Here are six cases where I was pretty confident in my understanding of the microeconomics of something, but then later found out I was missing an important consideration.

Thanks to Richard Ngo and Tristan Hume for helpful comments.

Here’s the list of mistakes:

  • I thought divesting from a company had no effect on the company.
  • I thought that the prices on a prediction market converged to the probabilities of the underlying event.
  • I thought that I shouldn’t expect to be able to make better investment decisions than buying index funds.
  • I had a bad understanding of externalities, which was improved by learning about Coase’s theorem.
  • I didn’t realize that regulations like minimum wages are analogous to taxes in that they disincentivize work.
  • I misunderstood the economics of price controls.

In each, I’m not talking about empirical situations at all—I’m just saying that I had a theoretical analysis which I think turned out to be wrong. It’s possible that in many real situations, the additional considerations I’ve learned about don’t actually affect the outcome very much. But it was still an error to not know that those considerations were potentially relevant.

1. Divestment

I used to believe that personally divesting in a company didn’t affect its share price, and therefore had no impact on the company. I guess my reasoning here was something like “If the share is worth $10 and you sell it, someone else will just buy it for $10, so the price won’t change”. I was treating shares as if they were worth some fixed amount of money.

The simplest explanation for why you can’t just model shares as being worth fixed amounts of money is that people are risk averse, and so the tenth Google share you buy is worth less to you than the first; and so as the price decreases, it becomes more worthwhile to take a bigger risk on the company.

As a result, divestment reduces the price of shares, in the same way that selling anything else reduces its price.

In the specific case of divestment, this means that when I sell some stocks, the price ends up lower than it was.

I first learned I was wrong about this from this Sideways View post, published May 2019.

2. Index funds

I used to think that it wasn’t possible for individuals like me to get higher returns than I’d get from just buying an index fund, because in an efficient market, every share is equally valuable.

This is wrong for a few reasons. One is that the prices of shares are determined by the risk aversion of other market participants; if your risk aversion is different from the average, some shares (specifically, risky ones) will be much better investments than others.

Secondly, because I’m risk averse, I prefer buying shares which are going to do relatively well in worlds where I’m relatively poorer. For example, if I’m a software engineer at a tech company, compared to a random shareholder I should invest more in companies which are as anticorrelated with software engineer salaries as possible. Or if I live in the US, I should consider investing in the markets of other countries.

I didn’t understand this fully until around April this year.

3. Prediction markets

Relatedly, I thought that the fair market price of a contract which pays out $1 if Trump gets elected is just the probability of Trump getting elected. This is wrong because Trump getting elected is correlated with how valuable other assets are. Suppose I thought that Trump has a 50% chance of getting reelected, and that if he gets re-elected, the stock market will crash. If I have a bunch of my money in the stock market, the contract is worth more than 50 cents, because it hedges against Trump winning.

(Here’s a maybe more intuitive way of seeing this: Suppose I could pick between getting $10 in the world where Trump won (in which we’re assuming the market would crash) and the world where Trump lost. Clearly the $10 would be more valuable to me in the world where he wins and my stocks are decimated. So the value of the “Trump wins” contract is higher than the value of the “Trump loses” contract, even though they correspond to events of equal probability.) And there is a potentially very high number of correlative outcomes that betters might be thinking about and hedging against, and the market computes these and reflects them in the price.

This is a more general version of the point that it’s hard to have a prediction market on whether the world will end. Paul Christiano has an old blog post on this topic which I first saw years ago but which I didn't understand properly at the time.

I first understood this fully around March this year.

All of these first three mistakes were the result of me not really understanding basic portfolio theory; thanks to spending a bunch of time talking to traders over the last few years, I now understand it better.

4. Coase’s arguments about externalities

I used to have an overly simplistic picture of externalities—I believed the Econ 101 story: normally markets are efficient, but when a good has an externality the wrong amount will be produced, and this is resolved by putting a tax or subsidy on the good to internalize the externality.

I changed my mind about this after reading David Friedman’s essay. I’ll just quote a few paragraphs:

The first step is to realize that an external cost is not simply a cost produced by the pollutor and born by the victim. In almost all cases, the cost is a result of decisions by both parties. I would not be coughing if your steel mill were not pouring out sulfur dioxide. But your steel mill would do no damage to me if I did not happen to live down wind from it. It is the joint decision—yours to pollute and mine to live where you are polluting—that produces the cost.
Suppose that, in a particular case, the pollution does $100,000 a year worth of damage and can be eliminated at a cost of only $80,000 a year (from here on, all costs are per year). Further assume that the cost of shifting all of the land down wind to a new use unaffected by the pollution—growing timber instead of renting out summer resorts, say—is only $50,000. If we impose an emission fee of a hundred thousand dollars a year, the steel mill stops polluting and the damage is eliminated—at a cost of $80,000. If we impose no emission fee the mill keeps polluting, the owners of the land stop advertising for tenants and plant trees instead, and the problem is again solved—at a cost of $50,000. In this case the result without Pigouvian taxes is efficient—the problem is eliminated at the lowest possible cost—and the result with Pigouvian taxes in inefficient.
Moving the victims may not be a very plausible solution in the case of air pollution; it seems fairly certain that even the most draconian limitations on emissions in southern California would be less expensive than evacuating that end of the state. But the problem of externalities applies to a wide range of different situations, in many of which it is far from obvious which party can avoid the problem at lower cost and in some of which it is not even obvious which one we should call the victim.

My previous position was missing this nuance. I first read that David Friedman essay midway through last year.

5. Non-tax regulations that increase equality have disincentive effects on work

I used to think that the way to decide whether a minimum wage was good was to look at the effect on unemployment and the effect on total income for minimum wage workers, and then figure out whether I thought that the increase in unemployment was worth the increase in income. I think this was wrong in two pretty different ways.

The first mistake is that I was neglecting the fact that policies aimed at transferring wealth from rich people to poor people disincentivize making money. Taxes are just a special case of this, and can be seen as part of a category of wealth-transferal policies that includes minimum wage. So when you’re arguing that a minimum wage would be part of the optimal policy portfolio, you have to argue that it would be better than a tax. I did not understand that this was part of the calculation.

I first learned this from a post by Paul Christiano which I think he incorporated into Objection 2 here; that blog post was published March 2019.

6. Price and quality controls

The second of the ways I was wrong about the minimum wage comes from a misunderstanding of the economics of price controls; in hindsight I think that my high school economics curriculum was just wrong about this. I think that I realized my misconception after reading The Dark Lord’s Answer, published in 2016.

In high school economics, I was taught that when the government imposes a price floor (e.g., a minimum wage), you’ll end up with more supply than demand for the good. This is beneficial to suppliers who still succeed at selling the good, it’s harmful to suppliers who can no longer sell the good, and it’s harmful to buyers.

I now think that that understanding was overly simplistic. Here’s my current understanding.

In a market, the supply and demand of a good must equilibrate somehow—for every loaf of bread that someone buys, someone had to sell a loaf of bread. One way that the market can equilibrate is that the price can change—if the price is higher, selling is more attractive and buying is less attractive. So if more people want to buy than sell at the current price, we might expect the price to rise until things are in equilibrium.

But there are other variables than price which can change in a way that allow the market to equilibrate. One obvious example is product quality—if you decrease the quality of a product, consumers are less enthusiastic about buying but suppliers are more enthusiastic about selling (because they can presumably make it for cheaper).

Often, fluctuations in quality rather than price are what cause markets to equilibrate. For example, restaurants often don’t have price hikes at busy times, they just have long waits. Customers like it less when they have to wait more, and restaurants like having customers waiting (because it helps them ensure that their restaurant is constantly full).

So when we talk about the equilibrium state of a market, we can’t just talk about price, we also need to talk about all the other variables which can change.

In the case where we only consider price and quantity, there’s always only one equilibrium, because as price increases, supply rises and demand falls. (Actually, supply and demand could be constant over some range of prices, in which case there is an interval of equilibrium prices. I’m going to ignore this.)

But if we’re allowed to vary quality too, there are now many possible settings of price and quality where supply equals demand. E.g., for any fixed quality level, there’s going to be one equilibrium price, for the same reason as before.

In a competitive market, the equilibrium will be the point on the supply-equals-demand curve which maximizes efficiency. E.g., if there’s a way that producers could increase quality that would make production cost $1 more, producers will only do that if it makes the product worth more than $1 more valuable to consumers. This is optimal.

(In real life, you usually have producers selling a variety of different similar goods at different price/quality points; I’m talking about this restricted case because it’s simpler.)

Now, suppose that the government imposes a restriction on price or quality. For example, they might set a maximum or minimum price, or they might make safety restrictions which restrict quality in certain ways. The market will reequilibriate by using whatever degrees of freedom it has left. Specifically, it will reequilibriate to the optimal point within the newly restricted space of points at which supply equals demand. In general, this will lead to a less efficient outcome.

For example, if the price of bread is $2 at equilibrium, and the government sets a maximum price of $1.50, then the equilibrium will move along the quality curve until it gets to the point where the equilibrium price is $1.50.

This analysis gets more realistic if you allow there to be more dimensions than price and quantity along which bread can vary. For example, I’d expect to see the following phenomena:

  • Producers trying to figure out ways to get paid under the table, e.g., by demanding favors in return for selling to people. This reduces efficiency inasmuch as producers weren’t already being compensated by miscellaneous favors.
  • Sellers changing in ways that are mildly more convenient for them but much more inconvenient for consumers. For example, having long lines outside stores, or treating customers worse.
  • Producers indulging weak preferences of theirs in who they sell to (e.g., nepotism).

In the case of minimum wages, I’d expect to see employers do things like engaging in wage theft which the employees tolerate (which is inefficient because it increases variance for employees) or being inflexible and unpleasant. This analysis would predict that wage theft is much more common among minimum wage employees than employees at higher wages.

One way of thinking about the efficiency of this is to think from the perspective of the producers. They have to pick some change that makes the price of the bread $1.50. There are many ways they could reduce the price to $1.50. They’re going to pick the way that is best for them.

In some cases, this leads to almost no value being destroyed at all. For example, in the bread case, sellers might sell smaller loaves, which might be almost as efficient if you dubiously assume that the main cost of bread is flour. The worst case is that there’s no way for the seller to change the product to keep it profitable which benefits them, and so they end up changing it in a way which makes them very little better off.

The welfare impact of this kind of regulation is also affected by redistributive effects. For example, if bakers decide to only sell bread to their friends and family, this has a positive redistributive effect if the friends and family of bakers are poorer than average.

An example where the redistributive effect might make the world much better: Suppose that there’s demand for 100 loaves of bread, where half of that comes from poor people who want to feed their children and the other half comes from a tech billionaire who wants to make a giant bread sculpture. If the baker ends up selling to people who are most willing to stand in lines, then this might lead to a better outcome. (Getting this result requires making some pretty strong assumptions about the shape of the relevant curves.)

Another example is that you might expect that in a world where the minimum wage causes low-paid jobs to be more unpleasant, teenagers will be less inclined to take the jobs and poor adults will end up having relatively more of the jobs. It’s possible to set things up such that this ends up increasing total welfare.


It’s embarrassing that I was confidently wrong about my understanding of so many things in the same domain. I’ve updated towards thinking that microeconomics is trickier than most other similarly straightforward-seeming subjects like physics, math, or computer science. I think that the above misconceptions are more serious than any misconceptions about other technical fields which I’ve discovered over the last few years (except maybe the aestivation hypothesis thing).

In three of these cases (4, 5, and 6), I had incorrect beliefs that came from my high school economics class. In those three cases, the correct understanding makes government intervention look worse. I think that this is not a coincidence—I think that the people who wrote the IB economics curriculum are probably leftist and this colored their perception.

On the other hand, in the other cases, I assumed that the equilibria of markets had a variety of intuitive properties that they turn out not to have.

One obvious question is: how many more of these am I going to discover over the next year or two?

I think my median guess is that over the next year I will learn two more items that I think deserve to go on this list. Of course, I’m now a lot more cautious about being confident about microeconomics arguments, so I don’t expect to be as confidently wrong as I was about some of these.

In most of these cases, there was a phase where I no longer believed the false thing but didn’t properly understand the true thing. During this phase, I wouldn’t have made bets. Currently I’m in the “not making bets” phase with regard to a few other topics in economics; hopefully in a year I’ll understand them.

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Regarding externalities, I think the correct way to calculate Pigovian tax is as the value the rest of society will lose, provided that they can react to the existence of the externality. So, in Friedman's example, the actual damage of pollution (and the tax to be levied on the steel mill) is only $50,000, because of the possibility to shift land use. Of course it does make it harder to evaluate externalities in practice, but the principle seems solid at least.

This seems to be relevant to calculations of climate change externalities, where the research is almost always based on the direct costs of climate change if no one modified their behaviour, rather than the cost of building a sea wall, or planting trees.

It’s embarrassing that I was confidently wrong about my understanding of so many things in the same domain. I’ve updated towards thinking that microeconomics is trickier than most other similarly simple-seeming subjects like physics, math, or computer science. I think that the above misconceptions are more serious than any misconceptions about other technical fields which I’ve discovered over the last few years

For some of these, I'm confused about your conviction that you were "confidently wrong" before. It seems that the general pattern here is that you used the Econ 101 model to interpret a situation, and then later discovered that there was a more complex model that provided different implications. But isn't it kind of obvious that for something in the social sciences, there's always going to be some sort of more complex model that gives slightly different predictions?

When I say that a basic model is wrong, I mean that it gives fundamentally incorrect predictions, and that a model of similar complexity would provide better ones. However (at least minimally in the cases of (3) and (4)) I'm not sure I'd really describe your previous models as "wrong" in this sense. And I think there's a meaningful distinction between saying you were wrong and saying you gained a more nuanced understanding of something.


I agree that there's some subtlety here, but I don't think that all that happened here is that my model got more complex.

I think I'm trying to say something more like "I thought that I understood the first-order considerations, but actually I didn't." Or "I thought that I understood the solution to this particular problem, but actually that problem had a different solution than I thought it did". Eg in the situations of 1, 2, and 3, I had a picture in my head of some idealized market, and I had false beliefs about what happens in that idealized market, just like I'd be able to be wrong about the Nash equilibrium of a game.

I wouldn't have included something on this list if I had just added complexity to the model in order to capture higher-order effects.

Agreed — I feel like it makes more sense to be proud of changing your mind when that entails acquiring a model of complexity similar to or lower than that of the model you used to have that makes better predictions, rather than merely making your model more complex.

For the externalities in (4), it’s important to remember that not internalizing the externality creates a lot of moral hazard, though, because Coase’s theorem rarely applies in practice. For example, the steel mill could often have been built at a different location for slightly more cost (say, $10k), which they will not do if they know the efficient move will be to not tax them. Thus a $40k inefficiency. And the theorem would rejoin with “well, the owners of the resorts will pay the mill >$10k to initially build on the new spot, which makes things efficient again”, but then of course you open up the opportunity for all sorts of inefficient blackmail if you don’t fulfill the perfect information requirement of Coase.

Obviously none of this contradicts the nuance you were adding, but I just wanted to spell this out lest we see anyone waver in their moral resolution to internalize most externalities.

lest we see anyone waver in their moral resolution to internalize most externalities.


If I find out that internalizing externalities is harmful, I don't want to do it!  It might be harmful to moralize this, in case it makes it harder to change our minds?

There are plenty of things you should still resolve to do. You don't want to throw the baby out with the bathwater by maintaining maximum irresolution so you'll never have difficulty changing your mind. Just change your mind when important evidence comes in—and in this case, I'm trying to point out that it is not important evidence against internalizing externalities. (It is evidence against levying the full externality cost and failing to try mitigating trades that reduce that externality cost.)

That makes sense.  I guess I'm mostly reacting to the last sentence, which adds a moral aspect.

(I'm also not 100% sure how much the last sentence is a joke, or deliberate exaggeration?)

I think I basically mean it straightforwardly. In my mind it is pretty similar to other moral injunctions like "tell the truth" or "speak up for the bullied"—it is important to resolve to do it ahead of time, because in the moment it might be quite hard and costly to do so. So if someone were to start talking about how actually the bullied need to learn to stick up for themselves, etc etc, I would want to remind myself and others that while this is true, it shouldn't change my moral resolution to stand up to bullying. (It's perfectly fine for people to discuss whether maybe we shouldn't stand up for them, but if someone gives an argument that doesn't apply, or evidence that later turns out to be false, I want to again reiterate the resolution.)

Maybe this is overkill or something but I think it feels pretty straightforward to me. I think sometimes my moral resolutions do in fact get eroded by people questioning them, and not "re-committing" afterward.

My understanding of banking and monetary policy was pretty wrong until very recently. Apparently the textbook I read in the 90s was explaining how banking and central banking worked in the 50s. John Wentsworth pointed me to a Coursera course by Perry Mehrling and here are the same lectures without having to register for the course.

Do you know of any source that gives the same explanations in text instead of video?

Edit: Never mind, the course has links to "Lecture PDF" that seem to summarize them. For the first lecture the summary is undetailed and I couldn't make sense of it without watching the videos, but they appear to get more detailed later on.

Another big update for me is that according to modern EMH, big stock market movements mostly reflect changes in risk premium, rather than changes in predicted future cash flows. (The recent COVID-19 crash however was perhaps driven even more by liquidity needs.)

Important thing to note here: the Fama and French crowd tend to call a lot of things "risk premiums" which may or may not reflect any actual taste for risk; they're just outputs of a factor model. That doesn't mean that they're meaningless, but calling it a "risk premium" is often rather misleading. I wouldn't be the least bit surprised if one of their time-dependent "risk premiums" were actually just a factor corresponding to liquidity needs.

Curated – and for the first time, edited!

(The LW team hired a professional editor to make line edits to the above post. Buck went through and accepted/rejected the edits, and we updated the post before curating, so that the many people on the curated email list got the edited version. This was an experiment, we may do more of this.)

Overall I continue to think it's very healthy to write down your major updates and mistakes, and I'm curating this for similar reasons I curated Buck's last piece. It feels to me like records of these updates allow one to do something like actually update on the highest level. Related, something about the insights in this piece feel very 'hard-earned', in a way where I think a person can only write this kind of post after a lot of time and effort and cycles of thought have passed. (Ray's Sunset at Noon feels similar to me, where I think that Ray will only be able to write that specific kind of post every 5 years or so, and shouldn't try to write another one much faster.)

And I learned a ton from this post. Everything is explained very simply and concisely, no section is written in a way that signalled to me "You should be afraid of math and experts" which happens to me often for stuff about econ, and I think I basically understood all your updates. I mean, I need to read Friedman's essay in full and think on it, and I also need to actually use the insight about there being many dimensions on which markets compete other than price (e.g. quality, employee work standards, etc) to feel like it's truly-part-of-me, but they were at least very effective pointers to ideas that I want to use when thinking about these questions.

I also really like your predictions at the end and meta-level updates.

Any ideas on how software engineers can specifically hedge against the risk of software salaries declining? I ask because in the case of software specifically it isn't intuitive to me whether in worlds where software salaries have gone down we should expect tech company valuations to have gone up or down. In any other industry it feels clearer cut to me that the way to hedge against your own career capital risk and salary risk is to divest from the industry your work experience is in.

Also note that many companies that you think of as tech companies and employ a lot of highly paid software engineers are not classified as tech companies in indices. For example, the S&P has Google and Facebook under "communications".

Start your own company and hire some software engineers? Only partly humor.

Perhaps one aspect of minimum wage that you are missing is that this is different from price control of fungible goods is several important aspects, that everything else being equal:

  1. Higher minimum wage means higher demand for goods consumed by minimum wage employees.
  2. Higher minimum wage incentivises employers to invest more in their employee productivity (training, better work conditions, etc)
  3. Same employees may be more productive if you pay them higher wages, and you may be able to get better employees.

In some cases 2+3 might means that there may be several equilibrium points that are roughly equally good for the employers - either hire high-turnover low-productivity people with lower wages, or hire lower-turnover higher-productivity people for higher wages, and effect #1 is enough for the higher minimum wage to just be a win-win (which is perhaps why some employers actually support minimum wage laws).


I think all these sort of fail on the basis of partial equilibrium rather then general equilibrium but here are a few thought that may or may not fit somewhere.

1. Is a bit of a Say's Law take. One thing that might be considered is just how quickly the realized new demand from increased wages (and how quickly some might react in terms of quantity of labor employed is reduced) transmits thought the local economy. If demand propagates quickly, 1 might hold.

2. That's an interesting approach. Could increased wages result in increased investment in human capital? Maybe, maybe not. An interesting historical debate might come back here. The old Cambridge Capital Controversy, as it was explained to be once, basically supports a multi equilibrium outcome. One is a high wage equilibrium with a low return to capital (the w and r in the model). While the debate was supposed to be been resolved and so the two outcomes not possible I never got the sense that all agreed so perhaps there might be something there.

3. Was a theory called Efficiency Wages.

All that said, I think the biggest problem with wage theory for economics is that "wages" are not really set as much in the market as in the corporate HR office. This is not to say that there is not linkage to external markets, but borrowing from old monetary policy terms, is only loosely linked. Within a medium to large (and probably even what would be called small these days) corporation the effort is very much a complex joint production activity and margins are poorly understood (and probably not even known in a lot of cases). The standard micro economic analysis only goes so far. The margin really should be some unit output from the corporate effort. Wages then become more a political economy setting where the issue is more distribution and less about allocation. (Include all the thinking about need for "slack" for productivity...)

I agree that the case where there are several equilibrium points that are almost as good for the employer is the case where the minimum wage looks best.

Re point 1, note that the minimum wage decreases total consumption, because it reduces efficiency.

Is there actual evidence that a minimum wage decreases total consumption? I've never heard that, or seen any study on it, and I'd like to learn more.

(Intuitively, it doesn't seem highly plausible to me, since my assumption would be that it transfers wealth from rich people to poor people, which should increase total consumption, because there's more room for consumption growth for poorer people, but I'm also not sure if that is true.)

(Edit: after a cursory search of current research on the topic, it seems that the consensus is rather that a minimum wage has a small positive effect on consumption, which is what I would have naively expected.)

Remember that I’m not interested in evidence here, this post is just about what the theoretical analysis says :)

In an economy where the relative wealth of rich and poor people is constant, poor people and rich people both have consumption equal to their income.

First, poor have lower savings rate, and consume faster, so money velocity is higher. Second, minimal wages are local, and I would imagine that poor people on average spend a bigger fraction of their consumption locally (but I am not as certain about this one).

In an economy where the relative wealth of rich and poor people is constant, poor people and rich people both have consumption equal to their income.

Don't rich people tend to die with a significant portion of their lifetime income unspent, while poor people don't?

A minimum wage decreases total consumption in some situations but not in all situations. In a world consisting of ten poor people and a single rich person, where buying the bare minimum food costs $1/day and buying comfort costs $10/day, the only way for the poor people to get money is to work for the rich person, and he is willing to hire them for any wage up to $100/day, the equilibrium wage would be $1/day. The result is that the rich person would only be spending $20/day (his own food, the wages of the nine poor people, and his own comfort) and each poor person would be spending $1/day, their entire wage. If a minimum wage of $11/day were instituted, all the poor people would be hired for $11/day, with all ten of the people having food to survive and having comfort. Consumption would go up significantly and everyone would be better off.

This hypothetical is more an analysis on the constraints (monopoly employer, closed system, static labor supply / demand, static prices) than on the effect of the minimum wage on consumption. It ignores that the minimum wage harms both employers and employees that would be hired absent a minimum wage.

A minimum wage will be inefficient in all situations relative to a taxing more inelastic economic activity and redistributing the proceeds.

Given a monopsony employer, setting a minimum wage equal to the competitive equilibrium wage is efficient because it removes the monopsony dead weight loss.

Agreed! Thanks, that is certainly the caveat I would add. In real world, monopsonies are however rare to nonexistent

The monopsony approach to the labor market says they're the rule. A company doesn't actually formally have to be the only buyer of labor power in its region to hold monopsony power.

I don't get the divestment argument, please help me understand why I'm wrong.

Here's how I understand it:

If Bob offers to pay Alice whatever Evil-Corp™ would have paid in stock dividends in exchange for what Alice would have paid for an Evil-Corp™ stock, Evil-Corp™ has to find another buyer. Since Alice was the buyer willing to pay the most, Evil-Corp™ now loses the difference between what Alice was willing to pay and the next-most willing buyer, Eve, is willing to pay.

Is that understanding correct, or am I missing something crucial?

If my understanding is right, then I don't understand why divestment works.

Lets assume I know Bob is doing this and I have the same risk-profile as Alice. I know the market price to be distorted, Evil-Corp™ stocks are being sold for less than what they're worth! After all, Alice deemed the stock to be worth more than what the stock was sold for. If it was not worth the price Alice was willing to pay for it, she wouldn't have offered to give that price.

Why wouldn't I just buy the stock from Eve offering to pay the price set by Alice?

So I think the divestment argument that Buck is making is the following:

Assume there are 25 investors, from Alice to Ysabel. Each investor is risk-averse, and so is willing to give up a bit of expected value in exchange for reduced variance, and the more anticorrelated their holdings, the less variance they'll have. This means Alice is willing to pay more for her first share of EvilCorp stock than she is for her second share, and so on; suppose EvilCorp has 100 shares, and the equilibrium is that each investor has 4 shares.

Suppose now Alice decides that the moral loss of holding EvilCorp stock is larger than the financial gain of having another less-correlated asset, and so offers to sell her EvilCorp shares. The value-to-Alice of those shares before was the 1st share value + 2nd share value + 3rd share value + 4th share value, but the value-to-buyers will be the 5th share value (times 4), which by risk aversion is lower than the 4th share value that it was at before. [This is why you wouldn't just buy it yourself; you already have 4 shares, and a fifth share is worth less to you than your fourth share.]

As more and more investors divest from EvilCorp, the remaining people willing to invest in EvilCorp find it becoming a larger and larger fraction of their holdings, meaning they pay more in variance, making it less attractive. If there are sufficiently large risk-neutral investors, or sufficiently many small risk-averse investors who don't own any shares of it yet, divestment barely shifts the value of EvilCorp; if there aren't, divestment can seriously restrict their access to capital.

Why is it that riskier investments should give higher expected returns?

I ask not because I don't get that the avg person would rather invest on something safe than something unsafe, all else being equal. I get that. I ask because I imagine that investors could bring their total risk down through diversification without harming the expected returns, so big money would prefer the higher expected returns even if they are risky, and in doing that, they'd bring down the extra returns from the riskier investments.

Is it because investments options are so correlated that diversification isn't enough to bring the risk of a portfolio down to acceptable levels? Or some other reason?

Investors can always use leverage to get higher risk and higher returns if they want. 

Do they really get higher expected returns from that?

I know they do when the market isn't efficient (relative to the specific investor), but that doesn't help me.


I think the answer is yes. I would say it is a very similar strategy to that of corporate financial management and using financial leverage to improve returns and earnings.

US taxes treat corporate debt financing more favorably than corporate equity financing, which may be distorting companies towards higher leverage.

re: Index funds, if it's just about risk tolerance, you're better off with options on indexes + index funds than you are picking stocks.

One thing this post makes me curious about: in the last section, you talk about the effects of price controls on people selling goods, and also jobs. Usually we think of the labor market as workers selling their labor, rather than companies selling jobs. But is there any problem with this inversion? I guess the former view is better when workers are very heterogeneous, whereas maybe in cases where the company cares less about worker quality (like minimum wage jobs) the latter is also viable.

Also, I expect service industries to in general adapt better to price controls, since worker time can often vary more continuously than other products. Although idk how helpful such generalisations are, since there will be many exceptions.

I think your update on divestment is in fact wrong; divestment has no or negligible effect.

There are two main cases:

1- Divestment without substantial coordination

This stands in for anything where you are divesting from a company you find distasteful, but with the expectation that there will not be substantial numbers of other people who follow the same logic. In this case, unless you control a large fund, your effect on the price will be nonzero, and downward, but negligible.

2 - Divestment with coordination.

(This covers both explicit coordination and amorphous implicit coordination like 'many people share my moral logic and this offense was made very public'.)

Assume for the moment that a mass movement to divest is not substantial evidence of the corporation's fundamentals being weaker. (This is often false, particularly for businesses which sell directly to consumers.) If so, the price will go down, but high-information observers (serious traders) will note the outside factor depressing prices, note that this outside factor is uncorrelated with future stock performance, and conclude that these stocks are now a substantially better deal than other stocks. Result: stocks bought up until the market price ~returns to the equilibrium price without divestment. (This is a longstanding phenomenon in the form of the 'sin fund'. There are mixed results on whether the P/E ratio is actually better for 'sin stocks' in a durable way, but they're not worse.)

If the company is actually likely to be negatively impacted on a non-stock level, the situation is more complicated, but not much better for the divestors. To the extent the skilled traders correctly estimate , the size of the divestment movement, and , the (size of the effect on the company's bottom line)/(size of divestment movement) quotient, the stock price will behave exactly as it would if the divestors had made some equally-costly signal of their opposition to the company but not actually divested. These estimates will be imperfect, but they seem likely to be a case where the EMH works well, and if they have errors don't seem likely to be systematically wrong in a particular direction.

Note also that if you want to lower the share price, the thing to do, given that competent traders will attempt to figure out the market price implied by the fundamentals and be fairly adequate in that task, is to maximize ; increasing the size is no good if the 'heat/light' ratio goes down by a bigger ratio than the size went up. If you consider a slightly more complicated model where you have movement size , fraction of movement which divests , and fraction of movement which takes direct actions that hurt the company's fundamentals , and , for a total effect of , divestment totally falling out of the picture. Any movement only has a finite amount of energy to spend convincing its members to take actions, so we should further expect and to be anticorrelated, i.e. it's not worth actively discouraging people from divestment but whenever there is a choice you should always choose the other action if it has a meaningful chance of hurting the company's fundamentals, possibly even down to dust-speck-level negligible-but-nonzero effects.

Thank you for writing this, I had some of the same misconceptions.

A question about point 1, divestment: Does a similar principle apply when companies pledge to only use renewable energy? If they also build capacities so more renewable energy is generated, then obviously yes.

But otherwise I don't see how there is risk aversion in using more non-renewable energy for the other energy consumers that would shift the price.

It's interesting that the first three are aggregation error - a focus on the mean rather than the distribution. And that the last 3 are politically-entangled enough that I see incentive to believe/teach the naive version.

Amazing post. But I am stuck at the "prediction market does not reflect probability" point. Currently Trump futures sell for 0.36$ and Metaculus predicts a 22% winning chance of Trump winning in 2024. This difference is what one would observe if many people are used these futures contracts for hedging. However, couldn't I just issue lots of futures contracts to bring the price down? Assuming that my assets are not meaningfully linked to Trump winning, that means 0.36$-0.22$=0.12$ expected return per issued contract. 

Relatedly, I thought that the fair market price of a contract which pays out $1 if Trump gets elected is just the probability of Trump getting elected. This is wrong because Trump getting elected is correlated with how valuable other assets are. Suppose I thought that Trump has a 50% chance of getting reelected, and if he gets re-elected, the stock market will crash. If I have a bunch of my money in the stock market, the contract is worth more than 50 cents, because it hedges against Trump winning.

Isn't this effect going to be very small for almost all markets, and still fairly moderate for presidential ones?

Not that you talked about effect size either way, I'm just wondering how much I should adjust predictions from markets for this reason.

I think it would be extremely material for the 2020 Presidential Election. Lets say for sake of argument that Biden winning means the TCJA gets partially reversed and corporate tax rates go up 2%. That would have an extremely large (downward) impact on stock prices.

The market cap for stocks is huge O(10^13) compared to amounts wagered on the Presidential Election O(10^8), so any effect is going to swamp prediction markets.

However, I don't believe that this effect is material to prediction markets at the moment.

1/ Prediction markets just aren't super efficient. Compare PredictIt (41%), Betfair (36%) and various other venues to see the kind of differences out there in estimates for the odds of Trump winning re-election.

2/ Volumes aren't super high, so this sort of hedging the author talks about is a long time away.

3/ Financial actors have much more liquid ways of hedging election risk than hedging in thin prediction markets.

Cliche at this point but still fun as the vast majority get it wrong. If you take out a mortgage with a bank, where does the money come from to pay off the old home owner?

Without looking it up:

My first impression is that the bank pays off the original homeowner in full, which they are willing to do because I pay back the bank over time with interest, or else they take my house. Is the real answer that they are middlemen who sell the right to foreclose my house to investors?

Edit: I asked my mom, who's a landlord, and in America the buyer borrows money from the bank (via a mortgage) and pays an escrow company, which pays off any liens (debts tied to the property that the original owner failed to pay such as unpaid property taxes or repair costs) and then pays the original owner the remaining. Unless the owner owed $3 million in liens and the house sold for $2 million, in which case the owner would owe the escrow company $1 million instead of getting paid. This way the house buyer buys just the house without worrying about liens. A bank makes sure a homebuyer is trustworthy before lending them money; an escrow company makes sure that the seller actually owns the house and that all their liens are accounted for.

On the other hand, if you buy a foreclosed house at auction then you are in charge of paying the liens as well, kind of like how when you buy a business, any debt the business owed comes with it.

> Is the real answer that they are middlemen who sell the right to foreclose my house to investors?

this is a big part of it, where people's intuitions go wrong is where the actual dollars come from though. e.g. " the buyer borrows money from the bank " where the bank actually gets the dollars.

In an immediate but not useful sense, from your bank, because while the calculations that make them determine this mortgage is a good investment involve other actors, none of the interaction with other actors is instantaneous.

On the time scale of a month (and probably a week), partially from the company who bought your mortgage for its risk-adjusted net present value (let's just call that ), and the rest from 'nowhere', i.e. the amount they're now allowed to lend by the fractional reserve banking regulations based on the fact that their reserves have just increased by . Trying to work out which of those portions is bigger is making my head hurt, mostly because I'm pretty sure the relative value of the risk-adjusted net present value of the mortgage's future cash flow, compared with the reserve fraction and the actual face value of the mortgage, matter, but I'm not quite sure how.

Yes, though the reserve requirement was recently dropped to zero.

Wat. Is there some more complicated picture, there, where they don't have to maintain real reserves but they do need to hold something like overnight loans from the Fed as reserves? Because if they're really untethered from reserves of any kind, they can 'print' as much money as they want, which seems...

It's not necessarily a terrible idea, but it does entail that the central bank give up its monopoly, and that seems like an insane move from the central bank's perspective.

There are complex rules which serve similar functions to reserve requirements. See here for a start.

I don't know the full picture on that, it confuses me too.

Excellent post. I have a small complaint on the Coase section though. Quoting for reference:

Suppose that, in a particular case, the pollution does $100,000 a year worth of damage and can be eliminated at a cost of only $80,000 a year (from here on, all costs are per year). Further assume that the cost of shifting all of the land down wind to a new use unaffected by the pollution—growing timber instead of renting out summer resorts, say—is only $50,000. If we impose an emission fee of a hundred thousand dollars a year, the steel mill stops polluting and the damage is eliminated—at a cost of $80,000. If we impose no emission fee the mill keeps polluting, the owners of the land stop advertising for tenants and plant trees instead, and the problem is again solved—at a cost of $50,000. In this case the result without Pigouvian taxes is efficient—the problem is eliminated at the lowest possible cost—and the result with Pigouvian taxes in inefficient.

With the numbers laid out, (and presuming the mill is more than $100k profitable), I agree that the "efficient" outcome is for the resort to convert to timber. However, the result with Pigouvian taxes is still efficient. This is because Friedman arrives at the wrong equilibrium result with taxes. It is possible this is because he has structured his taxes incorrectly -- they aren't properly taxing damages, but rather an intermediary which can cause damages.

I think the result that Coase would advocate is that in the presence of a tax on damages, the mill pays the resort owner $50k+1 to convert to timber. At that point, the damages are $0, and no Pigouvian tax is paid. This is central to Coase's realization. Conditional on the pre-existing endowments, we should arrive at the min-cost solution -- the question is who bears the cost. In this case, imposing a Pigouvian tax transfers the burden from the resort owner to the mill owner.

It is possible this is because he has structured his taxes incorrectly -- they aren't properly taxing damages, but rather an intermediary which can cause damages.

I think your complaint is missing his main argument, which is that the taxes are more difficult to structure correctly than it would first appear. To quote the last paragraph:

But the problem of externalities applies to a wide range of different situations, in many of which it is far from obvious which party can avoid the problem at lower cost and in some of which it is not even obvious which one we should call the victim.

On the externalities example I have also worried that conventional economic treatments also completely ignore corruption. In real life I think you have to assume that the government does not always act like an angel, and therefore there is an additional cost to allowing governments to correct externalities at all. And this cost will not just be limited to the example itself (where the government introduces a sub-par solution to the specific externality in question as the result of corruption), but instead applicable to broad swathes of economic interactions where, once allowed the power to correct externalities, governments may corruptly "correct" situations where no externality truly exists.

Thanks for this.

I wonder how common these misconceptions are among the public.

Regarding divestment, *who* owns equity can materially affect value independent of transacted price because other equity owners adjust the models of their long-term position value based on this information. This is reflected in concepts such as "dead equity" (implied dilution risk) in small companies and the notional-only value of founder equity in big public companies e.g. Bezos.

Regarding index funds, the (anti-)correlations are much more complex and less obvious, particularly in the modern globalized economy, than classic diversification and risk management heuristics allow for. The level of diversification within some single companies today does not have precedent. There is an emerging school of thought that a concentrated portfolio of companies with extremely high levels of internal diversification will have lower risk and consistently higher performance than when trying to reduce risk by diversification at the portfolio level. Anti-correlation has become so difficult in practice that optimizing for diversification efficiency and adaptivity is often the more effective strategy.

Andrew, I've never heard this emerging school of thought you name and I'm interested in it. Do you have any link or author you can name? Thanks in advance!