Angel Investing Returns
In my work for RSCM, one of the key questions is, “What is the return of angel investing?” There’s some general survey data and a couple of angel groups publish their returns, but the only fine-grained public dataset I’ve seen comes from Rob Wiltbank of Willamette University and the Kauffman Foundation’s Angel Investor Performance Project (AIPP).
In this paper, Wiltbank and Boeker calculate the internal rate of return (IRR) of AIPP investments as 27%, using the average payoff of 2.6x and the average hold time of 3.5 years. Now, the arithmetic is clearly wrong: 1.27^3.5 = 2.3. The correctly calculated IRR using this methodology is 31%. DeGenarro et al report (page 10) that this discrepancy is due to the fact that Wiltbank and Boeker did not weight investments appropriately.
In any case, the entire methodology of using average payoffs and hold times is somewhat iffy. When I read the paper, I immediately had flashbacks to my first engineering-economics class at Stanford. There was a mind-numbing problem set that beat into our skulls the fact that IRR calculations are extremely sensitive to the timing of cash outflows and inflows. I eventually got a Master’s degree in that department, so loyally adopted IRR sensitivity as a pet peeve.
To calculate the IRR for the AIPP dataset, what we really want is to account for the year of every outflow and inflow. The first step is to get a clean dataset. I started by downloading the public AIPP data. I then followed a three step cleansing process:
- Select only those records that correspond to an exited investment.
- Delete all records that do not have both dates and amounts for the investment and the exit.
- Delete all records where time runs backwards (e.g., payout before investment).
The result was 452 records. A good-sized sample. The next step was to normalize all investments so they started in the year 2000. While not strictly necessary, it greatly simplified the mechanics of collating outflows and inflows by year. Finally, I had to interpolate dates in two types of cases:
- While the dataset includes the years of the first and second follow on investment, it does not include the year for the “followxinvest”. For the affected 12 records, I interpolated by calculating the halfway point between the previous investment and the exit, rounding down. Note that this is a conservative assumption. Rounding down pushes the outflow associated with the investment earlier, which lowers the IRR.
- For 78 records, there are “midcash” entries where investors received some payout before the final exit. Unfortunately, there is no year associated with this payout. A conservative assumption pushes inflows later, so I assumed that the intermediate payout occurred either 0, 1, or 2 years before the final exit. I calculated the midpoint between the last investment and the final exit and rounded down. If it was more than 2 years before the final exit, I used 2 years.
With these steps completed, I simply added up outflows and inflows for every year and used the Excel IRR calculation.
The result was an IRR of 30% and a payoff multiple of 2.4x with an average hold time of 3.6 years.
Please note that this multiple is slightly lower than the 2.6x and the hold time is slightly higher than the 3.5 years Wiltbank and Boeker calculated for the entire dataset. Thus, my results do not depend on accidentally cherry-picking high-returning, quick-payout investments. If you want to double-check my work, you can download the Excel file here.
All in all, a satisfying result. Not too different from what’s other people have published, but I feel much more confident in the number. For anyone analyzing subsets of the AIPP data, I’ve found that my Excel file makes it pretty easy to calculate those returns. Just zero out all records you don’t care about by selecting the row and hitting the “Delete” key. The return results will update correctly. But don’t do a “Delete Row”. Then a bunch of the cell references will be broken. [Update 1/27/11: I’ve done a follow up post on using this method to test various hypotheses.]
Startups, Small Businesses, and Large Companies
One of the reasons I like my Production Function Space (PFS) hypothesis, is that it clarifies a lot of issues that have puzzled me for a while. For example, as part of my work on seed-stage startup investing with RSCM, I have struggled with two questions: (1) what’s the difference between a startup and a small business and (2) why do some large companies have initiatives like venture groups and startup incubators?
To answer these questions, I’m going to have to get a little mathematical. Don’t worry. No derivatives or integrals, but I need to introduce some notation to keep the story straight. First, let’s define production footprint and search area.
A production footprint is the surface that encloses a set of points in PFS.* If A is a production function for basketballs, B is a production function for baseballs, and C is a production function for golfballs, then pf(ABC) looks like this in two dimensions:
We can also talk about the production footprint of a company like Google. pf(Google) is the surface that encloses all the production functions that Google currently uses.
A search area is the surface defined by extending the production footprint outward by the search radius.** Imagine that we wanted to see if making basketballs, baseballs, and golfballs would enable a company to make footballs using production function F, we might want to compute sa(r, ABC). It looks like this in two dimensions:
We can also talk about search areas for a company. sa(r,Google) is the surface enclosing all the points in PFS within r units of Google’s current production footprint. If we write just sa(Google), we mean search area using Google’s actual search radius.
With these two basic concepts in place, I can now easily answer questions (1) and (2). SU stands for startup, SB stands for small business, and LC stands for large company. So what’s the difference between a startup and a small business? Well, when they are founded, a startup doesn’t have any production footprint at all and a small business does. To a first order, pf(SU)=0 and pf(SB)>0. A startup doesn’t know with any precision how it’s going to make stuff. A small business does. Whether it’s a dry cleaner, law office, or liquor distributor, the founders know pretty precisely what they’re going to do and how they’re going to do it. However, startups have a much larger search radius than small businesses. r(SU)>r(SB). Assuming that we can define a search area on a set of production functions the startup could currently implement (but hasn’t yet), I content that also sa(SU)>sa(SB).
This realization was an epiphany for me. Even though the average person thinks of startups and small businesses as similar, they are actually polar opposites. They may both have a few employees working in a small office, but one is widely focused on exploring a huge region of PFS while the other is narrowly focused on implementing production functions within a tiny region of PFS. I also realized that you need to evaluate two things in a startup: (a) its ability to search PFS and (b) the ability to implement a production function once it locates a promising region of PFS. But the magnitude of impact for (a) is at least as big as (b) in the very early stages.
Now on to the issue of large companies. The problem here is search costs. Remember that, in three-dimensional space, volume increases as the cube of distance. In PFS, volume increase as an exponent of distance equal to the dimensionality of PFS. I posit that PFS is high-dimension, so this volume increases very quickly indeed. Now try to visualize the production footprint and search area of a large company. A large company has a lot of production functions in play so pf(LC) is large. But sa(r,LC) increases exponentially from this large volume by a large exponent.
In three dimensions, imagine that pf(LC) is like a hot air balloon. Extending just 10 feet out from the hot air balloon’s surface encompasses a huge volume of additional air. But in high-dimension PFS, the effect is… well… exponentially greater. So a large company has a problem. On the one hand, increasing its search radius is enormously costly. On the other hand, we know that Black Swan shifts in the fabric of PFS will occasionally render a huge volume dramatically less profitable, probably killing companies limited to that volume. So it’s only a matter of time before sa(r,LC) is hit by one of these shifts, for any value of r.
Obviously, there will be some equilibrium value of r where the cost balances the risk, but that also implies there’s an equilibrium value for the expected time-to-live of large companies. Yikes! This explains why the average life expectancy of a Fortune 500 company is measured in decades. Another epiphany.
Internal venture groups and incubators represent a hack that attempts to circumvent this cold, hard calculation. The problem is that it’s difficult to explore a region of PFS without actually trying to implement a production function in that region. Sure, paper analysis and small experiments buy you some visibility, but not very much. Also, in most cases, you don’t get very good information from other firms on their explorations of PFS, unless you observe a massive success or failure, at which point it’s too late to do much about your position. That’s why search costs are so darn high. Enter corporate venture groups and startup incubators.
These initiatives require some capital investment by the large company. But this investment is then multiplied by the monetary capital of other investors as well as the human capital of the entrepreneurs. With careful management, a large company can get almost as much insight into explorations of PFS by these startups as it would from its own direct efforts. Moreover, because startups are willing to explore PFS farther from existing production footprints, the large company actually gets better search coverage of PFS.
This framework answers a key question about such initiatives. To what extent should corporate venture groups and startup incubators restrict the startups they back to those with a “strategic” fit”? If you believe in my PFS hypothesis, the answer is close to zero or perhaps even less than zero (look for startups in areas outside your company’s area of expertise). Otherwise, they’re biasing their searches to the region of PFS that’s close to the region they’re already searching. It doesn’t increase the ability to survive that much. As far as I know, Google is the only company that adopts this approach. I think they’re right and now I think I understand why. Epiphany number three.
* There are some mathematical details here that need to be fleshed out to define this surface. But I don’t think they add to the discussion and my topology is really rusty.
** More mathematical details omitted. The only important one is that the extension outward doesn’t have to be by a constant radius. It can be a function of the point on the pf. In that case, r is a global scaling parameter for the function.
Thoughts on the Theory of the Firm
One of the interesting questions in economics is why markets coordinate some forms of production but firms coordinate others. Or to put it more sharply, if centralized economic planning doesn’t work for countries, why does it work for firms?
In principle, it should be possible to coordinate production solely through market transactions among individuals. Everyone would be some combination of an independent contractor and a capital owner. The challenge of course would be establishing the necessarily fluid markets, not to mention all the time everyone would have to spend negotiating contracts for their labor and capital.
Thus the standard approach to explaining firms starts with the Transaction Cost theory (typically attributed to Coase). Whenever the cost of a market-based mechanism is higher than a firm-based mechanism, a firm will end up coordinating production. Of course, to anyone who has ever started a new firm or worked any length of time at a large one, this explanation is not terribly satisfying. How do you know the relative costs in the first place and then explain the apparently wasted resources at large companies? Newer theories have tried to do better, but none seem to tell the whole story. See here for an overview of the literature.
Another unsatisfying aspect of mainstream Theories of the Firm is that they don’t explain the observed interactions of firms with the macroeconomy very well. For example, firms don’t responsively lower existing salaries when the demand for labor goes down or the supply goes up. Firms also seem to forego internal price-based mechanisms that would allow them to respond more flexibly to macro shifts in cost and demand. Even more puzzling, there’s no good explanation of why and when some large firms grow dramatically while others die off. I’ve seen some attempts to address particular questions, but they seem like a patchwork rather than a coherent framework.
The always insightful Arnold Kling refers to a tweet from fellow GMU economist Garett Jones as one possible explanation: “Workers mostly build organizational capital, not final output”. Unfortunately, this is a tweet, not a theory. I was sort of playing around with the idea to see if I could get a decent theory out of it and I think I may have something. It ties together microeconomics, entrepreneurship, search theory, options theory, principal-agent theory, and group dynamics.
The basic idea is: firms don’t produce products; firms produce production functions. It seems obvious in retrospect, but a cursory search of the literature didn’t turn up anything similar. Someone has probably thought of this before. But perhaps I got lucky. So I’ll run with the ball for now.
What Is a Production Function?
In economics, a production function is an abstract model of how an economic actor turns inputs into outputs. Basically, it represents the formula or a recipe for a product. Typically, we write Q=f(X), where Q is a vector of output quantities, f is the production function, and X is a vector of input quantities. While “real” production functions have very specific outputs and inputs, economists often simplify the world by assuming each actor only produces one output, Goods, and there are a standard set of general inputs such as Labor, Capital, and Land. If we know the cost curves of Labor, Capital, and Land, we can calculate a cost curve for Goods and examine the tradeoffs and synergies among Labor, Capital, and Land.
Typically, economic theory defines a firm in terms of its production function. However, anyone who has ever founded a startup or worked in a large company should find this definition puzzling. When I’ve started companies, I could not even clearly define what our inputs and outputs would be, let alone the formula for turning the former into the latter. When I’ve interacted with big companies, I typically see a lot of people and groups who have nothing to do with turning inputs into outputs. For example, CTO, CIO, CFO, Corporate Development, Business Development, Product Management, Brand Management, and Market Research. In fact, when I think about the technology industry, the fraction of people actually involved in transforming of inputs to outputs, even if you count the relevant management hierarchy, seems pretty small.
So what is it that entrepreneurs and most of the of the people at large companies are actually doing? My hypothesis is that they are exploring alternative production functions: trying to figure out ways to improve existing businesses and explore opportunities for completely new businesses. Intuitively, this seems reasonable given my experience, but I’d never thought of how to formalize the concept.
Now some production functions are conceptually “near” current ones in that they represent small refinements to the manufacturing process or modest enhancement to existing products. Other production function are conceptually “far” from current ones in that they introduce radical new manufacturing technologies or generate revolutionary new products. I bet if you think about the people you’ve worked with, most of them are involved in figuring out how to produce things or what things to produce, rather than actually producing things. So they are producing production functions.
Production Function Space
The cool way to approach this kind of search problem is to posit a high-dimension space of all the alternatives with a structure that allows us to define the concepts of “near” and “far”. In this case we have production function space.
The challenge is that most points in this space are not economically viable. Some of them define products that nobody wants (e.g., Apple Newtons). Some of them define products that we can’t make at our current level of technology (e.g., flying cars). Some of them define products that we could make but whose demand curve never intersects its cost curve (e.g., diamond coated toothpicks).
Moreover, there are a lot of dependencies among points in production function space. So you can’t consider just one point in isolation; you have to consider configurations of points. Some Goods in one production function are Capital in another production function (e.g., Intel processors). In other cases, demand for some Goods exists only if there is also demand for other Goods (e.g., third party iPhone cases and Apple iPhones).
Most importantly, the goal is not just to find economically viable points. The goal is to find points that generate a lot of profit. Given that changes in technology and fashion cause these points to constantly shift relative to each other and the high dimensionality of the relationships among points, we have a rather complex optimization problem. I think of it as the potfolio optimization problem from finance, combined with the n-body problem from physics, combined with the protein folding problem from biology.
Given this level of complexity, we would expect that search strategies almost always use heuristics and trial-and-error rather than purely analytic optimization.
The Implications
In subsequent posts, I plan to analyze this hypothesis from several different angles. I also hope to come up with some predictions that someone could test. But I thought it would be useful to throw out some gross speculation right now to show how this insight crystallized my thinking and pique your interest in exploring further:
– The value of a firm is the present value of the profit stream from actual current production functions plus the option value of potential future production functions.
– Large firms tend to explore neighborhoods of production function space relatively near the surfaces defined by their current products.
– Startups tend to explore neighborhoods of production function space relatively distant from the surfaces defined by everyone else’s current products.
– Firms that have released successful new products are more valuable because this success implies greater skill in searching production functions space.
– Firms that have released successful new products are also more valuable because they then have a larger beachhead from which to explore greater regions of production function space in the future. Luck counts.
– Large firms acquire startups in part to increase their ability to search more distant regions of production function space.
– Due to network effects among colleagues and the uniqueness of each firm’s endowments, a given firm’s ability to search production function space is proportional to the number of employees it has and their length of service.
– It is harder to observe the true contribution of a particular employee to searching production function space than it is to observe the true contributions of an employee to a specific production function. Therefore, the principal-agent problem is worse than we think.
– Because the ability to search production function space increases with the number of people involved, “empire building” is a rational strategy for an employee to increase both his apparent and his actual value to the firm.
Explaining Money: Part III
In Part I, we saw how Money is an emergent phenomenon. In Part II, we analyzed how changes to the supply of Money affect trade. Now, we’re going to examine how expected changes to the supply of Money in the future affect trade today.
Earlier, we considered what would happen if Sally became ill and were unable to meet the ever-growing demand for new silver figurines created by population growth and innovation. We concluded that families would increase their reserves of figurines and the frequency of trades would decrease. A current event affected future activity. Now consider whether a future event could affect current activity.
Suppose Sally announces that she will retire in one year. Moreover, she declares that she has not seen any other metalsmith whose work matches her standards for beauty and quality (and most people trust Sally’s opinion). She’ll continue to manufacture figurines for a year, so there’s no effect on the actual supply of Money today. It will just stop growing a year from now. But what do you think will happen?
If I lived in this country, my wife and I would put a plan into place to accumulate a greater reserve of figurines over the next year. If there were a significant fraction of people like us, the frequency of trades would immediately begin decreasing , with the negative impact growing over time as those with less foresight began initiating reserve plans as well. You can see the potential for a snowball effect here: a constricting supply of figurines in circulation due to accumulating household reserves causes everyone to update their plans and desire… even greater household reserves!
We should also expect a general price decrease. Here’s why. Bob and Brad would probably tell their wives, Sue and Sara, that they need to accumulate a larger reserve of figurines to ensure they’ll be able to trade for necessities in the future. So Sue and Sara will thus want to increase their sales. But when Bob goes to buy clothes from Sara, he’s going to be less willing to part with his figurines due to his accumulation plan. How will Sara convince Bob to buy clothes so she can help Brad build their family’s reserves? That’s right, by lowering prices. Same for when Brad goes to buy milk and meat from Sue. So as the frequency of trade decreases due to greater demand for reserves, prices would go down.
But the worst part would be the effect on innovation. If I were an entrepreneur and I knew that the supply of Money would stop growing a year from now, how would I adjust my efforts at creating new products and services? I would probably reduce them because any innovation might end up in no man’s land; people want it, but they need to use their Money for higher priority items. Lower chance of a payoff means lower investment. Heck, entrepreneurs with currently successful products might well stop making improvements or even stop maintaining their means of production due to the combination of an expected future decrease in demand and their own desires to accumulate reserves. Our country could actually go backwards technologically! Not surprising though if you think of Money itself as a technology. You’d expect a similar effect if metal or computers became relatively scarce.
Of course, the opposite sequence of events would occur if everyone expected a future increase in the supply of Money. Suppose Sally announces that her daughter, Sunny, will finish her metalsmithing apprenticeship in a year and the capacity to product new silver figurines will increase (but not double, Sunny won’t be nearly as productive as Sally to start). I would expect the frequency of trades, prices, and investments in innovation to all increase.
Now, if Sally had ten apprentices and everyone expected the rate of new figurines introduced into the economy to skyrocket, our little economy might have a problem with runaway inflation. Similarly, if someone figured out a way to mass produce silver figurines equivalent in quality to Sally’s handcrafted ones, people’s trust in silver figurines as Money might erode. So more is not always better.
What we really want is for Sally and Sunny to have a fairy godfather who tells them exactly how many figurines they should make to keep up with population growth, innovation, and any changes in demand for household reserves. I like to think he’d be named Alan. Everyone would love Alan. Unfortunately, nobody lasts in the fairy godfather job forever. So people in our little country would eventually need to somehow harness their collective wisdom to determine how many figurines they need.
Explaining Money: Part II
(1) The seller must believe that, if she accepts the Money, her husband will be able to use it in future trades where he is the buyer. The extent to which she believes Money will be useful in future transactions affects the price at which she will be willing to sell.
(2) The buyer must believe that he will be able to acquire more Money from his wife’s selling activities to support future trades where he is the buyer. The extent to which he believes Money will be scarce affects the price at which he will be willing to buy.
Most people focus on expectation (1). They examine reasons why the seller might not like the buyer’s Money. Potential debasement (reducing the amount of a precious commodity represented by the Money) and inflation expectations are the chief worries.
But they forget all about expectation (2). Remember that Money enables transactions that would otherwise not be possible. If a buyer has only a limited amount of Money, he will make the most important of these trades first. When he runs out of Money, all the other potential trades will not happen. So if there isn’t enough Money in circulation, it will have a real effect on the economy.
Consider the following scenario, using the setup from the previous episode. Sally becomes so ill that she can’t produce figurines anymore. The economic success enabled by Money had caused a steady increase in demand for it. The geographic area where people use Money has grown, people have moved into the area to take advantage of the better life enabled by Money, and people are constantly discovering new products and services whose trade was profitable with Money. Now the Money supply can’t expand to meet this growing demand. What do you think will happen?
Obviously, there are a bunch of lower-value transactions that simply can’t occur because there isn’t enough Money in circulation to execute them once the higher-value transactions are completed. However, the situation is actually worse. Because people will feel uncertain about whether they will have enough Money to meet future critical and surprise needs, they won’t even spend all the Money they have! They’ll want a reserve. The worse the shortage, the higher the reserve they’ll want and the worse the decrease in Money-mediated transactions. It’s just common sense to increase your inventory when future resupply is uncertain. Whether it’s money or food.
Hopefully, you can now see the outlines of my argument for why commodity Money isn’t necessarily better than fiat Money. Sellers like commodity Money such as silver figurines because it has some intrinsic value: the value determined by its demand for use in products and services. If they accept silver figurines, at the very least their husbands will be able to use the silver as barter.
But when you take into account the buyer perspective, this intrinsic value is a double-edged sword. Inherently, the demand for the commodity as Money will always compete with the demand for the commodity as a good. So in our toy economy, if someone discovers a new use for silver or a new use for Sally’s metalsmithing skills, the supply of Money will come under pressure and potentially cause a Money shortage like the one discussed above.
I tend to think that human ingenuity will always come up with more uses for things over the long term, so I believe commodity Money tends to directly harm buyers more than sellers. However, sellers can get hurt directly too. If someone figures out a really good substitute for the commodity as good, its intrinsic value can drop dramatically. Consider the invention of white gold as a substitute for silver or machine stamping as a substitute for Sally’s smithing. Because the commodity Money would be worth fundamentally less as barter, every seller that accepted it would take a hit. What you really want is Money that has the common knowledge properties of silver figurines but whose supply can be directly managed, without competition from direct use in goods and services. That’s what fiat money is. Of course, someone has to properly manage the Money supply. But that’s a topic for Part III.
So in summary, shocks to the Money supply can affect real economic activity and commodity money is no panacea.
Explaining Money: Part I
I am undertaking a Quixotic quest. I am going to try to explain Money. I believe that hardly anyone (including me) fully understands Money. Even economists. A few appear to mostly understand it. The vast majority, even some charged with running government monetary authorities, seem to get confused by Money some of the time. Unfortunately, we are currently living during one of those times. In my opinion, much of the sphincter tightening economic news we have been reading about is due to fundamental misconceptions about Money by the very people charged with supervising our economy.
It will take several posts for me to complete this tilt at the windmill. But before I get started by laying out the overall plan, I would like to thank Scott Sumner. First, his informative blog posts on monetary policy inspired me to undertake this venture. Second, he graciously reviewed parts of my approach. All mistakes (and there will some, I’m sure) remain my own.
Step 1 will explain how Money is an emergent phenomenon. Step 2 will illustrate the concept of “monetary shocks”, culminating with dispelling the fallacy of commodity money’s superiority over fiat money. Step 3 will extend this illustration to show how expectations about Money help steer the economy. If I haven’t painted myself into a corner by then, I may try to push my luck even further.
So let’s tackle the concept of Money as an emergent phenomenon. I claim that Money will emerge out of a desire to trade. As a didactic device, I propose analyzing an imaginary country. All the adults are married, the women do all the selling, and the men do all the buying. Conveniently, all the women’s names start with S and all the men’s names start with B. The reason for this device to create an explicit need for households to coordinate production and consumption behaviors. So let’s start by examining this country back in a time before Money existed and barter was the only means of trade.
Sue is married to Bob and is shepherd. Sara is married to Brad and is a seamstress. Sally is married to Billy and is a metalsmith. Now, suppose that Billy needs clothes for his children. He must to go to Sara and trade metal objects made by his wife for those clothes. Unfortunately, Billy can’t just go and trade with Sara. Billy doesn’t have enough information about the relative production value of the various metal items his wife could make to trade. Moreover, Sara doesn’t have enough information about the relative consumption value of those metal items because that’s Brad’s responsibility. So Sally & Billy and Sara & Brad must all get together to arrange the trade. In many cases, the expected value from the trade won’t be worth the hassle of getting them all together, so they won’t bother.
Now, let’s consider trades between the Sue-Bob and Sally-Billy households. Sue always has a supply of wool and sometimes has a supply mutton. Of course, wool is useless by itself to Billy. So if Bob needs metal items from Sally and his wife hasn’t slaughtered any sheep lately, Bob has to first go to the Sara-Brad household. As a seamstress, Sara can always use wool. After he trades for clothes, he can go back to Sally-Billy who always have some demand for them. Of course, he doesn’t have enough information about the Sally-Billy clothing preferences to tell Sara what he wants. Moreover, we have the same household coordination problem as before. So Sue & Bob, Sally & Billy, and Sara & Brad all have to get together to hash out a trade or one person has to go back and forth among the others until they converge on an acceptable series of trades. This inter-household coordination cost is even higher than the intra-household coordination cost discussed above, so even fewer of these trades are worth the hassle.
Notice that a lot of potential trades won”t happen because the transaction costs are greater than the expected gains. Then one day, something important happens. Sally makes a little silver figurine for her and Billy’s daughter, Sunny. Bob sees it one day when he’s over completing a trade and wants one for his son, Bert. Pretty soon, all three families and everyone in their town is in the grip of a silver figurine collecting craze. Almost everyone wants to trade for figurines. Everyone knows almost everyone wants to trade for figurines. So even those people who don’t care much for the figurines know they can easily trade them to people who do want them.
Billy finds he no longer needs to bring Sally along when he trades with Sara. Sally can simply give him five figurines to trade for clothes because they know roughly how much clothing Sara will trade for figurines. Things also get easier for Bob when he needs metal items from Sally. He can just trade her some of his figurines for other metal items. Even though she can make figurines herself, especially because she makes them herself, she realizes their value in terms of trades that Billy can make down the line.
So Money has emerged. It didn’t have to be figurines. It could have been turquoise, salt, or leather. The key ingredients were that it was relatively portable and a group of people began expecting everyone in the group to accept it in trades. Within the group, the item’s trading value became common knowledge (in the game theory sense of the term). In this case, a collecting craze precipitated this mutual agreement. In other cases, it could arise out of established tradition, explicit negotiation, or random discovery.
Notice that Money adds value. It’s not merely an accounting fiction. All sorts or trades that weren’t possible before become possible, creating new sources of value. Moreover, a lot of trades that did occur previously now produce more value because they cost less to make. So there’s a lot of “pull” for Money to emerge. Once it happens, there’s an equilibrium that will tend to hold unless perturbed.
Moreover, once Money emerges, it’s like any other technological innovation such as electricity or steel. It becomes embedded in the pattern of trade across the economy. People will be out and about more often because there will be more trades to make. Hey, that means more restaurants and hotels. Smaller trades become possible. Hey, that means whole new markets for accessories to larger items. Trades across larger distances become practical. Hey, that means more regional specialization of industries. And so on.
But what happens to this network of effects if something undermines common knowledge foundation of Money? We’ll explore the possibilities in the next post.
a small country where all the adults are married, the women do all the selling, and the men do all buying. Conveniently, all the women's names start with S and all the men's names start with B. The reason for assuming such a fantasy world is to create an explicit need for coordinating production and consumption behaviors in households.
The Universe Is a Giant Computation Engine
This is my hypothesis based on a relatively consistent diet of physics books over the last couple of decades. Now, this hypothesis is by no means original to me (see here). But it is certainly not the dominant view of and most laypersons are probably unaware it even exists.
The latest bit of data that reinforces my belief in the Computation Engine Hypothesis is From Eternity to Here, by Sean Carroll. In this book, Carroll tries to explain the arrow of time using the concept of entropy from the perspective of statistical mechanics.
The basic idea behind entropy is to compute the number of physical microstates (e.g., positions of each molecule of oxygen) that correspond to the same physical macrostate (e.g., the physical distribution of those molecules in a jar). If a macrostate has lots of different corresponding microstates, it’s “ordinary” and has high entropy. If a macrostate, has only a few corresponding microstates, it’s “special” and has low entropy. There are a lot more ways to arrange a set of oxygen molecules so they are uniformly distributed than there are to arrange them in the shape of a duck, so the former has high entropy while the latter has low entropy.
High entropy states occur more frequently than low entropy states. So any interaction tends to increase entropy because transitions to more common states are more likely. Thus the arrow of time is a statistical property of dynamic behavior.
But now there’s a problem. One can apply this same type of analysis to the Universe as a whole (or more precisely, our “observable patch” of the Universe). You see, it has rather low entropy compared to its maximum (which we can calculate using concepts from statistical mechanics). There’s all this orderly clumping of matter into galaxies, solar systems, planets, animals, and humans. And that’s just not very likely. Now, you could try invoking the Anthropic Principle: that we wouldn’t be here to observe the Universe unless it were ordered this way. Sorry, but no. It’s actually much more likely that our brains would materialize out of the ether due to random quantum fluctuations (so called “Boltzmann Brains”).
Carroll has a loophole. What if our Universe (and indeed each Universe in the “Metaverse”) spawns new Universes? Then there is no maximum entropy and the configuration of our observable patch becomes much more likely. Here’s how it might happen. Even a Universe at maximum entropy still undergoes fluctuations, definitely of quantum fields and perhaps of spacetime itself. If a quantum fluctuation to a higher vacuum energy occurred at the same time that a bit of spacetime pinched off, you would get what looks like a new universe undergoing a Big Bang. Astronomically unlikely at any given time and place, but almost certain to happen eventually in a given Universe.
Aha! Problem solved. But think of the implications. There’s a huge proliferation of Universes. Now, add in the proliferation of different versions of the Universe from from the Many Worlds Interpretation (MWI) of quantum mechanics. Recall that the MWI explains apparently “spooky” quantum behavior by suggesting that the wavefunction does not actually collapse. Instead, every possible value of the wavefunction is realized in a different blob of amplitude, a process known as decoherence. Effectively, any time a quantum particle interacts with a macro objects, it generates a version of the universe for each possible outcome of that interaction.
So at the quantum level, we’ve got all this branching of the Universe every microsecond. Then at the astrophysics level, we’ve got new Universes spawning. Of course, this spawning also obeys the MWI, so you’ve actually got an exponential proliferation of baby Universes. If you squint, this whole process looks like a multi-dimensional forward-chaining computation. Every possibility in this Universe is realized, whole new Universes with slightly different rules get created, and every possibility in them is realized.
Going back to the concept of entropy, it turns out that the Thermodynamic Entropy we can calculate for objects is exactly the same as the Shannon Entropy we can calculate for information. Shannon Entropy measures how unique a piece of information is. Think of it in terms of compression. You can’t compress a file any smaller than its Shannon Entropy will allow. Structured files have low entropy and by encoding their structure, you can compress them more. A random string of bits in a file has maximum entropy, so you can’t compress it at all. Shannon Entropy is a measure of how potentially useful information is. Just like Thermodynamic Entropy is a measure of potential energy.
So there’s already a known equivalence between the physical and informational. Then if you buy into Carroll’s hypothesis and the MWI, it looks like the Metaverse is trying to compute every possible outcome. In fact, it may compute every possible outcome more than once. An infinite number of times if it runs an infinite amount of time. After it runs long enough, someone who could observe the whole Metaverse could actually calculate very precise odds of any outcome given any condition. You’d be statistically omnipotent.
Never bet against a statistically omnipotent being.
Yes, You Can Save the World with Startups
Dave Lambert pointed me to this new Kauffman Foundation paper by Tim Kane about job creation in the US. Then Will Ambrosini pointed to this Growthology post which reproduces the money diagram from page 5 :
Look carefully. Then think about this statement about US job creation:
The only firms that create jobs on average are brand new ones.
So yes, you can save the world with startups.
Simulating Angel Investment: Kevin’s Remix
Jeff Miller has done a couple of nice posts on “A Simulation of Angel Investing” here and here. I think it’s terrific that Jeff actually asked the question and tried to answer it with simulation. However, his answer of 20 is way too low because of two key oversimplifications. Using a more sophisticated methodology, I’ll show that a better answer is 100 to 150.
Saving the World with Startups
On a recent business trip trying to drum up support for RSCM, someone asked Dave and me why such obviously talented guys were starting a fund instead of a company. I’ve been thinking about that question for the last week and have a much better answer than the one I gave.
I want to make the world a better place. But it’s not clear precisely what interventions will lead to the best outcomes over the long term. I think I’m a really smart guy, but I’m quite sure I can’t evaluate all the potential interactions within a system as complex as the world society to figure out the optimal plan.
Luckily, I don’t have to be that smart. We just have to collectively be that smart. And economic markets are the best way I know to organize collective action. The more effectively we can all create value, the better off we’ll all be. Creating wealth won’t directly solve a lot of problems, but it enables the solution of an incredibly wide range of problems.
So here’s the math that leads to my conclusion that increasing the number of startups we can fund is the best thing I can do for the world. This study shows that a 5% improvement in startup creation leads to about a half a percentage point improvement in the economic growth rate. If we could increase the rate of startup creation by 10%, we could add a full percentage point to our economic growth rate.
From this dataset, I determined that the world GDP growth rate over the last 30 years has been about 4%. So we could probably achieve a 5% growth rate by increasing startup formation by 10%.
This seemingly small shift has dramatic results over the long term. In 50 years, world GDP would be 60% (1.6x) greater. In 100 years, GDP would be 160% (2.6x) greater. I think a world in which everyone were 2.6x richer would be pretty sweet. That’s a gift I want to give to my great-great grandchildren.
Seed-stage startups are the key because that’s where businesses are born. A larger pool of innovative seed stage companies will naturally attract a larger pool of investment in later stages. About $10B every year goes to professional investments in seed-stage startups in the US. So if we can add $1B, that’s 10%. Even better, if we develop a better process, this process can be copied all over the world. If it’s a lot better, I bet we can do significantly exceed a 10% improvement.
That’s why I’m focusing my time on revolutionizing the process for funding seed-stage startups.
Possible Insight 