随机金融网络：流动性注入与关键参与者的价值

[SQUEAKING] [RUSTLING] [CLICKING] ROBERT M. TOWNSEND: So let me just say from the beginning, there are some connections between the lecture today and the one last time, and I will try to point that out. And then there's a missing third lecture. If time permits, I will kind of outline that at the end of today, but let's see how it goes with these slides first. So this is stochastic financial networks, liquidity and the value of key players versus contagion dynamics.

Or to put it succinctly, do we enhance or limit markets? So here's an outline. Introduction to stochastic financial networks, showing you how markets vary over time and in principle with other shocks. I'll lay out the economic environment. We'll define a stochastic financial network with examples. Anyone who participates at all is in a centralized market and otherwise isolated, and in the second, the markets fragment.

They're partitioned. And then we'll think about ex-ante injections of liquidities as buffers against shocks, and in particular try to pinpoint who would be the most valued person to receive the injection of liquidity to carry it into subsequent markets in which that agent participates. And so we'll characterize the most valued player in that sense, in the baseline environment, and also for a more general class of environments.

And then we'll do some positive economics. What does this value correspond with in financial markets, go to Thai villages you've seen before and do some empirical work to see how well the theory is holding up, at least at an initial level, and end with financial centrality and contagion, disease, systemic risk. And the point is to compare and contrast the market making aspect of judiciously chosen liquidity injections with what is the current policy framework, which is to limit the interactions across players due to this concern about financial contagion.

All right. So I should say from the outset that when these slides were written and the draft of the paper, we were referring to our measure of the value of liquidity for key players as a measure of financial centrality. That has caused confusion because people associate financial centrality and network financial centrality with the contagion point of view. Our measure is not equivalent with other measures of financial centrality, and I'll show you that.

We are going to change the wording to be liquidity value of a player, rather than the financial centrality of a player. But I can't change the slides that quickly, so we're kind of stuck with it for today. The main thing here is to talk about disruption to markets. Disruptions take the form of shocks that limit market participation. There is a literature, at least three literatures, one a very famous paper by Darrell Duffie and coauthors having to do with over-the-counter markets, which has a search friction aspect to it and has to do with the broker-dealer markups and the volume of trade that can be supported.

And you may or not be familiar with a class of monetary models in which traders meet at random. There's a supplier of good and a potential buyer of a good, and then the issue is what to carry around with you to facilitate trade. Kyotki and Wright and others are born into that way of thinking, and it's quite influential. The point here is, again, we have this kind of random matching. And I should say, we've been studying partitioned setups almost from the get-go in this class.

Granted, deterministic pairings, but not everybody was paired with it, matched with everybody else all the time. And finally, we have this explicit random market participation, where there's a kind of borrowing and lending market, but some of the participants leave early, others arrive late, and this was used to model the need for the Federal Reserve to inject liquidity into the system. It's based on much earlier work of Milton Freeman and the need for the Federal Reserve to manage liquidity, which is by the logo on the door.

As you go into the New York Fed, it has this quote. It's not about full employment. It's not about price stability. The Fed was set up to manage these liquidity shortages. Financial centrality or liquidity value is the marginal social value of giving a little bit more purchasing power or goods to an agent, conditioned on that agent being able to trade with other people. So you don't carry the liquidity into autarky. It's of no use for it.

You can think of it as like a financial instrument that you can trade. It's a social point of view, and I've emphasized this before when we talk about money, what is the purpose of money. Here, quote, "The liquidity is to enhance the social value." So you give resources to an agent, which not only increases her consumption, but the consumption of other agents that trade with the recipient. And we'll formalize this. It's also possible that markets not only suffer from these exogenous shocks that determine who's in the market, but that, in addition to that, people can decide endogenously whether to go to the market or be attentive to get online and so on.

And it could, in principle, go either way. But intuitively, by subsidizing an agent who carries liquidity into the market, that may make the market more attractive to other agents who otherwise would bear a participation cost. So you can get these externality-like aspects going on, but we will formally model what we mean by community value. So here's a actually pretty well-known picture of interbank market, federal funds markets back in 2006.

So these are banks who are deficient or have excess reserves, and they're borrowing and lending with each other. But here, the point is breaking a typical day down into half-an-hour intervals, although not everything is shown here. And you can see, at the beginning and end of day, we have these classic kind of network pictures of who was trading with whom, and the market's thin. On the other hand, midday and so on, it's a much denser graph.

Now, this shows variation over time, so it doesn't really show you the shocks. But you could well imagine that if you picked a particular interview-- interval of time and looked at different days, you would see the extent of this kind of varying over time, which could be due to endogenous participation as well as potentially to shocks. A side note that I hope we can come back toward the end of class, people don't show pictures of the federal funds market anymore because it's essentially collapsed.

There's so much liquidity in the system that the banks don't really borrow and lend with each other, and instead there is an active repo market where you have money market mutual funds with excess liquidity, in other words, not commercial banks, a different type of player, effectively lending to hedge funds and pension funds over a very brief amount of time. And "repo" refers to the collateral, which is backing the loans.

So that's the principal. The repo market has become the principal venue for Federal Reserve monetary policy, not tracking the Fed funds rate anymore. STUDENT: What are the colors in the-- [INAUDIBLE] different colors? ROBERT M. TOWNSEND: Yeah, I don't know. Good question. It makes it look nice. It must have a meaning. I'll try to go back and find it. Oh, and this may remind you a bit of the network pictures that Tomaž was showing last time, but they're just nodes, and the edges here refer to trades.

So what's the underlying environment? It's a risk sharing environment. And I did show you a couple of slides on the third lecture about what is a reason for intervening or not, and how well do we do in accommodating risk. And I referred in one slide to Thai villages and another slide to Indian villages. And we'll do more of that later in 193. But here, it's all self-contained and laid out. So there's a finite number of agents, capital I.

The number of agents is little n. They are risk-averse agents with a concave utility function, strictly. Agents maximize expected utility by choices of