AGI and the EMH: markets are not expecting aligned or unaligned AI in the next 30 years
by Trevor Chow, Basil Halperin, and J. Zachary Mazlish
In this post, we point out that short AI timelines would cause real interest rates to be high, and would do so under expectations of either unaligned or aligned AI. However, 30- to 50-year real interest rates are low. We argue that this suggests one of two possibilities:
Long(er) timelines. Financial markets are often highly effective information aggregators (the “efficient market hypothesis”), and therefore real interest rates accurately reflect that transformative AI is unlikely to be developed in the next 30-50 years.
Market inefficiency. Markets are radically underestimating how soon advanced AI technology will be developed, and real interest rates are therefore too low. There is thus an opportunity for philanthropists to borrow while real rates are low to cheaply do good today; and/or an opportunity for anyone to earn excess returns by betting that real rates will rise.
In the rest of this post we flesh out this argument.
Both intuitively and under every mainstream economic model, the “explosive growth” caused by aligned AI would cause high real interest rates.
Both intuitively and under every mainstream economic model, the existential risk caused by unaligned AI would cause high real interest rates.
We show that in the historical data, indeed, real interest rates have been correlated with future growth.
Plugging the Cotra probabilities for AI timelines into the baseline workhorse model of economic growth implies substantially higher real interest rates today.
In particular, we argue that markets are decisively rejecting the shortest possible timelines of 0-10 years.
We argue that the efficient market hypothesis (EMH) is a reasonable prior, and therefore one reasonable interpretation of low real rates is that since markets are simply not forecasting short timelines, neither should we be forecasting short timelines.
Alternatively, if you believe that financial markets are wrong, then you have the opportunity to (1) borrow cheaply today and use that money to e.g. fund AI safety work; and/or (2) earn alpha by betting that real rates will rise.
An order-of-magnitude estimate is that, if markets are getting this wrong, then there is easily $1 trillion lying on the table in the US treasury bond market alone – setting aside the enormous implications for every other asset class.
Interpretation. We view our argument as the best existing outside view evidence on AI timelines – but also as only one model among a mixture of models that you should consider when thinking about AI timelines. The logic here is a simple implication of a few basic concepts in orthodox economic theory and some supporting empirical evidence, which is important because the unprecedented nature of transformative AI makes “reference class”-based outside views difficult to construct. This outside view approach contrasts with, and complements, an inside view approach, which attempts to build a detailed structural model of the world to forecast timelines (e.g. Cotra 2020; see also Nostalgebraist 2022).
Outline. If you want a short version of the argument, sections I and II (700 words) are the heart of the post. Additionally, the section titles are themselves summaries, and we use text formatting to highlight key ideas.
I. Long-term real rates would be high if the market was pricing advanced AI
Real interest rates reflect, among other things:
Time discounting, which includes the probability of death
Expectations of future economic growth
This claim is compactly summarized in the “Ramsey rule” (and the only math that we will introduce in this post), a version of the “Euler equation” that in one form or another lies at the heart of every theory and model of dynamic macroeconomics:
is the real interest rate over a given time horizon
is time discounting over that horizon
is a (positive) preference parameter reflecting how much someone cares about smoothing consumption over time
is the growth rate
(Internalizing the meaning of these Greek letters is wholly not necessary.)
While more elaborate macroeconomic theories vary this equation in interesting and important ways, it is common to all of these theories that the real interest rate is higher when either (1) the time discount rate is high or (2) future growth is expected to be high.
We now provide some intuition for these claims.
Time discounting and mortality risk. Time discounting refers to how much people discount the future relative to the present, which captures both (i) intrinsic preference for the present relative to the future and (ii) the probability of death.
The intuition for why the probability of death raises the real rate is the following. Suppose we expect with high probability that humanity will go extinct next year. Then there is no reason to save today: no one will be around to use the savings. This pushes up the real interest rate, since there is less money available for lending.
Economic growth. To understand why higher economic growth raises the real interest rate, the intuition is similar. If we expect to be wildly rich next year, then there is also no reason to save today: we are going to be tremendously rich, so we might as well use our money today while we’re still comparatively poor.
(For the formal math of the Euler equation, Baker, Delong, and Krugman 2005 is a useful reference. The core intuition is that either mortality risk or the prospect of utopian abundance reduces the supply of savings, due to consumption smoothing logic, which pushes up real interest rates.)
Transformative AI and real rates. Transformative AI would either raise the risk of extinction (if unaligned), or raise economic growth rates (if aligned).
Therefore, based on the economic logic above, the prospect of transformative AI – unaligned or aligned – will result in high real interest rates. This is the key claim of this post.
As an example in the aligned case, Davidson (2021) usefully defines AI-induced “explosive growth” as an increase in growth rates to at least 30% annually. Under a baseline calibration where and , and importantly assuming growth rates are known with certainty, the Euler equation implies that moving from 2% growth to 30% growth would raise real rates from 3% to 31%!
For comparison, real rates in the data we discuss below have never gone above 5%.
(In using terms like “transformative AI” or “advanced AI”, we refer to the cluster of concepts discussed in Yudkowsky 2008, Bostrom 2014, Cotra 2020, Carlsmith 2021, Davidson 2021, Karnofsky 2022, and related literature: AI technology that precipitates a transition comparable to the agricultural or industrial revolutions.)
II. But: long-term real rates are low
The US 30-year real interest rate ended 2022 at 1.6%. Over the full year it averaged 0.7%, and as recently as March was below zero. Looking at a shorter time horizon, the US 10-year real interest rate is 1.6%, and similarly was below negative one percent as recently as March.
(Data sources used here are explained in section V.)
The UK in autumn 2021 sold a 50-year real bond with a −2.4% rate at the time. Real rates on analogous bonds in other developed countries in recent years have been similarly low/negative for the longest horizons available. Austria has a 100-year nominal bond – being nominal should make its rate higher due to expected inflation – with yields less than 3%.
Thus the conclusion previewed above: financial markets, as evidenced by real interest rates, are not expecting a high probability of either AI-induced growth acceleration or elevated existential risk, on at least a 30-50 year time horizon.
III. Uncertainty, takeoff speeds, inequality, and stocks
In this section we briefly consider some potentially important complications.
Uncertainty. The Euler equation and the intuition described above assumed certainty about AI timelines, but taking into account uncertainty does not change the core logic. With uncertainty about the future economic growth rate, then the real interest rate reflects the expected future economic growth rate, where importantly the expectation is taken over the risk-neutral measure: in brief, probabilities of different states are reweighted by their marginal utility. We return to this in our quantitative model below.
Takeoff speeds. Nothing in the logic above relating growth to real rates depends on slow vs. fast takeoff speed; the argument can be reread under either assumption and nothing changes. Likewise, when considering the case of aligned AI, rates should be elevated whether economic growth starts to rise more rapidly before advanced AI is developed or only does so afterwards. What matters is that GDP – or really, consumption – ends up high within the time horizon under consideration. As long as future consumption will be high within the time horizon, then there is less motive to save today (“consumption smoothing”), pushing up the real rate.
Inequality. The logic above assumed that the development of transformative AI affects everyone equally. This is a reasonable assumption in the case of unaligned AI, where it is thought that all of humanity will be evaporated. However, when considering aligned AI, it may be thought that only some will benefit, and therefore real interest rates will not move much: if only an elite Silicon Valley minority is expected to have utopian wealth next year, then everyone else may very well still choose to save today.
It is indeed the case that inequality in expected gains from transformative AI would dampen the impact on real rates, but this argument should not be overrated. First, asset prices can be crudely thought of as reflecting a wealth-weighted average across investors. Even if only an elite minority becomes fabulously wealthy, it is their desire for consumption smoothing which will end up dominating the determination of the real rate. Second, truly transformative AI leading to 30%+ economy-wide growth (“Moore’s law for everything”) would not be possible without having economy-wide benefits.
Stocks. One naive objection to the argument here would be the claim that real interest rates sound like an odd, arbitrary asset price to consider; certainly stock prices are the asset price that receive the most media attention.
In appendix 1, we explain that the level of the real interest rate affects every asset price: stocks for instance reflect the present discounted value of future dividends; and real interest rates determine the discount rate used to discount those future dividends. Thus, if real interest rates are ‘wrong’, every asset price is wrong. If real interest rates are wrong, a lot of money is on the table, a point to which we return in section X.
We also argue that stock prices in particular are not a useful indicator of market expectations of AI timelines. Above all, high stock prices of chipmakers or companies like Alphabet (parent of DeepMind) could only reflect expectations for aligned AI and could not be informative of the risk of unaligned AI. Additionally, as we explain further in the appendix, aligned AI could even lower equity prices, by pushing up discount rates.
IV. Historical data on interest rates supports the theory: preliminaries
In section I, we gave theoretical intuition for why higher expected growth or higher existential risk would result in higher interest rates: expectations for such high growth or mortality risk would lead people to want to save less and borrow more today. In this section and the next two, we showcase some simple empirical evidence that the predicted relationships hold in the available data.
Measuring real rates. To compare historical real interest rates to historical growth, we need to measure real interest rates.
Most bonds historically have been nominal, where the yield is not adjusted for changes in inflation. Therefore, the vast majority of research studying real interest rates starts with nominal interest rates, attempts to construct an estimate of expected inflation using some statistical model, and then subtracts this estimate of expected inflation from the nominal rate to get an estimated real interest rate. However, constructing measures of inflation expectations is extremely difficult, and as a result most papers in this literature are not very informative.
Additionally, most bonds historically have had some risk of default. Adjusting for this default premium is also extremely difficult, which in particular complicates analysis of long-run interest rate trends.
The difficulty in measuring real rates is one of the main causes, in our view, of Tyler Cowen’s Third Law: “all propositions about real interest rates are wrong”. Throughout this piece, we are badly violating this (Gödelian) Third Law. In appendix 2, we expand on our argument that the source of Tyler’s Third Law is measurement issues in the extant literature, together with some separate, frequent conceptual errors.
Our approach. We take a more direct approach.
Real rates. For our primary analysis, we instead use market real interest rates from inflation-linked bonds. Because we use interest rates directly from inflation-linked bonds – instead of constructing shoddy estimates of inflation expectations to use with nominal interest rates – this approach avoids the measurement issue just discussed (and, we argue, allows us to escape Cowen’s Third Law).
To our knowledge, prior literature has not used real rates from inflation-linked bonds only because these bonds are comparatively new. Using inflation-linked bonds confines our sample to the last ~20 years in the US, the last ~30 in the UK/Australia/Canada. Before that, inflation-linked bonds didn’t exist. Other countries have data for even fewer years and less liquid bond markets.
(The yields on inflation-linked bonds are not perfect measures of real rates, because of risk premia, liquidity issues, and some subtle issues with the way these securities are structured. You can build a model and attempt to strip out these issues; here, we will just use the raw rates. If you prefer to think of these empirics as “are inflation-linked bond yields predictive of future real growth” rather than “are real rates predictive of future real growth”, that interpretation is still sufficient for the logic of this post.)
Nominal rates. Because there are only 20 or 30 years of data on real interest rates from inflation-linked bonds, we supplement our data by also considering unadjusted nominal interest rates. Nominal interest rates reflect real interest rates plus inflation expectations, so it is not appropriate to compare nominal interest rates to real GDP growth.
Instead, analogously to comparing real interest rates to real GDP growth, we compare nominal interest rates to nominal GDP growth. The latter is not an ideal comparison under economic theory – and inflation variability could swamp real growth variability – but we argue that this approach is simple and transparent.
Looking at nominal rates allows us to have a very large sample of countries for many decades: we use OECD data on nominal rates available for up to 70 years across 39 countries.
V. Historical data on interest rates supports the theory: graphs
The goal of this section is to show that real interest rates have correlated with future real economic growth, and secondarily, that nominal interest rates have correlated with future nominal economic growth. We also briefly discuss the state of empirical evidence on the correlation between real rates and existential risk.
Real rates vs. real growth. A first cut at the data suggests that, indeed, higher real rates today predict higher real growth in the future:
To see how to read these graphs, take the left-most graph (“10-year horizon”) for example. The x-axis shows the level of the real interest rate, as reflected on 10-year inflation linked bonds. The y-axis shows average real GDP growth over the following 10 years.
The middle and right hand graphs show the same, at the 15-year and 20-year horizons. The scatter plot shows all available data for the US (since 1999), the UK (since 1985), Australia (since 1995), and Canada (since 1991). (Data for Australia and Canada is only available at the 10-year horizon, and comes from Augur Labs.)
Eyeballing the figure, there appears to be a strong relationship between real interest rates today and future economic growth over the next 10-20 years.
To our knowledge, this simple stylized fact is novel.
Caveats. “Eyeballing it” is not a formal econometric method; but, this is a blog post not a journal article (TIABPNAJA). We do not perform any formal statistical tests here, but we do want to acknowledge some important statistical points and other caveats.
First, the data points in the scatter plot are not statistically independent: real rates and growth are both persistent variables; the data points contain overlapping periods; and growth rates in these four countries are correlated. These issues are evident even from eyeballing the time series. Second, of course this relationship is not causally identified: we do not have exogenous variation in real growth rates. (If you have ideas for identifying the causal effect of higher real growth expectations on real rates, we would love to discuss with you.)
Relatedly, many other things are changing in the world which are likely to affect real rates. Population growth is slowing, retirement is lengthening, the population is aging. But under AI-driven “explosive” growth – again say 30%+ annual growth, following the excellent analysis of Davidson (2021) – then, we might reasonably expect that this massive of an increase in the growth rate would drown out the impact of any other factors.
Nominal rates vs. nominal growth. Turning now to evidence from nominal interest rates, recall that the usefulness of this exercise is that while there only exists 20 or 30 years of data on real interest rates for two countries, there is much more data on nominal interest rates.
We simply take all available data on 10-year nominal rates from the set of 39 OECD countries since 1954. The following scatterplot compares the 10-year nominal interest versus nominal GDP growth over the succeeding ten years by country:
Again, there is a strong positive – if certainly not perfect – relationship. (For example, the outlier brown dots at the bottom of the graph are Greece, whose high interest rates despite negative NGDP growth reflect high default risk during an economic depression.)
The same set of nontrivial caveats apply to this analysis as above.
We consider this data from nominal rates to be significantly weaker evidence than the evidence from real rates, but corroboration nonetheless.
Backing out market-implied timelines. Taking the univariate pooled OLS results from the real rate data far too seriously, the fact that the 10-year real rate in the US ended 2022 at 1.6% would predict average annual real GDP growth of 2.6% over the next 10 years in the US; the analogous interest rate of −0.2% in the UK would predict 0.7% annual growth over the next 10 years in the UK. Such growth rates, clearly, are not compatible with the arrival of transformative aligned AI within this horizon.
VI. Empirical evidence on real rates and mortality risk
We have argued that in the theory, real rates should be higher in the face of high economic growth or high mortality risk; empirically, so far, we have only shown a relationship between real rates and growth, but not between real rates and mortality.
Showing that real rates accurately reflect changes in existential risk is very difficult, because there is no word-of-god measurement of how existential risk has evolved over time.
We would be very interested in pursuing new empirical research examining “asset pricing under existential risk”. In appendix 3, we perform a scorched-earth literature review and find essentially zero existing empirical evidence on real rates and existential risks.
Disaster risk. In particular, the extant literature does not study existential risks but instead “merely” disaster risks, under which real assets are devastated but humanity is not exterminated. Disaster risks do not necessarily raise real rates – indeed, such risks are thought to lower real rates due to precautionary savings. That notwithstanding, some highlights of the appendix review include a small set of papers finding that individuals with a higher perceived risk of nuclear conflict during the Cold War saved less, as well as a paper noting that equities which were headquartered in cities more likely to be targeted by Soviet missiles did worse during the Cuban missile crisis (see also). Our assessment is that these and the other available papers on disaster risks discussed in the appendix have severe limitations for the purposes here.
Individual mortality risk. We judge that the best evidence on this topic comes instead from examining the relationship between individual mortality risk and savings/investment behavior. The logic we provided was that if humanity will be extinct next year, then there is no reason to save, pushing up the real rate. Similar logic says that at the individual level, a higher risk of death for any reason should lead to lower savings and less investment in human capital. Examples of lower savings at the individual level need not raise interest rates at the economy-wide level, but do provide evidence for the mechanism whereby extinction risk should lead to lower saving and thus higher interest rates.
One example comes from Malawi, where the provision of a new AIDS therapy caused a significant increase in life expectancy. Using spatial and temporal variation in where and when these therapeutics were rolled out, it was found that increased life expectancy results in more savings and more human capital investment in the form of education spending. Another experiment in Malawi provided information to correct pessimistic priors about life expectancy, and found that higher life expectancy directly caused more investment in agriculture and livestock.
A third example comes from testing for Huntington’s disease, a disease which causes a meaningful drop in life expectancy to around 60 years. Using variation in when people are diagnosed with Huntington’s, it has been found that those who learn they carry the gene for Huntington’s earlier are 30 percentage points less likely to finish college, which is a significant fall in their human capital investment.
Studying the effect on savings and real rates from increased life expectancy at the population level is potentially intractable, but would be interesting to consider further. Again, in our assessment, the best empirical evidence available right now comes from the research on individual “existential” risks and suggests that real rates should increase with existential risk.
VII. Plugging the Cotra probabilities into a simple quantitative model of real interest rates predicts very high rates
Section VI used historical data to go from the current real rate to a very crude market-implied forecast of growth rates; in this section, we instead use a model to go from existing forecasts of AI timelines to timeline-implied real rates. We aim to show that under short AI timelines, real interest rates would be unrealistically elevated.
This is a useful exercise for three reasons. First, the historical data is only able to speak to growth forecasts, and therefore only able to provide a forecast under the possibly incorrect assumption of aligned AI. Second, the empirical forecast assumes a linear relationship between the real rate and growth, which may not be reasonable for a massive change caused by transformative AI. Third and quite important, the historical data cannot transparently tell us anything about uncertainty and the market’s beliefs about the full probability distribution of AI timelines.
We use the canonical (and nonlinear) version of the Euler equation – the model discussed in section I – but now allow for uncertainty on both how soon transformative AI will be developed and whether or not it will be aligned. The model takes as its key inputs (1) a probability of transformative AI each year, and (2) a probability that such technology is aligned.
The model is a simple application of the stochastic Euler equation under an isoelastic utility function. We use the following as a baseline, before considering alternative probabilities:
We use smoothed Cotra (2022) probabilities for transformative AI over the next 30 years: a 2% yearly chance until 2030, a 3% yearly chance through 2036, and a 4% yearly chance through 2052.
We use the FTX Future Fund’s median estimate of 15% for the probability that AI is unaligned conditional on the development of transformative AI.
With the arrival of aligned AI, we use the Davidson (2020) assumption of 30% annual economic growth; with the arrival of unaligned AI, we assume human extinction. In the absence of the development of transformative AI, we assume a steady 1.8% growth rate.
We calibrate the pure rate of subjective time preference to 0.01 and the consumption smoothing parameter (i.e. inverse of the elasticity of intertemporal substitution) as 1, following the economic literature.
Thus, to summarize: by default, GDP grows at 1.8% per year. Every year, there is some probability (based on Cotra) that transformative AI is developed. If it is developed, there is a 15% probability the world ends, and an 85% chance GDP growth jumps to 30% per year.
We have built a spreadsheet here that allows you to tinker with the numbers yourself, such as adjusting the growth rate under aligned AI, to see what your timelines and probability of alignment would imply for the real interest rate. (It also contains the full Euler equation formula generating the results, for those who want the mathematical details.) We first estimate real rates under the baseline calibration above, before considering variations in the critical inputs.
Baseline results. The model predicts that under zero probability of transformative AI, the real rate at any horizon would be 2.8%. In comparison, under the baseline calibration just described based on Cotra timelines, the real rate at a 30-year horizon would be pushed up to 5.9% – roughly three percentage points higher.
For comparison, the 30-year real rate in the US is currently 1.6%.
While the simple Euler equation somewhat overpredicts the level of the real interest rate even under zero probability of transformative AI – the 2.8% in the model versus the 1.6% in the data – this overprediction is explainable by the radical simplicity of the model that we use and is a known issue in the literature. Adding other factors (e.g. precautionary savings) to the model would lower the level. Changing the level does not change its directional predictions, which help quantitatively explain the fall in real rates over the past ~30 years.
Therefore, what is most informative is the three percentage point difference between the real rate under Cotra timelines (5.9%) versus under no prospect of transformative AI (2.8%): Cotra timelines imply real interest rates substantially higher than their current levels.
Now, from this baseline estimate, we can also consider varying the key inputs.
Varying assumptions on P(misaligned|AGI). First consider changing the assumption that advanced AI is 15% likely to be unaligned (conditional on the development of AGI). Varying this parameter does not have a large impact: moving from 0% to 100% probability of misalignment raises the model’s predicted real rate from 5.8% only to 6.3%.
Varying assumptions on timelines. Second, consider making timelines shorter or longer. In particular, consider varying the probability of development by 2043, which we use as a benchmark per the FTX Future Fund.
We scale the Cotra timelines up and down to vary the probability of development by 2043. (Specifically: we target a specific cumulative probability of development by 2043; and, following Cotra, if the annual probability up until 2030 is , then it is in the subsequent seven years up through 2036, and it is in the remaining years of the 30-year window.)
As the next figure shows and as one might expect, shorter AI timelines have a very large impact on the model’s estimate for the real rate.
The original baseline parameterization from Cotra corresponds to the FTX Future Fund “upper threshold” of a 45% chance of development by 2043, which generated the 3 percentage point increase in the 30-year real rate discussed above.
The Future Fund’s median of a 20% probability by 2043 generates a 1.1 percentage point increase in the 30-year real rate.
The Future Fund’s “lower threshold” of a 10% probability by 2043 generates a 0.5 percentage point increase in the real rate.
These results strongly suggest that any timeline shorter than or equal to the Cotra timeline is not being expected by financial markets.
VIII. Markets are decisively rejecting the shortest possible timelines
While it is not possible to back out exact numbers for the market’s implicit forecast for AI timelines, it is reasonable to say that the market is decisively rejecting – i.e., putting very low probability on – the development of transformative AI in the very near term, say within the next ten years.
Consider the following examples of extremely short timelines:
Five year timelines: With a 50% probability of transformative AI by 2027, and the same yearly probability thereafter, the model predicts 13.0pp higher 30-year real rates today!
Ten year timelines: With a 50% probability of transformative AI by 2032, and the same yearly probability thereafter, the model predicts 6.5pp higher 30-year real rates today.
Real rate movements of these magnitudes are wildly counterfactual. As previously noted, real rates in the data used above have never gone above even 5%.
Stagnation. As a robustness check, in the configurable spreadsheet we allow you to place some yearly probability on the economy stagnating and growing at 0% per year from thereon. Even with a 20% chance of stagnation by 2053 (higher than realistic), under Cotra timelines, the model generates a 2.1% increase in 30-year rates.
Recent market movements. Real rates have increased around two percentage points since the start of 2022, with the 30-year real rate moving from −0.4% to 1.6%, approximately the pre-covid level. This is a large enough move to merit discussion. While this rise in long-term real rates could reflect changing market expectations for timelines, it seems much more plausible that high inflation, the Russia-Ukraine war, and monetary policy tightening have together worked to drive up short-term real rates and the risk premium on long-term real rates.
IX. Financial markets are the most powerful information aggregators produced by the universe (so far)
Should we update on the fact that markets are not expecting very short timelines?
As a prior, we think that market efficiency is reasonable. We do not try to provide a full defense of the efficient markets hypothesis (EMH) in this piece given that it has been debated ad nauseum elsewhere, but here is a scaffolding of what such an argument would look like.
Loosely, the EMH says that the current price of any security incorporates all public information about it, and as such, you should not expect to systematically make money by trading securities.
This is simply a no-arbitrage condition, and certainly no more radical than supply and demand: if something is over- or under-priced, you’ll take action based on that belief until you no longer believe it. In other words, you’ll buy and sell it until you think the price is right. Otherwise, there would be an unexploited opportunity for profit that was being left on the table, and there are no free lunches when the market is in equilibrium.
As a corollary, the current price of a security should be the best available risk-adjusted predictor of its future price. Notice we didn’t say that the price is equal to the “correct” fundamental value. In fact, the current price is almost certainly wrong. What we did say is that it is the best guess, i.e. no one knows if it should be higher or lower.
Testing this hypothesis is difficult, in the same way that testing any equilibrium condition is difficult. Not only is the equilibrium always changing, there is also a joint hypothesis problem which Fama (1970) outlined: comparing actual asset prices to “correct” theoretical asset prices means you are simultaneously testing whatever asset pricing model you choose, alongside the EMH.
In this sense, it makes no sense to talk about “testing” the EMH. Rather, the question is how quickly prices converge to the limit of market efficiency. In other words, how fast is information diffusion? Our position is that for most things, this is pretty fast!
Here are a few heuristics that support our position:
For our purposes, the earlier evidence on the link between real rates and growth is a highly relevant example of market efficiency.
There are notable examples of markets seeming to be eerily good at forecasting hard-to-anticipate events:
In the wake of the Challenger explosion, despite no definitive public information being released, the market seems to have identified which firm was responsible.
Economist Armen Alchian observed that the stock price of lithium producers spiked 461% following the public announcement of the first hydrogen bomb tests in 1954, while the prices of producers of other radioactive metals were flat. He circulated a paper within RAND, where he was working, identifying lithium as the material used in the tests, before the paper was suppressed by leadership who were apparently aware that indeed lithium was used. The market was prescient even though zero public information was released about lithium’s usage.
Remember: if real interest rates are wrong, all financial assets are mispriced. If real interest rates “should” rise three percentage points or more, that is easily hundreds of billions of dollars worth of revaluations. It is unlikely that sharp market participants are leaving billions of dollars on the table.
X. If markets are not efficient, you could be earning alpha and philanthropists could be borrowing
While our prior in favor of efficiency is fairly strong, the market could be currently failing to anticipate transformative AI, due to various limits to arbitrage.
However, if you do believe the market is currently wrong about the probability of short timelines, then we now argue there are two courses of action you should consider taking:
Bet on real rates rising (“get rich or die trying”)
Borrow today, including in order to fund philanthropy (“impatient philanthropy”)
1. Bet on real rates rising (“get rich or die trying”)
Under the logic argued above, if you genuinely believe that AI timelines are short, then you should consider putting your money where your mouth is: bet that real rates will rise when the market updates, and potentially earn a lot of money if markets correct. Shorting (or going underweight) government debt is the simplest way of expressing this view.
Indeed, AI safety researcher Paul Christiano has written publicly that he is (or was) short 30-year government bonds.
If short timelines are your true belief in your heart of hearts, and not merely a belief in a belief, then you should seriously consider how much money you could earn here and what you could do with those resources.
Implementing the trade. For retail investors, betting against treasuries via ETFs is perhaps simplest. Such trades can be done easily with retail brokers, like Schwab.
(i) For example, one could simply short the LTPZ ETF, which holds long-term real US government debt (effective duration: 20 years).
(ii) Alternatively, if you would prefer to avoid engaging in shorting yourself, there are ETFs which will do the shorting for you, with nominal bonds: TBF is an ETF which is short 20+ year treasuries (duration: 18 years); TBT is the same, but levered 2x; and TTT is the same, but levered 3x. There are a number of other similar options. Because these ETFs do the shorting for you, all you need to do is purchase shares of the ETFs.
Back of the envelope estimate. A rough estimate of how much money is on the table, just from shorting the US treasury bond market alone, suggests there is easily $1 trillion in value at stake from betting that rates will rise.
In response to a 1 percentage point rise in interest rates, the price of a bond falls in percentage terms by its “duration”, to a first-order approximation.
The average value-weighted duration of (privately-held) US treasuries is approximately 4 years.
So, to a first-order approximation, if rates rise by 3 percentage points, then the value of treasuries will fall by 12% (that is, 3*4).
The market cap of (privately-held) treasuries is approximately $17 trillion.
Thus, if rates rise by 3 percentage points, then the total value of treasuries can be expected to fall by $2.04 trillion (that is, 12%*17 trillion).
Slightly more than half (55%) of the interest rate sensitivity of the treasury market comes from bonds with maturity beyond 10 years. Assuming that the 3 percentage point rise occurs only at this horizon, and rounding down, we arrive at the $1 trillion estimate.
Alternatively, returning to the LTPZ ETF with its duration of 20 years, a 3 percentage point rise in rates would cause its value to fall by 60%. Using the 3x levered TTT with duration of 18 years, a 3 percentage point rise in rates would imply a mouth-watering cumulative return of 162%.
While fully fleshing out the trade analysis is beyond the scope of this post, this illustration gives an idea of how large the possibilities are.
The alternative to this order-of-magnitude estimate would be to build a complete bond pricing model to estimate more precisely the expected returns of shorting treasuries. This would need to take into account e.g. the convexity of price changes with interest rate movements, the varied maturities of outstanding bonds, and the different varieties of instruments issued by the Treasury. Further refinements would include trading derivatives (e.g. interest rate futures) instead of shorting bonds directly, for capital efficiency, and using leverage to increase expected returns.
Additionally, the analysis could be extended beyond the US government debt market, again since changes to real interest rates would plausibly impact the price of every asset: stocks, commodities, real estate, everything.
(If you would be interested in fully scoping out possible trades, we would be interested in talking.)
Trade risk and foom risk. We want to be clear that – unless you are risk neutral, or can borrow without penalty at the risk-free rate, or believe in short timelines with 100% probability – then such a bet would not be a free lunch: this is not an “arbitrage” in the technical sense of a risk-free profit. One risk is that the market moves in the other direction in the short term, before correcting, and that you are unable to roll over your position for liquidity reasons.
The other risk that could motivate not making this bet is the risk that the market – for some unspecified reason – never has a chance to correct, because (1) transformative AI ends up unaligned and (2) humanity’s conversion into paperclips occurs overnight. This would prevent the market from ever “waking up”.
However, to be clear, expecting this specific scenario requires both:
Buying into specific stories about how takeoff will occur: specifically, Yudkowskian foom-type scenarios with fast takeoff.
Having a lot of skepticism about the optimization forces pushing financial markets towards informational efficiency.
You should be sure that your beliefs are actually congruent with these requirements, if you want to refuse to bet that real rates will rise. Additionally, we will see that the second suggestion in this section (“impatient philanthropy”) is not affected by the possibility of foom scenarios.
2. Borrow today, including in order to fund philanthropy (“impatient philanthropy”)
If prevailing interest rates are lower than your subjective discount rate – which is the case if you think markets are underestimating prospects for transformative AI – then simple cost-benefit analysis says you should save less or even borrow today.
An illustrative example. As an extreme example to illustrate this argument, imagine that you think that there is a 50% chance that humanity will be extinct next year, and otherwise with certainty you will have the same income next year as you do this year. Suppose the market real interest rate is 0%. That means that if you borrow $10 today, then in expectation you only need to pay $5 off, since 50% of the time you expect to be dead.
It is only if the market real rate is 100% – so that your $10 loan requires paying back $20 next year, or exactly $10 in expectation – that you are indifferent about borrowing. If the market real rate is less than 100%, then you want to borrow. If interest rates are “too low” from your perspective, then on the margin this should encourage you to borrow, or at least save less.
Note that this logic is not affected by whether or not the market will “correct” and real rates will rise before everyone dies, unlike the logic above for trading.
Borrowing to fund philanthropy today. While you may want to borrow today simply to fund wild parties, a natural alternative is: borrow today, locking in “too low” interest rates, in order to fund philanthropy today. For example: to fund AI safety work.
We can call this strategy “impatient philanthropy”, in analogy to the concept of “patient philanthropy”.
This is not a call for philanthropists to radically rethink their cost-benefit analyses. Instead, we merely point out: ensure that your financial planning properly accounts for any difference between your discount rate and the market real rate at which you can borrow. You should not be using the market real rate to do your financial planning. If you have a higher effective discount rate due to your AI timelines, that could imply that you should be borrowing today to fund philanthropic work.
Relationship to impatient philanthropy. The logic here has a similar flavor to Phil Trammell’s “patient philanthropy” argument (Trammell 2021) – but with a sign flipped. Longtermist philanthropists with a zero discount rate, who live in a world with a positive real interest rate, should be willing to save all of their resources for a long time to earn that interest, rather than spending those resources today on philanthropic projects. Short-timeliners have a higher discount rate than the market, and therefore should be impatient philanthropists.
(The point here is not an exact analog to Trammell 2021, because the paper there considers strategic game theoretic considerations and also takes the real rate as exogenous; here, the considerations are not strategic and the endogeneity of the real rate is the critical point.)
XI. Conclusion: outside views vs. inside views & future work
We do not claim to have special technical insight into forecasting the likely timeline for the development of transformative artificial intelligence: we do not present an inside view on AI timelines.
However, we do think that market efficiency provides a powerful outside view for forecasting AI timelines and for making financial decisions. Based on prevailing real interest rates, the market seems to be strongly rejecting timelines of less than ten years, and does not seem to be placing particularly high odds on the development of transformative AI even 30-50 years from now.
We argue that market efficiency is a reasonable benchmark, and consequently, this forecast serves as a useful prior for AI timelines. If markets are wrong, on the other hand, then there is an enormous amount of money on the table from betting that real interest rates will rise. In either case, this market-based approach offers a useful framework: either for forecasting timelines, or for asset allocation.
Opportunities for future work. We could have put 1000 more hours into the empirical side or the model, but, TIABPNAJA. Future work we would be interested in collaborating on or seeing includes:
More careful empirical analyses of the relationship between real rates and growth. In particular, (1) analysis of data samples with larger variation in growth rates (e.g. with the Industrial Revolution, China or the East Asian Tigers), where a credible measure of real interest rates can be used; and (2) causally identified estimates of the relationship between real rates and growth, rather than correlations. Measuring historical real rates is the key challenge, and the main reason why we have not tried to address these here.
Any empirical analysis of how real rates vary with changing existential risk. Measuring changes in existential risk is the key challenge.
Alternative quantitative models on the relationship between real interest rates and growth/x-risk with alternative preference specifications, incomplete markets, or disaster risk.
Tests of market forecasting ability at longer time horizons for any outcome of significance; and comparisons of market efficiency at shorter versus longer time horizons.
Creation of sufficiently-liquid genuine market instruments for directly measuring outcomes we care about like long-horizon GDP growth: e.g. GDP swaps, GDP-linked bonds, or binary GDP prediction markets. (We emphasize market instruments to distinguish from forecasting platforms like Metaculus or play-money sites like Manifold Markets where the forceful logic of financial market efficiency simply does not hold.)
An analysis of the most capital-efficient way to bet on short AI timelines and the possible expected returns (“the greatest trade of all time”).
Analysis of the informational content of infinitely-lived assets: e.g. the discount rates embedded in land prices and rental contracts. There is an existing literature related to this topic: , , , , , , .
This literature estimates risky, nominal discount rates embedded in rental contracts out as far as 1000 years, and finds surprisingly low estimates – certainly less than 10%. This is potentially extremely useful information, though this literature is not without caveats. Among many other things, we cannot have the presumption of informational efficiency in land/rental markets, unlike financial markets, due to severe frictions in these markets (e.g. inability to short sell).
Thanks especially to Leopold Aschenbrenner, Nathan Barnard, Jackson Barkstrom, Joel Becker, Daniele Caratelli, James Chartouni, Tamay Besiroglu, Joel Flynn, James Howe, Chris Hyland, Stephen Malina, Peter McLaughlin, Jackson Mejia, Laura Nicolae, Sam Lazarus, Elliot Lehrer, Jett Pettus, Pradyumna Prasad, Tejas Subramaniam, Karthik Tadepalli, Phil Trammell, and participants at ETGP 2022 for very useful conversations on this topic and/or feedback on drafts.
Update 1: we have now posted a comment summarising our responses to the feedback we have received so far.
OpenAI’s ChatGPT model on what will happen to real rates if transformative AI is developed:
Some framings you can use to interpret this post:
“This blog post takes Fama seriously” [a la Mankiw-Romer-Weil]
“The market-clearing price does not hate you nor does it love you” [a la Yudkowsky]
“Existential risk and asset pricing” [a la Aschenbrenner 2020, Trammell 2021]
“Get rich or hopefully don’t die trying” [a la 50 Cent]
“You can short the apocalypse.” [contra Peter Thiel, cf Alex Tabarrok]
“Tired: market monetarism. Inspired: market longtermism.” [a la Scott Sumner]
“This is not not financial advice.” [a la the standard disclaimer]
Lots of the comments here are pointing at details of the markets and whether it’s possible to profit off of knowing that transformative AI is coming. Which is all fine and good, but I think there’s a simple way to look at it that’s very illuminating.
The stock market is good at predicting company success because there are a lot of people trading in it who think hard about which companies will succeed, doing things like writing documents about those companies’ target markets, products, and leadership. Traders who do a good job at this sort of analysis get more funds to trade with, which makes their trading activity have a larger impact on the prices.
Now, when you say that:
I think what you’re claiming is that market prices are substantially controlled by traders who have a probability like that in their heads. Or traders who are following an algorithm which had a probability like that in the spreadsheet. Or something thing like that. Some sort of serious cognition, serious in the way that traders treat company revenue forecasts.
And I think that this is false. I think their heads don’t contain any probability for transformative AI at all. I think that if you could peer into the internal communications of trading firms, and you went looking for their thoughts about AI timelines affecting interest rates, you wouldn’t find thoughts like that. And if you did find an occasional trader who had such thoughts, and quantified how much impact they would have on the prices if they went all-in on trading based on that theory, you would find their impact was infinitesimal.
Market prices aren’t mystical, they’re aggregations of traders’ cognition. If the cognition isn’t there, then the market price can’t tell you anything. If the cognition is there but it doesn’t control enough of the capital to move the price, then the price can’t tell you anything.
I think this post is a trap for people who think of market prices as a slightly mystical source of information, who don’t have much of a model of what cognition is behind those prices.
(Comment cross-posted with the EA forum version of this post)
i agree that there’s the 3rd alternative future that the post does not consider (unless i missed it!):
3. markets remain in an inadequate equilibrium until the end of times, because those participants (like myself!) who consider short timelines remain in too small minority to “call the bluff”.
see the big short for a dramatic depiction of such situation.
great post otherwise. upvoted.
Coincidentally, that scene in The Big Short takes place on January 11 (2007) :D
I agree with this comment. Don’t treat markets as an oracle regarding some issue, if there’s no evidence that traders in the market have even thought about the issue.
And in this case, the question is not just whether AI is coming soon, the question is whether AI will soon cause extinction or explosive economic growth. Have there been any Bloomberg op-eds debating this?
Agreed. A recent example of this was the long delay in early 2020 between “everyone who pays attention can see that corona will become a pandemic” until stocks actually started falling.
Is there any evidence at all that markets are good at predicting paradigm shifts? Not my field but I would not be surprised by the “no” answer.
Markets as often-efficient in-sample predictors, and poor out-of-sample predictors, would be my base intuition.
Reposting my agreement from the EA forum! (Personally I feel like it would be nice to have EA/Lesswrong crossposts have totally synced comments, such that it is all one big community discussion. Anyways --)
Definitely agree with this. Consider for instance how markets seemed to have reacted strangely / too slowly to the emergence of the Covid-19 pandemic, and then consider how much more familiar and predictable is the idea of a viral pandemic compared to the idea of unaligned AI:
Peter Thiel (in his “Optimistic Thought Experiment” essay about investing under anthropic shadow, which I analyzed in a Forum post) also thinks that there is a “failure of imagination” going on here, similar to what Gwern describes:
In this comment, you are decisively rejecting the semi-strong form of the EMH, or at least carving out an exception where AI is concerned. Specifically, the semi-strong EMH states that “ because public information is part of a stock’s current price, investors cannot utilize either technical or fundamental analysis, though information not available to the public can help investors.”
The OP is explicitly and carefully written as an argument aimed at people who do subscribe to the (semi-strong or strong) EMH. For those people, it is correct to ascribe “semi-mystical” powers of prediction to the market. You can make a separate argument that the EMH is false, or that the reasoning of this article is flawed. But your comment makes it sound like it’s not the same thing to reject the EMH as it is to deny that “cognition is there” on this issue. I say that rejection of the EMH and denial of market cognition are the same belief.
It’s only an argument against the EMH if you take the exploitability of AI timeline prediction as axiomatic. If you unpack the EMH a little, traders not analyzing transformative AI can also be interpreted as evidence of inexploitability.
The OP described how a trader might exploit AI timeline prediction for financial gain if they believed in short timelines, such as by borrowing. Are you saying they are wrong, and that it’s not possible to exploit low real rates in this manner? I have to point out that this is not the argument you were making in the comment I responded to. Markets certainly are thinking very hard about AI, including the immediately transformative possibilities of LLMs like ChatGPT for search. Even if markets ignored the possibility of doom, it seems like they’d at least be focusing heavily on the possibility for mega-profits from controlling a beneficial AI. And it’s not like these ideas aren’t out there in the world—advances in AI are a major topic of world conversation.
At the very least, if markets were considering the possibility of AI takeoff and concluding it was inexploitable, that would not look like “if you could peer into the internal communications of trading firms, and you went looking for their thoughts about AI timelines affecting interest rates, you wouldn’t find thoughts like that.” It would look like firms thinking very hard about how to financially exploit AI takeoff and concluding explicitly that it is not possible.
I mostly agree with this post.
Note that ancient plagues provide more evidence on the relationship between interest rates and mortality. It’s likely hard to distinguish real rates from the inflationary effects, but the inflationary effects are likely due to the expectation that mortality will reduce the value of holding money (that kind of inflationary effect would tend to support your claims).
It looks harder than you indicate to profit from the bond market mispricings. Still, it looks promising enough that I feel foolish for not looking into it before this.
I’m unwilling to bet against t-bonds now. Investors likely overestimate near-term inflation. Changes in inflation forecasts are likely to dominate the t-bond market this year.
Shorting TIPS is a more pure way to bet on real rates. The 2040 TIPS (and later years) look weirdly overpriced.
A quick glance suggests that I can’t short TIPS directly, at least at IBKR.
Shorting LTPZ looks superficially great, but SLB rates on IBKR have been ranging from 4 to 6.44%. That eats up much of the expected profit, but is maybe still worth it.
Buying TIPD looks like currently the best choice. But if it’s doing a better job of what I’d like from shorting LTPZ, why are investors paying so much to short LTPZ?
If I evaluate TIPD (or shorting LTPZ) as a stand-alone investment, it’s unlikely to be as good a bet on AGI as semiconductor stocks. But it seems likely to be negatively correlated with my equity investments, which suggests it’s sort of like a free lunch.
I’ve found a better way to bet on real rates increasing sometime in the next decade: shorting long-dated Eurodollar futures, while being long 2025 Eurodollar futures (to bet on a nearer-term decline in expected inflation).
The Eurodollar markets are saying that interest rates will start slowly rising after about 2027, implying a mild acceleration of economic growth and/or inflation.
I spent nearly 2 months trying to short the December 2032 contract, slowly reducing my ask price. As far as I can tell, nobody is paying attention to that contract. At very least, nobody who thinks interest rates will be stable after 2030.
Recent events prompted me to look for other Eurodollar contract months. I ended up trading the September 2029 contracts, which have enough liquidity that I was able to trade a decent amount within a few days.
That gives me a fairly pure bet on short-term interest (nominal) rates rising between 2025 and 2029.
I feel like the correct take here is EMH false because market’s don’t really account for black swans well.
I agree that there’s money to be made here under certain circumstances, but also keep in mind that the best companies are not publicly traded. In a non-catastrophic scenario you can probably get decent exposure via public tech companies, but in a catastrophic scenario the winning strategy is to spend as much as possible before the world ends.
Suppose you have something like 50% catastrophic AI and 50% nothing happens for 2 decades, though, I’m not really sure what you should do. If nothing happens and you spend all your money you spend the rest of your life penniless. If the world does end, does buying that 2nd house really get you all that much utility? Most of the things I value (and haven’t already bought) are of the form “living a long and fulfilling life” or “seeing my grandchildren” which are impossible to invest for in the 50⁄50 scenario.
If the world does end, does buying that 2nd house really get you all that much utility?
Conversely what about the range of somewhat positive scenarios. The world doesn’t end, but general robotic AI works. You can simply write a file for the instructions for a robot and it can go do a task and it is much more likely to succeed than a typical human is.
Only the land under that 2nd house has any long term value in that scenario. The structure can be swapped like we swap flatscreen TVs today. (not that far fetched, in prior eras TVs were much more expensive and actually a significant investment)
And implicitly the reason we are all supposed to horde away huge piles of wealth for retirement is because:
1. medical care is delivered by humans and is mostly ineffective but when you are elderly it can burn away millions on marginally effective treatments to add a few extra weeks before you’re dead
2. prices for basic necessities could theoretically increase a lot and you need that huge pile of assets to pay for them
3. you have plans for all the activities you are going to do when elderly that you probably won’t actually do
Even somewhat positive AI scenarios where the world hasn’t ended but it is capable and commonplace may break all 3 assumptions. It definitely breaks #2, it might break #1. AI developed therapies for aging might break #3 though arguably if you weren’t appearing elderly and suffering from all the symptoms of untreated aging you could return to work.
Anyone know how the pricing of the long term securities linked work?
I’m guessing these rates aren’t high because the mechanisms that would make those numbers high aren’t able to be activated by “lots of the world’s wealthiest expect massive gains from AI”. And so no amount of EMH will fix that?
On my model, if you’re wealthy and expect AI soon, I expect you to invest what you can in AI stuff. You would affect interest rates only if you manage to take out a bunch of loans in order to put more money in AI stuff. But loans aren’t easy to get, and they can be risky (because the value of your collateral on the market can shift around lots, especially if you’re going very leveraged).
So, if someone can enlighten me: (1) Would private actors expecting AI be making leveraged AI bets with a good fraction of their wealth? [probably yes] (2) Do loans these actors obtain drive up that number on the US treasury site? [probably no]
ETA: I know the post goes into some detail as to why we’d expect rates to move around with folk’s expectations, but I find it hard to parse in my mechanism-brain
One possible explanation is an expectation of massive deflation (perhaps due to AI-caused decreases in production costs) which the structure of Treasury Inflation Protected Securities (TIPS) and other inflation-linked government bonds — the source of your real interest rate data — doesn’t account for.
While TIPS adjust the principal (and corresponding coupons) up and down over time according to changes in the consumer price index, you ALWAYS get at least the initial principal back at maturity. Typical “yield” calculations, however, are based on the assumption that you get your inflation-adjusted principal back (which you do if inflation was positive over its term, as it usually would be historically).
This means that iff there’s net deflation over its term, the “yield” underestimates your real rate of return with TIPS by the amount of that deflation.
1. Very interesting, thanks, I think this is the first or second most interesting comment we’ve gotten.
2. I see that you are suggesting this as a possibility, rather than a likelihood, but I’ll note at least for other readers that—I would bet against this occurring, given central banks’ somewhat successful record at maintaining stable inflation and desire to avoid deflation. But it’s possible!
3. Also, I don’t know if inflation-linked bonds in the other countries we sample—UK/Canada/Australia—have the deflation floor. Maybe they avoid this issue.
4. Long-term inflation swaps (or better yet, options) could test this hypothesis! i.e. by showing the market’s expectation of future inflation (or the full [risk-neutral] distribution, with options).
It appears the UK’s index-linked gilts, at least, don’t have this structural issue.
See “redemption payments” on page 6 of this document, or put in a sufficiently large negative inflation assumption here.
Thanks for this interesting and well-developed perspective. However, I disagree specifically with the claim “the existential risk caused by unaligned AI would cause high real interest rates”.
The idea seems to be that, anticipating doomsday, people will borrow money to spend on lavish consumption under the assumption that they won’t need to pay it back. But:
This is a bad strategy (in a game-theoretic and evolutionary sense).
I am skeptical that people actually act this way.
Studying a simple example may help to clarify.
Strategy: playing to your outs
There is a concept in card games of “playing to your outs”. The idea is, if you’re in a losing position, then the way to maximize your winning probability is to assume that future random events still provide a possibility of winning. A common example of this is to observe that you lose unless your next draw is a particular card, and as a result you play under the assumption that you will draw the card you need.
How the concept of playing to your outs applies to existential risk: if in fact extinction occurs, then it didn’t matter what you did. So you ought to plan for the scenario where extinction does not occur.
This same idea ought to apply to evolution for similar reasons that it applies to games. That said, obviously we’re not recalculating evolutionarily optimal strategies as we live our lives, so our actions may not be consistent with a good evolutionary strategy. Still, it makes me skeptical.
Do people actually act this way?
Section VI of the post discusses the empirical question of how people act if they expect doomsday, but I didn’t find it very persuasive. That said, I also haven’t done the work of finding contradictory evidence. (I’d propose looking at cases of religious movements with dated doomsday predictions.)
A lot of the cited evidence in section VI is about education, but I believe that’s a red herring. It makes sense that somebody would value education less if they expect to die before they can benefit from it. But that doesn’t necessarily mean they’re putting the resources towards lavish consumption instead: they might spend it on alternative investments that can outlive them (and therefore benefit their family). So it can’t tell us much about what doomsday does to consumption in particular.
I had originally hoped to settle the matter through an example, but that doesn’t quite work. Still, it’s instructive.
Consider two people, Alice and Bob. They agree that there’s a 50% probability that tomorrow the Earth will explode, destroying humanity. They contemplate the following deal:
Today (day 0), Bob gives Alice $1 million.
The day after tomorrow (day 2), Alice gives Bob her $1.5 million vacation home.
One way to look at this:
Alice gains $1 million for sure.
With 50% probability, Alice doesn’t need to give Bob the home (because humanity is extinct), so her expected loss is only 50% * $1.5 million = $750k.
Therefore, Alice’s net expected profit is $250k.
From this perspective, it’s a good deal for Alice. (This seems to be the perspective taken by the OP.)
But here’s a different way to look at it:
In the scenario where the world ends, Alice, her family, and her friends are all dead, regardless of whether she made the deal, so she nets nothing.
In the scenario where the world doesn’t end, Alice has lost net $500k.
Therefore, Alice has a net expected loss of $250k.
From this perspective, it’s a bad deal for Alice. (This is more in line with my intuition.)
The discrepancy presumably arises from the possibility of Alice consuming the $1 million today, for example by throwing a mega-party.
But that just feels wrong, doesn’t it? Is partying hard actually worth so much to Alice that she’s willing to make herself worse off in the substantial (50%!) chance that the world doesn’t end?
Here’s an attempt to formalize the “is partying hard worth so much” aspect of your example:
It’s common (with some empirical support) to approximate utility as proportional to log(consumption). Suppose Alice has $5M of savings and expected-future-income that she intends to consume at a rate of $100k/year over the next 50 years, and that her zero utility point is at $100/year of consumption (since it’s hard to survive at all on less than that). Then she’s getting log(100000/100) = 3 units of utility per year, or 150 over the 50 years.
Now she finds out that there’s a 50% chance that the world will be destroyed in 5 years. If she maintains her old spending patterns her expected utility is .5*log(1000)*50 + .5*log(1000)*5 = 82.5. Alternately, if interest rates were 0%, she might instead change her plan to spend $550k/year over the next 5 years and then $50k/year subsequently (if she survives). Then her expected utility is log(5500)*5+.5*log(50)*45 = 56.9, which is worse. In fact her expected utility is maximized by spending $182k over the next five years and $91k after that, yielding an expected utility of about 82.9, only a tiny increase in EV. If she has to pay extra interest to time-shift consumption (either via borrowing or forgoing investment returns) she probably just won’t bother. So it seems like you need very high confidence of very short timelines before it’s worth giving up the benefits of consumption-smoothing.
I like this comment. Where the intuition pump breaks down is that you haven’t realistically described what Alice would do with a million dollars, knowing that the Earth has a 50% chance of being destroyed tomorrow. She’d probably spend it trying to diminish that probability—a more realistic possibility that total confidence in 50% destruction and total helplessness to do anything about it.
If we presume Alice can diminish the probability of doom somewhat by spending her million dollars, then it could easily have sufficient positive expected value to make the trade with Bob clearly beneficial.
Why would you expect her to be able to diminish the probability of doom by spending her million dollars? Situations where someone can have a detectable impact on global-scale problems by spending only a million dollars are extraordinarily rare. It seems doubtful that there are even ways to spend a million dollars on decreasing AI xrisk now when timelines are measured in years (as the projects working on it do not seem to be meaningfully funding-constrained), much less if you expected the xrisk to materialize with 50% probability tomorrow (less time than it takes to e.g. get a team of researchers together).
I agree it’s rare to have a global impact with a million dollars. But if you’re 50% confident the world will be destroyed tomorrow, that implies you have some sort of specific knowledge about the mechanism of destruction. The reason it’s hard to spend a million dollars to have a big impact is often because of a lack of such specific information.
But if you are adding the stipulation that there’s nothing Alice can do to affect the probability of doom, then I agree that your math checks out.
How exactly would I go about doing that? A-priori this seems difficult: If there were opportunities to cheaply borrow money for eg 10 years, lots of people who have strong time discounting would take that option.
For 99% of people, the only viable option to achieve this is refinancing your mortgage to take any equity out and resetting terms to a 30 year loan duration.
The most surprising thing about the last year was that all the big tech companies reduced their headcount while AI advanced. That’s while those companies also have a lot of cash in the bank.
Maybe because existing big companies have a lot of bullshit jobs they will all be outcompeted by new smaller companies that leverage AI?
You don’t even need to expect it to occur overnight. It’s enough for the market update to predictably occur so late that having lots of money available at that point is no longer useful. If AGI ends the world next week, there’s not that much a hundred billion dollar influx can actually gain you. Any operation that actually stops the apocalypse from happening probably needs longer than that to set up, regardless of any additional funds available. And everything else you can do with a hundred billion dollars in that week is just not that fun or useful.
And if you do get longer than that, if we have an entire month somehow, a large fraction of market participants believing the apocalypse is coming would be the relevant part anyway. That many people taking the problem actually seriously might maybe be enough to put the brakes on things through political channels. For a little bit at least. Monetary concerns seem secondary to me in comparison.
I guess a short position by EA aligned people just in case that this edge scenario happens and a competent institutional actor with a hundred billion dollars is needed now now now could maybe make some sense?
Tl;dr markets are hard to beat, but it’s not impossible. Case in point, there is probably alpha in understanding AI’s impact but it’s very hard to time and finance the associated bets
The market doesn’t account for black swans.
Or, look at it another way. Is any demonstrated and existing AI system going to change the world? No. In short timeline worlds, there is rapid iteration, every few weeks, of better systems. At a certain point, instead of getting diminishing returns, where each iteration doesn’t result in much improvement, you get accelerating returns because the current AI system is good enough to accelerate the development of AI.
This may or may not be happen but it’s not written on the annual report of any company or a possibility known to the market as anything more than decades of AI hype which is already “priced in”.
If this does happen, it was possible because there is enormously more compute available. Something the market is apparently not pricing in.
In this comment, I merely want to focus on using the Challenger Disaster Reaction example of market capabilities. I think it’s a bad example.
I think it’s basically a very interesting story that would be good to tell people at a party or in a TED talk to introduce people to the idea of prediction markets by using an obviously extreme example.
I think it is a mistake to confuse good storytelling with good empirical evidence. I don’t think it’s valuable empirical evidence about the market being able to make these kinds of predictions.
At a quick naive approximation, there’s already a 25% chance that 1 out of 4 contractors of the mission would be coincidentally correctly identified as the one with most fault. Very low bar; shouldn’t cause you to update much in terms of bayesian evidence.
Even after extensive research after the events, analysts could not identify the mechanism by which the market was able to produce this result, if we assume it was not coincidence. The sources linked in this article quotes the researchers thusly:
”a perplexing situation that while markets appear to work in practice, we are not sure how they work in theory.”
Which is totally consistent with the null hypothesis of “win 2 coinflips”. As far as we can tell, it’s either insider info, or coincidence, because there is no causal mechanism to derive this result from public information!
It is especially concerning, that this seems like an appeal to the mysticism of markets. It seems like one is handwaving the lack of identifiable causal mechanisms and saying “markets work because they’re basically magic, look at this magical-seeming example we found”
If it really is that efficient and we simply can’t figure out the mechanism because we’re too stupid, at least we would see tons of other examples. Can we get like another 100 examples like this one? I just find it suspicious that we’re giving so much hype to an example that happened in 1986. Surely there would be some other flashy examples since then as well? If that is the case, it would be more convincing to list all of them instead of focusing on this single example.
I realize that’s asking for a lot more effort, but that would be what it would take to actually make this convincing, because I think picking one example from 1986 that could have happened due to 2 coinflips is close to useless in convincing me. But worse, it is using the Dark Art of storytelling which may convince people when they shouldn’t be convinced.
It’s hard to see how to use this knowledge to make a huge pile of money. A few people can take out a personal loan. The finance system has to handle people with terminal cancer who want to hold a massive party today and don’t care about the long term. (Mostly by not giving out massive unsecured loans)
There have been attempts here and elsewhere to recommend investments if you think AGI is more likely than “the market” seems to. Whether optimistic or pessimistic in outcome, the only agreement I’ve seen is “there are more out-of-distribution possibilities than we can account for, so it’s impossible to find alpha over 5-year or better horizons, unless you are deeply personally involved in some sector”.
I agree with the conclusion: most of the market volume is indicating a disbelief in massive transformation. But it could equally be a wager on transformation in directions whose probabilities cancel each other out. It’s important to realize that all prices, including interest rates, are ratios of values one thing to another. Interest is the ratio of the value of a currency now to the value later. And value is a ratio too—it’s what you can exchange or use a thing for. The problem with massive disruption is you get nonsense values when a value goes to 0 (if a lynchpin of the calculations becomes unnecessary) or infinite (a commodity in this valuation-ratio chain becomes completely unavailable).
“AGI and the EMH: markets are not expecting aligned or unaligned AI in the next 30 years”
Question: are you talking about expectation under the risk-neutral measure or the physical measure? Your parts about how EA’s could exploit arbitrage should be based on the risk-neutral measure, right? (I’m not super familiar with financial theory.)
Interesting discussion here :)
Just my 2 cents:
I am wondering about 2 things:
If/when TS (technological singularity) happens, then the economic actor having created SI (super intelligence) would very likely very quickly exponentially increase to some ultra-high/out-of-scale value while almost all the other economic actors value would decrease towards 0, wouldn’t it? It’s the concepts of “singularity” and “winner takes all” isn’t it?
The world (including the economic world) pre/during/post-TS is very difficult to predict / very speculative in nature (one of the basic concept of TS). Imho it would completely depend on by whom and how the SI is controlled, if it is controlled by a company intended on maximizing its profits then that company could easily dictate the level of inflation and interest rates it deems appropriate to maximize its profits which probably could be as close to zero as possible. It the SI is controlled by some sort of benevolent/utilitarianist entity then it would probably make everything free for everybody, just allocating goods/services in the most possible benevolent/utilitarianist way and things like “inflation”, “interest rate” might simply disappear having become essentially irrelevant (maybe except in some sort of (black) markets that might still operate more or less outside the super intelligence sphere of influence if that is still somewhat possible).
What happens just before, during and after the TS is ultra-speculative in nature.
But we have seen already that entities which work explicitely/implicitely on AGI/TS and which obtain tangible results tend to fair well in terms of valuation growth (Google, OpenAI, Amazon, etc...) and tend, at least at first, to have a deflationary effect on the cost of many products/services but might impede that deflationary effect if/when they start behaving in monopolistic and rent-seeking ways (then government(s) intervention comes into play).
Imho the effect on interest rates of a TS depends on so many difficult to predict variables either just before, during and after a TS that the EMH is kept safe by the markets not taking into account what impact TS will have on interest rates.
No. The economy and the market will be booming up until (and if) a complete transition out of the monetary system happens, including in the presence of ASI.
Thank you for your answer :)
Imho there will definitely be a flood of already existing products and services being produced at rock-bottom prices and a flood of new products and services at cheap prices, etc… coming from the entity having created / in control of the ASI, but will that make the economy as a whole booming? I am not sure.
To take an analogy imagine a whole new country appears from under the ocean (or an extraterrestrial alien spaceship, etc...) and flood the rest of the world with very cheap products and services as well as new products and services etc… at very cheap prices completely outcompeting each and every company in the rest of the world, what would that mean for the economy of the rest of the world: absolutely trashed, wouldn’t it?
All the companies, workers, means of production of the rest of the world would become very quickly valueless, even commodities as the SI could, if it wanted to, get them in almost unlimited quantity from outerspace and nuclear fusion etc...
Maybe Earth land would still have some value for people who enjoy living / traveling there rather than on giant artificial Earth satellites, etc...
The company having created / in control of ASI will be economically booming (in the short term at least) for sure but the rest of the economy and markets completely outcompeted by it, I am not sure, it would depend if the company having created / in control of ASI is willing to share some of its economic value / activity to the rest of the world or just quickly absorb all the economic activity into an economic singularity.
What do you think?
One actor having all the money and economic power in the world all all the rest “trashed” is not a coherent situation, under modern economics. For the products, businesses, services, etc. to be outcompeted you still need the trade happening, and this trade should necessarily be bidirectional.
If trade ceases it either means that the whole world is converted in a single corporation under the command of a single ASI (in which case the conventional market economics have ended, no more money and company valuations), or ASI just decouples from the rest of the economy and does its stuff, “moves atoms directly” as Yudkowsky puts it, but in this case the rest of the economy is also not destroyed (unless ASI also deliberately does this, of course).
Inequality, no matter how severe, even if could make 99.9% people worse off, couldn’t bring the corporations down.
Thank you for your interesting answer :)
I agree that in all likelihood a TS/ASI would be very disruptive for the economy.
Under some possible scenarios it would benefit most economic actors (existing and new) and lead to a general market boom.
But under some other possible scenarios (like for example as you mentioned a monopolistic single corporation swallowing up all the economic activity under the command of a single ASI) it would lead to an economic and market crash for all the other economic actors.
Note that a permanent economic and market crash would not necessarily mean that the standards of living would not drastically improve, in this scenario (the monopolistic ASI) the standards of living would not depend on an economic and market crash but on how benevolent/utilitarian the entity controlling the ASI is.
In economic/market terms there are plenty of possible scenarios depending mostly on what the entity controlling the ASI decides to do with regard to economic trade which is indeed the key word here as you rightly mentioned.
Given that it is imho impossible (or at least very speculative) to predict which economic trade configuration and economic scenario would be the most likely to emerge, it is also impossible (or at least very speculative) to predict what the interest rates would become (if they still exist at all).
So to come back to the original question about EMH and AGI/ASI/TS, as it is imho impossible (or very speculative) to predict the economic scenario that will emerge in case of the emergence of an AGI/ASI, the EMH is kept safe by the markets currently not taking into account what impact an AGI/ASI will have on interest rates.
Note that, as mentioned, imho, in case of an AGI/ASI/TS the standards of living would not depend on an economic and market boom or crash but on how benevolent/utilitarian the (entity controlling the) AGI/ASI is.
Please also take into account that TAI (~= AGI) is not the same thing as ASI. It’s now perhaps within the Overton window for normie traders to imagine the arrival of AGI/TAI that will radically automate the economy and will unlock abundance, but imagining that this stage will, perhaps, very soon will be followed by ASI is still outside the Overton window. For example, in the public discourse, there is plenty of discussion of powerful AI taking away human jobs (more often than not with the connotation that it will simultaneously create much more jobs and the economy will flourish, though), but not much if any discussion of powerful AI taking away human lives.
But it seems to me that the market doesn’t take into account the expected time of AGI arrival nonetheless.
Finally, I want to register that I’m not sure that “far superhuman AI” that can make something completely wild with the economy (and, in fact, the whole planet) as it wishes, is that assured idea. It could be that no matter how smart you are, you will still run into painful infrastructure limitations, will need to cooperate with dumb humans (the efficiency of which is capped by human irrationality itself), etc.
You make good/interesting points:
1) About AGI being different from ASI: basically this is the question of how fast we go from AGI to ASI i.e. how fast is the takeoff. This is debated and no one can exactly predict how much time it will take i.e. if it would/will be a slow/soft takeoff or a fast/hard takeoff. The question of what happens economically during the AGI to ASI takeoff is also difficult to predict. It would/will depend on what (the entity controlling) the self-improving AGI decides to do, how market actors are impacted, if they can adapt to it or not, government intervention (if the AGI/ASI makes it possible), etc...
2) With regard to the impact of an ASI on the economic world and society I would distinguish between
2a) The digital/knowledge/etc… economy basically everything that can be thought of as “data processing” that can be done by computing devices:
an ASI could take over all of that very quickly.
2b) The “physical” economy… i.e. basically everything that can be thought as “matter processing” that can be done by human bodies, machines, robots, …:
an ASI could take over all of that but it would take more time than the digital world of course as the ASI would/will need to produce many machines/robots/etc… and there could indeed be a bottleneck in terms of resources and laws of physics but if you imagine that the ASI would quickly master fast space travel, fast asteroid mining, fast nuclear fusion, fast robot production, etc… it might not take that long neither. The question of what would happen economically while this happens is also difficult to predict. Traditional/existing economic actors could for example just basically stop as soon as the ASI starts providing any imaginable amount of great quality goods and services to any living entities if the ASI is benovolent/utilitarian (within the constraints of the laws of physics if it is in the real/physical world and if the ASI don’t find ways to overcome the laws of physics in the real/physical world) basically what is called “post-scarcity”.
But there could be other scenarios including economic scenarios as well basically essentially depending on what (the entity controlling) the ASI decides to do, it could decide that people still need to be forced to work to keep some meaning of life so it could artificially maintain a working capitalist economy, etc...
When the digital and physical world are essentially mastered at will then basically it “just” becomes a question of how things are then organized/allocated. Money/interest rates/etc… become unnecessary to do that (but could still be used if that is the choice).
Cross-posting some thoughts of mine from the EA Forum (note that there is a lot of good discussion there, such as from Jakob and Eliezer):
Among other objections, I don’t find it plausible that a vision of impending TAI-induced utopia, an acceleration of technological progress and human flourishing even more significant than the industrial revolution, would… send stock prices plummeting?
If someone told me that humanity’s long-term future was totally assured and there was a gigantic economic boom just around the corner, I feel like my discount rate would go down rather than up, and I would care about the future much more rather than less, and I would consequently want to invest as much as possible now, so that I could have more influence over the long and wondrous future ahead of me.
You could make an analogy here between stable utopia and assured personal longevity (perhaps to hundreds of years of age), similar to the one you make between human extinction and personal death. The promise of a stable utopian future (or personal longevity) seems like it should lead to the opposite of the short-term behavior seen in the near-term-extinction (or personal death) scenario. But your post says that these two futures end up in the same place as far as the discount rate is concerned?
I have high confidence that the next few decades will be frothy but the distribution of possibilities does not give me high confidence that I should try to bet on that, certainly not in the form of a short position due to the high risk. Personally, I think there’s a significant likelihood that AI leads to more of a disaster scenario short of an existential threat. As mentioned in the post,
Disasters and accompanying global instability easily lead to monetary effects that are far more complex than simple models of an efficient market can account for. Long-term rates do seem unreasonably low but trying to make alpha from that observation or going deeply into debt to fund philanthropy feels dangerous to me. On the other hand, locking in a long-term loan seems reasonable if I had anything I wanted to spend it on that would retain intrinsic value (like a house).