happy New Year!

Giving it away

Carbon News reports:

THEY’VE declared a climate emergency and now the government is taking steps to ensure we can continue to drink chilled Sauvignon Blanc in a warming world.

Agriculture minister Damien O’Connor has announced the government is investing in a seven-year programme led by Bragato Research Institute to help future-proof the sustainability of New Zealand’s Sauvignon Blanc grapevines.

“Sauvignon Blanc comprises 87% of our wine exports. This new $18.7 million grapevine improvement programme will introduce genetic diversity into our vines, and ensure they continue to thrive in New Zealand conditions,”  O’Connor said.

“Many of our existing vines will need to be replaced in 10 to 15 years in order to avoid a loss in productivity.

“The new variants could also lead to new flavour and aroma profiles, resulting in exciting new styles of wine that will add further value to the sector.”

Seriously?

The government also gifted invested another $7.5 million through another MPI programme.

What is the problem the government thinks it is solving here? Does it think the horticulture sector has not heard of climate change? That growers could not possibly work out a way to cope with gradual changes in the distribution of temperatures, rain and humidity without someone to hold their hand?

“Anticipated climate change impacts require action now to ensure New Zealand continues to be considered the world’s Sauvignon Blanc capital.”

I’d guess there will be no shortage of action if the alternative is growers lose money or go out of business if they do not adapt to changing weather patterns.

If the standard for getting $26 million out of the government is that you might be affected by a changing climate – who does not qualify?

Of course, the problem the government is solving with its seemingly endless parade of nonsense on climate change is its own re-election in two years.

There is a fundamental problem across all of the government’s thinking on adaptation. The government is making no attempt to isolate the problems that property owners are not going to solve themselves.

Managed retreat from low lying land is a horribly exaggerated response to a problem that should mostly take care of itself. From the government’s perspective, 99% of the problem is going to be solved automatically by property owners responding to inundation risks. Nobody is better placed to weigh costs and benefits and tradeoffs between competing land uses than land owners.

The government’s magic bullet in all of this is finding a way to solve the commitment problem: the promise not to bailout wealthy landowners who suffer losses. Is there anybody in government thinking about adaptation in such gravy-free terms?

Did Rod Carr mislead the Environment Committee?

Yesterday, Rod Carr appeared before Parliament’s Environment Committee as Chair of the Climate Change Commission. Carr made the following statement (at 5:10):

I think the first thing to do is recognise not only as Chair but the Commission itself accepts that markets and prices will provide significant signals to producers, consumers and investors, that will play an important part in putting New Zealand on a pathway, which it is not currently on, to achieve the statutory targets for domestic emissions.

So, Carr told the Select Committee that New Zealand is not on track to deliver its “statutory targets for domestic emissions.”

There are two problems with his statement.

The first is that back in May the Climate Change Commission told the government that existing policies and an ETS price of $50 will deliver net zero emissions in about 2050.

Today, the ETS is at $68. At that higher price, the Commission’s models must show New Zealand getting to net zero emissions well before 2050.

I would say that puts New Zealand firmly on track to deliver statutory targets.

The second problem with Carr’s statement is his mention of “statutory targets for domestic emissions.”

What statutory domestic target?

The Climate Change Response Act defines net emissions as gross emissions minus domestic removals (for example, by forestry) minus offshore mitigation. The Act says emissions budgets must be met “as far as possible” by domestic reductions and domestic removals. But there is no “statutory targets for domestic emissions.”

I am perfectly willing to believe Carr misspoke, and that he meant “statutory targets.” But New Zealand is firmly on track to achieve its legislated targets.

So did Rod Carr mislead the Environment Committee by telling it New Zealand is “currently not on” track to deliver the targets Parliament has set?

Or did Rod Carr tell the Environment Committee New Zealand is not on track to achieve statutory targets which he invented?

My guess is that the unelected Carr is making an unstated political judgment about the acceptable level of tree planting. With its current settings, a $68 ETS is going to plant a lot of trees, probably more than Carr and the Climate Change Commission would like. Perfectly reasonable position for them to take.

But if that is Carr’s objection, he should be clear about it.

There is a world of difference between “more trees than we would like” and “currently not on [track].”

New Zealand is firmly on track, in the important sense that, according to the Commission’s modelling, it will achieve net zero emissions well before 2050 at an ETS price of $68.

Here is why Carr’s misleading statement matters.

If New Zealand is already on track to statutory targets, that is going to be relevant context for deciding whether the cost and pain of the upcoming Emissions Reduction Plan is really necessary.

Pretending New Zealand is off track is the foundation officials and ministers need to claim their draconian Emissions Reduction Plan is necessary.

It is not.

It is a choice. The trade-off is between a) willingness to pay more for a higher share of gross reductions in emissions, versus b) paying less and relying more on trees.

This is a legitimate political choice. That choice is pre-empted when unelected officials say New Zealand is ‘off track’ in order to maintain that their sweeping plans for how each of us lives is needed, as if we have no choice.

We already have congestion pricing

It’s a rainy morning in Wellington. There have been crashes on my road to work. The roads are full.

Uber wanted to charge me $84 to get to work by 9am. The usual price is $21. So I’m going to Zoom in for the 9am and come in after that when, I expect, prices will be more sensible. (Assuming I still have a job: missing the 9am might be a bigger deal than I think.)

So: one less road user at the peak of a particularly busy day. I’m sure I am not the only one. If it were desperate for me to be there in person for the 9am, I’d have swallowed the extra fee. Or perhaps been a bit more organised and picked up my car yesterday.

The system is working. Now scale.

Low expectations

Source: Wikipedia

The Herald reports:

Andersson, leader of the Social Democratic party, decided it was best to step down from the post [Prime Minister] more than seven hours after she made history by becoming the first woman to lead the country.

Myself, I would have gone with “less than eight hours.” Perhaps something was lost in translation. Perhaps this is Swedish humour. Perhaps the author is not a fan.

To Minister Shaw: Please explain

Yesterday, in the Herald ($), I challenged Climate Change Minister James Shaw to explain how his Emissions Reduction Plan lowers emissions.

Source: NZ Herald

In this post, I want to head off what he is going to say. His lines are, frankly, not right. So let’s get that on the table and go through the argument before he says it.

Shaw’s plan is vast. It covers every sector of the economy. The government could regulator, tax or subsidise anything or everything in the name of reducing emissions.

But Shaw’s plan is not going to reduce emissions.* The government has already placed a quantity cap, a sinking lid, on emissions with the ETS. Legislation passed in 2020. It is widely accepted that cap-and-trade schemes neutralise other emissions policies. If the cap determines total emissions, policies under the cap do not.

This neutralising effect of an emissions cap is called “the waterbed effect”.

Here is how a cap-and-trade scheme will neutralise an EV subsidy, for example:

Imagine an economy normally produces 100 tonnes of emissions. This year, the government decides to cap emissions at 80 tonnes. It issues 80 emissions permits and demands the surrender of one permit per tonne of CO2. Emissions fall to 80 tonnes.

Next year, the government issues another 80 permits and introduces a new EV subsidy. The subsidy successfully reduces transport emissions by five tonnes.

Total emissions remain at 80 tonnes. Why? Because there are still 80 emissions permits available. The five permits which transport no longer needs due to the subsidy will be used elsewhere. They will raise emissions (or postpone reductions) by exactly five tonnes somewhere else in the economy.

So, the EV subsidy reduces emissions from one sector. But overall emissions do not change. This is the waterbed effect.

Now, before I go any further, let me say that “The ETS Is Not Enough”™ is not an answer. That line is a mantra in Wellington. It is useless except for the fact it has fooled everybody who hears it.

Somehow, nobody has noticed “The ETS Is Not Enough”™ does not make any case for doing other policies if those policies are going to be neutralised by the cap.

Even if the ETS leaves you short of your emissions target (because it is Not Enough™), the waterbed effect is still in play.

So even if the “The ETS Is Not Enough,”™ complementary emissions policies don’t help. If they are neutralised by the cap, then those policies are going to leave you exactly as far short of your target as if you had not done them.

Every day, this advanced logic escapes hundreds of public servants who do nothing except think about climate change policy at your expense. You pay their salaries but I assure you they are not working for you.

Anyway, if Shaw’s Emissions Reduction Plan is to reduce emissions, it has to find a way around the waterbed effect.

Shaw has previously spoken about how to avoid the waterbed effect. His solution seems obvious: lower the cap as policies bring down emissions.

Here is Shaw speaking to Carbon News earlier this year:

[W]hat they’re talking about is something called the ‘waterbed effect’. If you cut emissions in one area and that takes things below the cap then it allows others to pollute more in the meantime.

But if you’re successfully lowering the cap every time then you minimise that effect because you’re saying, ‘Yes we’re taking emissions out here with the feebate and also with the ETS and then next time we set an emissions budget it will take account of the fact that emissions are lower.’

The way it works is you’ve got your 2050 target which is sort of long term. Then you’ve got your three five yearly budgets and each one is smaller than the one before. Every five years, at the start of each budget period, if circumstances dramatically change since you set the budget five years earlier, you can adjust at that time and say, ‘hey look things have moved far quicker or in unexpected ways we can adjust the budget to take account of that emissions budget.’

Shaw’s logic, as I understand it, is this: Ministers set the cap; Ministers can link the cap to complementary policies (EV subsidies, for example); complementary policies therefore lower emissions.

In the earlier example, emissions stayed at 80 tonnes after the EV subsidy had cut transport emissions. That is because there were still 80 emissions units in circulation. The intuitively obvious solution is to lower the emissions cap to 75 tonnes. Total emissions come down in line with the emissions benefits of the EV subsidy. Problem solved.

No. Problem not solved. That logic is not right.

Linking the cap to the policy does not make the policy lower emissions. It is the cap, not the policy, which lowers emissions. The policy is actually redundant. We explain why in our submission earlier this week on Shaw’s plan:

[Linking] the cap with complementary policies may imply the policies lowered emissions. However, this is an illusion. To see why consider this from the earlier example:

# If the government reduced the cap to 75 tonnes without the complementary policy, emissions would fall to 75 tonnes.

# If the government did the complementary policy but left the cap at 80 tonnes, emissions would remain at 80 tonnes.

The cap is doing all the work.

Accordingly, it is wrong to say that linking the cap to complementary policies means complementary policies reduce emissions. The connection is arbitrary. Ministers could link the cap to, say, cumulative rainfall, but nobody would suggest last week’s storm had lowered emissions. It is the cap, not the complementary policies, which lowers emissions. Complementary policies are still neutralised by the emissions cap. The waterbed effect is not avoided.

The cap is doing all the work. So long as the government has the option to reduce emissions simply by tightening the cap, other policies cannot cause emissions to come down (provided they are subject to the cap). The other policies are redundant.

The next obvious question is: what happens when the government does not have the option to simply tighten the cap? What if carbon prices rise to the point that voters or Parliament will not countenance any further tightening? Can complementary policies help further reduce emissions then?

This does open the door to complementary policies reducing emissions, but only by the smallest amount. Our submission walks through the weird permutations which are needed to get complementary policies to to cut emissions under an emissions cap. Short answer: we see no real way for complementary policies to cut more than a little extra emissions, at best.

If anything, complementary policies are more likely to raise emissions because of their lower economic efficiency and likely political inefficiency. The high cost of top-down emissions policies probably translates to a higher burn rate of political capital per tonne of emissions. That may seem like a fairly esoteric metric, but it matters in principle when the limiting factor on further reducing emissions is political feasibility.

Think about it this way: if the reason the ETS becomes politically constrained is because voters don’t like its cost of living effect, then how can policies which spend far more per tonne of abated emissions be any solution?

Complementary policies only have the opportunity to make any difference to emissions, up or down, if the ETS first becomes politically constrained.

It is hard to see any way the ETS is going to become politically constrained before 2050. New Zealand is already comfortably on track to achieve net zero emission in 2050 with existing policies. We include a list of reasons why in our submission. Nearly all of the evidence shows existing policies get us there.

I need to be clear about what “politically constrained” means. I mean it in the sense that a future government has no politically feasible way to net zero emissions.

Sure, the government could force the ETS price all the way to $500 if it stamps hard enough on trees and other removals technologies and rules out offshore mitigation entirely. That is what this government wants to do. And voters could well object to paying $500 per tonne of carbon.

But the ETS is not politically constrained if the government has the option to just stamp a bit less hard on trees or open the door slightly to offshore mitigation. Politically constrained is when the government cannot tighten the ETS any further, it cannot plant more trees, it cannot commission other removals technologies, and it cannot go offshore, and it is still short of net zero emissions.

Not going to happen. See the submission for why.

So, there is no question at all that right now we have legitimate, affordable, genuine pathways to net zero emissions, and we have options. We can plant a less trees and still get to net zero. We could plant no more trees and get to net zero. None.

Which means the government will always have the option to tighten the cap.

Which makes complementary policies under the cap redundant, including existing emissions policies.

Which means James Shaw’s vast plan is not going to reduce emissions. Not by one tonne.*

* For policies covered by the ETS cap, which is nearly everything except agriculture.

Why Reserve Bank independence matters

The case for Reserve Bank independence on monetary policy is obvious. If politicians have control of the money supply, they will use it to support their re-election.

But what is the case for Reserve Bank independence on financial regulation?*

The question arises because the Reserve Bank is looking at disclosure rules and possibly other regulations in response to climate change. The Bank can only consider these actions by maintaining climate change is a risk to financial stability. The Reserve Bank Act does not mention climate change but makes the Bank responsible for the stability of the financial system.

The Reserve Bank has not found any credible evidence that climate change threatens financial stability. Climate change is a big problem, to be sure, which demands a response. But its costs will be manageable and come with decades of warning. The idea that climate change is financial stability risk is absurd.

Accordingly, the Reserve Bank is outside its financial stability mandate by focusing on climate change. Its decision to target climate looks politically motivated.

John Cochrane explains why the combination of unlawful, politically-motivated actions by powerful financial regulators is toxic:

Of all the threats posed by a slowly warming climate, why is Ms. Yellen [the US Treasury Secretary] talking about financial stability? The answer is simple: Financial regulators are not supposed to implement each administration’s policies on non-financial matters. Financial regulators may only act if they think financial stability is at risk.

Why? Imagine that Trump returns. He declares, “Illegal immigration is an existential crisis. I can’t get Congress to do anything about it. Financial regulators: Tell banks to freeze the bank accounts of any customers who can’t prove legal status. Scour people’s accounts for payments to illegal employees. Freeze out any business that hires an illegal.” You would be shocked. The nation would be shocked. Ms. Yellen would be shocked. There is no financial risk here, we would all say. This is a vast abuse of power.

The Reserve Bank’s actions on climate change are not remotely in the same league of awfulness as this scenario. But it opens the door to that possibility in the future.

Climate risk to the financial system is a Big Lie. I don’t know how to put this politely. A little lie is a knowing untruth spouted by a devious individual. A Big Lie is a whopper, self-evidently false when parsed in standard English, passed around and around the bubbles of Davos, Glasgow, alphabet-soup financial agencies, philanthropies, and the narrative-endorsing media, until earnest do-gooders come to believe in its nonsense. Spouting it gains one the approval of the elite, and denying it quick expulsion and exclusion. A Big Lie justifies extraordinary grasps of political power.

Why repeat this Big Lie? Well, it’s obvious. Many people in our government and surrounding policy elites want to expand a particular kind of climate policy. That policy centers on stopping fossil-fuel development and use, before alternatives are available at scale, and subsidizing a particular kind of “green” projects. Windmills, solar panels, electric cars, rail, yes. Nuclear, carbon capture and storage — which would permit fossil-fuel burning — natural gas, hydrogen, geothermal, hydropower, innovation, zoning and land-use reform, adaptation, no.

Democratically elected legislatures and accountable administrations refuse to quickly implement this policy. Even the Biden administration, which on day one canceled the Keystone pipeline, quickly turned around to ask OPEC and the Russians to turn on the spigots when voters noticed gas prices rising.

What to do? Well, turn to financial regulation. What they can’t accomplish by accountable, democratic methods, they can accomplish by unleashing the awesome power of financial regulators to impose these policies, by denying funding to fossil-fuel companies and their customers, and freezing them out of the financial or payments system as we do to pot farmers, by demanding “disclosures.” The European Central Bank (ECB) is already printing money to buy “green” bonds, declaring them to be “undervalued.”

It is a particularly effective idea, because once thousands of pages of regulations are written, once the right people are appointed with all the protections of office, once the Twitter mob has silenced dissenters in the financial-regulatory community, once private businesses have gotten the message how to please regulators and hired hundreds of thousands of climate-disclosure compliance officers, the effort will be immune to the whims of pesky voters….

Most of all, it is blatantly illegal. In a democracy, independent agencies have broad but limited powers. Financial regulators are limited to financial risks. Securities regulators are supposed to enforce the “fiduciary rule” that asset managers must invest only on financial basis, not to please either the managers’ or politicians’ preferences. And there are great reasons for this limitation. If the Fed starts buying “green bonds,” the next Trump can force it to start buying “build the wall” bonds…

John Cochrane really is difficult to excerpt. Do read the whole thing.

In New Zealand, the order of events is slightly different. Climate change is more politically feasible here than in other countries, with the possible exception of agriculture. But it is the Governor driving the Bank’s focus on climate, rather than politicians forcing it onto the Bank. The end result is the same: an unelected body pushing a political agenda, compromising its independence, and opening the door to greater abuses in future. It is all fundamentally undemocratic.

Finally, a nice insight from Cochrane on the logic behind central banks’ focus on investment:

What they mean is not climate risk to the financial system, but the financial system’s risk to the climate, by financing the “wrong” investments. But they’re not allowed to regulate that. Hence the Big Lie: We looked for risks, and guess what, climate came out on top!

John Cochrane will deliver a public webinar for the New Zealand Initiative on Thursday 2 December at 11am. Sign up here.

Ian Harrison will deliver a public seminar on “Climate change and the risk to financial stability; Reality or overreaction?” next week on Friday 26 November at 11am Sign up here.

*To be clear, the independent application of financial regulation. Policy setting sits and should remain with the elected government.

Email to the Reserve Bank

The Reserve Bank says climate change is a risk to financial stability. It is proposing to regulate accordingly. A recent paper by the Federal Reserve Bank of New York finds weather disasters are profitable for large banks because they increase loans. In view of the apparent gulf in the two positions, and the lack of any credible evidence so far from the Reserve Bank for its position, the Bank needs to reconcile the gap between its position and the evidence.

Yesterday, I sent the following email to the Reserve Bank. It includes a promise to OIA the Bank at the end of February with a goal of finding out what the Bank has done with these papers:

From: Matt Burgess
Sent: Thursday, 18 November 2021 6:20 pm
To: xxxxxxxxxxxx@rbnz.govt.nz
Subject: Research on climate change and financial stability

Dear xxxxxxxx

In view the Reserve Bank’s interest in climate change, I attach a paper from the Federal Reserve Bank of New York titled “How Bad Are Weather Disasters for Banks?”

Here is the abstract:

Not very. We find that weather disasters over the last quarter century had insignificant or small effects on U.S. banks’ performance. This stability seems endogenous rather than a mere reflection of federal aid. Disasters increase loan demand, which offsets losses and actually boosts profits at larger banks. Local banks tend to avoid mortgage lending where floods are more common than official flood maps would predict, suggesting that local knowledge may also mitigate disaster impacts.[my emphasis]

The paper includes a literature review:

Our main findings are generally consistent with the few papers that study the bank stability effects of disaster. Looking across countries, Klomp (2014) finds that disasters do not effect default risk of banks in developed countries. Brei et al. (2019) find that hurricanes (the most destructive weather disaster) do not significantly weaken Caribbean banks. Koetter et al. (2019) finds increased lending and profits at German banks exposed to flooding along the Elbe River. The study closest to ours by Noth and Schuewer (2018) finds default risk increases at U.S. banks following disasters but the effects are small and short-lived. Barth et al. (2019) find higher profits and interest spreads at U.S. banks after disasters but did not look at bank risk. Based on four case studies of extreme disasters and small banks, FDIC (2005) concluded that …”historically, natural disasters did not appear to have a significant negative impact on bank performance.”

These findings appear to be directly relevant to and substantially at-odds with the Reserve Bank’s position on the financial stability effects of climate change. I have found no record of any of these papers on the Reserve Bank’s web site.

Here are the references to those cited papers with their abstracts:

Barth, J., Y. Sun, and S. Zhang (2019). Banks and natural disasters. SSRN Working Paper

Natural disasters are not rare and costless events. Indeed, the evidence indicates there has been an acceleration in the number of disasters and the associated costs over the past century. Such disasters can cause severe property damage in the communities affected. Typically, insurance policies and government disaster relief fail to cover the full amount of damages. In this case, banks can play an important supporting role in providing additional funding for the necessary reconstruction that takes place after disasters. We provide evidence that following natural disasters, banks with branches in the affected areas raise both deposit and loan rates, but the latter more than the former so that net interest margin increases. This, in turn, leads to an increase in return on assets for such banks, but not sufficiently large enough to indicate profiteering. At the same time, banks increase the use of brokered deposits after natural disasters to help fund the increased demand for loans by individuals and firms in affected communities. Thus banks located in the disaster-prone areas contribute to helping communities recover from natural disasters.

Brei, M., P. Mohan, and E. Strobl (2019). The impact of natural disasters on the banking sector: Evidence from hurricane strikes in the Caribbean. The Quarterly Review of Economics and Finance 72. https://ideas.repec.org/a/eee/quaeco/v72y2019icp232-239.html

While natural disasters cause considerable damage and a number of studies have attempted to investigate the nature and quantify the magnitude of these losses, there is a paucity of empirical evidence on the impact on the banking sector. In this paper we construct a panel of quarterly banking data and historical losses due to hurricane strikes for islands in the Eastern Caribbean to econometrically investigate the impact of these natural disasters on the banking industry. Our results suggest that, following a hurricane strike, banks face deposit withdrawals and experience a negative funding shock to which they respond by reducing the supply of lending and by drawing on liquid assets. There are no signs of deterioration in loan defaults and bank capital. Therefore, the withdrawal and use of deposits rather than an expansion in credit appears to play a significant role in funding post hurricane recovery in the region. This points to the importance of an active reserve requirement policy.

Klomp, J. (2014). Financial fragility and natural disasters: An empirical analysis. Journal of Financial Stability 13 https://doi.org/10.1016/j.jfs.2014.06.001

Using data for more than 160 countries in the period 1997 to 2010, we explore the impact of large-scale natural disasters on the distance-to-default of commercial banks. The financial consequences of natural catastrophes may stress and threaten the existence of a bank by adversely affecting their solvency. After extensive testing for the sensitivity of the results, our main findings suggest that natural disasters increase the likelihood of a banks’ default. More precisely, we conclude that geophysical and meteorological disasters reduce the distance-todefault the most due to their widespread damage caused. In addition, the impact of a natural disaster depends on the size and scope of the catastrophe, the rigorousness of financial regulation and supervision, and the level of financial and economic development of a particular country.

Koetter, M., F. Noth, and O. Rehbein (2019). Borrowers under water! Rare disasters, regional banks, and recovery lending. Journal of Financial Intermediation Forthcoming. https://libkey.io/10.1016/j.jfi.2019.01.003?utm_source=ideas

We show that local banks provide corporate recovery lending to firms affected by adverse regional macro shocks. Banks that reside in counties unaffected by the natural disaster that we specify as macro shock increase lending to firms inside affected counties by 3%. Firms domiciled in flooded counties, in turn, increase corporate borrowing by 16% if they are connected to banks in unaffected counties. We find no indication that recovery lending entails excessive risk-taking or rent-seeking. However, within the group of shock-exposed banks, those without access to geographically more diversified interbank markets exhibit more credit risk and less equity capital.

Noth, F. and U. Schuewer (2018). Natural disaster and bank stability: Evidence from the U.S. financial system. SAFE Working Paper 167.

Our analysis provides new evidence that weather-related disaster damages in the banks’ business regions indeed weaken bank stability and performance. This is reflected in significantly lower bank z-scores, higher probabilities of default, higher non-performing assets ratios, higher foreclosure ratios, lower return on assets and lower equity ratios in the two years following a natural disaster. For a relatively small number of (non-weather-related) geological disasters in the United States, such as earthquakes and tsunamis, we show that these disasters have even relatively stronger adverse effects on bank stability. Overall, the evidence reveals that natural disasters jeopardize borrowers’ financial solvency and decrease bank stability, despite potential insurance payments and public aid programs. On a more positive note, we find that banks generally manage to recover from the adverse shock from weather related disasters (but not from geological disasters) after some years, which is reflected in the bank stability and performance measures of affected banks that are not significantly worse than those of unaffected banks two or three years after a disaster.

Given the extent of the apparent gap between these research findings and the Reserve Bank’s position on the financial stability effects of climate change, I trust the Reserve Bank will consider this research seriously and be able to reconcile its position with these findings.

Given the public interest in this area and the significant steps the Reserve Bank is considering around disclosure and possibly other regulation, at the end of February 2022 we will submit a request to the Reserve Bank under the OIA for all documents and emails which refer to these articles.

I hope you will find this research interesting and useful.

Best regards,

Matt Burgess

And a reminder that none of those five papers appear anywhere on the Reserve Bank web site, according to Google on 17 November, despite their obvious relevance to the relationship between climate change and financial stability. #smh

Contrasting substance on climate

The Reserve Bank keeps saying climate change threatens financial stability. It has been saying that for three years. No previous Reserve Bank Governor agrees, judging by their silence on the matter. As I said in last week’s report on the Reserve Bank, after three years of looking the Reserve Bank has not been able to come up with any evidence for their theory. I’m sure it is due any minute now.

Via John Cochrane, the Federal Reserve Bank of New York has taken a different approach. It has actually looked at the evidence. Its paper, called “How Bad Are Weather Disasters for Banks?” includes this as its opening sentence in the abstract: “Not very.”

It goes on:

Disasters increase loan demand, which offsets losses and actually boosts profits at larger banks. Local banks tend to avoid mortgage lending where floods are more common than official flood maps would predict, suggesting that local knowledge may also mitigate disaster impacts.

Here is their literature review:

Our main findings are generally consistent with the few papers that study the bank stability effects of disaster. Looking across countries, Klomp (2014) finds that disasters do not effect default risk of banks in developed countries. Brei et al. (2019) find that hurricanes (the most destructive weather disaster) do not significantly weaken Caribbean banks. Koetter et al. (2019) finds increased lending and profits at German banks exposed to flooding along the Elbe River. The study closest to ours by Noth and Schuewer (2018) finds default risk increases at U.S. banks following disasters but the effects are small and short-lived. Barth et al. (2019) find higher profits and interest spreads at U.S. banks after disasters but did not look at bank risk. Based on four case studies of extreme disasters and small banks, FDIC (2005) concluded that …”historically, natural disasters did not appear to have a significant negative I impact on bank performance.”

So, a small, short lived increase in default (not stability) risk, followed by higher profits as a result of higher lending for the recovery. Larger banks see the greatest boost in profitability.

Oh.

There is more substance in that quote above than anything the Reserve Bank has written on climate change. Look at this tripe, from their the Reserve Bank’s Climate Changed report:

A key concern for us is the exposure of the financial sector, including banks and insurers, to climate-related risks… We take our role seriously, so in 2018 we launched our Climate Change Strategy to understand and manage our direct impacts on climate change, incorporate climate change into our core functions, and lead through collaboration…  Without significant action there will be serious impacts on our economies.

There is more that we can collectively do to integrate climate considerations throughout the financial system. It is encouraging to see national and global progress – for example, progress in setting a framework to disclose climate-related risks and some firms beginning to disclose, the delivery of the Climate Change Commission’s first set of advice, and the launch of Toitū Tahua, the Centre for Sustainable Finance. Internationally we are heartened by collaboration in international groups such as the Network of Central Banks and Supervisors for Greening the Financial System (NGFS) and the Sustainable Insurance Forum (SIF), and the focus on finance at this year’s United Nations Climate Change Conference (COP26).

A key challenge is that financial stability is best maintained when all relevant risks have been identified, priced and allocated to those best able to manage them. Work is underway to increase our global understanding of these risks.

Yet we need to be realistic in measuring our collective global progress against the scale of the risks before us and the transition required. While tools like disclosure and scenario analysis are critical in helping us understand and prepare for climate risks, we cannot let a desire to perfect such analysis paralyse us…

Etc. The Reserve Bank could have written that literature review quoted earlier. It decided not to. Instead, the Bank chose to pump out its risible agitprop which might as well have come from Greenpeace.

As Cochrane points out:

This is a courageous paper to write… “We looked and there is nothing here” is not going to go down well. It’s hard to publish papers and get jobs as climate and finance researchers these days if you come up with the “wrong” answers.

A reminder that John Cochrane is delivering a public seminar for the New Zealand Initiative on 2 December. You can sign up here.

Post script: The Fed’s literature review, the part that covers stability, has references to five academic papers. These papers have pertinent titles: “Financial fragility and natural disasters,” “The impact of natural disasters on the banking sector,” “Borrowers under water! rare disasters, regional banks, and recovery lending,” “Natural disaster and bank stability,” and “Banks and natural disasters.”

According to Google, none of those five papers are mentioned anywhere on the Reserve Bank’s web site. Quelle surprise.

Untrue statements as boilerplate

Stuff reports:

A group of more than 100 New Zealanders, including two former All Blacks and musician Neil Finn, has written an open letter to New Zealand Rugby saying it is going against its own leadership principles by making a major deal with an oil, gas and plastics company.

Good luck to those who have signed the open letter.

But where is the open letter that complains about all the emissions policies which the government says will cut emissions but don’t?

Just yesterday, for example, the government announced it will spend $13 million on a welter of new projects. Together these projects will reduce emissions by exactly zero tonnes because every one of them is in the ETS cap.

Thousands of officials continue not to understand that if an emissions cap decides total emissions then anything that is not an emissions cap does not affect total emissions. This advanced logic continues to elude public servants.

I’m sure former All Blacks are penning their outrage as you read this.

Stuff ends its article with this:

No, Stuff. The Earth is not basically on fire. It has warmed by 1 degree since 1850. The IPCC says so.

Untrue statements aren’t just in the news. They’re boilerplate.