WEBVTT 00:00:00.000 --> 00:00:02.428 align:middle line:90% [SQUEAKING] 00:00:02.428 --> 00:00:03.874 align:middle line:90% [RUSTLING] 00:00:03.874 --> 00:00:11.420 align:middle line:90% [CLICKING] 00:00:11.420 --> 00:00:13.600 align:middle line:84% ROBERT TOWNSEND: OK, we'll get started. 00:00:13.600 --> 00:00:14.680 align:middle line:90% Thank you for coming. 00:00:14.680 --> 00:00:19.600 align:middle line:84% Today is lecture 4, "Smart Contracts as a Solution 00:00:19.600 --> 00:00:21.640 align:middle line:90% to a Coordination Problem. 00:00:21.640 --> 00:00:23.620 align:middle line:84% It's still about distributed ledgers, 00:00:23.620 --> 00:00:29.040 align:middle line:84% but we're going to add on top of that not just information use, 00:00:29.040 --> 00:00:31.840 align:middle line:90% but also contracting. 00:00:31.840 --> 00:00:34.600 align:middle line:84% The longer subtitle, commodity space 00:00:34.600 --> 00:00:39.040 align:middle line:90% with location dates and states. 00:00:39.040 --> 00:00:41.100 align:middle line:84% The policy objective is the same. 00:00:41.100 --> 00:00:43.360 align:middle line:84% The Pareto criteria, we will also 00:00:43.360 --> 00:00:46.680 align:middle line:84% have fragmented markets the way we did last time. 00:00:46.680 --> 00:00:49.000 align:middle line:84% The implementation is going to-- problem 00:00:49.000 --> 00:00:51.400 align:middle line:84% is going to have something to do with privately 00:00:51.400 --> 00:00:56.680 align:middle line:84% issued securities, which are circulating around as monies. 00:00:56.680 --> 00:01:00.260 align:middle line:84% And without the ability to coordinate 00:01:00.260 --> 00:01:05.900 align:middle line:84% with their smart contract, there will be market crises. 00:01:05.900 --> 00:01:10.380 align:middle line:84% And so we're featuring this multi-agent smart contract. 00:01:10.380 --> 00:01:11.880 align:middle line:90% So a little more detail. 00:01:11.880 --> 00:01:14.340 align:middle line:84% Extensions of the theory that we started 00:01:14.340 --> 00:01:19.620 align:middle line:84% to cover last time, but this time, explicitly about time 00:01:19.620 --> 00:01:21.980 align:middle line:90% and risk. 00:01:21.980 --> 00:01:27.260 align:middle line:84% And then we'll talk about getting policy guidance 00:01:27.260 --> 00:01:28.280 align:middle line:90% from the data. 00:01:28.280 --> 00:01:35.140 align:middle line:84% As I said last time, I'm trying to put discipline 00:01:35.140 --> 00:01:38.700 align:middle line:84% on myself and the research, that we shouldn't just 00:01:38.700 --> 00:01:48.340 align:middle line:84% be exploring case studies or potential applications that 00:01:48.340 --> 00:01:50.600 align:middle line:84% potentially use these new technologies, 00:01:50.600 --> 00:01:53.940 align:middle line:84% we want to know what economic problem exists out 00:01:53.940 --> 00:01:59.970 align:middle line:84% there and whether or not we can help mitigate the problem. 00:01:59.970 --> 00:02:02.490 align:middle line:84% So we're going to use this efficiency benchmark 00:02:02.490 --> 00:02:05.330 align:middle line:84% that we did last time, and I'll show you 00:02:05.330 --> 00:02:09.530 align:middle line:84% how to use it with actual data, although that's 00:02:09.530 --> 00:02:12.490 align:middle line:90% a bit of a summary. 00:02:12.490 --> 00:02:16.450 align:middle line:84% And then we'll, like last time, do some policy guidance 00:02:16.450 --> 00:02:17.790 align:middle line:90% that comes from theory. 00:02:17.790 --> 00:02:22.290 align:middle line:84% What's the logic according to the theory 00:02:22.290 --> 00:02:25.130 align:middle line:84% of what can go wrong when you have privately 00:02:25.130 --> 00:02:27.810 align:middle line:90% issued circulating debt? 00:02:27.810 --> 00:02:30.130 align:middle line:84% The idea is not to get rid of the debt, 00:02:30.130 --> 00:02:36.730 align:middle line:84% but to provide some coordination to avoid these financial crises. 00:02:36.730 --> 00:02:46.610 align:middle line:84% And this comes up in at least four seemingly distinct venues, 00:02:46.610 --> 00:02:50.310 align:middle line:84% but they have in common this underlying theory. 00:02:50.310 --> 00:02:53.010 align:middle line:84% So again, I think you've seen the pattern here, which 00:02:53.010 --> 00:02:56.760 align:middle line:90% is, take the theory seriously. 00:02:56.760 --> 00:03:00.180 align:middle line:84% Even when it was designed and written 00:03:00.180 --> 00:03:03.100 align:middle line:84% without these kinds of considerations in mind, 00:03:03.100 --> 00:03:08.640 align:middle line:84% there are huge lessons to be learned from going back to it 00:03:08.640 --> 00:03:11.320 align:middle line:84% and thinking about the new technologies. 00:03:11.320 --> 00:03:14.520 align:middle line:84% So again, it's about multi-agent smart contracts 00:03:14.520 --> 00:03:19.280 align:middle line:84% on a common ledger, and in particular, at the end, 00:03:19.280 --> 00:03:22.800 align:middle line:84% we'll talk about Ethereum and what 00:03:22.800 --> 00:03:26.600 align:middle line:90% that is relative to Bitcoin. 00:03:26.600 --> 00:03:27.100 align:middle line:90% OK. 00:03:27.100 --> 00:03:31.880 align:middle line:84% So extensions of the theory to incorporate risk 00:03:31.880 --> 00:03:34.600 align:middle line:90% and intertemporal exchange. 00:03:34.600 --> 00:03:37.280 align:middle line:90% So we had apples and wheat. 00:03:37.280 --> 00:03:41.600 align:middle line:84% It's easier to think about borrowing and lending 00:03:41.600 --> 00:03:44.920 align:middle line:90% as in getting-- 00:03:44.920 --> 00:03:50.500 align:middle line:84% or giving goods up today and receiving goods tomorrow, 00:03:50.500 --> 00:03:52.400 align:middle line:90% so the time date is there. 00:03:52.400 --> 00:03:55.480 align:middle line:84% But in addition, we're going to have mother nature drawing 00:03:55.480 --> 00:04:02.900 align:middle line:84% rainfall and weather realizations. 00:04:02.900 --> 00:04:06.740 align:middle line:84% So we need to talk about the state of nature, 00:04:06.740 --> 00:04:09.860 align:middle line:90% and that's that little s t. 00:04:09.860 --> 00:04:13.180 align:middle line:84% And actually, it could be the entire history 00:04:13.180 --> 00:04:16.920 align:middle line:84% from the genesis of states that have been realized over time. 00:04:16.920 --> 00:04:22.220 align:middle line:84% So we index commodities by time and by this history, including 00:04:22.220 --> 00:04:25.020 align:middle line:90% contemporary realizations. 00:04:25.020 --> 00:04:30.340 align:middle line:84% So little t superscript denotes the history, sub t denotes 00:04:30.340 --> 00:04:33.220 align:middle line:90% the contemporary value. 00:04:33.220 --> 00:04:36.900 align:middle line:84% The utility of the agents is going to be-- 00:04:36.900 --> 00:04:40.640 align:middle line:84% I'll say it in words, discounted expected utility. 00:04:40.640 --> 00:04:46.420 align:middle line:84% So we're going to add up the utilities over the time horizon, 00:04:46.420 --> 00:04:48.460 align:middle line:84% and we're going to take expectations 00:04:48.460 --> 00:04:51.620 align:middle line:84% over these underlying states of nature. 00:04:51.620 --> 00:04:58.000 align:middle line:84% So it's discounted by beta, and the expectations 00:04:58.000 --> 00:05:00.360 align:middle line:84% are formed with these probabilities 00:05:00.360 --> 00:05:03.320 align:middle line:90% of states of nature. 00:05:03.320 --> 00:05:08.480 align:middle line:84% And then we're going to, with this notation, 00:05:08.480 --> 00:05:11.800 align:middle line:84% do what we said we were going to do last time, 00:05:11.800 --> 00:05:14.140 align:middle line:84% which is turn this into a programming problem. 00:05:14.140 --> 00:05:18.280 align:middle line:84% So we're going to maximize this lambda-weighted sum 00:05:18.280 --> 00:05:21.920 align:middle line:84% of the utilities of the participants subject 00:05:21.920 --> 00:05:23.880 align:middle line:90% to resource constraints. 00:05:23.880 --> 00:05:25.500 align:middle line:90% The words are easy. 00:05:25.500 --> 00:05:31.320 align:middle line:84% The notation is a little more demanding, 00:05:31.320 --> 00:05:34.640 align:middle line:84% but lambdas are the weights, here's 00:05:34.640 --> 00:05:39.960 align:middle line:84% the discounted expected utility summing over dates and states 00:05:39.960 --> 00:05:42.560 align:middle line:84% with that probability distribution. 00:05:42.560 --> 00:05:44.640 align:middle line:84% And this resource constraint says 00:05:44.640 --> 00:05:49.880 align:middle line:84% that consumption in a pure exchange economy, consumption 00:05:49.880 --> 00:05:51.300 align:middle line:90% should equal income. 00:05:51.300 --> 00:05:55.750 align:middle line:84% So we're just summing up over all the, quote, "endowments" 00:05:55.750 --> 00:05:57.670 align:middle line:90% of the finite number-- 00:05:57.670 --> 00:06:01.230 align:middle line:84% capital I, it is-- of participants. 00:06:01.230 --> 00:06:06.310 align:middle line:84% That's the resources available for, say, distribution. 00:06:06.310 --> 00:06:11.110 align:middle line:84% So consumptions can add up to more than that. 00:06:11.110 --> 00:06:16.670 align:middle line:84% Again, a very powerful tool, and I'm happy to elaborate on this. 00:06:16.670 --> 00:06:19.810 align:middle line:84% We set this max problem up as a Lagrangian, 00:06:19.810 --> 00:06:23.190 align:middle line:84% so we kind of repeat the objective function. 00:06:23.190 --> 00:06:26.830 align:middle line:84% And then we have these auxiliary terms 00:06:26.830 --> 00:06:30.670 align:middle line:84% which are shadow prices times constraint. 00:06:30.670 --> 00:06:33.390 align:middle line:84% So we have the resource constraint written out 00:06:33.390 --> 00:06:35.390 align:middle line:90% for each date and state. 00:06:35.390 --> 00:06:37.550 align:middle line:84% For every date in state, it's preceded 00:06:37.550 --> 00:06:42.470 align:middle line:84% by this shadow price, this Lagrange multiplier, theta, 00:06:42.470 --> 00:06:44.390 align:middle line:90% of s of t. 00:06:44.390 --> 00:06:47.390 align:middle line:84% And the very nice thing about Lagrangians 00:06:47.390 --> 00:06:51.980 align:middle line:84% is as long as we have concavity of the objective functions 00:06:51.980 --> 00:06:54.860 align:middle line:84% and convexity of the underlying constraints, 00:06:54.860 --> 00:06:57.820 align:middle line:84% the first-order conditions of this max problem 00:06:57.820 --> 00:07:02.300 align:middle line:84% are necessary and sufficient for characterizing an optimum. 00:07:02.300 --> 00:07:05.260 align:middle line:84% Here are the first-order conditions. 00:07:05.260 --> 00:07:08.740 align:middle line:84% And it simply states in words that 00:07:08.740 --> 00:07:14.900 align:middle line:84% the lambda-weighted discounted marginal utility of consumption 00:07:14.900 --> 00:07:20.820 align:middle line:84% in a certain history of states should equal the common Lagrange 00:07:20.820 --> 00:07:23.740 align:middle line:84% multiplier across all the households. 00:07:23.740 --> 00:07:26.380 align:middle line:84% For every date and state, we're equating-- 00:07:26.380 --> 00:07:28.700 align:middle line:84% we're reallocating consumption in a way 00:07:28.700 --> 00:07:32.240 align:middle line:84% that equates the weighted marginal utilities. 00:07:32.240 --> 00:07:35.660 align:middle line:90% 00:07:35.660 --> 00:07:39.480 align:middle line:84% So this is-- and we repeat the resource constraint. 00:07:39.480 --> 00:07:42.420 align:middle line:90% 00:07:42.420 --> 00:07:44.100 align:middle line:84% Just a word about the math, and I'm 00:07:44.100 --> 00:07:46.980 align:middle line:84% trying not to do too much of that, 00:07:46.980 --> 00:07:49.900 align:middle line:84% there's a lot of these guys for every date 00:07:49.900 --> 00:07:52.960 align:middle line:84% and every history of states, and we're 00:07:52.960 --> 00:07:57.840 align:middle line:84% writing it out conditionally, but there are tons of them-- 00:07:57.840 --> 00:08:02.120 align:middle line:84% of these constraints, tons of Lagrange multipliers. 00:08:02.120 --> 00:08:06.560 align:middle line:84% So this just says weighted marginal utilities for person 1 00:08:06.560 --> 00:08:10.000 align:middle line:84% should be equated to any other person i, 00:08:10.000 --> 00:08:13.440 align:middle line:84% repeat the resource constraints, and we get, 00:08:13.440 --> 00:08:18.760 align:middle line:84% as a solution, something that looks deceptively simple, which 00:08:18.760 --> 00:08:23.600 align:middle line:84% is that the consumption allocation for an agent type i 00:08:23.600 --> 00:08:29.220 align:middle line:84% can be captured by a household i specific function g 00:08:29.220 --> 00:08:37.600 align:middle line:84% i, which has, as its argument, only the aggregate income. 00:08:37.600 --> 00:08:45.120 align:middle line:84% Now the intuition for this is that we're operating kind 00:08:45.120 --> 00:08:48.280 align:middle line:90% of a mutual insurance society. 00:08:48.280 --> 00:08:54.150 align:middle line:84% And it's as if everybody were contributing their rice 00:08:54.150 --> 00:08:59.930 align:middle line:84% to a community fund, and then that is pooled together, 00:08:59.930 --> 00:09:02.070 align:middle line:90% here's the big pile of rice. 00:09:02.070 --> 00:09:05.790 align:middle line:84% And now, maybe under the auspices of the monks, 00:09:05.790 --> 00:09:07.810 align:middle line:84% that is handed back to households 00:09:07.810 --> 00:09:13.950 align:middle line:84% depending on whether their own harvest was high or low. 00:09:13.950 --> 00:09:16.390 align:middle line:84% So the implication is, individual harvests 00:09:16.390 --> 00:09:19.710 align:middle line:84% are in there, but they're in the stockpile. 00:09:19.710 --> 00:09:22.230 align:middle line:84% And once you control for the stockpile in terms 00:09:22.230 --> 00:09:27.950 align:middle line:84% of its aggregate income y, the individual harvests don't enter. 00:09:27.950 --> 00:09:31.070 align:middle line:84% So you have this surprising result 00:09:31.070 --> 00:09:34.630 align:middle line:84% that consumption should depend on the aggregate and not 00:09:34.630 --> 00:09:37.870 align:middle line:90% on the individual shocks. 00:09:37.870 --> 00:09:41.370 align:middle line:84% And that's, as you'll see, a benchmark, 00:09:41.370 --> 00:09:43.550 align:middle line:90% which is taken to data. 00:09:43.550 --> 00:09:46.230 align:middle line:84% There is another implication, because 00:09:46.230 --> 00:09:51.210 align:middle line:84% of the concavity, that you'll have co-movement in consumption. 00:09:51.210 --> 00:09:55.010 align:middle line:84% People's consumption should go up and down together. 00:09:55.010 --> 00:09:58.250 align:middle line:84% Not everyone should eat the same amount. 00:09:58.250 --> 00:10:00.390 align:middle line:84% Some will be eating more, some less, 00:10:00.390 --> 00:10:03.210 align:middle line:84% but if you track their consumption, 00:10:03.210 --> 00:10:05.010 align:middle line:90% it should never cross. 00:10:05.010 --> 00:10:07.810 align:middle line:84% You should never have any period where 00:10:07.810 --> 00:10:11.050 align:middle line:84% consumption of one household or region 00:10:11.050 --> 00:10:16.010 align:middle line:84% is going up while consumption in the other region is going down. 00:10:16.010 --> 00:10:20.170 align:middle line:90% And that's testable. 00:10:20.170 --> 00:10:23.910 align:middle line:84% So again, we're working on policy guidance from the data, 00:10:23.910 --> 00:10:26.750 align:middle line:84% and the idea is, OK, that's the implication of the theory. 00:10:26.750 --> 00:10:29.010 align:middle line:90% How well are people doing? 00:10:29.010 --> 00:10:30.750 align:middle line:90% Maybe they're doing just fine. 00:10:30.750 --> 00:10:32.050 align:middle line:90% That would be wonderful. 00:10:32.050 --> 00:10:34.170 align:middle line:90% It sometimes happens. 00:10:34.170 --> 00:10:37.250 align:middle line:84% Or in other instances, things that look terrible, 00:10:37.250 --> 00:10:39.570 align:middle line:90% is there a remedy? 00:10:39.570 --> 00:10:41.230 align:middle line:90% That's the simple logic of it. 00:10:41.230 --> 00:10:46.390 align:middle line:84% So we're going to take a peek at village India, village Thailand, 00:10:46.390 --> 00:10:50.550 align:middle line:84% and come back to this idea of targeting based 00:10:50.550 --> 00:10:52.530 align:middle line:90% on the theory more generally. 00:10:52.530 --> 00:10:55.630 align:middle line:84% So this is a picture of villages in India 00:10:55.630 --> 00:10:59.710 align:middle line:84% that were sampled for 10 years by a crops institute 00:10:59.710 --> 00:11:03.150 align:middle line:84% where the economists and business folks were not 00:11:03.150 --> 00:11:05.250 align:middle line:84% telling households how to grow crops, 00:11:05.250 --> 00:11:07.930 align:middle line:84% but they were gathering the data. 00:11:07.930 --> 00:11:10.150 align:middle line:90% ICRISAT data. 00:11:10.150 --> 00:11:14.450 align:middle line:84% And here, you can see the year, 70-- 00:11:14.450 --> 00:11:17.750 align:middle line:90% 10 years, basically. 00:11:17.750 --> 00:11:21.310 align:middle line:84% The numbers here are 76 through 84. 00:11:21.310 --> 00:11:24.630 align:middle line:90% And here are household numbers. 00:11:24.630 --> 00:11:26.790 align:middle line:84% And for every household, we're tracking 00:11:26.790 --> 00:11:28.990 align:middle line:90% the ups and downs of income. 00:11:28.990 --> 00:11:32.750 align:middle line:84% It's normalized around the overall average. 00:11:32.750 --> 00:11:37.710 align:middle line:84% So a negative number doesn't mean it's negative income, 00:11:37.710 --> 00:11:40.390 align:middle line:84% although incomes could go negative, 00:11:40.390 --> 00:11:44.130 align:middle line:84% it's just that you're below the average. 00:11:44.130 --> 00:11:48.340 align:middle line:90% So you see this gradient here. 00:11:48.340 --> 00:11:51.800 align:middle line:84% This has to do with landless small, medium, 00:11:51.800 --> 00:11:53.940 align:middle line:84% and large landholders the way they 00:11:53.940 --> 00:11:57.380 align:middle line:84% were assigned numbers in the data set. 00:11:57.380 --> 00:12:01.420 align:middle line:84% And not too surprisingly, large landowners are eating more-- 00:12:01.420 --> 00:12:08.060 align:middle line:84% or have more income than these landless laborers. 00:12:08.060 --> 00:12:09.980 align:middle line:84% When you look at the income, I sometimes 00:12:09.980 --> 00:12:14.180 align:middle line:84% refer to this as the Rocky Mountain picture 00:12:14.180 --> 00:12:16.700 align:middle line:84% because the peaks in front conceal 00:12:16.700 --> 00:12:23.620 align:middle line:84% what's going on behind the peak, which is arguably a valley. 00:12:23.620 --> 00:12:27.180 align:middle line:84% So incomes are not co-moving at all. 00:12:27.180 --> 00:12:29.540 align:middle line:90% They're very erratic. 00:12:29.540 --> 00:12:32.580 align:middle line:84% But when you look at consumption, 00:12:32.580 --> 00:12:34.900 align:middle line:84% in this case, of grain, which is sorghum, which 00:12:34.900 --> 00:12:37.860 align:middle line:84% is the dominant item in the diet, 00:12:37.860 --> 00:12:42.240 align:middle line:84% it looks-- forgive me if you're from Kansas, 00:12:42.240 --> 00:12:45.040 align:middle line:84% it looks like Kansas, it's really flat. 00:12:45.040 --> 00:12:46.740 align:middle line:90% There's not much going on. 00:12:46.740 --> 00:12:49.800 align:middle line:90% 00:12:49.800 --> 00:12:52.340 align:middle line:84% And yes, I've shown these pictures before. 00:12:52.340 --> 00:12:56.100 align:middle line:84% I've had a student in class who said, "I'm from Kansas, 00:12:56.100 --> 00:12:59.140 align:middle line:84% and you're right, there's not much going on in Kansas." 00:12:59.140 --> 00:13:03.680 align:middle line:84% The point here is how flat and a bit undulating 00:13:03.680 --> 00:13:07.780 align:middle line:84% waves of grain consumption are relative to income-- 00:13:07.780 --> 00:13:10.060 align:middle line:84% they are deliberately put on the same scale. 00:13:10.060 --> 00:13:13.840 align:middle line:84% I could blow this up if I change the scale, 00:13:13.840 --> 00:13:19.320 align:middle line:84% but the main message here is consumption is smooth. 00:13:19.320 --> 00:13:21.920 align:middle line:84% And then we can go to the data and see 00:13:21.920 --> 00:13:28.460 align:middle line:84% whether that more stringent test is consistent with the data, 00:13:28.460 --> 00:13:31.340 align:middle line:84% or whether we fail the statistical tests, 00:13:31.340 --> 00:13:34.760 align:middle line:90% and if we do, by how much. 00:13:34.760 --> 00:13:40.000 align:middle line:84% So roughly-- hard to draw one number from this. 00:13:40.000 --> 00:13:42.460 align:middle line:84% If it were in dollars, not rupees, 00:13:42.460 --> 00:13:47.730 align:middle line:84% but for every dollar increase in income, 00:13:47.730 --> 00:13:51.250 align:middle line:84% there's a $0.07 increase in consumption. 00:13:51.250 --> 00:13:56.430 align:middle line:84% So roughly only 7% of the income fluctuations 00:13:56.430 --> 00:14:00.950 align:middle line:84% are making their way into consumption. 00:14:00.950 --> 00:14:03.350 align:middle line:84% It's different for different groups. 00:14:03.350 --> 00:14:06.490 align:middle line:84% If you look at profits from trade and handicraft, 00:14:06.490 --> 00:14:09.510 align:middle line:84% then it's almost up to a quarter. 00:14:09.510 --> 00:14:14.590 align:middle line:84% Profits from animal husbandry in the two other villages, Shirapur 00:14:14.590 --> 00:14:21.350 align:middle line:84% and Kanzara, are, again, less than 25%, but close. 00:14:21.350 --> 00:14:24.470 align:middle line:84% So we're already into the, quote, "targeting aspect" 00:14:24.470 --> 00:14:30.910 align:middle line:84% of trying to identify sectors where the smoothing is not 00:14:30.910 --> 00:14:32.310 align:middle line:90% only-- 00:14:32.310 --> 00:14:36.070 align:middle line:84% overall it's not perfect, but the benchmark 00:14:36.070 --> 00:14:37.890 align:middle line:90% came surprisingly close. 00:14:37.890 --> 00:14:41.910 align:middle line:84% This actually created a firestorm among policymakers. 00:14:41.910 --> 00:14:43.610 align:middle line:90% They couldn't believe it. 00:14:43.610 --> 00:14:46.010 align:middle line:84% Their presumption was that households 00:14:46.010 --> 00:14:49.290 align:middle line:84% in a poor village in India, replete 00:14:49.290 --> 00:14:52.930 align:middle line:84% with the traditional caste system with the Brahmins 00:14:52.930 --> 00:14:56.450 align:middle line:84% and the untouchables and so on, there's 00:14:56.450 --> 00:15:00.890 align:middle line:84% no way they could be doing anything close to this well, 00:15:00.890 --> 00:15:03.530 align:middle line:84% but it is a statement about what's 00:15:03.530 --> 00:15:08.250 align:middle line:84% going on within the village in terms of storage of grain, gifts 00:15:08.250 --> 00:15:10.610 align:middle line:90% and transfers, and so on. 00:15:10.610 --> 00:15:12.290 align:middle line:90% But it isn't. 00:15:12.290 --> 00:15:14.650 align:middle line:84% It gets a little further away, and these guys 00:15:14.650 --> 00:15:20.090 align:middle line:84% suffer from more risk than some of the other groups do. 00:15:20.090 --> 00:15:26.290 align:middle line:84% OK, so I showed you the theory when there was pure exchange, 00:15:26.290 --> 00:15:28.410 align:middle line:90% as if endowments were-- 00:15:28.410 --> 00:15:30.570 align:middle line:90% income were given. 00:15:30.570 --> 00:15:35.030 align:middle line:84% It is possible to extend it to include production. 00:15:35.030 --> 00:15:38.330 align:middle line:84% So for the Thai villages, we have 00:15:38.330 --> 00:15:48.640 align:middle line:84% the output produced with capital inputs in sector I household J. 00:15:48.640 --> 00:15:52.780 align:middle line:84% And there, the idea is a bit unrealistic. 00:15:52.780 --> 00:15:54.620 align:middle line:84% You can always undo your projects. 00:15:54.620 --> 00:15:57.460 align:middle line:84% You have some of the consumption, 00:15:57.460 --> 00:16:00.800 align:middle line:84% you set it aside as investment, you 00:16:00.800 --> 00:16:03.400 align:middle line:84% acquire machinery and equipment and so on, that's 00:16:03.400 --> 00:16:05.640 align:middle line:90% helping with production. 00:16:05.640 --> 00:16:07.780 align:middle line:84% At the time of production you have, say, 00:16:07.780 --> 00:16:11.120 align:middle line:84% the harvest or some other revenue, 00:16:11.120 --> 00:16:15.560 align:middle line:84% and you decide how much to eat and how much to save. 00:16:15.560 --> 00:16:19.760 align:middle line:84% So the idea here is you get to eat potentially 00:16:19.760 --> 00:16:22.160 align:middle line:84% everything that's available, which 00:16:22.160 --> 00:16:25.740 align:middle line:84% is the output from these projects, 00:16:25.740 --> 00:16:28.560 align:middle line:84% like agriculture over something over all households, 00:16:28.560 --> 00:16:30.440 align:middle line:90% and the capital stock. 00:16:30.440 --> 00:16:37.640 align:middle line:84% But you can also reinvest, so it's not all consumed, 00:16:37.640 --> 00:16:43.010 align:middle line:84% but some residual is invested in the projects all over again. 00:16:43.010 --> 00:16:49.310 align:middle line:84% So sources and uses of wealth, you might say. 00:16:49.310 --> 00:16:54.190 align:middle line:84% Now here, we're focusing on the production aspect. 00:16:54.190 --> 00:16:57.190 align:middle line:84% And then the key issue is how much 00:16:57.190 --> 00:17:04.150 align:middle line:84% risk does a producer bear of the fluctuations. 00:17:04.150 --> 00:17:11.829 align:middle line:84% And the aggregate would move everybody's incomes like before. 00:17:11.829 --> 00:17:13.750 align:middle line:84% And if you're restricting attention 00:17:13.750 --> 00:17:15.690 align:middle line:84% to what's going on within the village, 00:17:15.690 --> 00:17:18.589 align:middle line:84% there's not much you can do about that. 00:17:18.589 --> 00:17:21.510 align:middle line:84% Someone has to bear the aggregate risk. 00:17:21.510 --> 00:17:26.470 align:middle line:84% But the idiosyncratic risk that hits one person's land and not 00:17:26.470 --> 00:17:31.070 align:middle line:84% another's, that's potentially smoothable in this mutual fund. 00:17:31.070 --> 00:17:35.190 align:middle line:84% So when we talk about a risk premium, 00:17:35.190 --> 00:17:40.010 align:middle line:84% it has to do with a financial object, the rate of return 00:17:40.010 --> 00:17:44.310 align:middle line:84% on these projects as if they were stock, equity. 00:17:44.310 --> 00:17:47.850 align:middle line:84% So the rate of return having to do with the net 00:17:47.850 --> 00:17:51.610 align:middle line:84% profits you get from the production activity divided 00:17:51.610 --> 00:17:53.850 align:middle line:90% by the capital stock. 00:17:53.850 --> 00:17:56.410 align:middle line:84% If they're bearing some risk, they 00:17:56.410 --> 00:17:58.850 align:middle line:90% need to be compensated for that. 00:17:58.850 --> 00:18:02.290 align:middle line:84% The rate of return needed would be 00:18:02.290 --> 00:18:08.170 align:middle line:84% higher than what it is for a risk-free asset, or just 00:18:08.170 --> 00:18:11.090 align:middle line:90% holding inventory or money. 00:18:11.090 --> 00:18:14.530 align:middle line:90% And that can be tested. 00:18:14.530 --> 00:18:18.410 align:middle line:84% The first-order conditions are equating 00:18:18.410 --> 00:18:20.070 align:middle line:90% weighted marginal utilities. 00:18:20.070 --> 00:18:24.670 align:middle line:84% That's an implication we already had from the previous slides. 00:18:24.670 --> 00:18:28.450 align:middle line:84% And then of Euler condition, which is telling us 00:18:28.450 --> 00:18:32.210 align:middle line:84% intertemporally how much to eat and how much to save 00:18:32.210 --> 00:18:33.950 align:middle line:90% and where to put the savings. 00:18:33.950 --> 00:18:38.350 align:middle line:84% So this is like an efficiency condition. 00:18:38.350 --> 00:18:42.950 align:middle line:84% And it turns out, just looking at the investment and rate 00:18:42.950 --> 00:18:47.190 align:middle line:84% of return data, the percentage of diversified, 00:18:47.190 --> 00:18:53.310 align:middle line:84% idiosyncratic risk is, on average, in the 90s. 00:18:53.310 --> 00:18:57.950 align:middle line:84% So it's like some of it, maybe 10%, 00:18:57.950 --> 00:19:01.190 align:middle line:84% requires a higher rate of return, but 90% of the risk 00:19:01.190 --> 00:19:02.670 align:middle line:90% is gone. 00:19:02.670 --> 00:19:06.830 align:middle line:84% They've pooled it away in this mutual fund. 00:19:06.830 --> 00:19:08.790 align:middle line:84% And another implication is what's 00:19:08.790 --> 00:19:12.230 align:middle line:84% aggregate has to be borne, but if you look at villages one 00:19:12.230 --> 00:19:18.550 align:middle line:84% at a time, the aggregate is not common. 00:19:18.550 --> 00:19:24.470 align:middle line:84% So it's as if each village had its idiosyncratic risk, 00:19:24.470 --> 00:19:28.270 align:middle line:84% and if you had a larger mutual fund, which they didn't have, 00:19:28.270 --> 00:19:33.750 align:middle line:84% could imagine a building a platform that would smooth risk 00:19:33.750 --> 00:19:35.360 align:middle line:90% across those villages. 00:19:35.360 --> 00:19:39.320 align:middle line:84% So a within-aspect and an across-aspect. 00:19:39.320 --> 00:19:40.080 align:middle line:90% Yes, Henry? 00:19:40.080 --> 00:19:43.300 align:middle line:84% AUDIENCE: So for the diversified, idiosyncratic risk 00:19:43.300 --> 00:19:47.300 align:middle line:84% that's above 100%, for instance, for the third village, 00:19:47.300 --> 00:19:50.860 align:middle line:84% is the interpretation there that there's some consumption that 00:19:50.860 --> 00:19:56.020 align:middle line:84% goes to perhaps making up for some lost crops 00:19:56.020 --> 00:19:59.580 align:middle line:84% or something that isn't actually like personal consumption that's 00:19:59.580 --> 00:20:02.080 align:middle line:84% meant to improve utility, but some sort of investment? 00:20:02.080 --> 00:20:03.580 align:middle line:90% Is it like mismeasurement? 00:20:03.580 --> 00:20:04.880 align:middle line:90% Otherwise, how should you-- 00:20:04.880 --> 00:20:08.860 align:middle line:84% ROBERT TOWNSEND: I think it's mismeasurement of four. 00:20:08.860 --> 00:20:14.280 align:middle line:84% Buriram had experienced an enormous amount of transitions. 00:20:14.280 --> 00:20:17.100 align:middle line:84% It's sitting right on the Cambodia border. 00:20:17.100 --> 00:20:20.605 align:middle line:84% There were incursions, for one thing. 00:20:20.605 --> 00:20:21.980 align:middle line:84% And then they were growing rubber 00:20:21.980 --> 00:20:23.520 align:middle line:84% and they were making a lot of money, 00:20:23.520 --> 00:20:26.180 align:middle line:84% then there was a huge amount of Danish tourists 00:20:26.180 --> 00:20:28.020 align:middle line:90% that go there to retire. 00:20:28.020 --> 00:20:30.580 align:middle line:90% So things weren't stable. 00:20:30.580 --> 00:20:34.250 align:middle line:84% And so I haven't tried to actually come up 00:20:34.250 --> 00:20:37.870 align:middle line:84% with a particular reason for the higher numbers, 00:20:37.870 --> 00:20:45.050 align:middle line:84% I've just attributed it to data, but good to point it out. 00:20:45.050 --> 00:20:45.590 align:middle line:90% OK. 00:20:45.590 --> 00:20:52.250 align:middle line:84% So just in case you're a little bit bewildered, back to the goal 00:20:52.250 --> 00:20:55.170 align:middle line:90% here. 00:20:55.170 --> 00:20:57.130 align:middle line:90% We have a criterion. 00:20:57.130 --> 00:21:00.570 align:middle line:84% I'm trying to illustrate going to the data 00:21:00.570 --> 00:21:05.190 align:middle line:84% and testing it, and then having guidance for policy. 00:21:05.190 --> 00:21:07.970 align:middle line:90% 00:21:07.970 --> 00:21:13.690 align:middle line:84% And there's a lot more to talk about today, 00:21:13.690 --> 00:21:18.370 align:middle line:84% but these slides come, for example, from other work. 00:21:18.370 --> 00:21:22.130 align:middle line:84% I've mentioned, from time to time, 193 00:21:22.130 --> 00:21:25.610 align:middle line:84% or the second half of 772, and there, we 00:21:25.610 --> 00:21:30.570 align:middle line:84% go over in much more detail the theory of risk-sharing, 00:21:30.570 --> 00:21:34.670 align:middle line:84% these two papers, and also what I 00:21:34.670 --> 00:21:38.870 align:middle line:84% began to allude to, the building of a digital risk-sharing 00:21:38.870 --> 00:21:41.350 align:middle line:90% platform. 00:21:41.350 --> 00:21:46.030 align:middle line:84% But you don't have to wait to gain access to that material. 00:21:46.030 --> 00:21:49.030 align:middle line:84% I've already reviewed the lecture slides iterated 00:21:49.030 --> 00:21:52.710 align:middle line:84% with my administrative assistant, Deb, 00:21:52.710 --> 00:21:54.470 align:middle line:84% and those slides are ready to go. 00:21:54.470 --> 00:22:01.550 align:middle line:84% So we can post them if you like, and you can read ahead and-- 00:22:01.550 --> 00:22:06.630 align:middle line:84% well, read in parallel would be a much better way to put this. 00:22:06.630 --> 00:22:10.590 align:middle line:84% All right, so the last word on the targeting 00:22:10.590 --> 00:22:14.590 align:middle line:84% is, it's not just Thai villages, although that here 00:22:14.590 --> 00:22:17.630 align:middle line:84% has to do with the networks within the village 00:22:17.630 --> 00:22:21.110 align:middle line:84% distinguishing the risk-sharing network from those that aren't 00:22:21.110 --> 00:22:24.750 align:middle line:84% in it, and the exposure to idiosyncratic shocks 00:22:24.750 --> 00:22:27.625 align:middle line:84% and how they channel through these networks. 00:22:27.625 --> 00:22:30.250 align:middle line:84% But you could look at the whole country of Thailand-- and Angus 00:22:30.250 --> 00:22:34.590 align:middle line:84% Deaton, who's report here doing this for Cote d'Ivoire, 00:22:34.590 --> 00:22:39.890 align:middle line:84% you can see these cross-regional decompositions. 00:22:39.890 --> 00:22:42.990 align:middle line:84% It's not a developing country thing exclusively. 00:22:42.990 --> 00:22:44.190 align:middle line:90% You could go to the US. 00:22:44.190 --> 00:22:48.410 align:middle line:84% These workers beta-- betas, finance terminology, 00:22:48.410 --> 00:22:53.650 align:middle line:84% having to do with co-movements, distinguishing various groups 00:22:53.650 --> 00:22:55.110 align:middle line:90% using US data. 00:22:55.110 --> 00:22:59.770 align:middle line:84% And this paper from the EU has to do 00:22:59.770 --> 00:23:04.330 align:middle line:84% with the countries in the monetary union 00:23:04.330 --> 00:23:11.650 align:middle line:84% are not in a fiscal union and their movements of consumption. 00:23:11.650 --> 00:23:14.890 align:middle line:84% Well, they don't co move much, so there 00:23:14.890 --> 00:23:21.730 align:middle line:84% is gains to thinking about having a better unemployment-- 00:23:21.730 --> 00:23:27.210 align:middle line:84% cross-country unemployment scheme for the eurozone. 00:23:27.210 --> 00:23:32.640 align:middle line:84% OK, so now we get to policy guidance from theory. 00:23:32.640 --> 00:23:36.760 align:middle line:84% And we're going to focus on high-velocity private debt, 00:23:36.760 --> 00:23:41.280 align:middle line:84% or, for short, privately issued monies. 00:23:41.280 --> 00:23:44.280 align:middle line:84% A little more provocative to put it that way, 00:23:44.280 --> 00:23:47.240 align:middle line:84% although I will say, immediately, this 00:23:47.240 --> 00:23:49.920 align:middle line:84% is the monetary theory definition 00:23:49.920 --> 00:23:54.840 align:middle line:84% of a money as an object-- in this case, a security that 00:23:54.840 --> 00:23:58.840 align:middle line:90% appears frequently in exchange. 00:23:58.840 --> 00:24:01.480 align:middle line:84% Hence, privately issued securities 00:24:01.480 --> 00:24:07.240 align:middle line:84% are candidates to be money depending on how often-- 00:24:07.240 --> 00:24:09.640 align:middle line:90% what their velocity is. 00:24:09.640 --> 00:24:13.920 align:middle line:84% And we'll look at these bills of exchange 00:24:13.920 --> 00:24:18.920 align:middle line:84% after we go through the theory that were being used in London. 00:24:18.920 --> 00:24:21.480 align:middle line:90% I have touched on that already-- 00:24:21.480 --> 00:24:24.680 align:middle line:90% in England and traded in London. 00:24:24.680 --> 00:24:28.260 align:middle line:84% We'll look at the first welfare theorem again as a review. 00:24:28.260 --> 00:24:32.320 align:middle line:84% View will attempt to implement the competitive equilibrium, 00:24:32.320 --> 00:24:36.380 align:middle line:84% but with fragmented markets and limited securities. 00:24:36.380 --> 00:24:40.540 align:middle line:84% And we're going to bump into this huge coordination problem. 00:24:40.540 --> 00:24:44.900 align:middle line:84% So English inland bills of exchange-- 00:24:44.900 --> 00:24:47.860 align:middle line:90% so this is within England-- 00:24:47.860 --> 00:24:51.100 align:middle line:84% were used as a medium of exchange during the Industrial 00:24:51.100 --> 00:24:55.700 align:middle line:84% Revolution in the north of England in the 18th and first 00:24:55.700 --> 00:24:58.220 align:middle line:90% half of the 19th centuries. 00:24:58.220 --> 00:25:04.180 align:middle line:84% So if I say privately issued monies, and the comeback is, 00:25:04.180 --> 00:25:08.580 align:middle line:84% we only have fiat monies, that would be wrong. 00:25:08.580 --> 00:25:11.980 align:middle line:84% Historically, we have seen these privately issued notes 00:25:11.980 --> 00:25:14.320 align:middle line:84% circulating as media of exchange, 00:25:14.320 --> 00:25:18.700 align:middle line:90% as in these inland bills. 00:25:18.700 --> 00:25:22.180 align:middle line:90% And we'll come back to that. 00:25:22.180 --> 00:25:23.720 align:middle line:90% So what is the welfare theorem? 00:25:23.720 --> 00:25:25.460 align:middle line:90% And this is a review. 00:25:25.460 --> 00:25:30.970 align:middle line:84% We have a candidate star allocation and prices p, 00:25:30.970 --> 00:25:34.010 align:middle line:84% and we have, say, a way of raising equilibrium. 00:25:34.010 --> 00:25:35.890 align:middle line:84% And then under certain conditions 00:25:35.890 --> 00:25:40.130 align:middle line:84% that, while raising an equilibrium, is Pareto-optimal. 00:25:40.130 --> 00:25:44.990 align:middle line:84% Despite the dates and the states and the risk and so on, 00:25:44.990 --> 00:25:48.490 align:middle line:84% it's the same theorem as it was last time. 00:25:48.490 --> 00:25:54.930 align:middle line:84% So we are going to, as a continuation from last time, 00:25:54.930 --> 00:25:57.430 align:middle line:90% retain these fragmented markets. 00:25:57.430 --> 00:26:01.570 align:middle line:84% It's as if traders are meeting pairwise, or at least 00:26:01.570 --> 00:26:03.250 align:middle line:90% in subgroups. 00:26:03.250 --> 00:26:06.170 align:middle line:84% But we're going to extend this to the dynamics, which are now 00:26:06.170 --> 00:26:10.450 align:middle line:84% going to be explicit, as in maximizing 00:26:10.450 --> 00:26:14.210 align:middle line:90% discounted utility over time. 00:26:14.210 --> 00:26:16.850 align:middle line:84% And the agents are no longer just code 00:26:16.850 --> 00:26:21.850 align:middle line:84% where we were trying to figure out how much information would 00:26:21.850 --> 00:26:23.850 align:middle line:84% be needed as an input into the code 00:26:23.850 --> 00:26:27.270 align:middle line:90% to achieve an objective here. 00:26:27.270 --> 00:26:32.710 align:middle line:84% The agents are self-interested, they're maximizing. 00:26:32.710 --> 00:26:34.770 align:middle line:84% And it's always a bit uncomfortable, 00:26:34.770 --> 00:26:36.670 align:middle line:84% at least for economists, to think 00:26:36.670 --> 00:26:39.310 align:middle line:84% about agents that don't max something, 00:26:39.310 --> 00:26:42.830 align:middle line:84% so now we're in more familiar ground. 00:26:42.830 --> 00:26:45.030 align:middle line:84% But we're going to still need the computer science 00:26:45.030 --> 00:26:52.070 align:middle line:84% to talk about the code and how to correct the problem that will 00:26:52.070 --> 00:26:54.350 align:middle line:90% become clear when we get there. 00:26:54.350 --> 00:26:56.390 align:middle line:84% So the focus-- the economic focus 00:26:56.390 --> 00:27:01.030 align:middle line:84% is on asset issue and ownership change of those assets, 00:27:01.030 --> 00:27:02.970 align:middle line:84% and I've already talked about money. 00:27:02.970 --> 00:27:08.070 align:middle line:84% So this is a paper I wrote with Neal Wallace. 00:27:08.070 --> 00:27:10.750 align:middle line:84% Each trader-- here's the environment. 00:27:10.750 --> 00:27:13.230 align:middle line:84% Traders are endowed with a single good, 00:27:13.230 --> 00:27:15.870 align:middle line:84% it's an endowment economy, but there 00:27:15.870 --> 00:27:19.230 align:middle line:90% are multiple dates and states. 00:27:19.230 --> 00:27:22.270 align:middle line:90% Or at least multiple dates. 00:27:22.270 --> 00:27:24.940 align:middle line:84% And their endowments vary over time. 00:27:24.940 --> 00:27:29.260 align:middle line:84% They're going to meet in these trading venues, which are 00:27:29.260 --> 00:27:33.140 align:middle line:90% segmented markets or platforms. 00:27:33.140 --> 00:27:38.580 align:middle line:84% And when they meet, they're only in one place in a given date, 00:27:38.580 --> 00:27:43.980 align:middle line:84% but different households are in different locations. 00:27:43.980 --> 00:27:49.180 align:middle line:84% And they will try to maximize their utility, which 00:27:49.180 --> 00:27:51.820 align:middle line:84% is derived from end of period of consumption. 00:27:51.820 --> 00:27:56.020 align:middle line:84% Obviously just intuitively from the get-go, 00:27:56.020 --> 00:28:01.500 align:middle line:84% if your income is low, you might want to be a borrower 00:28:01.500 --> 00:28:03.660 align:middle line:84% or sell securities that you've already 00:28:03.660 --> 00:28:07.180 align:middle line:84% acquired to get your consumption to be higher than your income 00:28:07.180 --> 00:28:10.740 align:middle line:84% and vice versa if your income is high. 00:28:10.740 --> 00:28:16.740 align:middle line:84% They're all interested in smoothing the path. 00:28:16.740 --> 00:28:20.860 align:middle line:84% So agents are going to maximize intertemporal utility 00:28:20.860 --> 00:28:23.800 align:middle line:84% at each date, taking into account 00:28:23.800 --> 00:28:29.080 align:middle line:84% the future, including the future prices of securities. 00:28:29.080 --> 00:28:31.820 align:middle line:84% Yeah, and we're going to get rid of the states of the world, 00:28:31.820 --> 00:28:36.360 align:middle line:84% so it's entirely about time variation. 00:28:36.360 --> 00:28:39.320 align:middle line:84% So here's a-- not just an example, 00:28:39.320 --> 00:28:43.360 align:middle line:84% really the prime motivator for what we're going to do, 00:28:43.360 --> 00:28:48.280 align:middle line:90% is two locations. 00:28:48.280 --> 00:28:51.800 align:middle line:90% Again, agents meet pairwise. 00:28:51.800 --> 00:28:58.680 align:middle line:84% So agents 1 and 2 at date 1 are in location 1, agents 3 and 4 00:28:58.680 --> 00:29:01.840 align:middle line:90% at date 1 or in location 2. 00:29:01.840 --> 00:29:05.460 align:middle line:84% In this case, trader 1 stays put in location 1, 00:29:05.460 --> 00:29:08.740 align:middle line:84% trader 4 stays put in location 2, 00:29:08.740 --> 00:29:12.420 align:middle line:84% but the other two guys numbered agents 2 and 3, 00:29:12.420 --> 00:29:17.880 align:middle line:84% they're flipping back and forth, back and forth. 00:29:17.880 --> 00:29:20.040 align:middle line:84% So, again, for Ostroy-Starr, these 00:29:20.040 --> 00:29:22.530 align:middle line:90% would be the pairwise matchings. 00:29:22.530 --> 00:29:26.230 align:middle line:84% And it's deterministic, the sequence is known. 00:29:26.230 --> 00:29:30.850 align:middle line:90% So I'm going to focus on-- 00:29:30.850 --> 00:29:32.830 align:middle line:90% well, let me do it now. 00:29:32.830 --> 00:29:37.150 align:middle line:84% If you notice, agents 1 and 2 are together again at date 3 00:29:37.150 --> 00:29:39.190 align:middle line:90% as they were at date 1. 00:29:39.190 --> 00:29:41.530 align:middle line:84% So depending on the endowment profiles, 00:29:41.530 --> 00:29:44.390 align:middle line:84% you can imagine that 1 or 2 are borrowing and lending 00:29:44.390 --> 00:29:47.950 align:middle line:84% with each other depending on who's high and who's low 00:29:47.950 --> 00:29:49.750 align:middle line:90% and when. 00:29:49.750 --> 00:29:51.370 align:middle line:90% There's a lot of that going on. 00:29:51.370 --> 00:29:55.470 align:middle line:84% 1 and 3 are together, and 2, 4, and there's symmetry over here 00:29:55.470 --> 00:29:57.150 align:middle line:90% at location 2. 00:29:57.150 --> 00:30:01.530 align:middle line:84% So there's the potential for these debts, but in this case, 00:30:01.530 --> 00:30:06.830 align:middle line:84% they would be the more familiar debt where the borrower 00:30:06.830 --> 00:30:12.870 align:middle line:84% and lender agree to the loan, and the loan 00:30:12.870 --> 00:30:17.110 align:middle line:84% is to be paid back two dates later, 00:30:17.110 --> 00:30:20.780 align:middle line:90% not passed to third parties. 00:30:20.780 --> 00:30:26.100 align:middle line:84% But, in addition, you have these chains 00:30:26.100 --> 00:30:31.140 align:middle line:84% going on where one issues a security, which is a promise 00:30:31.140 --> 00:30:34.100 align:middle line:90% to repay at date 4. 00:30:34.100 --> 00:30:40.300 align:middle line:84% And 2 could buy that and then trade it to 4 at day 2, 00:30:40.300 --> 00:30:46.900 align:middle line:84% 4 could trade it back to 3 at date 3, and 3 could cash it in. 00:30:46.900 --> 00:30:50.000 align:middle line:84% Now let's just suppose, for the sake of argument, 00:30:50.000 --> 00:30:52.540 align:middle line:90% that there's no reneging. 00:30:52.540 --> 00:30:56.820 align:middle line:84% These debts have to be repaid when they're presented, 00:30:56.820 --> 00:31:01.660 align:middle line:84% otherwise, you go to debtor's prison which they had, 00:31:01.660 --> 00:31:03.740 align:middle line:90% severe penalties. 00:31:03.740 --> 00:31:06.220 align:middle line:90% So we abstract from that. 00:31:06.220 --> 00:31:10.200 align:middle line:84% Again, without too much by way of apology, 00:31:10.200 --> 00:31:14.220 align:middle line:84% because the more we simplify and yet still encounter 00:31:14.220 --> 00:31:17.700 align:middle line:84% a problem that needs a solution, the more clear 00:31:17.700 --> 00:31:20.600 align:middle line:84% it is how pervasive of the problem could be. 00:31:20.600 --> 00:31:22.680 align:middle line:90% So no reneging. 00:31:22.680 --> 00:31:27.720 align:middle line:84% But it's also true that 4 could issue this stuff to 3, 00:31:27.720 --> 00:31:33.260 align:middle line:84% 3 could issue it to 1, 1 to 2, and 2 redeems it to 4. 00:31:33.260 --> 00:31:35.460 align:middle line:90% So you're getting the idea here. 00:31:35.460 --> 00:31:41.680 align:middle line:84% We can look at these chains that connect the issuer at the issue 00:31:41.680 --> 00:31:45.360 align:middle line:84% date to redemption of the issuer at the redemption 00:31:45.360 --> 00:31:50.740 align:middle line:84% date with the change going through other parties. 00:31:50.740 --> 00:31:54.280 align:middle line:84% And those create the possibility of these circulating 00:31:54.280 --> 00:31:57.800 align:middle line:90% privately issued IOUs. 00:31:57.800 --> 00:32:01.000 align:middle line:84% If we just looked at the first two dates 00:32:01.000 --> 00:32:05.720 align:middle line:84% and restrict ourselves as we are to these kinds of debt 00:32:05.720 --> 00:32:10.840 align:middle line:84% securities, then we're kind of in trouble. 00:32:10.840 --> 00:32:12.400 align:middle line:90% Why? 00:32:12.400 --> 00:32:16.360 align:middle line:84% Because the debt cannot be redeemed. 00:32:16.360 --> 00:32:18.740 align:middle line:84% You could imagine, one still issues 00:32:18.740 --> 00:32:22.120 align:middle line:90% this note due at date 4 to 2-- 00:32:22.120 --> 00:32:25.220 align:middle line:90% 00:32:25.220 --> 00:32:26.660 align:middle line:90% sorry. 00:32:26.660 --> 00:32:35.180 align:middle line:84% 1 borrows from 2, 2 carries it to 4, 00:32:35.180 --> 00:32:37.000 align:middle line:90% but that's the end of the world. 00:32:37.000 --> 00:32:42.220 align:middle line:84% If there's only two dates, so it cannot be redeemed. 00:32:42.220 --> 00:32:44.620 align:middle line:84% Now this is interesting because it 00:32:44.620 --> 00:32:49.320 align:middle line:84% means the simple debt equilibrium gives us autarky, 00:32:49.320 --> 00:32:52.260 align:middle line:90% which is a horrible outcome. 00:32:52.260 --> 00:32:56.900 align:middle line:84% So the restriction to pairwise trading 00:32:56.900 --> 00:33:02.940 align:middle line:84% and to limiting ourselves to debt security trades 00:33:02.940 --> 00:33:05.620 align:middle line:90% can be quite damaging. 00:33:05.620 --> 00:33:12.660 align:middle line:84% If we had allowed the complete market solution with these four 00:33:12.660 --> 00:33:17.010 align:middle line:84% guys, you could potentially see some trade 00:33:17.010 --> 00:33:20.410 align:middle line:90% even though it's not bilateral. 00:33:20.410 --> 00:33:27.970 align:middle line:84% It's like 1 borrows from 2, and then 3 00:33:27.970 --> 00:33:31.810 align:middle line:84% provides the flow going back in the other direction at date 2. 00:33:31.810 --> 00:33:34.990 align:middle line:84% So it's a four-person multilateral agreement 00:33:34.990 --> 00:33:39.590 align:middle line:84% if we allowed, as the theory would have suggested, 00:33:39.590 --> 00:33:44.290 align:middle line:84% a decentralized competitive equilibrium in state and date 00:33:44.290 --> 00:33:46.650 align:middle line:90% contingent securities. 00:33:46.650 --> 00:33:49.850 align:middle line:84% But we're ruling that out for now. 00:33:49.850 --> 00:33:53.410 align:middle line:90% But we'll come back to it. 00:33:53.410 --> 00:33:57.130 align:middle line:84% It is pretty much in the spirit of Ostroy-Starr, in the sense 00:33:57.130 --> 00:34:00.010 align:middle line:84% that not everybody's together all the time-- they're 00:34:00.010 --> 00:34:04.010 align:middle line:84% in this fragmented, spatially separated market, 00:34:04.010 --> 00:34:06.010 align:middle line:84% there's quid pro quo requirements 00:34:06.010 --> 00:34:08.469 align:middle line:84% as per the competitive equilibrium. 00:34:08.469 --> 00:34:12.770 align:middle line:84% They have a budget constraint, and then the issue 00:34:12.770 --> 00:34:17.110 align:middle line:84% is how much can they achieve with these kinds 00:34:17.110 --> 00:34:19.590 align:middle line:90% of sequential restrictions? 00:34:19.590 --> 00:34:21.590 align:middle line:90% It's multilateral. 00:34:21.590 --> 00:34:25.429 align:middle line:90% Ostroy-Starr was not bilateral. 00:34:25.429 --> 00:34:29.429 align:middle line:84% It was about what the community can do as a whole 00:34:29.429 --> 00:34:34.870 align:middle line:84% even if the actual trading is restricted to pairwise. 00:34:34.870 --> 00:34:36.723 align:middle line:90% OK. 00:34:36.723 --> 00:34:41.190 align:middle line:84% That's what this says, basically. 00:34:41.190 --> 00:34:45.690 align:middle line:84% If you look here, and restricted it to two dates, 00:34:45.690 --> 00:34:50.010 align:middle line:84% you would see that the objects that agents care about, 00:34:50.010 --> 00:34:55.010 align:middle line:84% which depends on the location and date, is never common. 00:34:55.010 --> 00:34:58.350 align:middle line:90% 00:34:58.350 --> 00:35:00.870 align:middle line:90% Agent 1 cares about location. 00:35:00.870 --> 00:35:05.270 align:middle line:84% Agent 1 cares about location 1 goods, 4 about location 2 goods, 00:35:05.270 --> 00:35:08.930 align:middle line:84% and the other guys keep flipping places. 00:35:08.930 --> 00:35:16.060 align:middle line:84% So there's no common date-state pairing if the economy ends 00:35:16.060 --> 00:35:17.740 align:middle line:90% with only two dates. 00:35:17.740 --> 00:35:20.460 align:middle line:84% Obviously with four, more is possible. 00:35:20.460 --> 00:35:23.680 align:middle line:84% So these rules, traders can issue securities. 00:35:23.680 --> 00:35:26.180 align:middle line:90% They have to be redeemed. 00:35:26.180 --> 00:35:28.460 align:middle line:84% We allow short- and long-term debt. 00:35:28.460 --> 00:35:30.860 align:middle line:90% We allow circulating debt. 00:35:30.860 --> 00:35:33.820 align:middle line:84% Traders can buy previously issued assets 00:35:33.820 --> 00:35:37.160 align:middle line:90% and then sell them for value. 00:35:37.160 --> 00:35:41.020 align:middle line:84% This is like the quid pro quo or value for delivery swaps 00:35:41.020 --> 00:35:43.380 align:middle line:90% at any given date and location. 00:35:43.380 --> 00:35:47.820 align:middle line:84% It's as if, though, that they carry these paper securities 00:35:47.820 --> 00:35:50.980 align:middle line:90% around, but goods can't move. 00:35:50.980 --> 00:35:52.840 align:middle line:90% Again, that's a restriction. 00:35:52.840 --> 00:35:57.860 align:middle line:84% We're not having endowments or carrying of the commodities 00:35:57.860 --> 00:35:58.740 align:middle line:90% around. 00:35:58.740 --> 00:36:00.940 align:middle line:84% That would change the outcome, they 00:36:00.940 --> 00:36:03.900 align:middle line:84% could do some smoothing that way. 00:36:03.900 --> 00:36:06.460 align:middle line:84% Here, they're restricted to use the securities 00:36:06.460 --> 00:36:08.320 align:middle line:90% for the smoothing. 00:36:08.320 --> 00:36:08.820 align:middle line:90% OK. 00:36:08.820 --> 00:36:13.210 align:middle line:84% So if you think about that economy, 00:36:13.210 --> 00:36:17.250 align:middle line:84% we could talk about payment matrices and velocity. 00:36:17.250 --> 00:36:20.330 align:middle line:84% For payment matrices, I have shown 00:36:20.330 --> 00:36:22.490 align:middle line:90% you versions of this earlier. 00:36:22.490 --> 00:36:25.850 align:middle line:84% For simplicity, just imagine we have 00:36:25.850 --> 00:36:29.690 align:middle line:84% rows and columns in a big square matrix, 00:36:29.690 --> 00:36:33.550 align:middle line:84% and the objects consist of these consumption goods, 00:36:33.550 --> 00:36:36.930 align:middle line:84% but they're indexed by dates and locations. 00:36:36.930 --> 00:36:39.690 align:middle line:84% So you have eight of those guys because there are 00:36:39.690 --> 00:36:42.530 align:middle line:90% two locations and four dates. 00:36:42.530 --> 00:36:47.450 align:middle line:84% There's also the potential of these non-circulating debts, 00:36:47.450 --> 00:36:51.250 align:middle line:84% and they can trade against consumption. 00:36:51.250 --> 00:36:53.290 align:middle line:84% If, in fact, each consumption good 00:36:53.290 --> 00:36:56.170 align:middle line:84% gets traded for one circulating security and one 00:36:56.170 --> 00:36:59.130 align:middle line:84% non-circulating security, then there's 00:36:59.130 --> 00:37:03.690 align:middle line:84% a non-zero element in each row corresponding to a consumption 00:37:03.690 --> 00:37:06.330 align:middle line:90% good or a non-circulating debt. 00:37:06.330 --> 00:37:10.130 align:middle line:84% And for circulating debt, there are basically 00:37:10.130 --> 00:37:13.710 align:middle line:84% four checks because that debt could 00:37:13.710 --> 00:37:18.250 align:middle line:84% be traded in dates and locations and it's circulating around. 00:37:18.250 --> 00:37:23.550 align:middle line:84% So that's one way to think about the circulating stuff appearing 00:37:23.550 --> 00:37:25.330 align:middle line:90% more frequently in exchange. 00:37:25.330 --> 00:37:28.510 align:middle line:90% It fills in more boxes. 00:37:28.510 --> 00:37:31.830 align:middle line:84% Velocity is related, but not identical. 00:37:31.830 --> 00:37:36.510 align:middle line:84% So velocity means the amount traded in a given date divided 00:37:36.510 --> 00:37:38.910 align:middle line:90% by the stock outstanding. 00:37:38.910 --> 00:37:43.150 align:middle line:84% And we take the average over all dates 00:37:43.150 --> 00:37:46.510 align:middle line:84% where the security is in existence. 00:37:46.510 --> 00:37:51.550 align:middle line:84% So for that same table economy, a consumption 00:37:51.550 --> 00:37:56.030 align:middle line:84% good at location i at date t, the stock outstanding 00:37:56.030 --> 00:38:00.630 align:middle line:84% would be the endowment, and the amount traded would arguably 00:38:00.630 --> 00:38:01.730 align:middle line:90% be something less. 00:38:01.730 --> 00:38:04.790 align:middle line:84% This has to do with excess demand and excess supply. 00:38:04.790 --> 00:38:08.330 align:middle line:84% Rarely is it the case that if you're endowed with it, 00:38:08.330 --> 00:38:12.210 align:middle line:84% you give it all up to somebody else. 00:38:12.210 --> 00:38:15.170 align:middle line:84% So it's always a fraction of the total. 00:38:15.170 --> 00:38:17.850 align:middle line:90% So that's a number less than 1. 00:38:17.850 --> 00:38:21.650 align:middle line:84% If you consider the non-circulating debt, 00:38:21.650 --> 00:38:27.770 align:middle line:84% it comes into existence when the borrowing-lending contract 00:38:27.770 --> 00:38:28.710 align:middle line:90% is signed. 00:38:28.710 --> 00:38:32.730 align:middle line:90% All of it is traded-- 00:38:32.730 --> 00:38:36.290 align:middle line:84% all of the stock is now held by somebody else. 00:38:36.290 --> 00:38:39.730 align:middle line:84% They hold it for one period, nothing happens, 00:38:39.730 --> 00:38:40.910 align:middle line:90% and then it's redeemed. 00:38:40.910 --> 00:38:42.690 align:middle line:90% All of it is redeemed. 00:38:42.690 --> 00:38:46.450 align:middle line:84% So that has a velocity of two-thirds 00:38:46.450 --> 00:38:50.610 align:middle line:84% because there's three dates and it's completely traded 00:38:50.610 --> 00:38:54.730 align:middle line:84% in two of them and not traded at all in the intermediate date. 00:38:54.730 --> 00:38:59.410 align:middle line:84% And likewise, the circulating debts, of it 00:38:59.410 --> 00:39:06.850 align:middle line:84% is traded every date, so it has a velocity of 1. 00:39:06.850 --> 00:39:12.400 align:middle line:84% Either way you can think about these circulating debts 00:39:12.400 --> 00:39:16.680 align:middle line:84% as monies that appear frequently in exchange 00:39:16.680 --> 00:39:20.440 align:middle line:84% and have a high velocity relative to other securities 00:39:20.440 --> 00:39:22.560 align:middle line:90% and relative to consumption. 00:39:22.560 --> 00:39:30.520 align:middle line:84% So it turns out to be useful to create more general notation 00:39:30.520 --> 00:39:33.600 align:middle line:84% that would cover additional economies, not just 00:39:33.600 --> 00:39:35.480 align:middle line:90% the one in the table. 00:39:35.480 --> 00:39:38.400 align:middle line:84% So let J be the number of locations, 00:39:38.400 --> 00:39:43.080 align:middle line:84% T the number of dates, the commodity space 00:39:43.080 --> 00:39:47.140 align:middle line:84% has dimension J times T. Same idea here. 00:39:47.140 --> 00:39:49.640 align:middle line:84% People get utility from commodities. 00:39:49.640 --> 00:39:52.800 align:middle line:84% They have positive endowments, but only in the locations 00:39:52.800 --> 00:39:54.960 align:middle line:90% where they're in residence. 00:39:54.960 --> 00:39:58.000 align:middle line:84% If there are capital G people and they're 00:39:58.000 --> 00:40:01.980 align:middle line:84% living for these T periods, each person, little g, 00:40:01.980 --> 00:40:05.740 align:middle line:84% can be paired with another person or no one. 00:40:05.740 --> 00:40:07.480 align:middle line:84% Remember, in Ostroy-Starr, we had 00:40:07.480 --> 00:40:12.260 align:middle line:84% that a stand alone because trade was pairwise 00:40:12.260 --> 00:40:14.220 align:middle line:90% and there were five traders. 00:40:14.220 --> 00:40:18.140 align:middle line:84% So here again, we can allow these isolated pairings 00:40:18.140 --> 00:40:22.620 align:middle line:84% of singletons and isolated location. 00:40:22.620 --> 00:40:24.580 align:middle line:84% So you're either assigned to be alone 00:40:24.580 --> 00:40:28.700 align:middle line:84% or you're assigned with someone, and that's the itineraries. 00:40:28.700 --> 00:40:32.020 align:middle line:84% There's one commodity still for every date. 00:40:32.020 --> 00:40:34.820 align:middle line:84% And location, goods are indexed that way, 00:40:34.820 --> 00:40:37.820 align:middle line:84% and there's no transportation, production, or storage 00:40:37.820 --> 00:40:40.380 align:middle line:84% of the goods, but of course these assets 00:40:40.380 --> 00:40:43.020 align:middle line:90% can be carried around. 00:40:43.020 --> 00:40:48.180 align:middle line:84% So if we have person g in location i at date t, 00:40:48.180 --> 00:40:51.220 align:middle line:84% that person, if they are in that location, 00:40:51.220 --> 00:40:56.320 align:middle line:84% would have an endowment w g of it of the consumption. 00:40:56.320 --> 00:41:01.680 align:middle line:84% If you thought about a vector over all dates and states, 00:41:01.680 --> 00:41:04.940 align:middle line:84% they would have, say, positive endowments in the locations 00:41:04.940 --> 00:41:08.050 align:middle line:84% and dates that they visit and 0 elsewhere because they're just 00:41:08.050 --> 00:41:09.610 align:middle line:90% not there. 00:41:09.610 --> 00:41:13.036 align:middle line:84% Likewise, for consumption, c g, c 00:41:13.036 --> 00:41:17.130 align:middle line:84% g i d being a typical element of non-negative consumption 00:41:17.130 --> 00:41:21.130 align:middle line:84% for person g in location i at date t. 00:41:21.130 --> 00:41:23.090 align:middle line:84% Well, now what I promise is coming back 00:41:23.090 --> 00:41:25.170 align:middle line:84% with a vengeance in the notation. 00:41:25.170 --> 00:41:29.690 align:middle line:84% We're indexing everything in sight by locations and dates, 00:41:29.690 --> 00:41:31.530 align:middle line:90% and then we have these people. 00:41:31.530 --> 00:41:36.850 align:middle line:84% i location, date t, and g for the person. 00:41:36.850 --> 00:41:40.470 align:middle line:84% But they get utility from the consumption vectors, 00:41:40.470 --> 00:41:43.270 align:middle line:84% and now we have these securities, 00:41:43.270 --> 00:41:48.250 align:middle line:84% which would be the number of units of consumption promised 00:41:48.250 --> 00:41:54.170 align:middle line:84% by person f issued at date s coming due at date t. 00:41:54.170 --> 00:41:58.950 align:middle line:84% And we looked at this from the point of view of agent 1, 00:41:58.950 --> 00:42:05.720 align:middle line:84% for example, issuing a promise at date 1 coming due at date 4. 00:42:05.720 --> 00:42:08.720 align:middle line:84% And this is the general notation. 00:42:08.720 --> 00:42:13.960 align:middle line:84% But we're only going to consider issuers f at date 00:42:13.960 --> 00:42:18.760 align:middle line:84% s coming due at t for paths or chains which 00:42:18.760 --> 00:42:21.540 align:middle line:84% allow this kind of interconnectedness. 00:42:21.540 --> 00:42:25.080 align:middle line:84% That hopefully was clear from the table. 00:42:25.080 --> 00:42:30.680 align:middle line:84% So when there is a chain, which is active on both the supply 00:42:30.680 --> 00:42:34.520 align:middle line:84% side and the demand side, we can determine a price. 00:42:34.520 --> 00:42:39.440 align:middle line:84% So we'll have this price of security f 00:42:39.440 --> 00:42:45.150 align:middle line:84% issued at s coming due at t, but priced at a different location 00:42:45.150 --> 00:42:47.720 align:middle line:90% i and some date u. 00:42:47.720 --> 00:42:52.120 align:middle line:84% Yeah, so sorry, we're up to five superscripts and subscripts 00:42:52.120 --> 00:42:56.100 align:middle line:90% and objects, p of st at i, u. 00:42:56.100 --> 00:42:59.440 align:middle line:84% But where we don't need to price them everywhere, 00:42:59.440 --> 00:43:04.380 align:middle line:84% if traders h and g, say, are meeting at location i at date u, 00:43:04.380 --> 00:43:09.440 align:middle line:84% h may not want to acquire that security, 00:43:09.440 --> 00:43:15.860 align:middle line:84% there has to be some route from when agent h could acquire it, 00:43:15.860 --> 00:43:19.380 align:middle line:84% either directly presenting it to the issuer later 00:43:19.380 --> 00:43:23.620 align:middle line:84% or through other people who, in turn, are connected 00:43:23.620 --> 00:43:25.900 align:middle line:84% to other people who, in turn, are connected 00:43:25.900 --> 00:43:30.180 align:middle line:84% to the issuer at the redemption date. 00:43:30.180 --> 00:43:32.860 align:middle line:84% So that's on the, quote, "demand side." 00:43:32.860 --> 00:43:36.580 align:middle line:84% Likewise, who's bringing this security in? 00:43:36.580 --> 00:43:39.580 align:middle line:84% They must have been either directly connected 00:43:39.580 --> 00:43:43.980 align:middle line:84% with the issuer at date s or connected 00:43:43.980 --> 00:43:47.140 align:middle line:84% with someone else who was connected to the issuer 00:43:47.140 --> 00:43:51.220 align:middle line:84% from whom they have acquired securities which they are now 00:43:51.220 --> 00:43:53.760 align:middle line:90% basically supplying. 00:43:53.760 --> 00:43:56.820 align:middle line:90% 00:43:56.820 --> 00:44:03.920 align:middle line:84% So you can capture these rules for security markets and trades. 00:44:03.920 --> 00:44:08.440 align:middle line:84% The no redemption rule says that basically, 00:44:08.440 --> 00:44:11.500 align:middle line:84% the issuer is like a demander and a supplier, 00:44:11.500 --> 00:44:15.260 align:middle line:84% they're a supplier initially when they issue the security, 00:44:15.260 --> 00:44:17.580 align:middle line:84% but they also have to demand it back. 00:44:17.580 --> 00:44:21.200 align:middle line:90% That's the no redemption aspect. 00:44:21.200 --> 00:44:24.220 align:middle line:84% And they have to demand back everything that they issued. 00:44:24.220 --> 00:44:28.200 align:middle line:90% 00:44:28.200 --> 00:44:33.040 align:middle line:84% And these are the notions that you 00:44:33.040 --> 00:44:36.760 align:middle line:84% have to acquire an asset before you sell it. 00:44:36.760 --> 00:44:38.680 align:middle line:84% Somehow, the English is a lot easier 00:44:38.680 --> 00:44:41.500 align:middle line:84% to say than the notation is to understand, 00:44:41.500 --> 00:44:47.320 align:middle line:84% but that's what this means, that the demand is non-negative 00:44:47.320 --> 00:44:50.060 align:middle line:84% when you're summing over previous histories. 00:44:50.060 --> 00:44:53.720 align:middle line:84% You have to demand it first before you can supply it. 00:44:53.720 --> 00:44:55.640 align:middle line:90% And then this is key. 00:44:55.640 --> 00:45:01.790 align:middle line:84% This is the budget constraint of a person g at some location i 00:45:01.790 --> 00:45:06.070 align:middle line:84% and date t, and this is his or her endowment, 00:45:06.070 --> 00:45:07.450 align:middle line:90% and this is consumption. 00:45:07.450 --> 00:45:10.510 align:middle line:84% So if you subtracted consumption off 00:45:10.510 --> 00:45:13.470 align:middle line:84% from the left-hand side-- from both sides, 00:45:13.470 --> 00:45:15.910 align:middle line:84% you would see the difference between endowment 00:45:15.910 --> 00:45:18.050 align:middle line:90% minus consumption on the left. 00:45:18.050 --> 00:45:23.570 align:middle line:84% So that would be excess supply if it's positive. 00:45:23.570 --> 00:45:27.390 align:middle line:84% The amount that you own over and above what 00:45:27.390 --> 00:45:32.590 align:middle line:84% you eat, so you're a supplier of the good at that location 00:45:32.590 --> 00:45:33.610 align:middle line:90% i and date u. 00:45:33.610 --> 00:45:35.290 align:middle line:84% But what are these other objects? 00:45:35.290 --> 00:45:40.630 align:middle line:84% These are the valuation at these prices p of the security trades. 00:45:40.630 --> 00:45:45.190 align:middle line:84% So you could take this excess value 00:45:45.190 --> 00:45:47.630 align:middle line:90% and basically buy securities. 00:45:47.630 --> 00:45:51.050 align:middle line:84% Or alternatively, when it's excess demand, 00:45:51.050 --> 00:45:53.510 align:middle line:84% how do you accommodate excess demand? 00:45:53.510 --> 00:45:56.310 align:middle line:84% How do you manage to eat more than you have? 00:45:56.310 --> 00:46:00.490 align:middle line:84% Basically you have to sell securities you previously 00:46:00.490 --> 00:46:01.810 align:middle line:90% acquired. 00:46:01.810 --> 00:46:03.470 align:middle line:84% So when you're running surpluses, 00:46:03.470 --> 00:46:05.330 align:middle line:90% you're acquiring securities. 00:46:05.330 --> 00:46:09.010 align:middle line:84% When you're running deficits, you're selling securities. 00:46:09.010 --> 00:46:15.090 align:middle line:84% And that's what this budget balance equation is saying. 00:46:15.090 --> 00:46:17.970 align:middle line:84% But again, you're not-- we're not 00:46:17.970 --> 00:46:21.650 align:middle line:84% allowing direct commitments for location 00:46:21.650 --> 00:46:24.370 align:middle line:84% and date-specific goods, we are only 00:46:24.370 --> 00:46:28.570 align:middle line:84% allowing these non-circulating and circulating 00:46:28.570 --> 00:46:35.770 align:middle line:84% securities all captured by this d f of st notation. 00:46:35.770 --> 00:46:40.850 align:middle line:84% So a securities equilibrium-- a debt equilibrium would specify 00:46:40.850 --> 00:46:45.770 align:middle line:84% consumption and debt demands for each person and prices 00:46:45.770 --> 00:46:49.450 align:middle line:84% such that consumption in the debt demands 00:46:49.450 --> 00:46:55.610 align:middle line:84% are maximizing utility by date and location 00:46:55.610 --> 00:46:58.370 align:middle line:84% subject to the debt trading rules, 00:46:58.370 --> 00:47:00.460 align:middle line:90% and we need market clearing. 00:47:00.460 --> 00:47:02.680 align:middle line:84% And market clearing is just saying 00:47:02.680 --> 00:47:06.680 align:middle line:84% that the excess demands of consumption sum up to 0, 00:47:06.680 --> 00:47:11.280 align:middle line:84% but that also the security demand is equal to the security 00:47:11.280 --> 00:47:15.040 align:middle line:84% supply for every potential circulating or non-circulating 00:47:15.040 --> 00:47:16.240 align:middle line:90% security. 00:47:16.240 --> 00:47:20.520 align:middle line:84% This thing is summing up over g over both of them, 00:47:20.520 --> 00:47:22.800 align:middle line:90% over the total number of agents. 00:47:22.800 --> 00:47:24.400 align:middle line:84% So again, apart from the struggle 00:47:24.400 --> 00:47:27.520 align:middle line:84% of absorbing all the notation, it's 00:47:27.520 --> 00:47:29.440 align:middle line:84% very similar to what we had before 00:47:29.440 --> 00:47:33.000 align:middle line:84% in a competitive equilibrium, except here, we 00:47:33.000 --> 00:47:36.160 align:middle line:90% are doing it with securities. 00:47:36.160 --> 00:47:41.160 align:middle line:84% OK, so finally, we can look at our target, 00:47:41.160 --> 00:47:45.800 align:middle line:84% and the target is going to be as if we had the complete markets 00:47:45.800 --> 00:47:48.100 align:middle line:90% equilibrium all along. 00:47:48.100 --> 00:47:52.640 align:middle line:84% So remember, in Ostroy-Starr, we had the excess demands 00:47:52.640 --> 00:47:57.750 align:middle line:84% and prices that corresponded to a competitive equilibrium, 00:47:57.750 --> 00:47:59.950 align:middle line:90% allowing multiple goods. 00:47:59.950 --> 00:48:03.710 align:middle line:84% Here, goods are indexed by locations and dates, 00:48:03.710 --> 00:48:07.150 align:middle line:84% so we could imagine a competitive equilibrium 00:48:07.150 --> 00:48:10.830 align:middle line:84% in date- and location-specific commodities 00:48:10.830 --> 00:48:15.870 align:middle line:84% where we price them all out initially at some initial date, 00:48:15.870 --> 00:48:20.430 align:middle line:84% and agents can trade them there, taking prices 00:48:20.430 --> 00:48:24.590 align:middle line:90% as given, maximizing utility. 00:48:24.590 --> 00:48:28.390 align:middle line:84% And in an equilibrium, prices will be such that excess demand 00:48:28.390 --> 00:48:29.990 align:middle line:90% sum to 0. 00:48:29.990 --> 00:48:34.150 align:middle line:84% So those are the words of Ostroy-Starr 00:48:34.150 --> 00:48:40.610 align:middle line:84% and Walrasian equilibria in the context of this location, date. 00:48:40.610 --> 00:48:44.550 align:middle line:84% So these excess demands are consumption 00:48:44.550 --> 00:48:49.430 align:middle line:84% over endowments of person g at location i and date t. 00:48:49.430 --> 00:48:53.690 align:middle line:84% The sit are these unit of account prices-- 00:48:53.690 --> 00:48:55.470 align:middle line:90% you have to pick a numeraire. 00:48:55.470 --> 00:48:59.370 align:middle line:84% Maybe it's the ghost currency sit, 00:48:59.370 --> 00:49:03.730 align:middle line:84% the price of consumption at location i and date t. 00:49:03.730 --> 00:49:09.810 align:middle line:84% And every person is going to have their budget constraint, 00:49:09.810 --> 00:49:12.730 align:middle line:84% which is that when you sum up over all the goods, 00:49:12.730 --> 00:49:19.090 align:middle line:84% sum up over locations and dates, the valuation of excess demands 00:49:19.090 --> 00:49:25.410 align:middle line:84% is 0 for each household, just as it was before. 00:49:25.410 --> 00:49:29.370 align:middle line:84% And also, the sum of the excess demands 00:49:29.370 --> 00:49:35.330 align:middle line:84% would be 0 when we sum up over g over the households. 00:49:35.330 --> 00:49:36.050 align:middle line:90% Yes? 00:49:36.050 --> 00:49:39.170 align:middle line:84% AUDIENCE: The prices we had earlier, were we pricing goods 00:49:39.170 --> 00:49:42.013 align:middle line:90% or were we pricing the debt? 00:49:42.013 --> 00:49:42.930 align:middle line:90% ROBERT TOWNSEND: Debt. 00:49:42.930 --> 00:49:44.330 align:middle line:84% AUDIENCE: So those aren't the same? 00:49:44.330 --> 00:49:45.130 align:middle line:90% ROBERT TOWNSEND: Not the same. 00:49:45.130 --> 00:49:46.547 align:middle line:84% AUDIENCE: So you want to convert-- 00:49:46.547 --> 00:49:48.130 align:middle line:90% ROBERT TOWNSEND: Yes. 00:49:48.130 --> 00:49:49.030 align:middle line:90% Exactly. 00:49:49.030 --> 00:49:52.170 align:middle line:90% 00:49:52.170 --> 00:49:54.950 align:middle line:84% So we're going to get to exactly that on I 00:49:54.950 --> 00:49:59.550 align:middle line:84% think the next slide, but first, just a statement. 00:49:59.550 --> 00:50:02.590 align:middle line:84% What is the relationship between this complete market, 00:50:02.590 --> 00:50:07.990 align:middle line:84% date-location market initially and its equilibrium 00:50:07.990 --> 00:50:11.310 align:middle line:90% with the debt equilibrium? 00:50:11.310 --> 00:50:13.670 align:middle line:84% So a debt equilibrium would consist 00:50:13.670 --> 00:50:21.310 align:middle line:84% of those debt prices and non-negative debt quantities 00:50:21.310 --> 00:50:26.190 align:middle line:84% such that the debt quantities and our target, 00:50:26.190 --> 00:50:28.990 align:middle line:84% complete market's excess demands, 00:50:28.990 --> 00:50:33.070 align:middle line:84% satisfy each person's debt budget constraints, 00:50:33.070 --> 00:50:35.950 align:middle line:84% which I wrote down on the previous slide, 00:50:35.950 --> 00:50:39.710 align:middle line:84% and the debt quantities and these excess demands 00:50:39.710 --> 00:50:44.390 align:middle line:84% are utility maximizing for each person given the debt prices. 00:50:44.390 --> 00:50:50.210 align:middle line:84% So that's what it means to achieve the date, location, 00:50:50.210 --> 00:50:56.300 align:middle line:84% complete markets equilibrium by way of these debts. 00:50:56.300 --> 00:51:00.580 align:middle line:84% So here, I'm kind of reminding myself not 00:51:00.580 --> 00:51:04.480 align:middle line:84% to get too carried away on each one of these slides. 00:51:04.480 --> 00:51:11.500 align:middle line:84% I just want to tell you what's going on, and then if you like, 00:51:11.500 --> 00:51:14.220 align:middle line:84% you can look at the algebra later. 00:51:14.220 --> 00:51:18.620 align:middle line:84% So this, Rafa, is the answer to your question. 00:51:18.620 --> 00:51:23.300 align:middle line:84% Let's guess what these debt prices ought to be. 00:51:23.300 --> 00:51:27.700 align:middle line:84% The debt prices are telling you how much consumption you 00:51:27.700 --> 00:51:31.560 align:middle line:84% get when you issue it relative to redemption, 00:51:31.560 --> 00:51:33.200 align:middle line:90% and redemption is one to one. 00:51:33.200 --> 00:51:36.140 align:middle line:84% You have to honor the number of consumption goods 00:51:36.140 --> 00:51:39.440 align:middle line:90% you promised in the d f of ft. 00:51:39.440 --> 00:51:44.820 align:middle line:84% So you could think about the ratio of these complete markets' 00:51:44.820 --> 00:51:47.780 align:middle line:84% prices as how much consumption you're 00:51:47.780 --> 00:51:54.160 align:middle line:84% getting at redemption dates relative to the issue dates, 00:51:54.160 --> 00:51:58.120 align:middle line:84% and hopefully that's enough without getting too involved 00:51:58.120 --> 00:51:58.660 align:middle line:90% with it. 00:51:58.660 --> 00:52:02.940 align:middle line:84% So the relationship between, say, 00:52:02.940 --> 00:52:07.400 align:middle line:84% the security issued by agent 1 coming due at date 4 traded 00:52:07.400 --> 00:52:12.200 align:middle line:84% at location 1 and date 1 is this Arrow-Debreu-- 00:52:12.200 --> 00:52:17.640 align:middle line:84% Arrow complete markets price in unit of account at date 4 00:52:17.640 --> 00:52:19.880 align:middle line:90% relative to date 1. 00:52:19.880 --> 00:52:21.720 align:middle line:90% So that's the guess. 00:52:21.720 --> 00:52:26.000 align:middle line:84% Which means at the guess, we can fill in all the debt prices, 00:52:26.000 --> 00:52:28.920 align:middle line:84% and then we see if it works or not. 00:52:28.920 --> 00:52:32.140 align:middle line:84% It's a very large system if you consider all these people, 00:52:32.140 --> 00:52:34.200 align:middle line:90% dates, and locations. 00:52:34.200 --> 00:52:38.800 align:middle line:84% Fortunately, we don't have to solve explicitly for all 00:52:38.800 --> 00:52:41.700 align:middle line:90% of the budget constraints. 00:52:41.700 --> 00:52:47.280 align:middle line:84% If we judiciously choose five of them, we'll be fine. 00:52:47.280 --> 00:52:50.400 align:middle line:84% So there's two statements on this slide. 00:52:50.400 --> 00:52:54.750 align:middle line:84% One is important, which is that using 00:52:54.750 --> 00:52:59.550 align:middle line:84% our candidate for the prices and the target excess demands, 00:52:59.550 --> 00:53:03.890 align:middle line:84% and then we sum up over the budget constraints, 00:53:03.890 --> 00:53:07.110 align:middle line:84% but we're going to have those prices filled in here. 00:53:07.110 --> 00:53:10.190 align:middle line:84% We sum up over these sequential budget constraints 00:53:10.190 --> 00:53:13.270 align:middle line:84% with the debt prices filled in at the Arrow-Debreu unit 00:53:13.270 --> 00:53:18.590 align:middle line:84% of account, prices we can show that we 00:53:18.590 --> 00:53:23.390 align:middle line:84% will get out of this the complete markets single budget 00:53:23.390 --> 00:53:25.110 align:middle line:90% constraint. 00:53:25.110 --> 00:53:30.510 align:middle line:84% So if we are able to come up with debt quantities that 00:53:30.510 --> 00:53:33.830 align:middle line:84% satisfy these constraints sequentially, 00:53:33.830 --> 00:53:36.590 align:middle line:84% we automatically have maximization 00:53:36.590 --> 00:53:41.270 align:middle line:84% because the complete market specification, 00:53:41.270 --> 00:53:44.030 align:middle line:84% they were maximizing utility there, 00:53:44.030 --> 00:53:46.550 align:middle line:84% and if we can find debt quantities that 00:53:46.550 --> 00:53:49.070 align:middle line:84% satisfy these sequential constraints, 00:53:49.070 --> 00:53:53.020 align:middle line:84% then they can get that utility level. 00:53:53.020 --> 00:53:55.300 align:middle line:84% And then the next part is, we don't 00:53:55.300 --> 00:53:58.020 align:middle line:84% need to solve this for every person, every date, 00:53:58.020 --> 00:53:59.740 align:middle line:90% and every location. 00:53:59.740 --> 00:54:04.300 align:middle line:84% There are, in fact, 32 excess demands, 00:54:04.300 --> 00:54:09.500 align:middle line:84% but we have constraints for the way excess demands sum up 00:54:09.500 --> 00:54:12.440 align:middle line:84% for the location and date, market clearing conditions, 00:54:12.440 --> 00:54:17.900 align:middle line:84% and for places where things are not visited. 00:54:17.900 --> 00:54:21.380 align:middle line:90% So we end up with more-- 00:54:21.380 --> 00:54:28.220 align:middle line:84% we end up with five things we have to fill out, not 32. 00:54:28.220 --> 00:54:31.980 align:middle line:84% And again, forgive me, but I'm at risk 00:54:31.980 --> 00:54:36.420 align:middle line:84% of falling into the trap going through that algebra too much. 00:54:36.420 --> 00:54:39.540 align:middle line:84% Let's just say we're counting equations and unknowns, 00:54:39.540 --> 00:54:42.500 align:middle line:90% and there are five unknowns. 00:54:42.500 --> 00:54:45.220 align:middle line:84% We just have to choose them very carefully. 00:54:45.220 --> 00:54:49.920 align:middle line:84% This is a matrix notation with five rows, 00:54:49.920 --> 00:54:53.860 align:middle line:84% and the columns correspond to the potential debts, 00:54:53.860 --> 00:54:55.680 align:middle line:90% which are being traded. 00:54:55.680 --> 00:54:58.820 align:middle line:84% And then we end up with two systems. 00:54:58.820 --> 00:55:01.560 align:middle line:84% We actually did a little linear algebra 00:55:01.560 --> 00:55:05.800 align:middle line:84% and took one row multiplied by a constant 00:55:05.800 --> 00:55:07.460 align:middle line:90% and then add it to another row. 00:55:07.460 --> 00:55:11.200 align:middle line:84% That's perfectly permitted matrix algebra. 00:55:11.200 --> 00:55:14.360 align:middle line:84% The advantage of that is the first four rows 00:55:14.360 --> 00:55:20.080 align:middle line:84% will pin down the non-circulating debts that 00:55:20.080 --> 00:55:23.040 align:middle line:84% are part of achieving the target allocation, 00:55:23.040 --> 00:55:28.400 align:middle line:84% and the fifth row is this equation. 00:55:28.400 --> 00:55:32.860 align:middle line:84% So this-- if this equation is satisfied, 00:55:32.860 --> 00:55:36.160 align:middle line:90% then we can achieve the target. 00:55:36.160 --> 00:55:40.400 align:middle line:84% And this equation has the valuation 00:55:40.400 --> 00:55:44.600 align:middle line:84% of excess demands on the left of what 00:55:44.600 --> 00:55:48.900 align:middle line:84% would have been the target complete market's equilibrium 00:55:48.900 --> 00:55:52.780 align:middle line:84% and a configuration of debts on the right. 00:55:52.780 --> 00:55:57.980 align:middle line:84% So for example, if this valuation of excess demands 00:55:57.980 --> 00:56:04.020 align:middle line:84% were positive, all we need to do is 00:56:04.020 --> 00:56:06.340 align:middle line:84% issue this quantity of the debt issued 00:56:06.340 --> 00:56:08.740 align:middle line:84% by person one coming due at date 4 00:56:08.740 --> 00:56:12.460 align:middle line:90% and ignore all the other debts. 00:56:12.460 --> 00:56:18.180 align:middle line:84% Or, instead of doing it with person 1 at location 1, 00:56:18.180 --> 00:56:23.780 align:middle line:84% we could do it with person 4 at location 2. 00:56:23.780 --> 00:56:26.980 align:middle line:84% There's two negative signs here, so this is a-- 00:56:26.980 --> 00:56:31.460 align:middle line:84% so a positive number here with all the other debts at 0 00:56:31.460 --> 00:56:35.020 align:middle line:90% will also work. 00:56:35.020 --> 00:56:38.140 align:middle line:84% And now we're inching up on the problem. 00:56:38.140 --> 00:56:42.340 align:middle line:84% How can agents know in the decentralized world, where 00:56:42.340 --> 00:56:46.090 align:middle line:84% they're born into a certain location, what is going on 00:56:46.090 --> 00:56:48.570 align:middle line:90% in the other location? 00:56:48.570 --> 00:56:51.510 align:middle line:84% And again, it's very akin to Ostroy-Starr 00:56:51.510 --> 00:56:55.090 align:middle line:84% where you don't know what's happening, unless it's all 00:56:55.090 --> 00:57:00.850 align:middle line:84% recorded on the ledger, what happened in other pairings. 00:57:00.850 --> 00:57:04.410 align:middle line:84% So there's an infinite number of equilibria. 00:57:04.410 --> 00:57:08.290 align:middle line:84% The underlying allocations are unique and identical, 00:57:08.290 --> 00:57:11.410 align:middle line:84% but the way of achieving them through the debt, there's 00:57:11.410 --> 00:57:14.610 align:middle line:84% an infinite number of ways of doing it. 00:57:14.610 --> 00:57:16.210 align:middle line:84% They could get it right, but they're 00:57:16.210 --> 00:57:18.130 align:middle line:90% going to need to coordinate. 00:57:18.130 --> 00:57:20.530 align:middle line:84% To get it right, they're going to need some information 00:57:20.530 --> 00:57:24.610 align:middle line:84% about what's happening in the other location. 00:57:24.610 --> 00:57:28.570 align:middle line:84% So this compares to Ostroy-Starr where 00:57:28.570 --> 00:57:32.510 align:middle line:84% we said money might potentially work if there's enough of it 00:57:32.510 --> 00:57:35.850 align:middle line:84% but they would have to know which object is the money, 00:57:35.850 --> 00:57:37.850 align:middle line:84% and the budget balance information had 00:57:37.850 --> 00:57:41.610 align:middle line:84% to do with information being recorded on the distributed 00:57:41.610 --> 00:57:42.150 align:middle line:90% ledger. 00:57:42.150 --> 00:57:46.210 align:middle line:84% So the point this is akin to Ostroy-Starr. 00:57:46.210 --> 00:57:49.830 align:middle line:84% It's not different, it's a different context 00:57:49.830 --> 00:57:51.730 align:middle line:90% and a bit of a different model. 00:57:51.730 --> 00:57:52.230 align:middle line:90% Yes? 00:57:52.230 --> 00:57:52.810 align:middle line:90% AUDIENCE: Sorry. 00:57:52.810 --> 00:57:54.310 align:middle line:84% The question went a little too fast. 00:57:54.310 --> 00:57:55.790 align:middle line:90% Can we go back to last slide? 00:57:55.790 --> 00:57:59.390 align:middle line:84% So this is something that has to hold at every debt 00:57:59.390 --> 00:58:04.350 align:middle line:84% equilibrium that implements the Walrasian allocation of this? 00:58:04.350 --> 00:58:07.470 align:middle line:84% And how can we see from there that-- 00:58:07.470 --> 00:58:11.830 align:middle line:84% what the chains are and how the debt is circulating, 00:58:11.830 --> 00:58:13.250 align:middle line:90% and what the possibilities are? 00:58:13.250 --> 00:58:14.830 align:middle line:90% So what does this mean? 00:58:14.830 --> 00:58:17.470 align:middle line:84% ROBERT TOWNSEND: Well, this is the stable economy. 00:58:17.470 --> 00:58:19.870 align:middle line:90% AUDIENCE: OK. 00:58:19.870 --> 00:58:23.570 align:middle line:84% ROBERT TOWNSEND: And this-- we don't have a statement, 00:58:23.570 --> 00:58:28.302 align:middle line:84% we have an example of where you can actually reach the target. 00:58:28.302 --> 00:58:30.010 align:middle line:84% AUDIENCE: And it satisfies that equation? 00:58:30.010 --> 00:58:31.690 align:middle line:84% ROBERT TOWNSEND: And it satisfies this equation. 00:58:31.690 --> 00:58:32.315 align:middle line:90% AUDIENCE: Yeah. 00:58:32.315 --> 00:58:34.210 align:middle line:84% And where are the degrees of freedom? 00:58:34.210 --> 00:58:37.230 align:middle line:90% What could you vary now as you-- 00:58:37.230 --> 00:58:40.230 align:middle line:84% ROBERT TOWNSEND: This is the given as an Ostroy-Starr. 00:58:40.230 --> 00:58:43.260 align:middle line:84% The excess demands are given and the prices are given. 00:58:43.260 --> 00:58:45.500 align:middle line:84% And the statement-- that it corresponds 00:58:45.500 --> 00:58:48.493 align:middle line:84% to the complete market's equilibrium. 00:58:48.493 --> 00:58:49.660 align:middle line:90% AUDIENCE: So once you pick-- 00:58:49.660 --> 00:58:51.360 align:middle line:84% ROBERT TOWNSEND: So that's data, right? 00:58:51.360 --> 00:58:52.032 align:middle line:90% AUDIENCE: Right, that's data. 00:58:52.032 --> 00:58:53.140 align:middle line:84% And then on the right-hand side-- 00:58:53.140 --> 00:58:55.057 align:middle line:84% ROBERT TOWNSEND: How do we get to this number? 00:58:55.057 --> 00:58:56.420 align:middle line:90% Choose. 00:58:56.420 --> 00:58:57.300 align:middle line:90% AUDIENCE: Any one? 00:58:57.300 --> 00:59:00.540 align:middle line:84% ROBERT TOWNSEND: Any one that satisfies the equation. 00:59:00.540 --> 00:59:03.300 align:middle line:84% AUDIENCE: You don't need to specify all the different d's 00:59:03.300 --> 00:59:04.860 align:middle line:90% that are possible? 00:59:04.860 --> 00:59:07.260 align:middle line:84% You only need these four d's or are there-- 00:59:07.260 --> 00:59:10.380 align:middle line:84% ROBERT TOWNSEND: That's true, you don't even need all of them 00:59:10.380 --> 00:59:11.380 align:middle line:90% if you-- 00:59:11.380 --> 00:59:15.780 align:middle line:84% you can choose one at a time depending on this number. 00:59:15.780 --> 00:59:16.500 align:middle line:90% AUDIENCE: Yeah. 00:59:16.500 --> 00:59:21.180 align:middle line:84% ROBERT TOWNSEND: What I featured was this is, say, positive, 00:59:21.180 --> 00:59:23.060 align:middle line:90% then just choose this one. 00:59:23.060 --> 00:59:28.520 align:middle line:84% But another is to set it to 0 and choose this one. 00:59:28.520 --> 00:59:29.020 align:middle line:90% Right. 00:59:29.020 --> 00:59:31.560 align:middle line:84% And I didn't go through the other cases. 00:59:31.560 --> 00:59:35.420 align:middle line:84% If this is negative, something like this also happens. 00:59:35.420 --> 00:59:39.020 align:middle line:84% AUDIENCE: And the one that would say minimize-- 00:59:39.020 --> 00:59:41.213 align:middle line:84% velocity is always 1, we said, in all of them? 00:59:41.213 --> 00:59:42.130 align:middle line:90% ROBERT TOWNSEND: Yeah. 00:59:42.130 --> 00:59:43.370 align:middle line:84% AUDIENCE: So that's not going to change? 00:59:43.370 --> 00:59:43.870 align:middle line:90% OK. 00:59:43.870 --> 00:59:45.330 align:middle line:90% ROBERT TOWNSEND: Yeah. 00:59:45.330 --> 00:59:48.730 align:middle line:84% Yeah, all the work that I didn't really 00:59:48.730 --> 00:59:51.730 align:middle line:84% share in the algebra is going through all those debt budget 00:59:51.730 --> 00:59:54.890 align:middle line:84% constraints and making sure they're satisfied that these gas 00:59:54.890 --> 00:59:56.050 align:middle line:90% prices-- 00:59:56.050 --> 00:59:59.290 align:middle line:84% so that we are achieving the excess demand of-- 00:59:59.290 --> 01:00:03.810 align:middle line:84% which is just popping up here at the end. 01:00:03.810 --> 01:00:06.130 align:middle line:84% So yeah, so just like Ostroy-Starr 01:00:06.130 --> 01:00:08.850 align:middle line:84% said need some kind of coordination, 01:00:08.850 --> 01:00:11.090 align:middle line:84% either information directly or agreement 01:00:11.090 --> 01:00:13.490 align:middle line:84% about what the money is in the case 01:00:13.490 --> 01:00:16.090 align:middle line:84% that that works, for us here, you 01:00:16.090 --> 01:00:19.850 align:middle line:84% need some information about the security issues. 01:00:19.850 --> 01:00:24.850 align:middle line:84% So the question is, what happens if somehow they get it wrong? 01:00:24.850 --> 01:00:30.490 align:middle line:84% What happens in the model if location 1 believes 01:00:30.490 --> 01:00:33.350 align:middle line:84% they're the only issuer of the circulating stuff, 01:00:33.350 --> 01:00:38.850 align:middle line:84% location 2 believes they are the only issuer? 01:00:38.850 --> 01:00:41.350 align:middle line:90% And then this is an outline. 01:00:41.350 --> 01:00:44.210 align:middle line:84% We'll come back to Bagehot's London Money Markets, 01:00:44.210 --> 01:00:48.830 align:middle line:84% low and middle-income countries, and fragmentation of liquidity 01:00:48.830 --> 01:00:51.430 align:middle line:90% in decentralized finance. 01:00:51.430 --> 01:00:55.870 align:middle line:84% So the answer is, if they get it wrong 01:00:55.870 --> 01:01:00.150 align:middle line:84% and they're both issuing this circulating money in such a way 01:01:00.150 --> 01:01:02.910 align:middle line:84% as to violate the equation, the people 01:01:02.910 --> 01:01:06.410 align:middle line:84% who have gotten a hold of the circulating debt in, say, 01:01:06.410 --> 01:01:10.430 align:middle line:84% location 1 thinking that they will be able to unload 01:01:10.430 --> 01:01:13.950 align:middle line:84% it are going to discover that its price has plummeted when 01:01:13.950 --> 01:01:15.350 align:middle line:90% they get there. 01:01:15.350 --> 01:01:17.550 align:middle line:84% There's enough information for everyone 01:01:17.550 --> 01:01:22.750 align:middle line:84% to realize the mistake at date 2, but it's too late to undo it. 01:01:22.750 --> 01:01:27.630 align:middle line:84% They will start changing their borrowing and lending that's 01:01:27.630 --> 01:01:32.110 align:middle line:84% done at day 2 and coming due at date 4, but it's not enough, 01:01:32.110 --> 01:01:35.190 align:middle line:84% it's not enough of an adjustment. 01:01:35.190 --> 01:01:38.390 align:middle line:84% It's really kind of a slow-moving crisis. 01:01:38.390 --> 01:01:41.410 align:middle line:84% Even though the prices change abruptly, 01:01:41.410 --> 01:01:43.990 align:middle line:84% it's partially mitigated, as I said. 01:01:43.990 --> 01:01:46.770 align:middle line:84% And in the third date, the people 01:01:46.770 --> 01:01:48.950 align:middle line:84% who are carrying around this circulating stuff, 01:01:48.950 --> 01:01:51.670 align:middle line:84% they just take a big hit in terms of consumption. 01:01:51.670 --> 01:01:54.570 align:middle line:90% 01:01:54.570 --> 01:01:58.490 align:middle line:90% And we work out-- 01:01:58.490 --> 01:02:01.250 align:middle line:84% Spector and I work out an example 01:02:01.250 --> 01:02:07.090 align:middle line:84% with log utilities, constant aggregate endowments that vary, 01:02:07.090 --> 01:02:10.490 align:middle line:84% and who has what fraction of it over time, 01:02:10.490 --> 01:02:16.170 align:middle line:84% and we're able to compute the solution. 01:02:16.170 --> 01:02:19.050 align:middle line:84% This table is a bit confusing because there's 01:02:19.050 --> 01:02:20.190 align:middle line:90% so much going on. 01:02:20.190 --> 01:02:22.290 align:middle line:90% There's the two locations. 01:02:22.290 --> 01:02:25.850 align:middle line:84% Scenario 1 is where they get the debt issues correct. 01:02:25.850 --> 01:02:28.610 align:middle line:84% Scenario 2 is where they guess wrong. 01:02:28.610 --> 01:02:31.290 align:middle line:84% And here's where you can see that consumption 01:02:31.290 --> 01:02:35.850 align:middle line:84% is getting buffeted around, often severely. 01:02:35.850 --> 01:02:39.520 align:middle line:84% Eventually in day 3, you can see, 01:02:39.520 --> 01:02:41.680 align:middle line:84% when you have time to study this, 01:02:41.680 --> 01:02:45.520 align:middle line:84% that the prices are collapsing because otherwise, 01:02:45.520 --> 01:02:49.240 align:middle line:84% in the complete market, the prices are all equal to 1. 01:02:49.240 --> 01:02:54.160 align:middle line:84% And here are the utility consequences. 01:02:54.160 --> 01:02:58.880 align:middle line:84% Namely persons 2 and 3 who acquire and carry 01:02:58.880 --> 01:03:05.040 align:middle line:84% the circulating stuff have a loss in utility. 01:03:05.040 --> 01:03:08.700 align:middle line:84% Summed with the units, this log utility is negative, 01:03:08.700 --> 01:03:11.260 align:middle line:84% but you want something to be less negative, 01:03:11.260 --> 01:03:14.200 align:middle line:90% that's a good thing. 01:03:14.200 --> 01:03:15.280 align:middle line:90% OK. 01:03:15.280 --> 01:03:22.000 align:middle line:84% So oddly, also, agents 1 and 4 actually benefit from this, 01:03:22.000 --> 01:03:24.640 align:middle line:84% and we haven't thought that through. 01:03:24.640 --> 01:03:28.640 align:middle line:84% The impact is heterogeneous given all the heterogeneity 01:03:28.640 --> 01:03:31.560 align:middle line:90% in the economy. 01:03:31.560 --> 01:03:36.080 align:middle line:84% So, again, things could go really bad in the model, 01:03:36.080 --> 01:03:40.000 align:middle line:84% and the fix is to coordinate on the issues. 01:03:40.000 --> 01:03:43.800 align:middle line:84% You could imagine respecting the itineraries-- 01:03:43.800 --> 01:03:47.620 align:middle line:84% so people are only allowed to trade consumption when they're 01:03:47.620 --> 01:03:51.340 align:middle line:84% in a date and location and paired with someone, 01:03:51.340 --> 01:03:56.600 align:middle line:84% but the big accounting matrix is keeping track-- 01:03:56.600 --> 01:04:04.300 align:middle line:84% and now restricting especially the security issues. 01:04:04.300 --> 01:04:08.720 align:middle line:84% So I'll get-- and now I'm going to get to applications. 01:04:08.720 --> 01:04:11.000 align:middle line:84% But everyone is talking about digital assets, 01:04:11.000 --> 01:04:14.980 align:middle line:84% we're going to focus a lot on that in the next class, 01:04:14.980 --> 01:04:18.060 align:middle line:90% and tokenization and so on. 01:04:18.060 --> 01:04:22.040 align:middle line:84% This risk has not been articulated so far as I know. 01:04:22.040 --> 01:04:24.440 align:middle line:90% It's a somewhat nuanced message. 01:04:24.440 --> 01:04:26.720 align:middle line:84% It's not like the singleness of money. 01:04:26.720 --> 01:04:28.500 align:middle line:84% It's not the idea that you should 01:04:28.500 --> 01:04:33.640 align:middle line:84% ban private securities or the circulating stuff, 01:04:33.640 --> 01:04:36.870 align:middle line:84% but rather, coordinate in the issue of that stuff 01:04:36.870 --> 01:04:41.490 align:middle line:84% if you know enough about the underlying economy. 01:04:41.490 --> 01:04:44.370 align:middle line:84% There's a lot of literature, It's quite the rage 01:04:44.370 --> 01:04:49.390 align:middle line:84% now on tokenization and what you can do with dynamic ledgers, 01:04:49.390 --> 01:04:55.770 align:middle line:84% but so far as I know, no policymaker has taken on board 01:04:55.770 --> 01:05:00.250 align:middle line:84% and talked about this kind of coordination problem. 01:05:00.250 --> 01:05:01.810 align:middle line:90% Back to London. 01:05:01.810 --> 01:05:05.010 align:middle line:84% We had those inland bills of exchange. 01:05:05.010 --> 01:05:07.650 align:middle line:84% They were circulating around as the money. 01:05:07.650 --> 01:05:12.070 align:middle line:84% And the brokers were making money off of this. 01:05:12.070 --> 01:05:18.970 align:middle line:84% So you could think about a small-medium enterprise selling 01:05:18.970 --> 01:05:19.810 align:middle line:90% stuff. 01:05:19.810 --> 01:05:23.330 align:middle line:90% The purchaser has issued an IOU. 01:05:23.330 --> 01:05:26.870 align:middle line:84% The small business is suffering from low liquidity, 01:05:26.870 --> 01:05:31.770 align:middle line:84% so they go to a bank or, in this case, a bill broker, 01:05:31.770 --> 01:05:35.410 align:middle line:84% and for a discount, are able to get liquidity. 01:05:35.410 --> 01:05:38.770 align:middle line:84% They're selling the security to the bank. 01:05:38.770 --> 01:05:42.810 align:middle line:84% And the bank is a broker-dealer, so they trade to other people. 01:05:42.810 --> 01:05:45.050 align:middle line:84% So this was the London money market, 01:05:45.050 --> 01:05:49.330 align:middle line:84% so it's a familiar institution, these kinds of IOUs, 01:05:49.330 --> 01:05:52.190 align:middle line:84% and it was a big part of what was going on in England, 01:05:52.190 --> 01:05:54.990 align:middle line:90% except that there was a crisis. 01:05:54.990 --> 01:05:57.510 align:middle line:84% And, yeah, the model actually predicts 01:05:57.510 --> 01:06:00.710 align:middle line:84% that can happen if you don't have 01:06:00.710 --> 01:06:03.390 align:middle line:90% coordination over these IOUs. 01:06:03.390 --> 01:06:05.550 align:middle line:84% It's entirely plausible that that 01:06:05.550 --> 01:06:07.790 align:middle line:90% was the source of the crisis. 01:06:07.790 --> 01:06:11.770 align:middle line:84% In any event, then there was an issue about what to do, 01:06:11.770 --> 01:06:14.990 align:middle line:84% and this book of Bagehot has to do 01:06:14.990 --> 01:06:17.910 align:middle line:90% with the role of central banks. 01:06:17.910 --> 01:06:19.830 align:middle line:84% The way to summarize this literature 01:06:19.830 --> 01:06:22.910 align:middle line:84% is real bills versus the quantity theory, 01:06:22.910 --> 01:06:27.070 align:middle line:84% and this debate is alive and well today, 01:06:27.070 --> 01:06:29.010 align:middle line:90% what causes inflation? 01:06:29.010 --> 01:06:32.890 align:middle line:84% And one view is, you take any money or money-like object, 01:06:32.890 --> 01:06:35.900 align:middle line:84% that's the quantity, then you have to restrict it 01:06:35.900 --> 01:06:38.420 align:middle line:90% in order to keep prices stable. 01:06:38.420 --> 01:06:43.160 align:middle line:84% The intermediation point of view is, no, intermediation is fine, 01:06:43.160 --> 01:06:46.020 align:middle line:84% that's what the financial system should be doing. 01:06:46.020 --> 01:06:49.060 align:middle line:84% These banks were basically lending 01:06:49.060 --> 01:06:54.420 align:middle line:84% backed by the eventual receipt of value from businesses, 01:06:54.420 --> 01:06:59.300 align:middle line:84% hence real bills linked to Main Street. 01:06:59.300 --> 01:07:03.420 align:middle line:84% And Wallace and Sargent have a paper about this. 01:07:03.420 --> 01:07:06.780 align:middle line:84% The same issue comes up with low- and middle-income 01:07:06.780 --> 01:07:10.340 align:middle line:84% countries, although, again, they have not yet 01:07:10.340 --> 01:07:12.100 align:middle line:90% made the connection. 01:07:12.100 --> 01:07:17.820 align:middle line:84% This has to do with the double use of both electronic accounts 01:07:17.820 --> 01:07:21.780 align:middle line:84% and currency, and I actually referenced this 01:07:21.780 --> 01:07:24.180 align:middle line:90% in a different way last time. 01:07:24.180 --> 01:07:28.240 align:middle line:84% All of this literature is on the syllabus. 01:07:28.240 --> 01:07:32.000 align:middle line:84% So if any of it interests you, that's a candidate, 01:07:32.000 --> 01:07:34.320 align:middle line:84% either a two-page review of it to share 01:07:34.320 --> 01:07:40.600 align:middle line:84% with your fellow students or adopt it as your bigger research 01:07:40.600 --> 01:07:42.460 align:middle line:90% project on this. 01:07:42.460 --> 01:07:49.320 align:middle line:84% And here's something about fragmentation is killing DeFi. 01:07:49.320 --> 01:07:53.640 align:middle line:84% So again, you could make a connection to the lecture today. 01:07:53.640 --> 01:07:56.160 align:middle line:84% The last thing I want to end with-- 01:07:56.160 --> 01:08:00.440 align:middle line:84% I haven't really allowed myself enough time, 01:08:00.440 --> 01:08:06.400 align:middle line:84% is to review what we mean by smart contracts on a blockchain. 01:08:06.400 --> 01:08:10.760 align:middle line:90% And these slides are from Sam. 01:08:10.760 --> 01:08:13.160 align:middle line:90% Thank you. 01:08:13.160 --> 01:08:18.920 align:middle line:84% So basically, in about three minutes, 01:08:18.920 --> 01:08:22.359 align:middle line:84% I can tell you what the content is. 01:08:22.359 --> 01:08:24.080 align:middle line:90% This is a review slide. 01:08:24.080 --> 01:08:27.000 align:middle line:84% A blockchain is a distributed ledger. 01:08:27.000 --> 01:08:29.840 align:middle line:90% That was lecture 2. 01:08:29.840 --> 01:08:34.710 align:middle line:84% It keeps track of transactions, which are recorded in blocks. 01:08:34.710 --> 01:08:39.010 align:middle line:84% And it's a common listing of these transactions. 01:08:39.010 --> 01:08:41.910 align:middle line:84% There's a consensus algorithm to come 01:08:41.910 --> 01:08:45.750 align:middle line:84% to an agreement about which blocks are valid. 01:08:45.750 --> 01:08:49.830 align:middle line:84% And the transactions in Bitcoin involve 01:08:49.830 --> 01:08:53.670 align:middle line:84% movement of cryptocurrency from the owner to someone 01:08:53.670 --> 01:08:55.750 align:middle line:90% of a different address. 01:08:55.750 --> 01:08:58.710 align:middle line:84% And there is this consensus going on. 01:08:58.710 --> 01:09:00.370 align:middle line:90% The blocks are being proposed. 01:09:00.370 --> 01:09:03.069 align:middle line:90% There's a validation algorithm. 01:09:03.069 --> 01:09:04.850 align:middle line:84% And we've talked about this before, 01:09:04.850 --> 01:09:10.430 align:middle line:84% so this is really a review, and we'll come back to it 01:09:10.430 --> 01:09:16.810 align:middle line:84% in other lectures featuring Bitcoin as the state machine. 01:09:16.810 --> 01:09:20.750 align:middle line:84% And finally, we come to smart contracts in Ethereum. 01:09:20.750 --> 01:09:26.950 align:middle line:84% So the main slide here is we're generalizing the notion 01:09:26.950 --> 01:09:31.740 align:middle line:90% of the state of the blockchain. 01:09:31.740 --> 01:09:37.380 align:middle line:84% And with Ethereum, we have a complete language 01:09:37.380 --> 01:09:41.819 align:middle line:84% for coding which allows arbitrary functionality. 01:09:41.819 --> 01:09:45.979 align:middle line:84% I will say that, according to the literature, almost 01:09:45.979 --> 01:09:49.620 align:middle line:84% immediately after the advent of Bitcoin, 01:09:49.620 --> 01:09:53.460 align:middle line:84% people were trying to do more with the coin other 01:09:53.460 --> 01:09:56.020 align:middle line:90% than just transfer balances. 01:09:56.020 --> 01:09:58.900 align:middle line:84% Trying to put some kind of conditionality. 01:09:58.900 --> 01:10:02.020 align:middle line:84% Maybe limiting the issuance, or directing it 01:10:02.020 --> 01:10:05.100 align:middle line:84% to certain participants, or you can imagine 01:10:05.100 --> 01:10:06.800 align:middle line:90% umpteen other possibilities. 01:10:06.800 --> 01:10:10.700 align:middle line:84% So Ethereum was born from Bitcoin. 01:10:10.700 --> 01:10:14.900 align:middle line:84% And this is really the main slide here, which 01:10:14.900 --> 01:10:17.880 align:middle line:90% is the two types of accounts. 01:10:17.880 --> 01:10:23.400 align:middle line:84% There's the Bitcoin type account for balances and transfers 01:10:23.400 --> 01:10:25.980 align:middle line:90% and there are contract accounts. 01:10:25.980 --> 01:10:28.080 align:middle line:84% And the contract accounts contain 01:10:28.080 --> 01:10:31.240 align:middle line:90% the code and the data storage. 01:10:31.240 --> 01:10:36.000 align:middle line:84% The contract accounts receive, quote, "messages--" say, 01:10:36.000 --> 01:10:41.160 align:middle line:84% transactions, and the contract accounts update the state 01:10:41.160 --> 01:10:48.040 align:middle line:84% and send transactions out as part of the outcome 01:10:48.040 --> 01:10:52.560 align:middle line:90% of the contract being executed. 01:10:52.560 --> 01:10:55.160 align:middle line:90% So what's the point here? 01:10:55.160 --> 01:10:57.440 align:middle line:90% There's a common language. 01:10:57.440 --> 01:10:59.580 align:middle line:84% And I mentioned this at the beginning. 01:10:59.580 --> 01:11:03.040 align:middle line:84% State in Bitcoin or money means balances and transfers 01:11:03.040 --> 01:11:04.200 align:middle line:90% of balances. 01:11:04.200 --> 01:11:07.200 align:middle line:84% Here, state is generalized, so not as 01:11:07.200 --> 01:11:09.840 align:middle line:84% to preclude balances and transfers, 01:11:09.840 --> 01:11:14.480 align:middle line:90% but to accommodate contracts. 01:11:14.480 --> 01:11:17.320 align:middle line:84% And currency, currency, and then you 01:11:17.320 --> 01:11:20.460 align:middle line:84% run into these contract accounts, which are nodes, 01:11:20.460 --> 01:11:24.640 align:middle line:84% they're valid nodes, but they have different functionality 01:11:24.640 --> 01:11:30.310 align:middle line:84% relative to the other agents who are doing transactions. 01:11:30.310 --> 01:11:35.590 align:middle line:84% So as a database, you can talk about the transaction structure, 01:11:35.590 --> 01:11:40.230 align:middle line:84% which distinguishes the contracts from the currency. 01:11:40.230 --> 01:11:44.890 align:middle line:84% And I'm not able to do justice to all of this. 01:11:44.890 --> 01:11:46.850 align:middle line:84% So you can take a look at these slides, 01:11:46.850 --> 01:11:52.670 align:middle line:84% and Sam's here also as a go-to for you 01:11:52.670 --> 01:11:56.870 align:middle line:84% to absorb more of these details, including 01:11:56.870 --> 01:11:58.830 align:middle line:90% Ethereum's virtual machine. 01:11:58.830 --> 01:12:03.490 align:middle line:84% It seemed like today was the day to talk about smart contracts 01:12:03.490 --> 01:12:08.910 align:middle line:84% because we talked about how to use them and couple them 01:12:08.910 --> 01:12:11.510 align:middle line:84% with the distributed ledger, and on Ethereum, this 01:12:11.510 --> 01:12:16.860 align:middle line:84% is what those contracts are building on. 01:12:16.860 --> 01:12:26.000 align:middle line:90%