This paper considers a simple model of credit cycles driven by moral hazard in financial intermediation. Investment advisers or bankers must earn moral-hazard rents, but the cost of these rents can be efficiently spread over a banker's entire career, by promising large back-loaded rewards if the banker achieves a record of consistently successful investments. The dynamic interactions among different generations of bankers can create equilibrium credit cycles with repeated booms and recessions. We find conditions when taxing workers to subsidize bankers can increase investment and employment enough to make the workers better off.

The full paper is available at

http://home.uchicago.edu/~rmyerson/research/bankers.pdf

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I think today I’d like to present a real model and let’s do the details because I want to talk about what I think is one of the most important problems I could think of, we all know that we need fundamental new approaches to macro economics, a new paradigm is needed. We need to think more carefully, something seems to be missing. From my perspective we each have to bring our own intuition to this hugely important question of deepening our understanding of the macro economy. My intuition is that what's driving this model is that moral hazard in banking were absolutely central to everything we seem to, most of what we saw happening in the last several years of global financial crisis. And yet banking and moral hazard are not prominent in most of the traditional macro economic theories. So I would like to try to remedy that by proposing a model that puts moral hazard and banking at the very centre of the macro economy. And what we will discover is that for absolutely fundamental reasons, taking a very standard principle agent model and simply putting it in a macro context that principle agent analysis creates macro economic instability in a way that I think hasn’t been recognised. That may without claiming that this is going to be a model that abstracts away from all the other things you normally think about in macro economic analysis, there’s no money, no long-term or liquid assets, no asset pricing bubbles. It’s going to be completely stationary environment, no stochastic shocks, no nothing going on except moral hazard in banking. And I do that not because I believe that all of those things that are in most, in virtually every other model, macro model aren’t important but because I want to show you that this one which certainly seem to be important can all by itself drive macro economic instability. So that if we see problems with financial moral hazards seeming to cause a financial crisis, you could say yes it can. So in order to get a dynamic in an economy which is absolutely stationary, we have to have some state variable that is inherited from past history so the only thing that’s going to be long lived in this model are people and in particular bankers and their contractual wealths are going to form the state of the dynamic system. What we’re going to do is we’re going to find boom and bust cycles, multiple dynamic equilibria, unless the economy starts with exactly the right profile of bankers of all ages it will not be in the steady state without some stabilisation policies. But we’ll find that when investment is weak a bale out or stabilisation or stimulus that uses workers taxes to subsidise rich bankers can actually make the workers better off. So that the model is rich enough to allow us to consider the possible benefits of some policies. Let me show you, I think time is short in here and precious so let’s go right to the end of the whole talk and see the picture. There’s a bottle behind all this, but let’s see if I can, at least on the middle screen, yes point to things. So here’s a picture that shows the unstable economy, what's going on here is that bankers, we’re looking at an economy where investments are going to be handled by different cohorts of bankers with 10 year careers. And never mind what the parameters are, I’ll introduce the parameters in a few minutes but there’s a steady state which would have, let’s see the young bankers are green in the top, middle aged bankers of various ages, there are 8 cohorts of middle aged bankers are in the middle. And on the bottom, the dark are the old bankers. And what I’m showing you on the bar is in a steady state how much investment is being handled, you know in the macro economy by, in this little model by the young bankers and each of the 8 grades of middle aged bankers and the old bankers who are about to retire in a steady state. And the dark brown bar, the bars get larger, as we move from green to dark brown, the spaces get larger because the rewards are back loaded in a career. A standard result in dynamic agency theory is that when someone is subject to moral hazard temptations in every period the efficient way to motivate that person and we’ll go to extreme point, assuming risk neutrality and standard discounting. And the simplest possible model of risk neutrality and standard discounting is give them a big prize at the end of their career if they maintain a good record and the desire to get that good prize will motivate them and they get cut off if they ever turn a bad outcome. But the result of that is as the bankers get older they get closer to the big prize at retirement and they can be trusted with larger responsibilities and that’s what it looks like. Now let’s start with 80% of the contractual positions of these mid-career bankers. We don’t have enough middle aged and old bankers to get to the steady state output so we hire a lot of young bankers. But what's going to happen is, I’m going to follow this cohort of young bankers as they get older through time, this is the time axis, over here is just the steady state, we’re starting with 20% less than the steady state of our inherited middle aged and old bankers. So we hire a lot of young bankers in the trough to get started but not enough to get to full employment because their going to sign contracts with investors that involve their responsibilities growing over time. And if we hired enough young bankers to get to steady state in the first period then as this cohort gets older and older and here’s, period 10 is where they’re finally old bankers about to retire. Then we would go above the steady state. What that would mean is there would be too much investment going on, the returns to investment would be too small, there wouldn’t be enough returns to investment to pay for the moral hazard rents for the bankers and the investor’s dividends. So the economy must have a trough for several years, then it must go into a boom and then when these guys retire we get another recession and this economy goes on forever like that. Just to make, this is a model that says absolutely nothing, this is a picture of the absolutely analogues model except that instead of having, it’s a standard capital model, where capital is invested at the beginning, lives for 10 years, depreciating over time. And then is retired just like the people. One big payment for a banker at retirement motivates a whole career. The standard investment model that everybody learns, and it’s not a stupid model, it’s a simplification but a good approximation to reality, is capital, you spend a lot of money at the beginning to buy the capital and then it serves you over a period of time but it depreciates in value over time. And then at some point it’s scrapped. The point is, the only point is that standard model would not give you an unstable dynamic because the big expenses at the end and the value of the capital depreciates but all of that is reversed in our standard agency models because the big expense. I’m sorry the big expense for capital is at the beginning and it depreciates. The big expense in an agency model for motivating a long-term career is at the end and the value of that motivation increases over time. So it’s like a form, if you wanted, the only way you can understand it is to go back to old fashioned capital theory. You have to think people and their motivation careers as being like a form of capital where the expense is at the end and the capital gets more efficient until it’s suddenly scrapped at retirement. And then you would have a much more unstable traditional model. But the traditional capital model that we all studied in growth theory doesn’t have the dynamic, even though it’s very similar and the only difference is because in agency theory, agency theory is different from capital theory. So now the overview of the model. So the simple world, imagine a little island, an island in a world full of islands. And the one thing about the island is that bankers are limited to investments on the island where they live, only on our island. There’s one commodity call it grain. The central thing I want to emphasise, the central insight is that in a modern industrial economy, much of the miracles of modern production depend on concentrations of capital that are much larger than any individual worker could hope to earn in a lifetime. And so the savings of many people have to be pooled to achieve these investments. So think about, I’m going to say that good investments of size H great than or equal to 1, but think when I think about investments that a banker handles, think of them as being in billions. So billions of whatever currency you like, except for a currency where billions are what you have in your pocket now. So good investments and billions are found by entrepreneurs who are say people, old experienced people about to, late before retirement. But anybody, they’re good investments. But also anybody can find a bad investment. We need, the bulk of us consumers need, workers and consumers need to pool our savings and there’s cost to identifying a good investment so we want one person to pay those costs, eta down here is going to be those costs. Now an investment of size H which is how much billions we put into it, at time T, if it succeeds then a time T plus 1 is going to return either R sub T plus 1 of H, if it succeeds, if it fails it returns zero, so there are 2 possible outcomes. There’s a subscript on that rate of return for successful investments, I said this was a stationary economy, every period the same. What’s stationary is that the R T plus 1 depends on the aggregate investment on the island. We’re going to have workers harvesting the successful investments and if there’s more investment in any given period then the next period when there’s a lot of harvesting to do the wage rate will be higher. So the net profit, the net retunes will be a stationary function of aggregate investment. So there’s some decreasing investment demand function that says when there’s more investment on the island the rate of return to successful investments will be lower. But no matter what the probability of success is some big number, alpha, some high probability alpha, if it’s a good investment, some smaller probability beta if it’s a bad investment. I’ll make some parametric assumptions that will guarantee that in all of the equilibria of the model that nobody would ever want to make a bad investment. So we don’t have to worry about that. Moral hazard, I’m going to put 2 kinds of moral hazard in there because this Bernanke and Gertler’s model is really one of the predecessors of this, I should also mention more recently Suarez and Sussman as a related model. But I think that Bernanke and Gertler really wanted to have a model of banking but what they ended up with was a moral hazard model of entrepreneurship. To make sure that you really see that I’ve got a banking and not entrepreneurship I’ve got to put them both in there. So the entrepreneurs are, essentially are senior people who have the good idea and a banker is a person of any age who is going to go find a good entrepreneur and a banker in any one period can identify and verify one investment in a range of sizes. But the entrepreneur who has to manage his investment project could divert a gamma fraction of it. So that’s one of the parameters and just steel it and consume it in that second period, in that subsequent period. The banker also could not bother, that diversion would make the good project bad and instead of having an alpha probability of success would only have a beta probability of success. Similarly the banker could divert some fraction, call it eta by not bothering to verify the quality of investment. So let me show you the base. I’ll assume limited liability, entrepreneurs and bankers cannot get worse than zero, I’m assuming everything is risk neutral and discounts, what was the parameter, discount rate row down at the bottom, everyone is going to live, N periods, N plus 1 periods which means that people could do banking services in N periods and still have an N plus 1 period where we know the outcome of all their work and they can still have a nice party on the billions that they could be paid. So limited liability, nobody can get worse than zero if they fail. I’m going to show you the derivation but I’m going to make some simplifying assumptions that are actually theorems because you can guess that since the reason we’re going to pay these entrepreneurs and bankers a lot is because we want to make sure that they don’t do the bad things, that they don’t steel from divert resources. So the entrepreneur is going to be paid some amount, E if it’s a success and if you could have some parameter F that’s how much the entrepreneur is paid if failure, but the optimum is going to be pay F equals zero if it fails, you don’t pay entrepreneurs for failure and you're not going to pay the banker anything. The banker’s rewards will be zero if she offers a project that’s a failure. So let’s just focus on 2 numbers, we have given a project of size H the sum amount, E that the entrepreneur that will get if successful and zero if failure, B is the amount that the banker will get if the project succeeds and zero failure. The entrepreneur’s moral hazard constraint is he has an alpha probability of getting the reward E if he doesn’t divert the resources. But he could take the gamma fraction of the investment amount H and consume it and still have a beta probability of winning the prize E. So this inequality has to be satisfied and it’s easy to see and this is an absolutely standard result, that H times gamma over alpha minus beta is the least amount E that you could pay and satisfy this inequality, this moral hazard constraint. And so this constant capital E which is gamma over alpha minus beta, you’ve seen that formula before you’ve seen any of these moral hazard models, there are formulas just like it with whatever letters are in the model. And that is the entrepreneurs ex post moral hazard rent for success. Now the banker’s moral hazard constraint, I’ve set a bunch of words, this one line here summarises everything the banker could do. So the banker, if she does the right thing, she’s going to go find a good project, she’s going to make sure the entrepreneur doesn’t steel the resources and there’ll be an alpha probability of success. She’ll get B, so alpha probability she’ll get B, she’ll get a reward worth B in the next period and that’s alpha times B is her expected reward next period. But what she could do is first of all not do any work on searching for a good project, save the eta. Then she could just turn to her brother in law and ask him to manage the project but since she knows he has a bad project, he can steal the gamma but she’s not going to let him do it, he kicks the gamma fraction back to her so she gets eta plus gamma times H. She just diverts for both of them and then she says to her brother in law you don’t get to keep your entrepreneur payment either, you’re a stooge for me. And so he has to pay her back. She gets both her B and E in the beta probability that this fraudulent project succeeds. So that’s the moral hazard constraint. I’m looking at the worst possible collusion between entrepreneur and banker and the banker gets her stooge to kick back almost everything but this is a constraint, we know what E is, it’s H times capital E and then it’s just linear and H and then can solve for B and B is some function. In terms of the fundamental parameters, there it is, I’m going to call that constant, everything is proportional to the investment size. So capital B times H is the value of rewards that we must give the banker in case of success. The expected value of the rewards that the banker would get in case of success next period per unit of investment that she’s handling, period, and that’s it, that’s the bankers moral hazard rents. Ok, now the simplest, with models like this, these bankers, I’m going to assume bankers, in every generation there’s no shortage of people who have the talent to be bankers, maybe not all of us can do it but there’s lots of them, lots of people who would like to have a career that could culminate in retiring with billions paid to them. So I’m going to choose, I want to make it as hard as possible to have a recession. So I’m going to assume in this, for simplicity that investors can go out and hire bankers and they can in fact, I’m going to assume and this is going to be an important assumption, that the investors can make a long-term contract with the banker. So the investors almost without loss of generality but this is a theorem, might as well hire a young banker. So in fact they are going to want to hire young bankers, we’ll see that. So a consortium of investors are going to go and find a young banker and say ok you're going to intermediate for us, we’re going to give you an incentive system and at various points in your life H T will represent how much you get to invest for us as long as you’ve not failed and at the end of your career if you succeed you’ll do some B N, without loss of generality it will turn out, we’ll assume that they’ll start her with the minimal amount of investment which is 1 billion. There are no investments smaller than a billion, no good project smaller than a billion. But I am assuming in this slide and I could show you at the end a detailed slide that proves that this is optimal. That the contract has maximal punishment and maximal back loading. Maximal punishment means that as soon as there’s ever a failed project, this banker is never going to get anything again and since she’s never going to get anything again she can’t handle any responsibilities because she would cheat. So they’ll terminate. And so she only gets to a period T in her life, she only gets to invest H T if she’s been always successful up through that period. And she’s only going to get paid at the end, this is the result of an assumption of risk neutrality and that everybody, the investors and the bankers discount at the same rate. I’ve been looking at the risk adverse bankers and many of the results turn out to be numerically very similar. When you introduce risk adverse bankers some things change but these results can be extended to risk adverse bankers, but today for simplicity risk neutral bankers and then one big payment at the end motivates throughout the life. Now this long formula here is the present discounted value for the consortium. At the end there’s an alpha to the N probability that in the N plus first period they’ll have to pay B N to the banker and that’s discounted of course because it’s N period is in the future. And at every previous period, let’s see here’s the amount that the banker is investing, if with alpha to the T probability she hasn’t failed yet, then she’s going to get some R to the T returns. We’re going to have to pay capital E times that to the entrepreneur who has just, the difference between an entrepreneur and a banker is the entrepreneur is tied to a real investment opportunity and so we can’t have long-term relationships, these are unique to every period, we can’t have long-term relationships with them. The banker is not tied to any particular opportunity, the investors can have a long-term relationship with her as she goes out and hunts for different investment opportunities. But this particular bracketed term is funds in the period after the investment, so the money you have to do to pay off, the returns we have to set aside as dividends to the entrepreneurs to pay for the H T that went into it is 1 plus row divided by alpha. It’s one period later, row is the discount rate and divided by alpha because there’s only an alpha probability will get there and all of this will happen with alpha to the T plus 1 because alpha to the T is the probability that we’ll still be in business at this period T and another alpha because there’s only an alpha probability for succeeding. And these net rewards are in period, these dividends that can be claimed by the investors are going to be achieved in the period T plus 1 so we have to discount it back to the time of contract. Ok the one period analysis can be replied recursively. First of all it’s obvious that in the macro economy, this bracketed term here must be non-negative at every period. If it were ever negative in any period then nobody would want to invest in this economy and if R T was so small that it couldn’t cover the entrepreneurial moral hazard rents and the cost of capital, the cost of investment, then nobody would want to invest and let’s just assume that when investment is, the investment to man curve is such that if nobody invests then this would be positive. R is a function of aggregate investment. So this is always going to be non-negative. That’s one constraint of our equilibrium, one. We’re going to have 3 constraints. Therefore in every period, given the B N which is out there, you going to want to have the highest H T possible. Given the final reward, given B N, the optimal investment at each period T is, this here is the present discounted value of the great career we’ve got you on, you're going to get this but you have to, there’s some probability every period you might not succeed, it’s in the future, this is how many periods you have to wait for the big party at retirement. At H T multiplied by capital B has to be that, because that is the present discounted value, that is the value of the reward at period T plus 1 that the banker is getting from success. It’s not a monitory reward, it’s a career reward. It’s the opportunity to go forward with a lottery that has this present discounted value. That’s the maximum amount you can do, you can see that H T is multiplied by a non-negative number so you want to make it binding. But as I said without loss of generality. We can assume we start the banker at H zero equals 1, so that enables us at zero to figure out what B N is, B N is, oh of course B N is the moral hazard rent you have to give the banker, multiplied by the, whatever it takes because it’s being paid long in the future and because there’s some risk about getting there. But now once you have that we can feed that back into this equation and we get something very simple, you start at 1 billion and then every period, of course every period the prize is becoming one discounted thing closer and it’s one less alpha probability that you have to get through so the responsibilities. My responsibilities in my career as a professor might have grown because maybe I learned something during my career, I don’t think so but maybe I might have. In this model I’m not having any learning, if you added learning you get even more of the effect but simply getting closer to retirement means that these bankers can be trusted with larger responsibilities as they get closer. When you take that and plug it back into the initial formula for the investor's present discounted values, almost everything cancels out and you’re left with something that has very few T’s in it. And in fact, but now you say wait a minute, we’re living in a world where I’m going to assume funds, there’s global savings, there’s a global savings glut and people are willing to save in the world at the discount rate row, at the personal discount rate row. So if the present discounted value of this was negative nobody would hire young bankers. If it was positive then there’d be infinite investment in our island and that would drive the investment returns down to zero. So it must be that infinitively elastically supplied global investments must get zero returns and that simply says that these terms which are the, this we could call the banking surplus, the returns to the island in any given period minus what the entrepreneurs get, minus the cost of capital, the sum of these over the N periods that any banker can live, must add up to the moral hazard rents that bankers have to get. The result of having long lived bankers as N gets larger, bankers can be trusted over longer careers, you can spread the banking moral hazard rents over more periods. But in every period, it’s going to turn out, in every period in equilibrium people are going to be willing to, it’s called sigma, this banking surplus, and in every period, starting in period T plus 1, starting in period T, these have to sum to B because in every period entrepreneurs have to get zero profits from hiring new young bankers on this island. But that cyclically means that R T plus N has to be R T. This model is going to perfectly cycle. It wouldn’t cycle, the cycles would dampen with risk aversion. If we add noise other things will happen. But the model is going to have to cycle. I don’t have time to go through. It turns out these contracts are going to have actually no external funding after H zero but it’s going to turn out that the investors are going to have to be committed to reinvest. Let me just pause for a moment and say the long-term relationship between, it’s going to turn out that at any point in time after the first period, the present discounted value of future dividends to the investors will be less than the amount being reinvested. That means that the investors need to be committed. This was a model in which without any long-term investments, Diamond-Dybvig, other models of banking have typically assumed that real investments were long-term. This is a simple model with only short term investments, just one period, just 3 time model. And yet we’ve discovered for agency reasons there is a liquidity problem. Investors must be committed to reinvest, that means that yes if you can sell your investment but only if you can find some other person who is willing to buy it from you. These bankers, these investors must make some kind of long-term commitment in this model and there must be some illiquidity in the system for the investors, not because of the investments being long-term but efficiency agency relationships and this is absolutely standard, are long-term. And that in itself creates an illiquidity. But I’ve only shown you 2 of the 3 equilibrium conditions, there’s one more and it’s rather surprising. So what were the 2 equilibrium conditions, one was in every period the rate of return has to yield after entrepreneurs moral hazard rents and after the cost of, the basic present discounted value cost, expected present discounted value cost of capital, have to yield non-negative banking surplus. The banking surpluses over a banker’s life time have to add up to a certain constant, the moral hazard rents that comes from the moral hazard parameters. There’s one more constraint and this took me a long time to find it. Let J T denote the total investment handled by young bankers at time T. At any time period T the total investment handled by young bankers at time T minus S, the S year old bankers, every period a banker succeeds, her responsibilities grow by 1 plus row divided by alpha. But only an alpha fraction of them can go forward. Therefore in the cohort they grow by a factor of 1 plus row, the discount factor. They grow as the discounting. And the sum over the N cohorts. That gives us a system of equations, they have a cyclical solution only if it satisfies this and this. But J T has to be non-negative and that says that 1 plus row times the aggregate investment in period T minus 1 has to be at least I T. Investment at time T, aggregate investment IT. What that says is down here, this is a model in which investment can grow gradually, there’s an upper bound on how fast macro economic investment can grow, it cannot grow faster than the personal discount rate. But there is no lower bound, there is no corresponding lower bound on how fast investment can crash, that was a surprise to me. That’s another, we’re getting a liquidity problem, we also have gotten just from basic agency models and insight into how macro economies can grow gradually and crash as opposed to spike suddenly and gradually decline. And that’s everything, an equilibrium credit cycle, cyclical return sequence that satisfies these and there’s an equation that says we’re on the aggregate demand, the given investment demand function. I’m basically out of time so let me just show briefly. I’m going to add a linier investment demand function and it’s going to be linear because workers wages will be part of the, the workers have to harvest it, there’s their wages, workers have a quadratic disutility of effort so their wages go up linearly with how hard they work. The only reason I want to mention that is because I want to emphasise, I’m going to calculate workers welfare and I’m going to do the right thing and remember to take from their aggregate wages the cost, their quadratic cost of effort and their net utility in a standard quadratic effort model is half of the wage bill. So then with this, 2 things, here is the steady state which is the cost of capital, the entrepreneurial moral hazard rent plus one Nth of the moral hazard rent. This is an important chart showing how the steady state income distribution in this little toy economy looks depending on how long people can trust bankers. What I want to say only is the differences resemble those of development, a country where you can’t have long-term relationships with financial intermediaries is in this model a desperately poor country. If you could have infinitely, it would be much better. Finally I’m going to show you the picture here again, this is the same picture you saw at the beginning, a picture of a model where we start with 80% of the steady state in period zero I’m calling it. And we hire a large number of bankers, young bankers but then they crowd out the new young bankers over a period of time. And then, it’s not shown here, when they retire the next period we go into a recession, finally here’s all it takes to calculate how much, in order to stabilise the economy, you would have to subsidies investors to hire middle aged bankers. Investors don’t spontaneously want to hire middle aged bankers because they can’t amortise the moral hazard rents over such along period. That’s why they only want to hire young bankers. But we could subsidise it and you can calculate how much would you have to subsidise the investors to hire middle aged bankers. Then you can calculate, let’s have the workers' pay the taxes that pay for that subsidy and in some numerical examples you can find that the gains to the workers exceed the cost of the subsidy. Because of financial moral hazard bankers need long-term relationships with investors and these relationships can create macro economic, complex macro economic dynamics which macro economic theory needs to take into account. In the recessions of our model productive investment is reduced by a scarcity of trusted financial intermediaries. Kind of sounds like today. Competitive recruitment of new bankers cannot fully remedy such undersupply because bankers can be efficiently hired only with long-term contracts in which their responsibilities are expected to grow during their careers. So a large adjustment to reach steady state financial capacity in one period would create an over supply in future periods. Thus a financial recovery has to grow gradually up hill into the next boom which in turns creates the seeds of the next recession. A tax on workers to subsidise bankers, they’d benefit workers by more than the tax but some of the workers gains are coming at the expense of past long-term investors. Sorry for running over, thank you so much.

# Roger B. Myerson (2011)

## A Model of Moral-Hazard Credit Cycles

# Roger B. Myerson (2011)

## A Model of Moral-Hazard Credit Cycles

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