WEBVTT 00:00:00.000 --> 00:00:01.960 align:middle line:90% [SQUEAKING] 00:00:01.960 --> 00:00:02.460 align:middle line:90% 00:00:02.460 --> 00:00:03.930 align:middle line:90% [RUSTLING] 00:00:03.930 --> 00:00:05.400 align:middle line:90% [CLICKING] 00:00:05.400 --> 00:00:10.443 align:middle line:90% 00:00:10.443 --> 00:00:12.860 align:middle line:84% ROBERT M. TOWNSEND: So let me just say from the beginning, 00:00:12.860 --> 00:00:15.560 align:middle line:84% there are some connections between the lecture 00:00:15.560 --> 00:00:20.880 align:middle line:84% today and the one last time, and I will try to point that out. 00:00:20.880 --> 00:00:25.600 align:middle line:84% And then there's a missing third lecture. 00:00:25.600 --> 00:00:29.720 align:middle line:84% If time permits, I will kind of outline that 00:00:29.720 --> 00:00:31.600 align:middle line:84% at the end of today, but let's see how it 00:00:31.600 --> 00:00:33.580 align:middle line:90% goes with these slides first. 00:00:33.580 --> 00:00:38.880 align:middle line:84% So this is stochastic financial networks, liquidity 00:00:38.880 --> 00:00:43.480 align:middle line:84% and the value of key players versus contagion dynamics. 00:00:43.480 --> 00:00:50.800 align:middle line:84% Or to put it succinctly, do we enhance or limit markets? 00:00:50.800 --> 00:00:52.960 align:middle line:90% So here's an outline. 00:00:52.960 --> 00:00:56.440 align:middle line:84% Introduction to stochastic financial networks, 00:00:56.440 --> 00:00:59.850 align:middle line:84% showing you how markets vary over time and in principle 00:00:59.850 --> 00:01:02.210 align:middle line:90% with other shocks. 00:01:02.210 --> 00:01:04.230 align:middle line:84% I'll lay out the economic environment. 00:01:04.230 --> 00:01:08.850 align:middle line:84% We'll define a stochastic financial network with examples. 00:01:08.850 --> 00:01:12.610 align:middle line:84% Anyone who participates at all is in a centralized market 00:01:12.610 --> 00:01:15.730 align:middle line:84% and otherwise isolated, and in the second, 00:01:15.730 --> 00:01:17.470 align:middle line:90% the markets fragment. 00:01:17.470 --> 00:01:19.010 align:middle line:90% They're partitioned. 00:01:19.010 --> 00:01:22.610 align:middle line:84% And then we'll think about ex-ante injections 00:01:22.610 --> 00:01:26.890 align:middle line:84% of liquidities as buffers against shocks, 00:01:26.890 --> 00:01:29.290 align:middle line:84% and in particular try to pinpoint 00:01:29.290 --> 00:01:33.650 align:middle line:84% who would be the most valued person 00:01:33.650 --> 00:01:36.050 align:middle line:84% to receive the injection of liquidity 00:01:36.050 --> 00:01:39.450 align:middle line:84% to carry it into subsequent markets in which that agent 00:01:39.450 --> 00:01:40.770 align:middle line:90% participates. 00:01:40.770 --> 00:01:44.050 align:middle line:84% And so we'll characterize the most valued player 00:01:44.050 --> 00:01:46.430 align:middle line:84% in that sense, in the baseline environment, 00:01:46.430 --> 00:01:51.130 align:middle line:84% and also for a more general class of environments. 00:01:51.130 --> 00:01:54.550 align:middle line:84% And then we'll do some positive economics. 00:01:54.550 --> 00:02:00.620 align:middle line:84% What does this value correspond with in financial markets, 00:02:00.620 --> 00:02:04.940 align:middle line:84% go to Thai villages you've seen before 00:02:04.940 --> 00:02:07.940 align:middle line:84% and do some empirical work to see how well the theory is 00:02:07.940 --> 00:02:11.660 align:middle line:84% holding up, at least at an initial level, 00:02:11.660 --> 00:02:16.340 align:middle line:84% and end with financial centrality and contagion, 00:02:16.340 --> 00:02:20.180 align:middle line:90% disease, systemic risk. 00:02:20.180 --> 00:02:23.940 align:middle line:84% And the point is to compare and contrast the market 00:02:23.940 --> 00:02:28.220 align:middle line:84% making aspect of judiciously chosen liquidity 00:02:28.220 --> 00:02:35.140 align:middle line:84% injections with what is the current policy framework, which 00:02:35.140 --> 00:02:38.980 align:middle line:84% is to limit the interactions across players 00:02:38.980 --> 00:02:43.520 align:middle line:84% due to this concern about financial contagion. 00:02:43.520 --> 00:02:46.180 align:middle line:90% 00:02:46.180 --> 00:02:46.720 align:middle line:90% All right. 00:02:46.720 --> 00:02:53.260 align:middle line:84% So I should say from the outset that when these slides were 00:02:53.260 --> 00:02:56.470 align:middle line:84% written and the draft of the paper, 00:02:56.470 --> 00:03:00.470 align:middle line:84% we were referring to our measure of the value of liquidity 00:03:00.470 --> 00:03:05.310 align:middle line:84% for key players as a measure of financial centrality. 00:03:05.310 --> 00:03:09.950 align:middle line:84% That has caused confusion because people associate 00:03:09.950 --> 00:03:13.670 align:middle line:84% financial centrality and network financial centrality 00:03:13.670 --> 00:03:16.510 align:middle line:84% with the contagion point of view. 00:03:16.510 --> 00:03:19.990 align:middle line:84% Our measure is not equivalent with other measures 00:03:19.990 --> 00:03:23.490 align:middle line:84% of financial centrality, and I'll show you that. 00:03:23.490 --> 00:03:26.190 align:middle line:84% We are going to change the wording 00:03:26.190 --> 00:03:32.930 align:middle line:84% to be liquidity value of a player, 00:03:32.930 --> 00:03:36.550 align:middle line:84% rather than the financial centrality of a player. 00:03:36.550 --> 00:03:39.010 align:middle line:84% But I can't change the slides that quickly, 00:03:39.010 --> 00:03:41.910 align:middle line:84% so we're kind of stuck with it for today. 00:03:41.910 --> 00:03:46.790 align:middle line:84% The main thing here is to talk about disruption to markets. 00:03:46.790 --> 00:03:50.590 align:middle line:84% Disruptions take the form of shocks that 00:03:50.590 --> 00:03:53.870 align:middle line:90% limit market participation. 00:03:53.870 --> 00:03:58.720 align:middle line:84% There is a literature, at least three literatures, 00:03:58.720 --> 00:04:01.800 align:middle line:84% one a very famous paper by Darrell Duffie 00:04:01.800 --> 00:04:06.520 align:middle line:84% and coauthors having to do with over-the-counter markets, which 00:04:06.520 --> 00:04:08.720 align:middle line:84% has a search friction aspect to it 00:04:08.720 --> 00:04:13.200 align:middle line:84% and has to do with the broker-dealer markups 00:04:13.200 --> 00:04:17.040 align:middle line:84% and the volume of trade that can be supported. 00:04:17.040 --> 00:04:22.880 align:middle line:84% And you may or not be familiar with a class of monetary models 00:04:22.880 --> 00:04:26.020 align:middle line:90% in which traders meet at random. 00:04:26.020 --> 00:04:32.100 align:middle line:84% There's a supplier of good and a potential buyer of a good, 00:04:32.100 --> 00:04:34.160 align:middle line:84% and then the issue is what to carry around 00:04:34.160 --> 00:04:36.920 align:middle line:90% with you to facilitate trade. 00:04:36.920 --> 00:04:41.020 align:middle line:84% Kyotki and Wright and others are born into that way of thinking, 00:04:41.020 --> 00:04:43.380 align:middle line:90% and it's quite influential. 00:04:43.380 --> 00:04:45.280 align:middle line:84% The point here is, again, we have 00:04:45.280 --> 00:04:46.900 align:middle line:90% this kind of random matching. 00:04:46.900 --> 00:04:51.200 align:middle line:84% And I should say, we've been studying partitioned setups 00:04:51.200 --> 00:04:55.090 align:middle line:84% almost from the get-go in this class. 00:04:55.090 --> 00:04:57.530 align:middle line:84% Granted, deterministic pairings, but not 00:04:57.530 --> 00:05:01.410 align:middle line:84% everybody was paired with it, matched with everybody else 00:05:01.410 --> 00:05:02.230 align:middle line:90% all the time. 00:05:02.230 --> 00:05:06.010 align:middle line:84% And finally, we have this explicit random market 00:05:06.010 --> 00:05:09.810 align:middle line:84% participation, where there's a kind of borrowing and lending 00:05:09.810 --> 00:05:12.570 align:middle line:84% market, but some of the participants 00:05:12.570 --> 00:05:15.770 align:middle line:84% leave early, others arrive late, and this 00:05:15.770 --> 00:05:19.450 align:middle line:84% was used to model the need for the Federal Reserve 00:05:19.450 --> 00:05:22.070 align:middle line:84% to inject liquidity into the system. 00:05:22.070 --> 00:05:25.690 align:middle line:84% It's based on much earlier work of Milton Freeman 00:05:25.690 --> 00:05:28.610 align:middle line:84% and the need for the Federal Reserve 00:05:28.610 --> 00:05:32.230 align:middle line:84% to manage liquidity, which is by the logo on the door. 00:05:32.230 --> 00:05:36.290 align:middle line:84% As you go into the New York Fed, it has this quote. 00:05:36.290 --> 00:05:38.490 align:middle line:90% It's not about full employment. 00:05:38.490 --> 00:05:40.770 align:middle line:90% It's not about price stability. 00:05:40.770 --> 00:05:44.670 align:middle line:84% The Fed was set up to manage these liquidity shortages. 00:05:44.670 --> 00:05:49.050 align:middle line:90% 00:05:49.050 --> 00:05:52.660 align:middle line:84% Financial centrality or liquidity value 00:05:52.660 --> 00:05:55.980 align:middle line:84% is the marginal social value of giving a little bit 00:05:55.980 --> 00:06:00.700 align:middle line:84% more purchasing power or goods to an agent, conditioned 00:06:00.700 --> 00:06:04.340 align:middle line:84% on that agent being able to trade with other people. 00:06:04.340 --> 00:06:07.040 align:middle line:84% So you don't carry the liquidity into autarky. 00:06:07.040 --> 00:06:09.200 align:middle line:90% It's of no use for it. 00:06:09.200 --> 00:06:11.660 align:middle line:84% You can think of it as like a financial instrument 00:06:11.660 --> 00:06:14.300 align:middle line:90% that you can trade. 00:06:14.300 --> 00:06:17.180 align:middle line:84% It's a social point of view, and I've emphasized this 00:06:17.180 --> 00:06:20.860 align:middle line:84% before when we talk about money, what is the purpose of money. 00:06:20.860 --> 00:06:25.280 align:middle line:84% Here, quote, "The liquidity is to enhance the social value." 00:06:25.280 --> 00:06:28.060 align:middle line:84% So you give resources to an agent, 00:06:28.060 --> 00:06:31.580 align:middle line:84% which not only increases her consumption, 00:06:31.580 --> 00:06:34.380 align:middle line:84% but the consumption of other agents 00:06:34.380 --> 00:06:38.740 align:middle line:90% that trade with the recipient. 00:06:38.740 --> 00:06:41.740 align:middle line:90% And we'll formalize this. 00:06:41.740 --> 00:06:44.900 align:middle line:84% It's also possible that markets not only 00:06:44.900 --> 00:06:48.180 align:middle line:84% suffer from these exogenous shocks that 00:06:48.180 --> 00:06:52.690 align:middle line:84% determine who's in the market, but that, in addition to that, 00:06:52.690 --> 00:06:56.310 align:middle line:84% people can decide endogenously whether to go to the market 00:06:56.310 --> 00:06:59.590 align:middle line:84% or be attentive to get online and so on. 00:06:59.590 --> 00:07:02.330 align:middle line:84% And it could, in principle, go either way. 00:07:02.330 --> 00:07:07.790 align:middle line:84% But intuitively, by subsidizing an agent who carries liquidity 00:07:07.790 --> 00:07:12.070 align:middle line:84% into the market, that may make the market more attractive 00:07:12.070 --> 00:07:16.650 align:middle line:84% to other agents who otherwise would bear a participation cost. 00:07:16.650 --> 00:07:22.230 align:middle line:84% So you can get these externality-like aspects going 00:07:22.230 --> 00:07:28.650 align:middle line:84% on, but we will formally model what we mean by community value. 00:07:28.650 --> 00:07:33.390 align:middle line:84% So here's a actually pretty well-known picture 00:07:33.390 --> 00:07:39.750 align:middle line:84% of interbank market, federal funds markets back in 2006. 00:07:39.750 --> 00:07:43.950 align:middle line:84% So these are banks who are deficient or have 00:07:43.950 --> 00:07:47.920 align:middle line:84% excess reserves, and they're borrowing and lending 00:07:47.920 --> 00:07:49.800 align:middle line:90% with each other. 00:07:49.800 --> 00:07:55.240 align:middle line:84% But here, the point is breaking a typical day down 00:07:55.240 --> 00:07:58.440 align:middle line:84% into half-an-hour intervals, although not everything 00:07:58.440 --> 00:07:59.840 align:middle line:90% is shown here. 00:07:59.840 --> 00:08:04.180 align:middle line:84% And you can see, at the beginning and end of day, 00:08:04.180 --> 00:08:09.360 align:middle line:84% we have these classic kind of network pictures 00:08:09.360 --> 00:08:14.440 align:middle line:84% of who was trading with whom, and the market's thin. 00:08:14.440 --> 00:08:21.800 align:middle line:84% On the other hand, midday and so on, it's a much denser graph. 00:08:21.800 --> 00:08:26.400 align:middle line:84% Now, this shows variation over time, 00:08:26.400 --> 00:08:29.960 align:middle line:84% so it doesn't really show you the shocks. 00:08:29.960 --> 00:08:32.840 align:middle line:84% But you could well imagine that if you 00:08:32.840 --> 00:08:36.640 align:middle line:84% picked a particular interview-- interval of time 00:08:36.640 --> 00:08:38.240 align:middle line:84% and looked at different days, you 00:08:38.240 --> 00:08:43.320 align:middle line:84% would see the extent of this kind of varying 00:08:43.320 --> 00:08:46.610 align:middle line:84% over time, which could be due to endogenous participation 00:08:46.610 --> 00:08:50.530 align:middle line:84% as well as potentially to shocks. 00:08:50.530 --> 00:08:52.610 align:middle line:84% A side note that I hope we can come back 00:08:52.610 --> 00:08:55.170 align:middle line:84% toward the end of class, people don't 00:08:55.170 --> 00:08:57.210 align:middle line:84% show pictures of the federal funds market 00:08:57.210 --> 00:09:01.170 align:middle line:84% anymore because it's essentially collapsed. 00:09:01.170 --> 00:09:03.890 align:middle line:84% There's so much liquidity in the system 00:09:03.890 --> 00:09:07.930 align:middle line:84% that the banks don't really borrow and lend with each other, 00:09:07.930 --> 00:09:11.930 align:middle line:84% and instead there is an active repo market 00:09:11.930 --> 00:09:15.450 align:middle line:84% where you have money market mutual funds 00:09:15.450 --> 00:09:18.610 align:middle line:84% with excess liquidity, in other words, not 00:09:18.610 --> 00:09:20.210 align:middle line:84% commercial banks, a different type 00:09:20.210 --> 00:09:24.170 align:middle line:84% of player, effectively lending to hedge funds and pension 00:09:24.170 --> 00:09:30.350 align:middle line:84% funds over a very brief amount of time. 00:09:30.350 --> 00:09:32.390 align:middle line:84% And "repo" refers to the collateral, 00:09:32.390 --> 00:09:35.650 align:middle line:90% which is backing the loans. 00:09:35.650 --> 00:09:37.230 align:middle line:90% So that's the principal. 00:09:37.230 --> 00:09:42.650 align:middle line:84% The repo market has become the principal venue 00:09:42.650 --> 00:09:45.900 align:middle line:84% for Federal Reserve monetary policy, 00:09:45.900 --> 00:09:50.860 align:middle line:84% not tracking the Fed funds rate anymore. 00:09:50.860 --> 00:09:54.312 align:middle line:84% STUDENT: What are the colors in the-- 00:09:54.312 --> 00:09:55.520 align:middle line:90% [INAUDIBLE] different colors? 00:09:55.520 --> 00:09:57.300 align:middle line:84% ROBERT M. TOWNSEND: Yeah, I don't know. 00:09:57.300 --> 00:09:58.820 align:middle line:90% Good question. 00:09:58.820 --> 00:10:01.620 align:middle line:90% It makes it look nice. 00:10:01.620 --> 00:10:02.960 align:middle line:90% It must have a meaning. 00:10:02.960 --> 00:10:06.700 align:middle line:90% I'll try to go back and find it. 00:10:06.700 --> 00:10:11.900 align:middle line:84% Oh, and this may remind you a bit of the network pictures 00:10:11.900 --> 00:10:16.200 align:middle line:84% that Tomaž was showing last time, but they're just nodes, 00:10:16.200 --> 00:10:19.860 align:middle line:84% and the edges here refer to trades. 00:10:19.860 --> 00:10:23.900 align:middle line:84% So what's the underlying environment? 00:10:23.900 --> 00:10:26.040 align:middle line:90% It's a risk sharing environment. 00:10:26.040 --> 00:10:30.340 align:middle line:84% And I did show you a couple of slides 00:10:30.340 --> 00:10:36.180 align:middle line:84% on the third lecture about what is a reason for intervening 00:10:36.180 --> 00:10:40.420 align:middle line:84% or not, and how well do we do in accommodating risk. 00:10:40.420 --> 00:10:44.510 align:middle line:84% And I referred in one slide to Thai villages and another slide 00:10:44.510 --> 00:10:49.030 align:middle line:90% to Indian villages. 00:10:49.030 --> 00:10:54.470 align:middle line:84% And we'll do more of that later in 193. 00:10:54.470 --> 00:10:56.970 align:middle line:84% But here, it's all self-contained and laid out. 00:10:56.970 --> 00:10:59.490 align:middle line:84% So there's a finite number of agents, 00:10:59.490 --> 00:11:03.230 align:middle line:84% capital I. The number of agents is little n. 00:11:03.230 --> 00:11:08.810 align:middle line:84% They are risk-averse agents with a concave utility function, 00:11:08.810 --> 00:11:10.470 align:middle line:90% strictly. 00:11:10.470 --> 00:11:17.350 align:middle line:84% Agents maximize expected utility by choices of various things, 00:11:17.350 --> 00:11:23.430 align:middle line:84% and they have random incomes, so of the n guys, this vector 1 00:11:23.430 --> 00:11:29.370 align:middle line:84% through n of realized incomes drawn from some distribution. 00:11:29.370 --> 00:11:33.270 align:middle line:84% So that's one of the fundamental shocks in the system, 00:11:33.270 --> 00:11:36.910 align:middle line:90% exogenous random endowments. 00:11:36.910 --> 00:11:41.560 align:middle line:84% An example would be these constant absolute risk-averse 00:11:41.560 --> 00:11:47.400 align:middle line:84% utility functions, which are basically exponential, 00:11:47.400 --> 00:11:52.420 align:middle line:84% coupled with parameterized risk distributions, 00:11:52.420 --> 00:11:57.080 align:middle line:84% so that this vector of incomes has 00:11:57.080 --> 00:12:02.040 align:middle line:84% a mean mu vector in [? RN, ?] and 00:12:02.040 --> 00:12:07.360 align:middle line:84% this variance-covariance matrix, which is an n by n matrix 00:12:07.360 --> 00:12:10.160 align:middle line:84% that captures the correlation of one person's income 00:12:10.160 --> 00:12:14.360 align:middle line:90% with any other person's income. 00:12:14.360 --> 00:12:17.858 align:middle line:84% So let's look at the other shock, 00:12:17.858 --> 00:12:20.400 align:middle line:84% and we're going to treat it like an income shock in the sense 00:12:20.400 --> 00:12:23.240 align:middle line:84% that it's an exogenous random shock. 00:12:23.240 --> 00:12:27.680 align:middle line:84% We want to enumerate all possible shocks to the economy. 00:12:27.680 --> 00:12:35.060 align:middle line:84% This xi, this guy here, is a vector of them over the n guys, 00:12:35.060 --> 00:12:37.220 align:middle line:90% and they take on binary values. 00:12:37.220 --> 00:12:38.820 align:middle line:90% They're either 0 or 1. 00:12:38.820 --> 00:12:42.730 align:middle line:84% 0 obviously means not in the market. 00:12:42.730 --> 00:12:44.710 align:middle line:90% 1 means in the market. 00:12:44.710 --> 00:12:47.505 align:middle line:90% 00:12:47.505 --> 00:12:49.130 align:middle line:84% When they're not in the market, they're 00:12:49.130 --> 00:12:52.850 align:middle line:90% doomed to just eat their income. 00:12:52.850 --> 00:12:58.570 align:middle line:84% But when they are in the market, they may be able to share risk, 00:12:58.570 --> 00:13:04.330 align:middle line:84% the income risk, subject to the resource constraint that agents 00:13:04.330 --> 00:13:09.750 align:middle line:84% who are in the market cannot eat more, in the aggregate, 00:13:09.750 --> 00:13:13.890 align:middle line:84% than the amount of income that's available in the aggregate. 00:13:13.890 --> 00:13:16.830 align:middle line:84% So those xi's are just zeros or ones, 00:13:16.830 --> 00:13:19.370 align:middle line:84% so we're adding up over everyone. 00:13:19.370 --> 00:13:23.470 align:middle line:84% But the guys who aren't in the market are getting a 0 xi, 00:13:23.470 --> 00:13:27.330 align:middle line:84% so they're really not in that constraint. 00:13:27.330 --> 00:13:31.130 align:middle line:84% So what's the community objective here 00:13:31.130 --> 00:13:35.890 align:middle line:84% is to maximize expected utility to maximize 00:13:35.890 --> 00:13:39.420 align:middle line:84% lambda weighted expected utilities, where 00:13:39.420 --> 00:13:42.660 align:middle line:84% the expectations over the underlying income shocks 00:13:42.660 --> 00:13:46.380 align:middle line:84% as well as over the market participation shocks. 00:13:46.380 --> 00:13:49.860 align:middle line:84% And the choice variables are consumption, 00:13:49.860 --> 00:13:51.380 align:middle line:84% and again, if you're alone, you're 00:13:51.380 --> 00:13:53.360 align:middle line:90% doomed to eat your income. 00:13:53.360 --> 00:13:57.740 align:middle line:84% But otherwise there is this resource constraint repeated out 00:13:57.740 --> 00:14:04.560 align:middle line:84% here that applies for all possible configurations. 00:14:04.560 --> 00:14:09.260 align:middle line:84% No matter what the realized income and market participation 00:14:09.260 --> 00:14:13.440 align:middle line:84% shocks are, you cannot violate the resource constraint. 00:14:13.440 --> 00:14:16.500 align:middle line:84% So there's a whole series of these guys 00:14:16.500 --> 00:14:21.860 align:middle line:84% depending on the xi vector and the y vector. 00:14:21.860 --> 00:14:25.500 align:middle line:84% Yeah, so the idea of choosing consumption is to pool risk, 00:14:25.500 --> 00:14:26.000 align:middle line:90% right? 00:14:26.000 --> 00:14:29.720 align:middle line:84% So ex-ante, for example, and we'll look at it. 00:14:29.720 --> 00:14:33.300 align:middle line:84% It's a very special case, but it's intuitive. 00:14:33.300 --> 00:14:34.600 align:middle line:90% Everybody's all alike. 00:14:34.600 --> 00:14:37.110 align:middle line:90% They have concave utility. 00:14:37.110 --> 00:14:39.010 align:middle line:90% Incomes could be high or low. 00:14:39.010 --> 00:14:41.390 align:middle line:90% They're drawn at random. 00:14:41.390 --> 00:14:42.950 align:middle line:84% Ex-ante, you don't know if you're 00:14:42.950 --> 00:14:45.010 align:middle line:84% going to be on the high side or the low side, 00:14:45.010 --> 00:14:48.150 align:middle line:84% so you enter into a mutual agreement 00:14:48.150 --> 00:14:53.590 align:middle line:84% that if one of the realizations is one person is high 00:14:53.590 --> 00:14:56.030 align:middle line:84% and the other is low, then the high person 00:14:56.030 --> 00:14:59.910 align:middle line:84% is going to give up purchasing power to the low guy, 00:14:59.910 --> 00:15:02.630 align:middle line:90% and vice versa. 00:15:02.630 --> 00:15:05.090 align:middle line:84% If they're, in this case, both high or both low, 00:15:05.090 --> 00:15:07.350 align:middle line:84% there's not much you can do, and that's 00:15:07.350 --> 00:15:11.270 align:middle line:90% kind of the aggregate state. 00:15:11.270 --> 00:15:15.750 align:middle line:84% So let's start talking about the network aspect of this, 00:15:15.750 --> 00:15:19.510 align:middle line:84% refer to a centralized market you're in or not, 00:15:19.510 --> 00:15:22.510 align:middle line:84% and I'll come back to these bilateral connections 00:15:22.510 --> 00:15:24.730 align:middle line:84% when we get to the relevant slide. 00:15:24.730 --> 00:15:27.670 align:middle line:90% So let's look at an example. 00:15:27.670 --> 00:15:33.270 align:middle line:84% We have a network given, and these participation shocks 00:15:33.270 --> 00:15:35.660 align:middle line:90% are modeled as a process. 00:15:35.660 --> 00:15:41.400 align:middle line:84% So it's as if one node in the network, one trader, 00:15:41.400 --> 00:15:46.240 align:middle line:84% is randomly chosen to be the host with some probability, 00:15:46.240 --> 00:15:49.860 align:middle line:84% maybe just 1 over n, that everyone is equally chosen, 00:15:49.860 --> 00:15:52.560 align:middle line:84% or it could be pretty special, and then 00:15:52.560 --> 00:15:57.380 align:middle line:84% that host is sending out messages to other traders. 00:15:57.380 --> 00:16:01.340 align:middle line:84% And if they get the message, let's just say for simplicity, 00:16:01.340 --> 00:16:04.760 align:middle line:84% they join with the host and have a party. 00:16:04.760 --> 00:16:07.760 align:middle line:90% They're in a market. 00:16:07.760 --> 00:16:10.580 align:middle line:84% You do see this process in actual markets. 00:16:10.580 --> 00:16:14.880 align:middle line:84% You'll see, especially now with the internet, 00:16:14.880 --> 00:16:20.480 align:middle line:84% you have someone with something to sell, 00:16:20.480 --> 00:16:24.440 align:middle line:84% and they'll send out invitations. 00:16:24.440 --> 00:16:28.440 align:middle line:84% It's good for 10 minutes, and whoever shows up 00:16:28.440 --> 00:16:31.100 align:middle line:84% can potentially bid for the asset. 00:16:31.100 --> 00:16:36.390 align:middle line:84% It's like a mini auction and it's very focused in time. 00:16:36.390 --> 00:16:39.590 align:middle line:84% And obviously, not everyone participates. 00:16:39.590 --> 00:16:41.790 align:middle line:84% So you start to get into these shocks. 00:16:41.790 --> 00:16:42.930 align:middle line:90% What is it? 00:16:42.930 --> 00:16:45.170 align:middle line:90% It could just be latency. 00:16:45.170 --> 00:16:48.290 align:middle line:84% We haven't even said what the frequency is here. 00:16:48.290 --> 00:16:53.540 align:middle line:84% I mean, these could be markets that are occurring every 10 00:16:53.540 --> 00:16:57.090 align:middle line:84% seconds, but with latency in computers 00:16:57.090 --> 00:17:01.070 align:middle line:84% and so on, there's a "technological reason," 00:17:01.070 --> 00:17:03.770 align:middle line:84% quote unquote, that not everybody receives 00:17:03.770 --> 00:17:09.290 align:middle line:84% the invitation, or at least they don't get it on a timely basis. 00:17:09.290 --> 00:17:12.730 align:middle line:84% STUDENT: If you receive an invitation and someone else 00:17:12.730 --> 00:17:15.710 align:middle line:84% also receives an invitation, can those two trade with each other? 00:17:15.710 --> 00:17:15.770 align:middle line:90% ROBERT M. TOWNSEND: Yeah. 00:17:15.770 --> 00:17:17.190 align:middle line:84% STUDENT: Or do they all just trade with the one-- 00:17:17.190 --> 00:17:19.349 align:middle line:84% they don't just trade with the one trader, then [INAUDIBLE]. 00:17:19.349 --> 00:17:20.807 align:middle line:84% ROBERT M. TOWNSEND: Yeah, the slide 00:17:20.807 --> 00:17:23.390 align:middle line:84% I skipped, you'll see it in the graph. 00:17:23.390 --> 00:17:26.210 align:middle line:90% They all trade with each other. 00:17:26.210 --> 00:17:29.930 align:middle line:84% Exactly how they do that, we'll come back to it. 00:17:29.930 --> 00:17:33.540 align:middle line:84% So with what probability do you get an invitation? 00:17:33.540 --> 00:17:36.560 align:middle line:84% Well, something to do, say, for example, 00:17:36.560 --> 00:17:40.740 align:middle line:84% with the distance of the two traders, in the sense of whether 00:17:40.740 --> 00:17:43.520 align:middle line:84% or not they're adjacent in the network map. 00:17:43.520 --> 00:17:47.280 align:middle line:84% Remember, we're taking as a primitive here the network. 00:17:47.280 --> 00:17:49.640 align:middle line:90% So let me show you the picture. 00:17:49.640 --> 00:17:54.780 align:middle line:84% Here's the network with the nodes and the edges. 00:17:54.780 --> 00:17:59.000 align:middle line:84% In this case, almost everyone's connected to everyone else. 00:17:59.000 --> 00:18:02.740 align:middle line:84% There's a few isolated things going on here. 00:18:02.740 --> 00:18:06.400 align:middle line:84% And then we see this network with the host, 00:18:06.400 --> 00:18:08.500 align:middle line:90% so that guy is chosen at random. 00:18:08.500 --> 00:18:12.620 align:middle line:84% And then he or she is sending out invitations, 00:18:12.620 --> 00:18:20.620 align:middle line:84% and the adjacent nodes are more likely, with probability q, 00:18:20.620 --> 00:18:23.060 align:middle line:90% to get the invite. 00:18:23.060 --> 00:18:29.790 align:middle line:84% If you're two nodes away, it's q squared, so it's diminishing. 00:18:29.790 --> 00:18:36.090 align:middle line:84% And this picture acts as if, after traversing three nodes, 00:18:36.090 --> 00:18:38.470 align:middle line:84% the probabilities are 0, but you can imagine 00:18:38.470 --> 00:18:40.210 align:middle line:90% that's just an approximation. 00:18:40.210 --> 00:18:43.170 align:middle line:84% Occasionally, you might get a q4, 00:18:43.170 --> 00:18:46.430 align:middle line:84% but not too many of them, and so on. 00:18:46.430 --> 00:18:50.070 align:middle line:84% So this is a market formation process 00:18:50.070 --> 00:18:54.670 align:middle line:84% emanating from some underlying fundamental network map. 00:18:54.670 --> 00:18:59.170 align:middle line:84% The obvious thing that comes to mind here is distance. 00:18:59.170 --> 00:19:02.590 align:middle line:84% And again, at this level of abstraction, it could be-- 00:19:02.590 --> 00:19:14.070 align:middle line:84% it could be geographic, in terms of who's adjacent to you or not. 00:19:14.070 --> 00:19:17.990 align:middle line:84% More generally, there could be some underlying characteristics 00:19:17.990 --> 00:19:23.830 align:middle line:84% that we're not modeling, some kind of affinity or similarity 00:19:23.830 --> 00:19:28.570 align:middle line:84% across agents that make some people close to you 00:19:28.570 --> 00:19:34.025 align:middle line:84% and easier to communicate with and other people further away. 00:19:34.025 --> 00:19:35.650 align:middle line:84% STUDENT: Could do equivalently to think 00:19:35.650 --> 00:19:38.290 align:middle line:84% about these distances being defined 00:19:38.290 --> 00:19:41.030 align:middle line:84% in terms of the probabilities of trading? 00:19:41.030 --> 00:19:45.290 align:middle line:84% Or is it important that the structure of the network 00:19:45.290 --> 00:19:46.590 align:middle line:90% implies these probabilities? 00:19:46.590 --> 00:19:47.490 align:middle line:90% It's not [INAUDIBLE] 00:19:47.490 --> 00:19:49.590 align:middle line:84% ROBERT M. TOWNSEND: The former is the main-- 00:19:49.590 --> 00:19:51.370 align:middle line:90% no, it doesn't matter. 00:19:51.370 --> 00:19:57.450 align:middle line:84% This is an example to show how you could have a network 00:19:57.450 --> 00:20:02.710 align:middle line:84% and that that will generate the stochastic market participation. 00:20:02.710 --> 00:20:05.970 align:middle line:84% What we need for the theory is only that market participation 00:20:05.970 --> 00:20:09.990 align:middle line:84% is random, and I'll show you another way of doing that. 00:20:09.990 --> 00:20:12.770 align:middle line:90% 00:20:12.770 --> 00:20:13.430 align:middle line:90% Oh, yeah. 00:20:13.430 --> 00:20:17.050 align:middle line:84% This is what's left after they're connected. 00:20:17.050 --> 00:20:18.910 align:middle line:90% I deleted some slides here. 00:20:18.910 --> 00:20:21.150 align:middle line:84% You can imagine the seed is this guy, 00:20:21.150 --> 00:20:23.450 align:middle line:84% and then you'll get a different picture 00:20:23.450 --> 00:20:25.350 align:middle line:90% of who's connected to whom. 00:20:25.350 --> 00:20:29.260 align:middle line:84% So this is the market chosen stochastically 00:20:29.260 --> 00:20:32.020 align:middle line:90% through that underlying process. 00:20:32.020 --> 00:20:33.940 align:middle line:90% Determined, I should have said. 00:20:33.940 --> 00:20:34.620 align:middle line:90% OK. 00:20:34.620 --> 00:20:37.260 align:middle line:84% More generally, you could think, not 00:20:37.260 --> 00:20:39.680 align:middle line:84% that everyone is either in or out of a market, 00:20:39.680 --> 00:20:43.460 align:middle line:84% but that they're getting divided into fragmented 00:20:43.460 --> 00:20:46.020 align:middle line:84% or getting divided into segments. 00:20:46.020 --> 00:20:49.020 align:middle line:84% So in this case, we have capital I here. 00:20:49.020 --> 00:20:50.680 align:middle line:90% It's the set of all agents. 00:20:50.680 --> 00:20:53.500 align:middle line:90% 00:20:53.500 --> 00:20:59.020 align:middle line:84% This power notation is the set of all subsets 00:20:59.020 --> 00:21:06.340 align:middle line:84% that you could form with n agents. 00:21:06.340 --> 00:21:11.820 align:middle line:84% And so this is a cluster, one subset, 00:21:11.820 --> 00:21:18.060 align:middle line:84% say, proper subset, of the set of possibilities of all of them. 00:21:18.060 --> 00:21:23.740 align:middle line:84% And their intersection is null, so they're partitioning 00:21:23.740 --> 00:21:26.130 align:middle line:90% themselves into these clusters. 00:21:26.130 --> 00:21:28.790 align:middle line:90% 00:21:28.790 --> 00:21:32.670 align:middle line:90% And this is a typo. 00:21:32.670 --> 00:21:37.990 align:middle line:84% So if you take the population in-- 00:21:37.990 --> 00:21:43.310 align:middle line:84% you're somewhere, maybe isolated, 00:21:43.310 --> 00:21:47.510 align:middle line:84% or paired or matched with other people, 00:21:47.510 --> 00:21:52.910 align:middle line:84% you'll get just a set of agents back at the end. 00:21:52.910 --> 00:21:58.430 align:middle line:84% So we're randomly partitioning the set of all traders here. 00:21:58.430 --> 00:22:01.070 align:middle line:84% So you could imagine we have a probability, 00:22:01.070 --> 00:22:05.830 align:middle line:84% to answer Laurel's question, we have a probability distribution 00:22:05.830 --> 00:22:07.950 align:middle line:90% over these clusters. 00:22:07.950 --> 00:22:11.990 align:middle line:84% Mu would be the probability of a particular cluster drawn 00:22:11.990 --> 00:22:14.910 align:middle line:90% from some known distribution. 00:22:14.910 --> 00:22:16.167 align:middle line:90% STUDENT: So what is k? 00:22:16.167 --> 00:22:17.750 align:middle line:84% If you just take the previous picture, 00:22:17.750 --> 00:22:20.770 align:middle line:84% you have either a group was chosen and the rest was out, 00:22:20.770 --> 00:22:23.200 align:middle line:84% and here we're picking a partition that contains 00:22:23.200 --> 00:22:24.360 align:middle line:90% possibly more than two? 00:22:24.360 --> 00:22:25.360 align:middle line:90% ROBERT M. TOWNSEND: Yes. 00:22:25.360 --> 00:22:27.120 align:middle line:84% STUDENT: And then that means that-- 00:22:27.120 --> 00:22:28.260 align:middle line:84% ROBERT M. TOWNSEND: Where did it go? 00:22:28.260 --> 00:22:30.343 align:middle line:84% STUDENT: What's the difference between the groups? 00:22:30.343 --> 00:22:32.400 align:middle line:84% ROBERT M. TOWNSEND: Here's a network, 00:22:32.400 --> 00:22:35.680 align:middle line:84% and then we have a random variable that chooses 00:22:35.680 --> 00:22:37.660 align:middle line:90% who is active in the network. 00:22:37.660 --> 00:22:44.760 align:middle line:84% And in this case, if you're concentrating, 00:22:44.760 --> 00:22:47.740 align:middle line:84% this guy, because this guy's not active, 00:22:47.740 --> 00:22:50.060 align:middle line:84% this guy's going to be completely isolated. 00:22:50.060 --> 00:22:51.560 align:middle line:90% These two are connected. 00:22:51.560 --> 00:22:53.440 align:middle line:84% STUDENT: Oh, those are the partitions. 00:22:53.440 --> 00:22:54.482 align:middle line:90% ROBERT M. TOWNSEND: Yeah. 00:22:54.482 --> 00:22:56.880 align:middle line:90% So these will end up being-- 00:22:56.880 --> 00:23:01.520 align:middle line:84% and likewise you could-- oh, and so now I'll answer your question 00:23:01.520 --> 00:23:05.680 align:middle line:90% about the dotted lines here. 00:23:05.680 --> 00:23:11.000 align:middle line:84% So if they're sharing risk and they're in a group, 00:23:11.000 --> 00:23:14.320 align:middle line:84% in this case, the group of three, 00:23:14.320 --> 00:23:18.920 align:middle line:84% we will determine the extent to which they're 00:23:18.920 --> 00:23:23.450 align:middle line:84% getting or giving consumption relative to their endowments. 00:23:23.450 --> 00:23:30.010 align:middle line:84% And you could well imagine that effectively they're 00:23:30.010 --> 00:23:32.070 align:middle line:84% all connected, all three with each other. 00:23:32.070 --> 00:23:39.010 align:middle line:84% This dotted line is a way of saying, don't burden me 00:23:39.010 --> 00:23:41.770 align:middle line:84% with the math of figuring out how much this guy should 00:23:41.770 --> 00:23:43.410 align:middle line:90% give to this guy. 00:23:43.410 --> 00:23:46.890 align:middle line:84% But likewise, you could imagine that they 00:23:46.890 --> 00:23:51.730 align:middle line:84% are perfectly able to achieve the optimal risk 00:23:51.730 --> 00:23:56.050 align:middle line:84% sharing just by going through the central node. 00:23:56.050 --> 00:24:00.850 align:middle line:84% Whereas last time, what Tomaž was emphasizing in the pictures 00:24:00.850 --> 00:24:08.810 align:middle line:84% was you're only connected bilaterally 00:24:08.810 --> 00:24:10.490 align:middle line:84% with the people who owe you money 00:24:10.490 --> 00:24:13.210 align:middle line:84% or to whom you owe money, although there 00:24:13.210 --> 00:24:17.170 align:middle line:84% was a multilateral aspect to it in the sense of forming 00:24:17.170 --> 00:24:19.830 align:middle line:84% those chains and those cycles here. 00:24:19.830 --> 00:24:22.260 align:middle line:84% We just kind cut to the chase and allow 00:24:22.260 --> 00:24:28.500 align:middle line:84% full interconnectedness among any subgroup. 00:24:28.500 --> 00:24:31.940 align:middle line:84% And it's really without loss of generality. 00:24:31.940 --> 00:24:37.300 align:middle line:84% So I skipped in order to answer [? Raffa's ?] question. 00:24:37.300 --> 00:24:39.040 align:middle line:90% So what are we doing? 00:24:39.040 --> 00:24:44.700 align:middle line:84% We're, again, maximizing utility subject to resource constraints. 00:24:44.700 --> 00:24:50.300 align:middle line:84% This is the resource constraint for a particular cluster, 00:24:50.300 --> 00:24:54.620 align:middle line:90% [? ML ?] in the previous slide. 00:24:54.620 --> 00:25:02.100 align:middle line:84% And yeah, somehow the notation is getting a little sparse here. 00:25:02.100 --> 00:25:04.740 align:middle line:84% So the relevant state is going to be 00:25:04.740 --> 00:25:07.860 align:middle line:84% income within this partition, although the larger 00:25:07.860 --> 00:25:15.660 align:middle line:84% state is the determination of these clusters, randomly chosen. 00:25:15.660 --> 00:25:17.420 align:middle line:84% So a stochastic financial network 00:25:17.420 --> 00:25:21.430 align:middle line:84% is a network formed by a collection of complete isolated 00:25:21.430 --> 00:25:22.370 align:middle line:90% subgraphs. 00:25:22.370 --> 00:25:28.550 align:middle line:90% 00:25:28.550 --> 00:25:33.550 align:middle line:84% So you can have the graph, which is given, 00:25:33.550 --> 00:25:38.270 align:middle line:84% characterized by the nodes and the edges. 00:25:38.270 --> 00:25:42.790 align:middle line:84% And we have links, in this case, not directed, undirected links. 00:25:42.790 --> 00:25:45.230 align:middle line:90% i and j are linked or not. 00:25:45.230 --> 00:25:48.910 align:middle line:84% There's an edge connecting them or not. 00:25:48.910 --> 00:25:54.250 align:middle line:84% And if there is, we say that the Gij is equal to 1, 00:25:54.250 --> 00:25:55.530 align:middle line:90% and otherwise it's 0. 00:25:55.530 --> 00:25:59.750 align:middle line:90% 00:25:59.750 --> 00:26:01.590 align:middle line:84% And then I went through these examples 00:26:01.590 --> 00:26:10.450 align:middle line:90% already, although I'm not sure-- 00:26:10.450 --> 00:26:16.430 align:middle line:90% 00:26:16.430 --> 00:26:22.000 align:middle line:84% this was one randomly chosen partition 00:26:22.000 --> 00:26:25.020 align:middle line:84% and this was a second randomly chosen partition. 00:26:25.020 --> 00:26:28.840 align:middle line:84% I think I cut myself off and didn't show this comparison 00:26:28.840 --> 00:26:32.800 align:middle line:84% slide, just to illustrate how very different the thickness 00:26:32.800 --> 00:26:36.880 align:middle line:84% of the market can be and who's participating and participating 00:26:36.880 --> 00:26:38.060 align:middle line:90% in which cluster. 00:26:38.060 --> 00:26:42.160 align:middle line:90% 00:26:42.160 --> 00:26:44.040 align:middle line:84% The international markets these days 00:26:44.040 --> 00:26:48.120 align:middle line:84% are becoming much more fragmented 00:26:48.120 --> 00:26:53.720 align:middle line:84% than they used to be, partly as a consequence of trade embargoes 00:26:53.720 --> 00:26:58.660 align:middle line:84% and financial sequestering of value, and so on. 00:26:58.660 --> 00:27:02.120 align:middle line:90% 00:27:02.120 --> 00:27:05.440 align:middle line:90% Just a comment. 00:27:05.440 --> 00:27:07.480 align:middle line:84% So financial centrality, let's think 00:27:07.480 --> 00:27:13.000 align:middle line:84% about the value of liquidity where we increase income 00:27:13.000 --> 00:27:19.890 align:middle line:84% by agent i by epsilon, where epsilon is a small number, just 00:27:19.890 --> 00:27:25.890 align:middle line:84% an infinitesimal variation around their income endowment. 00:27:25.890 --> 00:27:31.530 align:middle line:84% And we do it ex-ante before the market shocks are determined 00:27:31.530 --> 00:27:34.690 align:middle line:84% and before incomes are determined. 00:27:34.690 --> 00:27:37.570 align:middle line:84% So it's an ex-ante commitment to this named 00:27:37.570 --> 00:27:41.570 align:middle line:84% trader without knowing what exact situation she's 00:27:41.570 --> 00:27:42.750 align:middle line:90% going to be in. 00:27:42.750 --> 00:27:46.090 align:middle line:90% 00:27:46.090 --> 00:27:49.530 align:middle line:84% So a liquidity injection, in essence, 00:27:49.530 --> 00:27:52.890 align:middle line:90% is marginally increasing income. 00:27:52.890 --> 00:27:56.410 align:middle line:84% You could write it out a little bit more formally. 00:27:56.410 --> 00:27:59.790 align:middle line:84% Income is the sum of endowments plus assets. 00:27:59.790 --> 00:28:03.030 align:middle line:84% There's some asset which is very liquid. 00:28:03.030 --> 00:28:07.850 align:middle line:84% Its price is set to 1, so it converts into consumption goods 00:28:07.850 --> 00:28:10.450 align:middle line:90% on a 1 to 1 basis. 00:28:10.450 --> 00:28:15.340 align:middle line:84% And you have that asset set and the value of it 00:28:15.340 --> 00:28:18.720 align:middle line:84% as your starting income if you're in the market, 00:28:18.720 --> 00:28:21.320 align:middle line:90% But it's a liquid asset. 00:28:21.320 --> 00:28:27.100 align:middle line:84% So if you're in autarky, you don't have anyone to trade with. 00:28:27.100 --> 00:28:30.140 align:middle line:84% And this is equivalent with agent i 00:28:30.140 --> 00:28:32.620 align:middle line:84% having this initial asset position 00:28:32.620 --> 00:28:35.000 align:middle line:84% and then getting epsilon more of it. 00:28:35.000 --> 00:28:37.860 align:middle line:90% 00:28:37.860 --> 00:28:41.140 align:middle line:84% So you could think about it as money, 00:28:41.140 --> 00:28:45.980 align:middle line:84% except we're not really closing the model, "money," quote, 00:28:45.980 --> 00:28:50.480 align:middle line:84% from the Federal Reserve being arguably, if it's the US, 00:28:50.480 --> 00:28:53.140 align:middle line:90% a very liquid asset. 00:28:53.140 --> 00:28:56.380 align:middle line:84% When I say, not closing the model, 00:28:56.380 --> 00:28:59.580 align:middle line:84% if we gave out too much money, we'll 00:28:59.580 --> 00:29:02.340 align:middle line:84% start to influence the price level. 00:29:02.340 --> 00:29:07.780 align:middle line:84% But this experiment is starting with an infinitesimally small 00:29:07.780 --> 00:29:13.950 align:middle line:84% amount that would have virtually zero impact on the price level, 00:29:13.950 --> 00:29:20.690 align:middle line:84% with the goal of figuring out who are the valued players. 00:29:20.690 --> 00:29:23.630 align:middle line:90% 00:29:23.630 --> 00:29:26.930 align:middle line:84% The Fed does not do this explicitly. 00:29:26.930 --> 00:29:30.390 align:middle line:90% 00:29:30.390 --> 00:29:33.150 align:middle line:84% They intervene in the repo market 00:29:33.150 --> 00:29:43.190 align:middle line:84% by, say, lending liquidity, or they have market facilities 00:29:43.190 --> 00:29:51.850 align:middle line:84% that allow banks and so on to borrow a window from the Fed. 00:29:51.850 --> 00:29:54.390 align:middle line:84% But this is like saying, no, suppose 00:29:54.390 --> 00:29:57.190 align:middle line:84% a monetary authority were proactive and could 00:29:57.190 --> 00:30:02.890 align:middle line:84% identify these key players who bridge across other players. 00:30:02.890 --> 00:30:06.350 align:middle line:84% And the frequency of the shocks is so high 00:30:06.350 --> 00:30:12.340 align:middle line:84% that you can't wait for Silicon Valley Bank to do something bad. 00:30:12.340 --> 00:30:19.680 align:middle line:84% You've got to decide in advance, and so you could very well 00:30:19.680 --> 00:30:24.440 align:middle line:84% interpret this as the value of monetary injections 00:30:24.440 --> 00:30:27.560 align:middle line:90% and who they should go to. 00:30:27.560 --> 00:30:31.440 align:middle line:84% But it is on the assumption that the traders 00:30:31.440 --> 00:30:35.520 align:middle line:84% have entered into a risk sharing agreement with each other. 00:30:35.520 --> 00:30:40.080 align:middle line:84% So the definition of financial centrality, 00:30:40.080 --> 00:30:45.440 align:middle line:84% or our value of liquidity, is how much the community objective 00:30:45.440 --> 00:30:48.540 align:middle line:84% function is enhanced, in this case, 00:30:48.540 --> 00:30:53.040 align:middle line:84% if it's an injection to trader i, how the community value 00:30:53.040 --> 00:30:56.720 align:middle line:84% function is enhanced as we change the value of epsilon 00:30:56.720 --> 00:30:58.800 align:middle line:90% around 0. 00:30:58.800 --> 00:31:01.580 align:middle line:84% We're trying to find who is central, 00:31:01.580 --> 00:31:04.920 align:middle line:84% so we want to run this calculation over all the agents 00:31:04.920 --> 00:31:07.040 align:middle line:90% and rank them. 00:31:07.040 --> 00:31:11.090 align:middle line:84% And again, what was that Vi of Epsilon? 00:31:11.090 --> 00:31:16.050 align:middle line:84% V of lambda was the value function given fixed weights 00:31:16.050 --> 00:31:18.610 align:middle line:84% lambda over the community of people 00:31:18.610 --> 00:31:21.770 align:middle line:90% participating in the market. 00:31:21.770 --> 00:31:27.210 align:middle line:84% Vi, i for injecting something to agent i, which 00:31:27.210 --> 00:31:32.110 align:middle line:84% will alter this resource constraint by epsilon. 00:31:32.110 --> 00:31:35.570 align:middle line:84% And we're then taking the derivative with respect 00:31:35.570 --> 00:31:37.890 align:middle line:90% to that injection. 00:31:37.890 --> 00:31:40.890 align:middle line:84% STUDENT: So here, the consumption you choose 00:31:40.890 --> 00:31:45.010 align:middle line:90% can depend on y and-- 00:31:45.010 --> 00:31:47.250 align:middle line:84% what's this letter called xi, psi? 00:31:47.250 --> 00:31:49.130 align:middle line:84% ROBERT M. TOWNSEND: Yeah, I'm saying xi, 00:31:49.130 --> 00:31:51.310 align:middle line:84% but I'm probably getting it wrong. 00:31:51.310 --> 00:31:53.150 align:middle line:84% STUDENT: But it could also depend on-- 00:31:53.150 --> 00:31:56.830 align:middle line:84% or is that implied by xi what the realized partition is? 00:31:56.830 --> 00:31:58.070 align:middle line:90% Because I mean, if I'm-- 00:31:58.070 --> 00:32:00.570 align:middle line:84% ROBERT M. TOWNSEND: It's implied by xi, yes. 00:32:00.570 --> 00:32:01.110 align:middle line:90% Yeah. 00:32:01.110 --> 00:32:04.090 align:middle line:90% 00:32:04.090 --> 00:32:08.500 align:middle line:84% So let's do a policy experiment where 00:32:08.500 --> 00:32:12.580 align:middle line:84% we imagine we have more than just epsilon 00:32:12.580 --> 00:32:14.600 align:middle line:90% close to 0 amount of liquidity. 00:32:14.600 --> 00:32:22.160 align:middle line:84% Suppose it's a finite amount A that's available for injection. 00:32:22.160 --> 00:32:25.620 align:middle line:84% So in principle, we could be injecting to multiple, but not 00:32:25.620 --> 00:32:28.620 align:middle line:90% necessarily all agents. 00:32:28.620 --> 00:32:33.780 align:middle line:84% The sum of the injections cannot exceed the amount 00:32:33.780 --> 00:32:36.820 align:middle line:90% that's available. 00:32:36.820 --> 00:32:41.140 align:middle line:84% So the larger objective would be to choose 00:32:41.140 --> 00:32:45.700 align:middle line:84% the injections over potentially all the people in such a way 00:32:45.700 --> 00:32:52.420 align:middle line:84% to maximize the social value function subject to this limit 00:32:52.420 --> 00:32:53.680 align:middle line:90% on availability. 00:32:53.680 --> 00:32:56.380 align:middle line:90% 00:32:56.380 --> 00:33:01.860 align:middle line:84% But if there are finite number of players, 00:33:01.860 --> 00:33:10.190 align:middle line:84% then we go back to our other infinitesimal measure and rank 00:33:10.190 --> 00:33:12.110 align:middle line:90% order all the players. 00:33:12.110 --> 00:33:16.730 align:middle line:84% So you can imagine that there is diminishing value, 00:33:16.730 --> 00:33:18.970 align:middle line:84% but maybe not diminishing so quickly. 00:33:18.970 --> 00:33:23.470 align:middle line:84% So if the total available is not very big, 00:33:23.470 --> 00:33:27.990 align:middle line:84% you might still want to inject it all to just one guy. 00:33:27.990 --> 00:33:32.990 align:middle line:84% If the amount available A is slightly bigger than that, 00:33:32.990 --> 00:33:36.370 align:middle line:84% then you might want to go to a second person, and so on. 00:33:36.370 --> 00:33:39.350 align:middle line:90% 00:33:39.350 --> 00:33:41.650 align:middle line:90% So that's all this said. 00:33:41.650 --> 00:33:53.550 align:middle line:90% 00:33:53.550 --> 00:33:57.710 align:middle line:84% There exist these critical values, A bar, 00:33:57.710 --> 00:34:01.350 align:middle line:84% such that if the amount available is, say, less 00:34:01.350 --> 00:34:04.720 align:middle line:84% than that, we're still going to want to give the money to just 00:34:04.720 --> 00:34:07.680 align:middle line:90% one person. 00:34:07.680 --> 00:34:09.978 align:middle line:84% So what's the value of giving the liquidity? 00:34:09.978 --> 00:34:11.520 align:middle line:84% Well, the risk sharing effect is what 00:34:11.520 --> 00:34:14.679 align:middle line:84% we're emphasizing that propagates through the risk 00:34:14.679 --> 00:34:15.820 align:middle line:90% sharing network. 00:34:15.820 --> 00:34:19.320 align:middle line:84% There's a participation effect, which I don't have time 00:34:19.320 --> 00:34:20.940 align:middle line:90% to talk much about today. 00:34:20.940 --> 00:34:24.639 align:middle line:84% It's like a subsidy for participation in the market. 00:34:24.639 --> 00:34:26.960 align:middle line:84% And there's an income distribution effect 00:34:26.960 --> 00:34:30.560 align:middle line:84% that the injection can start changing, basically, 00:34:30.560 --> 00:34:38.080 align:middle line:84% their endowments in a model that's more articulate about how 00:34:38.080 --> 00:34:41.199 align:middle line:90% the endowments are determined. 00:34:41.199 --> 00:34:44.480 align:middle line:90% These are interesting formulas. 00:34:44.480 --> 00:34:47.360 align:middle line:84% But then again, we don't do much more with it, 00:34:47.360 --> 00:34:49.320 align:middle line:84% so I'm just going to today continue 00:34:49.320 --> 00:34:54.280 align:middle line:84% to focus on these exogenous shocks, market shocks. 00:34:54.280 --> 00:35:02.330 align:middle line:84% So if we think about the Lagrangian, as always, 00:35:02.330 --> 00:35:06.850 align:middle line:84% the repeat of the objective function is the lambda weighted 00:35:06.850 --> 00:35:12.270 align:middle line:84% expected utilities with expectation over the states, 00:35:12.270 --> 00:35:17.890 align:middle line:84% including market participation and income enhanced 00:35:17.890 --> 00:35:26.610 align:middle line:84% by the resource constraints, where qs is the Lagrange 00:35:26.610 --> 00:35:32.400 align:middle line:84% multiplier, or the shadow price, of the particular constraint s 00:35:32.400 --> 00:35:40.250 align:middle line:84% that the sum of incomes cannot be less than the sum 00:35:40.250 --> 00:35:43.250 align:middle line:90% of consumptions. 00:35:43.250 --> 00:35:49.050 align:middle line:84% So qs is the Lagrange multiplier, and not 00:35:49.050 --> 00:35:51.810 align:middle line:84% too surprisingly, it as a shadow price 00:35:51.810 --> 00:35:54.730 align:middle line:84% reflects how much the objective function 00:35:54.730 --> 00:35:59.890 align:middle line:84% could be increased if you were to slacken or weaken 00:35:59.890 --> 00:36:04.100 align:middle line:84% this constraint by a tiny amount. 00:36:04.100 --> 00:36:11.480 align:middle line:84% So it's like a price of resources in that state. 00:36:11.480 --> 00:36:15.420 align:middle line:84% In fact, when you're thinking about what prices 00:36:15.420 --> 00:36:18.860 align:middle line:84% are in a decentralized competitive equilibrium, 00:36:18.860 --> 00:36:22.340 align:middle line:84% they're essentially marginal utility prices. 00:36:22.340 --> 00:36:24.340 align:middle line:84% You have to pick a numeraire, and then it's 00:36:24.340 --> 00:36:26.200 align:middle line:90% really only relative prices. 00:36:26.200 --> 00:36:31.260 align:middle line:84% But a decentralized competitive equilibrium 00:36:31.260 --> 00:36:36.180 align:middle line:84% is using marginal utility pricing. 00:36:36.180 --> 00:36:40.660 align:middle line:90% So there's a proposition. 00:36:40.660 --> 00:36:44.500 align:middle line:84% What is the liquidity value for agent i, 00:36:44.500 --> 00:36:47.740 align:middle line:84% this financial centrality for agent i? 00:36:47.740 --> 00:36:53.940 align:middle line:84% It's just the expected product of i's participation shock 00:36:53.940 --> 00:36:56.820 align:middle line:90% with those shadow prices. 00:36:56.820 --> 00:37:00.110 align:middle line:84% If agent i is not in the market, then 00:37:00.110 --> 00:37:05.390 align:middle line:84% xi i, under a given realization of shocks, then xi i is 0. 00:37:05.390 --> 00:37:07.430 align:middle line:90% So this goes away. 00:37:07.430 --> 00:37:11.230 align:middle line:84% And if xi i is 1, agent i is in the market, 00:37:11.230 --> 00:37:14.110 align:middle line:90% and what is i's contribution? 00:37:14.110 --> 00:37:16.470 align:middle line:84% The epsilon is small, so it's just 00:37:16.470 --> 00:37:19.710 align:middle line:84% the value of liquidity in that market, which 00:37:19.710 --> 00:37:24.550 align:middle line:84% is reflected in the shadow price, the qs price. 00:37:24.550 --> 00:37:30.150 align:middle line:84% So that is the measure of liquidity value of player i, 00:37:30.150 --> 00:37:33.270 align:middle line:84% and now we can go through some examples. 00:37:33.270 --> 00:37:36.510 align:middle line:84% How does that value vary as a function 00:37:36.510 --> 00:37:38.050 align:middle line:90% of the underlying environment? 00:37:38.050 --> 00:37:42.470 align:middle line:84% So one example is everyone has an equal weight. 00:37:42.470 --> 00:37:46.690 align:middle line:84% This weight could be 1 over n so that it sums to 1, 00:37:46.690 --> 00:37:49.270 align:middle line:84% but that's entirely arbitrary because we can 00:37:49.270 --> 00:37:52.110 align:middle line:90% rescale the objective function. 00:37:52.110 --> 00:37:55.510 align:middle line:84% So they're all going to get equal weight in this example. 00:37:55.510 --> 00:37:59.680 align:middle line:84% They all have a common utility function, no i, 00:37:59.680 --> 00:38:06.160 align:middle line:84% and their incomes are drawn from a distribution, which 00:38:06.160 --> 00:38:09.520 align:middle line:84% is independent across all the agents. 00:38:09.520 --> 00:38:13.440 align:middle line:84% And it has a mean mu, which is common, 00:38:13.440 --> 00:38:16.520 align:middle line:90% and a variance sigma squared. 00:38:16.520 --> 00:38:19.740 align:middle line:84% So if we were filling out that variance-covariance matrix, 00:38:19.740 --> 00:38:22.480 align:middle line:84% there would be sigma squares on the diagonal and 0 00:38:22.480 --> 00:38:25.480 align:middle line:90% everywhere else. 00:38:25.480 --> 00:38:30.560 align:middle line:84% And these participation shocks are orthogonal to the income 00:38:30.560 --> 00:38:32.760 align:middle line:90% shocks. 00:38:32.760 --> 00:38:39.780 align:middle line:84% So in a given market size state xi, 00:38:39.780 --> 00:38:42.900 align:middle line:84% which is summing up over all of them, but many could be 0. 00:38:42.900 --> 00:38:46.200 align:middle line:84% So we get the total number who are participating 00:38:46.200 --> 00:38:51.960 align:middle line:84% is just the sum of those across the objects of the vector. 00:38:51.960 --> 00:38:56.450 align:middle line:84% And what is the solution to the risk sharing problem? 00:38:56.450 --> 00:39:01.130 align:middle line:84% Essentially, you give everyone the average 00:39:01.130 --> 00:39:06.730 align:middle line:84% of the incomes of the people participating in the market. 00:39:06.730 --> 00:39:11.070 align:middle line:84% The market's random here, so just kind of a word of caution, 00:39:11.070 --> 00:39:17.050 align:middle line:84% but whatever x is take the-- oops. 00:39:17.050 --> 00:39:20.970 align:middle line:90% I should have had a xi in here. 00:39:20.970 --> 00:39:23.450 align:middle line:84% So we just add up over the incomes 00:39:23.450 --> 00:39:27.330 align:middle line:84% of those people in the market and divide 00:39:27.330 --> 00:39:29.930 align:middle line:84% by the number of people in the market, 00:39:29.930 --> 00:39:32.970 align:middle line:84% and that's going to be the average income. 00:39:32.970 --> 00:39:35.430 align:middle line:84% And that's going to be the target for these people. 00:39:35.430 --> 00:39:37.710 align:middle line:84% Their consumption is going to be the average. 00:39:37.710 --> 00:39:40.690 align:middle line:90% 00:39:40.690 --> 00:39:45.990 align:middle line:84% So it's like the two agent example, high-low, low-high, 00:39:45.990 --> 00:39:49.730 align:middle line:84% and so on, except now the number of agents in this mutual fund 00:39:49.730 --> 00:39:51.610 align:middle line:90% is random. 00:39:51.610 --> 00:39:55.780 align:middle line:84% But whatever it turns out to be, with identical preferences 00:39:55.780 --> 00:39:57.900 align:middle line:84% in IID shocks and so on, they just 00:39:57.900 --> 00:40:01.700 align:middle line:84% share all the risk because they're all risk 00:40:01.700 --> 00:40:04.740 align:middle line:90% averse to the same degree. 00:40:04.740 --> 00:40:09.380 align:middle line:84% And so the marginal utility, the shadow price of that resource 00:40:09.380 --> 00:40:14.260 align:middle line:84% constraint is just the marginal utility of the common utility 00:40:14.260 --> 00:40:16.872 align:middle line:84% functions evaluated at that average income, 00:40:16.872 --> 00:40:18.580 align:middle line:84% because they're all alike and they're all 00:40:18.580 --> 00:40:19.760 align:middle line:90% getting the same thing. 00:40:19.760 --> 00:40:22.300 align:middle line:90% 00:40:22.300 --> 00:40:25.220 align:middle line:84% We can do a little more, generally, 00:40:25.220 --> 00:40:27.440 align:middle line:90% especially with approximations. 00:40:27.440 --> 00:40:28.800 align:middle line:90% This we had before. 00:40:28.800 --> 00:40:31.820 align:middle line:84% Financial centrality is the expected product 00:40:31.820 --> 00:40:35.100 align:middle line:84% of participation with the shadow price, 00:40:35.100 --> 00:40:41.580 align:middle line:84% and that's going to be equal to mu, the mean of the income 00:40:41.580 --> 00:40:46.100 align:middle line:84% distribution plus the marginal utility at that mean 00:40:46.100 --> 00:40:50.940 align:middle line:84% plus the expected value of this guy here. 00:40:50.940 --> 00:40:58.310 align:middle line:84% So it's the product of xi i with this. 00:40:58.310 --> 00:41:09.030 align:middle line:84% And this gamma has to do with the third derivative of utility. 00:41:09.030 --> 00:41:15.070 align:middle line:84% It's called prudence, and the idea is the more prudent 00:41:15.070 --> 00:41:19.910 align:middle line:84% you are, the more you will want to save 00:41:19.910 --> 00:41:24.390 align:middle line:84% when you're facing a risky situation in the future. 00:41:24.390 --> 00:41:28.730 align:middle line:84% Of course, not all utility functions display prudence, 00:41:28.730 --> 00:41:33.790 align:middle line:84% but some of the familiar ones do, like the power 00:41:33.790 --> 00:41:39.470 align:middle line:84% functions, C to the omega or something. 00:41:39.470 --> 00:41:41.610 align:middle line:90% So we have prudence times this. 00:41:41.610 --> 00:41:46.990 align:middle line:84% So the higher is the variance, then 00:41:46.990 --> 00:41:51.960 align:middle line:84% the bigger is the ex-ante expected utility 00:41:51.960 --> 00:41:59.600 align:middle line:84% of the liquidity injection, because there's more risk, more 00:41:59.600 --> 00:42:03.780 align:middle line:84% diversity across realizations of income shocks, 00:42:03.780 --> 00:42:06.120 align:middle line:90% so there's more gain to pooling. 00:42:06.120 --> 00:42:09.920 align:middle line:84% On the other hand, it diminishes with the number 00:42:09.920 --> 00:42:12.760 align:middle line:90% of agents in the market. 00:42:12.760 --> 00:42:15.260 align:middle line:84% Well, that's kind of like a diminishing returns. 00:42:15.260 --> 00:42:20.280 align:middle line:84% I mean, you're getting closer and closer to the average. 00:42:20.280 --> 00:42:22.940 align:middle line:84% Having one more person doesn't really help much. 00:42:22.940 --> 00:42:26.200 align:middle line:90% 00:42:26.200 --> 00:42:29.160 align:middle line:84% If we had the segmented market, rather than you're in 00:42:29.160 --> 00:42:35.440 align:middle line:84% or you're out, we get a familiar almost equivalent expression, 00:42:35.440 --> 00:42:38.280 align:middle line:84% except that now we're not dividing by the number of agents 00:42:38.280 --> 00:42:39.700 align:middle line:90% in the centralized market. 00:42:39.700 --> 00:42:41.160 align:middle line:84% We're just dividing by the number 00:42:41.160 --> 00:42:46.560 align:middle line:84% of agents in the cluster in which you're randomly located. 00:42:46.560 --> 00:42:49.170 align:middle line:84% And again, you're taking expectations 00:42:49.170 --> 00:42:53.310 align:middle line:84% over all these guys, over all these clusters, because it's 00:42:53.310 --> 00:42:56.250 align:middle line:90% entirely an ex-ante measure. 00:42:56.250 --> 00:43:02.590 align:middle line:84% If you think about these xi's, xi i, it's binary. 00:43:02.590 --> 00:43:05.410 align:middle line:90% It's either a 0 or 1. 00:43:05.410 --> 00:43:09.610 align:middle line:84% So you could imagine writing two branches here, 00:43:09.610 --> 00:43:14.250 align:middle line:84% the probability that it's 1 plus the probability that it's 0. 00:43:14.250 --> 00:43:18.610 align:middle line:84% But if it's 0, this whole thing goes away, 00:43:18.610 --> 00:43:24.010 align:middle line:84% so you're left with the branch where xi i is 1. 00:43:24.010 --> 00:43:27.770 align:middle line:84% And so then we're able to pull that out here conditioned 00:43:27.770 --> 00:43:30.330 align:middle line:90% on xi i being 1. 00:43:30.330 --> 00:43:36.570 align:middle line:84% That measure of liquidity value is just this probability. 00:43:36.570 --> 00:43:39.010 align:middle line:84% I mean, the intuition is pretty brutal, 00:43:39.010 --> 00:43:41.570 align:middle line:84% so why am I giving liquidity to a guy that doesn't show up 00:43:41.570 --> 00:43:43.970 align:middle line:90% very much in the market? 00:43:43.970 --> 00:43:46.970 align:middle line:90% It's kind of worthless. 00:43:46.970 --> 00:43:53.680 align:middle line:84% So you're weighting positively in the liquidity formula 00:43:53.680 --> 00:43:59.180 align:middle line:84% someone who is around a lot in the market. 00:43:59.180 --> 00:44:01.440 align:middle line:84% STUDENT: So this is an ex-ante measure, I understand. 00:44:01.440 --> 00:44:06.260 align:middle line:84% But everything we did, also consumption 00:44:06.260 --> 00:44:09.300 align:middle line:84% and the injection, all depends on realization-- 00:44:09.300 --> 00:44:10.560 align:middle line:90% can depend on realization. 00:44:10.560 --> 00:44:12.500 align:middle line:90% So it's all exposed. 00:44:12.500 --> 00:44:14.920 align:middle line:84% So then why do we care about an exact measure? 00:44:14.920 --> 00:44:18.880 align:middle line:84% If we can make our injection depend on the realized clusters, 00:44:18.880 --> 00:44:21.940 align:middle line:84% and we can make the consumption that they have depend 00:44:21.940 --> 00:44:24.780 align:middle line:84% on the realized clusters, and [? y's. ?] 00:44:24.780 --> 00:44:27.540 align:middle line:84% ROBERT M. TOWNSEND: Yeah I mean, that is 00:44:27.540 --> 00:44:29.080 align:middle line:90% what we're doing mechanically. 00:44:29.080 --> 00:44:33.460 align:middle line:84% We're taking realizations of income, realizations of shocks, 00:44:33.460 --> 00:44:35.940 align:middle line:84% and then allocating across the agents. 00:44:35.940 --> 00:44:39.000 align:middle line:84% The ex-ante part starts to enter in when you say, well, 00:44:39.000 --> 00:44:42.000 align:middle line:84% look, if we waited to trade, and I'm high and you're low, 00:44:42.000 --> 00:44:44.020 align:middle line:90% I'm not giving up stuff. 00:44:44.020 --> 00:44:46.570 align:middle line:84% So it has to be mutually beneficial, 00:44:46.570 --> 00:44:48.470 align:middle line:84% and they're in a smart contract that 00:44:48.470 --> 00:44:53.870 align:middle line:90% commits them to share the risk. 00:44:53.870 --> 00:44:57.610 align:middle line:84% And then this is ex-ante for sure. 00:44:57.610 --> 00:45:00.990 align:middle line:90% It's a probability object. 00:45:00.990 --> 00:45:03.430 align:middle line:84% Yeah, so we're starting with your point 00:45:03.430 --> 00:45:07.610 align:middle line:84% but then integrating back before anything happens. 00:45:07.610 --> 00:45:11.990 align:middle line:90% 00:45:11.990 --> 00:45:14.990 align:middle line:84% But it is crucial here that the injection 00:45:14.990 --> 00:45:17.550 align:middle line:84% has to-- the site of the injection 00:45:17.550 --> 00:45:21.470 align:middle line:84% has to be determined ex-ante also before anything happens, 00:45:21.470 --> 00:45:22.923 align:middle line:90% like a buffer stock. 00:45:22.923 --> 00:45:24.590 align:middle line:84% STUDENT: Oh, but I thought the injection 00:45:24.590 --> 00:45:26.910 align:middle line:84% was allowed to depend on the realization 00:45:26.910 --> 00:45:28.032 align:middle line:90% of the fragmentations. 00:45:28.032 --> 00:45:28.990 align:middle line:90% ROBERT M. TOWNSEND: No. 00:45:28.990 --> 00:45:35.510 align:middle line:90% 00:45:35.510 --> 00:45:36.010 align:middle line:90% Yeah. 00:45:36.010 --> 00:45:39.110 align:middle line:84% It's all about hedging the income risk 00:45:39.110 --> 00:45:42.790 align:middle line:84% and hedging the market participation risk. 00:45:42.790 --> 00:45:46.120 align:middle line:84% And this guy, the second term, looks very 00:45:46.120 --> 00:45:47.700 align:middle line:90% similar to what we had before. 00:45:47.700 --> 00:45:50.650 align:middle line:84% It's just that you're conditioning on this branch. 00:45:50.650 --> 00:45:52.400 align:middle line:84% STUDENT: So you're not injecting liquidity 00:45:52.400 --> 00:45:55.540 align:middle line:84% to the guy with the highest shadow price, 00:45:55.540 --> 00:45:58.200 align:middle line:84% but you're injecting liquidity with the guy with the highest 00:45:58.200 --> 00:46:01.000 align:middle line:84% expected shadow price or [? something. ?] 00:46:01.000 --> 00:46:03.200 align:middle line:84% I thought it was a shadow price or something that 00:46:03.200 --> 00:46:05.840 align:middle line:90% determined the [INAUDIBLE]. 00:46:05.840 --> 00:46:07.800 align:middle line:84% ROBERT M. TOWNSEND: It's the expected thing. 00:46:07.800 --> 00:46:09.488 align:middle line:90% STUDENT: Expected, [INAUDIBLE]. 00:46:09.488 --> 00:46:10.780 align:middle line:90% ROBERT M. TOWNSEND: Here it is. 00:46:10.780 --> 00:46:13.680 align:middle line:90% 00:46:13.680 --> 00:46:16.080 align:middle line:84% Yeah, so this is the shadow price conditioned 00:46:16.080 --> 00:46:20.040 align:middle line:84% on a given draw of the income shocks and the market 00:46:20.040 --> 00:46:24.500 align:middle line:84% participation shocks, and you're taking expectations over that. 00:46:24.500 --> 00:46:31.120 align:middle line:90% 00:46:31.120 --> 00:46:32.680 align:middle line:90% All right. 00:46:32.680 --> 00:46:35.240 align:middle line:90% So another example. 00:46:35.240 --> 00:46:36.700 align:middle line:90% We're back to the host. 00:46:36.700 --> 00:46:43.490 align:middle line:84% Suppose you pick agent i as the host with probability 1 over n, 00:46:43.490 --> 00:46:47.790 align:middle line:84% and then the markets are formed, as I said, by this invitation. 00:46:47.790 --> 00:46:55.050 align:middle line:84% In fact, a version of that is that agent can connect only 00:46:55.050 --> 00:47:02.570 align:middle line:84% to adjacent nodes, so that's like his or her neighborhood. 00:47:02.570 --> 00:47:05.210 align:middle line:84% A neighborhood of i is just a set 00:47:05.210 --> 00:47:08.970 align:middle line:84% of adjacent nodes in the network, 00:47:08.970 --> 00:47:15.010 align:middle line:84% and di is the number of people in that to which 00:47:15.010 --> 00:47:17.970 align:middle line:90% agent i is directly connected. 00:47:17.970 --> 00:47:20.350 align:middle line:84% But there's a bit more to the formula than that, 00:47:20.350 --> 00:47:21.930 align:middle line:90% even though it's additive. 00:47:21.930 --> 00:47:27.010 align:middle line:84% This other component has to do with the variance, the prudence. 00:47:27.010 --> 00:47:31.810 align:middle line:84% And a bit counterintuitively, perhaps it's 00:47:31.810 --> 00:47:35.890 align:middle line:84% divided by the extent of the neighborhoods 00:47:35.890 --> 00:47:38.850 align:middle line:84% of the other traders j to whom agent i would 00:47:38.850 --> 00:47:41.740 align:middle line:90% be connected as the host. 00:47:41.740 --> 00:47:46.500 align:middle line:84% So let me show you a picture two different networks. 00:47:46.500 --> 00:47:54.860 align:middle line:84% Here's agent i immediately connected to 1, 2, 3, 4 guys. 00:47:54.860 --> 00:48:00.880 align:middle line:84% Here's an agent-- it's kind of bad notation. 00:48:00.880 --> 00:48:05.020 align:middle line:84% It should be i prime, some other configuration, 00:48:05.020 --> 00:48:08.300 align:middle line:84% and he's connected directly to 4. 00:48:08.300 --> 00:48:12.480 align:middle line:84% But now these guys, like 5, is connected to three people, 00:48:12.480 --> 00:48:14.340 align:middle line:90% not to two people. 00:48:14.340 --> 00:48:19.740 align:middle line:84% So in every instance, the number of connections of the periphery 00:48:19.740 --> 00:48:26.580 align:middle line:84% guys is larger on the right than it is on the left. 00:48:26.580 --> 00:48:29.700 align:middle line:84% You might have thought that this guy would be connected 00:48:29.700 --> 00:48:32.580 align:middle line:84% because he's directly and indirectly connected to more 00:48:32.580 --> 00:48:40.030 align:middle line:84% people, and this is the disease contagion, systemic risk point 00:48:40.030 --> 00:48:44.990 align:middle line:84% of view, that this guy is dangerous 00:48:44.990 --> 00:48:50.110 align:middle line:84% because he's quite connected to almost everybody, at least 00:48:50.110 --> 00:48:51.510 align:middle line:90% indirectly. 00:48:51.510 --> 00:48:54.950 align:middle line:84% But our measure of liquidity is about market making. 00:48:54.950 --> 00:48:59.150 align:middle line:84% So why is this guy more valued in terms of liquidity? 00:48:59.150 --> 00:49:02.570 align:middle line:84% The answer is that if these guys come in, 00:49:02.570 --> 00:49:04.670 align:middle line:84% they come in with their own players. 00:49:04.670 --> 00:49:07.430 align:middle line:84% And the more players you have in the market, 00:49:07.430 --> 00:49:10.890 align:middle line:84% the less the incremental value of the liquidity injection. 00:49:10.890 --> 00:49:15.750 align:middle line:90% 00:49:15.750 --> 00:49:21.230 align:middle line:84% And you'll see this summarized in a minute. 00:49:21.230 --> 00:49:24.390 align:middle line:84% Valued players are players who are 00:49:24.390 --> 00:49:28.270 align:middle line:84% in the market when the market is thin, on average, 00:49:28.270 --> 00:49:30.670 align:middle line:90% in expectation. 00:49:30.670 --> 00:49:33.910 align:middle line:84% And when people in the market don't have a lot of income, 00:49:33.910 --> 00:49:36.590 align:middle line:84% when the risk is high, when they're 00:49:36.590 --> 00:49:42.920 align:middle line:84% valued a lot in the sense of lambda weights, 00:49:42.920 --> 00:49:47.040 align:middle line:84% yeah, so we changed the environment 00:49:47.040 --> 00:49:51.140 align:middle line:84% to have a more general variance-covariance matrix, 00:49:51.140 --> 00:49:53.540 align:middle line:84% not necessarily identical Pareto weights, 00:49:53.540 --> 00:49:57.680 align:middle line:84% not necessarily the same mean incomes. 00:49:57.680 --> 00:50:01.700 align:middle line:84% And they're not IID, heterogeneous preferences. 00:50:01.700 --> 00:50:04.360 align:middle line:84% The utility functions don't have to be all alike. 00:50:04.360 --> 00:50:08.800 align:middle line:84% And there are shocks to these, quote, fundamentals. 00:50:08.800 --> 00:50:13.860 align:middle line:84% So this is what I was already beginning to enunciate. 00:50:13.860 --> 00:50:16.340 align:middle line:84% Agents are more central if the market is small, 00:50:16.340 --> 00:50:19.480 align:middle line:84% if the average volatility is high, 00:50:19.480 --> 00:50:24.200 align:middle line:84% or income shocks are positively correlated. 00:50:24.200 --> 00:50:27.700 align:middle line:84% I mean, when income shocks are positively correlated, 00:50:27.700 --> 00:50:29.340 align:middle line:84% there's a lot of aggregate risks. 00:50:29.340 --> 00:50:34.280 align:middle line:84% So you can't use the IID aspect adding up over independent draws 00:50:34.280 --> 00:50:38.410 align:middle line:90% to get the mutual fund benefit. 00:50:38.410 --> 00:50:41.330 align:middle line:84% So even if the market is large but the incomes are highly 00:50:41.330 --> 00:50:43.570 align:middle line:84% correlated, there's a lot of risk, 00:50:43.570 --> 00:50:47.130 align:middle line:84% and hence an agent could be more central if he's 00:50:47.130 --> 00:50:50.650 align:middle line:90% likely to be in those clusters. 00:50:50.650 --> 00:50:54.850 align:middle line:84% This has to do with the Pareto weights, the average Pareto 00:50:54.850 --> 00:51:00.090 align:middle line:84% weights of those participating in the market. 00:51:00.090 --> 00:51:04.090 align:middle line:84% The average agent is poor, the incomes are low, 00:51:04.090 --> 00:51:09.010 align:middle line:84% or the average of risk aversion is high. 00:51:09.010 --> 00:51:12.110 align:middle line:84% So all those things I think are intuitive. 00:51:12.110 --> 00:51:15.090 align:middle line:90% 00:51:15.090 --> 00:51:19.450 align:middle line:84% So let's talk about positive counterparts 00:51:19.450 --> 00:51:23.410 align:middle line:90% to financial centrality. 00:51:23.410 --> 00:51:26.850 align:middle line:84% And there are two pieces, and one piece of it 00:51:26.850 --> 00:51:31.050 align:middle line:90% is really sparse but important. 00:51:31.050 --> 00:51:34.130 align:middle line:84% In a constrained-- means constrained 00:51:34.130 --> 00:51:37.080 align:middle line:84% by the environment with the shocks-- 00:51:37.080 --> 00:51:41.060 align:middle line:84% complete market implementation of the optimal risk sharing 00:51:41.060 --> 00:51:42.620 align:middle line:90% contract. 00:51:42.620 --> 00:51:43.680 align:middle line:90% OK, so what are we doing? 00:51:43.680 --> 00:51:46.980 align:middle line:84% We're taking the planning problem in the fragmented 00:51:46.980 --> 00:51:49.360 align:middle line:90% environment, solving it. 00:51:49.360 --> 00:51:53.380 align:middle line:84% So with a smart contract, we implement the risk sharing. 00:51:53.380 --> 00:51:57.700 align:middle line:84% They're committed to do what they said they're going to do. 00:51:57.700 --> 00:52:00.060 align:middle line:84% And we've been focusing on the normative part 00:52:00.060 --> 00:52:02.020 align:middle line:84% of solving the planner's problem, which 00:52:02.020 --> 00:52:05.420 align:middle line:84% is equivalent with determining the constrained Pareto optimal 00:52:05.420 --> 00:52:06.780 align:middle line:90% allocations. 00:52:06.780 --> 00:52:09.500 align:middle line:84% We could talk about a market where 00:52:09.500 --> 00:52:12.060 align:middle line:90% there are financial assets. 00:52:12.060 --> 00:52:16.660 align:middle line:84% We can decentralize the risk sharing environment 00:52:16.660 --> 00:52:24.380 align:middle line:84% where they're entering into risk contracts, 00:52:24.380 --> 00:52:29.180 align:middle line:84% and those contracts are priced, contract determining 00:52:29.180 --> 00:52:31.900 align:middle line:84% premia and indemnity and so on, and the price 00:52:31.900 --> 00:52:38.070 align:middle line:84% being what you would pay to enter into that contract. 00:52:38.070 --> 00:52:40.750 align:middle line:84% And there could be things like bonds. 00:52:40.750 --> 00:52:44.950 align:middle line:84% So a bond would be a financial asset that pays off, 00:52:44.950 --> 00:52:49.030 align:middle line:84% maybe all the time, but maybe it's contingent. 00:52:49.030 --> 00:52:55.070 align:middle line:84% So you could imagine a bond that pays off when some event happens 00:52:55.070 --> 00:52:57.630 align:middle line:90% and 0 otherwise. 00:52:57.630 --> 00:53:00.590 align:middle line:84% And the event could be a hurricane or whatever, 00:53:00.590 --> 00:53:03.110 align:middle line:84% but here the event could be having something 00:53:03.110 --> 00:53:06.350 align:middle line:84% to do with the market, and in particular having something 00:53:06.350 --> 00:53:09.390 align:middle line:84% to do with whether agent i is in the market. 00:53:09.390 --> 00:53:12.950 align:middle line:84% So you can imagine a bond that pays off 00:53:12.950 --> 00:53:19.830 align:middle line:84% if you're the holder only when agent i is in the market. 00:53:19.830 --> 00:53:23.270 align:middle line:84% And that bond, the price of that bond, 00:53:23.270 --> 00:53:28.710 align:middle line:84% is exactly our measure of the value of liquidity of trader i. 00:53:28.710 --> 00:53:33.840 align:middle line:84% And maybe you could imagine how to derive this 00:53:33.840 --> 00:53:37.480 align:middle line:84% because we did those qs's, the qs's, the shadow 00:53:37.480 --> 00:53:41.540 align:middle line:84% price of the state contingent resource constraint, 00:53:41.540 --> 00:53:44.960 align:middle line:84% and we were summing up over all those prices. 00:53:44.960 --> 00:53:49.560 align:middle line:84% It's like if you're familiar with arrow 00:53:49.560 --> 00:53:53.780 align:middle line:84% indexation of securities, you can price any security you want. 00:53:53.780 --> 00:53:57.540 align:middle line:84% You just pick the states over which it pays out, 00:53:57.540 --> 00:54:06.040 align:middle line:84% and then you add up over the pure bonds that pay 1, 0 00:54:06.040 --> 00:54:07.220 align:middle line:90% depending on the state. 00:54:07.220 --> 00:54:09.420 align:middle line:84% You add up over all the states that are relevant, 00:54:09.420 --> 00:54:10.520 align:middle line:90% and that's what-- 00:54:10.520 --> 00:54:13.480 align:middle line:84% it's just this somewhat weird state here is 00:54:13.480 --> 00:54:15.460 align:middle line:90% that agent i is participating. 00:54:15.460 --> 00:54:19.880 align:middle line:84% You could call it a personalized bond. 00:54:19.880 --> 00:54:25.840 align:middle line:84% Obviously, here the exogeneity matters. 00:54:25.840 --> 00:54:30.870 align:middle line:84% We don't want to enter into people entering into a trade. 00:54:30.870 --> 00:54:32.930 align:middle line:84% If i shows up and then i gets to choose 00:54:32.930 --> 00:54:34.530 align:middle line:84% whether he's showing up or not, that 00:54:34.530 --> 00:54:38.010 align:middle line:90% could be a very bad outcome. 00:54:38.010 --> 00:54:40.990 align:middle line:84% It could be all kinds of moral hazard considerations. 00:54:40.990 --> 00:54:45.490 align:middle line:84% But mainly this is to share conceptually 00:54:45.490 --> 00:54:48.970 align:middle line:84% what our measure of the value of liquidity, 00:54:48.970 --> 00:54:51.170 align:middle line:84% or our measure of financial centrality 00:54:51.170 --> 00:54:53.070 align:middle line:90% is not an alien concept. 00:54:53.070 --> 00:54:58.290 align:middle line:84% It's basically standard asset pricing formula. 00:54:58.290 --> 00:55:05.250 align:middle line:84% This one is another interpretation, 00:55:05.250 --> 00:55:08.570 align:middle line:84% and it's if agents are getting together ex-ante, 00:55:08.570 --> 00:55:11.730 align:middle line:84% before anything happens, to bargain over 00:55:11.730 --> 00:55:14.770 align:middle line:90% who's going to get what, when. 00:55:14.770 --> 00:55:18.770 align:middle line:90% So we can think about-- 00:55:18.770 --> 00:55:20.950 align:middle line:84% I think it starts on the next slide. 00:55:20.950 --> 00:55:23.770 align:middle line:90% 00:55:23.770 --> 00:55:27.050 align:middle line:84% Let me-- not really written out, so 00:55:27.050 --> 00:55:31.180 align:middle line:90% let me just say it in English. 00:55:31.180 --> 00:55:37.700 align:middle line:84% The Nash bargaining solution would be determined 00:55:37.700 --> 00:55:41.620 align:middle line:90% by what people would threaten. 00:55:41.620 --> 00:55:44.740 align:middle line:84% You have a higher bargaining position 00:55:44.740 --> 00:55:47.380 align:middle line:90% if your threat point is high. 00:55:47.380 --> 00:55:51.140 align:middle line:84% So in this case, the threat is you're not going to participate, 00:55:51.140 --> 00:55:54.660 align:middle line:84% and the utility value of that is autarky. 00:55:54.660 --> 00:56:00.020 align:middle line:84% So the terms in the objective function in the Nash bargaining 00:56:00.020 --> 00:56:03.900 align:middle line:84% objective function is the product 00:56:03.900 --> 00:56:06.060 align:middle line:84% of the difference of each agent's 00:56:06.060 --> 00:56:10.580 align:middle line:90% utility relative to autarky. 00:56:10.580 --> 00:56:16.300 align:middle line:84% It's that raised to a power and multiplied. 00:56:16.300 --> 00:56:19.780 align:middle line:84% So that's the Nash version of bargaining, and there's this-- 00:56:19.780 --> 00:56:21.840 align:middle line:84% I don't think it's [? Kaliaj ?] Minsky, 00:56:21.840 --> 00:56:26.100 align:middle line:84% but there's a guy beginning with K, whose name I'm forgetting, 00:56:26.100 --> 00:56:28.270 align:middle line:90% that also works. 00:56:28.270 --> 00:56:30.850 align:middle line:84% So let's actually spell it out a little more. 00:56:30.850 --> 00:56:33.030 align:middle line:84% Suppose we have those constant absolute risk 00:56:33.030 --> 00:56:34.710 align:middle line:90% averse preferences. 00:56:34.710 --> 00:56:38.310 align:middle line:84% Then we determine a Pareto efficient allocation. 00:56:38.310 --> 00:56:41.470 align:middle line:84% So this is a risk sharing formula. 00:56:41.470 --> 00:56:46.310 align:middle line:84% Because it's absolute risk aversion, 00:56:46.310 --> 00:56:49.710 align:middle line:84% they're all going to get the mean income plus or minus 00:56:49.710 --> 00:56:51.790 align:middle line:90% this intercept. 00:56:51.790 --> 00:56:56.790 align:middle line:84% And this intercept is high for agents with a high Pareto 00:56:56.790 --> 00:57:01.110 align:middle line:84% weight, lambda i, relative to the average weight 00:57:01.110 --> 00:57:03.550 align:middle line:90% of the others. 00:57:03.550 --> 00:57:07.030 align:middle line:84% And again, it's all conditioned in this case on xi, the market 00:57:07.030 --> 00:57:11.510 align:middle line:84% participation, because you're only sharing risk 00:57:11.510 --> 00:57:15.630 align:middle line:90% in these segmented markets. 00:57:15.630 --> 00:57:17.290 align:middle line:90% So this is like an intercept. 00:57:17.290 --> 00:57:19.030 align:middle line:84% If you were going to run a risk sharing 00:57:19.030 --> 00:57:21.770 align:middle line:84% regression, and we do all the time-- 00:57:21.770 --> 00:57:24.880 align:middle line:90% 00:57:24.880 --> 00:57:32.240 align:middle line:84% I'll show you that this term is going to be like a fixed effect. 00:57:32.240 --> 00:57:35.020 align:middle line:84% Oh, that would have been a better slide. 00:57:35.020 --> 00:57:36.540 align:middle line:84% I talked you through the English. 00:57:36.540 --> 00:57:40.680 align:middle line:90% 00:57:40.680 --> 00:57:45.600 align:middle line:84% So you run this regression in data 00:57:45.600 --> 00:57:52.000 align:middle line:84% over time of the consumption of agent i with an intercept. 00:57:52.000 --> 00:57:54.260 align:middle line:84% You allow for the counterfactual, 00:57:54.260 --> 00:58:00.320 align:middle line:84% which should be 0, that individual income matters. 00:58:00.320 --> 00:58:04.140 align:middle line:84% You allow a time-varying fixed effect. 00:58:04.140 --> 00:58:07.440 align:middle line:84% This captures the aggregate risk. 00:58:07.440 --> 00:58:11.440 align:middle line:84% And epsilon is an orthogonal error term, 00:58:11.440 --> 00:58:14.600 align:middle line:84% could be measurement error or something else. 00:58:14.600 --> 00:58:16.860 align:middle line:84% So we want to focus on this intercept. 00:58:16.860 --> 00:58:21.640 align:middle line:84% We ran this regression in my Thai data, 00:58:21.640 --> 00:58:24.020 align:middle line:84% and so we know what these intercepts are. 00:58:24.020 --> 00:58:27.720 align:middle line:84% And yeah, intuitively, the higher is your lambda weight, 00:58:27.720 --> 00:58:31.900 align:middle line:84% the higher is this intercept relative to the lambda weights 00:58:31.900 --> 00:58:32.840 align:middle line:90% of others. 00:58:32.840 --> 00:58:35.900 align:middle line:90% 00:58:35.900 --> 00:58:38.980 align:middle line:84% And if you do this Nash bargaining thing, 00:58:38.980 --> 00:58:44.340 align:middle line:84% you get an expression for the lambda, 00:58:44.340 --> 00:58:47.420 align:middle line:84% except it's a bit more complicated 00:58:47.420 --> 00:58:50.880 align:middle line:84% because lambda appears on both sides of the equation. 00:58:50.880 --> 00:58:54.420 align:middle line:90% 00:58:54.420 --> 00:58:56.640 align:middle line:84% This is like financial centrality. 00:58:56.640 --> 00:59:00.060 align:middle line:84% The higher is the value of liquidity, 00:59:00.060 --> 00:59:01.640 align:middle line:90% the higher should be lambda. 00:59:01.640 --> 00:59:07.820 align:middle line:90% 00:59:07.820 --> 00:59:09.220 align:middle line:90% Why? 00:59:09.220 --> 00:59:12.460 align:middle line:84% Because if you're financially central 00:59:12.460 --> 00:59:14.540 align:middle line:84% or you have a high liquidity value, 00:59:14.540 --> 00:59:18.780 align:middle line:90% that's socially beneficial. 00:59:18.780 --> 00:59:22.790 align:middle line:84% That's what the number represents. 00:59:22.790 --> 00:59:25.270 align:middle line:84% So if you're bargaining ex-ante, you 00:59:25.270 --> 00:59:27.350 align:middle line:90% should get more out of the pie. 00:59:27.350 --> 00:59:34.710 align:middle line:84% You have more sway in determining the social contract. 00:59:34.710 --> 00:59:37.670 align:middle line:84% But as you've seen, these formulas 00:59:37.670 --> 00:59:40.870 align:middle line:84% for financial centrality depend on the lambda's too, 00:59:40.870 --> 00:59:43.110 align:middle line:84% because we're maximizing a lambda weighted sum 00:59:43.110 --> 00:59:44.630 align:middle line:90% of utilities. 00:59:44.630 --> 00:59:49.430 align:middle line:84% So we really, in principle, have to come to grips with the fixed 00:59:49.430 --> 00:59:52.110 align:middle line:90% point aspect of the lambdas. 00:59:52.110 --> 00:59:57.190 align:middle line:84% Instead, what we do is go back to the basics. 00:59:57.190 --> 01:00:00.390 align:middle line:84% As I was saying, who are the valued players? 01:00:00.390 --> 01:00:03.590 align:middle line:84% They're in the market when the market is small, 01:00:03.590 --> 01:00:06.570 align:middle line:84% and they're in the market when there's a lot of risk 01:00:06.570 --> 01:00:08.270 align:middle line:90% and so on and so forth. 01:00:08.270 --> 01:00:12.830 align:middle line:84% And so in the Thai data, we did that. 01:00:12.830 --> 01:00:15.630 align:middle line:84% We know who's borrowing and lending and giving gifts 01:00:15.630 --> 01:00:17.330 align:middle line:90% to whom in a given month. 01:00:17.330 --> 01:00:20.080 align:middle line:90% Those are the edges. 01:00:20.080 --> 01:00:22.580 align:middle line:90% We see those things. 01:00:22.580 --> 01:00:26.440 align:middle line:84% And we know how many people were doing that as well as-- 01:00:26.440 --> 01:00:28.720 align:middle line:84% but let's imagine they're all connected to each other 01:00:28.720 --> 01:00:31.320 align:middle line:84% or some people just aren't there. 01:00:31.320 --> 01:00:33.240 align:middle line:84% That's the way we deal with the data. 01:00:33.240 --> 01:00:37.420 align:middle line:84% So this is the covariance of the participation shock being there, 01:00:37.420 --> 01:00:43.640 align:middle line:84% say, with the number of agents who are also there. 01:00:43.640 --> 01:00:46.040 align:middle line:84% So these are objects that are varying, each 01:00:46.040 --> 01:00:47.720 align:middle line:90% one of them over time. 01:00:47.720 --> 01:00:49.100 align:middle line:90% They're random variables. 01:00:49.100 --> 01:00:51.320 align:middle line:90% We take the covariance of that. 01:00:51.320 --> 01:00:56.300 align:middle line:84% That's this rho xi for the participation shock. 01:00:56.300 --> 01:01:02.280 align:middle line:84% And this one is having to do with the variance of these two 01:01:02.280 --> 01:01:04.400 align:middle line:84% random variables, the participation 01:01:04.400 --> 01:01:11.280 align:middle line:84% shocks, and the average variance of the players who are there. 01:01:11.280 --> 01:01:15.700 align:middle line:84% For each player, we have their incomes, each household, 01:01:15.700 --> 01:01:19.850 align:middle line:84% so we can use all of the data to determine 01:01:19.850 --> 01:01:24.050 align:middle line:84% the variance-covariance structure of the incomes. 01:01:24.050 --> 01:01:31.130 align:middle line:84% And then we look at those variance-covariance numbers, 01:01:31.130 --> 01:01:39.770 align:middle line:84% the sigma ij's, conditioned on the participation shocks. 01:01:39.770 --> 01:01:42.950 align:middle line:84% And that becomes this random variable, 01:01:42.950 --> 01:01:44.730 align:middle line:84% and then we look at the covariance with h 01:01:44.730 --> 01:01:51.370 align:middle line:84% and i's participation to get the variance value of agent i. 01:01:51.370 --> 01:01:53.150 align:middle line:90% And then we run this regression. 01:01:53.150 --> 01:01:58.070 align:middle line:84% These [? Ai's ?] were the intercept terms from before, 01:01:58.070 --> 01:01:59.910 align:middle line:84% and we know how to run that regression. 01:01:59.910 --> 01:02:04.410 align:middle line:90% So this isn't deep science. 01:02:04.410 --> 01:02:08.050 align:middle line:84% There's even disagreements or questions 01:02:08.050 --> 01:02:11.010 align:middle line:84% we have about whether we should include this, but I can't help 01:02:11.010 --> 01:02:19.460 align:middle line:84% but be wanting to share it with you because it turned 01:02:19.460 --> 01:02:23.060 align:middle line:84% out quite remarkably well in the sense 01:02:23.060 --> 01:02:29.900 align:middle line:84% that the higher is the intercept-- 01:02:29.900 --> 01:02:33.300 align:middle line:84% the higher are these two terms, the participation term 01:02:33.300 --> 01:02:36.680 align:middle line:84% and the variance term, the higher is the intercept. 01:02:36.680 --> 01:02:39.260 align:middle line:90% 01:02:39.260 --> 01:02:40.360 align:middle line:90% And what is it saying? 01:02:40.360 --> 01:02:43.140 align:middle line:84% It's saying, somehow or other, it's 01:02:43.140 --> 01:02:50.220 align:middle line:84% as if this community is aware not only of the income shocks, 01:02:50.220 --> 01:02:53.580 align:middle line:84% but the participation shocks and the fact 01:02:53.580 --> 01:02:57.220 align:middle line:84% that not everyone is around all the time. 01:02:57.220 --> 01:03:06.140 align:middle line:84% So if someone is a steadfast moneylender or gift giver, 01:03:06.140 --> 01:03:08.180 align:middle line:84% that's a good thing, and they're valued. 01:03:08.180 --> 01:03:10.860 align:middle line:84% And they get a higher average consumption 01:03:10.860 --> 01:03:14.560 align:middle line:84% than other people do, as if they're getting a premium. 01:03:14.560 --> 01:03:16.310 align:middle line:84% I mean, de facto, of course, they're not 01:03:16.310 --> 01:03:19.110 align:middle line:84% entering into an explicit insurance contract, 01:03:19.110 --> 01:03:24.230 align:middle line:84% but they are, we know, in the data getting higher consumption 01:03:24.230 --> 01:03:29.150 align:middle line:84% pretty much along the lines that the theory would predict. 01:03:29.150 --> 01:03:30.830 align:middle line:84% Now, I would love to do something 01:03:30.830 --> 01:03:35.510 align:middle line:84% like this in the New York financial markets 01:03:35.510 --> 01:03:38.670 align:middle line:90% or in the Swiss markets. 01:03:38.670 --> 01:03:42.830 align:middle line:90% I've gone fishing. 01:03:42.830 --> 01:03:45.610 align:middle line:84% Those data sets are pretty confidential, 01:03:45.610 --> 01:03:51.750 align:middle line:84% and it's not obvious either exactly which variables 01:03:51.750 --> 01:03:53.790 align:middle line:90% we would want to measure. 01:03:53.790 --> 01:03:56.850 align:middle line:84% We should probably have to change the theory, 01:03:56.850 --> 01:04:00.070 align:middle line:84% but we do think that the theory is 01:04:00.070 --> 01:04:04.470 align:middle line:84% capturing something important about stochastic markets, 01:04:04.470 --> 01:04:06.930 align:middle line:84% and that that's a fundamental risk, 01:04:06.930 --> 01:04:11.070 align:middle line:84% and liquidity injections could help. 01:04:11.070 --> 01:04:12.390 align:middle line:90% So yes. 01:04:12.390 --> 01:04:14.000 align:middle line:84% STUDENT: If some policy like this 01:04:14.000 --> 01:04:16.960 align:middle line:84% are implemented in some markets, will that 01:04:16.960 --> 01:04:21.720 align:middle line:84% create some more [? harder? ?] [INAUDIBLE] 01:04:21.720 --> 01:04:24.683 align:middle line:90% those who are [INAUDIBLE] 01:04:24.683 --> 01:04:26.600 align:middle line:84% ROBERT M. TOWNSEND: So we have partial answers 01:04:26.600 --> 01:04:28.560 align:middle line:90% to that in the paper. 01:04:28.560 --> 01:04:34.440 align:middle line:84% We have a model of market participation where it's costly, 01:04:34.440 --> 01:04:36.800 align:middle line:84% and you can choose to go or not, depending 01:04:36.800 --> 01:04:39.080 align:middle line:90% on who else you think is going. 01:04:39.080 --> 01:04:45.080 align:middle line:84% And we characterize a Nash equilibrium and the impact 01:04:45.080 --> 01:04:49.120 align:middle line:84% on effort, or whether or not you're 01:04:49.120 --> 01:04:53.520 align:middle line:84% making an effort to be in the market is the moral hazard part. 01:04:53.520 --> 01:05:00.360 align:middle line:84% But on the one hand, you're not the first 01:05:00.360 --> 01:05:01.700 align:middle line:90% to ask us this question. 01:05:01.700 --> 01:05:04.000 align:middle line:84% That's why we include in the paper 01:05:04.000 --> 01:05:07.160 align:middle line:84% a discussion about endogenous participation. 01:05:07.160 --> 01:05:11.360 align:middle line:84% On the other hand, I don't think we got far enough along with it. 01:05:11.360 --> 01:05:14.850 align:middle line:84% It always seems to be very special to depend 01:05:14.850 --> 01:05:19.770 align:middle line:84% on the particular structure of a model. 01:05:19.770 --> 01:05:22.550 align:middle line:84% And you can imagine lots of different models. 01:05:22.550 --> 01:05:25.890 align:middle line:90% 01:05:25.890 --> 01:05:32.290 align:middle line:84% OK, so the other branch, contagion, that's 01:05:32.290 --> 01:05:33.230 align:middle line:90% the title of the book. 01:05:33.230 --> 01:05:39.250 align:middle line:84% It actually has an exclamation mark in the title, Contagion! 01:05:39.250 --> 01:05:42.970 align:middle line:84% Systemic Risk in Financial Networks. 01:05:42.970 --> 01:05:45.290 align:middle line:84% This is a book reviewing the literature 01:05:45.290 --> 01:05:48.090 align:middle line:84% and contributing to the literature 01:05:48.090 --> 01:05:52.930 align:middle line:84% that financial contagion is analogous to disease. 01:05:52.930 --> 01:05:55.050 align:middle line:84% Damaging financial crises are better 01:05:55.050 --> 01:05:58.930 align:middle line:84% understood by this conceptualization 01:05:58.930 --> 01:06:02.530 align:middle line:84% of the problem, and the policy implication 01:06:02.530 --> 01:06:05.290 align:middle line:84% would be manage the systemic risk, 01:06:05.290 --> 01:06:10.180 align:middle line:84% as you would in epidemiology, to identify situations 01:06:10.180 --> 01:06:15.220 align:middle line:84% where the danger is high and make targeted interventions 01:06:15.220 --> 01:06:22.020 align:middle line:84% or ex-ante policy rules to try to mitigate systemic risk. 01:06:22.020 --> 01:06:26.626 align:middle line:84% So this book, it's on the reading list. 01:06:26.626 --> 01:06:31.260 align:middle line:84% It would always be tempting to choose as something 01:06:31.260 --> 01:06:33.620 align:middle line:90% you might want to write up. 01:06:33.620 --> 01:06:35.580 align:middle line:84% The book presents a mathematical framework 01:06:35.580 --> 01:06:39.740 align:middle line:84% for the transmission channels of damaging shocks 01:06:39.740 --> 01:06:43.220 align:middle line:84% that cause instability in [? financial. ?] This all 01:06:43.220 --> 01:06:50.140 align:middle line:84% really took shape with the great financial crisis. 01:06:50.140 --> 01:06:55.340 align:middle line:84% And then somehow they made this leap to networks, and it stuck. 01:06:55.340 --> 01:06:56.880 align:middle line:90% They're still stuck on it. 01:06:56.880 --> 01:07:00.260 align:middle line:90% 01:07:00.260 --> 01:07:02.400 align:middle line:90% There's a lot of disclaimers. 01:07:02.400 --> 01:07:06.020 align:middle line:84% So there's the systemic risk basics 01:07:06.020 --> 01:07:08.630 align:middle line:84% in the introductory chapter, the features 01:07:08.630 --> 01:07:11.250 align:middle line:84% of past historical financial crises, 01:07:11.250 --> 01:07:13.570 align:middle line:84% the characteristics of banks, their balance sheets, 01:07:13.570 --> 01:07:18.510 align:middle line:84% how they're regulated, and then these cascade models, 01:07:18.510 --> 01:07:22.650 align:middle line:84% network effects, like default contagion, 01:07:22.650 --> 01:07:28.910 align:middle line:84% liquidity hoarding by banks and through their interbank 01:07:28.910 --> 01:07:29.610 align:middle line:90% exposure. 01:07:29.610 --> 01:07:36.470 align:middle line:84% For example, if there's wind in the air about a crisis brewing 01:07:36.470 --> 01:07:40.630 align:middle line:84% and it starts to impact, people may sell their assets 01:07:40.630 --> 01:07:43.870 align:middle line:84% to mitigate the problem, to gain some value, 01:07:43.870 --> 01:07:45.990 align:middle line:90% because the markets are thin. 01:07:45.990 --> 01:07:49.410 align:middle line:84% And that exacerbates the problem because it's like a fire sale, 01:07:49.410 --> 01:07:51.190 align:middle line:84% and so the asset prices are going down 01:07:51.190 --> 01:07:54.170 align:middle line:84% and everyone else has fewer buffers. 01:07:54.170 --> 01:07:59.270 align:middle line:90% 01:07:59.270 --> 01:08:03.070 align:middle line:84% And there are other kinds of cascade mechanisms. 01:08:03.070 --> 01:08:07.340 align:middle line:84% So it becomes very real when you read the book. 01:08:07.340 --> 01:08:10.800 align:middle line:84% I'm not taking away from it at all. 01:08:10.800 --> 01:08:14.800 align:middle line:84% Instead, what I want to compare is this notion 01:08:14.800 --> 01:08:20.120 align:middle line:84% of, let's make sure traders have limited exposure, especially 01:08:20.120 --> 01:08:24.960 align:middle line:84% the bigger ones, because if something were to go wrong, 01:08:24.960 --> 01:08:26.840 align:middle line:84% they're going to spread their problems 01:08:26.840 --> 01:08:29.140 align:middle line:84% around the entire financial market. 01:08:29.140 --> 01:08:31.840 align:middle line:90% 01:08:31.840 --> 01:08:35.880 align:middle line:84% So it's kind of an ex-post measure, 01:08:35.880 --> 01:08:39.920 align:middle line:90% but it's guiding ex-ante policy. 01:08:39.920 --> 01:08:42.720 align:middle line:84% And it leads you to different conclusion. 01:08:42.720 --> 01:08:44.840 align:middle line:84% The spirit of what we're doing is 01:08:44.840 --> 01:08:50.220 align:middle line:84% to try to allow ex-ante policy to mitigate adverse shocks, 01:08:50.220 --> 01:08:55.040 align:middle line:84% to keep the market thick or as functioning as well. 01:08:55.040 --> 01:09:00.120 align:middle line:84% Now, that's not to say you have to choose one or the other. 01:09:00.120 --> 01:09:09.649 align:middle line:84% There's a whole branch here of ex-ante thoughts about risk 01:09:09.649 --> 01:09:14.210 align:middle line:84% sharing versus ex-post, unexpected shocks, and maybe 01:09:14.210 --> 01:09:21.090 align:middle line:84% deriving some hybrid policy that is some kind of policy that 01:09:21.090 --> 01:09:24.069 align:middle line:90% reflects both strands. 01:09:24.069 --> 01:09:26.729 align:middle line:84% There seems to be nothing like that in the literature 01:09:26.729 --> 01:09:28.069 align:middle line:90% that we are aware of. 01:09:28.069 --> 01:09:35.090 align:middle line:90% 01:09:35.090 --> 01:09:38.330 align:middle line:84% In the few minutes that remain, I 01:09:38.330 --> 01:09:41.370 align:middle line:84% want to live up to my hope and promise 01:09:41.370 --> 01:09:45.210 align:middle line:84% to take you through a third model 01:09:45.210 --> 01:09:48.330 align:middle line:84% we really don't have time to do, and that's 01:09:48.330 --> 01:09:52.330 align:middle line:90% back to the US repo markets. 01:09:52.330 --> 01:09:59.930 align:middle line:84% So just a word about the repo markets. 01:09:59.930 --> 01:10:02.810 align:middle line:84% As I was saying earlier, you've got these money market 01:10:02.810 --> 01:10:10.660 align:middle line:84% funds looking for with, say, excess liquidity, 01:10:10.660 --> 01:10:14.740 align:middle line:84% and they're happy to lend it out for a return. 01:10:14.740 --> 01:10:16.980 align:middle line:84% They're restricted by regulation and who 01:10:16.980 --> 01:10:19.220 align:middle line:90% they are allowed to deal with. 01:10:19.220 --> 01:10:21.920 align:middle line:84% They're not allowed to trade directly with hedge funds, 01:10:21.920 --> 01:10:24.000 align:middle line:84% but they can trade with broker-dealers, 01:10:24.000 --> 01:10:30.140 align:middle line:84% especially if broker-dealers are associated with large banks. 01:10:30.140 --> 01:10:33.240 align:middle line:84% And they take treasuries as the collateral for their loans. 01:10:33.240 --> 01:10:38.340 align:middle line:84% The other side of it are the hedge funds and pension funds, 01:10:38.340 --> 01:10:42.660 align:middle line:84% and they're involved in all kinds of security trades 01:10:42.660 --> 01:10:44.740 align:middle line:90% and derivatives and so on. 01:10:44.740 --> 01:10:46.630 align:middle line:90% And they want to finance that. 01:10:46.630 --> 01:10:48.380 align:middle line:84% So they're short of liquidity, and they're 01:10:48.380 --> 01:10:51.380 align:middle line:84% very eager to borrow, even overnight, 01:10:51.380 --> 01:10:56.220 align:middle line:84% in order to adjust their asset position. 01:10:56.220 --> 01:10:58.720 align:middle line:84% So that's the basis of the repo market, 01:10:58.720 --> 01:11:02.610 align:middle line:90% and the dealers are in between. 01:11:02.610 --> 01:11:07.110 align:middle line:84% They are the nodes in the network that 01:11:07.110 --> 01:11:12.770 align:middle line:84% are connected to these clients, the mutual funds or, say, 01:11:12.770 --> 01:11:13.810 align:middle line:90% the hedge funds. 01:11:13.810 --> 01:11:17.470 align:middle line:90% 01:11:17.470 --> 01:11:23.270 align:middle line:84% Well, one thought, how are they coordinating if they're not 01:11:23.270 --> 01:11:24.890 align:middle line:90% in touch with one another? 01:11:24.890 --> 01:11:29.750 align:middle line:84% How thick will the market be depends on the arrangements 01:11:29.750 --> 01:11:34.350 align:middle line:84% that money market funds have with their clients or risk 01:11:34.350 --> 01:11:36.630 align:middle line:84% managers have with their clients, 01:11:36.630 --> 01:11:39.630 align:middle line:84% so there's a bit of an anticipation problem. 01:11:39.630 --> 01:11:41.750 align:middle line:84% And indeed, formally, you can show 01:11:41.750 --> 01:11:45.550 align:middle line:84% there are multiple equilibria in the repo market. 01:11:45.550 --> 01:11:48.870 align:middle line:84% That should remind you of the paper 01:11:48.870 --> 01:11:53.850 align:middle line:84% I went through in lecture 3 with Neil Wallace, 01:11:53.850 --> 01:11:58.430 align:middle line:84% having to do with the circulating IOUs and the fact 01:11:58.430 --> 01:12:03.540 align:middle line:84% that there were multiple perfectly valid configurations, 01:12:03.540 --> 01:12:06.800 align:middle line:84% but it requires some kind of coordination, 01:12:06.800 --> 01:12:10.300 align:middle line:84% in that case, among who was issuing assets, 01:12:10.300 --> 01:12:12.800 align:middle line:84% or in this case, how much of a position 01:12:12.800 --> 01:12:17.240 align:middle line:84% to take on behalf of your client before you enter 01:12:17.240 --> 01:12:20.840 align:middle line:90% the inter-dealer repo market. 01:12:20.840 --> 01:12:26.040 align:middle line:84% Second aspect has to do with the regulation 01:12:26.040 --> 01:12:27.800 align:middle line:90% and this financial contagion. 01:12:27.800 --> 01:12:34.160 align:middle line:84% As a result of the great financial crisis, 01:12:34.160 --> 01:12:41.760 align:middle line:84% it was judged that simple risk-weighted portfolios are not 01:12:41.760 --> 01:12:51.360 align:middle line:84% enough to allow a true measure of the risk 01:12:51.360 --> 01:12:53.160 align:middle line:90% of financial players. 01:12:53.160 --> 01:12:55.200 align:middle line:84% You just want, in addition, to look 01:12:55.200 --> 01:12:58.080 align:middle line:84% at the size of their balance sheets. 01:12:58.080 --> 01:13:00.990 align:middle line:84% So what's going on with these broker-dealers? 01:13:00.990 --> 01:13:04.450 align:middle line:84% And then you should be thinking about Tomaž's diagrams. 01:13:04.450 --> 01:13:09.290 align:middle line:84% So they're broker-dealers, so if they're in touch 01:13:09.290 --> 01:13:14.410 align:middle line:84% with a mutual fund, that means they're kind of accepting money 01:13:14.410 --> 01:13:19.610 align:middle line:84% to pass along in return for passing the securities 01:13:19.610 --> 01:13:21.090 align:middle line:90% in the other direction. 01:13:21.090 --> 01:13:23.850 align:middle line:84% But they are connected to another broker 01:13:23.850 --> 01:13:26.530 align:middle line:90% who's taking the same position. 01:13:26.530 --> 01:13:28.590 align:middle line:90% It's called rehypothecation. 01:13:28.590 --> 01:13:33.090 align:middle line:84% Basically, you're borrowing and lending simultaneously, 01:13:33.090 --> 01:13:36.490 align:middle line:84% but that expands your balance sheet. 01:13:36.490 --> 01:13:39.450 align:middle line:84% The assets and the liabilities match. 01:13:39.450 --> 01:13:42.930 align:middle line:84% But under Basel regulations, that's 01:13:42.930 --> 01:13:45.950 align:middle line:84% a bad thing, that you've expanded the balance sheet. 01:13:45.950 --> 01:13:51.290 align:middle line:84% So the policy directive was that these broker-dealers are limited 01:13:51.290 --> 01:13:54.010 align:middle line:84% in the amount of their participation in the repo 01:13:54.010 --> 01:14:00.660 align:middle line:84% market, and then you get these shortfalls of liquidity. 01:14:00.660 --> 01:14:03.340 align:middle line:84% And the big banks are saying we can't intermediate 01:14:03.340 --> 01:14:06.700 align:middle line:90% more because it would violate-- 01:14:06.700 --> 01:14:12.180 align:middle line:84% if you take it at face value, they 01:14:12.180 --> 01:14:14.220 align:middle line:84% may be getting what they want in the sense 01:14:14.220 --> 01:14:18.060 align:middle line:84% that they succeed in lobbying the Fed to inject 01:14:18.060 --> 01:14:19.840 align:middle line:90% more liquidity into the market. 01:14:19.840 --> 01:14:22.000 align:middle line:84% In fact, they don't need to lobby. 01:14:22.000 --> 01:14:24.380 align:middle line:84% The repo rate goes through the roof. 01:14:24.380 --> 01:14:29.260 align:middle line:84% It hit 10% at one point when the Federal Reserve policy 01:14:29.260 --> 01:14:35.100 align:middle line:84% rate was, like, 3% and the repo rate was 9% or 10% 01:14:35.100 --> 01:14:37.600 align:middle line:90% in October of 2023, I think. 01:14:37.600 --> 01:14:39.940 align:middle line:84% I don't remember exactly the date. 01:14:39.940 --> 01:14:44.820 align:middle line:84% And the Fed enters as a node, providing liquidity 01:14:44.820 --> 01:14:47.640 align:middle line:84% to the system as a lender, reverse repo. 01:14:47.640 --> 01:14:50.460 align:middle line:90% 01:14:50.460 --> 01:14:53.700 align:middle line:84% The third thing I want to say is there 01:14:53.700 --> 01:14:58.270 align:middle line:84% a policy to get around to mitigate this balance sheet 01:14:58.270 --> 01:14:59.630 align:middle line:90% regulation? 01:14:59.630 --> 01:15:02.910 align:middle line:84% Well, it's kind of weird because you're 01:15:02.910 --> 01:15:05.310 align:middle line:84% both a borrower nor a lender, and you're passing it 01:15:05.310 --> 01:15:07.070 align:middle line:90% right along the chain. 01:15:07.070 --> 01:15:11.350 align:middle line:84% So like Tomaž's paper that he presented, 01:15:11.350 --> 01:15:15.550 align:middle line:84% you can imagine being explicit about the interconnectedness 01:15:15.550 --> 01:15:18.270 align:middle line:84% and only worry about the source and the sink 01:15:18.270 --> 01:15:21.670 align:middle line:84% as the source and point of the flow. 01:15:21.670 --> 01:15:29.070 align:middle line:84% So you can, and we are, taking the data from the repo market. 01:15:29.070 --> 01:15:31.350 align:middle line:84% And fortunately, we have collaboration 01:15:31.350 --> 01:15:33.630 align:middle line:90% with the US Treasury on this. 01:15:33.630 --> 01:15:38.510 align:middle line:84% We are able to do the flow decomposition algorithm, one 01:15:38.510 --> 01:15:44.030 align:middle line:84% of them, and look at all these interconnected 01:15:44.030 --> 01:15:50.750 align:middle line:84% edges among the dealers, and separate out cycles, 01:15:50.750 --> 01:15:55.080 align:middle line:90% closed cycles from chains. 01:15:55.080 --> 01:15:57.480 align:middle line:84% And the chains gives you a way to order 01:15:57.480 --> 01:16:01.040 align:middle line:84% the source and the sink, but we don't 01:16:01.040 --> 01:16:02.620 align:middle line:90% eliminate the underwriting. 01:16:02.620 --> 01:16:07.520 align:middle line:84% We're saying even if this stuff isn't on the balance sheet, 01:16:07.520 --> 01:16:11.000 align:middle line:84% they've still entered into a bilateral agreement 01:16:11.000 --> 01:16:15.640 align:middle line:84% to absorb the risk if the person they passed the loan to 01:16:15.640 --> 01:16:18.280 align:middle line:90% does not pay it back. 01:16:18.280 --> 01:16:20.880 align:middle line:84% So they're willing to take that risk, 01:16:20.880 --> 01:16:26.520 align:middle line:84% but that's still a change relative to-- 01:16:26.520 --> 01:16:29.600 align:middle line:84% so I had thought for quite a while 01:16:29.600 --> 01:16:31.960 align:middle line:84% about taking through the details about all of this 01:16:31.960 --> 01:16:35.640 align:middle line:84% because it links up closely, although not identical with what 01:16:35.640 --> 01:16:38.480 align:middle line:90% Tomaž is doing. 01:16:38.480 --> 01:16:41.840 align:middle line:84% But enough said about that for today. 01:16:41.840 --> 01:16:42.340 align:middle line:90% All right. 01:16:42.340 --> 01:16:44.350 align:middle line:90% Thank you very much. 01:16:44.350 --> 01:16:53.000 align:middle line:90%