Computational Challenges in Macroeconomics, Thomas Sargent (New York University, USA)

okay good evening ladies and gentlemen it's my great pleasure and honor to introduce Professor Thomas Hart mr. speaker tonight professor scientist at New York University and a senior fellow at the Hoover Institution he had professorships at University of Minnesota University of Chicago Stanford University he has an endless list of honors and awards which I'm not going to list instead I'm going to take two minutes to explain what I'm personally very happy that agreed that he agreed to give this lecture so this is my personal view uh tom is going to kill me afterwards my colleagues might also kill me but it might be useful for you to sort of have a little bit of an idea what's going on so he doesn't look like it but when he entered the profession macroeconomics was in the dark ages okay so these people use very reduced form orders and they try to model the economy without economic agents so they didn't realize that you know to understand the miracle economy would be useful to understand that it's populated of firms and households who try to maximize profits try to maximize utility and have expectations about the future and start and together with lucas wallace prescott and several others they went out and in the early seventies revolutionized their so it's often referred to as a rational expectations revolution and they will change the way macroeconomists are thinking about the world so you know if you read the New York Times or the newspaper you might not realize this but you know for economists it's clearly they've won the war so their models are the models we work with now and so what makes us great now that he's here is that these models if you take them serious and if you try to model heterogeneity if you try to model you know complex environments you need to use computational methods so it's a theory that economics you are now at a position where we need to you know use your help in order to solve the models we write down so we need to use up-to-date American methods we need to use supercomputers because the models we have become so complicated that they cannot longer be solved analytically and so Tom being now as part of a second mini revolution its call it which is to use computational methods and economics on excuse me happy ok so it's off and it's an honor to be here so I'm going to so I'm here to learn and and I'd rather be listening than talking but I agreed to talk so I'm gonna tell you some things about the structure of economic models and I'm not going to use any equations I'm just going to use words which are which are imperfect so I'm going to tell you about the structure of our models so here's what I mean by ad I not did not dynamic economic model and I'm gonna repeat myself so the first thing is it's it's going to have a collection of people and they have purposes beliefs and constraints so you might ask what I mean by a person and so for me a person is going to be a constrained intertemporal stochastic optimization problem that's what I mean by a person just like us it's gonna be dynamic because we we live a while it's gonna be stochastic because we don't because there's shocks hitting us and perhaps because our our models are imperfect is that's what's best for B so purposes beliefs in constraints and then there's going to be another entity it's called a government I'll come back and tell you the government is gonna have the power to tax to spend to redistribute to borrow maybe to repay maybe not to repay okay now what's the government that's going to be different so it's gonna be our government itself is going to be a collection of people which collection it depends on where you live and when you live in some places even today it's a very small number of people in other places it's various kinds of coalition's now sir I mean by government so and as Felix said when we write down models our models are going to have people in them and you know a good model is you should be I don't know the difference between us you should either be able to sympathize or empathize with them one of those two things maybe both so you should be able to get inside their problems and appreciate them and the next thing is there's going to be technologies for producing goods services and capital and some kind of cattle the most important kind of capital is human capital what we call human capital and what I mean by that is that's that's the stuff in s that allows us to think better and produce better and that's created by we would devote resources into that we you know takes people and money and time to produce that so there's technologies for doing that some better ones and worse ones okay then the next thing is there's going to be stochastic processes and you know what I mean by a stochastic processes is going to be a a probability distribution over a sequence so when I say stochastic process it's going to be a joint probability distribution and we're going to use those to describe information flows and economic shocks so there's going to be shocks hitting the system like financial shocks and there's going to be some information that people have about each other and about how the nature of the economy so there's gonna be all these all those things and then the next thing we're gonna have is an equilibrium concept and because there every equilibrium concept that I know of has some has some notion of a system at rest in some sense in some sense now the our equilibrium concept the sense its what it's going to be in at rest is going to be a little bit subtle it's good and what it's going to be is it's gonna be no person is going to have an incentive to deviate from what he's doing and what he's doing what he or she's doing pretty complicated he's at rest in the sense that you ask him shouldn't you be behaving in some different way given the environment and that person is seen no that's what's in rest the system itself is moving along around like everything it's moving around stochastically but every every person is playing a best strategy given everybody else's strategy that's a sense in which it's at rest and that's a great economist who just died that's the notion of a Nash equilibrium that's his sense of at rest and he introduced that probably wasn't him okay if we did history probably wasn't the first one there were 19th century Europeans who were on to that like Cornell okay so so what this equilibrium concept is going to do it's going to describe how all these diverse purposes and possibilities are reconciled and they're going to be reconciled through markets where people voluntarily trade and government activities or statements which in some sense may be voluntary or involuntary so there everything is going to have to be tied together so there so it's going to fit together and be coherent in that sense so that's when you could have modelers so I could stop now so I'm just gonna say more and more about this so so so why do we do this so there's several reasons we do this the first reason is it's beautiful some of the mathematics are beautiful and the way you know the notion of an equilibrium disequilibrium concept the way you could take in this diverse set of people with different purposes and beliefs conflicts of interest and through this market system with this government system everything is reconciled and fit together so if you actually look at the mathematics it's beautiful but that's not a good enough reason and you don't go tell people that in public so so the purposes of quantitative economics and this is serious is you know you know there's there's a minority in economics so so some people accuse economists like Ken Judd and Felix and me of having physics Envy and I plead guilty happily because I because I think you know their goal is to make economics more like physics in the sense uh take models seriously and take them to the data and there's an intimate interaction between the successes and the failures of data of the model and explaining the data and revisions of the model that's a business that we aspire to be in and we also have physics Envy in that in that we are ruthless and importing mathematics from from every place we can get it and we're limited only by our ability so their purpose is to interpret historical data in ways that distinguish cause from poisonous you could ask me what I mean by cause and what I mean by coincidence what do you mean by well cause is it some relationship that's invariant with respect to certain kinds of interventions or changes in government policies perhaps so the reason we want to do this is we want to evaluate the consequences of alternative government policies we want to there are proposals that are coming on line all the while and we want to have a machine for saying whether these are good ones or bad ones and and and all of these things are going to they're going to affect different people differently and we want to understand the quantitative implications of them so the way we're going to do that is we're going to build models like this and hopefully take them to the data estimate them and then do policy evaluation that's that's the business world in okay okay so now I'm going to tell you a little bit about remember I told you about these people and I told you what a person was a person is a constrained intertemporal stochastic optimization problem and I and I'm gonna tell you what I'm a model well for us a model is going to be a collection of people who are interacting in a coherent environment that's our vision so let's drill down a little bit and talk about these these people inside this model and we're going to run into something that's going to be very costly in a minute okay so the people inside our model have incentives to forecast forecast what just like you so their decisions the way I'm going to say this is their decision they're gonna make decisions at time T that are going to depend on prices and taxes and other people's decisions at times T plus J for all J greater or equal to zero so what I do what I do now depends on what other people in the society are going to do in the future or what my expect them to do and simply any like you play soccer or baseball or football any that anytime any to any player in a game I was doing this all the time is forecasting the decisions of his teammates and his his his opponents doing it all the time so so so this definition of a person is solving intertemporal optimization from that's not so silly now because a soccer player does it all the time okay so this leads us to the obvious inference that people's beliefs about the future affects their current decisions so if you want to think about the arrows of time there's a there's an era where so now we're I'm going to use the notion of a state just like Laplace or physicists did but now what's going to happen is there's going to be a bi-directional influence of of future and past things on what's going on today the past is going to impinge on what our opportunities are today but our expectations about the future are going to influence what we do today you know if I I could I could elaborate on this if you're a if you're a businessman and you're living in in Moscow in 1920 you're gonna make one set of decisions and if you're living in if you're living in West Germany and 1990 you're gonna make others and it's because of your beliefs about the future they can affect your present decisions okay so now we have to model beliefs okay so the way ken Jed put this our agents are elements the elementary objects in our model are people and not particles and what our people are I'll tell you again what we call an agent sequence intertemporal optimization problem and to make that problem well posed to write it down so that in a respectful way I have to tell you how something about people's beliefs about the future in order to make that problem will post one way to say it is if you're a dynamic programming or a pontryagin intertemporal guy I have to mount write down the law of motion that you think belongs in that optimization problem have to write that down that's your law of motion or a great statistician savage would say that's your subjective belief so what I'm going to write down here's what I well you could say is I told you there's a people there's a collection of people you got to write down beliefs for every person about how the futures can unfold to make this these problems coherent with me so I'm gonna write down police and now what's a belief well if you kind of think about it a belief is a probability distribution over sequence that's what I mean so they're the people inside our models have to have models because the way I think of a model is a probability distribution over sequence index by some parameters if we're gonna make progress so the people inside our models have to have models that's can judge their people and not particles and those model the stochastic brought the part of the stochastic processes they care about it's a future because the way they're gonna when I write down this control problem if I sit an optimal control problem once I write down their model the world everything is dictated okay so now something is okay so you have heard you may have heard that so the kind of economics can judge my doer you'd call it chicago-style economics I don't know why they call it that and you may have heard the University Chicago doesn't like communists okay but that's it's false because I'm going to talk about heroic assumption that's going to be communism so the way the idea of rational expectations is communism so instead of saying every single agent has his own set of beliefs that it's a model we're going to impute the same model to everybody in the economy and we're going to go beyond that so there's going to be a communism of beliefs who's going to share this model remember what I said is a model it's a joint probability distribution over sequences it's going to be shared by everybody inside the model it's going to be shared by God or or nature and it's going to be shared by the economy trician or the outside observer and there's gonna be one model that's shared by everybody inside the model and why are we doing that it's a huge simplification that's one reason it's a data it's a dimension reduction instead of having to have one set of beliefs for everybody it's going to be it's just gonna be one thing and furthermore many of these this stochastic process itself is going to be endogenous and the people inside the model are forming beliefs about stuff that they're you know that's being determined by the model so essentially this rational expectations assumption is going to be um it's going to be a fixed point in a space of stochastic processes and it's going to compete it's going to reduce dimensionality in an immense way that's one reason it's a scientific convenience and if you try to do something else the curse of dimensionality is going to get worse than it already is so that's one reason we're doing the other reason we do it is the following okay it's just relates to something can jetsedder its economists get asked this they get asked to forecast a stock market and and one question always comes up is if you're so smart why aren't you rich okay so if you're a rational expectations person the answer is you you just you tell the person why you're not rich it's because you know the best you know your model is not any better than the model of the agents inside your model and those guys are trying to forecast stock prices and they do it just as well as you do so it's it's a coherent answer to that and furthermore okay so that bears a lot of thinking about that's a very attractive answer so the fact of the matter is rational expectations for a combination of these reasons is used to rout Applied Economics it's used in and it's it's used by left wingers right wingers it's it's a it's a scientific data dimension good model dimension reduction my friend Lars Hanson mine actually we worked on rational expectations London we're trying to go a little beyond rational expectations and we actually encounter lots of opposition from young people but that's another story what kind of okay so right right so here's the here's what I just said again a model is a stochastic process I'm gonna keep saying the same thing at different ways because it's kind of hard to digest that implied forecasts about the future and our forecasts are going to be mathematical conditional expectations Reese where's the forecast again I like this the people inside the model themselves have a model you know like if you're an economist and you have uncles or dads or aunts you'll find out they'll say I go to a party and say I want to talk to you about economics that means they want to tell me their model of the economy that happens to all of us they don't want to hear about our model okay okay so good so so here's here's them here's what this does there's a self-referential aspect which is beautiful about rational expectations model and what you can think about is it's it's a fixed point in a space of there's what different ways you could formulate the space it's either in a space of stochastic processes where I take people's beliefs about the stochastic process and then I find out what that implies about what actually happens and then I ate on that mapping so there's a mapping from believe stochastic processes to actual stochastic processes irrational expectations and is a fixed point of that question you might ask based on some talks I went to is that fixed point unique and if it's not unique how do you select among them we'll get back to that because that's going to be key okay okay so what's also true is you should notice is this definition allows information discrepancies so you and I may make we have the common stochastic process but you have more information than I do so your conditional expectations are conditioned on more expectation on more information you make better forecasts I would make the same forecast as you if I had your information but I don't have it so this is going to be a framework that's going to accommodate some what looks like some differences in forecasts but not really their information differences we'll come back to that that's going to be important when we talk a little bit about the financial crisis okay okay so now this is going to be a cut I'm going to say that the same thing of different so my definite that definition I gave is a fixed point think about this given the past the present and the future are simultaneously deterrent so I'm going to say this in a different way dynamics is a special case of statics I'm just gonna solve a whole bunch of stuff I'm gonna just solve a whole bunch of simultaneously I'm gonna solve the future and the present simultaneously because they're interacting and I have to solve them simultaneously to get to this fixed point so you didn't like that I'll say in an even more flight let me tell you wait uncertainty is actually a special case of certainty and they gave several people a Nobel Prize for for recognizing it because and that that is actually you that's that's the foundation of and here's the idea there I'm just gonna all sorts of commodities they're traded the dynamics is a special case of statics I'm just going to index all commodities by time and I'm going to solve for all mall simultaneously prices and quantities different dates I have to solve them simultaneously okay so then Kenneth arrow saw that somebody did that Kenneth arrow said well why not index prices and quantities by events random events and I'm gonna solve for them all simultaneously what you get on a particular event is going to be determined as as a result it is simultaneously so so this notion time zeroes this brings out the importance of the details of timing protocols in theory and practice so when I write down an economic model and in a description of this collection of people in effect I have to write down a timing protocol and what that means is that's the Constitution for social Constitution it's a description of who chooses what when tying protocol but who chooses first and that matters so and so a mathematician was it explaining to way he described us today to me whether it's online or offline so one thing is one way you could one way we sometimes say this is here's a tiny protocol the government commits to a policy it sends the Constitution it can't change it at times zero for the United States it's eight 1789 we make up some rules and we're not gonna change him and we're not gonna go back there but then other people choose every period that's different then the government makes up its mind about the rules every period those are different time across those are very important ok ok so now I'm going to tell you ok now I've told you all about rational expectations I'm going to tell you this is no one to three thousand years ago in China like everything else ancient Chinese ancient Chinese proverb that's it okay now it's surprising as it may say is is the when Felix said when I went into macro in like in 1852 that every model violated that every model violated debt it said that private people strategies were fixed for all time and the government could have adjusted strategies to take advantage of their foolishness to correct for their foolishness and that violated that okay so now so now what I'm going to do is I'm going to apply these ideas to two models of the financial crisis okay so here's a young here's here's kind of a little story it's my baby so the kind of economics that I'm describing is by the people the kind of economics that of people who actually write down models and take them put them on computers and take them to data and all of us do things like I've described but there are other people who write about economics especially in the press who do not like this wonder they don't like the math and they and they don't like the computers and so he criticized what we've done and they and they don't like yeah they don't like this the assumption that a my description of a person as a constrained intertemporal optimization problem I don't like any of that so they say oh that's wrong they when the financial crisis happened there's people were writing op-eds person is like I could tell you names of the people like Robert Skidelsky in the Financial Times saying the financial crisis proves that modern dynamic macro that uses computers and mathematics is wrong because if those guys were right so smart we wouldn't have financial crisis so the fact of the matter is and those so those people don't fit models to data they don't write down models we're just gonna warn you this and and what I'm going to submit now is the only models of financial crisis that are actually used by by by by people in authority and by scientifically use rational expectations and very heavily I'm going to show you that and I'm going to describe two different models of there's simplified models of financial crisis they're actually too simple although one of them is very widely believed and they're gonna have all the elements that I talked about and they're both going to work rational expectations really hard so you'll hear there's a field called behavioral economics which is defined by the following it's not rational expectations and a person is not solving a constrained intertemporal optimization problem it's not that so as various people have pointed out there's an infinity of ways you cannot be something and and so those people that in the behavioral economics there's no there's no contributions to the ongoing scientific problem of trying to figure out financial crisis and prevent them so far you were still waiting for them and now they're going to need some first principles ok so watch for the appearance of rational expectations when I describe these models so there's two polar models and also watch for the influence of these models on Ben Bernanke and Mario Draghi one of these models is going to have a huge effect on them and you might wish the other model did or would or maybe not and you can make up your mind about dose that's where I'm going so here's these two polar models one is it's going to have a it's going to be a rational expectation model and you'll see how heavily this is stress of multiple equilibria and this is going to be the leading model of bank runs it's going to explain why there are bank runs and the other is going to be polar opposite model in many ways the people who wrote these models respect each other but they realize they're doing different things and one reason they're doing different things is they don't have the they didn't have the computational power that we think we're going to have soon to combine these in reality the moral hazard is going to be adverse incentive effects of bailing out banks so both of these models used ratification so I want to explain these to you and please ask me questions if you if you want so it's gonna be a model of bank runs you so you know what a bank have you doing a bank run this you know it's a bunch of people actually I can tell you some place to go if you want to see one in purpose so here's what banks do they supply intermediating and they do maturity and risk transformation so they do something that's math actually there's great economist wrote something called statistical theory of banks so they actually use kind of a law of large numbers say what they do is they take deposits and they tell the depositor you can come and get your money whenever you want so so it's short maturity instantaneous the person has a call option I'm getting his money when everyone's with the bank counts on the people and that most people leaving their money in for a while and the only people that come in and get their money are impatient they want their money now so most people aren't impatient and what the bank then does is it it take it borrows short couldn't borrow any shorter it's the banks an intermediary it borrows short and it lends long so what it does is if it finds some businessman or entrepreneur and that entrepreneur has a project and it's not going to be short-term it's gonna be medium-term it might be it might be risky it might be risky so it it the bank takes these depositors as short-term in it and buys a portfolio of longer-term stuff if it buys enough of a portfolio can use a law of large numbers and be pretty sure it has a get so it gets a return okay and then all this is going to this is all going to work if people leave their money you know it's going to do some statistics hire some math math math math petition figure out what's the you know arrival rate at which people in good times withdraw their money you can figure out how long it can be in there and can do cash management and under normal times this is all going to work and the bank's doing something socially useful it's it's it's actually taking money from the depositors who want to lend in a convenient way giving it to people who want to borrow longer-term and it's going to do risk sharing and under right circumstances it can actually give the depositors a return you can pay interest on that it works really well so the problem is this system under certain circumstances this is a famous model that had a huge impact in my view I never talked to him about it there's got to be true on Ben Bernanke this model has multiple equilibria and here's the deal banks are really good if they do this but they're vulnerable to runs and house of run go so the run goes like this I'm happy to leave my money in the bank and I'm patient I don't want to I don't want to run I see some people going to the bank and most of the time they go to the bank it's just because they want to get you know some money to buy a coke or something like that so I see that I see I don't get disturbed but now it's like this I see you on the street and you see me and we're walking by the bank and you see and you see me and you realize I don't I've got my money at the bank and I don't read much talk and you see me kind of taking a step toward the bank and I see you I think I see you so I go to the bank and I withdraw my money and then you withdraw your money and everybody sees us withdrawing and they go to the bank and if it's in my best interest to run to the bank if I think it's in your if you're gonna run and you think if I'm gonna run you're gonna run so you won't run if I don't run and vice versa so we go like this and we create one additional equilibrium which is a bank loan equivalent and a clever guy like kindred can create more for you okay a lot more of them so the idea is if there's a bank run then what happens is the bank has to liquidate the project early these projects early and intermediation collapses that's what happens there's multiple equilibria and it's all about notice notice these expectations are Rasha it's not the you're not running because you're stupid you're running cuz you're smart and sing with me so rational expectations does not when we do this fixed point and we do that there's multiple equilibria and there's zillions of them and most of them are bad awesome have this run to okay so so the people that wrote this paper this is a setup they wrote this paper and they said suppose there's the following thing there's a government and I have to tell you the way the bank operates here there's a rule by which the bank operates its first come first serve the contract is you know the implicit contract is if you come if you have a bank deposit I'm gonna give you the dollars and then the implicit thing is until they run out and when I run out of course simply I'm not going to run out if you don't run but if if I if I run out and you run you're gonna get you better be first you better be really this gives you an incentive to okay so what the authors of this did the falling they looked at this is a bad they're gonna do some engineering just notice how this is having every element that I said about why we want to do quantitative or theoretical economics we want to write down this model when examine its characteristics and then we want to describe government policy or some kind of policy that's going to make the world better and the people that wrote this Paul did this and so what they did is suppose there was government Deposit Insurance which I'm gonna come back and wait government deposit insurance work says if there's a run what the government does is it transfers resources from the taxpayer and gives the depositors our money that's what it is everyone understand its government and let's just make it free you'll see why we make it free it's close to free in the United States we're gonna make it free so make it free now go back hand the model with the deposit insurance to you know Simon and Ken Judd and now compute the equilibria there's only one equilibrium because no one has an incentive to run now this is beautiful just offering this Deposit Insurance knocks out the bad equilibria and how much does this cost the government in the event zero this is beautiful this is just a promise okay so the way a sophisticated economist and there are some here would say on the equilibrium path it doesn't cost anything if there's some crazy people and they go off the glass it would cost but there aren't any so this is a Costas intervention so so the way I think of it as government promises the bailouts are costless what we call equilibrium selection devices they they amend the model to knock out these equilibria that are socially bad so this is this is the defense that people who like Deposit Insurance appeal to so deposit insurance was put in the United States by in 1935 bill called the glass-steagall Act which Franklin Roosevelt signed and you know standard undergraduate textbook say one of the things you should credit Franklin Roosevelt with is putting in Deposit Insurance the fact of the matter is Franklin Roosevelt hated Deposit Insurance and he tried to get this out of the law I'll tell you about this more okay so why did he hate it so here's moral hazard now if you're here's what moral hazard is this is my second polar model and this is going to just this is going to be a rational expectations model so I'm changing the environment but I'm still using rational expectations so so there's a lesson in this which I mean for you to take away rational expectations is not one model it's an equilibrium concept that we as part of an equilibrium concept that we use we can build lots of models with this and the art so there's no rational expectation school there's no such thing so there's gonna be a polar model that's gonna use rational expectations and instead of having deposit insurance be really a good thing it's gonna be a horrible thing and Franklin Roosevelt knew this model even though he hated math wasn't good at it but it is his he had this in his blood and I'll tell you why so here's it the effects of a deposit insurance and a lender of last resort like we will do whatever it takes I've heard that and believe me it will be enough without telling you whatever it takes is so what this is this model focuses on the effects of deposit insurance and lender of last resort on the incentives of two groups of people the depositors and the bank managers and their shareholders and this has nothing to do with it the bank managers being greedy and ended up they're supposed to be greedy and the shareholders are supposed to be okay so so what happens in this model is the the depositors are if there's no if there's no vision here is it that if the depositors if there's no Deposit Insurance they have an incentive to do what the great English political scientist Walter Paget said was have preservative apprehension meaning if I would have put my money in that Bank I might want to know what kind of loans that banks making so the depositor has an incentive to monitor the bank and I want some evidence that its portfolio is safe if I want to hold a safe asset I better be holding in a pretty responsible Bank good so what Deposit Insurance does innocent in this setting is it completely eliminates the incentive for depositors to to care about the portfolio's of the institution's I can give you quotes from some relatives of mine and furthermore if you if you do a study of what the bank managers and shareholders should do is they should become as risky as possible and as big as possible when you do a little calculation they should become as big as possible and as risky as possible and eventually with probability one the banks going to fail and there's going to be a financial crisis it's all about Deposit Insurance and there was this was all pointed out in the 1970s by some rational expectations economist named Kerrigan Ross who said that one of them wrote a paper called the cart before the horse that if you're going to deregulate banks you better reform deposit insurance you better withdraw deposit insurance and Franklin Roosevelt knew this because there was there was experiments with state deposit insurance schemes in the 1910s and 20s and about a third of the states put in those ski and they all went bust precisely because the banks became too risky so Franklin Roosevelt knew that he'd wanted to eat a lot so I'll tell you the story sometime about why he signed it because of logrolling okay so that's it so those are two polar models I believe if you look at the first model that's the model that inspired the Fed and inspires with Draghi to bail out everything in sight because they think with what they see they ignore they're ignoring the moral hazard and the effects of incentives down the line and they think if you can stop a run you would be welfare improving and the danger is that model leads out the moral hazard and the adverse incentives so if you bail out somebody once might you have to bail them out again okay so now I'll just conclude by saying what are our tools and why I'm here trying to learn something at this conference well our tulip turn is a stochastic process that's why is it a joint density it's gonna be indexed by some parameters theta and I learned this phrase here in several seminars what some people call the inverse problem is I have some data and I want to back out I want to make inferences about theta and I see picked some papers and other subjects they're exactly the tools we want to use and that's why we have things to learn from you what's one of our tools a Markov process and then finding the states in art and then two of our tools are sequential analysis we're going to convert a problem in a in a stochastic process to a recursive representation of that stochastic process some functions of which map today and tomorrow today and some shocks in tomorrow Abraham Wald and Richard bellman invented us and our estimation method is to get either to be maximum likely or Bayesian same things I said see Caracas I find it really encouraging what's our tool a bellman equation it's a functional equation I'll just tell you for me that's a person that's what I mean by a person you know my wife would say that's just like you so what V is these ants are visa so dynamic programming is a big Bluff it's a big Bluff that turns out to be okay v of X is the optimum value of the problem starting from X so I pretend like I know that answer and then it turns out that's the answer today and then but then that's going to be related star means a next period value that's a functional equation that's the same V on the left and the right and have to solve that so so for for problems where that's kind of a single that's our canonical problem it's to be solved for a function I've learned a lot of things about how to solve that I'm better at solving that today than I was two days ago or I know how to get better okay so this problem is is paralyzed able because you have to repeatedly solve this Optima problem and you can you can you can naturally you got to solve it for a whole bunch of axis which acts as you saw there's some art and a science I learned a lot about that she got us all that and there's the curse of dimensionality what impedes us from sauce bigger models is it many of our problems have naturally big states the curse of dimensionality is this gets harder to solve the bigger these are and that's one of the frontiers I'm learning about here so that's a bellman equation now let me show you something that really that I really like one more minute this is called dynamic programming squared and for financial crisis you want to I made this term up nobody else uses this term for financial crisis we want to solve dynamic programming square process those are bellman equations that have bellman equation inside them and the interior bellman equations capture the incentive effects of people whose incentives are affected by government policies so these are that looks like double-talk right so I'll show you a bellman equation a dynamic programming squared so the V that's a set of these the same V I wrote down below you know that there's a dense that the transition density that's my functional equation but that little V that's that's the the V of a citizen the Big W is the value function for a government it's doing some policy well one of the state variables are they vector in the Big W is that and that's kind of a that's kind of the value okay so you look at that what the policy maker is actually going to do is going to choose the continuation value of the other guys subject to that equation now that equation is beautiful because it's going forward it's looking forward and that's one of the frontier things so and I've learned how to solve that better from some people here and I expect to learn more in the coming days so thanks for I was funny we have time for one or two questions so are there any comments questions question in my opinion yeah so this is what my friend Lars Hanson I do is what validates or tells you how to revise it in a better direction which is more often so I'll do meant I'll often do maximum likelihood we do one of these inverse problems and then if I do a maximum likelihood I'll do a likelihood ratio test against some kind of alternatives and then I'll look at directions in which I'm failing if I if I succeed I'll try to apply to model I'll usually fail and I'll try to find directions in which I can improve the model so I like it that's a great quick okay so make sure understand ah there's layers of this sorry so here's what we're going to do so here's kind of the program so you saw something so what we're gonna do is for a given government policy for a given government policy we're gonna actually when we do historical data that given government's policy is the kind of one that governed the data historically we're gonna do a rational expectations equilibrium so we're gonna go for a fixed point for that now what you said is if I'm going to change the government the policy design problem is I'm going to change the government policy now I'm going to have to have recompute a fixed point and now some things could happen there might be multiple fix points so there might be none it could happen there's an existence and uniqueness question if there's none it's a question is are you sure that policies as coherent as you thought if there's multiple okay now I'm in a run situation so it's a machine for for attacking that and and all those things possible is that you kind of hinted at are there

Channel: cscsch

Views: 9,714

Rating: 5 out of 5

Keywords: CSCS, HPC, Economics (Field Of Study)

Id: VM7UtaR5wHw

Length: 52min 48sec (3168 seconds)

Published: Tue Jun 09 2015