Recall the example from the previous post. We had a small world consisting of three jobs and three people. The people were called Yvonne, Jacqueline, and Babette, and the jobs that they could have (we need one person doing each job) were manager, electro technician, and recycling expert. The following table states the potential added value (recall post on GDP) in thousands of euros per year that each person could create by working in one of the possible jobs.

Recall that this little job market had only one possible stable allocation (or matching) of people to jobs, the unique total added value maximizing one, in which Yvonne is technician, Jacqueline is manager, and Babette recycling expert. The total added value in this case is 160+200+180=540 thousand of euros per year. We also noted that this model does not allow us to make strong conclusions about the salaries in this job market. There is a range of possible (unequal) splits of value added between employees and employers. It was clear, however, that Jacqueline, by virtue of her high levels of added value, would have to make considerably more than Yvonne in this highly stylized job market. In fact, I believe it was 60 thousand euros a year more. But otherwise salaries can be higher or lower on the whole. It is just as stable to pay Yvonne and Babette 50 thousand a year and Jacqueline 110 thousand a year as it is to pay everyone 30 thousand a year more. This is so in this model and I am not completely sure whether this would hold up in better models that we would build if our primary interest was salaries. But as it is, this model leaves room for unionized bargaining, which does happen in many countries in the world (Austria, for instance). So perhaps this feature is not completely silly either. With unionized bargaining I mean that the employees all get together and negotiate a sort of base wage together as one negotiator against the also possibly unionized collective of employers as one other negotiator.

But I wanted to address a different problem in this post. What do we expect to happen if we do and if we don’t have equal opportunities? One could argue that education is a way for people’s potential added value numbers to be generated. A person without an education could do very few jobs, that’s the idea at least. To be an engineer, for instance, you probably need to study engineering at least. Let us suppose for the moment that Yvonne simply has no access to education. And without education the added value she can provide is very limited in all three positions. In fact assume it is limited to 20 thousand a year in each job. The new situation can then be depicted in the following table.

Given the insight from the previous post we know that the only stable allocation or matching is the total added value maximizing one. Here this means that Yvonne will be manager (a very bad one and also badly paid), Jacqueline technician, and Yvonne recycling expert. The total added value is 20+220+180=420 thousand a year. By assumption this is less than in the case when Yvonne is educated. But more interestingly, now Jacqueline has less competition (when educated Yvonne is also not such a bad manager) and now Jacqueline needs to be paid at least 180 thousand a year. Also Babette now needs to be paid at least 80 thousand a year. This means that if you ask Jacqueline and Babette in this small world if they would like Yvonne to be educated they might well say no. Because then Yvonne could compete with them for these jobs which might mean that they might be paid less.

As I said before, this post should be taken with a grain of salt. The model completely ignores the realistic possibility that an educated (and this could also mean well-trained, it does not have to mean “high-brow” education) person could create altogether new job possibilities, from which (almost) everyone in the economy could benefit. As an example consider someone who is educated in specific ways that enables him or her to start something like Microsoft or Google. Such a person then becomes a new employer and, in our model here, would create a fourth column in the matrix and thus new scope for added value.

But I could imagine that in some societies the elites, being the only ones with access to education, worry that if everyone gets an education, then their possibly not so clever offspring will have a hard time getting well-paid jobs. It is otherwise difficult to see how one could be against equal opportunities, not for fairness but for efficiency reasons. But the model is probably really too simple to provide the definite answer to this question.

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In this post I am perhaps being a bit eclectic but I want to think about which person gets which job. That is, I want to think about how the job market allocates people to jobs.

And I will do this in a highly idealized setting. So the key feature of the world that I will focus on are these: In this model different people have very different skills and one person’s job cannot easily be done by a random other person. I keep the rest of the model as simple and idealized as possible. Jobs are just there, for instance. Nobody creates these. There is no innovation either. Everyone is super active on the job market, constantly checking to see if there are better jobs out there, and everyone cares only about money. These are huge simplifications and in their extreme form all these assumptions are empirically wrong. But this is how modelling works, and if you are unhappy with something, especially with the final insight this model provides, then have a go at creating your own model. This is in fact how scientific progress is made and how research in economics works.

With these excuses let me turn to the story I want to tell here. You can see for yourself in the end if you feel that you learnt something from it. Let me consider a slice of the world (somewhat independent of the rest) of three jobs and three people. The people are called Yvonne, Jacqueline, and Babette, and the jobs that they could have (we need one person doing each job) are manager, electro technician, and recycling expert.

As I said, I want these three people to be differently good at the various possible jobs, so this table above captures this. In this table, each cell describes the value added (recall the post on GDP) in thousands of euros a year that would result if a person does a particular job. So for instance, Yvonne would generate a value added of 120 thousand euros a year if she works as a manager and 160 thousand euros a year if she works as a technician, whereas Babette would generate 100 thousand euros a year if she worked as a manager and 180 thousand euros a year if she worked as a recycling expert.

So who will get which job in this job market? Let us begin by considering the following possible allocation of people to jobs: Yvonne is manager, Jacqueline technician, and Babette recycling expert. Suppose furthermore that employer and employee divide the generated value added equally. In other words Yvonne and her employer get 60 thousand a year each, Jacqueline and her employer 110 thousand a year each, and Babette and her employer 90 thousand a year each. Do we think that this is a “stable” job market outcome? Or is there a pair of person and employer that could negotiate a better deal between them and, thus, “block” the current situation. You may want to think about it for yourself for some time.

Well? Consider Jacqueline and the management position. In this position Jacqueline could generate a value added of 200 thousand a year much more than the 120 thousand a year that Yvonne can generate in this position. To attract Jacqueline to the management position she would need to be paid her current salary of at least 110 thousand a year. Suppose the management position offers Jacqueline 125. This still leaves 75 for the employer who at the moment only receives 60 by employing Yvonne. So this new situation is an improvement for both Jacqueline and her new employer. In this fictitious world in which the two only care about money (and the job market is as flexible as we assume here) they would then probably go through with this change.

Let us suppose Jacqueline does move to the management position. What do we have now? Yvonne is unemployed (earning zero), Jacqueline works in the management position and earns 125 thousand a year, Babette works as a recycling expert and earns 90 thousand a year. On the employer’s side we have that the employer seeking a manager employs Jacqueline and earns 75 thousand a year, the employer of the technician has nobody at the moment (earning zero), and the employer of the recycling expert, currently Babette, earns 90 thousand a year. So what happens to Yvonne and the employer seeking a technician? Well, they could team up. How much would Yvonne have to get paid so that she does not go back to knock on the door of the management position to accept the job at lower salary? How much does Yvonne’s new employer need to earn so that they don’t call up Jacqueline again and offer her her old job back at a higher salary? Well, looking at the numbers Yvonne needs to earn at least 45 thousand a year, otherwise she could offer a deal to the management employer that this employer would find attractive. Yvonne’s new employer would request at least 95 thousand a year, otherwise they would offer a new deal to Jacqueline that Jacqueline would find attractive. But this could work out. Together they create an added value of 160 thousand a year, so they could for instance split it 55 thousand for Yvonne and 95 for the employer. This way neither of them can find a better opportunity elsewhere.

Is this new allocation of people to jobs with the given salaries stable? What do we need for a job market outcome to be stable in our fictitious job market?

Well, an allocation (often also called matching) of people to jobs is considered stable if there is no pair of employee and employer that could block the allocation by getting together and that way both improving their income.

If you think about it, this means that the matching has to be such that employees and employers get so much that for any pair of them the sum of what they get is at least as much as they could both get together if they work together. This is not an easy sentence to read. So let us go through some examples.

Let us first go back to the beginning where we had Yvonne as manager, Jacqueline as technician, and Babette as the recycling expert such that in each employee employer pair they split the value added by them equally. That meant that Yvonne and her employer have 60 thousand a year each, Jacqueline and her employer 110 thousand a year each, and Babette and her employer 90 thousand a year each.

So why was this not stable? This is so because Jacqueline (getting 110) and the employer of the manager (getting 60) together could create a value added of 200, which is more than the sum of what they both currently make. This is why they could come to a mutually beneficial agreement to block the current matching. This is why the original matching is not stable.

What about the final matching that we found? How was it? We had Jacqueline (125) as manager (75), Yvonne (55) as technician (95), and Babette (90) as recycling expert (90), with numbers in brackets the amount of money the employee or employer makes. Is this stable now? To see this we need to check how much any pair of employee and employer could generate together and compare this with what they currently make. Let us go through all of these cases.

Jacqueline (125) and the employer of the technician (95) have a joint income of 125+95=220, which is just as much as they could generate if they were to get together. So they cannot strike a mutually beneficial deal. In any deal in which Jacqueline gets more than 125 the employer gets less than 95 as the sum has to be 220.

Jacqueline (125) and the employer of the recycling expert (90) have a joint income of 125+90=215, which is more than the 140 that they could generate together. So they cannot strike a mutually beneficial deal. In any deal in which Jacqueline gets more than 125 the employer gets less than 15 as the sum has to be 140.

These are the two possibilities Jacqueline has. Let us turn to Yvonne.

Yvonne (55) and the employer of the manager (75) have a joint income of 55+75=130, which is more than the 120 that they could generate together. So they cannot strike a mutually beneficial deal. In any deal in which Yvonne gets more than 55 the employer gets less than 65 as the sum has to be 120.

Yvonne (55) and the employer of the recycling expert (90) have a joint income of 55+90=145, which is more than the 40 that they could generate together. So they cannot strike a mutually beneficial deal. There is not even a possible deal in which Yvonne could get more than 40.

We can finally turn to Babette.

Babette (90) and the employer of the manager (75) have a joint income of 90+75=165, which is more than the 100 that they could generate together. So they cannot strike a mutually beneficial deal. In any deal in which Babette gets more than 90 the employer gets less than 10 as the sum has to be 100.

Babette (90) and the employer of the technician (95) have a joint income of 90+95=185, which is more than the 100 that they could generate together. So they cannot strike a mutually beneficial deal. In any deal in which Babette gets more than 90 the employer gets less than 10 as the sum has to be 100.

We therefore have a stable matching of people to jobs. But is this the only stable matching? It turns out that, actually yes, this is the only one. What is not uniquely determined, however, is the set of salaries and employer earnings. But none of the other 5 possible allocation of people to jobs can be made stable with any feasible salary – profit arrangement. I would encourage you to try to do this for yourself (for instance in a spreadsheet document).

But is there an easier way to find the stable matching in this and other cases? Can we find another (easier to check and possible insightful) property that a matching needs to have to be stable?

Yes! In fact a matching has to be Pareto-efficient, which, given we have money in this problem, means that it must maximize the total sum of value added over all possible matchings. To see this for our specific problem let us have a look at the table of all possible added values generated by different pairs of employee and employer.

Using what I hope are self-explanatory abbreviations, we can compute the total added value generate by any matching in the following table.

We can see that the unique total added value maximizing matching is the matching of Yvonne to the technical job, Jacqueline to the management job, and Yvonne to the recycling job. And this is also the only stable matching in this job market, and is therefore supposedly the outcome of this (admittedly highly fictitious) job market.

I would like to leave it to you to think about why this always has to be so in such a highly fictitious job market: only Pareto-efficient (that is overall added value maximizing) matchings can be stable.

Please note that, as we had so often before in this class, that Pareto-efficiency has again nothing to do with fairness. While this example gives us some hope that the real job market might allocate people to jobs perhaps close to a Pareto-efficient manner, we should note that it does not necessarily do so in a fair manner. While I do not here want to take a stance on what might be considered fair, it is at least clear that in this fictitious job market not everyone can expect the same salary. You can play with this example as much as you want but you will always find that to get a stable job market outcome you need to give Jacqueline a higher salary than Yvonne.

There are many more things we can discuss using this example, but I will leave this to separate posts.

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where is the repayment amount that you pay back to the investor in case of the project being successful. We argued (in a previous post) that the range of feasible interest rates is 12,5% to 200%. Anything outside that will certainly not be accepted by either the investor or by you.

Suppose that you and the investor are close to agreeing to an interest rate of just over 12,5%. Put yourself in the shoes of the investor for a moment. What might worry you in this case?

There is something I perhaps didn’t emphasize enough. I sort of glanced over the problem of how the various investors come up with their assessment of the risk involved in your project. Clearly most investors will try to carefully assess the risks in a project before they make any investment. I believe that many banks, for instance, use an internal rating system similar to those used be the big rating agencies such as Standard and Poor’s or Moody’s or Fitch. These companies typically rate risks, for instance of countries defaulting on their bonds or other financial obligations, on a letter scale, such as in the case of Standard and Poor’s from AAA (almost no chance of default) to D (has already defaulted). Banks then translate their ratings into probabilities of various outcomes, with special focus on the probability that the entity that they giving their money to will default (i.e., not be able to pay their loan back).

Different banks or other investors will typically not necessarily completely agree in their assessment of the risks in your project. So now put yourself in the shoes of an investor (such as a bank) and imagine that this bank has made you the offer of a 12,5% interest rate and, after you shopped around at other banks, you decide to take up their offer. So, why might this bank now be worried? Well, it seems that they were the ones making the best offer to you. Why did the other banks not make a better offer? Probably because the other banks didn’t assess your project as favorably as this bank did. But if this is so, is it not now possible that this bank has overestimated the likelihood of success of your project? If this is the case, then perhaps this bank should also not offer you a 12,5% interest rate.

This phenomenon, that when you make the best offer you possibly overestimated the value of whatever you are buying, is generally often called the winner’s curse. You can easily imagine suffering from the winner’s curse when you buy a house at what seemed to you a low price only later to find out that it had all sorts of problems. That may explain why you were able to buy it for such a low price in the first place: because you overlooked something. If you worry about the winner’s curse in such cases, as your bank might when giving you a loan, you might ask for an even lower price to compensate for this – or a higher interest rate in the bank’s case.

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where is the repayment amount that you pay back to the investor in case of the project being successful. We argued (in a previous post) that the range of feasible interest rates is 12,5% to 200%. Anything outside that will certainly not be accepted by either the investor or by you.

Suppose that you and the investor are close to agreeing to an interest rate of almost 200%. Put yourself in the shoes of the investor for a moment. What might worry you in this case?

Well, if I were the investor I would realize that you have very little to gain from the success of the project if we indeed agree a 200% interest rate. You may recall that, in the very beginning, we said that the project required two things: startup money that you need to raise somehow and a lot of work from you. So I would then worry that, given that you have little to gain from the success of the project, you will not try very hard to make the project a success. And if you don’t try very hard I might have to revise my assessment of the likelihood of a successful outcome downwards. This new risk that I, as your investor, am now facing is often called “moral hazard”.

I believe the term comes from the insurance industry who face moral hazard for instance when they insure you against burglaries and then you stop locking your house when you are on holiday. Well, you might not do something quite as extreme – and in fact the insurance contract details will state that in such cases they do not cover your damages – but you might not do everything to help prevent burglaries that you would do if you were not insured. Or when you have full coverage car insurance you might not be quite as careful with your car as you would be if you had only the basic insurance. The term moral hazard is used more generally in economics whenever there is a contractual arrangement between two or more parties, in which the two parties do not have exactly the same interest and the contract cannot completely specify (or this cannot be enforced) what one party wants the other to do. If, to just give one example, you employ a cleaning person, this person might not care as much about how clean it is under your bed as you might do, and this person might not put as much effort into cleaning there (especially if you can’t check it easily) than you might like them to.

Anyway, in our case, a 200% interest rate agreement might well lead to moral hazard and a resulting increase in the probability of the project being unsuccessful. This might even be so severe that the investor might refuse this 200% interest rate.

]]>Suppose then that you live in one of these cities and are considering buying insurance against flooding. When I say “against flooding” I, of course, mean that the insurance will pay out some money in the event of a flood and that this amount is so that it covers the costs of all repairs that become necessary because of the damage caused by the flood. Suppose furthermore that there is no other insurance already in place (such as the local or national government paying out some emergency funds in such cases). In this post I want to address the following question: Will you have to pay a large risk-premium on your flood-insurance?

I believe the answer is “probably not”. But the argument behind it comes in two steps. Of course you have to pay at least so much that the insurance company “expects” a non-negative return from giving you insurance. Suppose that according to the assessment of all insurance companies (and they spend a lot of time and care assessing these things) the risk of a flood for your house in one given year is one in ten thousand. Suppose your house is worth half a million Euros. Then you will have to pay at least 500.000 * 1/10.000 = 50 Euros per year for your insurance. The insurance company will certainly not accept anything less. But will they demand a substantial risk premium on top of these 50 Euros? Suppose you are considering getting insurance from a local insurance company that mostly insures people in Graz (or wherever you live). For such a local company, though, the risk of a flooding at your house is probably highly correlated with the risks of flooding of other houses in Graz (even if they may not all have the same risk – depending on how far away in distance and especially altitude your house is from the river). So for such a local insurance company all these risks are highly correlated and, by the argument of one of the previous post, they would probably demand a risk-premium for these risks.

But will they? I don’t think so. Why? Well, there are of course many cities in this world in which there is some flood risk (or other risk). Moreover the risk of flooding in Graz, Austria, is probably not very highly correlated with the risk of flooding in Houston, Texas, or Santiago, Chile, or Canberra, Australia. Does this mean that our local insurance company needs to operate globally, so that they can diversify their risks, as in this post? No. It is in fact quite ok for them to operate locally and offer flood-insurance only in Graz, but buy themselves insurance against the event of a mass-flooding in Graz from a global re-insurance company. This insurance should not demand a risk-premium and this would allow the Graz based insurance company to offer flood-insurance in Graz without a risk premium.

So one would expect that you would get a competitive insurance offer from your local insurance provider (of course you should compare a few and negotiate). The insurance fee will not entail a large risk premium, but will of course (by the usual supply and demand argument) be a bit more than 50 Euros.

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In the previous post we considered the case that this risk inherent in your project is stochastically independent of the risks in other potential investment opportunities. In this case we figured out that the interest rate you might get for your project might be as low as 12.5% (but certainly not below that). This is so low that, due to the risk in the investment, investors expect actually a zero return on their investment. The actual interest rate would then probably be a bit higher, determined by supply and demand.

All this depends, however, on the fact the risk is stochastically independent of other risks. Expressed differently, one could say that the financial market generates no risk premium on any stochastically independent risk in an investment opportunity. This is because investors can hedge independent risks away by diversifying their investment portfolio. They can invest small amounts in many such independent risks and then, by force of the law of large numbers, actually have no risk in their diversified portfolio.

In this post, which I am now finally getting to, I want to consider how this analysis changes when the risk inherent in this investment opportunity is not stochastically independent of other risks, but is correlated with them.

I find it easiest to talk about this considering a concrete example. For the same project as before suppose now that the risk can be split into two components. First there is the “market” risk (at least in the investors’ view). Suppose there is a 50% chance of a global recession and a 50% chance of a global boom period. Then our project can be summarized as follows.

Now suppose that conditional on being in the bad or good world, all risks are again stochastically independent. But note that overall the risks are correlated because there is a 50% chance that all risks are more severe and a 50% chance that all risks are less severe.

If this is how investors see your (and others’) investment opportunity, how would they feel about a 12.5% interest rate for your loan? Well, at 12.5% investors will get an expected (or average) payout of in the bad world and in the good world. But this means that, if the world happens to go into a recession, the investor loses money on average, and diversification across investment opportunities does not cancel out this risk.

If the investor in our example is extremely risk averse, i.e., she wants to guarantee a non-negative return on her investment in both worlds, she will ask for an interest rate of at least 16.66%, because

This means that only non-independent risk will typically have risk-premia in the financial markets.

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We figured out that you will not accept the loan if the repayment amount is more than € 200.000 (that would be an interest rate of 200%). Because then you have nothing to gain from this project. In reality, you might not even accept anything close to 200%, but we will come back to this problem later.

We also figured out that the investor will (almost) certainly not accept an interest rate below 12.5%, as otherwise the investor expects a negative return on their investment and would then be better off just putting her or his money under a mattress or, I guess, in a safe or vault. By the way, for a very long time the Catholic Church (and other religions) considered positive interest rates morally wrong. In such a world, you probably wouldn’t get a loan for your great project, unless you find a way around this problem. And that would probably be a shame (see previous post).

In this post I want to think about whether an investor will really accept an interest of 12.5% (or slightly above) given that the investor now takes all the risk and at an interest rate of 12.5% only expects a zero return. The answer to this question, it turns out, all depends on whether the risk in this project is essentially stochastically independent of all other risks inherent in all other projects or not.

Imagine that your investor, perhaps a bank, has a lot of money and your project is just one of many that they invest in. Assume, for simplicity, that all projects that they could invest in are just like yours, and that all risks inherent in these projects are stochastically independent of each other. This means, for instance, that if your project fails, this has no effect on the chances of other projects failing. This is not always a plausible assumption, and we will think about what happens when it is not satisfied a little further down. But if they are all independent of each other, then something magical, the law of large numbers, happens. Then investing in all of these essentially has zero risk. To see this suppose that the interest rate is 20% for all these projects. Then from each project there is a 20% chance the investor loses € 50.000 and an 80% chance the investor gains € 20.000 ().

Now I have two ways to try to convince you that there is essentially zero risk when you invest in all these projects. My first attempt assumes that you know a bit about probability theory, the second makes you work something out in a spreadsheet such as Excel.

So here is the first attempt. Let us call the random gain / loss the investor makes from each project by the random amount . So can be either – € 50.000 (with probability 20%) or + € 20.000 (with probability 80%). Statisticians or probability theorists would say that each follows a (rescaling of a) Bernoulli distribution. Note that, on average, these projects pay out So on average, the investor gains money for each project. But what about the risk?

The investor in the end receives the sum of all , summed over all projects . Let us assume that there are such projects and that is a large number (think 1000 for instance). Then the risk inherent in the sum of all these random payments can be described by the standard deviated of this sum of all payments. The standard deviation of one is given by the square root of and is equal to . So, relative to the expected gain of € 6.000, there is a substantial risk in one (as we already know). One could say that for every € 1 of expected gain there is a risk of By the way this is essentially the inverse of the so-called Sharpe ratio in finance, where a low Sharpe ratio means high risk relative to the potential gain.

So how does the risk change if we can invest in not one, but very many such projects? It turns out that, for independent random variables, such as ours, the square of the standard deviation, called the variance, of the sum of all is just the sum of the individual variances. This means that the standard deviation of the sum of all payments is here given by the somewhat ugly expression of . What interests us is how this is related to the expected gain from the sum of all payments which is the sum of all expected gains from the individual projects and, therefore, equal to Investing in such independent projects, thus, gives us a per € 1 risk of

Imagine that there are 1000 projects like this, then this per € 1 risk is equal to approximately , which is a lot lower than the per € 1 risk of approximately that we had in one project. Or in other words, while we expect a € 6.000 gain on average from each project, if we invest in all projects we get a standard deviation for the average gain from all projects of . As zero is more than 6 standard deviations away from 6000, this means that the chances of getting a negative total amount from investing in all these projects is essentially zero.

Here is my second attempt to try to convince you that there is essentially zero risk in investing in many independent projects. If you don’t enjoy this probability theory argument, I would recommend you open a spreadsheet such Excel and generate a column of 1000 random numbers that are uniformly distributed between zero and one. In Excel you can do this with the command “rand()”. In the next column you write a 0 for failure if the random number on the left is below 0,2 and 1 otherwise. In Excel you can do this with the command “if(A1<0,2;0;1)” (and pulling this all the way down the column). This means you are generating a Bernoulli random variable (as in my first attempt). In the third column you multiply the entry from the second column with 70.000 and subtract 50.000. Now, in this column, you have the outcome of all 1000 projects. Then in some cell you compute the average payment from all these projects. In Excel this is done with the command “average(C1:C1000)”. Then by pressing space and then enter in an empty cell (or some other activity) you simulate the outcome of these 1000 projects once. Do this over and over and watch the average payment cell. You will see that it varies around € 6000, half the time it is somewhat higher, half the time it is somewhat lower. But no matter how often you try this number is virtually never below zero. In other words we come to the same conclusion as in my probability theory explanation: that there is essentially no risk if you invest in a 1000 such (stochastically independent!) projects.

Because of this, and because big investors do have a lot of money so that they can invest in many projects at the same time, in principle such investors would (in the absence of any better investment opportunities) accept an interest rate for your loan even as low as 12.5% (at which they make on average zero profits) or let’s say they would accept any interest that is at least a little bit above 12.5%.

The actual interest you will get in the end depends on the overall supply and demand of money. See the end of the previous post.

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Suppose you have an idea for a new product or a new project that you believe many people would find useful, and that, because of that, you would make some money with it. For instance, suppose you happen to own a cave in the mountains and you think it would be a great place for a server farm: a bunch of large scale computers. One of the biggest costs in running such a farm, supposedly, is the cost of cooling and you think that, as your cave is always pretty cool, it would be a good place for such a server farm. You could save on cooling costs and could thus be more competitive (or profitable) than other server farms. Suppose that you believe that this idea of yours most likely will make you a decent amount of money. In other words, you believe that there will be substantial demand for the services of your server farm so that you could make some money with this. The catch, however, is this: installing your server farm requires a certain amount of money to begin with. You need to buy the servers and make sure you have access to electricity and the internet, et cetera. You probably have to do a bit of construction work to install the servers as well. The catch, now really, is this: You do not have that sort of money. So, what do you do?

Well, you try and get a loan from someone who has money and doesn’t quite know what to do with it (doesn’t perhaps have such a great idea as yours). So, will someone (like this) lend you this money? The answer, of course, is that it all depends. But we can now figure out what it depends on.

So the first thing, I guess, that your bank or other potential financier would demand from you is a business plan. Then they will assess for themselves how they see the potential of your project. This is obviously pretty difficult. In other classes, I am hoping, you can learn how to assess the potential future demand for your product or services and how to translate this into a probability assessment about potential future revenue that you might make with your product or services. Let us here simply assume that this was done, to the best of everyone’s ability. And that the general assessment among people who might give you money about your project is this:

You will need to borrow about € 100.000 for the initial investment. You will need to put in one year of hard work. Then people believe that there is 20% chance that things will not go so well (that the future demand for your servers is low). In this case they estimate that you would be able to recoup only about € 50.000 (so you are making a loss of € 50.000 – even without counting the time you put into it). But, they also think that there is an 80% chance that things will go very well (that the future demand for your servers is high). They estimate that in that case your server farm would make about € 300.000. That is you make a net profit of €200.000 (still not counting your time investment).

So will you get a loan for € 100.000? Should you get this loan? Let’s put all this information into a table.

Let us first start with the question, assuming this assessment is correct and the best we can do, whether you should get a loan. Note that the expected income, according to this assessment, is Does this mean you should get this loan? Well, my answer would be: “probably yes!” To give a firm answer, we need to know a bit more about the risk inherent in this project.

Note first that it is clear that there is some risk. It is also clear that if the project turns out to be bad, then ex post (I mean after it is all done and turns out to be bad) we regret that you pursued your project. Why? Well, the project in that case cost more than it made and that’s probably because people didn’t really use its services, which in turn means that it probably did not provide much benefit to anyone. But this is with the benefit of hindsight. At this moment when we have to decide we do not know whether the project will turn out to be bad or good. If it does turn out to be good, it is likely not only good for you but also for the people who use the services that they buy from you. If you recall how things enter GDP, your project would in this good case, enter with € 200.000 and possibly would have provided more benefit than this (that we cannot quite measure).

Now why do I say it is probably a good idea that you get this loan? Suppose for a moment that the risk inherent in your project is largely uncorrelated with any other risk in this world. This is probably not completely justified. It means that whether your project turns out to be good or bad has little to with the success of any other project other people are pursuing. But then, imagine lots of such projects. Then on average they would make a net profit of € 150.000, which means that on average the project creates net benefits that measured in monetary terms exceed at least € 150.000. Now, it is possible that while the project creates some benefits to its paying customers it might also create some costs (of some kind) for other customers. I will assume that this is not the case here, but we should come back to this, and we will, when we talk about externalities. And the total risk is then very small. I will come back to this in one moment. So you probably should get the loan (under these assumptions).

But will you get a loan? And if so, under what conditions? Let us think about the range of feasible loan conditions. We can here think about a loan as a repayment amount in case the project turns out to be good. If the project turns out to be bad, let us here assume, for simplicity, that then there is only the € 50.000 left to be repaid. This means that the risk inherent in this project is then fully borne by the investor, the person who lent you the money. Let us call this repayment amount . What is then the range of feasible values for ? Consider this table:

As a function of this repayment amount the expected earnings are

The best you can hope for is a value in which case the investor expects to make on average The investor would certainly not accept anything lower than this, assuming she or he wants to make money with her investment. Your interest rate would then be 12.5\%. You borrow €100.000 and, in case things go well, pay back €112.500, and in case things go badly, the loss is the investor’s.

The worst for you, that you might just accept, but probably wouldn’t, would be a value You certainly wouldn’t accept a higher value. So let us assume that the possible range of interest rates that the two of you (you and the investor) might agree on is between 12.5% and 200%. You might now say, that you don’t really expect that the investor would accept an interest rate of 12.5% (seeing that this would give the investor zero expected return from her investment and there is risk for her or him as well) and also that you don’t really expect that you would accept such a high rate of 200% (and you are probably right). I will come back to both of these questions in the next two or three blog posts. These are central questions, indeed. But for the moment let us assume that they both would. So what interest will the two parties then agree on?

To answer this, at least to a satisfactory first approximation, we can turn to our supply and demand idea. Money is really a pretty homogenous good. With that I mean that any € 10 you own I would also value at € 10 and vice versa. Or in other words, people typically don’t care whether they get €10 from one person or another. People feel, on the whole, that pecunia non olet. This isn’t always true. A university, for instance, might decide not to accept money from someone considered to have made their money illegally or to have otherwise committed crimes. But I guess it is fair to say that whether you get your loan from bank A or bank B is really not that important as long as the conditions are the same. This means, that you are likely to go to many banks and to try to get the best deal. Investors (such as banks), on the other hand, probably consider various investment opportunities and pursue those that they find most lucrative. So we can imagine a demand function for loans (of various riskiness) and a supply function of money for such loans. The interest rate for your loan will then probably be more or less the market interest rate for loans with such riskiness that more or less equates the demand and supply of money. If there is a lot of money around and only few ideas, as it seems to be a little bit at the moment, then you would expect to get a pretty good rate close to 12.5% (for your loan). If unused money is rare and there is an abundance of great ideas, we would not expect such a low rate (for your loan).

]]>In einem kürzlich erschienen Artikel im American Economic Review: Insights sind die AutorInnen Gneezy, List, Livingston, Qin, Sadoff, und Xu der Frage nachgegangen, welche Anreize wohl die Kinder haben, die an der PISA-Studie beteiligt waren. Wie gut ein Kind in der Studie abschneidet, hat ja für das Kind selbst keine Konsequenzen. Man bekommt dadurch keine bessere Note und dadurch auch keine bessere Chance auf einen Job; es bringt ja eigentlich nicht viel. Wenn man nun davon ausgeht, dass es auch ein bisschen anstrengend ist, einen solchen Test gut zu absolvieren, kann man sich schon fragen, wie sehr sich die Kinder da überhaupt ins Zeug legen werden.

Die AutorInnen dieses Artikels haben folgendes Experiment gemacht. Sie haben zwei Gruppen von Kindern Mathetests gegeben, einer Gruppe in Shanghai und einer in den USA. Sie haben diese Gruppen jeweils in zwei zufällig gewählte Teilgruppen aufgeteilt. Eine Teilgruppe, die Kontrollgruppe, bekam jeweils den Mathetest einfach so (also wie bei der PISA-Studie zum Beispiel) und die andere bekam den Test mit finanziellen Anreizen: Ihnen wurde zu Beginn des Tests gesagt und versprochen, dass Sie für Ihr Testresultat bezahlt werden; je besser der Test, umso mehr.

Interessanterweise ergab sich nun, dass die Kinder in Shanghai sich in beiden Gruppen gleich anstrengten und die Testergebnisse mit oder ohne finanzielle Anreize im Schnitt gleich waren. Die AutorInnen interpretieren dies so, dass sich die Kinder in Shanghai auch ohne Aussicht auf Geld bemühen, so gut wie möglich zu antworten. Mit den Kindern in den USA war das aber nicht so. Die Kinder mit finanziellen Anreizen haben sich um einiges mehr angestrengt und um einiges besser im Test abgeschnitten. Der Effekt war so groß, dass die USA, umgelegt auf das PISA-Ranking, sich vom 36. auf den 19. Platz verbessert hätten.

Wir wissen jetzt natürlich nicht genau, wie die Testergebnisse in anderen Ländern (wie zum Beispiel in Österreich) gewesen wären, wenn man den Kindern finanzielle Anreize gegeben hätte, aber man sollte vielleicht aus der anreizschwachen PISA-Studie keine voreiligen Schlüsse ziehen.

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I feel this is best done by going through a series of (semi)fictitious examples in which we find it relatively easy to judge how much value is really generated and where we can then see how this is reflected in the GDP calculation.

Example 1

Suppose we have two countries A and B. Suppose in country A someone has a monopoly on milk, while in country B the milk market is quite competitive. This means milk prices in country B are more or less such that market supply is equal to market demand. The market price for milk in country A, however, is set not so much by market forces but by the milk monopolist. As we have discussed earlier, this means that the price of milk in country A is likely “too high” and there is likely “too little” milk sold. Now suppose that milk price multiplied with milk quantity sold is nevertheless equal in both countries. In which country does milk contribute more to GDP? In which country would we think people are better off? You may want to think about it for a moment.

Well, one way of calculating how milk enters the GDP (see previous post) is to compute the final value to consumers: that is price (or value) per liter of milk multiplied by how many liters of milk are consumed. As we have assumed that this number is the same for both countries, milk, thus, enters the GDP calculation in exactly the same way in both countries. So according to GDP, if we think of GDP measuring the “market value”, milk provides the same value in both countries. But this is clearly odd, as the value of milk as measured by its price in country A is high probably not because so many people love milk so much more in country A than in country B, but rather because the milk monopolist is able to charge such a high price for milk simply because it is a monopolist. We would therefore think that milk-related welfare is much higher in country B than in country A, even though this does not show up in the GDP calculation.

Example 2

This one is about all the valuable production in a country that do not enter the GDP calculation. Compare the three situations A, B and C. In situation A, I spend a specific Saturday on my couch, doing nothing. In situation B, I instead spend this same Saturday trimming the hedge in my father’s garden. In situation C, I spend Saturday on the couch again, while my father hires a gardening firm to trim his hedge. In which situation is this Saturday’s contribution to GDP the highest? In which situation do we have the highest welfare? You may want to think about it a bit.

Well, situations A and B yield the same GDP. As long as no money changes hands (in such a way that it is recorded somewhere) activities such as me trimming my father’s hedge do not enter the GDP calculation. In situation C, as money does change hands (presumably in a recorded manner), GDP is higher. As to welfare, I don’t know. One could quite possibly argue that situations B and C are similar in total welfare, although one could also argue that I would really enjoy a Saturday on the couch, much more so than my father enjoys a neatly trimmed hedge.

But the point of all this is this. Any, no matter how productive activity that is not officially paid for, cannot enter the GDP calculations. Any work you do at home, cooking, cleaning, gardening, shopping, et cetera, no matter how valuable it is to you and others, does not enter GDP. Nor does any only unofficially paid work, i.e. black market work. If you build a house by yourself, possibly with the help of “friends”, and if you never sell this house, then not much of all this activity enters the GDP calculation.

Example 3

Suppose that football (soccer) games in City A are very peaceful, while in City B they are rather violent affairs. With violent I mean fan violence: they break rear-view mirrors of cars, break windows, fight and injure each other. Because of this, City B requires much more police personnel than City A does. Suppose that this is the only difference between these two cities. Which city has a higher GDP? Where is welfare higher? Think about it for a bit.

Well, City B has a higher GDP as police work certainly enters into the GDP calculation. Yet, I would consider welfare higher in City A. In fact, if the hooligans in city B manage to destroy a few things, GDP will likely be even higher still. Consider the damaging of cars. The car owners might then have to buy new rear-view mirrors and the payment they (or their insurance company) make for that enters the GDP as well. In fact GDP does not at all measure whether anything deteriorates in value. The GDP of a given country in a given year measures the “market value” of anything officially produced in that country in that year. No more and no less. It does not measure the value of everything that is already there (perhaps produced in previous years). A hurricane or volcano eruption might therefore increase GDP as it destroys things that were already there (which does not enter the GDP calculation) and thereby creates a “demand” for having these things rebuilt. Whether or not it does, depends on what exactly is destroyed and how much of it is rebuilt and how much of what was originally planned can now not be done.

Summing up, I think it is fair to say that GDP is no measure of welfare.

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