WEBVTT 00:00:00.000 --> 00:00:01.964 align:middle line:90% [SQUEAKING] 00:00:01.964 --> 00:00:04.404 align:middle line:90% [RUSTLING] 00:00:04.404 --> 00:00:07.332 align:middle line:90% [CLICKING] 00:00:07.332 --> 00:00:11.010 align:middle line:90% 00:00:11.010 --> 00:00:12.760 align:middle line:84% ROBERT TOWNSEND: Thank you all for coming. 00:00:12.760 --> 00:00:18.560 align:middle line:84% Today is the third lecture, the second after the introduction 00:00:18.560 --> 00:00:24.000 align:middle line:84% to the class, focusing on distributed ledgers 00:00:24.000 --> 00:00:27.760 align:middle line:84% as a solution to an information problem. 00:00:27.760 --> 00:00:33.080 align:middle line:84% The longer title is "Fragmented Markets, Policy Objectives, 00:00:33.080 --> 00:00:37.800 align:middle line:84% Regulatory Solutions, and Distributed Ledgers 00:00:37.800 --> 00:00:41.120 align:middle line:90% as a Technology Solution." 00:00:41.120 --> 00:00:46.160 align:middle line:84% And largely, this lecture involves 00:00:46.160 --> 00:00:51.620 align:middle line:84% statics or kind of pseudo dynamics, but not real time. 00:00:51.620 --> 00:00:55.840 align:middle line:90% 00:00:55.840 --> 00:00:59.810 align:middle line:90% So here's the outline. 00:00:59.810 --> 00:01:04.650 align:middle line:84% Efficiency as the objective of public policy and private sector 00:01:04.650 --> 00:01:06.410 align:middle line:90% innovations. 00:01:06.410 --> 00:01:08.450 align:middle line:84% I want to dwell on that for a second, 00:01:08.450 --> 00:01:15.730 align:middle line:84% because so often you will see central banks coming up 00:01:15.730 --> 00:01:21.750 align:middle line:84% with a use case and trying to work it out, 00:01:21.750 --> 00:01:24.210 align:middle line:90% spending resources and so on. 00:01:24.210 --> 00:01:28.450 align:middle line:84% I have no idea sometimes why they pick that use case. 00:01:28.450 --> 00:01:32.050 align:middle line:84% They never give the motivation for it. 00:01:32.050 --> 00:01:35.570 align:middle line:84% It's more like something they think 00:01:35.570 --> 00:01:39.290 align:middle line:84% they can do with the technology, rather than 00:01:39.290 --> 00:01:45.930 align:middle line:84% something that's motivated by the underlying economic need. 00:01:45.930 --> 00:01:50.650 align:middle line:84% So I'm going to take the time to go through efficiency the way 00:01:50.650 --> 00:01:54.130 align:middle line:90% economists think about it. 00:01:54.130 --> 00:01:56.990 align:middle line:84% Then problems from fragmented markets. 00:01:56.990 --> 00:02:00.940 align:middle line:84% So we're going to take the standard setup 00:02:00.940 --> 00:02:05.300 align:middle line:84% and chop it up, create some frictions, 00:02:05.300 --> 00:02:09.300 align:middle line:84% and then see what happens and potentially how to overcome 00:02:09.300 --> 00:02:11.420 align:middle line:90% those frictions. 00:02:11.420 --> 00:02:16.140 align:middle line:84% When you have frictions like fragmented markets, 00:02:16.140 --> 00:02:20.140 align:middle line:84% it's typical that regulators get involved. 00:02:20.140 --> 00:02:24.260 align:middle line:84% Being well intended, they will try to remedy the problem. 00:02:24.260 --> 00:02:28.180 align:middle line:84% And you'll see that in the US, this is the case. 00:02:28.180 --> 00:02:33.067 align:middle line:84% But even imposing common prices, we're 00:02:33.067 --> 00:02:34.900 align:middle line:84% still going to be left with this information 00:02:34.900 --> 00:02:38.740 align:middle line:84% problem and a natural role for distributed ledgers. 00:02:38.740 --> 00:02:42.260 align:middle line:84% This, by the way, quite a few years ago 00:02:42.260 --> 00:02:45.940 align:middle line:84% was my first entry point into thinking 00:02:45.940 --> 00:02:50.940 align:middle line:84% about distributed ledgers, because I made this connection. 00:02:50.940 --> 00:02:54.180 align:middle line:90% OK, so that's a little long. 00:02:54.180 --> 00:02:57.740 align:middle line:84% Efficiency is an objective of public policy, private sector 00:02:57.740 --> 00:02:59.700 align:middle line:90% innovations as well. 00:02:59.700 --> 00:03:03.980 align:middle line:84% So these slides are about Pareto efficient allocations 00:03:03.980 --> 00:03:08.020 align:middle line:84% through the planner's problem and competitive markets. 00:03:08.020 --> 00:03:12.280 align:middle line:84% Now, you saw some of this material on Friday, 00:03:12.280 --> 00:03:16.740 align:middle line:84% for those of you in the recitation. 00:03:16.740 --> 00:03:20.540 align:middle line:84% Repetition arguably is a good thing, 00:03:20.540 --> 00:03:24.260 align:middle line:84% so I'm not going to skip over it too, too fast. 00:03:24.260 --> 00:03:27.980 align:middle line:84% Let me just say, especially for those of you who 00:03:27.980 --> 00:03:30.340 align:middle line:84% weren't in the recitation section, 00:03:30.340 --> 00:03:32.460 align:middle line:84% those slides are available, and also 00:03:32.460 --> 00:03:36.180 align:middle line:84% [? Ralph ?] and I are available to walk you through. 00:03:36.180 --> 00:03:44.660 align:middle line:84% We certainly recognize that the economic background is something 00:03:44.660 --> 00:03:47.380 align:middle line:84% that you may need some help with, 00:03:47.380 --> 00:03:52.260 align:middle line:84% and we're here to provide that background. 00:03:52.260 --> 00:03:56.090 align:middle line:84% That said, this treatment, Pareto efficient allocations, 00:03:56.090 --> 00:03:59.890 align:middle line:84% competitive equilibria, it's all self-contained. 00:03:59.890 --> 00:04:03.590 align:middle line:84% It's not like you need another reference to understand 00:04:03.590 --> 00:04:06.390 align:middle line:84% the definitions and the concepts. 00:04:06.390 --> 00:04:11.010 align:middle line:84% And we will be working with it a lot today. 00:04:11.010 --> 00:04:14.590 align:middle line:84% So you'll see the basic definitions and then 00:04:14.590 --> 00:04:17.290 align:middle line:90% how we use that in analysis. 00:04:17.290 --> 00:04:23.230 align:middle line:84% So long story short, this is a pure exchange economy 00:04:23.230 --> 00:04:27.510 align:middle line:84% with two goods and two households. 00:04:27.510 --> 00:04:30.270 align:middle line:84% We're going to have a representation 00:04:30.270 --> 00:04:36.510 align:middle line:84% of an efficient allocation that has the property that you can't 00:04:36.510 --> 00:04:38.750 align:middle line:84% make one party better off without making 00:04:38.750 --> 00:04:40.590 align:middle line:90% the other worse off. 00:04:40.590 --> 00:04:44.950 align:middle line:84% And that's going to be this dotted orange line. 00:04:44.950 --> 00:04:49.510 align:middle line:84% Note that these indifference curves representing preferences 00:04:49.510 --> 00:04:52.850 align:middle line:84% are tangent, a little bit of jargon. 00:04:52.850 --> 00:04:55.480 align:middle line:84% The marginal rates of substitution of the households 00:04:55.480 --> 00:04:56.420 align:middle line:90% are equated. 00:04:56.420 --> 00:05:01.620 align:middle line:84% And if you pick one good as a numeraire, 00:05:01.620 --> 00:05:05.720 align:middle line:84% the prices at which they're trading are equated. 00:05:05.720 --> 00:05:08.720 align:middle line:84% So there's a whole bunch of these efficient allocations, 00:05:08.720 --> 00:05:13.520 align:middle line:84% and a lot of allocations which are not efficient. 00:05:13.520 --> 00:05:18.100 align:middle line:84% When we're off the Pareto front, the Pareto set, 00:05:18.100 --> 00:05:19.460 align:middle line:90% we might want to fix something. 00:05:19.460 --> 00:05:24.360 align:middle line:84% Another way to find these efficient allocations 00:05:24.360 --> 00:05:28.280 align:middle line:84% is to convert it into a programming problem, which 00:05:28.280 --> 00:05:33.040 align:middle line:84% is to maximize weighted sums of the utility of the agents 00:05:33.040 --> 00:05:36.320 align:middle line:90% subject to resource constraints. 00:05:36.320 --> 00:05:41.400 align:middle line:84% So here the weighted sum is represented by this red tangent 00:05:41.400 --> 00:05:42.440 align:middle line:90% line. 00:05:42.440 --> 00:05:47.560 align:middle line:84% And given the weights lambda of the agents, 00:05:47.560 --> 00:05:52.170 align:middle line:84% u star would be the solution to the programming problem. 00:05:52.170 --> 00:05:56.250 align:middle line:84% And u star would be some particular allocation 00:05:56.250 --> 00:05:57.890 align:middle line:90% in this Pareto set. 00:05:57.890 --> 00:06:01.130 align:middle line:84% If you change the weights, you'll 00:06:01.130 --> 00:06:04.290 align:middle line:84% rotate along that frontier, and you 00:06:04.290 --> 00:06:09.490 align:middle line:84% would be tracing out all of these efficient allocations. 00:06:09.490 --> 00:06:14.130 align:middle line:84% So the programming problem makes it easy to find stuff. 00:06:14.130 --> 00:06:17.530 align:middle line:84% In fact, we can convert them to linear programs. 00:06:17.530 --> 00:06:22.530 align:middle line:84% And finally, a particular economy 00:06:22.530 --> 00:06:25.730 align:middle line:84% may be characterized by private ownership 00:06:25.730 --> 00:06:27.810 align:middle line:90% where we have endowments. 00:06:27.810 --> 00:06:33.090 align:middle line:84% Their starting point, we have prices and a trading line 00:06:33.090 --> 00:06:36.770 align:middle line:84% running through the endowment, the slopes 00:06:36.770 --> 00:06:40.790 align:middle line:84% being the prices and the outcome, 00:06:40.790 --> 00:06:45.010 align:middle line:84% the competitive equilibrium outcome is a particular Pareto 00:06:45.010 --> 00:06:48.570 align:middle line:90% optimal allocation. 00:06:48.570 --> 00:06:51.690 align:middle line:84% So hopefully these three pictures 00:06:51.690 --> 00:06:56.190 align:middle line:84% are worth thousands of words and a little bit of notation, 00:06:56.190 --> 00:07:00.790 align:middle line:84% but I will go through some of the notation in more generality. 00:07:00.790 --> 00:07:05.370 align:middle line:90% 00:07:05.370 --> 00:07:09.530 align:middle line:84% Commodities could be apples and oranges. 00:07:09.530 --> 00:07:11.490 align:middle line:84% General equilibrium theory has a bit 00:07:11.490 --> 00:07:15.410 align:middle line:84% of a stigma that somehow it kind fell out 00:07:15.410 --> 00:07:20.570 align:middle line:84% of fashion in favor of partial equilibrium and game theory 00:07:20.570 --> 00:07:22.010 align:middle line:90% and so on. 00:07:22.010 --> 00:07:26.370 align:middle line:84% I think part of that is just not realizing the applicability. 00:07:26.370 --> 00:07:30.570 align:middle line:84% When you start to index goods by time 00:07:30.570 --> 00:07:35.010 align:middle line:84% or by realized states of the world, 00:07:35.010 --> 00:07:38.070 align:middle line:84% we can deal with intertemporal allocations and uncertainty, 00:07:38.070 --> 00:07:39.610 align:middle line:84% and we don't have to change anything 00:07:39.610 --> 00:07:43.930 align:middle line:84% at all about the underlying way of proceeding. 00:07:43.930 --> 00:07:49.280 align:middle line:84% So it's really quite a robust thing. 00:07:49.280 --> 00:07:54.700 align:middle line:84% So the economy consists of more than two potentially goods. 00:07:54.700 --> 00:07:57.100 align:middle line:90% L is the number of commodities. 00:07:57.100 --> 00:07:59.740 align:middle line:84% A finite number of households, say more than 2, 00:07:59.740 --> 00:08:03.440 align:middle line:84% capital I. We're going to add production and firms 00:08:03.440 --> 00:08:05.580 align:middle line:90% J, finite number. 00:08:05.580 --> 00:08:10.980 align:middle line:84% And then consumers have sets of feasible allocations, 00:08:10.980 --> 00:08:12.840 align:middle line:90% which could generate utility. 00:08:12.840 --> 00:08:15.380 align:middle line:84% They have preferences over those bundles. 00:08:15.380 --> 00:08:18.660 align:middle line:84% Firms have technologies characterized 00:08:18.660 --> 00:08:20.820 align:middle line:90% by production sets. 00:08:20.820 --> 00:08:23.840 align:middle line:84% And there is potentially, in addition, 00:08:23.840 --> 00:08:27.020 align:middle line:84% some aggregate resources available. 00:08:27.020 --> 00:08:29.960 align:middle line:84% So L is the dimension of the commodity space. 00:08:29.960 --> 00:08:31.920 align:middle line:90% I is number of households. 00:08:31.920 --> 00:08:34.260 align:middle line:90% J is the number of firms. 00:08:34.260 --> 00:08:40.280 align:middle line:84% And then we have this utility possibility set for any economy. 00:08:40.280 --> 00:08:45.860 align:middle line:84% So economies are now being summarized by consumption sets 00:08:45.860 --> 00:08:47.810 align:middle line:84% and utilities for each household, 00:08:47.810 --> 00:08:51.630 align:middle line:84% production sets for each firm, and this aggregate endowment. 00:08:51.630 --> 00:08:54.510 align:middle line:84% And we're going to experimentally think 00:08:54.510 --> 00:08:59.750 align:middle line:84% about varying the consumption and the production allocation 00:08:59.750 --> 00:09:02.410 align:middle line:84% to be feasible for households and consumers 00:09:02.410 --> 00:09:10.390 align:middle line:84% and look at the requirement that you can't consume more than 00:09:10.390 --> 00:09:12.270 align:middle line:90% what's available. 00:09:12.270 --> 00:09:15.030 align:middle line:84% What's available in this case being 00:09:15.030 --> 00:09:20.110 align:middle line:84% from the aggregate endowment or from production. 00:09:20.110 --> 00:09:22.270 align:middle line:84% And for any feasible allocation, we're 00:09:22.270 --> 00:09:26.010 align:middle line:84% going to generate this utility possibility set. 00:09:26.010 --> 00:09:30.630 align:middle line:84% So this example was two goods, two households, 00:09:30.630 --> 00:09:36.390 align:middle line:84% feasible allocations in the box, generating this pink area 00:09:36.390 --> 00:09:38.450 align:middle line:90% of utility possibilities. 00:09:38.450 --> 00:09:41.550 align:middle line:90% 00:09:41.550 --> 00:09:52.760 align:middle line:84% The utility possibility frontier is the outer locus 00:09:52.760 --> 00:09:54.880 align:middle line:90% of feasible points. 00:09:54.880 --> 00:10:00.160 align:middle line:84% Here there's nothing northeast of any of these points. 00:10:00.160 --> 00:10:03.040 align:middle line:84% If you had a point on the frontier 00:10:03.040 --> 00:10:04.680 align:middle line:84% with something northeast of it, you 00:10:04.680 --> 00:10:06.920 align:middle line:84% could make one household better off 00:10:06.920 --> 00:10:08.560 align:middle line:84% without hurting the other one, and that 00:10:08.560 --> 00:10:12.240 align:middle line:84% would violate the definition of Pareto efficiency. 00:10:12.240 --> 00:10:15.260 align:middle line:84% There is nothing northeast if you're on the frontier. 00:10:15.260 --> 00:10:18.600 align:middle line:90% 00:10:18.600 --> 00:10:21.520 align:middle line:84% And likewise, the formal definition of Pareto 00:10:21.520 --> 00:10:26.480 align:middle line:84% optimality is an allocation for consumers and firms 00:10:26.480 --> 00:10:30.720 align:middle line:84% that is feasible, and such that there 00:10:30.720 --> 00:10:35.760 align:middle line:84% is no other feasible allocation with primes here 00:10:35.760 --> 00:10:41.160 align:middle line:84% that would make no household worse off and one 00:10:41.160 --> 00:10:46.040 align:middle line:84% or potential subset of households better off. 00:10:46.040 --> 00:10:50.480 align:middle line:84% So Pareto optimality is defined by what it is not. 00:10:50.480 --> 00:10:55.920 align:middle line:84% You cannot find such a bundle that Pareto dominates, 00:10:55.920 --> 00:11:01.160 align:middle line:84% that would make some better off without hurting the others. 00:11:01.160 --> 00:11:07.880 align:middle line:84% And then as a final step, we talk about competitive markets 00:11:07.880 --> 00:11:10.800 align:middle line:84% as a way, hopefully, to implement 00:11:10.800 --> 00:11:13.320 align:middle line:90% an efficient allocation. 00:11:13.320 --> 00:11:17.000 align:middle line:84% Let there be markets in everything in sight. 00:11:17.000 --> 00:11:20.680 align:middle line:84% And then we have to specify ownership. 00:11:20.680 --> 00:11:24.720 align:middle line:84% So not just the aggregate endowment, 00:11:24.720 --> 00:11:32.840 align:middle line:84% but the vector for household I of its endowments of goods. 00:11:32.840 --> 00:11:36.160 align:middle line:84% Some of the components of that vector could be 0, 00:11:36.160 --> 00:11:39.240 align:middle line:90% but some could be positive. 00:11:39.240 --> 00:11:43.530 align:middle line:84% And these theta IJ's are the equity market. 00:11:43.530 --> 00:11:46.730 align:middle line:84% So theta IJ is the share that household 00:11:46.730 --> 00:11:51.490 align:middle line:84% I has in the profits of firm J. In other words, 00:11:51.490 --> 00:11:55.070 align:middle line:84% net profits will be distributed according to those thetas. 00:11:55.070 --> 00:11:59.490 align:middle line:90% 00:11:59.490 --> 00:12:05.490 align:middle line:84% So of all raising equilibrium, competitive equilibrium 00:12:05.490 --> 00:12:16.290 align:middle line:84% is a specification of prices, a particular price p 00:12:16.290 --> 00:12:22.810 align:middle line:84% star, and these allocations for consumers and firms 00:12:22.810 --> 00:12:26.370 align:middle line:84% also with stars, x star, y star, such 00:12:26.370 --> 00:12:32.290 align:middle line:84% that each firm is maximizing profits, 00:12:32.290 --> 00:12:36.730 align:middle line:84% scanning over all feasible bundles in its production set. 00:12:36.730 --> 00:12:42.580 align:middle line:84% Each household is maximizing utility subject to two 00:12:42.580 --> 00:12:47.140 align:middle line:84% requirements that the bundles be feasible for household I 00:12:47.140 --> 00:12:49.100 align:middle line:90% and its consumption set. 00:12:49.100 --> 00:12:55.060 align:middle line:84% And in this case, that the value of expenditures on goods 00:12:55.060 --> 00:13:01.480 align:middle line:84% not exceed the value of its available resources, 00:13:01.480 --> 00:13:04.420 align:middle line:84% which is the valuation of endowment 00:13:04.420 --> 00:13:08.140 align:middle line:84% plus the distributed profits from firms. 00:13:08.140 --> 00:13:10.820 align:middle line:84% And allocation should be feasible. 00:13:10.820 --> 00:13:15.060 align:middle line:84% You can't eat more in the aggregate than what's available. 00:13:15.060 --> 00:13:20.540 align:middle line:84% Now, let me just convert something in words. 00:13:20.540 --> 00:13:22.540 align:middle line:90% Excess demand. 00:13:22.540 --> 00:13:28.460 align:middle line:84% So excess demand for household I would be the positive difference 00:13:28.460 --> 00:13:32.460 align:middle line:84% between its consumption allocation and its endowment. 00:13:32.460 --> 00:13:35.340 align:middle line:84% It could have little or no endowment. 00:13:35.340 --> 00:13:39.300 align:middle line:84% Who wants to eat more in a competitive equilibrium? 00:13:39.300 --> 00:13:42.150 align:middle line:90% So we could relabel this. 00:13:42.150 --> 00:13:45.070 align:middle line:84% We could get rid of production and just 00:13:45.070 --> 00:13:50.670 align:middle line:84% say the valuation at price is p star of excess demand 00:13:50.670 --> 00:13:55.030 align:middle line:90% is less than or equal to 0. 00:13:55.030 --> 00:13:57.510 align:middle line:84% Likewise, this resource constraint 00:13:57.510 --> 00:14:00.390 align:middle line:84% getting rid of production just says 00:14:00.390 --> 00:14:03.770 align:middle line:84% the sum of the excess demands are equal to 0. 00:14:03.770 --> 00:14:07.030 align:middle line:90% 00:14:07.030 --> 00:14:10.190 align:middle line:84% I'm mentioning this because shortly when 00:14:10.190 --> 00:14:12.190 align:middle line:84% we get to this information problem 00:14:12.190 --> 00:14:15.230 align:middle line:84% of decentralized exchange, it's written down 00:14:15.230 --> 00:14:17.830 align:middle line:90% in terms of excess demands. 00:14:17.830 --> 00:14:21.710 align:middle line:84% But you can go back and forth between the underlying demands, 00:14:21.710 --> 00:14:24.510 align:middle line:84% keeping track of the endowment versus just talking 00:14:24.510 --> 00:14:26.030 align:middle line:90% about excess demands. 00:14:26.030 --> 00:14:29.710 align:middle line:84% Excess demands are negative when you're 00:14:29.710 --> 00:14:31.490 align:middle line:90% supplying more than you eat. 00:14:31.490 --> 00:14:35.190 align:middle line:90% 00:14:35.190 --> 00:14:39.210 align:middle line:84% And these great theorems without here 00:14:39.210 --> 00:14:42.550 align:middle line:84% all the qualifications of all Walrasian equilibrium 00:14:42.550 --> 00:14:43.850 align:middle line:90% is Pareto optimal. 00:14:43.850 --> 00:14:46.430 align:middle line:84% So it has these efficiency properties. 00:14:46.430 --> 00:14:49.390 align:middle line:84% And in fact, any Pareto optimal allocation 00:14:49.390 --> 00:14:53.310 align:middle line:84% can be supported as a competitive equilibrium 00:14:53.310 --> 00:15:00.190 align:middle line:84% if you're able to redistribute wealth lump sum. 00:15:00.190 --> 00:15:07.630 align:middle line:84% So that's a 10 minute summary of these theorems. 00:15:07.630 --> 00:15:12.550 align:middle line:84% And now we'll launch into these two problems 00:15:12.550 --> 00:15:15.630 align:middle line:84% that we get from fragmented markets. 00:15:15.630 --> 00:15:20.430 align:middle line:84% The first is the intention that everyone should 00:15:20.430 --> 00:15:22.790 align:middle line:90% be trading at a common price. 00:15:22.790 --> 00:15:26.910 align:middle line:84% And the second has to do with this impossibility theorem 00:15:26.910 --> 00:15:28.270 align:middle line:90% of Ostroy-Starr. 00:15:28.270 --> 00:15:34.010 align:middle line:84% So a reminder, again, the Edgeworth box. 00:15:34.010 --> 00:15:35.830 align:middle line:90% We start with an endowment. 00:15:35.830 --> 00:15:39.600 align:middle line:90% We have a competitive price. 00:15:39.600 --> 00:15:43.300 align:middle line:84% Trader one is moving, giving up good one and getting good two. 00:15:43.300 --> 00:15:46.480 align:middle line:84% Trader two is moving in the opposite direction. 00:15:46.480 --> 00:15:48.840 align:middle line:84% The valuation of the excess demands 00:15:48.840 --> 00:15:53.620 align:middle line:90% are equal to 0 for both parties. 00:15:53.620 --> 00:15:56.480 align:middle line:84% And in particular, if you thought about the good 00:15:56.480 --> 00:15:59.680 align:middle line:84% on the x-axis, so to speak, as a numeraire, 00:15:59.680 --> 00:16:02.840 align:middle line:84% they're trading at a common price. 00:16:02.840 --> 00:16:05.760 align:middle line:84% The price of good two relative to good one 00:16:05.760 --> 00:16:07.500 align:middle line:90% is the same for both. 00:16:07.500 --> 00:16:13.200 align:middle line:90% 00:16:13.200 --> 00:16:18.280 align:middle line:84% The US has lots of financial markets. 00:16:18.280 --> 00:16:20.900 align:middle line:84% In particular, it has multiple equity markets. 00:16:20.900 --> 00:16:24.720 align:middle line:84% Not just the New York Stock Exchange, but also 00:16:24.720 --> 00:16:33.960 align:middle line:84% local exchanges in the Midwest and so on for other securities. 00:16:33.960 --> 00:16:36.930 align:middle line:84% But it's regulated and there's something 00:16:36.930 --> 00:16:43.450 align:middle line:84% called the US national marketing system that 00:16:43.450 --> 00:16:46.050 align:middle line:84% seeks to remedy a potential failure that 00:16:46.050 --> 00:16:48.730 align:middle line:84% could happen when you have multiple exchanges quoting 00:16:48.730 --> 00:16:50.330 align:middle line:90% different prices. 00:16:50.330 --> 00:16:52.930 align:middle line:84% Trades could be executed on one exchange 00:16:52.930 --> 00:16:58.410 align:middle line:84% at a price different from what would happen on the other one. 00:16:58.410 --> 00:17:02.970 align:middle line:84% And the Security Exchange Commission framework, again, 00:17:02.970 --> 00:17:09.849 align:middle line:84% called National Marketing System, NMS, from 2005 00:17:09.849 --> 00:17:14.410 align:middle line:84% is order protection to ensure that retail orders are executed 00:17:14.410 --> 00:17:19.130 align:middle line:84% at the exchange with the most favorable pricing. 00:17:19.130 --> 00:17:24.010 align:middle line:84% Or another way to put this, an exchange as an institution 00:17:24.010 --> 00:17:29.570 align:middle line:84% has to match the best quote from any other exchange. 00:17:29.570 --> 00:17:33.170 align:middle line:84% So exchanges are competing for orders. 00:17:33.170 --> 00:17:35.900 align:middle line:84% Broker dealers are placing those orders. 00:17:35.900 --> 00:17:40.340 align:middle line:84% There are other things that happen, like giving discounts 00:17:40.340 --> 00:17:44.620 align:middle line:84% to brokers who bring in more volume, trying 00:17:44.620 --> 00:17:50.380 align:middle line:84% to attract traders, and other obvious things 00:17:50.380 --> 00:17:53.440 align:middle line:90% that happen with exchanges. 00:17:53.440 --> 00:17:58.820 align:middle line:84% But the outcome is checked against this standard. 00:17:58.820 --> 00:18:02.700 align:middle line:84% Chester Spatt at Carnegie Mellon and his colleague have just 00:18:02.700 --> 00:18:08.940 align:middle line:84% written a rather lengthy paper called "Regulating Market 00:18:08.940 --> 00:18:10.000 align:middle line:90% Microstructure." 00:18:10.000 --> 00:18:14.020 align:middle line:84% Oh, so now that reminds me to say something, which 00:18:14.020 --> 00:18:16.060 align:middle line:90% I forgot to say last time. 00:18:16.060 --> 00:18:18.160 align:middle line:84% When I scroll through these slides, 00:18:18.160 --> 00:18:23.420 align:middle line:84% I am mentioning, briefly, other papers. 00:18:23.420 --> 00:18:30.300 align:middle line:84% And those papers are on the syllabus often with stars. 00:18:30.300 --> 00:18:34.030 align:middle line:90% So this is like a reminder. 00:18:34.030 --> 00:18:36.030 align:middle line:84% Maybe you're interested in getting 00:18:36.030 --> 00:18:39.670 align:middle line:84% into the nitty gritty of what the National Marketing 00:18:39.670 --> 00:18:46.550 align:middle line:84% System is about, as summarized by Chester and his colleague. 00:18:46.550 --> 00:18:47.290 align:middle line:90% Maybe not. 00:18:47.290 --> 00:18:49.070 align:middle line:84% There's lots of other options, but I just 00:18:49.070 --> 00:18:52.310 align:middle line:84% wanted to highlight these when I go through it. 00:18:52.310 --> 00:18:56.090 align:middle line:90% So they've amended this. 00:18:56.090 --> 00:18:58.870 align:middle line:84% The Securities and Exchange Commission 00:18:58.870 --> 00:19:03.030 align:middle line:84% changed the National Marketing System regulations. 00:19:03.030 --> 00:19:08.530 align:middle line:84% The key idea would be minimum pricing increments, 00:19:08.530 --> 00:19:13.510 align:middle line:84% making those increments smaller, dealing with access fees that 00:19:13.510 --> 00:19:17.230 align:middle line:84% are charged by the Securities exchanges, 00:19:17.230 --> 00:19:21.430 align:middle line:84% and making orders more transparent. 00:19:21.430 --> 00:19:25.910 align:middle line:84% I will spare you the details, although they're written down 00:19:25.910 --> 00:19:26.790 align:middle line:90% here. 00:19:26.790 --> 00:19:29.630 align:middle line:84% But I wanted to compare this with something else 00:19:29.630 --> 00:19:33.510 align:middle line:84% the SEC was doing, which has to do 00:19:33.510 --> 00:19:38.750 align:middle line:84% with an antitrust suit against Amazon, which I presume has now 00:19:38.750 --> 00:19:40.550 align:middle line:90% been dropped. 00:19:40.550 --> 00:19:43.250 align:middle line:84% But when I wrote up these slides, 00:19:43.250 --> 00:19:49.950 align:middle line:84% it was still being argued in court. 00:19:49.950 --> 00:19:53.070 align:middle line:84% Amazon was charged with antitrust. 00:19:53.070 --> 00:19:56.870 align:middle line:84% They filed a motion to dismiss the charges, 00:19:56.870 --> 00:19:58.830 align:middle line:84% arguing that, well, all they're doing 00:19:58.830 --> 00:20:03.030 align:middle line:84% is innovations that lead to consumer benefits, 00:20:03.030 --> 00:20:05.810 align:middle line:84% and they're pushing their competitors to follow suit. 00:20:05.810 --> 00:20:08.790 align:middle line:84% In particular, Amazon matches the discounts 00:20:08.790 --> 00:20:10.690 align:middle line:90% provided by competitors. 00:20:10.690 --> 00:20:13.550 align:middle line:90% 00:20:13.550 --> 00:20:17.450 align:middle line:84% Also, if the items are high priced or overpriced, 00:20:17.450 --> 00:20:19.110 align:middle line:90% it will feature deals. 00:20:19.110 --> 00:20:22.910 align:middle line:84% And it also features efficient delivery options 00:20:22.910 --> 00:20:25.608 align:middle line:90% for Prime subscribers. 00:20:25.608 --> 00:20:27.150 align:middle line:84% Well, at this point, hopefully you're 00:20:27.150 --> 00:20:30.760 align:middle line:84% feeling a little bit puzzled, because the spirit 00:20:30.760 --> 00:20:36.840 align:middle line:84% of the antitrust suit goes against-- 00:20:36.840 --> 00:20:43.840 align:middle line:84% in a commodity, Amazon as a merchandise platform 00:20:43.840 --> 00:20:49.200 align:middle line:84% go against the standards of the National Marketing System. 00:20:49.200 --> 00:20:51.460 align:middle line:84% So this is not a uniform standard. 00:20:51.460 --> 00:20:53.480 align:middle line:84% I don't know whether there's something 00:20:53.480 --> 00:20:56.160 align:middle line:84% about financial markets that makes regulation 00:20:56.160 --> 00:20:59.400 align:middle line:84% of those markets different or more difficult 00:20:59.400 --> 00:21:04.320 align:middle line:84% than regulation of other markets. 00:21:04.320 --> 00:21:08.680 align:middle line:84% So something provocative to think about. 00:21:08.680 --> 00:21:11.360 align:middle line:90% The second leg of this. 00:21:11.360 --> 00:21:17.320 align:middle line:84% And let me again just say regulation is a tough thing 00:21:17.320 --> 00:21:18.960 align:middle line:90% to do. 00:21:18.960 --> 00:21:25.080 align:middle line:84% If you had technology available that you could implement, 00:21:25.080 --> 00:21:30.890 align:middle line:84% it sometimes mitigates the need for the regulation. 00:21:30.890 --> 00:21:32.810 align:middle line:84% So when you're advising central banks 00:21:32.810 --> 00:21:36.570 align:middle line:84% in other countries about distributed ledger technologies, 00:21:36.570 --> 00:21:39.030 align:middle line:84% this kind of discussion comes up. 00:21:39.030 --> 00:21:42.010 align:middle line:90% 00:21:42.010 --> 00:21:45.610 align:middle line:84% Better to use the new technologies if possible 00:21:45.610 --> 00:21:49.770 align:middle line:84% rather than be stuck with a regulatory problem. 00:21:49.770 --> 00:21:53.130 align:middle line:84% So Ostroy-Starr I wrote this paper, granted, 00:21:53.130 --> 00:21:58.450 align:middle line:84% in 1974, which will hopefully through the slides, you'll see, 00:21:58.450 --> 00:22:01.530 align:middle line:84% make it even more remarkable, called 00:22:01.530 --> 00:22:04.530 align:middle line:84% something about the information problem 00:22:04.530 --> 00:22:07.290 align:middle line:84% of decentralized exchange or the heading 00:22:07.290 --> 00:22:11.110 align:middle line:84% here is the information problem of fragmented markets. 00:22:11.110 --> 00:22:17.370 align:middle line:84% So we're going to again partition agents exogenously 00:22:17.370 --> 00:22:19.250 align:middle line:90% into pairs. 00:22:19.250 --> 00:22:23.510 align:middle line:84% They can trade with each other at common prices in these pairs. 00:22:23.510 --> 00:22:29.140 align:middle line:84% In fact, to make it "easy," quote, 00:22:29.140 --> 00:22:31.360 align:middle line:90% we just impose common prices. 00:22:31.360 --> 00:22:36.020 align:middle line:84% So the pricing is not the issue, but the fragmentation still 00:22:36.020 --> 00:22:37.480 align:middle line:90% creates frictions. 00:22:37.480 --> 00:22:40.660 align:middle line:84% So in this model, first in English, 00:22:40.660 --> 00:22:45.300 align:middle line:84% there's a finite number of goods like the apples and oranges. 00:22:45.300 --> 00:22:49.540 align:middle line:84% But as I said, they could be assets, even digital assets. 00:22:49.540 --> 00:22:51.640 align:middle line:90% The same framework works. 00:22:51.640 --> 00:22:53.820 align:middle line:84% They own stuff and they want to get other stuff 00:22:53.820 --> 00:22:56.060 align:middle line:90% and they're willing to trade. 00:22:56.060 --> 00:23:00.420 align:middle line:84% So they're endowed with goods or securities, 00:23:00.420 --> 00:23:02.580 align:middle line:90% depending on the interpretation. 00:23:02.580 --> 00:23:05.980 align:middle line:84% They have utility functions over end of period holdings 00:23:05.980 --> 00:23:07.200 align:middle line:90% of these assets. 00:23:07.200 --> 00:23:11.940 align:middle line:84% And the goal is to achieve the Walrasian equilibrium 00:23:11.940 --> 00:23:13.120 align:middle line:90% allocation. 00:23:13.120 --> 00:23:14.780 align:middle line:90% That's the target. 00:23:14.780 --> 00:23:16.160 align:middle line:90% It's a good target. 00:23:16.160 --> 00:23:20.800 align:middle line:84% It's Pareto efficient to achieve that, 00:23:20.800 --> 00:23:26.900 align:middle line:84% even though they're doomed to have to trade with one another 00:23:26.900 --> 00:23:29.700 align:middle line:90% in the sequence of markets. 00:23:29.700 --> 00:23:33.580 align:middle line:84% What you can't do here is have everyone trade with everybody 00:23:33.580 --> 00:23:37.020 align:middle line:84% else initially in a completely centralized market. 00:23:37.020 --> 00:23:39.820 align:middle line:84% We're going to respect the fragmentation 00:23:39.820 --> 00:23:43.100 align:middle line:84% and nevertheless try to achieve the objective. 00:23:43.100 --> 00:23:45.120 align:middle line:84% So traders are matched pair wise. 00:23:45.120 --> 00:23:49.020 align:middle line:84% The pairings are known in advance. 00:23:49.020 --> 00:23:54.220 align:middle line:84% Equilibrium prices are used to value these swaps or trades 00:23:54.220 --> 00:23:56.320 align:middle line:90% as if they were digital assets. 00:23:56.320 --> 00:23:59.260 align:middle line:90% Atomic swaps of digital assets. 00:23:59.260 --> 00:24:03.540 align:middle line:84% Each bilateral exchange satisfies a quid pro quo 00:24:03.540 --> 00:24:05.980 align:middle line:84% condition that the value of goods received 00:24:05.980 --> 00:24:09.820 align:middle line:84% is going to be equal to the value of goods sold, 00:24:09.820 --> 00:24:13.700 align:middle line:84% exchanged with your trading partner. 00:24:13.700 --> 00:24:20.540 align:middle line:84% And traders are nothing more here than code. 00:24:20.540 --> 00:24:25.470 align:middle line:84% So we're used to thinking they should be maximizing something. 00:24:25.470 --> 00:24:28.350 align:middle line:90% Here the objective is given. 00:24:28.350 --> 00:24:33.550 align:middle line:84% It's to achieve, if possible, the Walrasian allocation. 00:24:33.550 --> 00:24:37.830 align:middle line:84% And the question is, what information 00:24:37.830 --> 00:24:45.270 align:middle line:84% would each trader as a node need as an input into the code 00:24:45.270 --> 00:24:47.610 align:middle line:84% in order to achieve the objective? 00:24:47.610 --> 00:24:50.230 align:middle line:90% 00:24:50.230 --> 00:24:55.870 align:middle line:84% It's like algorithmic trading without the max part. 00:24:55.870 --> 00:25:00.750 align:middle line:84% Now, things seem to be pretty special here in the sense 00:25:00.750 --> 00:25:03.230 align:middle line:90% they're matched pairwise. 00:25:03.230 --> 00:25:05.250 align:middle line:90% Maybe there could be triplets. 00:25:05.250 --> 00:25:08.430 align:middle line:90% 00:25:08.430 --> 00:25:11.170 align:middle line:84% If they're singletons, that's fine. 00:25:11.170 --> 00:25:13.710 align:middle line:90% That's going to be allowed. 00:25:13.710 --> 00:25:15.850 align:middle line:84% And the pairings are known in advance. 00:25:15.850 --> 00:25:18.550 align:middle line:84% And things are going to get even more complicated 00:25:18.550 --> 00:25:26.240 align:middle line:84% if the ordering is random and is maybe even revealed over time. 00:25:26.240 --> 00:25:27.660 align:middle line:90% This is quite simple. 00:25:27.660 --> 00:25:31.180 align:middle line:84% It's completely forecastable, and yet the problem emerges. 00:25:31.180 --> 00:25:33.260 align:middle line:84% So this is the way we want to go. 00:25:33.260 --> 00:25:37.120 align:middle line:84% We want to make it as easy as possible 00:25:37.120 --> 00:25:40.780 align:middle line:84% and still show that it's potentially hard. 00:25:40.780 --> 00:25:44.380 align:middle line:90% 00:25:44.380 --> 00:25:49.920 align:middle line:84% So in notation, there are J traders 00:25:49.920 --> 00:25:53.040 align:middle line:84% and a finite number of commodities 00:25:53.040 --> 00:25:56.360 align:middle line:90% with this price vector p. 00:25:56.360 --> 00:26:00.600 align:middle line:84% And we're going to have a Walrasian environment. 00:26:00.600 --> 00:26:05.000 align:middle line:84% So I was anticipating this a minute ago. 00:26:05.000 --> 00:26:07.240 align:middle line:84% Each trader has an endowment vector. 00:26:07.240 --> 00:26:08.220 align:middle line:90% I apologize. 00:26:08.220 --> 00:26:10.580 align:middle line:84% The notation changes across papers. 00:26:10.580 --> 00:26:13.880 align:middle line:84% This is the notation that Ostroy and Starr used. 00:26:13.880 --> 00:26:16.680 align:middle line:84% Each trader has an endowment vector, 00:26:16.680 --> 00:26:22.970 align:middle line:84% and each trader has excess demand at that price p. 00:26:22.970 --> 00:26:26.970 align:middle line:84% So if you start with the endowment B 00:26:26.970 --> 00:26:32.450 align:middle line:84% and you get your excess demand, your final consumption 00:26:32.450 --> 00:26:34.930 align:middle line:84% or holdings would be B plus C. Remember, 00:26:34.930 --> 00:26:37.170 align:middle line:90% things can be negative here. 00:26:37.170 --> 00:26:40.490 align:middle line:84% C could be negative excess supply. 00:26:40.490 --> 00:26:45.130 align:middle line:84% And as in a competitive equilibrium, 00:26:45.130 --> 00:26:46.990 align:middle line:90% the budget constraint is this. 00:26:46.990 --> 00:26:51.650 align:middle line:84% It just says the value of excess demand is 0. 00:26:51.650 --> 00:26:55.010 align:middle line:84% We've shut down the distinction between endowments 00:26:55.010 --> 00:26:57.490 align:middle line:84% and final allocation, taken the difference, 00:26:57.490 --> 00:27:01.290 align:middle line:90% and valued it at the price p. 00:27:01.290 --> 00:27:05.130 align:middle line:84% And also the sum of the excess demands is 0. 00:27:05.130 --> 00:27:10.450 align:middle line:84% So this is in even more succinct notation 00:27:10.450 --> 00:27:16.810 align:middle line:84% the standard definition of a competitive equilibrium starting 00:27:16.810 --> 00:27:23.850 align:middle line:84% with the objects, three of them, B, Z, and P. So any 00:27:23.850 --> 00:27:28.650 align:middle line:84% BZP satisfying this is a competitive equilibrium. 00:27:28.650 --> 00:27:33.570 align:middle line:84% Forgot to say you can't sell more than you own. 00:27:33.570 --> 00:27:35.530 align:middle line:90% Z is excess demand. 00:27:35.530 --> 00:27:37.650 align:middle line:84% Take the negative sign through both. 00:27:37.650 --> 00:27:39.570 align:middle line:84% You'll have excess supply is less than 00:27:39.570 --> 00:27:41.230 align:middle line:90% or equal to your endowment. 00:27:41.230 --> 00:27:45.010 align:middle line:90% 00:27:45.010 --> 00:27:52.050 align:middle line:84% So the Ostroy-Starr paper refers to this block u 00:27:52.050 --> 00:27:55.770 align:middle line:90% as the underlying economy. 00:27:55.770 --> 00:27:58.890 align:middle line:90% The underlying objective. 00:27:58.890 --> 00:28:00.850 align:middle line:84% You'll see the theorems are going to-- 00:28:00.850 --> 00:28:04.930 align:middle line:84% for any blah, blah, blah in x, y, z, and for every u 00:28:04.930 --> 00:28:07.850 align:middle line:84% there exists a so-called-- so the u is going 00:28:07.850 --> 00:28:10.970 align:middle line:90% to appear in the theorems. 00:28:10.970 --> 00:28:12.310 align:middle line:90% The mechanics of trading. 00:28:12.310 --> 00:28:16.380 align:middle line:84% There are T periods where traders are matched pairwise, 00:28:16.380 --> 00:28:20.580 align:middle line:84% unless the number of traders is odd, in which case 00:28:20.580 --> 00:28:23.020 align:middle line:84% at every date, one trader has to stand out, 00:28:23.020 --> 00:28:27.220 align:middle line:90% because there's no pairing left. 00:28:27.220 --> 00:28:33.580 align:middle line:84% And this is such that every trader meets every other trader 00:28:33.580 --> 00:28:36.720 align:middle line:90% eventually and only once. 00:28:36.720 --> 00:28:40.800 align:middle line:90% 00:28:40.800 --> 00:28:47.860 align:middle line:84% A. A are actions or outcomes that happen for trader I, 00:28:47.860 --> 00:28:52.600 align:middle line:84% AIT, trader I in period T, gets a positive number 00:28:52.600 --> 00:28:56.080 align:middle line:84% if you're acquiring a good, negative if you're giving it up. 00:28:56.080 --> 00:29:00.020 align:middle line:84% These are vectors, again, over the underlying commodities. 00:29:00.020 --> 00:29:03.780 align:middle line:84% And the restrictions on actions is 00:29:03.780 --> 00:29:07.460 align:middle line:84% they should not result in a negative holding of any good. 00:29:07.460 --> 00:29:11.500 align:middle line:84% And traders are trading pairwise. 00:29:11.500 --> 00:29:16.190 align:middle line:84% So what one guy gets, the other guy gives up for each good. 00:29:16.190 --> 00:29:20.550 align:middle line:84% So the sum of the vectors of actions sums to 0 00:29:20.550 --> 00:29:24.830 align:middle line:84% and trades are fair at those given prices p 00:29:24.830 --> 00:29:27.870 align:middle line:90% of the underlying environment. 00:29:27.870 --> 00:29:31.750 align:middle line:84% For each trader, they're kind of on their budget line 00:29:31.750 --> 00:29:33.930 align:middle line:90% for this pairwise trade. 00:29:33.930 --> 00:29:36.590 align:middle line:90% 00:29:36.590 --> 00:29:39.830 align:middle line:84% The valuation of the actions is quid pro quo. 00:29:39.830 --> 00:29:42.550 align:middle line:84% The value of what you give up, you 00:29:42.550 --> 00:29:45.570 align:middle line:90% get equivalent value in return. 00:29:45.570 --> 00:29:49.910 align:middle line:90% 00:29:49.910 --> 00:29:54.190 align:middle line:84% So the capital A denotes the set of all these actions 00:29:54.190 --> 00:29:55.690 align:middle line:90% with these restrictions. 00:29:55.690 --> 00:30:00.300 align:middle line:90% 00:30:00.300 --> 00:30:04.230 align:middle line:84% So we could think about what information 00:30:04.230 --> 00:30:08.750 align:middle line:84% might be needed starting with something minimal. 00:30:08.750 --> 00:30:14.200 align:middle line:84% In fact, they proposed three types of limited information 00:30:14.200 --> 00:30:16.180 align:middle line:90% or decentralized information. 00:30:16.180 --> 00:30:18.240 align:middle line:90% D1, D2, D3. 00:30:18.240 --> 00:30:22.240 align:middle line:84% And then finally, which they will need, 00:30:22.240 --> 00:30:29.360 align:middle line:84% the centralizing restriction C. So D for decentralized, C 00:30:29.360 --> 00:30:31.960 align:middle line:90% for centralized. 00:30:31.960 --> 00:30:38.160 align:middle line:84% D is the minimal specifying that when traders I and J meet 00:30:38.160 --> 00:30:42.840 align:middle line:84% at day T, their actions can depend 00:30:42.840 --> 00:30:51.600 align:middle line:84% on their initial excess demands of the two on their endowment. 00:30:51.600 --> 00:30:56.120 align:middle line:84% And if this is not the first pairing, 00:30:56.120 --> 00:31:04.120 align:middle line:84% the sum of the actions of each one 00:31:04.120 --> 00:31:06.720 align:middle line:84% up to and through the previous date. 00:31:06.720 --> 00:31:11.920 align:middle line:84% Now, I was thinking about Bitcoin with this. 00:31:11.920 --> 00:31:16.410 align:middle line:90% 00:31:16.410 --> 00:31:21.670 align:middle line:84% Bitcoin doesn't directly report the balances. 00:31:21.670 --> 00:31:23.490 align:middle line:84% You have to figure out the balances 00:31:23.490 --> 00:31:28.730 align:middle line:84% from the entire history of trades since the genesis state. 00:31:28.730 --> 00:31:31.950 align:middle line:84% And this requirement says, all you need are the balances. 00:31:31.950 --> 00:31:35.450 align:middle line:84% It doesn't matter what the individual components 00:31:35.450 --> 00:31:38.190 align:middle line:84% were over time, leading up to the current balance. 00:31:38.190 --> 00:31:41.090 align:middle line:90% 00:31:41.090 --> 00:31:43.970 align:middle line:84% Now, this always comes as a surprise. 00:31:43.970 --> 00:31:46.690 align:middle line:90% We finally name these guys. 00:31:46.690 --> 00:31:50.710 align:middle line:84% So we have their identities, I and J. 00:31:50.710 --> 00:31:54.670 align:middle line:84% So this actually meant that whenever I and J meet, 00:31:54.670 --> 00:31:56.868 align:middle line:84% they put on blinders about who they're meeting. 00:31:56.868 --> 00:31:58.410 align:middle line:84% They don't know their names, but they 00:31:58.410 --> 00:32:03.490 align:middle line:84% do know these excess demands without knowing 00:32:03.490 --> 00:32:04.870 align:middle line:90% the name of the people. 00:32:04.870 --> 00:32:08.110 align:middle line:84% So in some sense, we have anonymity here. 00:32:08.110 --> 00:32:10.370 align:middle line:90% We drop it. 00:32:10.370 --> 00:32:15.390 align:middle line:84% D3 is the same as D2 with the names and excess demands, 00:32:15.390 --> 00:32:19.570 align:middle line:84% except that now we do spell out the entire history of trades 00:32:19.570 --> 00:32:24.370 align:middle line:84% of the two, I and J. And that's going to be crucial. 00:32:24.370 --> 00:32:28.130 align:middle line:90% But it's not enough. 00:32:28.130 --> 00:32:31.170 align:middle line:84% The centralizing one is the same as D3, 00:32:31.170 --> 00:32:36.290 align:middle line:84% except that when any two get together, 00:32:36.290 --> 00:32:40.330 align:middle line:84% the code has available not just the history of trades 00:32:40.330 --> 00:32:43.730 align:middle line:84% of each of those two, I and J, but the history of trades 00:32:43.730 --> 00:32:48.850 align:middle line:84% of all the traders in the whole system. 00:32:48.850 --> 00:32:56.290 align:middle line:84% In other words, even if I and J have never 00:32:56.290 --> 00:33:00.770 align:middle line:84% met any of the other people other than I and J, 00:33:00.770 --> 00:33:03.970 align:middle line:84% they still know what those other traders have been doing. 00:33:03.970 --> 00:33:09.190 align:middle line:84% Or at least if they had that information, 00:33:09.190 --> 00:33:13.420 align:middle line:84% then the theorem is they are able to get 00:33:13.420 --> 00:33:20.220 align:middle line:84% to the competitive equilibrium in one round of trading. 00:33:20.220 --> 00:33:23.840 align:middle line:84% So here's a formal statement of the theorem, 00:33:23.840 --> 00:33:28.860 align:middle line:84% which I called fast, efficient chains. 00:33:28.860 --> 00:33:31.260 align:middle line:90% We'll come back to that maybe. 00:33:31.260 --> 00:33:38.300 align:middle line:84% There is a trading rule that uses this information in C. 00:33:38.300 --> 00:33:43.220 align:middle line:84% It satisfies the restrictions of action set A 00:33:43.220 --> 00:33:50.340 align:middle line:84% and it completes trading in a single round for any environment 00:33:50.340 --> 00:33:56.420 align:middle line:90% u, for any p, Z, B satisfying u. 00:33:56.420 --> 00:33:59.940 align:middle line:84% Not just some of them, but all of them. 00:33:59.940 --> 00:34:06.580 align:middle line:84% But likewise, the twin, there is no trading rule that 00:34:06.580 --> 00:34:12.310 align:middle line:84% uses the most information, but still decentralized D3 that 00:34:12.310 --> 00:34:15.070 align:middle line:84% satisfies the restrictions in A and completes trading 00:34:15.070 --> 00:34:22.630 align:middle line:84% with a single round satisfying any p, Z, B. In other words, 00:34:22.630 --> 00:34:28.270 align:middle line:84% starting from D3, you try to implement the solution 00:34:28.270 --> 00:34:29.530 align:middle line:90% for any environment. 00:34:29.530 --> 00:34:31.530 align:middle line:84% You should be able to find a counterexample. 00:34:31.530 --> 00:34:33.210 align:middle line:84% That's what the theorem is saying. 00:34:33.210 --> 00:34:36.330 align:middle line:84% You can't do it for all environments u. 00:34:36.330 --> 00:34:39.790 align:middle line:90% 00:34:39.790 --> 00:34:41.690 align:middle line:84% But you may need some extra assumptions. 00:34:41.690 --> 00:34:45.969 align:middle line:84% And if those assumptions are satisfied in addition, 00:34:45.969 --> 00:34:50.710 align:middle line:84% then you may be able to get there. 00:34:50.710 --> 00:34:53.489 align:middle line:84% So we want to look at what I'm calling on the slides here 00:34:53.489 --> 00:34:55.790 align:middle line:90% institutional workaround. 00:34:55.790 --> 00:35:00.510 align:middle line:84% In this case, it's my language, but it's Ostroy-Starr with this 00:35:00.510 --> 00:35:05.470 align:middle line:84% paper written in the '70s about to describe to us the current 00:35:05.470 --> 00:35:09.120 align:middle line:84% set of contemporary institutional arrangements 00:35:09.120 --> 00:35:16.160 align:middle line:84% and highlighting the problems with those arrangements some 50 00:35:16.160 --> 00:35:19.320 align:middle line:84% years after they wrote their article. 00:35:19.320 --> 00:35:22.213 align:middle line:84% STUDENT: Can we talk about whether or not 00:35:22.213 --> 00:35:23.880 align:middle line:84% we're supposed to think of these traders 00:35:23.880 --> 00:35:27.560 align:middle line:84% as when they're engaging in trades, trying to maximize 00:35:27.560 --> 00:35:29.240 align:middle line:90% some objective function? 00:35:29.240 --> 00:35:31.520 align:middle line:84% Because you said the goal is to try and achieve 00:35:31.520 --> 00:35:33.400 align:middle line:84% some Pareto equilibrium, which kind of 00:35:33.400 --> 00:35:37.500 align:middle line:84% implies the existence of some selfish behavior of the agents. 00:35:37.500 --> 00:35:40.600 align:middle line:84% But then you also said that it kind of 00:35:40.600 --> 00:35:44.920 align:middle line:84% seemed like the objective function of the traders 00:35:44.920 --> 00:35:47.480 align:middle line:84% was to just to achieve a Pareto equilibrium. 00:35:47.480 --> 00:35:50.680 align:middle line:84% ROBERT TOWNSEND: In this paper, it is only the latter. 00:35:50.680 --> 00:35:55.320 align:middle line:84% So they have a consensus about the social objective, 00:35:55.320 --> 00:35:58.480 align:middle line:84% and the issue is whether they can achieve it 00:35:58.480 --> 00:36:01.020 align:middle line:84% given this kind of partitioning of agents. 00:36:01.020 --> 00:36:04.080 align:middle line:84% So the maximization of individual agents, 00:36:04.080 --> 00:36:07.320 align:middle line:84% other than the fact that their preference got used in defining 00:36:07.320 --> 00:36:09.800 align:middle line:90% the social objective, is gone. 00:36:09.800 --> 00:36:14.680 align:middle line:84% We will next time weaken that and have agents maximizing 00:36:14.680 --> 00:36:16.920 align:middle line:84% utility in the way that we're used to thinking 00:36:16.920 --> 00:36:19.540 align:middle line:90% about it date by date by date. 00:36:19.540 --> 00:36:22.720 align:middle line:84% But here it's like pseudo time, and it's just 00:36:22.720 --> 00:36:27.800 align:middle line:84% the design of an algorithm that dictates what they're 00:36:27.800 --> 00:36:29.340 align:middle line:90% supposed to do when they meet. 00:36:29.340 --> 00:36:31.650 align:middle line:84% STUDENT: So the utility, or the I 00:36:31.650 --> 00:36:34.840 align:middle line:84% guess, objective function of the traders kind of only factors 00:36:34.840 --> 00:36:37.018 align:middle line:84% into the definition of what constitutes a Pareto? 00:36:37.018 --> 00:36:38.060 align:middle line:90% ROBERT TOWNSEND: Correct. 00:36:38.060 --> 00:36:40.640 align:middle line:90% 00:36:40.640 --> 00:36:42.260 align:middle line:90% And still there's a problem. 00:36:42.260 --> 00:36:45.920 align:middle line:90% 00:36:45.920 --> 00:36:52.720 align:middle line:84% So these workarounds have to do with money, with a big broker 00:36:52.720 --> 00:36:57.920 align:middle line:84% dealer, and with some kind of overdraft facility. 00:36:57.920 --> 00:37:01.200 align:middle line:90% So we'll do each one at a time. 00:37:01.200 --> 00:37:04.890 align:middle line:90% Money is a medium of exchange. 00:37:04.890 --> 00:37:07.410 align:middle line:90% So we pick one security. 00:37:07.410 --> 00:37:10.210 align:middle line:90% More on that momentarily. 00:37:10.210 --> 00:37:14.010 align:middle line:84% One commodity, if you wish, that has the property 00:37:14.010 --> 00:37:19.130 align:middle line:84% that at the specified price, each and every trader 00:37:19.130 --> 00:37:22.810 align:middle line:84% can use it in pairwise meetings to buy 00:37:22.810 --> 00:37:27.410 align:middle line:84% the requisite target, regardless of the order 00:37:27.410 --> 00:37:30.610 align:middle line:90% or timing of the meetings. 00:37:30.610 --> 00:37:33.910 align:middle line:84% The intuition being that they have enough of it. 00:37:33.910 --> 00:37:38.290 align:middle line:84% So that if they happen to be buying before selling, 00:37:38.290 --> 00:37:42.310 align:middle line:84% they can buy out of the value of this security. 00:37:42.310 --> 00:37:46.450 align:middle line:90% 00:37:46.450 --> 00:37:51.810 align:middle line:84% I mentioned on the second lecture 00:37:51.810 --> 00:37:55.850 align:middle line:84% that monetary theorists think of money as having properties, 00:37:55.850 --> 00:37:59.490 align:middle line:84% like a unit of account store of value and medium of exchange. 00:37:59.490 --> 00:38:02.180 align:middle line:84% Medium of exchange being it appears frequently 00:38:02.180 --> 00:38:04.620 align:middle line:90% in a transaction matrix. 00:38:04.620 --> 00:38:06.940 align:middle line:90% And that's what's going on here. 00:38:06.940 --> 00:38:10.060 align:middle line:84% It will be necessary, in fact, that they're using 00:38:10.060 --> 00:38:14.940 align:middle line:90% this money security a lot. 00:38:14.940 --> 00:38:19.060 align:middle line:84% It's a little more subtle than that, but we'll get to that part 00:38:19.060 --> 00:38:22.260 align:middle line:90% when we look at the theorem. 00:38:22.260 --> 00:38:26.580 align:middle line:84% Now, there's still kind of a centralization aspect to this. 00:38:26.580 --> 00:38:27.900 align:middle line:90% Which good? 00:38:27.900 --> 00:38:31.340 align:middle line:90% Which security? 00:38:31.340 --> 00:38:33.800 align:middle line:84% If they pick it right and there's enough of it, 00:38:33.800 --> 00:38:35.660 align:middle line:90% it's great. 00:38:35.660 --> 00:38:39.200 align:middle line:84% But you may need some social consensus. 00:38:39.200 --> 00:38:42.940 align:middle line:90% 00:38:42.940 --> 00:38:45.500 align:middle line:90% And you could choose wrong. 00:38:45.500 --> 00:38:49.700 align:middle line:84% It might work for one possible choice and not for another one. 00:38:49.700 --> 00:38:52.940 align:middle line:84% So here's the definition in theorem-- 00:38:52.940 --> 00:38:55.460 align:middle line:84% formal statement in theorem four. 00:38:55.460 --> 00:38:59.220 align:middle line:84% There is a trading rule that uses D1. 00:38:59.220 --> 00:39:01.890 align:middle line:90% And that's pretty interesting. 00:39:01.890 --> 00:39:08.430 align:middle line:84% D1 is the weakest information requirement. 00:39:08.430 --> 00:39:11.830 align:middle line:90% Doesn't even use their names. 00:39:11.830 --> 00:39:14.170 align:middle line:84% And the spirit of that is I don't care who you are, 00:39:14.170 --> 00:39:15.690 align:middle line:84% and I don't care about your history. 00:39:15.690 --> 00:39:18.470 align:middle line:90% Just show me the money. 00:39:18.470 --> 00:39:19.890 align:middle line:90% The other guys got the money. 00:39:19.890 --> 00:39:22.550 align:middle line:90% That's all I need to know. 00:39:22.550 --> 00:39:25.410 align:middle line:84% So this satisfies the restrictions on actions. 00:39:25.410 --> 00:39:29.950 align:middle line:84% It completes trade within a single round. 00:39:29.950 --> 00:39:32.750 align:middle line:84% But we need this extra condition that there's 00:39:32.750 --> 00:39:35.990 align:middle line:84% this commodity, little m for money, 00:39:35.990 --> 00:39:41.670 align:middle line:84% such that for every trader I, the valuation at those prices 00:39:41.670 --> 00:39:47.910 align:middle line:84% of the environment u, the valuation of that good 00:39:47.910 --> 00:39:54.030 align:middle line:84% is not less than the demands for goods 00:39:54.030 --> 00:39:56.010 align:middle line:90% of all the other commodities. 00:39:56.010 --> 00:39:59.390 align:middle line:84% This bracket plussing operator just 00:39:59.390 --> 00:40:02.910 align:middle line:84% picks out positive components and sets negative components 00:40:02.910 --> 00:40:03.610 align:middle line:90% to 0. 00:40:03.610 --> 00:40:09.030 align:middle line:84% So it's just valuing at these prices C for commodity C's where 00:40:09.030 --> 00:40:12.110 align:middle line:90% the excess demand is positive. 00:40:12.110 --> 00:40:15.430 align:middle line:84% Remember, Z, excess demand, is a feature 00:40:15.430 --> 00:40:23.510 align:middle line:84% of the underlying environment along with P and B. So 00:40:23.510 --> 00:40:24.770 align:middle line:90% that's the condition. 00:40:24.770 --> 00:40:27.790 align:middle line:90% 00:40:27.790 --> 00:40:34.270 align:middle line:84% So every trader has enough of it to purchase his excess demands. 00:40:34.270 --> 00:40:36.230 align:middle line:90% This statement is interesting. 00:40:36.230 --> 00:40:39.310 align:middle line:84% Without quid pro quo, which I was arguing 00:40:39.310 --> 00:40:42.370 align:middle line:84% was a natural condition, without it, though, 00:40:42.370 --> 00:40:45.110 align:middle line:84% it would be easy to find a trading process that 00:40:45.110 --> 00:40:50.230 align:middle line:84% completes trade within a single round without these assumptions. 00:40:50.230 --> 00:40:53.750 align:middle line:84% Now, here, please forgive me, but I'm not going 00:40:53.750 --> 00:40:56.350 align:middle line:90% to show you more of the proof. 00:40:56.350 --> 00:40:58.800 align:middle line:84% And in fact, that would be something 00:40:58.800 --> 00:41:03.460 align:middle line:84% very useful to do if any one of you are interested in it. 00:41:03.460 --> 00:41:08.640 align:middle line:84% I'm showing you the nuances, but not actually digging out 00:41:08.640 --> 00:41:11.400 align:middle line:90% the notation of the proof. 00:41:11.400 --> 00:41:14.200 align:middle line:84% So this statement is left hanging here. 00:41:14.200 --> 00:41:17.280 align:middle line:84% However, with the restriction of quid pro quo, 00:41:17.280 --> 00:41:19.800 align:middle line:84% when two traders meet, the excess demands 00:41:19.800 --> 00:41:23.480 align:middle line:84% do not precisely offset one another. 00:41:23.480 --> 00:41:26.640 align:middle line:84% Then they would need to decide what subset of their demands 00:41:26.640 --> 00:41:31.160 align:middle line:84% would be met at the meeting if you didn't have the money. 00:41:31.160 --> 00:41:34.280 align:middle line:84% But when you have the money, they're 00:41:34.280 --> 00:41:39.120 align:middle line:84% trading what they can to match excess demands. 00:41:39.120 --> 00:41:43.805 align:middle line:84% And the difference would be filled in by this money object. 00:41:43.805 --> 00:41:46.180 align:middle line:84% So in other words, when you're going through the theorem, 00:41:46.180 --> 00:41:48.360 align:middle line:84% it's kind of sounds like they don't do anything 00:41:48.360 --> 00:41:50.800 align:middle line:90% but give or get the money. 00:41:50.800 --> 00:41:52.760 align:middle line:84% And the theorem is actually proved, 00:41:52.760 --> 00:41:56.730 align:middle line:84% allowing some trades to happen without the money, 00:41:56.730 --> 00:42:00.850 align:middle line:84% and it's the residual that's getting filled in. 00:42:00.850 --> 00:42:04.050 align:middle line:84% I don't know if that's an essential part of the proof, 00:42:04.050 --> 00:42:06.090 align:middle line:84% and they could have done it the easy way. 00:42:06.090 --> 00:42:12.730 align:middle line:84% But the main thing here is the theorem, ample ex-ante 00:42:12.730 --> 00:42:13.630 align:middle line:90% liquidity. 00:42:13.630 --> 00:42:16.930 align:middle line:90% 00:42:16.930 --> 00:42:21.010 align:middle line:84% So that brings us to contemporary economies, 00:42:21.010 --> 00:42:23.910 align:middle line:84% sufficient liquidity savings mechanisms. 00:42:23.910 --> 00:42:28.970 align:middle line:84% So large value payment systems used by central banks 00:42:28.970 --> 00:42:31.530 align:middle line:84% to settle the claims of commercial banks 00:42:31.530 --> 00:42:33.770 align:middle line:90% play a crucial role. 00:42:33.770 --> 00:42:38.530 align:middle line:84% This is delegated to the public sector in almost all countries. 00:42:38.530 --> 00:42:41.210 align:middle line:84% It's a natural role for a central bank 00:42:41.210 --> 00:42:45.530 align:middle line:84% to operate these settlement systems. 00:42:45.530 --> 00:42:49.610 align:middle line:84% And the value is huge, in the US 100 times GDP. 00:42:49.610 --> 00:42:54.210 align:middle line:84% And these systems have been improved over time. 00:42:54.210 --> 00:43:00.420 align:middle line:84% It used to be something like end of day settlement, 00:43:00.420 --> 00:43:03.580 align:middle line:84% but then people didn't come up with the money. 00:43:03.580 --> 00:43:06.120 align:middle line:84% So that was deemed to be very risky. 00:43:06.120 --> 00:43:09.260 align:middle line:84% So they moved to real time gross settlement, 00:43:09.260 --> 00:43:13.900 align:middle line:84% which sounds like whenever an order is placed by one bank 00:43:13.900 --> 00:43:18.660 align:middle line:84% to pay another bank, it's kind of instantaneously settled. 00:43:18.660 --> 00:43:21.020 align:middle line:90% That's not quite right. 00:43:21.020 --> 00:43:22.300 align:middle line:90% Why? 00:43:22.300 --> 00:43:25.020 align:middle line:84% Because then a participating commercial bank 00:43:25.020 --> 00:43:28.940 align:middle line:84% would have to come in at the beginning of the trading day 00:43:28.940 --> 00:43:31.540 align:middle line:84% with an enormous amount of liquidity 00:43:31.540 --> 00:43:36.200 align:middle line:84% put in escrow in order to honor potential demands on it, 00:43:36.200 --> 00:43:39.460 align:middle line:84% to make payments from other banks. 00:43:39.460 --> 00:43:41.340 align:middle line:84% And so almost immediately, people 00:43:41.340 --> 00:43:45.620 align:middle line:84% were searching for ways to cut back 00:43:45.620 --> 00:43:48.480 align:middle line:84% on the requisite amount of liquidity. 00:43:48.480 --> 00:43:51.100 align:middle line:84% And that's the terminology, liquidity 00:43:51.100 --> 00:43:53.300 align:middle line:90% saving mechanisms systems. 00:43:53.300 --> 00:43:58.740 align:middle line:84% And in particular, you can imagine putting money in escrow 00:43:58.740 --> 00:44:03.060 align:middle line:84% and have it available by the algorithm to use, 00:44:03.060 --> 00:44:06.740 align:middle line:84% but that it is not used right away. 00:44:06.740 --> 00:44:12.540 align:middle line:84% And as an example, this is from the Bank of England. 00:44:12.540 --> 00:44:16.500 align:middle line:84% They have one of the best liquidity savings 00:44:16.500 --> 00:44:18.720 align:middle line:90% mechanisms you can go. 00:44:18.720 --> 00:44:25.660 align:middle line:84% It's in the syllabus if you're of the mind to invest some more. 00:44:25.660 --> 00:44:31.220 align:middle line:84% Provides details about how the liquidity savings mechanism 00:44:31.220 --> 00:44:34.780 align:middle line:90% works for the Bank of England. 00:44:34.780 --> 00:44:40.140 align:middle line:84% And these money market managers of banks 00:44:40.140 --> 00:44:45.620 align:middle line:84% follow instructions for sequestering liquidity. 00:44:45.620 --> 00:44:49.500 align:middle line:84% It's kind of a funny argument in the sense 00:44:49.500 --> 00:44:52.050 align:middle line:84% that they don't want to mandate too much. 00:44:52.050 --> 00:44:55.670 align:middle line:84% They want to leave optionality to the commercial banks. 00:44:55.670 --> 00:44:58.190 align:middle line:84% So they basically tell them, oh, don't 00:44:58.190 --> 00:45:03.270 align:middle line:84% worry about reporting the fact that you're 00:45:03.270 --> 00:45:04.690 align:middle line:90% supposed to make a payment. 00:45:04.690 --> 00:45:07.550 align:middle line:84% We don't necessarily process it right away. 00:45:07.550 --> 00:45:09.670 align:middle line:90% We'll put it in the queue. 00:45:09.670 --> 00:45:15.030 align:middle line:84% And odds are you might get some liquidity paid to you 00:45:15.030 --> 00:45:17.930 align:middle line:90% by other banks in advance. 00:45:17.930 --> 00:45:22.950 align:middle line:84% And you'll never have to use this liquidity in escrow. 00:45:22.950 --> 00:45:26.950 align:middle line:84% Of course, the opposite could be happening. 00:45:26.950 --> 00:45:29.690 align:middle line:84% So commercial banks went along with this, 00:45:29.690 --> 00:45:33.390 align:middle line:84% and they're basically using less liquidity overall 00:45:33.390 --> 00:45:37.150 align:middle line:84% than they would if they had to sequester the amount for all 00:45:37.150 --> 00:45:38.210 align:middle line:90% of the payments. 00:45:38.210 --> 00:45:40.950 align:middle line:90% 00:45:40.950 --> 00:45:45.910 align:middle line:84% I find myself wondering what can you mandate? 00:45:45.910 --> 00:45:51.480 align:middle line:84% Customers go to their bank say, sellers, and they say, 00:45:51.480 --> 00:45:54.280 align:middle line:90% this customer owes me money. 00:45:54.280 --> 00:45:59.760 align:middle line:84% My customer to whom I sold goods owes me money. 00:45:59.760 --> 00:46:03.720 align:middle line:84% And so they go to the bank of the customer, effectively. 00:46:03.720 --> 00:46:09.420 align:middle line:84% And they say, we owe you on behalf of the supplier. 00:46:09.420 --> 00:46:12.680 align:middle line:90% 00:46:12.680 --> 00:46:17.880 align:middle line:84% We owe the supplier the money coming from the customer. 00:46:17.880 --> 00:46:19.180 align:middle line:90% But banks are strategic. 00:46:19.180 --> 00:46:22.560 align:middle line:84% They don't place all the payment orders right away. 00:46:22.560 --> 00:46:26.320 align:middle line:84% I showed you that reference in the first slide 00:46:26.320 --> 00:46:29.120 align:middle line:84% of the first lecture, this tension 00:46:29.120 --> 00:46:36.240 align:middle line:84% between store of value and medium of exchange. 00:46:36.240 --> 00:46:39.100 align:middle line:84% So they conserve their liquidity and they play this game. 00:46:39.100 --> 00:46:41.540 align:middle line:84% They wait till the end of the day to submit their orders. 00:46:41.540 --> 00:46:46.620 align:middle line:84% Of course, if the orders were on a registry to begin with, 00:46:46.620 --> 00:46:48.200 align:middle line:84% there would be nothing to conceal 00:46:48.200 --> 00:46:50.410 align:middle line:84% and the central bank would just run the algorithm 00:46:50.410 --> 00:46:51.310 align:middle line:90% from the get go. 00:46:51.310 --> 00:46:53.590 align:middle line:84% But that's not the way it works in practice. 00:46:53.590 --> 00:46:56.410 align:middle line:90% 00:46:56.410 --> 00:46:59.130 align:middle line:90% Second institutional workaround. 00:46:59.130 --> 00:47:03.930 align:middle line:84% One large trader or broker dealer. 00:47:03.930 --> 00:47:07.450 align:middle line:84% So here's another thing that would work. 00:47:07.450 --> 00:47:12.890 align:middle line:84% If a condition is satisfied, we designate 00:47:12.890 --> 00:47:17.690 align:middle line:84% one of the traders as the intermediary broker dealer. 00:47:17.690 --> 00:47:22.570 align:middle line:84% And effectively, all trade can happen through that dealer only, 00:47:22.570 --> 00:47:25.490 align:middle line:90% like a giant warehouse facility. 00:47:25.490 --> 00:47:28.770 align:middle line:84% This key broker dealer has to have 00:47:28.770 --> 00:47:33.370 align:middle line:84% sufficiently large inventories of each of the securities so as 00:47:33.370 --> 00:47:38.330 align:middle line:84% to be able to honor the demands for any security exchange placed 00:47:38.330 --> 00:47:43.010 align:middle line:84% upon it by any customer coming to trade, regardless 00:47:43.010 --> 00:47:48.300 align:middle line:84% of who comes early, their identity, who is coming late. 00:47:48.300 --> 00:47:52.980 align:middle line:90% It's like inventory on demand. 00:47:52.980 --> 00:47:56.360 align:middle line:84% And if this condition is not met, 00:47:56.360 --> 00:47:58.420 align:middle line:90% then there is no such dealer. 00:47:58.420 --> 00:48:01.100 align:middle line:90% What is the statement? 00:48:01.100 --> 00:48:05.060 align:middle line:90% With an embarrassing typo. 00:48:05.060 --> 00:48:07.300 align:middle line:90% There is no prices here. 00:48:07.300 --> 00:48:11.140 align:middle line:84% This is all about endowments and excess demands. 00:48:11.140 --> 00:48:17.140 align:middle line:84% And we're saying, say, this key agent as broker dealer, I, has 00:48:17.140 --> 00:48:24.420 align:middle line:84% to have enough in endowments of each commodity 00:48:24.420 --> 00:48:29.900 align:middle line:84% C such that the excess demands of all the other traders-- 00:48:29.900 --> 00:48:34.940 align:middle line:84% the typo here is that this should be a J and not an I. 00:48:34.940 --> 00:48:35.940 align:middle line:90% This is I over here. 00:48:35.940 --> 00:48:39.260 align:middle line:84% We want to sum up over all the other guys on the right hand 00:48:39.260 --> 00:48:41.300 align:middle line:90% side. 00:48:41.300 --> 00:48:48.100 align:middle line:84% And the sum of their positive excess demands cannot exceed-- 00:48:48.100 --> 00:48:50.980 align:middle line:84% in other words, trader I here has the capacity 00:48:50.980 --> 00:48:54.980 align:middle line:84% to honor the excess demands for everybody else. 00:48:54.980 --> 00:48:59.700 align:middle line:84% So a giant facilitator of trade, you might say. 00:48:59.700 --> 00:49:01.120 align:middle line:90% There is a trading rule. 00:49:01.120 --> 00:49:04.760 align:middle line:90% It uses a bit more than D1. 00:49:04.760 --> 00:49:08.920 align:middle line:84% It needs names, evidently, and I have no intuition for that. 00:49:08.920 --> 00:49:12.140 align:middle line:90% So again, hoping you will. 00:49:12.140 --> 00:49:17.700 align:middle line:84% One of you might take a stab at the underlying proofs. 00:49:17.700 --> 00:49:24.140 align:middle line:84% So you do have to know who's who to implement the algorithm that 00:49:24.140 --> 00:49:26.180 align:middle line:90% could work. 00:49:26.180 --> 00:49:29.980 align:middle line:90% So what's the problem? 00:49:29.980 --> 00:49:33.500 align:middle line:90% The problem is market power. 00:49:33.500 --> 00:49:40.580 align:middle line:84% One guy who could, in principle, set prices despite the theorem, 00:49:40.580 --> 00:49:45.030 align:middle line:90% in contrast to the theorem. 00:49:45.030 --> 00:49:50.390 align:middle line:84% He or she would be acting like a monopolist. 00:49:50.390 --> 00:49:53.990 align:middle line:84% And should we be worried about market power? 00:49:53.990 --> 00:49:54.870 align:middle line:90% Yes. 00:49:54.870 --> 00:50:00.590 align:middle line:84% Again, the Kansas City Fed I referenced earlier with respect 00:50:00.590 --> 00:50:01.830 align:middle line:90% to Fed Now. 00:50:01.830 --> 00:50:03.670 align:middle line:84% And the technological difference here 00:50:03.670 --> 00:50:06.710 align:middle line:84% is another report of the Kansas City 00:50:06.710 --> 00:50:13.670 align:middle line:84% Fed documenting market structure of core banking services. 00:50:13.670 --> 00:50:16.190 align:middle line:84% And there's something called aggregators. 00:50:16.190 --> 00:50:24.470 align:middle line:84% Basically, a retail shop or a department store 00:50:24.470 --> 00:50:25.470 align:middle line:90% could take cash. 00:50:25.470 --> 00:50:26.750 align:middle line:90% They could take credit cards. 00:50:26.750 --> 00:50:28.630 align:middle line:90% They could take debit cards. 00:50:28.630 --> 00:50:30.330 align:middle line:84% There's multiple means of payment, 00:50:30.330 --> 00:50:33.190 align:middle line:84% and you have these aggregators who basically 00:50:33.190 --> 00:50:37.230 align:middle line:84% act as agents on behalf of the stores 00:50:37.230 --> 00:50:45.840 align:middle line:84% in order to process the place, to facilitate the flow of funds 00:50:45.840 --> 00:50:47.600 align:middle line:90% to settle the trades. 00:50:47.600 --> 00:50:52.200 align:middle line:84% The three in the US are Fiserv, Jack Henry, and FIS. 00:50:52.200 --> 00:50:59.320 align:middle line:84% And Fiserv has 42% of the market of all clearing of banks 00:50:59.320 --> 00:51:01.240 align:middle line:90% in the United States. 00:51:01.240 --> 00:51:06.000 align:middle line:84% In fact, I happened to become aware of Fiserv 00:51:06.000 --> 00:51:11.000 align:middle line:84% when I was talking to someone at the Federal Reserve. 00:51:11.000 --> 00:51:13.520 align:middle line:84% It was either the Federal Reserve or the Department 00:51:13.520 --> 00:51:21.520 align:middle line:84% of the Census, because they had this amazing transactions data 00:51:21.520 --> 00:51:24.240 align:middle line:90% proprietary. 00:51:24.240 --> 00:51:26.340 align:middle line:84% And there are two others, and it depends. 00:51:26.340 --> 00:51:30.520 align:middle line:84% So there's a lot of concentration. 00:51:30.520 --> 00:51:33.280 align:middle line:90% This is on the syllabus. 00:51:33.280 --> 00:51:36.000 align:middle line:90% The question is huge. 00:51:36.000 --> 00:51:39.400 align:middle line:84% Is this something to do with the technology 00:51:39.400 --> 00:51:45.010 align:middle line:84% or is it just market power and distortions? 00:51:45.010 --> 00:51:47.890 align:middle line:84% This is for foreign exchange markets. 00:51:47.890 --> 00:51:50.850 align:middle line:84% So what's being traded are fiat monies. 00:51:50.850 --> 00:51:55.150 align:middle line:84% They're being traded through broker dealers such as Citibank, 00:51:55.150 --> 00:52:01.250 align:middle line:84% Deutsche Bank, and UBS. And the largest is Citibank. 00:52:01.250 --> 00:52:09.210 align:middle line:84% This table is showing you year by year by year by annual 00:52:09.210 --> 00:52:23.170 align:middle line:84% that Citibank had, in this case, was one of the top three dealers 00:52:23.170 --> 00:52:29.730 align:middle line:84% by market share, and actually, for almost every year. 00:52:29.730 --> 00:52:35.330 align:middle line:84% The others, Deutsche Bank and UBS, 00:52:35.330 --> 00:52:40.370 align:middle line:84% have less concentration in some years. 00:52:40.370 --> 00:52:42.970 align:middle line:84% Of course, now this raises the issue. 00:52:42.970 --> 00:52:47.810 align:middle line:84% What currencies are these guys trading in? 00:52:47.810 --> 00:52:49.090 align:middle line:90% Hint. 00:52:49.090 --> 00:52:51.330 align:middle line:84% Not every fiat money in the world 00:52:51.330 --> 00:52:54.850 align:middle line:84% is being traded through these broker dealers. 00:52:54.850 --> 00:53:00.370 align:middle line:84% The US dollar, the yen, pound, those 00:53:00.370 --> 00:53:05.770 align:middle line:84% are still the dominant international currencies. 00:53:05.770 --> 00:53:09.010 align:middle line:84% If you're from Brazil and you want 00:53:09.010 --> 00:53:14.930 align:middle line:84% to trade with Colombia, a sister country in Latin America, 00:53:14.930 --> 00:53:18.035 align:middle line:84% you don't trade bilaterally in those FX markets. 00:53:18.035 --> 00:53:19.410 align:middle line:84% You have to get a hold of dollars 00:53:19.410 --> 00:53:24.930 align:middle line:84% to buy the other country's exchange. 00:53:24.930 --> 00:53:27.550 align:middle line:84% So then you could raise this question. 00:53:27.550 --> 00:53:34.890 align:middle line:84% What if we were to implement the FX markets on a distributed 00:53:34.890 --> 00:53:36.530 align:middle line:90% ledger? 00:53:36.530 --> 00:53:41.900 align:middle line:84% Could we design it in a way that more currencies would 00:53:41.900 --> 00:53:48.520 align:middle line:84% be traded and potentially mitigate, if not eliminate, 00:53:48.520 --> 00:53:52.380 align:middle line:90% this concentration? 00:53:52.380 --> 00:53:54.860 align:middle line:90% I'm not saying it's all evil. 00:53:54.860 --> 00:53:57.200 align:middle line:84% The idea is if you're a broker dealer, 00:53:57.200 --> 00:54:01.140 align:middle line:84% you have to stand ready to trade foreign currencies. 00:54:01.140 --> 00:54:03.640 align:middle line:90% So you have an acquisition cost. 00:54:03.640 --> 00:54:09.260 align:middle line:84% They have to be on your balance sheet and a fairly high level. 00:54:09.260 --> 00:54:13.340 align:middle line:84% So how do you finance the acquisition of currencies? 00:54:13.340 --> 00:54:16.700 align:middle line:84% Plus you're going to hold them, their exchange rate 00:54:16.700 --> 00:54:17.920 align:middle line:90% fluctuations. 00:54:17.920 --> 00:54:22.180 align:middle line:90% So there's a risk component. 00:54:22.180 --> 00:54:24.620 align:middle line:84% So the acquisition costs and the risks 00:54:24.620 --> 00:54:28.280 align:middle line:84% already mean you have to price to cover those costs. 00:54:28.280 --> 00:54:31.860 align:middle line:90% Those are real costs. 00:54:31.860 --> 00:54:36.390 align:middle line:84% But likewise, if you could envision a blockchain chain 00:54:36.390 --> 00:54:40.970 align:middle line:84% where many more currencies could be traded, 00:54:40.970 --> 00:54:46.430 align:middle line:84% you don't necessarily have to have the security in a buffer 00:54:46.430 --> 00:54:51.370 align:middle line:84% stock if you can contract, as in a dynamic ledger, 00:54:51.370 --> 00:54:53.210 align:middle line:84% to sell things you don't currently own, 00:54:53.210 --> 00:54:55.990 align:middle line:84% but you will acquire from somebody else. 00:54:55.990 --> 00:54:59.050 align:middle line:84% And so I guess two lectures from now, 00:54:59.050 --> 00:55:02.950 align:middle line:84% we'll talk about tokenization and dynamic ledgers 00:55:02.950 --> 00:55:07.230 align:middle line:90% and atomic settlements. 00:55:07.230 --> 00:55:11.350 align:middle line:84% So we're kind of anticipating that here. 00:55:11.350 --> 00:55:14.990 align:middle line:84% And this is icing on the cake, in the sense 00:55:14.990 --> 00:55:18.710 align:middle line:84% of finding other things that are going on in the foreign exchange 00:55:18.710 --> 00:55:21.350 align:middle line:84% markets that are really interesting 00:55:21.350 --> 00:55:24.790 align:middle line:90% and beg for an explanation. 00:55:24.790 --> 00:55:27.310 align:middle line:84% Namely, even though there are, say, 00:55:27.310 --> 00:55:30.110 align:middle line:84% a non-trivial number of broker dealers, 00:55:30.110 --> 00:55:36.000 align:middle line:84% you can categorize them as being on the periphery or in the core. 00:55:36.000 --> 00:55:39.120 align:middle line:84% And it's the few core dealers who are absorbing 00:55:39.120 --> 00:55:40.480 align:middle line:90% the risk of exchange rates. 00:55:40.480 --> 00:55:43.340 align:middle line:84% And otherwise the periphery dealers, 00:55:43.340 --> 00:55:45.463 align:middle line:84% when they get a hold of a currency, 00:55:45.463 --> 00:55:46.880 align:middle line:84% they tend to want to get rid of it 00:55:46.880 --> 00:55:50.520 align:middle line:84% right away, referring to it as a hot potato. 00:55:50.520 --> 00:55:53.060 align:middle line:90% So why is it designed like that? 00:55:53.060 --> 00:55:57.840 align:middle line:84% That to me is a good challenging economic question. 00:55:57.840 --> 00:56:00.880 align:middle line:90% But this is the way it is. 00:56:00.880 --> 00:56:04.720 align:middle line:84% And then you would think that if it's down to a few core 00:56:04.720 --> 00:56:07.520 align:middle line:84% dealers, that the exchange rates would be determined 00:56:07.520 --> 00:56:11.120 align:middle line:84% in part by the underlying conditions 00:56:11.120 --> 00:56:15.780 align:middle line:84% of those dealers in terms of their capital ratios, 00:56:15.780 --> 00:56:17.160 align:middle line:90% for example. 00:56:17.160 --> 00:56:18.800 align:middle line:84% And people who have looked at the data 00:56:18.800 --> 00:56:22.640 align:middle line:90% are finding that that is true. 00:56:22.640 --> 00:56:24.100 align:middle line:90% I'm fascinated by this. 00:56:24.100 --> 00:56:27.720 align:middle line:90% I love economics. 00:56:27.720 --> 00:56:30.740 align:middle line:84% But anyway, if you want to explore further, 00:56:30.740 --> 00:56:32.860 align:middle line:84% this would be an interesting thing. 00:56:32.860 --> 00:56:40.320 align:middle line:84% Now, a third workaround is overdraft credit facility. 00:56:40.320 --> 00:56:43.620 align:middle line:84% Ostroy-Starr wanted to get everything done in one round, 00:56:43.620 --> 00:56:47.720 align:middle line:84% but you could imagine two more rounds, an initial round 00:56:47.720 --> 00:56:54.080 align:middle line:84% in which traders are given overdraft facilities, credit 00:56:54.080 --> 00:56:57.120 align:middle line:84% effectively, and they can use those credits 00:56:57.120 --> 00:56:58.640 align:middle line:90% when they go shopping. 00:56:58.640 --> 00:57:02.080 align:middle line:84% And the requirement is that they got a payback, essentially, 00:57:02.080 --> 00:57:05.920 align:middle line:84% the amount of the overdraft at the end, one way or another, 00:57:05.920 --> 00:57:07.380 align:middle line:90% in equivalent value. 00:57:07.380 --> 00:57:11.180 align:middle line:84% So then it's like the money that we had before, 00:57:11.180 --> 00:57:14.440 align:middle line:84% but the money from before was one of the goods 00:57:14.440 --> 00:57:16.520 align:middle line:90% or one of the securities. 00:57:16.520 --> 00:57:20.440 align:middle line:90% And here it's another object. 00:57:20.440 --> 00:57:23.800 align:middle line:90% It's just a credit. 00:57:23.800 --> 00:57:26.680 align:middle line:84% Well, then it's easy to have enough of it, 00:57:26.680 --> 00:57:29.880 align:middle line:84% because you can create it in arbitrary amounts, 00:57:29.880 --> 00:57:34.010 align:middle line:90% as long as these guys pay back. 00:57:34.010 --> 00:57:37.130 align:middle line:90% A hint of things to come. 00:57:37.130 --> 00:57:40.850 align:middle line:84% And I was thinking about this this morning 00:57:40.850 --> 00:57:42.390 align:middle line:90% reviewing the slide. 00:57:42.390 --> 00:57:45.570 align:middle line:84% This also means the amount of credit 00:57:45.570 --> 00:57:50.010 align:middle line:84% would be agent specific, because the value 00:57:50.010 --> 00:57:52.250 align:middle line:84% of the excess demands of each trader 00:57:52.250 --> 00:57:54.490 align:middle line:90% are going to be different. 00:57:54.490 --> 00:57:56.510 align:middle line:84% Some may be not trading much at all. 00:57:56.510 --> 00:57:58.690 align:middle line:90% Others need a lot of credit. 00:57:58.690 --> 00:58:02.190 align:middle line:84% So if it's repaid at the end, that's the second round, 00:58:02.190 --> 00:58:04.490 align:middle line:90% and you have three in total. 00:58:04.490 --> 00:58:09.490 align:middle line:84% So it works, but as we're already anticipating, 00:58:09.490 --> 00:58:12.730 align:middle line:84% there might be the possibility of default. 00:58:12.730 --> 00:58:16.330 align:middle line:84% So let me make this a little more tangible 00:58:16.330 --> 00:58:20.650 align:middle line:90% and go to medieval trade fairs. 00:58:20.650 --> 00:58:24.290 align:middle line:90% So this is a credit system. 00:58:24.290 --> 00:58:28.130 align:middle line:84% In principle, bankers were sitting at a table 00:58:28.130 --> 00:58:30.120 align:middle line:90% and they had their ledgers. 00:58:30.120 --> 00:58:33.220 align:middle line:84% And in principle, you could, say, 00:58:33.220 --> 00:58:39.000 align:middle line:84% deposit your gold or silver coin for safekeeping, like a deposit. 00:58:39.000 --> 00:58:41.600 align:middle line:84% And you would be credited on the books of the bank. 00:58:41.600 --> 00:58:43.840 align:middle line:90% The bank owes you money. 00:58:43.840 --> 00:58:45.180 align:middle line:90% It's your money. 00:58:45.180 --> 00:58:48.860 align:middle line:84% You get an IOU, and you could use that for trading. 00:58:48.860 --> 00:58:52.840 align:middle line:84% These giant trade fairs in France, 00:58:52.840 --> 00:58:55.900 align:middle line:84% they tried to minimize the amount of coin 00:58:55.900 --> 00:58:57.560 align:middle line:84% that traders would bring to the fair, 00:58:57.560 --> 00:59:00.860 align:middle line:84% because it was risky to be hauling around all that gold 00:59:00.860 --> 00:59:02.060 align:middle line:90% and silver. 00:59:02.060 --> 00:59:03.740 align:middle line:90% Not to mention the goods. 00:59:03.740 --> 00:59:07.220 align:middle line:84% So the fair would designate a sequence 00:59:07.220 --> 00:59:11.300 align:middle line:84% of trades, first in cloth, then in leather, then drugs 00:59:11.300 --> 00:59:14.880 align:middle line:84% and spices, and finally at the end for settlement. 00:59:14.880 --> 00:59:17.860 align:middle line:90% Those were the rules. 00:59:17.860 --> 00:59:24.420 align:middle line:84% So if you basically were bringing in spices, 00:59:24.420 --> 00:59:27.500 align:middle line:84% then you don't get value from stuff sold. 00:59:27.500 --> 00:59:30.690 align:middle line:90% You got to buy first. 00:59:30.690 --> 00:59:32.150 align:middle line:90% These are big traders. 00:59:32.150 --> 00:59:37.790 align:middle line:84% So they're trying to bring goods that they have access to 00:59:37.790 --> 00:59:40.850 align:middle line:84% and get other goods that their customers would like, 00:59:40.850 --> 00:59:45.590 align:middle line:84% and spices being a great example. 00:59:45.590 --> 00:59:51.690 align:middle line:84% So then comes the credits on the book of the banker. 00:59:51.690 --> 00:59:54.070 align:middle line:84% Instead of bringing a lot of coins, say, 00:59:54.070 --> 00:59:55.810 align:middle line:90% they brought no coin at all. 00:59:55.810 --> 00:59:58.470 align:middle line:84% Every person would be credited with 00:59:58.470 --> 01:00:00.410 align:middle line:90% a certain overdraft facility. 01:00:00.410 --> 01:00:04.550 align:middle line:84% You should still think about it as an IOU owed back 01:00:04.550 --> 01:00:06.790 align:middle line:84% to the banker, although in other ways, 01:00:06.790 --> 01:00:12.370 align:middle line:84% you can think of it as a loan that has to be repaid. 01:00:12.370 --> 01:00:13.730 align:middle line:90% It's overdraft. 01:00:13.730 --> 01:00:17.190 align:middle line:84% You're not expected to carry that overdraft balance 01:00:17.190 --> 01:00:19.270 align:middle line:90% indefinitely. 01:00:19.270 --> 01:00:21.190 align:middle line:84% And then they come together in the settlement 01:00:21.190 --> 01:00:23.970 align:middle line:84% period, which I gather was also a couple of weeks. 01:00:23.970 --> 01:00:27.760 align:middle line:84% And I think there is some interesting stories there 01:00:27.760 --> 01:00:32.800 align:middle line:90% of exactly how that worked. 01:00:32.800 --> 01:00:35.160 align:middle line:84% It could work perfectly if the prices were all 01:00:35.160 --> 01:00:38.720 align:middle line:84% posted in advance and cleared the markets, as in a Walrasian 01:00:38.720 --> 01:00:39.800 align:middle line:90% setup. 01:00:39.800 --> 01:00:42.420 align:middle line:84% But obviously, they weren't doing that. 01:00:42.420 --> 01:00:47.880 align:middle line:90% 01:00:47.880 --> 01:00:52.240 align:middle line:84% Just because I can't help but mention it, 01:00:52.240 --> 01:00:55.440 align:middle line:84% what was the unit of account being used 01:00:55.440 --> 01:00:58.000 align:middle line:90% on the books of the banker? 01:00:58.000 --> 01:00:59.420 align:middle line:90% There were different coins. 01:00:59.420 --> 01:01:01.520 align:middle line:90% Gold coins, silver coins. 01:01:01.520 --> 01:01:06.000 align:middle line:84% In fact, the king would occasionally 01:01:06.000 --> 01:01:08.160 align:middle line:84% call in all the pre-existing coins 01:01:08.160 --> 01:01:13.840 align:middle line:84% and melt them down and give out new coins that had less metal. 01:01:13.840 --> 01:01:16.020 align:middle line:90% So that's a classic debasement. 01:01:16.020 --> 01:01:20.360 align:middle line:84% Central banks have other ways of doing that now. 01:01:20.360 --> 01:01:23.840 align:middle line:84% So they would continue to keep the unit of account 01:01:23.840 --> 01:01:27.880 align:middle line:84% they had before, even though it no longer corresponded 01:01:27.880 --> 01:01:30.160 align:middle line:90% to a circulating coin. 01:01:30.160 --> 01:01:34.080 align:middle line:84% In fact, that was called ghost currency. 01:01:34.080 --> 01:01:36.720 align:middle line:90% I love it. 01:01:36.720 --> 01:01:41.060 align:middle line:84% Making the point that the unit of account is one function, 01:01:41.060 --> 01:01:44.880 align:middle line:84% and it's not inextricably wedded to store 01:01:44.880 --> 01:01:47.580 align:middle line:90% value and medium of exchange. 01:01:47.580 --> 01:01:50.200 align:middle line:90% 01:01:50.200 --> 01:01:53.280 align:middle line:84% Anyway, these guys would meet at the end of the fair, 01:01:53.280 --> 01:01:54.460 align:middle line:90% settle the accounts. 01:01:54.460 --> 01:01:59.440 align:middle line:84% But some people were owing back and they couldn't pay back 01:01:59.440 --> 01:02:00.920 align:middle line:90% the overdraft. 01:02:00.920 --> 01:02:04.680 align:middle line:84% So then they would issue an IOU, which 01:02:04.680 --> 01:02:09.320 align:middle line:84% was the order of I'll pay you later 01:02:09.320 --> 01:02:15.240 align:middle line:84% at a specified date and location when we meet up again. 01:02:15.240 --> 01:02:20.760 align:middle line:84% In fact, there was this huge international affair at Lyon 01:02:20.760 --> 01:02:23.720 align:middle line:84% where eventually it was all about clearing 01:02:23.720 --> 01:02:29.130 align:middle line:84% during these promissory IOUs rather than trading goods. 01:02:29.130 --> 01:02:33.150 align:middle line:84% So I've mentioned in lecture one, and we'll come back to it, 01:02:33.150 --> 01:02:39.050 align:middle line:84% these IOUs were letters of the fair, lettres de foire. 01:02:39.050 --> 01:02:44.970 align:middle line:90% And they are basically-- 01:02:44.970 --> 01:02:50.850 align:middle line:84% well anyways, they will arise as circulating notes 01:02:50.850 --> 01:02:55.550 align:middle line:84% in England and other places and led to financial crises. 01:02:55.550 --> 01:02:58.770 align:middle line:84% But that's the lecture for next time, not for today. 01:02:58.770 --> 01:03:00.650 align:middle line:84% So even in medieval times, they're 01:03:00.650 --> 01:03:04.290 align:middle line:84% working really hard to get an operational system with goods 01:03:04.290 --> 01:03:12.730 align:middle line:84% and finance to go against some of these overdraft problems. 01:03:12.730 --> 01:03:17.570 align:middle line:84% In practice, there's default. So I think arguably the largest 01:03:17.570 --> 01:03:20.990 align:middle line:84% market in the world, the US repo market, 01:03:20.990 --> 01:03:24.820 align:middle line:84% which is used by the Federal Reserve for monetary policy. 01:03:24.820 --> 01:03:28.420 align:middle line:84% They discovered, to their dismay, 01:03:28.420 --> 01:03:35.380 align:middle line:84% in around 2008 or '09 that these broker dealers were basically 01:03:35.380 --> 01:03:39.700 align:middle line:84% assuming the obligations of some of the people they were paired 01:03:39.700 --> 01:03:46.180 align:middle line:84% with, with intraday credit was being provided by these clearing 01:03:46.180 --> 01:03:51.460 align:middle line:84% banks during repo transactions greater than the US monetary 01:03:51.460 --> 01:03:52.940 align:middle line:90% stock. 01:03:52.940 --> 01:03:55.820 align:middle line:84% So the reforms, among other things, 01:03:55.820 --> 01:03:57.980 align:middle line:84% I'll just focus on the first one, 01:03:57.980 --> 01:04:02.060 align:middle line:84% was to alter the timing in such a way 01:04:02.060 --> 01:04:08.860 align:middle line:84% that the broker dealers had more balance on their balance sheet. 01:04:08.860 --> 01:04:10.380 align:middle line:90% But these things come up. 01:04:10.380 --> 01:04:13.180 align:middle line:84% They came up the other day when we were 01:04:13.180 --> 01:04:14.960 align:middle line:90% talking about emerging markets. 01:04:14.960 --> 01:04:20.100 align:middle line:84% So this is still a potential problem. 01:04:20.100 --> 01:04:24.750 align:middle line:84% Talked about potential remedies, but institutions 01:04:24.750 --> 01:04:26.910 align:middle line:84% that would require it sometimes suffer 01:04:26.910 --> 01:04:29.430 align:middle line:90% from their own big problems. 01:04:29.430 --> 01:04:33.350 align:middle line:84% Is there a solution with the new technologies? 01:04:33.350 --> 01:04:36.030 align:middle line:84% Which brings us back to distributed ledgers 01:04:36.030 --> 01:04:37.910 align:middle line:90% on the blockchain. 01:04:37.910 --> 01:04:41.270 align:middle line:84% The impossibility theorem is that you 01:04:41.270 --> 01:04:44.350 align:middle line:84% can't do it if you're decentralized 01:04:44.350 --> 01:04:46.190 align:middle line:90% in the information. 01:04:46.190 --> 01:04:48.490 align:middle line:90% D3 won't do it for you. 01:04:48.490 --> 01:04:53.270 align:middle line:84% You need C. So the idea is kind of intuitive 01:04:53.270 --> 01:04:56.090 align:middle line:84% that even if traders are meeting pairwise, 01:04:56.090 --> 01:05:00.070 align:middle line:84% those trades are reported to the ledger. 01:05:00.070 --> 01:05:04.150 align:middle line:84% In fact, you could have all their value 01:05:04.150 --> 01:05:09.350 align:middle line:84% sequestered in escrow to begin with to be used for the trading. 01:05:09.350 --> 01:05:12.750 align:middle line:84% With that history, it will be possible for people 01:05:12.750 --> 01:05:18.430 align:middle line:84% to coordinate to achieve this socially desirable outcome. 01:05:18.430 --> 01:05:23.910 align:middle line:84% A little bit of a story here before I 01:05:23.910 --> 01:05:28.510 align:middle line:84% get into a limited amount of detail. 01:05:28.510 --> 01:05:32.290 align:middle line:84% Ostroy-Starr showed an example-- again, 01:05:32.290 --> 01:05:35.910 align:middle line:84% the idea is proof by counterexample. 01:05:35.910 --> 01:05:38.790 align:middle line:90% Try D3. 01:05:38.790 --> 01:05:40.590 align:middle line:90% Claim for any environment. 01:05:40.590 --> 01:05:44.030 align:middle line:84% You can succeed to get to the Walrasian outcome. 01:05:44.030 --> 01:05:47.110 align:middle line:84% All you need is an example where it isn't true, 01:05:47.110 --> 01:05:50.630 align:middle line:84% that a price, excess demand, and endowments 01:05:50.630 --> 01:05:54.150 align:middle line:84% corresponding to the underlying u conditions 01:05:54.150 --> 01:05:56.390 align:middle line:90% would not be achievable. 01:05:56.390 --> 01:05:59.990 align:middle line:84% And I'm about to show you the example that 01:05:59.990 --> 01:06:03.870 align:middle line:84% proves the theorem as a counterexample 01:06:03.870 --> 01:06:07.710 align:middle line:90% to the theorem that isn't true. 01:06:07.710 --> 01:06:14.110 align:middle line:84% However, Kyungmin was a graduate student here, was my student. 01:06:14.110 --> 01:06:19.280 align:middle line:84% And as I do sometimes, and Sam can testify to this, 01:06:19.280 --> 01:06:21.720 align:middle line:84% I ask my students to help prepare 01:06:21.720 --> 01:06:24.720 align:middle line:90% lecture notes and material. 01:06:24.720 --> 01:06:28.240 align:middle line:84% And you've already seen some of Sam's slides 01:06:28.240 --> 01:06:29.840 align:middle line:90% in earlier lectures. 01:06:29.840 --> 01:06:33.860 align:middle line:84% So I asked for Kyungmin to do this for the Ostroy-Starr paper, 01:06:33.860 --> 01:06:37.460 align:middle line:84% and he went away for a while, came back, and he said, 01:06:37.460 --> 01:06:41.680 align:middle line:84% Professor Townsend, there seems to be a problem. 01:06:41.680 --> 01:06:46.840 align:middle line:90% So their example wasn't working. 01:06:46.840 --> 01:06:54.280 align:middle line:84% And I know Ostroy and Starr, so I wrote them an email. 01:06:54.280 --> 01:06:56.460 align:middle line:84% And they're like, oh, that was so many years ago. 01:06:56.460 --> 01:07:00.120 align:middle line:84% Why don't you get some graduate student to work it out? 01:07:00.120 --> 01:07:01.720 align:middle line:90% Which is, of course-- 01:07:01.720 --> 01:07:08.240 align:middle line:84% so we don't know for sure if this example is validated by-- 01:07:08.240 --> 01:07:10.660 align:middle line:84% it is not validated by Ostroy and Starr. 01:07:10.660 --> 01:07:14.560 align:middle line:90% They haven't acknowledged. 01:07:14.560 --> 01:07:16.690 align:middle line:90% But anyway, how does it go? 01:07:16.690 --> 01:07:21.130 align:middle line:84% So their big picture is the most important thing. 01:07:21.130 --> 01:07:25.770 align:middle line:84% We want to find two economies such that in a certain trade, 01:07:25.770 --> 01:07:30.330 align:middle line:84% only takes one, two traders cannot decide what economy they 01:07:30.330 --> 01:07:31.530 align:middle line:90% are in. 01:07:31.530 --> 01:07:35.090 align:middle line:84% When they look at their history and their own endowments 01:07:35.090 --> 01:07:37.970 align:middle line:84% and so on, they get some information, 01:07:37.970 --> 01:07:41.550 align:middle line:84% but it's not enough to know the excess demands of everyone. 01:07:41.550 --> 01:07:45.850 align:middle line:84% Hence, they have no guidance about what to trade to whom 01:07:45.850 --> 01:07:47.770 align:middle line:90% when they're meeting. 01:07:47.770 --> 01:07:49.970 align:middle line:90% So that's the big picture. 01:07:49.970 --> 01:07:55.210 align:middle line:84% The economy is kind of special, but that's good, 01:07:55.210 --> 01:07:58.170 align:middle line:84% because all you need is a counterexample. 01:07:58.170 --> 01:08:04.770 align:middle line:84% Again, it helps to understand too the aspects of Ostroy-Starr. 01:08:04.770 --> 01:08:06.570 align:middle line:90% Traders are meeting pairwise. 01:08:06.570 --> 01:08:09.490 align:middle line:90% Two, five meet pairwise. 01:08:09.490 --> 01:08:12.810 align:middle line:84% Three, four meet pairwise, and one's standing out alone. 01:08:12.810 --> 01:08:15.900 align:middle line:84% If you look at this, two meets five, two meets three, two 01:08:15.900 --> 01:08:17.899 align:middle line:90% meets one, two meets four. 01:08:17.899 --> 01:08:20.779 align:middle line:84% Every trader is matched with every other trader 01:08:20.779 --> 01:08:25.080 align:middle line:84% once, not just for trader two, but every other one. 01:08:25.080 --> 01:08:31.920 align:middle line:84% And of course, because there are five people at each period, 01:08:31.920 --> 01:08:37.740 align:middle line:84% one guy is kind of standing out all alone and is not trading. 01:08:37.740 --> 01:08:43.748 align:middle line:84% Then there is the price vector, which in principle, you 01:08:43.748 --> 01:08:45.540 align:middle line:84% would think there would be different prices 01:08:45.540 --> 01:08:47.340 align:middle line:90% for different goods. 01:08:47.340 --> 01:08:54.540 align:middle line:84% But all they do is say if this good costs $0.50, 01:08:54.540 --> 01:08:59.120 align:middle line:84% we're going to relabel the size of it to be two units. 01:08:59.120 --> 01:09:00.819 align:middle line:90% So then it costs $1. 01:09:00.819 --> 01:09:03.740 align:middle line:84% So we just normalize the units in which everything 01:09:03.740 --> 01:09:07.920 align:middle line:84% is measured in such a way that the prices are all equal to 1. 01:09:07.920 --> 01:09:10.420 align:middle line:84% That kind of helps keep track of values. 01:09:10.420 --> 01:09:15.180 align:middle line:84% And this is the matrix of excess demands. 01:09:15.180 --> 01:09:16.840 align:middle line:84% For trader one, two, three, four, 01:09:16.840 --> 01:09:20.140 align:middle line:84% five as the rows, and the columns represent the goods. 01:09:20.140 --> 01:09:24.060 align:middle line:84% So trader one has an excess demand of four for good one 01:09:24.060 --> 01:09:31.779 align:middle line:84% and excess supply of good two in the amount of two, et cetera. 01:09:31.779 --> 01:09:36.260 align:middle line:84% So you have these matrices with rows and columns 01:09:36.260 --> 01:09:38.700 align:middle line:90% for traders and goods. 01:09:38.700 --> 01:09:41.220 align:middle line:84% And you have their endowment vectors. 01:09:41.220 --> 01:09:46.899 align:middle line:84% Curious thing about this example is trader five is worthless. 01:09:46.899 --> 01:09:50.740 align:middle line:90% Trader five has 0 of everything. 01:09:50.740 --> 01:09:52.939 align:middle line:84% So whenever you're matched with five 01:09:52.939 --> 01:09:57.140 align:middle line:84% and we have this quid pro quo requirement, no trade happens. 01:09:57.140 --> 01:10:00.860 align:middle line:84% So we can just focus on the one remaining pair 01:10:00.860 --> 01:10:04.660 align:middle line:84% where something active might be going on. 01:10:04.660 --> 01:10:10.260 align:middle line:84% I'm just sketching how the counterexample goes, 01:10:10.260 --> 01:10:11.950 align:middle line:90% because you'll get bogged down. 01:10:11.950 --> 01:10:15.310 align:middle line:84% I always do when I start going through the details. 01:10:15.310 --> 01:10:16.970 align:middle line:90% Trader two meets five. 01:10:16.970 --> 01:10:18.370 align:middle line:90% Trader three meets four. 01:10:18.370 --> 01:10:20.630 align:middle line:90% At date one, five is worthless. 01:10:20.630 --> 01:10:23.290 align:middle line:84% Trader three and four have one good four. 01:10:23.290 --> 01:10:24.110 align:middle line:90% It's the same good. 01:10:24.110 --> 01:10:26.350 align:middle line:90% They don't trade. 01:10:26.350 --> 01:10:28.330 align:middle line:84% At day two, trader one meets five. 01:10:28.330 --> 01:10:29.170 align:middle line:90% Two meets three. 01:10:29.170 --> 01:10:32.970 align:middle line:84% Only two and three can be engaged in a non-trivial trade. 01:10:32.970 --> 01:10:34.430 align:middle line:90% Now, something more interesting. 01:10:34.430 --> 01:10:39.590 align:middle line:84% After trading at two, date two, trader three 01:10:39.590 --> 01:10:43.750 align:middle line:84% does not trade with anyone until he trades with trader one 01:10:43.750 --> 01:10:45.150 align:middle line:90% at date five. 01:10:45.150 --> 01:10:49.170 align:middle line:84% So there's a backwards and forwards looking aspect to this. 01:10:49.170 --> 01:10:51.310 align:middle line:84% Whenever you trade, you naturally 01:10:51.310 --> 01:10:54.070 align:middle line:84% have to think of the social objective function. 01:10:54.070 --> 01:10:56.630 align:middle line:84% So you think about the current state 01:10:56.630 --> 01:11:02.750 align:middle line:84% where you are in endowments, but endowments get transformed. 01:11:02.750 --> 01:11:06.910 align:middle line:84% This is classic computer science coding. 01:11:06.910 --> 01:11:08.610 align:middle line:90% Let B be the endowment. 01:11:08.610 --> 01:11:10.390 align:middle line:84% Then you relabel the endowment to be 01:11:10.390 --> 01:11:14.740 align:middle line:84% what it is now endogenously after two periods of trade, 01:11:14.740 --> 01:11:18.800 align:middle line:84% and similarly for the excess demands, which are moving around 01:11:18.800 --> 01:11:21.900 align:middle line:84% if they're actively engaged in trade. 01:11:21.900 --> 01:11:27.160 align:middle line:90% 01:11:27.160 --> 01:11:30.000 align:middle line:90% So I'm going to skip. 01:11:30.000 --> 01:11:35.280 align:middle line:84% The idea is to go through and determine at day three 01:11:35.280 --> 01:11:40.440 align:middle line:84% what traders one and three have to give to each other 01:11:40.440 --> 01:11:42.480 align:middle line:90% that you could work out. 01:11:42.480 --> 01:11:46.240 align:middle line:84% Then you change the underlying economy 01:11:46.240 --> 01:11:50.480 align:middle line:84% by switching these two rows around. 01:11:50.480 --> 01:11:52.960 align:middle line:90% It's another valid economy. 01:11:52.960 --> 01:11:56.800 align:middle line:84% And it turns out the sequence of trades 01:11:56.800 --> 01:12:00.480 align:middle line:90% would be the same up to a point. 01:12:00.480 --> 01:12:05.120 align:middle line:84% And you realize that they're going 01:12:05.120 --> 01:12:06.960 align:middle line:84% to have to do something different than what 01:12:06.960 --> 01:12:09.050 align:middle line:90% they did in the first example. 01:12:09.050 --> 01:12:11.650 align:middle line:84% But looking at what they know, there's 01:12:11.650 --> 01:12:14.650 align:middle line:84% no way that they would know at that point, given 01:12:14.650 --> 01:12:18.250 align:middle line:84% the trades that they were engaged in or that they saw, 01:12:18.250 --> 01:12:20.930 align:middle line:84% that they're in a different economy. 01:12:20.930 --> 01:12:23.290 align:middle line:90% So that's kind of the way-- 01:12:23.290 --> 01:12:25.850 align:middle line:90% it's quite tedious. 01:12:25.850 --> 01:12:27.650 align:middle line:90% I've double checked it. 01:12:27.650 --> 01:12:29.770 align:middle line:84% Every time I read it, I get involved 01:12:29.770 --> 01:12:34.150 align:middle line:84% with going back and verifying all the claims and so on. 01:12:34.150 --> 01:12:37.730 align:middle line:84% But I think it's better just to take away the spirit of how 01:12:37.730 --> 01:12:39.030 align:middle line:90% the proof is working. 01:12:39.030 --> 01:12:41.550 align:middle line:84% And you can do this at your leisure. 01:12:41.550 --> 01:12:45.130 align:middle line:84% So we talked about the distributed ledger 01:12:45.130 --> 01:12:48.230 align:middle line:84% and how the trades are recorded there, 01:12:48.230 --> 01:12:51.730 align:middle line:84% and everyone has access to them, that it solves this information 01:12:51.730 --> 01:12:57.370 align:middle line:84% problem that arises from having partitioned trade. 01:12:57.370 --> 01:12:59.030 align:middle line:84% And do we see something like this? 01:12:59.030 --> 01:13:02.210 align:middle line:84% Yeah, a big aspect of what we see on the blockchain, not 01:13:02.210 --> 01:13:04.670 align:middle line:90% the only thing, is tracking. 01:13:04.670 --> 01:13:09.030 align:middle line:84% So Walmart Canada is involved in shipping goods. 01:13:09.030 --> 01:13:12.410 align:middle line:84% And there are lots of problems plaguing the transportation 01:13:12.410 --> 01:13:13.410 align:middle line:90% industry. 01:13:13.410 --> 01:13:16.570 align:middle line:84% There's discrepancies in the invoices 01:13:16.570 --> 01:13:19.410 align:middle line:84% and the payments and fights about whether 01:13:19.410 --> 01:13:22.690 align:middle line:84% or not you were paid or that the goods were not there, 01:13:22.690 --> 01:13:24.850 align:middle line:84% because they could have been stolen. 01:13:24.850 --> 01:13:26.890 align:middle line:84% And so they have this tracker running 01:13:26.890 --> 01:13:30.850 align:middle line:84% on the distributed ledger to mitigate those problems. 01:13:30.850 --> 01:13:33.330 align:middle line:84% And another example are diamonds, although I don't know, 01:13:33.330 --> 01:13:37.690 align:middle line:84% you may not like diamonds coming from the Congo. 01:13:37.690 --> 01:13:41.010 align:middle line:84% But De Beers, the big diamond company, 01:13:41.010 --> 01:13:43.130 align:middle line:84% has a tracker on a distributed ledger 01:13:43.130 --> 01:13:45.890 align:middle line:84% that allows you, in principle, to know 01:13:45.890 --> 01:13:48.330 align:middle line:90% the origin of the diamond. 01:13:48.330 --> 01:13:52.110 align:middle line:84% So I could not find on their website 01:13:52.110 --> 01:13:55.130 align:middle line:84% exactly how they do that, because this 01:13:55.130 --> 01:13:57.430 align:middle line:84% has to do with the origin of the goods, 01:13:57.430 --> 01:14:02.050 align:middle line:84% not money that's changing hands along the way. 01:14:02.050 --> 01:14:06.300 align:middle line:90% But likewise with trade finance. 01:14:06.300 --> 01:14:08.400 align:middle line:90% Ghana has this prototype. 01:14:08.400 --> 01:14:15.300 align:middle line:84% And as Henry can tell you, Hong Kong has similar designs. 01:14:15.300 --> 01:14:18.780 align:middle line:84% Ghana is collaborating with Singapore, 01:14:18.780 --> 01:14:23.480 align:middle line:84% and they've got proof of concept for trade finance. 01:14:23.480 --> 01:14:29.140 align:middle line:84% So these very small merchants in Ghana who are exporting goods 01:14:29.140 --> 01:14:33.740 align:middle line:84% want to know that they're going to get paid in an Asian currency 01:14:33.740 --> 01:14:35.480 align:middle line:90% and that the goods are there. 01:14:35.480 --> 01:14:40.140 align:middle line:84% There's a tracking for the shipping of the goods and so on. 01:14:40.140 --> 01:14:45.120 align:middle line:84% And the goods, the money is held in escrow and it's not released. 01:14:45.120 --> 01:14:48.660 align:middle line:84% That last part has to do with the smart contract, which 01:14:48.660 --> 01:14:54.090 align:middle line:84% we didn't talk about today, but we will talk about it next time. 01:14:54.090 --> 01:15:06.000 align:middle line:90%