WEBVTT 00:00:00.000 --> 00:00:02.958 align:middle line:90% [SQUEAKING] 00:00:02.958 --> 00:00:03.944 align:middle line:90% [RUSTLING] 00:00:03.944 --> 00:00:06.902 align:middle line:90% [CLICKING] 00:00:06.902 --> 00:00:12.340 align:middle line:90% 00:00:12.340 --> 00:00:14.720 align:middle line:84% ROBERT TOWNSEND: So let's get started today. 00:00:14.720 --> 00:00:19.180 align:middle line:84% First of all, are there any questions from last time? 00:00:19.180 --> 00:00:19.840 align:middle line:90% All right. 00:00:19.840 --> 00:00:23.380 align:middle line:84% Well, please feel free to ask questions along the way. 00:00:23.380 --> 00:00:29.380 align:middle line:84% In terms of the reading list, we're up to lecture 9 today. 00:00:29.380 --> 00:00:31.540 align:middle line:90% We're sharing with production. 00:00:31.540 --> 00:00:34.160 align:middle line:84% It's our second lecture on applications. 00:00:34.160 --> 00:00:36.280 align:middle line:90% There are two starred papers. 00:00:36.280 --> 00:00:38.860 align:middle line:84% And we're going to be going through the first one 00:00:38.860 --> 00:00:42.250 align:middle line:84% with Samphantharak in detail, and then 00:00:42.250 --> 00:00:46.510 align:middle line:84% a few selected slides on the Kinnon et al paper. 00:00:46.510 --> 00:00:49.930 align:middle line:84% But like all starred papers, I hope you will be reading them, 00:00:49.930 --> 00:00:53.050 align:middle line:84% because I know you're very well trained now. 00:00:53.050 --> 00:00:55.630 align:middle line:84% And you will be able to read those articles. 00:00:55.630 --> 00:00:59.270 align:middle line:84% So I think you would get a lot out of it. 00:00:59.270 --> 00:01:02.960 align:middle line:84% But we will cover most of it today. 00:01:02.960 --> 00:01:06.500 align:middle line:84% The other thing for the study guide-- 00:01:06.500 --> 00:01:11.390 align:middle line:84% so let me ask you guys some questions. 00:01:11.390 --> 00:01:17.060 align:middle line:84% Last time was our first applied lecture on risk sharing. 00:01:17.060 --> 00:01:21.740 align:middle line:84% We did it in both village India and medieval villages. 00:01:21.740 --> 00:01:24.710 align:middle line:84% And today, I want to give a little bit more emphasis 00:01:24.710 --> 00:01:29.000 align:middle line:84% to the economics combined with the analysis-- 00:01:29.000 --> 00:01:30.290 align:middle line:90% more than I usually do. 00:01:30.290 --> 00:01:32.300 align:middle line:84% But it seems like the time to do that, 00:01:32.300 --> 00:01:35.040 align:middle line:84% since we're talking about applications. 00:01:35.040 --> 00:01:37.940 align:middle line:90% So the first one I picked here-- 00:01:37.940 --> 00:01:42.740 align:middle line:84% describe in words why villages in India are a risky place, 00:01:42.740 --> 00:01:46.490 align:middle line:84% how to quantify that risk and its sources, 00:01:46.490 --> 00:01:50.810 align:middle line:84% and how that risk might be mitigated or potentially 00:01:50.810 --> 00:01:56.410 align:middle line:84% mitigated via individual or social diversification. 00:01:56.410 --> 00:02:02.770 align:middle line:84% So I have lately been taking volunteers. 00:02:02.770 --> 00:02:03.550 align:middle line:90% But let me ask. 00:02:03.550 --> 00:02:07.290 align:middle line:84% Dexin, do you want to take a stab at that? 00:02:07.290 --> 00:02:09.229 align:middle line:90% AUDIENCE: Yeah, sure. 00:02:09.229 --> 00:02:13.250 align:middle line:84% So villages are a risky place, because it's mostly 00:02:13.250 --> 00:02:14.030 align:middle line:90% agriculture. 00:02:14.030 --> 00:02:16.530 align:middle line:84% And it's not a stable source of income. 00:02:16.530 --> 00:02:20.720 align:middle line:84% And I think we can quantify that risk by just looking 00:02:20.720 --> 00:02:22.640 align:middle line:84% at the variation through the years 00:02:22.640 --> 00:02:25.820 align:middle line:84% and how it really changes, and how a lot of things 00:02:25.820 --> 00:02:28.760 align:middle line:84% are linked with each other in terms of their risk. 00:02:28.760 --> 00:02:33.670 align:middle line:84% And it can be mitigated by planting 00:02:33.670 --> 00:02:39.190 align:middle line:84% different kinds of plants, or planting far apart-- 00:02:39.190 --> 00:02:40.150 align:middle line:90% that's individually. 00:02:40.150 --> 00:02:45.230 align:middle line:84% And social diversification-- giving gifts or transfers. 00:02:45.230 --> 00:02:45.730 align:middle line:90% Yeah. 00:02:45.730 --> 00:02:47.440 align:middle line:90% ROBERT TOWNSEND: Great. 00:02:47.440 --> 00:02:49.610 align:middle line:90% Very, very good answer. 00:02:49.610 --> 00:02:50.180 align:middle line:90% Thank you. 00:02:50.180 --> 00:02:54.410 align:middle line:84% So we quantify the risk by the coefficient 00:02:54.410 --> 00:03:00.080 align:middle line:84% of variation of a given crop or a given crop in a certain soil 00:03:00.080 --> 00:03:04.370 align:middle line:90% type or a certain income source. 00:03:04.370 --> 00:03:06.170 align:middle line:90% Just to add a few more details-- 00:03:06.170 --> 00:03:08.090 align:middle line:90% your answer was fine. 00:03:08.090 --> 00:03:11.240 align:middle line:84% The covariance across those things 00:03:11.240 --> 00:03:14.113 align:middle line:84% actually helps mitigate the risk. 00:03:14.113 --> 00:03:15.530 align:middle line:84% And that's what you're saying when 00:03:15.530 --> 00:03:21.750 align:middle line:84% you said different crops or different spots on the field. 00:03:21.750 --> 00:03:23.070 align:middle line:90% Those are ex-ante. 00:03:23.070 --> 00:03:26.930 align:middle line:84% So there's individual things that people can do. 00:03:26.930 --> 00:03:30.155 align:middle line:84% And the ex-post-- social diversification is the gifts. 00:03:30.155 --> 00:03:33.105 align:middle line:90% 00:03:33.105 --> 00:03:33.605 align:middle line:90% OK. 00:03:33.605 --> 00:03:36.780 align:middle line:90% 00:03:36.780 --> 00:03:37.380 align:middle line:90% Next one. 00:03:37.380 --> 00:03:41.140 align:middle line:84% Comparing incomes over households and time 00:03:41.140 --> 00:03:44.290 align:middle line:84% with consumption over households and time, 00:03:44.290 --> 00:03:48.260 align:middle line:84% what can you infer from the data alone? 00:03:48.260 --> 00:03:51.640 align:middle line:84% So let me stop there and not read the second part. 00:03:51.640 --> 00:03:52.480 align:middle line:90% Let's see. 00:03:52.480 --> 00:03:54.400 align:middle line:90% Who would like to? 00:03:54.400 --> 00:03:56.530 align:middle line:84% Charles, do you want to take a stab at that? 00:03:56.530 --> 00:03:57.670 align:middle line:90% Are you there? 00:03:57.670 --> 00:03:59.560 align:middle line:90% AUDIENCE: Yeah. 00:03:59.560 --> 00:04:00.640 align:middle line:90% Let me think. 00:04:00.640 --> 00:04:02.470 align:middle line:84% If I remember correctly, this is something 00:04:02.470 --> 00:04:07.660 align:middle line:84% like you can compare the incomes, which is basically 00:04:07.660 --> 00:04:11.650 align:middle line:84% the crop harvest, and then what you end up receiving. 00:04:11.650 --> 00:04:14.680 align:middle line:84% And I remember, you can infer from-- 00:04:14.680 --> 00:04:18.459 align:middle line:84% you can see that it's definitely much-- 00:04:18.459 --> 00:04:23.250 align:middle line:84% you end up getting is much flatter than what's produced. 00:04:23.250 --> 00:04:25.750 align:middle line:84% I guess I'm trying to answer the second part of the question 00:04:25.750 --> 00:04:26.250 align:middle line:90% now. 00:04:26.250 --> 00:04:30.040 align:middle line:84% But that is data that suggests that we're risk sharing. 00:04:30.040 --> 00:04:34.510 align:middle line:84% I don't think that's enough to prove causation, 00:04:34.510 --> 00:04:35.987 align:middle line:90% but it's definitely suggestive. 00:04:35.987 --> 00:04:37.445 align:middle line:84% ROBERT TOWNSEND: Yeah, that's good. 00:04:37.445 --> 00:04:40.900 align:middle line:90% 00:04:40.900 --> 00:04:43.740 align:middle line:90% Maybe the second sentence helps. 00:04:43.740 --> 00:04:46.080 align:middle line:84% If average consumption of households 00:04:46.080 --> 00:04:50.520 align:middle line:84% increased when average income of households increased, 00:04:50.520 --> 00:04:53.010 align:middle line:84% would that be consistent with risk sharing or not? 00:04:53.010 --> 00:04:58.240 align:middle line:90% 00:04:58.240 --> 00:04:59.150 align:middle line:90% AUDIENCE: Oh, for me? 00:04:59.150 --> 00:05:01.073 align:middle line:90% ROBERT TOWNSEND: Yeah, for you. 00:05:01.073 --> 00:05:01.740 align:middle line:90% AUDIENCE: So OK. 00:05:01.740 --> 00:05:04.800 align:middle line:84% So OK, average consumption has to increase, but-- 00:05:04.800 --> 00:05:12.380 align:middle line:90% 00:05:12.380 --> 00:05:15.060 align:middle line:84% I don't think it rolls out to some sort of big sharing, 00:05:15.060 --> 00:05:15.650 align:middle line:90% I don't think. 00:05:15.650 --> 00:05:20.210 align:middle line:84% Because I think you have to parse a degree of risk sharing 00:05:20.210 --> 00:05:22.940 align:middle line:84% that wouldn't completely annihilate everything. 00:05:22.940 --> 00:05:26.010 align:middle line:84% But I don't think that would be enough. 00:05:26.010 --> 00:05:28.340 align:middle line:84% I think that would still be consistent with some level, 00:05:28.340 --> 00:05:29.840 align:middle line:90% right? 00:05:29.840 --> 00:05:32.810 align:middle line:84% ROBERT TOWNSEND: Yeah, actually, the sentence 00:05:32.810 --> 00:05:34.610 align:middle line:90% is not terribly well worded. 00:05:34.610 --> 00:05:39.340 align:middle line:90% But it is worthwhile to clarify. 00:05:39.340 --> 00:05:40.810 align:middle line:84% So the first part that we looked at 00:05:40.810 --> 00:05:45.040 align:middle line:84% is just the levels of stuff over households and over time. 00:05:45.040 --> 00:05:47.290 align:middle line:84% We referred to the Rocky Mountain picture 00:05:47.290 --> 00:05:52.390 align:middle line:84% as incomes going up concealing the valley behind, 00:05:52.390 --> 00:05:56.950 align:middle line:84% and very, very jagged rocky pictures 00:05:56.950 --> 00:06:00.580 align:middle line:84% as opposed to consumption, which was very flat. 00:06:00.580 --> 00:06:04.600 align:middle line:84% And we were even joking around a bit-- very boring, 00:06:04.600 --> 00:06:06.500 align:middle line:90% as in Kansas. 00:06:06.500 --> 00:06:09.580 align:middle line:84% So then, the issue would be with the theory 00:06:09.580 --> 00:06:11.230 align:middle line:90% that we're about to look at. 00:06:11.230 --> 00:06:13.960 align:middle line:84% Apart from the data alone, would you 00:06:13.960 --> 00:06:15.970 align:middle line:84% think household consumption ought 00:06:15.970 --> 00:06:17.320 align:middle line:90% to move with household income? 00:06:17.320 --> 00:06:19.570 align:middle line:84% Actually, I think there's a question below. 00:06:19.570 --> 00:06:22.450 align:middle line:84% And what's ambiguous about that sentence is, 00:06:22.450 --> 00:06:26.920 align:middle line:84% household consumption is increased with average income 00:06:26.920 --> 00:06:28.800 align:middle line:90% of households. 00:06:28.800 --> 00:06:31.960 align:middle line:84% Yeah, that's very treacherously worded. 00:06:31.960 --> 00:06:35.170 align:middle line:84% Average income meaning overall the dates 00:06:35.170 --> 00:06:37.150 align:middle line:90% of a given household-- 00:06:37.150 --> 00:06:39.220 align:middle line:90% that sets the levels of things. 00:06:39.220 --> 00:06:45.070 align:middle line:84% And maybe the household with higher average income over time 00:06:45.070 --> 00:06:48.410 align:middle line:84% has a higher average consumption over time. 00:06:48.410 --> 00:06:51.300 align:middle line:90% And I'll ask for volunteers. 00:06:51.300 --> 00:06:56.670 align:middle line:84% If we have this regression where we run household consumption, 00:06:56.670 --> 00:06:59.160 align:middle line:84% on the left, as the dependent variable 00:06:59.160 --> 00:07:02.550 align:middle line:84% onto aggregate consumption and individual income, 00:07:02.550 --> 00:07:06.150 align:middle line:84% on the right, throwing in some intercepts-- so 00:07:06.150 --> 00:07:08.040 align:middle line:84% what restrictions from the theory 00:07:08.040 --> 00:07:13.620 align:middle line:84% are placed on the coefficient of individual income? 00:07:13.620 --> 00:07:16.610 align:middle line:84% And I'll take a volunteer for that. 00:07:16.610 --> 00:07:20.510 align:middle line:84% AUDIENCE: I think the coefficient individual income 00:07:20.510 --> 00:07:21.915 align:middle line:90% should be 0, right? 00:07:21.915 --> 00:07:22.790 align:middle line:90% ROBERT TOWNSEND: Yes. 00:07:22.790 --> 00:07:24.620 align:middle line:84% AUDIENCE: Because it's just related 00:07:24.620 --> 00:07:32.870 align:middle line:84% to the aggregate in average income of the household. 00:07:32.870 --> 00:07:35.060 align:middle line:90% And I have a question here. 00:07:35.060 --> 00:07:37.850 align:middle line:84% It's that I remember in the slides-- 00:07:37.850 --> 00:07:42.560 align:middle line:84% saying that when all the households have the same risk 00:07:42.560 --> 00:07:52.130 align:middle line:84% aversion, then the coefficient between the aggregate 00:07:52.130 --> 00:07:56.570 align:middle line:90% consumption should be 1. 00:07:56.570 --> 00:07:57.740 align:middle line:90% ROBERT TOWNSEND: Yes. 00:07:57.740 --> 00:08:00.140 align:middle line:90% AUDIENCE: But why? 00:08:00.140 --> 00:08:06.710 align:middle line:84% I think the coefficient on the average consumption 00:08:06.710 --> 00:08:11.395 align:middle line:84% should be when not the aggregate consumption. 00:08:11.395 --> 00:08:13.020 align:middle line:84% ROBERT TOWNSEND: Oh, well there's, say, 00:08:13.020 --> 00:08:14.350 align:middle line:90% a fixed number of households. 00:08:14.350 --> 00:08:17.640 align:middle line:84% So taking the aggregate and dividing 00:08:17.640 --> 00:08:22.620 align:middle line:84% by the number of households gives you the average. 00:08:22.620 --> 00:08:26.848 align:middle line:84% It's just a renormalization of the units, that's all. 00:08:26.848 --> 00:08:27.390 align:middle line:90% AUDIENCE: Oh. 00:08:27.390 --> 00:08:29.432 align:middle line:84% ROBERT TOWNSEND: But you're right that it's meant 00:08:29.432 --> 00:08:30.960 align:middle line:90% to represent the aggregate. 00:08:30.960 --> 00:08:34.270 align:middle line:90% 00:08:34.270 --> 00:08:35.740 align:middle line:90% So you can think of it that way. 00:08:35.740 --> 00:08:36.309 align:middle line:90% AUDIENCE: OK. 00:08:36.309 --> 00:08:38.900 align:middle line:84% ROBERT TOWNSEND: Because the economics makes more sense. 00:08:38.900 --> 00:08:42.890 align:middle line:84% The aggregate is going up, coming up 00:08:42.890 --> 00:08:45.910 align:middle line:90% over all the individuals. 00:08:45.910 --> 00:08:50.710 align:middle line:84% And if there's constant absolute risk aversion and the same risk 00:08:50.710 --> 00:08:53.620 align:middle line:84% aversion for all the households, then whenever 00:08:53.620 --> 00:08:56.200 align:middle line:84% the aggregate goes up, every individual household 00:08:56.200 --> 00:08:58.660 align:middle line:90% consumption goes up 1 to 1. 00:08:58.660 --> 00:08:59.433 align:middle line:90% AUDIENCE: Yeah. 00:08:59.433 --> 00:09:01.100 align:middle line:84% ROBERT TOWNSEND: Which is what you said. 00:09:01.100 --> 00:09:01.930 align:middle line:90% OK. 00:09:01.930 --> 00:09:03.380 align:middle line:90% AUDIENCE: Thank you. 00:09:03.380 --> 00:09:04.297 align:middle line:90% ROBERT TOWNSEND: Yeah. 00:09:04.297 --> 00:09:10.270 align:middle line:84% And the emphasis here is the household-specific income. 00:09:10.270 --> 00:09:12.100 align:middle line:90% It has a coefficient of 0. 00:09:12.100 --> 00:09:16.390 align:middle line:84% That's the salient restriction that the theory 00:09:16.390 --> 00:09:19.325 align:middle line:90% places on the data as well. 00:09:19.325 --> 00:09:21.890 align:middle line:90% 00:09:21.890 --> 00:09:27.140 align:middle line:84% And then finally, we looked at the division of land 00:09:27.140 --> 00:09:30.560 align:middle line:90% in these medieval village. 00:09:30.560 --> 00:09:34.710 align:middle line:84% And the question is, would scattering 00:09:34.710 --> 00:09:38.460 align:middle line:84% of an individual household's plots 00:09:38.460 --> 00:09:42.510 align:middle line:84% across the different fields be enough to achieve 00:09:42.510 --> 00:09:46.600 align:middle line:84% an optimal allocation of risk sharing? 00:09:46.600 --> 00:09:49.705 align:middle line:84% Paolo, do you want to take a crack at that? 00:09:49.705 --> 00:09:50.330 align:middle line:90% AUDIENCE: Sure. 00:09:50.330 --> 00:09:54.020 align:middle line:84% I think the answer is no, just because it's not necessarily 00:09:54.020 --> 00:09:59.900 align:middle line:84% that each field is a random draw. 00:09:59.900 --> 00:10:02.240 align:middle line:84% You can have correlations like, it's just a drought here 00:10:02.240 --> 00:10:03.530 align:middle line:90% and there's no rain anywhere. 00:10:03.530 --> 00:10:06.800 align:middle line:84% That's a risk, which would be a shock to all of your crops, 00:10:06.800 --> 00:10:10.370 align:middle line:90% essentially. 00:10:10.370 --> 00:10:11.870 align:middle line:90% ROBERT TOWNSEND: Yeah. 00:10:11.870 --> 00:10:15.950 align:middle line:84% So it's correct that it's not necessarily enough, 00:10:15.950 --> 00:10:19.830 align:middle line:84% unless you have very special characteristics 00:10:19.830 --> 00:10:21.600 align:middle line:90% of those plots-- 00:10:21.600 --> 00:10:24.900 align:middle line:90% 00:10:24.900 --> 00:10:28.140 align:middle line:84% how they move with various states of the world. 00:10:28.140 --> 00:10:29.820 align:middle line:84% In the lecture, we gave an example-- 00:10:29.820 --> 00:10:32.870 align:middle line:90% 00:10:32.870 --> 00:10:37.100 align:middle line:84% two examples, really-- one where there 00:10:37.100 --> 00:10:43.670 align:middle line:84% are two types of land and both are increasing 00:10:43.670 --> 00:10:44.885 align:middle line:90% as the states increase. 00:10:44.885 --> 00:10:48.320 align:middle line:90% 00:10:48.320 --> 00:10:55.100 align:middle line:84% And then, it would be enough to have each household have 00:10:55.100 --> 00:10:59.480 align:middle line:84% a share, a constant share over the two types of land. 00:10:59.480 --> 00:11:03.420 align:middle line:84% That would result in a linear risk sharing schedule. 00:11:03.420 --> 00:11:06.570 align:middle line:84% So for certain utility functions, 00:11:06.570 --> 00:11:10.580 align:middle line:84% including an examination of the slope and the intercepts, 00:11:10.580 --> 00:11:13.740 align:middle line:90% that would be enough. 00:11:13.740 --> 00:11:16.710 align:middle line:84% So in special cases, it might work. 00:11:16.710 --> 00:11:20.150 align:middle line:84% But in general, you have two different types of land. 00:11:20.150 --> 00:11:21.650 align:middle line:90% And the output goes up in one. 00:11:21.650 --> 00:11:23.450 align:middle line:84% It may go down in the other, depending 00:11:23.450 --> 00:11:28.220 align:middle line:84% on the state of the world, in which case, handing out 00:11:28.220 --> 00:11:35.370 align:middle line:84% shares of each type is not going to work, necessarily. 00:11:35.370 --> 00:11:39.000 align:middle line:84% And we explore that further in the lecture. 00:11:39.000 --> 00:11:42.270 align:middle line:84% So that whole lecture culminated at the end 00:11:42.270 --> 00:11:47.070 align:middle line:84% with an example where we had more states of the world 00:11:47.070 --> 00:11:51.480 align:middle line:84% than we had land types and restricted them 00:11:51.480 --> 00:11:57.560 align:middle line:84% to having shares of each type as if they could not transfer 00:11:57.560 --> 00:11:58.430 align:middle line:90% stuff around. 00:11:58.430 --> 00:12:03.740 align:middle line:84% And it was clear that it was constrained optimal. 00:12:03.740 --> 00:12:07.220 align:middle line:84% Taking that allocation of land with the harvest as given, 00:12:07.220 --> 00:12:09.920 align:middle line:84% we could do better by, add to welfare 00:12:09.920 --> 00:12:15.590 align:middle line:84% by having exposed redistribution of the grain via transfers. 00:12:15.590 --> 00:12:16.100 align:middle line:90% OK. 00:12:16.100 --> 00:12:19.030 align:middle line:84% So that's probably enough of a review. 00:12:19.030 --> 00:12:21.530 align:middle line:84% As always, there are many more questions in the study guide. 00:12:21.530 --> 00:12:23.300 align:middle line:84% And probably, spend quite a lot of time 00:12:23.300 --> 00:12:26.270 align:middle line:84% just deciding which ones to ask in class. 00:12:26.270 --> 00:12:28.980 align:middle line:90% You should look at all of them. 00:12:28.980 --> 00:12:34.910 align:middle line:84% And let's get to lecture 9, is what we're doing today. 00:12:34.910 --> 00:12:37.550 align:middle line:84% And this is risk sharing with production. 00:12:37.550 --> 00:12:39.740 align:middle line:90% Three main topics, really. 00:12:39.740 --> 00:12:42.560 align:middle line:84% Risk and return in production-- and that part 00:12:42.560 --> 00:12:45.110 align:middle line:84% is continuation of some of the themes, 00:12:45.110 --> 00:12:48.290 align:middle line:84% although we didn't really put all the pieces together. 00:12:48.290 --> 00:12:50.900 align:middle line:84% We had production in the dynamics lecture. 00:12:50.900 --> 00:12:55.100 align:middle line:84% We had risk as in yields coming from land plots. 00:12:55.100 --> 00:12:58.310 align:middle line:84% But we never talked about inputs into land plots, 00:12:58.310 --> 00:13:00.570 align:middle line:84% and associated outputs, and so on. 00:13:00.570 --> 00:13:03.140 align:middle line:84% So we'll put those two pieces together. 00:13:03.140 --> 00:13:05.360 align:middle line:84% Another feature of this lecture is 00:13:05.360 --> 00:13:08.540 align:middle line:84% that we're going to use data on production but also 00:13:08.540 --> 00:13:09.930 align:middle line:90% on consumption. 00:13:09.930 --> 00:13:12.060 align:middle line:90% So both things will be there. 00:13:12.060 --> 00:13:15.680 align:middle line:84% And this is illustrative of how powerful this risk sharing 00:13:15.680 --> 00:13:16.880 align:middle line:90% framework is. 00:13:16.880 --> 00:13:20.030 align:middle line:84% It extends to more and more complicated situations. 00:13:20.030 --> 00:13:22.080 align:middle line:84% We're able to do more and more with it. 00:13:22.080 --> 00:13:24.230 align:middle line:84% And finally, I have some words at the end 00:13:24.230 --> 00:13:27.560 align:middle line:84% about social networks and sharing risk, 00:13:27.560 --> 00:13:31.460 align:middle line:84% and in particular, an example that will remind you 00:13:31.460 --> 00:13:34.220 align:middle line:84% for better or worse of COVID, and what's 00:13:34.220 --> 00:13:38.610 align:middle line:84% going on when people get sick with the economics. 00:13:38.610 --> 00:13:39.110 align:middle line:90% OK. 00:13:39.110 --> 00:13:42.290 align:middle line:84% So this first starred paper on the reading list 00:13:42.290 --> 00:13:44.750 align:middle line:90% with Krislert Samphantharak. 00:13:44.750 --> 00:13:46.880 align:middle line:84% It'll tie, if you haven't guessed, 00:13:46.880 --> 00:13:49.380 align:middle line:84% extensions of the theory project selection. 00:13:49.380 --> 00:13:54.050 align:middle line:84% So we studied a model with risk and return in productive assets 00:13:54.050 --> 00:13:57.390 align:middle line:84% in developing economies-- namely, Thailand. 00:13:57.390 --> 00:14:00.650 align:middle line:84% We're going to measure idiosyncratic and aggregate 00:14:00.650 --> 00:14:01.430 align:middle line:90% risk premia. 00:14:01.430 --> 00:14:03.650 align:middle line:84% Those words probably don't make a whole lot of sense, 00:14:03.650 --> 00:14:07.820 align:middle line:84% although we've been talking about related things just now 00:14:07.820 --> 00:14:10.910 align:middle line:84% with the risk sharing regression, idiosyncratic 00:14:10.910 --> 00:14:13.850 align:middle line:84% being household-specific income, and aggregate 00:14:13.850 --> 00:14:16.040 align:middle line:90% being aggregate consumption. 00:14:16.040 --> 00:14:19.940 align:middle line:84% And we're going to be able to quantify those two 00:14:19.940 --> 00:14:24.230 align:middle line:84% different premia and analyze what households are doing, 00:14:24.230 --> 00:14:26.730 align:middle line:90% how exposed they are to risk. 00:14:26.730 --> 00:14:28.940 align:middle line:84% And finally, in principle, one could 00:14:28.940 --> 00:14:31.910 align:middle line:84% take not just the straight-out returns, 00:14:31.910 --> 00:14:34.640 align:middle line:84% but risk-adjusted returns and look 00:14:34.640 --> 00:14:38.120 align:middle line:84% for patterns across households, like whether poor households 00:14:38.120 --> 00:14:41.090 align:middle line:84% are more vulnerable or less vulnerable, 00:14:41.090 --> 00:14:43.590 align:middle line:84% does education matter, and so on. 00:14:43.590 --> 00:14:45.110 align:middle line:90% So here's the model. 00:14:45.110 --> 00:14:49.730 align:middle line:84% There are capital J households indexed by j, 00:14:49.730 --> 00:14:51.620 align:middle line:90% little j for an individual. 00:14:51.620 --> 00:14:53.210 align:middle line:84% J is the number for the aggregate. 00:14:53.210 --> 00:14:56.930 align:middle line:84% There are I production activities, little i, big I. 00:14:56.930 --> 00:14:59.210 align:middle line:84% And you can think of those production activities 00:14:59.210 --> 00:15:03.350 align:middle line:84% as production sets or production technologies. 00:15:03.350 --> 00:15:05.630 align:middle line:90% The inputs are capital. 00:15:05.630 --> 00:15:08.210 align:middle line:84% And I'll say some words a bit later 00:15:08.210 --> 00:15:13.070 align:middle line:84% about where labor and materials and seed and other things went. 00:15:13.070 --> 00:15:15.200 align:middle line:84% But for now, just think of there being 00:15:15.200 --> 00:15:17.840 align:middle line:90% a single input called capital. 00:15:17.840 --> 00:15:22.130 align:middle line:84% And the outputs are in the same units of a single consumption 00:15:22.130 --> 00:15:23.060 align:middle line:90% good. 00:15:23.060 --> 00:15:26.660 align:middle line:84% So we're going to be looking at a household running 00:15:26.660 --> 00:15:29.130 align:middle line:90% a portfolio of assets. 00:15:29.130 --> 00:15:33.410 align:middle line:84% Now, actually, the way you think about this in finance 00:15:33.410 --> 00:15:36.680 align:middle line:84% is, you want to engage in a certain activity. 00:15:36.680 --> 00:15:41.120 align:middle line:84% You acquire the assets necessary to do that activity. 00:15:41.120 --> 00:15:45.150 align:middle line:84% And a household could be doing one or multiple activities. 00:15:45.150 --> 00:15:47.250 align:middle line:90% This will generate a return. 00:15:47.250 --> 00:15:50.000 align:middle line:84% So we want to know how well the project is doing 00:15:50.000 --> 00:15:52.160 align:middle line:84% and whether it was selected properly. 00:15:52.160 --> 00:15:54.710 align:middle line:84% So you want to compare the rate of return 00:15:54.710 --> 00:15:59.130 align:middle line:84% to the best alternative use of funds 00:15:59.130 --> 00:16:01.200 align:middle line:84% except that here, we're going to put risk in. 00:16:01.200 --> 00:16:04.230 align:middle line:84% So it makes it much more interesting. 00:16:04.230 --> 00:16:08.100 align:middle line:84% In particular, these set returns are stochastic. 00:16:08.100 --> 00:16:11.340 align:middle line:84% And they can be correlated over activities 00:16:11.340 --> 00:16:14.340 align:middle line:90% and correlated over households. 00:16:14.340 --> 00:16:17.310 align:middle line:84% So again, you can think about the previous lecture 00:16:17.310 --> 00:16:19.020 align:middle line:84% with village India, although this 00:16:19.020 --> 00:16:22.200 align:middle line:84% happens to be village Thailand and its different kinds 00:16:22.200 --> 00:16:24.660 align:middle line:84% of crops and different soils, different income 00:16:24.660 --> 00:16:26.650 align:middle line:90% sources, and so on. 00:16:26.650 --> 00:16:30.115 align:middle line:84% So I mentioned early on in lecture 1 00:16:30.115 --> 00:16:31.740 align:middle line:84% that we were going to go back and forth 00:16:31.740 --> 00:16:38.340 align:middle line:84% between actual real agrarian economies and associated 00:16:38.340 --> 00:16:39.600 align:middle line:90% metaphors. 00:16:39.600 --> 00:16:44.400 align:middle line:84% So we can talk about trees bearing fruit literally 00:16:44.400 --> 00:16:45.180 align:middle line:90% in the data. 00:16:45.180 --> 00:16:47.280 align:middle line:84% But we can also talk about a tree 00:16:47.280 --> 00:16:50.070 align:middle line:84% as an asset in financial markets, households' 00:16:50.070 --> 00:16:51.510 align:middle line:90% whole assets. 00:16:51.510 --> 00:16:52.830 align:middle line:90% And they pay dividends. 00:16:52.830 --> 00:16:55.360 align:middle line:84% And there may be correlations in stock returns. 00:16:55.360 --> 00:16:58.770 align:middle line:84% So exactly the same theory is being applied 00:16:58.770 --> 00:17:00.910 align:middle line:90% to two very different settings. 00:17:00.910 --> 00:17:04.349 align:middle line:84% And in fact, we're reverse engineering in this paper. 00:17:04.349 --> 00:17:08.640 align:middle line:84% We're taking measures of risk reduction and risk premia that 00:17:08.640 --> 00:17:12.569 align:middle line:84% have been applied to stocks in the New York Stock Exchange 00:17:12.569 --> 00:17:15.599 align:middle line:84% and applying it to all these activities 00:17:15.599 --> 00:17:20.369 align:middle line:84% across various households in a typical Thai village. 00:17:20.369 --> 00:17:20.910 align:middle line:90% OK. 00:17:20.910 --> 00:17:22.710 align:middle line:84% So a little bit more in notation. 00:17:22.710 --> 00:17:25.950 align:middle line:84% We have F production function for activity 00:17:25.950 --> 00:17:30.420 align:middle line:84% I run by household J. And it has as a single input 00:17:30.420 --> 00:17:32.560 align:middle line:84% the level at which it's capitalized, 00:17:32.560 --> 00:17:36.180 align:middle line:84% the capital input in activity I run by household J. 00:17:36.180 --> 00:17:40.020 align:middle line:84% So we can sum overall activities and sum overall households 00:17:40.020 --> 00:17:42.790 align:middle line:84% and get an aggregate production function. 00:17:42.790 --> 00:17:46.230 align:middle line:84% So again, early on in one of those lectures on production, 00:17:46.230 --> 00:17:49.800 align:middle line:84% we talked about aggregating two example production 00:17:49.800 --> 00:17:51.540 align:middle line:90% sets into one. 00:17:51.540 --> 00:17:54.370 align:middle line:90% So this is a version of that. 00:17:54.370 --> 00:17:57.870 align:middle line:84% So the economy starts out with an aggregate amount 00:17:57.870 --> 00:18:01.720 align:middle line:84% of wealth, which is coming from two sources. 00:18:01.720 --> 00:18:05.670 align:middle line:84% One, the trees, and two, the fruit. 00:18:05.670 --> 00:18:10.200 align:middle line:84% Now, let me just say that as is standard in a lot-- not all, 00:18:10.200 --> 00:18:12.340 align:middle line:84% but a lot-- of economic models, we're 00:18:12.340 --> 00:18:15.480 align:middle line:84% going to have what we call a putty putty, meaning that you 00:18:15.480 --> 00:18:19.740 align:middle line:84% take the putty in terms of very malleable consumption, what 00:18:19.740 --> 00:18:23.280 align:middle line:84% could be consumption, and invest it into capital. 00:18:23.280 --> 00:18:25.140 align:middle line:90% And then, that yields a return. 00:18:25.140 --> 00:18:28.530 align:middle line:84% You can certainly eat the fruit, but you can also eat the tree. 00:18:28.530 --> 00:18:33.030 align:middle line:84% So the putty putty part comes from undoing the tree. 00:18:33.030 --> 00:18:35.400 align:middle line:84% Of course, in many actual situations, 00:18:35.400 --> 00:18:37.260 align:middle line:90% you can't eat the machine. 00:18:37.260 --> 00:18:39.600 align:middle line:84% But it's as if you could sell the machine 00:18:39.600 --> 00:18:41.640 align:middle line:84% and get the consumption equivalent. 00:18:41.640 --> 00:18:44.040 align:middle line:84% If you wanted to eat all of it, you could. 00:18:44.040 --> 00:18:47.070 align:middle line:84% And you'll see that right now in the notation. 00:18:47.070 --> 00:18:50.520 align:middle line:84% We're going to have, quote unquote, "a social planner." 00:18:50.520 --> 00:18:52.830 align:middle line:84% But of course, you know now, that just 00:18:52.830 --> 00:18:55.110 align:middle line:84% means that we're going to have these programming 00:18:55.110 --> 00:18:58.570 align:middle line:84% problems for the determination of Pareto optimal allocation. 00:18:58.570 --> 00:19:01.020 align:middle line:84% And we're going to act as if the planner is doing it. 00:19:01.020 --> 00:19:03.600 align:middle line:84% But it's really a math problem that we 00:19:03.600 --> 00:19:06.660 align:middle line:84% can solve to go back and forth between solutions to the math 00:19:06.660 --> 00:19:11.430 align:middle line:84% problem and various Pareto optimal allocations. 00:19:11.430 --> 00:19:15.810 align:middle line:84% So consumption of household J at a given moment-- 00:19:15.810 --> 00:19:20.700 align:middle line:84% say a year-- the sources of potential consumption 00:19:20.700 --> 00:19:25.410 align:middle line:84% would be the fruit, how much activity I is yielding 00:19:25.410 --> 00:19:29.040 align:middle line:84% a fruit run by household J as a function of previously 00:19:29.040 --> 00:19:32.640 align:middle line:90% determined capitalization KIJ. 00:19:32.640 --> 00:19:36.490 align:middle line:84% We sum overall I. And we have the tree itself, 00:19:36.490 --> 00:19:39.330 align:middle line:84% which as I've said now could be potentially eaten. 00:19:39.330 --> 00:19:42.460 align:middle line:84% But from these available resources, 00:19:42.460 --> 00:19:46.710 align:middle line:84% we can subtract off the capitalization for next period. 00:19:46.710 --> 00:19:49.620 align:middle line:84% Prime means tomorrow or next year. 00:19:49.620 --> 00:19:54.750 align:middle line:84% And KIJ is the level of capital carried out from this year 00:19:54.750 --> 00:19:56.260 align:middle line:90% into next year. 00:19:56.260 --> 00:20:00.720 align:middle line:84% So this is like storage in that dynamic medieval village 00:20:00.720 --> 00:20:03.000 align:middle line:90% economy. 00:20:03.000 --> 00:20:04.320 align:middle line:90% That's one activity. 00:20:04.320 --> 00:20:08.760 align:middle line:84% Seed planted in the ground is another type of activity. 00:20:08.760 --> 00:20:11.310 align:middle line:90% This is a generalization. 00:20:11.310 --> 00:20:14.670 align:middle line:84% And finally, we have these transfers, tau. 00:20:14.670 --> 00:20:17.610 align:middle line:84% These are going to be, among other things, key control 00:20:17.610 --> 00:20:19.890 align:middle line:84% variables of the so-called planner, 00:20:19.890 --> 00:20:23.010 align:middle line:84% adding potentially to the resources of the household, 00:20:23.010 --> 00:20:26.790 align:middle line:90% or if negative, taking away. 00:20:26.790 --> 00:20:29.490 align:middle line:84% So then, we come to this programming problem 00:20:29.490 --> 00:20:34.800 align:middle line:84% for the determination of Pareto optimal allocations. 00:20:34.800 --> 00:20:37.890 align:middle line:84% And despite some heavy looking notation, 00:20:37.890 --> 00:20:40.590 align:middle line:84% you'll probably understand this pretty readily. 00:20:40.590 --> 00:20:44.550 align:middle line:84% First of all, here's the utility function of household J. 00:20:44.550 --> 00:20:49.140 align:middle line:84% And all the slide does is stick into what would be consumption. 00:20:49.140 --> 00:20:51.540 align:middle line:84% The consumption is defined at the bottom 00:20:51.540 --> 00:20:53.100 align:middle line:90% of the previous slide-- 00:20:53.100 --> 00:20:56.400 align:middle line:84% resources available minus resources 00:20:56.400 --> 00:21:00.930 align:middle line:84% utilized for next period year plus the transfer. 00:21:00.930 --> 00:21:02.910 align:middle line:84% These lambdas are the Pareto weights 00:21:02.910 --> 00:21:07.920 align:middle line:84% for maximizing a lambda-weighted sum of utilities today. 00:21:07.920 --> 00:21:10.530 align:middle line:84% And the control variables for the planner 00:21:10.530 --> 00:21:13.170 align:middle line:84% are these transfers, as I've already said, 00:21:13.170 --> 00:21:17.020 align:middle line:84% plus the level of capitalization of all the projects. 00:21:17.020 --> 00:21:21.570 align:middle line:84% So we're trying to find an optimal allocation of capital 00:21:21.570 --> 00:21:26.040 align:middle line:84% as well as an optimal allocation of the transfers. 00:21:26.040 --> 00:21:30.810 align:middle line:84% Small apology-- this apostrophe-looking object 00:21:30.810 --> 00:21:33.430 align:middle line:84% shouldn't be there on top of the taus. 00:21:33.430 --> 00:21:37.480 align:middle line:84% It's not a prime, because the transfers are decided today, 00:21:37.480 --> 00:21:39.060 align:middle line:90% not next period. 00:21:39.060 --> 00:21:42.150 align:middle line:84% But there's definitely a prime on this capital, 00:21:42.150 --> 00:21:45.540 align:middle line:84% because the current state has already given the projects 00:21:45.540 --> 00:21:47.400 align:middle line:90% with their capitalizations. 00:21:47.400 --> 00:21:51.060 align:middle line:84% The thing to be decided upon is how much capital 00:21:51.060 --> 00:21:53.970 align:middle line:84% you want to invest in all the various possible projects 00:21:53.970 --> 00:21:55.830 align:middle line:90% for tomorrow. 00:21:55.830 --> 00:21:58.860 align:middle line:84% AUDIENCE: Is it is it better to add a depreciation here? 00:21:58.860 --> 00:22:05.230 align:middle line:84% Because if instead of a tree, if you think of a machine? 00:22:05.230 --> 00:22:07.300 align:middle line:90% It will definitely depreciate. 00:22:07.300 --> 00:22:11.560 align:middle line:84% ROBERT TOWNSEND: Yeah, it's loaded into this output. 00:22:11.560 --> 00:22:13.300 align:middle line:90% And you'll see this in the data. 00:22:13.300 --> 00:22:16.570 align:middle line:84% You take net profits but you subtract off 00:22:16.570 --> 00:22:19.180 align:middle line:90% as an expense the depreciation. 00:22:19.180 --> 00:22:21.700 align:middle line:84% But it's true it's not there explicitly, 00:22:21.700 --> 00:22:23.590 align:middle line:90% but that's where it is. 00:22:23.590 --> 00:22:27.280 align:middle line:84% So yeah, it should be and it is included, OK? 00:22:27.280 --> 00:22:28.240 align:middle line:90% AUDIENCE: OK. 00:22:28.240 --> 00:22:30.657 align:middle line:84% ROBERT TOWNSEND: Now the other thing that makes this thing 00:22:30.657 --> 00:22:33.340 align:middle line:84% complicated-- but again, you're already tooled up to get this 00:22:33.340 --> 00:22:34.360 align:middle line:90% right away-- 00:22:34.360 --> 00:22:37.930 align:middle line:90% these are these value functions. 00:22:37.930 --> 00:22:41.140 align:middle line:84% So what is the state of the world today? 00:22:41.140 --> 00:22:44.950 align:middle line:84% It's total wealth that's available at the bottom 00:22:44.950 --> 00:22:47.950 align:middle line:84% of the slide summing over all activities and households, 00:22:47.950 --> 00:22:49.630 align:middle line:90% all fruit and all trees. 00:22:49.630 --> 00:22:53.950 align:middle line:84% This capital lambda is just the individual Pareto weights. 00:22:53.950 --> 00:22:56.350 align:middle line:90% And they're fixed for all time. 00:22:56.350 --> 00:22:59.320 align:middle line:84% And then, you decide on these control variables 00:22:59.320 --> 00:23:01.480 align:middle line:84% how much to eat and how much to save 00:23:01.480 --> 00:23:03.190 align:middle line:90% in the various technologies. 00:23:03.190 --> 00:23:06.260 align:middle line:84% That's going to deliver a state for tomorrow, 00:23:06.260 --> 00:23:09.190 align:middle line:90% which is wealth tomorrow. 00:23:09.190 --> 00:23:11.410 align:middle line:90% It would be W prime. 00:23:11.410 --> 00:23:16.040 align:middle line:84% Just like W is this period, W prime would be for next period. 00:23:16.040 --> 00:23:19.210 align:middle line:84% And you would have a prime on all of these objects. 00:23:19.210 --> 00:23:22.450 align:middle line:84% You'd have the fruit in the trees next period at prime. 00:23:22.450 --> 00:23:23.920 align:middle line:90% That's the W prime. 00:23:23.920 --> 00:23:27.580 align:middle line:84% This value function is as if they lived 00:23:27.580 --> 00:23:30.040 align:middle line:90% in an infinite horizon economy. 00:23:30.040 --> 00:23:34.090 align:middle line:84% They're discounting next period by this fee. 00:23:34.090 --> 00:23:35.200 align:middle line:90% Usually, we use beta. 00:23:35.200 --> 00:23:38.260 align:middle line:84% But beta in this lecture is reserved for something else, 00:23:38.260 --> 00:23:39.920 align:middle line:90% like a regression coefficient. 00:23:39.920 --> 00:23:44.380 align:middle line:84% So fee is the common discount rate across all the households. 00:23:44.380 --> 00:23:46.750 align:middle line:84% And you remember how we got these Vs, right? 00:23:46.750 --> 00:23:49.120 align:middle line:84% We had a slide at the end of one of the-- 00:23:49.120 --> 00:23:51.340 align:middle line:90% at the dynamic lecture. 00:23:51.340 --> 00:23:53.390 align:middle line:90% Act like it's a finite period. 00:23:53.390 --> 00:23:57.100 align:middle line:84% So for the optimum, which would be, don't fund everything, 00:23:57.100 --> 00:23:58.480 align:middle line:90% eat everything in sight. 00:23:58.480 --> 00:24:00.910 align:middle line:84% And then, go to the next to last period and third 00:24:00.910 --> 00:24:02.210 align:middle line:90% to last period. 00:24:02.210 --> 00:24:04.630 align:middle line:84% And then, keep iterating as far back 00:24:04.630 --> 00:24:06.680 align:middle line:90% into the present as possible. 00:24:06.680 --> 00:24:10.840 align:middle line:84% And this value function, which would have a T on it 00:24:10.840 --> 00:24:15.070 align:middle line:84% for the length of horizon, will go to something stable, 00:24:15.070 --> 00:24:18.140 align:middle line:84% as if we had solved the infinite horizon problem. 00:24:18.140 --> 00:24:20.410 align:middle line:84% So that's all loaded up in here, too. 00:24:20.410 --> 00:24:23.660 align:middle line:90% Questions about this slide? 00:24:23.660 --> 00:24:25.790 align:middle line:90% Oh, one last thing. 00:24:25.790 --> 00:24:29.480 align:middle line:84% You can't put negative capital into the ground. 00:24:29.480 --> 00:24:31.910 align:middle line:84% Capital could be 0, in which case 00:24:31.910 --> 00:24:33.740 align:middle line:90% you're not doing that activity. 00:24:33.740 --> 00:24:37.520 align:middle line:84% Or it's positive, in which case you are doing the activity. 00:24:37.520 --> 00:24:42.020 align:middle line:84% This is true over all projects I in all households J. 00:24:42.020 --> 00:24:45.470 align:middle line:84% You can set that thing up as a Lagrangian with the shadow 00:24:45.470 --> 00:24:46.980 align:middle line:90% prices and solve. 00:24:46.980 --> 00:24:50.690 align:middle line:84% And you'll get a familiar condition. 00:24:50.690 --> 00:24:52.520 align:middle line:84% If you differentiate with respect 00:24:52.520 --> 00:24:56.840 align:middle line:84% to consumptions or the transfers, for that matter, 00:24:56.840 --> 00:25:00.410 align:middle line:84% you will get that these lambda weighted margin utilities 00:25:00.410 --> 00:25:03.140 align:middle line:84% should be the same over all households 00:25:03.140 --> 00:25:06.020 align:middle line:84% and equal to a common Lagrange multiplier 00:25:06.020 --> 00:25:09.410 align:middle line:84% on the current resource constraint mu. 00:25:09.410 --> 00:25:11.570 align:middle line:84% So you've actually seen this before. 00:25:11.570 --> 00:25:15.350 align:middle line:84% It's exactly equal to what we had before in village 00:25:15.350 --> 00:25:18.770 align:middle line:84% India without consideration of production. 00:25:18.770 --> 00:25:20.420 align:middle line:84% But we're going to get something else. 00:25:20.420 --> 00:25:23.180 align:middle line:84% Namely, when we look at the control variable 00:25:23.180 --> 00:25:26.090 align:middle line:84% the capital control variables, we're 00:25:26.090 --> 00:25:29.900 align:middle line:84% going to get something that links marginal utility today 00:25:29.900 --> 00:25:33.320 align:middle line:84% to effectively to marginal utility next period. 00:25:33.320 --> 00:25:35.600 align:middle line:84% And that is that the lambda weighted 00:25:35.600 --> 00:25:39.320 align:middle line:84% marginal utility of consumption today for household J-- 00:25:39.320 --> 00:25:41.390 align:middle line:90% if this were set equal-- 00:25:41.390 --> 00:25:44.330 align:middle line:84% should be equal to the future margin utility. 00:25:44.330 --> 00:25:47.420 align:middle line:84% Well, if you take a unit of resource today 00:25:47.420 --> 00:25:50.330 align:middle line:84% infinitesimally small, and instead of eating it 00:25:50.330 --> 00:25:52.610 align:middle line:84% you invest it, what you'll get tomorrow 00:25:52.610 --> 00:25:54.590 align:middle line:84% would be the derivative off the production 00:25:54.590 --> 00:25:56.120 align:middle line:90% function of that investment. 00:25:56.120 --> 00:25:59.690 align:middle line:84% Plus you get the tree back, that one unit back. 00:25:59.690 --> 00:26:03.560 align:middle line:84% And that return stream is going to be evaluated 00:26:03.560 --> 00:26:05.730 align:middle line:84% at the marginal utility of wealth, 00:26:05.730 --> 00:26:09.530 align:middle line:84% which is the derivative of this value function at tomorrow's 00:26:09.530 --> 00:26:10.200 align:middle line:90% wealth. 00:26:10.200 --> 00:26:12.170 align:middle line:84% So again, we're just taking a derivative 00:26:12.170 --> 00:26:14.930 align:middle line:90% of this right-hand side term. 00:26:14.930 --> 00:26:16.040 align:middle line:90% Questions? 00:26:16.040 --> 00:26:18.470 align:middle line:84% So it's written as a weak inequality. 00:26:18.470 --> 00:26:19.850 align:middle line:90% It could be less than 0. 00:26:19.850 --> 00:26:22.610 align:middle line:84% If it's less than 0, let's take the margin utility 00:26:22.610 --> 00:26:25.190 align:middle line:84% of consumption today, which is minus, 00:26:25.190 --> 00:26:28.520 align:middle line:84% and on the left-hand side, put it on the right-hand side. 00:26:28.520 --> 00:26:30.590 align:middle line:84% And that would say, the weighted margin utility 00:26:30.590 --> 00:26:35.850 align:middle line:84% of consumption today is strictly greater than the margin utility 00:26:35.850 --> 00:26:37.375 align:middle line:90% you would get tomorrow. 00:26:37.375 --> 00:26:38.750 align:middle line:84% So they're going to hit a corner. 00:26:38.750 --> 00:26:42.320 align:middle line:84% They would like, actually, the capital level to go negative, 00:26:42.320 --> 00:26:44.480 align:middle line:84% because they're desperate to eat today. 00:26:44.480 --> 00:26:47.090 align:middle line:84% The marginal utility return today is higher 00:26:47.090 --> 00:26:49.310 align:middle line:90% than it will be next period. 00:26:49.310 --> 00:26:50.840 align:middle line:84% But of course, we're not allowing 00:26:50.840 --> 00:26:55.580 align:middle line:84% them to go negative, hence the inequality. 00:26:55.580 --> 00:26:58.310 align:middle line:84% To remind you in other contexts, we write out 00:26:58.310 --> 00:26:59.780 align:middle line:90% the full Lagrangian program. 00:26:59.780 --> 00:27:01.790 align:middle line:84% We put an extra Lagrange multiplier 00:27:01.790 --> 00:27:03.830 align:middle line:84% on these non-negativity constraints. 00:27:03.830 --> 00:27:06.350 align:middle line:84% Then this whole thing would be at an equality. 00:27:06.350 --> 00:27:09.380 align:middle line:84% But it would have as well the potentially positive 00:27:09.380 --> 00:27:11.400 align:middle line:90% Lagrange multiplier. 00:27:11.400 --> 00:27:15.450 align:middle line:84% Anyway, the conclusion is, not all activities need be funded. 00:27:15.450 --> 00:27:18.600 align:middle line:84% You might actually want to unfund them and draw resources 00:27:18.600 --> 00:27:20.190 align:middle line:90% out of them that aren't there. 00:27:20.190 --> 00:27:21.460 align:middle line:90% You can't do that. 00:27:21.460 --> 00:27:23.520 align:middle line:90% So you set them equal to 0. 00:27:23.520 --> 00:27:26.220 align:middle line:84% Others get funded at a positive level. 00:27:26.220 --> 00:27:29.130 align:middle line:84% We will be focusing a lot on these set 00:27:29.130 --> 00:27:33.240 align:middle line:84% of activities over households for which this is equal to 0. 00:27:33.240 --> 00:27:35.570 align:middle line:90% And those are funded projects. 00:27:35.570 --> 00:27:39.400 align:middle line:84% OK, so it looks like this is entirely closed economy. 00:27:39.400 --> 00:27:41.490 align:middle line:84% But as I said, these techniques generalize. 00:27:41.490 --> 00:27:45.450 align:middle line:84% So we can think of a village as a small open economy. 00:27:45.450 --> 00:27:47.970 align:middle line:84% And maybe they can go to an outside bank 00:27:47.970 --> 00:27:50.220 align:middle line:84% and borrow money, in which case we'd 00:27:50.220 --> 00:27:53.490 align:middle line:84% have to change the wealth variable to subtract off 00:27:53.490 --> 00:27:55.890 align:middle line:84% the principal and interest that's coming due today, 00:27:55.890 --> 00:27:59.610 align:middle line:84% but add in the debt that they enter into today. 00:27:59.610 --> 00:28:01.440 align:middle line:84% That will come due the next period. 00:28:01.440 --> 00:28:02.580 align:middle line:90% Nothing changes. 00:28:02.580 --> 00:28:04.920 align:middle line:84% These first order conditions don't change. 00:28:04.920 --> 00:28:07.680 align:middle line:84% Oh, it's good for them in terms of smoothing. 00:28:07.680 --> 00:28:10.650 align:middle line:84% If the village wealth is low, the village as a whole 00:28:10.650 --> 00:28:11.850 align:middle line:90% might want to borrow. 00:28:11.850 --> 00:28:13.110 align:middle line:90% That's fine. 00:28:13.110 --> 00:28:15.690 align:middle line:84% So the quantitative solution can change, 00:28:15.690 --> 00:28:18.630 align:middle line:84% but our characterization in terms of these first order 00:28:18.630 --> 00:28:20.800 align:middle line:90% conditions will not change. 00:28:20.800 --> 00:28:24.430 align:middle line:84% So we do not need to assume a closed economy. 00:28:24.430 --> 00:28:24.930 align:middle line:90% All right. 00:28:24.930 --> 00:28:27.910 align:middle line:90% So what the heck is this? 00:28:27.910 --> 00:28:32.270 align:middle line:84% Well, this mu is the lambda weighted marginal utility. 00:28:32.270 --> 00:28:35.300 align:middle line:84% I substituted that into this left-hand side 00:28:35.300 --> 00:28:39.950 align:middle line:84% of the second expression, set it equal to 0. 00:28:39.950 --> 00:28:42.470 align:middle line:90% And then, you've got two terms. 00:28:42.470 --> 00:28:45.770 align:middle line:84% Dividing through by this, you would 00:28:45.770 --> 00:28:47.780 align:middle line:90% set everything equal to 1. 00:28:47.780 --> 00:28:50.990 align:middle line:84% So it's actually easier to look at the algebra 00:28:50.990 --> 00:28:54.150 align:middle line:90% than it is to say it in words. 00:28:54.150 --> 00:28:57.350 align:middle line:84% We take mu here and divide this term 00:28:57.350 --> 00:29:00.200 align:middle line:84% by mu, which makes it equal to unity, 00:29:00.200 --> 00:29:02.570 align:middle line:84% and the second term by mu, which is 00:29:02.570 --> 00:29:05.300 align:middle line:90% what is being displayed here. 00:29:05.300 --> 00:29:08.590 align:middle line:84% And then, the rest is algebra, although it's 00:29:08.590 --> 00:29:11.680 align:middle line:84% revealing that we can take this expectation 00:29:11.680 --> 00:29:15.100 align:middle line:84% operator outside the whole expression, 00:29:15.100 --> 00:29:17.110 align:middle line:90% that these returns are random. 00:29:17.110 --> 00:29:20.670 align:middle line:84% I'm not sure I've been emphasizing that enough. 00:29:20.670 --> 00:29:22.920 align:middle line:84% It looked like constants, because you just 00:29:22.920 --> 00:29:24.690 align:middle line:90% have the level of capital. 00:29:24.690 --> 00:29:28.710 align:middle line:84% But the return on a unit of capital is random. 00:29:28.710 --> 00:29:31.080 align:middle line:84% Where did that first start to happen? 00:29:31.080 --> 00:29:33.840 align:middle line:84% I should have said it right here when we had that expectation 00:29:33.840 --> 00:29:35.050 align:middle line:90% operator. 00:29:35.050 --> 00:29:38.430 align:middle line:84% So anyway, bring the expectation operator out 00:29:38.430 --> 00:29:40.050 align:middle line:90% in front of everything. 00:29:40.050 --> 00:29:45.390 align:middle line:84% And then, adopt some very cryptic notation, M-- 00:29:45.390 --> 00:29:50.580 align:middle line:84% actually, M prime-- for this term, which is essentially 00:29:50.580 --> 00:29:53.310 align:middle line:84% the discounted Lagrange multiplier next period 00:29:53.310 --> 00:29:56.550 align:middle line:84% divided by the Lagrange multiplier today. 00:29:56.550 --> 00:29:59.430 align:middle line:90% So that's a discount factor. 00:29:59.430 --> 00:30:03.840 align:middle line:84% Call it M prime, and this R, capital R, 00:30:03.840 --> 00:30:07.200 align:middle line:84% is the total return on the project being run, 00:30:07.200 --> 00:30:09.840 align:middle line:84% the activity R run by household J. 00:30:09.840 --> 00:30:13.270 align:middle line:84% The return-- you get the tree back, plus you get the fruit. 00:30:13.270 --> 00:30:15.450 align:middle line:90% And this is a prime here. 00:30:15.450 --> 00:30:18.593 align:middle line:84% It's the marginal return, obviously. 00:30:18.593 --> 00:30:20.760 align:middle line:84% Because when we looked at the first order condition, 00:30:20.760 --> 00:30:22.870 align:middle line:84% we were varying the level of capital. 00:30:22.870 --> 00:30:25.510 align:middle line:84% So we picked up a derivative in the production function. 00:30:25.510 --> 00:30:27.120 align:middle line:90% So this is just notation. 00:30:27.120 --> 00:30:30.150 align:middle line:84% But it's very convenient notation. 00:30:30.150 --> 00:30:32.270 align:middle line:84% So it's saying that for all activities 00:30:32.270 --> 00:30:38.240 align:middle line:84% R run by households J, this product, this expected product, 00:30:38.240 --> 00:30:40.420 align:middle line:90% is equal to 1. 00:30:40.420 --> 00:30:44.410 align:middle line:84% Furthermore, looking at that expected product, 00:30:44.410 --> 00:30:46.780 align:middle line:84% there's a result in statistics that we 00:30:46.780 --> 00:30:50.260 align:middle line:84% didn't put into the lecture on uncertainty. 00:30:50.260 --> 00:30:52.690 align:middle line:84% But it's easy enough to state, which 00:30:52.690 --> 00:30:55.510 align:middle line:84% is, expectation of two random variables 00:30:55.510 --> 00:30:58.840 align:middle line:84% is equal to the product of the expectations adjusted 00:30:58.840 --> 00:31:02.200 align:middle line:84% by the covariance of the two variables. 00:31:02.200 --> 00:31:07.150 align:middle line:84% If the covariance is 0, then these individual variables 00:31:07.150 --> 00:31:08.000 align:middle line:90% are independent. 00:31:08.000 --> 00:31:10.360 align:middle line:84% And it's just the product of the expectations. 00:31:10.360 --> 00:31:12.160 align:middle line:84% But the covariance is an easy way 00:31:12.160 --> 00:31:14.090 align:middle line:84% to adjust if they're not independent. 00:31:14.090 --> 00:31:16.120 align:middle line:84% So now, we just substitute in that formula 00:31:16.120 --> 00:31:19.340 align:middle line:84% in the previous slide, which had this expression on the left. 00:31:19.340 --> 00:31:22.300 align:middle line:84% We now substitute in the expression on the right 00:31:22.300 --> 00:31:25.940 align:middle line:84% and manipulate by dividing through this expectation of M 00:31:25.940 --> 00:31:26.440 align:middle line:90% prime. 00:31:26.440 --> 00:31:28.280 align:middle line:90% And we get this object here. 00:31:28.280 --> 00:31:33.820 align:middle line:84% So the expected return on activity I run by household J-- 00:31:33.820 --> 00:31:35.770 align:middle line:90% expected return next period-- 00:31:35.770 --> 00:31:39.520 align:middle line:84% has an intercept in some kind of product term. 00:31:39.520 --> 00:31:42.310 align:middle line:84% And I'm about to give you an interpretation of what 00:31:42.310 --> 00:31:43.480 align:middle line:90% these are. 00:31:43.480 --> 00:31:46.030 align:middle line:84% And in some respects, this beta is going 00:31:46.030 --> 00:31:48.260 align:middle line:90% to be a regression coefficient. 00:31:48.260 --> 00:31:52.330 align:middle line:84% And the lambda is going to be a measure of social risk. 00:31:52.330 --> 00:31:57.700 align:middle line:84% In particular, finally, if we imagine those production 00:31:57.700 --> 00:32:01.510 align:middle line:84% functions are linear, then the return on activity 00:32:01.510 --> 00:32:05.590 align:middle line:84% I run by household J is linear in the capital. 00:32:05.590 --> 00:32:07.670 align:middle line:90% Constant returns to scale. 00:32:07.670 --> 00:32:11.110 align:middle line:84% However, as I have been trying to say, this return-- 00:32:11.110 --> 00:32:12.430 align:middle line:90% this little r thing-- 00:32:12.430 --> 00:32:14.260 align:middle line:90% is a random variable. 00:32:14.260 --> 00:32:17.320 align:middle line:84% Anyway, the marginal return is that little r. 00:32:17.320 --> 00:32:20.420 align:middle line:84% So also, it's the average return, for that matter. 00:32:20.420 --> 00:32:24.490 align:middle line:84% And we can talk about the growth rate of return equal 1 00:32:24.490 --> 00:32:28.690 align:middle line:84% plus the net rate of return as a definition of capital R. 00:32:28.690 --> 00:32:32.740 align:middle line:84% Just so you might feel a bit more comfortable, if we have 00:32:32.740 --> 00:32:36.070 align:middle line:84% a constant returns to scale production function actually 00:32:36.070 --> 00:32:39.700 align:middle line:84% finally modeling other inputs like labor and materials 00:32:39.700 --> 00:32:44.020 align:middle line:84% and so on, if you optimize that and put the optimized inputs 00:32:44.020 --> 00:32:45.460 align:middle line:84% back into the function, you would 00:32:45.460 --> 00:32:49.700 align:middle line:84% get this derived function, which is linear in the capital stock. 00:32:49.700 --> 00:32:51.520 align:middle line:84% So that's where it's coming from. 00:32:51.520 --> 00:32:53.560 align:middle line:84% But I didn't give you that algebra. 00:32:53.560 --> 00:32:55.780 align:middle line:84% Secondly, what about preferences? 00:32:55.780 --> 00:32:59.260 align:middle line:84% Let's let the value function be quadratic. 00:32:59.260 --> 00:33:02.050 align:middle line:90% So you've seen these before. 00:33:02.050 --> 00:33:04.390 align:middle line:90% W star is a bliss point. 00:33:04.390 --> 00:33:07.340 align:middle line:90% And less than W star-- 00:33:07.340 --> 00:33:09.310 align:middle line:84% so that the marginal utility of wealth 00:33:09.310 --> 00:33:11.000 align:middle line:90% is always strictly positive. 00:33:11.000 --> 00:33:15.430 align:middle line:84% So if we go back to this guy here and start substituting 00:33:15.430 --> 00:33:19.930 align:middle line:84% in what we assumed about the production function and utility 00:33:19.930 --> 00:33:22.210 align:middle line:84% function, then we're actually going 00:33:22.210 --> 00:33:27.820 align:middle line:84% to get an expression which says, the average or expected return 00:33:27.820 --> 00:33:32.170 align:middle line:84% on household J's activities less the risk free rate 00:33:32.170 --> 00:33:36.010 align:middle line:84% is equal to beta J for household J times 00:33:36.010 --> 00:33:38.830 align:middle line:84% the expected return in the whole village 00:33:38.830 --> 00:33:40.750 align:middle line:90% minus the risk free rate. 00:33:40.750 --> 00:33:43.990 align:middle line:84% In fact, you can put this R prime F, the risk free rate, 00:33:43.990 --> 00:33:45.320 align:middle line:90% on the right-hand side. 00:33:45.320 --> 00:33:47.480 align:middle line:90% So that would be the constant. 00:33:47.480 --> 00:33:50.830 align:middle line:84% So it's constant plus theta times this guy. 00:33:50.830 --> 00:33:53.500 align:middle line:84% And let me define these terms a little bit. 00:33:53.500 --> 00:33:56.680 align:middle line:84% R prime J no longer has an I on it, 00:33:56.680 --> 00:34:01.270 align:middle line:84% because it's the weighted return over all the activities run 00:34:01.270 --> 00:34:05.680 align:middle line:84% by household J. Likewise, the return for the whole village-- 00:34:05.680 --> 00:34:06.970 align:middle line:90% market, if you like-- 00:34:06.970 --> 00:34:09.610 align:middle line:84% M, is the weighted average return 00:34:09.610 --> 00:34:13.480 align:middle line:84% over all activities and all households. 00:34:13.480 --> 00:34:16.630 align:middle line:84% So you take the capitalization of activity 00:34:16.630 --> 00:34:21.370 align:middle line:84% I run by household J, look at the return on that as a peer 00:34:21.370 --> 00:34:25.449 align:middle line:84% activity I run by household J, sum over for the household 00:34:25.449 --> 00:34:29.679 align:middle line:84% all activities I, sum over all households J, 00:34:29.679 --> 00:34:33.219 align:middle line:84% you're getting a total return over all activities 00:34:33.219 --> 00:34:34.239 align:middle line:90% in all households. 00:34:34.239 --> 00:34:36.850 align:middle line:84% And to get a rate of return, you divide 00:34:36.850 --> 00:34:39.280 align:middle line:90% by the level of capitalization. 00:34:39.280 --> 00:34:41.380 align:middle line:84% And the total level of capitalization 00:34:41.380 --> 00:34:44.440 align:middle line:84% is just the sum of the capitals over all activities 00:34:44.440 --> 00:34:45.790 align:middle line:90% and projects. 00:34:45.790 --> 00:34:47.409 align:middle line:90% And what is this beta? 00:34:47.409 --> 00:34:52.000 align:middle line:84% This beta is just a covariance divided by a variance. 00:34:52.000 --> 00:34:55.600 align:middle line:84% As I've said, it's going to be a regression coefficient. 00:34:55.600 --> 00:34:58.210 align:middle line:84% If you're used to ordinary least squares, 00:34:58.210 --> 00:35:00.370 align:middle line:84% you know that a regression coefficient 00:35:00.370 --> 00:35:03.730 align:middle line:90% is x prime x inverse x prime y. 00:35:03.730 --> 00:35:07.490 align:middle line:84% So x must be in the denominator here, 00:35:07.490 --> 00:35:11.110 align:middle line:84% which means that we're running on the right-hand side, 00:35:11.110 --> 00:35:13.820 align:middle line:90% the total market village return. 00:35:13.820 --> 00:35:17.260 align:middle line:84% And on the left-hand side, the dependent variable 00:35:17.260 --> 00:35:19.930 align:middle line:84% is going to be the return of household J. 00:35:19.930 --> 00:35:24.640 align:middle line:84% So we're going to regress the return of household J 00:35:24.640 --> 00:35:27.400 align:middle line:84% over all the periods of the sample 00:35:27.400 --> 00:35:31.030 align:middle line:84% onto the aggregated village level return 00:35:31.030 --> 00:35:32.960 align:middle line:84% and get a regression coefficient. 00:35:32.960 --> 00:35:35.230 align:middle line:84% And that's going to be beta J. And that's 00:35:35.230 --> 00:35:39.880 align:middle line:84% going to capture how much the activities run by household J 00:35:39.880 --> 00:35:45.110 align:middle line:84% are covarying with what the village is doing as a whole. 00:35:45.110 --> 00:35:49.210 align:middle line:84% Now, as I think I explained to you last time, 00:35:49.210 --> 00:35:52.430 align:middle line:90% I could go from here to here. 00:35:52.430 --> 00:35:55.930 align:middle line:84% And it would all just look like some kind of claim. 00:35:55.930 --> 00:35:57.250 align:middle line:90% Go see the paper. 00:35:57.250 --> 00:36:00.550 align:middle line:84% If you don't read the paper, it remains mysterious. 00:36:00.550 --> 00:36:02.560 align:middle line:84% You have an extra level of abstraction. 00:36:02.560 --> 00:36:04.000 align:middle line:90% You don't believe the results. 00:36:04.000 --> 00:36:07.420 align:middle line:84% So I actually wrote in the algebra. 00:36:07.420 --> 00:36:09.610 align:middle line:84% I am not going to go through it today, 00:36:09.610 --> 00:36:12.370 align:middle line:84% because it is nothing other than algebra. 00:36:12.370 --> 00:36:15.220 align:middle line:84% But it's how to take those two assumptions 00:36:15.220 --> 00:36:19.270 align:middle line:84% about quadratic utility and production functions, 00:36:19.270 --> 00:36:22.960 align:middle line:84% and actually manipulate the equations we already had, 00:36:22.960 --> 00:36:26.800 align:middle line:84% substituting in these particular expressions 00:36:26.800 --> 00:36:30.040 align:middle line:84% and getting, at the bottom, the expression that 00:36:30.040 --> 00:36:33.230 align:middle line:90% corresponds to this, OK? 00:36:33.230 --> 00:36:34.460 align:middle line:90% But I'm going to skip that. 00:36:34.460 --> 00:36:39.070 align:middle line:84% So again, mechanically, take the return of household J 00:36:39.070 --> 00:36:46.150 align:middle line:84% at year T. Regress it onto constant and onto the time 00:36:46.150 --> 00:36:49.330 align:middle line:90% series of the market return. 00:36:49.330 --> 00:36:52.180 align:middle line:84% And this is actually a prime here. 00:36:52.180 --> 00:36:55.710 align:middle line:84% We're having trouble editing these latex files, I guess. 00:36:55.710 --> 00:36:57.700 align:middle line:90% So this is a prime. 00:36:57.700 --> 00:36:58.560 align:middle line:90% So we have prime. 00:36:58.560 --> 00:37:00.570 align:middle line:84% This could be all today, today, or it could 00:37:00.570 --> 00:37:02.100 align:middle line:90% be next period, next period. 00:37:02.100 --> 00:37:04.120 align:middle line:90% Just be consistent about it. 00:37:04.120 --> 00:37:07.350 align:middle line:84% So the return of household J at day T regressed 00:37:07.350 --> 00:37:11.370 align:middle line:84% on to the village level return at dates T, 00:37:11.370 --> 00:37:14.370 align:middle line:84% running over all T. So the sample could-- 00:37:14.370 --> 00:37:15.600 align:middle line:90% I'll show you in a minute-- 00:37:15.600 --> 00:37:19.080 align:middle line:84% something like 10 years of data, a bit more. 00:37:19.080 --> 00:37:21.510 align:middle line:84% Plus, an epsilon is the error term. 00:37:21.510 --> 00:37:24.000 align:middle line:84% After you run this regression using the time 00:37:24.000 --> 00:37:26.850 align:middle line:84% series for each household, one at a time, 00:37:26.850 --> 00:37:30.060 align:middle line:84% and having estimated these beta Js, 00:37:30.060 --> 00:37:33.270 align:middle line:84% we now run the next regression, which is entirely 00:37:33.270 --> 00:37:35.520 align:middle line:90% cross-sectional regression. 00:37:35.520 --> 00:37:39.360 align:middle line:84% We compute for each household the average return 00:37:39.360 --> 00:37:42.960 align:middle line:84% over the entire sample, which is a proxy for the household's 00:37:42.960 --> 00:37:46.300 align:middle line:84% expected return, the data analog to that. 00:37:46.300 --> 00:37:50.910 align:middle line:84% And we regress that for each household J onto its beta J 00:37:50.910 --> 00:37:53.970 align:middle line:84% as derived in the first equation-- so 1. 00:37:53.970 --> 00:37:58.290 align:middle line:84% So the economics here is, the return on the project 00:37:58.290 --> 00:38:02.580 align:middle line:84% run by household J, the expected return, should equal, 00:38:02.580 --> 00:38:04.620 align:middle line:90% say roughly, the risk free rate. 00:38:04.620 --> 00:38:06.480 align:middle line:90% But it has a risk premium-- 00:38:06.480 --> 00:38:10.020 align:middle line:84% first time I've use that now with the notation. 00:38:10.020 --> 00:38:13.410 align:middle line:84% And the risk premium has to do with the comovement 00:38:13.410 --> 00:38:17.680 align:middle line:84% of household J's activity with the village aggregate. 00:38:17.680 --> 00:38:20.430 align:middle line:84% So we talked about diversification 00:38:20.430 --> 00:38:22.240 align:middle line:90% at the beginning of class. 00:38:22.240 --> 00:38:26.610 align:middle line:84% And the idea here is, if the things household J is doing 00:38:26.610 --> 00:38:29.190 align:middle line:84% are highly correlated with returns 00:38:29.190 --> 00:38:31.650 align:middle line:84% on what other people are doing, then household J 00:38:31.650 --> 00:38:34.060 align:middle line:84% isn't doing very much worthwhile. 00:38:34.060 --> 00:38:37.210 align:middle line:84% Household J is not diversifying the village level risk. 00:38:37.210 --> 00:38:40.620 align:middle line:84% So in order to justify the set of activities 00:38:40.620 --> 00:38:44.220 align:middle line:84% that household J is doing, we have to bump up 00:38:44.220 --> 00:38:46.200 align:middle line:90% its expected rate of return. 00:38:46.200 --> 00:38:49.140 align:middle line:84% In some sense, we use the word risk premium, 00:38:49.140 --> 00:38:52.620 align:middle line:84% meaning household J's activities are pretty risky. 00:38:52.620 --> 00:38:53.700 align:middle line:90% Why? 00:38:53.700 --> 00:38:56.560 align:middle line:84% Because they're correlated with the village average. 00:38:56.560 --> 00:38:58.890 align:middle line:84% So diversification is not-- and we 00:38:58.890 --> 00:39:01.770 align:middle line:84% need to compensate for that lack of diversification. 00:39:01.770 --> 00:39:04.200 align:middle line:84% The opposite is more revealing, perhaps, 00:39:04.200 --> 00:39:08.520 align:middle line:84% which is, if this correlation is low or even 0, 00:39:08.520 --> 00:39:10.380 align:middle line:90% it's a wonderful hedge. 00:39:10.380 --> 00:39:13.350 align:middle line:84% Even if not many households are doing those things, 00:39:13.350 --> 00:39:17.250 align:middle line:84% if household J does them and manages to produce a return 00:39:17.250 --> 00:39:20.400 align:middle line:84% stream, which is not so correlated with the return 00:39:20.400 --> 00:39:24.400 align:middle line:84% streams of the other households, that's great, in which case, 00:39:24.400 --> 00:39:27.570 align:middle line:84% we don't need to have a high risk premium. 00:39:27.570 --> 00:39:30.100 align:middle line:84% Because actually, it's reducing risk. 00:39:30.100 --> 00:39:32.190 align:middle line:90% So that's the economics of it. 00:39:32.190 --> 00:39:36.580 align:middle line:84% It's all, also, entirely here in terms of the equations. 00:39:36.580 --> 00:39:37.127 align:middle line:90% All right. 00:39:37.127 --> 00:39:37.960 align:middle line:90% AUDIENCE: I'm sorry. 00:39:37.960 --> 00:39:41.873 align:middle line:84% I have a question about a previous slide. 00:39:41.873 --> 00:39:42.790 align:middle line:90% ROBERT TOWNSEND: Yeah? 00:39:42.790 --> 00:39:47.590 align:middle line:84% AUDIENCE: So it's more like econometrics stuff, 00:39:47.590 --> 00:39:50.890 align:middle line:84% because I think there should be some estimation error here, 00:39:50.890 --> 00:39:53.740 align:middle line:90% because the beta is estimated. 00:39:53.740 --> 00:39:56.470 align:middle line:90% And in step 2, you just regress. 00:39:56.470 --> 00:40:01.800 align:middle line:84% You regressive return on some estimated beta, right? 00:40:01.800 --> 00:40:12.310 align:middle line:84% So you just regress some true data, or some estimated data? 00:40:12.310 --> 00:40:15.820 align:middle line:84% And I think the lambda here will have some error rate. 00:40:15.820 --> 00:40:19.360 align:middle line:84% ROBERT TOWNSEND: Well, there are two things to adjust for. 00:40:19.360 --> 00:40:23.570 align:middle line:84% One, this is a regression coefficient. 00:40:23.570 --> 00:40:25.150 align:middle line:90% So it is measured with error. 00:40:25.150 --> 00:40:26.920 align:middle line:90% It has a standard error. 00:40:26.920 --> 00:40:29.560 align:middle line:84% And we do adjust the beta that we're using 00:40:29.560 --> 00:40:32.350 align:middle line:90% to allow for that uncertainty. 00:40:32.350 --> 00:40:35.240 align:middle line:84% That's part of what you're asking. 00:40:35.240 --> 00:40:36.615 align:middle line:84% Is that what you're asking about? 00:40:36.615 --> 00:40:40.780 align:middle line:90% 00:40:40.780 --> 00:40:41.830 align:middle line:90% AUDIENCE: Yeah, probably. 00:40:41.830 --> 00:40:43.030 align:middle line:90% But yeah, OK. 00:40:43.030 --> 00:40:46.340 align:middle line:90% OK, yeah. 00:40:46.340 --> 00:40:53.860 align:middle line:84% ROBERT TOWNSEND: The other thing is that here, we're 00:40:53.860 --> 00:40:57.620 align:middle line:84% regressing an individual J return on the village average. 00:40:57.620 --> 00:41:01.640 align:middle line:84% So you do have to be worried about regressing 00:41:01.640 --> 00:41:04.210 align:middle line:84% dependent variables on the left with their average 00:41:04.210 --> 00:41:05.930 align:middle line:90% on the right. 00:41:05.930 --> 00:41:11.840 align:middle line:84% And that tends to bias this beta toward 1. 00:41:11.840 --> 00:41:13.850 align:middle line:84% That's another econometric problem, 00:41:13.850 --> 00:41:18.400 align:middle line:84% except that here, we're actually interested in dispersion 00:41:18.400 --> 00:41:21.200 align:middle line:90% across the different betas. 00:41:21.200 --> 00:41:22.530 align:middle line:90% So we're OK. 00:41:22.530 --> 00:41:23.540 align:middle line:90% AUDIENCE: OK. 00:41:23.540 --> 00:41:27.190 align:middle line:84% ROBERT TOWNSEND: And this is Fama, French, 00:41:27.190 --> 00:41:29.143 align:middle line:90% which I suspect you know. 00:41:29.143 --> 00:41:30.560 align:middle line:84% AUDIENCE: Yeah, I know that, yeah. 00:41:30.560 --> 00:41:31.477 align:middle line:90% ROBERT TOWNSEND: Yeah. 00:41:31.477 --> 00:41:35.470 align:middle line:84% So we're just doing what they did with the New York stocks-- 00:41:35.470 --> 00:41:41.260 align:middle line:84% doing it here in the Thai villages, OK? 00:41:41.260 --> 00:41:45.940 align:middle line:84% We started our survey in 1998 with a big baseline. 00:41:45.940 --> 00:41:50.110 align:middle line:84% We update it every month thereafter. 00:41:50.110 --> 00:41:52.900 align:middle line:84% This said, at the time we were writing the paper, 00:41:52.900 --> 00:41:56.140 align:middle line:84% the survey was still ongoing, although even then, 00:41:56.140 --> 00:41:57.970 align:middle line:90% the later months were not ready. 00:41:57.970 --> 00:42:02.500 align:middle line:84% So we ended up using monthly data from month 5 00:42:02.500 --> 00:42:05.600 align:middle line:90% to month 160 of the survey. 00:42:05.600 --> 00:42:07.420 align:middle line:84% The other thing that's misleading-- it's 00:42:07.420 --> 00:42:09.310 align:middle line:90% not ongoing anymore. 00:42:09.310 --> 00:42:12.760 align:middle line:84% The project ended about 18 months ago. 00:42:12.760 --> 00:42:16.880 align:middle line:84% But we did end up with almost 20 years of monthly data. 00:42:16.880 --> 00:42:21.370 align:middle line:84% So it's a vast warehouse of potential projects 00:42:21.370 --> 00:42:22.720 align:middle line:90% that can be done with it. 00:42:22.720 --> 00:42:24.280 align:middle line:90% And I'm happy to tell you more. 00:42:24.280 --> 00:42:27.320 align:middle line:84% But today, I want to focus on this paper. 00:42:27.320 --> 00:42:29.710 align:middle line:84% So we only included the households 00:42:29.710 --> 00:42:32.710 align:middle line:84% that were actually in the village for the whole period. 00:42:32.710 --> 00:42:36.430 align:middle line:84% Sometimes, entire households picked up stakes and leave. 00:42:36.430 --> 00:42:37.490 align:middle line:90% We excluded them. 00:42:37.490 --> 00:42:39.820 align:middle line:84% We also are looking only at households 00:42:39.820 --> 00:42:41.830 align:middle line:90% with production activities. 00:42:41.830 --> 00:42:45.940 align:middle line:84% Farm is included, but also fish, shrimp, livestock, trade 00:42:45.940 --> 00:42:46.930 align:middle line:90% and handicrafts. 00:42:46.930 --> 00:42:49.250 align:middle line:90% But not just wage earnings-- 00:42:49.250 --> 00:42:49.750 align:middle line:90% why? 00:42:49.750 --> 00:42:51.220 align:middle line:84% Because with wage earnings, they're 00:42:51.220 --> 00:42:52.900 align:middle line:90% not really producing anything. 00:42:52.900 --> 00:42:55.550 align:middle line:84% They're earning something by working for others. 00:42:55.550 --> 00:42:57.230 align:middle line:90% So they're not entrepreneurs. 00:42:57.230 --> 00:42:59.690 align:middle line:90% So we did not include them. 00:42:59.690 --> 00:43:02.780 align:middle line:84% And there are extensive networks of family in these villages. 00:43:02.780 --> 00:43:05.390 align:middle line:84% And I'm going to come back to that a little bit later 00:43:05.390 --> 00:43:06.690 align:middle line:90% toward the end. 00:43:06.690 --> 00:43:10.670 align:middle line:84% So just to give you a feeling of the data, 00:43:10.670 --> 00:43:14.540 align:middle line:84% we've got net income, which means income 00:43:14.540 --> 00:43:16.550 align:middle line:90% from household enterprise. 00:43:16.550 --> 00:43:19.070 align:middle line:84% It's the difference between revenue and costs 00:43:19.070 --> 00:43:20.600 align:middle line:90% of all the inputs. 00:43:20.600 --> 00:43:25.550 align:middle line:84% Revenue is realized at the time of sale, or if it's a crop, 00:43:25.550 --> 00:43:26.510 align:middle line:90% it could be eaten. 00:43:26.510 --> 00:43:31.210 align:middle line:84% It could be given as a gift from others at all counts. 00:43:31.210 --> 00:43:33.190 align:middle line:90% We add them all up. 00:43:33.190 --> 00:43:35.620 align:middle line:84% Revenue even comes from renting out assets. 00:43:35.620 --> 00:43:37.090 align:middle line:90% We include that. 00:43:37.090 --> 00:43:40.280 align:middle line:84% Costs are all the inputs used in production, 00:43:40.280 --> 00:43:42.820 align:middle line:84% whether they're acquired in cash or in-kind 00:43:42.820 --> 00:43:44.920 align:middle line:90% with credit or gifts. 00:43:44.920 --> 00:43:45.880 align:middle line:90% We count them all. 00:43:45.880 --> 00:43:48.460 align:middle line:84% We put a valuation on them if it's not 00:43:48.460 --> 00:43:50.900 align:middle line:90% acquired in the market. 00:43:50.900 --> 00:43:54.220 align:middle line:84% So we take revenue minus costs, include depreciation-- 00:43:54.220 --> 00:43:55.450 align:middle line:90% that came up earlier. 00:43:55.450 --> 00:43:56.740 align:middle line:90% Subtract it. 00:43:56.740 --> 00:43:59.590 align:middle line:90% And we get net income. 00:43:59.590 --> 00:44:02.410 align:middle line:84% And these assets we're talking about-- 00:44:02.410 --> 00:44:06.250 align:middle line:84% we have agricultural, business, livestock assets. 00:44:06.250 --> 00:44:08.800 align:middle line:84% We've also got land and household assets. 00:44:08.800 --> 00:44:11.740 align:middle line:84% The agricultural assets, to give you an example, 00:44:11.740 --> 00:44:14.465 align:middle line:84% includes walking tractors-- you might remember 00:44:14.465 --> 00:44:16.840 align:middle line:84% in the production lecture, I showed you a picture of that 00:44:16.840 --> 00:44:19.390 align:middle line:84% guy walking around with the tractor-- 00:44:19.390 --> 00:44:24.100 align:middle line:84% or larger four wheel tractors, aerators for ponds, machines 00:44:24.100 --> 00:44:27.070 align:middle line:84% to put seeds in the ground, machines 00:44:27.070 --> 00:44:29.170 align:middle line:90% like sprinklers, et cetera. 00:44:29.170 --> 00:44:30.940 align:middle line:90% So you're in the village now. 00:44:30.940 --> 00:44:32.830 align:middle line:84% You can imagine living there, I think. 00:44:32.830 --> 00:44:35.190 align:middle line:84% This is the level of detail that we have. 00:44:35.190 --> 00:44:37.060 align:middle line:90% We did put household assets in. 00:44:37.060 --> 00:44:40.630 align:middle line:84% That's a decision, because some of the things that 00:44:40.630 --> 00:44:44.170 align:middle line:84% look like a durable good end up being used in farming, 00:44:44.170 --> 00:44:45.460 align:middle line:90% like a pickup truck. 00:44:45.460 --> 00:44:46.160 align:middle line:90% They use it. 00:44:46.160 --> 00:44:49.060 align:middle line:84% So rather than-- but we've done robustness checks. 00:44:49.060 --> 00:44:51.490 align:middle line:84% But here, we include them all, OK? 00:44:51.490 --> 00:44:54.040 align:middle line:90% So let me just jump here. 00:44:54.040 --> 00:44:59.630 align:middle line:84% If we look at that data, this is the return on assets, 00:44:59.630 --> 00:45:04.690 align:middle line:84% the expected return on household J. Each J corresponds to a dot 00:45:04.690 --> 00:45:05.470 align:middle line:90% here. 00:45:05.470 --> 00:45:08.350 align:middle line:84% And it's just the average return for household J. 00:45:08.350 --> 00:45:12.100 align:middle line:84% On the y-axis and the beta, the regression coefficient 00:45:12.100 --> 00:45:15.800 align:middle line:84% on the village average is on the x-axis. 00:45:15.800 --> 00:45:20.530 align:middle line:84% So you can see that households that have higher returns 00:45:20.530 --> 00:45:26.600 align:middle line:84% are households that have higher betas for three of the four, 00:45:26.600 --> 00:45:30.380 align:middle line:84% potentially all four, although Buriram is not the greatest 00:45:30.380 --> 00:45:32.010 align:middle line:90% example. 00:45:32.010 --> 00:45:34.500 align:middle line:84% And I have shown this picture to guys 00:45:34.500 --> 00:45:38.910 align:middle line:84% working in finance with New York Stock Exchange or Swedish Data. 00:45:38.910 --> 00:45:40.860 align:middle line:84% And they see this degree of correlation. 00:45:40.860 --> 00:45:43.750 align:middle line:84% And they're like, wow, that's really amazing. 00:45:43.750 --> 00:45:48.090 align:middle line:84% So the theory is working pretty well. 00:45:48.090 --> 00:45:50.000 align:middle line:90% And this is the regression. 00:45:50.000 --> 00:45:51.420 align:middle line:90% Doesn't really add more. 00:45:51.420 --> 00:45:55.880 align:middle line:84% This is the regression from that step 1 with the corresponding-- 00:45:55.880 --> 00:45:59.870 align:middle line:84% sorry, step 2, it is, with the corresponding betas. 00:45:59.870 --> 00:46:01.670 align:middle line:84% And it's not significant in Buriram, 00:46:01.670 --> 00:46:04.950 align:middle line:84% but it is in the other three provinces. 00:46:04.950 --> 00:46:06.960 align:middle line:84% Not sure if I've shown you this map. 00:46:06.960 --> 00:46:08.480 align:middle line:90% I don't think we did. 00:46:08.480 --> 00:46:13.010 align:middle line:84% Chachoengsao and Lopburi are relatively near to Bangkok. 00:46:13.010 --> 00:46:17.210 align:middle line:84% And Buriram and Srisaket are out in the agrarian regions 00:46:17.210 --> 00:46:18.560 align:middle line:90% of the northeast. 00:46:18.560 --> 00:46:21.600 align:middle line:84% So very different types of sample. 00:46:21.600 --> 00:46:24.470 align:middle line:84% OK, so let's talk about idiosyncratic risk. 00:46:24.470 --> 00:46:28.610 align:middle line:84% The return on household J is determined by beta J 00:46:28.610 --> 00:46:29.870 align:middle line:90% that we've been talking about. 00:46:29.870 --> 00:46:32.540 align:middle line:84% X is to make the argument more general. 00:46:32.540 --> 00:46:36.860 align:middle line:84% So regression coefficient times the object, 00:46:36.860 --> 00:46:38.520 align:middle line:90% and then an error term. 00:46:38.520 --> 00:46:41.970 align:middle line:84% So if you take the variance of both sides doing 00:46:41.970 --> 00:46:46.190 align:middle line:84% a variance decomposition, the variance of the return 00:46:46.190 --> 00:46:49.700 align:middle line:84% is the variance explained by the dependent variable 00:46:49.700 --> 00:46:53.700 align:middle line:84% with its coefficient plus the variance of the error term. 00:46:53.700 --> 00:46:56.630 align:middle line:84% So when we talk about idiosyncratic risk, 00:46:56.630 --> 00:47:00.050 align:middle line:84% we're talking about the error term here as opposed 00:47:00.050 --> 00:47:03.320 align:middle line:84% to how much of the variance is determined by the village 00:47:03.320 --> 00:47:04.590 align:middle line:90% aggregate. 00:47:04.590 --> 00:47:08.090 align:middle line:84% And so you can just imagine taking this variance term 00:47:08.090 --> 00:47:10.460 align:middle line:84% and dividing it through both sides. 00:47:10.460 --> 00:47:13.520 align:middle line:84% And then, you'll have one like, 100% 00:47:13.520 --> 00:47:16.670 align:middle line:84% is equal to the contribution of the village 00:47:16.670 --> 00:47:20.510 align:middle line:84% return plus the contribution of the idiosyncratic 00:47:20.510 --> 00:47:22.200 align:middle line:90% variance to the total. 00:47:22.200 --> 00:47:23.660 align:middle line:90% So this is not theory. 00:47:23.660 --> 00:47:27.470 align:middle line:84% This is a way of quantifying how much aggregate village 00:47:27.470 --> 00:47:31.190 align:middle line:84% average risk there is and how much idiosyncratic risk there 00:47:31.190 --> 00:47:34.130 align:middle line:90% is in an individual J's return. 00:47:34.130 --> 00:47:36.590 align:middle line:84% Now, the next thing-- back to the regression-- 00:47:36.590 --> 00:47:39.110 align:middle line:84% as I have been saying, in the baseline, 00:47:39.110 --> 00:47:42.050 align:middle line:84% we're running the average return on household J 00:47:42.050 --> 00:47:47.870 align:middle line:84% onto a constant plus the beta J coefficient times beta J. 00:47:47.870 --> 00:47:50.390 align:middle line:90% And now, we do something extra. 00:47:50.390 --> 00:47:53.630 align:middle line:84% We add in sigma J, where sigma J here 00:47:53.630 --> 00:47:56.420 align:middle line:84% is the variance of this epsilon term. 00:47:56.420 --> 00:47:58.520 align:middle line:84% How much is it moving-- oh, it's right here, 00:47:58.520 --> 00:48:00.830 align:middle line:84% except that I didn't call it sigma J here. 00:48:00.830 --> 00:48:03.500 align:middle line:84% The variance of epsilon J is sigma J. Stick 00:48:03.500 --> 00:48:05.930 align:middle line:84% that into this cross-sectional regression 00:48:05.930 --> 00:48:08.210 align:middle line:84% as an extra right-hand side variable. 00:48:08.210 --> 00:48:10.410 align:middle line:90% And get a coefficient on it. 00:48:10.410 --> 00:48:13.310 align:middle line:84% So now, we can do a similar calculation. 00:48:13.310 --> 00:48:15.830 align:middle line:84% We can take the risk premium, which 00:48:15.830 --> 00:48:19.550 align:middle line:84% is the sum of both the return over above the risk free rate 00:48:19.550 --> 00:48:21.230 align:middle line:84% that's due to the aggregate return 00:48:21.230 --> 00:48:23.880 align:middle line:84% and also due to the idiosyncratic risk. 00:48:23.880 --> 00:48:26.810 align:middle line:84% And so we can decompose the aggregate risk 00:48:26.810 --> 00:48:29.570 align:middle line:84% as a proportion of the total, and likewise, 00:48:29.570 --> 00:48:33.410 align:middle line:84% the idiosyncratic risk as a proportion of the total. 00:48:33.410 --> 00:48:35.770 align:middle line:90% Question? 00:48:35.770 --> 00:48:40.190 align:middle line:84% So doing that, we summarize the results-- 00:48:40.190 --> 00:48:42.460 align:middle line:84% the contribution of idiosyncratic 00:48:42.460 --> 00:48:45.700 align:middle line:84% risk to total risk and the contribution 00:48:45.700 --> 00:48:49.300 align:middle line:84% of idiosyncratic risk to the risk premium. 00:48:49.300 --> 00:48:51.610 align:middle line:84% The contribution of idiosyncratic risk 00:48:51.610 --> 00:48:54.770 align:middle line:90% to the total variance is huge. 00:48:54.770 --> 00:48:58.150 align:middle line:84% This row here running across the villages 00:48:58.150 --> 00:49:00.880 align:middle line:84% and looking at the quartiles including the median, 00:49:00.880 --> 00:49:06.340 align:middle line:84% you've got 98% of it, 97% of it, 94% of it. 00:49:06.340 --> 00:49:13.210 align:middle line:84% 65% of the risk is coming from the idiosyncratic component, 00:49:13.210 --> 00:49:15.640 align:middle line:90% coming from this guy. 00:49:15.640 --> 00:49:16.540 align:middle line:90% Let me back up. 00:49:16.540 --> 00:49:18.900 align:middle line:90% Coming from this guy. 00:49:18.900 --> 00:49:22.560 align:middle line:84% Second row of this table is a contribution 00:49:22.560 --> 00:49:25.410 align:middle line:84% to the risk premium of the idiosyncratic risk. 00:49:25.410 --> 00:49:26.940 align:middle line:90% And it's pretty small. 00:49:26.940 --> 00:49:28.590 align:middle line:90% Two things to note-- 00:49:28.590 --> 00:49:33.190 align:middle line:84% it's almost always lower than the quantity. 00:49:33.190 --> 00:49:37.350 align:middle line:84% So the risk premium here is also small. 00:49:37.350 --> 00:49:39.870 align:middle line:84% Here, it's 21%, which isn't trivial. 00:49:39.870 --> 00:49:41.970 align:middle line:90% Or even here, 45%. 00:49:41.970 --> 00:49:45.690 align:middle line:84% But the 45% is still less than the 99%. 00:49:45.690 --> 00:49:48.060 align:middle line:84% So the contribution to the risk premium 00:49:48.060 --> 00:49:51.480 align:middle line:84% in terms of the compensating returns required 00:49:51.480 --> 00:49:56.610 align:middle line:84% for the household to run those technologies is always-- 00:49:56.610 --> 00:49:58.530 align:middle line:84% the contribution to the total risk 00:49:58.530 --> 00:50:02.050 align:middle line:84% is always greater than the risk premium. 00:50:02.050 --> 00:50:04.880 align:middle line:84% Except Buriram screws up over here. 00:50:04.880 --> 00:50:08.090 align:middle line:84% But as you've seen, Buriram screws up in other ways. 00:50:08.090 --> 00:50:10.645 align:middle line:84% And then, we do a robustness check. 00:50:10.645 --> 00:50:11.145 align:middle line:90% Question? 00:50:11.145 --> 00:50:14.670 align:middle line:90% 00:50:14.670 --> 00:50:17.160 align:middle line:90% OK, back to the economics. 00:50:17.160 --> 00:50:20.130 align:middle line:84% And in medieval villages scattered around, 00:50:20.130 --> 00:50:22.440 align:middle line:90% random returns. 00:50:22.440 --> 00:50:24.120 align:middle line:90% Should they diversify? 00:50:24.120 --> 00:50:26.940 align:middle line:84% Do they do different activities, et cetera? 00:50:26.940 --> 00:50:30.300 align:middle line:84% Well, that depends on the level of risk. 00:50:30.300 --> 00:50:33.780 align:middle line:84% And it turns out, there's a lot of risk, but a lot of it 00:50:33.780 --> 00:50:38.790 align:middle line:84% is plot-specific or activity-specific. 00:50:38.790 --> 00:50:42.630 align:middle line:84% Most of it is idiosyncratic and not aggregate. 00:50:42.630 --> 00:50:45.540 align:middle line:84% It is not true that the returns are comoving much 00:50:45.540 --> 00:50:48.570 align:middle line:90% across all these activities. 00:50:48.570 --> 00:50:51.780 align:middle line:84% So it's a very risky place, as in India. 00:50:51.780 --> 00:50:54.740 align:middle line:84% But there are plenty of diversification possibilities 00:50:54.740 --> 00:50:57.740 align:middle line:84% by holding multiple activities, et cetera. 00:50:57.740 --> 00:51:00.080 align:middle line:84% So we're back to a version of what we did 00:51:00.080 --> 00:51:01.640 align:middle line:90% in medieval villages, right? 00:51:01.640 --> 00:51:03.860 align:middle line:84% How much did they hold different plots? 00:51:03.860 --> 00:51:07.160 align:middle line:84% Here, we are asking, how much do they hold different activities 00:51:07.160 --> 00:51:09.900 align:middle line:84% and what can be accomplished by doing that? 00:51:09.900 --> 00:51:12.680 align:middle line:84% And moreover, since it's idiosyncratic, 00:51:12.680 --> 00:51:15.770 align:middle line:90% you can hope that it might get-- 00:51:15.770 --> 00:51:18.350 align:middle line:84% the risk premium for the idiosyncratic stuff 00:51:18.350 --> 00:51:19.820 align:middle line:90% might get small. 00:51:19.820 --> 00:51:22.380 align:middle line:84% Anyway, all of this is from the production data. 00:51:22.380 --> 00:51:24.800 align:middle line:84% Let's look at the consumption data, and in particular, 00:51:24.800 --> 00:51:26.210 align:middle line:90% look at the gifts. 00:51:26.210 --> 00:51:29.600 align:middle line:84% So now, we're going from medieval villages, 00:51:29.600 --> 00:51:32.630 align:middle line:84% so to speak, in terms of plots and production, 00:51:32.630 --> 00:51:37.350 align:middle line:84% to India in terms of ex-post consumption smoothing. 00:51:37.350 --> 00:51:40.650 align:middle line:84% The gifts and transfers are the ex-post part. 00:51:40.650 --> 00:51:45.360 align:middle line:84% It's how much they would give money to each other starting 00:51:45.360 --> 00:51:45.960 align:middle line:90% from-- 00:51:45.960 --> 00:51:48.960 align:middle line:84% do actually give money to each other-- 00:51:48.960 --> 00:51:53.970 align:middle line:84% starting from the yields on their production activities. 00:51:53.970 --> 00:52:00.360 align:middle line:84% So if you look back here again, you would see these epsilons. 00:52:00.360 --> 00:52:02.000 align:middle line:90% So this could be high. 00:52:02.000 --> 00:52:03.350 align:middle line:90% This could be low. 00:52:03.350 --> 00:52:07.220 align:middle line:84% If the variance is big it's moving the returns around. 00:52:07.220 --> 00:52:09.900 align:middle line:84% What happens when it's really big? 00:52:09.900 --> 00:52:11.390 align:middle line:90% Then, this household got lucky. 00:52:11.390 --> 00:52:12.710 align:middle line:90% It had a high return. 00:52:12.710 --> 00:52:14.150 align:middle line:90% Just lucky. 00:52:14.150 --> 00:52:15.140 align:middle line:90% What does it do? 00:52:15.140 --> 00:52:17.350 align:middle line:90% It gives stuff away. 00:52:17.350 --> 00:52:19.900 align:middle line:84% Or another version-- they get unlucky. 00:52:19.900 --> 00:52:21.370 align:middle line:90% The epsilon is low. 00:52:21.370 --> 00:52:22.300 align:middle line:90% What do they do? 00:52:22.300 --> 00:52:24.310 align:middle line:90% People give them gifts. 00:52:24.310 --> 00:52:26.390 align:middle line:84% Well, I haven't actually shown your result. 00:52:26.390 --> 00:52:30.100 align:middle line:84% But that's exactly what is going on in the data. 00:52:30.100 --> 00:52:35.670 align:middle line:84% So if you regress those shocks, those idiosyncratic shocks 00:52:35.670 --> 00:52:40.050 align:middle line:84% on the right-hand side onto gifts and net lending, et 00:52:40.050 --> 00:52:42.600 align:middle line:90% cetera, you can see both. 00:52:42.600 --> 00:52:45.390 align:middle line:84% There is an ultimate impact on consumption, yes, 00:52:45.390 --> 00:52:48.480 align:middle line:84% but it's small relative to the way 00:52:48.480 --> 00:52:50.040 align:middle line:90% they're mitigating the risk. 00:52:50.040 --> 00:52:53.310 align:middle line:84% Namely, when the shock is high, they're 00:52:53.310 --> 00:52:56.580 align:middle line:84% giving stuff away and lending it out. 00:52:56.580 --> 00:52:58.590 align:middle line:84% And conversely, when the shock is low, 00:52:58.590 --> 00:53:00.060 align:middle line:90% they're getting this stuff in. 00:53:00.060 --> 00:53:01.320 align:middle line:90% It depends on the sign. 00:53:01.320 --> 00:53:04.920 align:middle line:84% This is net gift outflow when the shock is high. 00:53:04.920 --> 00:53:05.623 align:middle line:90% It's positive. 00:53:05.623 --> 00:53:06.915 align:middle line:90% It's statistically significant. 00:53:06.915 --> 00:53:09.960 align:middle line:84% You can add up both gifts and borrowing and lending 00:53:09.960 --> 00:53:11.610 align:middle line:84% and get a bigger coefficient here. 00:53:11.610 --> 00:53:12.360 align:middle line:90% It's 40. 00:53:12.360 --> 00:53:16.980 align:middle line:84% So 40 relative to the impact on consumption, which is 4. 00:53:16.980 --> 00:53:21.150 align:middle line:84% In other words, for every unit of idiosyncratic shock, 00:53:21.150 --> 00:53:25.510 align:middle line:84% roughly 10% of it is making its way into consumption, 00:53:25.510 --> 00:53:26.490 align:middle line:90% which it shouldn't. 00:53:26.490 --> 00:53:28.650 align:middle line:84% It violates the risk sharing theory. 00:53:28.650 --> 00:53:34.590 align:middle line:84% But 90% of it is being pooled away by this village 00:53:34.590 --> 00:53:36.850 align:middle line:90% gift-giving mechanism. 00:53:36.850 --> 00:53:39.520 align:middle line:90% Questions? 00:53:39.520 --> 00:53:42.190 align:middle line:84% In economics, we call this the smoking gun. 00:53:42.190 --> 00:53:43.900 align:middle line:90% You theorize a lot. 00:53:43.900 --> 00:53:45.400 align:middle line:84% You think you know what happened. 00:53:45.400 --> 00:53:47.300 align:middle line:90% But what's the evidence? 00:53:47.300 --> 00:53:48.400 align:middle line:90% Well, they smoothed a lot. 00:53:48.400 --> 00:53:49.930 align:middle line:90% Must be the gifts. 00:53:49.930 --> 00:53:50.830 align:middle line:90% OK, fine. 00:53:50.830 --> 00:53:52.090 align:middle line:90% If you think so. 00:53:52.090 --> 00:53:53.350 align:middle line:90% Well, here's the evidence. 00:53:53.350 --> 00:53:55.040 align:middle line:90% They're actually doing it. 00:53:55.040 --> 00:53:58.390 align:middle line:84% And not only that, they openly tell us they're doing it. 00:53:58.390 --> 00:54:01.280 align:middle line:84% They are very aware that they help each other. 00:54:01.280 --> 00:54:05.150 align:middle line:84% I think you might have seen the video by now-- my movie, 00:54:05.150 --> 00:54:05.710 align:middle line:90% so to speak. 00:54:05.710 --> 00:54:07.000 align:middle line:90% If not, take a look at it. 00:54:07.000 --> 00:54:09.310 align:middle line:84% Because it describes-- you'll actually 00:54:09.310 --> 00:54:11.140 align:middle line:84% see the setting of these Thai villages 00:54:11.140 --> 00:54:13.720 align:middle line:84% and how we've gathered the data, and so on. 00:54:13.720 --> 00:54:16.760 align:middle line:84% Michael is planning to show that at one point. 00:54:16.760 --> 00:54:18.490 align:middle line:90% But it's available. 00:54:18.490 --> 00:54:19.940 align:middle line:90% It's a 32-minute movie. 00:54:19.940 --> 00:54:22.430 align:middle line:90% It's not so much of a burden. 00:54:22.430 --> 00:54:25.510 align:middle line:84% And you'll see how I spend 20 years of my life. 00:54:25.510 --> 00:54:28.280 align:middle line:84% OK, so we've talked about in this. 00:54:28.280 --> 00:54:32.210 align:middle line:84% Now, let's come back to health shocks. 00:54:32.210 --> 00:54:34.160 align:middle line:90% No, it's not COVID. 00:54:34.160 --> 00:54:38.090 align:middle line:84% But it is an illness experienced by the household. 00:54:38.090 --> 00:54:40.460 align:middle line:84% And it's not covered by insurance. 00:54:40.460 --> 00:54:43.140 align:middle line:90% And the expenditures go up. 00:54:43.140 --> 00:54:47.300 align:middle line:84% So this is normalized so that the event happens here. 00:54:47.300 --> 00:54:50.510 align:middle line:84% And health spending is big, and other things like, 00:54:50.510 --> 00:54:51.500 align:middle line:90% they say they're sick. 00:54:51.500 --> 00:54:53.220 align:middle line:84% They're reporting symptoms to us. 00:54:53.220 --> 00:54:55.020 align:middle line:90% We also measure that. 00:54:55.020 --> 00:54:56.660 align:middle line:84% So we're pretty much sure that we 00:54:56.660 --> 00:54:58.310 align:middle line:90% nailed the episode, et cetera. 00:54:58.310 --> 00:55:01.790 align:middle line:84% And sick days goes up and stays up for a while 00:55:01.790 --> 00:55:03.530 align:middle line:90% before it comes back down again. 00:55:03.530 --> 00:55:04.230 align:middle line:90% OK. 00:55:04.230 --> 00:55:05.330 align:middle line:90% And what happens? 00:55:05.330 --> 00:55:07.490 align:middle line:90% There come the gifts. 00:55:07.490 --> 00:55:11.900 align:middle line:84% Again, centered around the episode, the event. 00:55:11.900 --> 00:55:15.530 align:middle line:84% As soon as the event happens, it's actually minus 1. 00:55:15.530 --> 00:55:17.990 align:middle line:84% As soon as the event happens, the gifts 00:55:17.990 --> 00:55:20.600 align:middle line:84% are positive and statistically different 00:55:20.600 --> 00:55:24.980 align:middle line:84% than for households that did not experience those health shocks. 00:55:24.980 --> 00:55:29.220 align:middle line:84% Here, we're comparing placebo households, if you like, 00:55:29.220 --> 00:55:31.370 align:middle line:84% which is a dangerous metaphor given the illness 00:55:31.370 --> 00:55:32.840 align:middle line:90% part of it and the COVID. 00:55:32.840 --> 00:55:37.460 align:middle line:84% We're taking households pairwise conceptually-- one set have 00:55:37.460 --> 00:55:41.480 align:middle line:84% experienced these health shocks, and ones that have not, 00:55:41.480 --> 00:55:44.675 align:middle line:84% and looking at the difference in the gifts that they get. 00:55:44.675 --> 00:55:46.880 align:middle line:84% So if they're sick, they're much more 00:55:46.880 --> 00:55:49.710 align:middle line:84% likely to be getting gifts than the others. 00:55:49.710 --> 00:55:53.510 align:middle line:84% This is the same setting as what I showed you 00:55:53.510 --> 00:55:57.560 align:middle line:84% in rates of return, except we've changed the subject from shocks 00:55:57.560 --> 00:56:00.120 align:middle line:90% to production to illness shocks. 00:56:00.120 --> 00:56:04.580 align:middle line:84% Now actually related, they're still producing or trying to. 00:56:04.580 --> 00:56:06.110 align:middle line:84% And the fact that they've doubled, 00:56:06.110 --> 00:56:09.560 align:middle line:84% say, their health expenditure is a big problem for them. 00:56:09.560 --> 00:56:11.870 align:middle line:84% Because they have only so much liquidity. 00:56:11.870 --> 00:56:13.800 align:middle line:84% And they're supposed to be buying inputs 00:56:13.800 --> 00:56:16.950 align:middle line:84% and so on to fund their agriculture and so on. 00:56:16.950 --> 00:56:18.690 align:middle line:90% So this is a liquidity shock. 00:56:18.690 --> 00:56:20.100 align:middle line:90% It's not just a health shock. 00:56:20.100 --> 00:56:22.130 align:middle line:84% In fact, sometimes, it's an elderly person 00:56:22.130 --> 00:56:23.600 align:middle line:84% in the household that is not even 00:56:23.600 --> 00:56:25.910 align:middle line:90% contributing to production. 00:56:25.910 --> 00:56:28.120 align:middle line:84% So we're looking at the economic impact 00:56:28.120 --> 00:56:31.795 align:middle line:84% of someone taking money away from their budget, essentially. 00:56:31.795 --> 00:56:35.320 align:middle line:84% OK, there are various kinds of networks in these villages. 00:56:35.320 --> 00:56:38.800 align:middle line:84% This is the kinship network, who's related to whom. 00:56:38.800 --> 00:56:41.560 align:middle line:84% This is the financial network in terms 00:56:41.560 --> 00:56:44.060 align:middle line:90% of giving gifts to one another. 00:56:44.060 --> 00:56:48.100 align:middle line:84% This is the sales network, who they sell to in the village. 00:56:48.100 --> 00:56:51.740 align:middle line:90% And this is who they hire from. 00:56:51.740 --> 00:56:53.950 align:middle line:84% So the way these pictures are produced 00:56:53.950 --> 00:56:56.440 align:middle line:84% with the software, roughly speaking, 00:56:56.440 --> 00:56:59.140 align:middle line:84% households in the middle are connected 00:56:59.140 --> 00:57:01.810 align:middle line:90% to many other households. 00:57:01.810 --> 00:57:05.170 align:middle line:84% Households on the fringe don't have that many connections, 00:57:05.170 --> 00:57:07.360 align:middle line:90% depending on the variable. 00:57:07.360 --> 00:57:10.210 align:middle line:84% And the gift giving financial network 00:57:10.210 --> 00:57:13.450 align:middle line:84% is different from the sales and production network. 00:57:13.450 --> 00:57:16.960 align:middle line:84% And I'm going to show you what happens because of that. 00:57:16.960 --> 00:57:18.730 align:middle line:84% I don't have a slide to show you this, 00:57:18.730 --> 00:57:22.810 align:middle line:84% but if they're in this gift giving network measured 00:57:22.810 --> 00:57:25.750 align:middle line:84% by how many times they got gifts before the shell 00:57:25.750 --> 00:57:30.760 align:middle line:84% shock happened, then most of the impact of the shock 00:57:30.760 --> 00:57:33.260 align:middle line:90% is covered by incoming gifts. 00:57:33.260 --> 00:57:35.350 align:middle line:90% But what do we have in the US? 00:57:35.350 --> 00:57:36.310 align:middle line:90% This is an issue. 00:57:36.310 --> 00:57:38.230 align:middle line:90% A household gets sick. 00:57:38.230 --> 00:57:41.420 align:middle line:84% Is the government going to be able to help them? 00:57:41.420 --> 00:57:46.150 align:middle line:84% We have these PPP Paycheck Protection Programs and so on. 00:57:46.150 --> 00:57:47.410 align:middle line:90% Are relatives helping? 00:57:47.410 --> 00:57:48.310 align:middle line:90% Probably so. 00:57:48.310 --> 00:57:49.790 align:middle line:90% We don't know the extent of it. 00:57:49.790 --> 00:57:51.250 align:middle line:90% It's not measured. 00:57:51.250 --> 00:57:53.680 align:middle line:84% We tend to think households are standalone. 00:57:53.680 --> 00:57:54.790 align:middle line:90% They're vulnerable. 00:57:54.790 --> 00:57:57.130 align:middle line:84% Households running businesses in particular 00:57:57.130 --> 00:57:58.570 align:middle line:90% get a liquidity shock. 00:57:58.570 --> 00:58:02.140 align:middle line:84% And mainly, they don't have sales with COVID. 00:58:02.140 --> 00:58:05.710 align:middle line:84% Or their employees aren't able to work. 00:58:05.710 --> 00:58:09.110 align:middle line:84% So they're not generating revenue. 00:58:09.110 --> 00:58:11.350 align:middle line:84% Well, if it were covered with gifts, 00:58:11.350 --> 00:58:14.320 align:middle line:84% as it is for some people in Thailand, 00:58:14.320 --> 00:58:17.290 align:middle line:90% then they pool that risk away. 00:58:17.290 --> 00:58:18.640 align:middle line:90% Great system. 00:58:18.640 --> 00:58:21.890 align:middle line:84% If they're not, there are other consequences. 00:58:21.890 --> 00:58:25.510 align:middle line:84% So in particular, we can look at who's 00:58:25.510 --> 00:58:28.420 align:middle line:84% connected to whom in terms of the network. 00:58:28.420 --> 00:58:31.840 align:middle line:84% Households who experience shocks and were 00:58:31.840 --> 00:58:36.443 align:middle line:84% selling to other households-- their sales go down. 00:58:36.443 --> 00:58:38.110 align:middle line:84% It's a bit counterintuitive, because you 00:58:38.110 --> 00:58:41.140 align:middle line:84% would think they would want the money from the sales. 00:58:41.140 --> 00:58:43.930 align:middle line:84% But the problem is, they had to reduce the inputs. 00:58:43.930 --> 00:58:46.790 align:middle line:84% They had to scale production down. 00:58:46.790 --> 00:58:49.570 align:middle line:84% And so they have less revenue as a result. 00:58:49.570 --> 00:58:50.860 align:middle line:90% Sales are down. 00:58:50.860 --> 00:58:53.290 align:middle line:90% Inventories are up. 00:58:53.290 --> 00:58:55.420 align:middle line:84% Well, I should-- let me come back and clarify. 00:58:55.420 --> 00:59:00.430 align:middle line:84% These are households connected to the household that 00:59:00.430 --> 00:59:02.680 align:middle line:90% has experienced a shock. 00:59:02.680 --> 00:59:04.330 align:middle line:90% These guys were selling-- 00:59:04.330 --> 00:59:05.170 align:middle line:90% I said it wrong. 00:59:05.170 --> 00:59:06.310 align:middle line:90% I'm sorry. 00:59:06.310 --> 00:59:09.490 align:middle line:84% These guys were selling revenue to the household 00:59:09.490 --> 00:59:10.810 align:middle line:90% that had the shock. 00:59:10.810 --> 00:59:12.610 align:middle line:90% Now, they sell less. 00:59:12.610 --> 00:59:15.400 align:middle line:84% Likewise, because they sell less, 00:59:15.400 --> 00:59:17.020 align:middle line:90% they're accumulating inventory. 00:59:17.020 --> 00:59:19.750 align:middle line:84% And they're holding onto inventory longer. 00:59:19.750 --> 00:59:23.140 align:middle line:84% This is this inventory turnover ratio. 00:59:23.140 --> 00:59:24.310 align:middle line:90% That's a measure of-- 00:59:24.310 --> 00:59:26.770 align:middle line:84% I'm going to [? tie it-- ?] It's a measure of inefficiency. 00:59:26.770 --> 00:59:30.010 align:middle line:84% It's also negative with an adverse effect. 00:59:30.010 --> 00:59:33.250 align:middle line:84% We do this for all the shocks and do it for the large shocks. 00:59:33.250 --> 00:59:36.280 align:middle line:84% So now, we see the COVID connection, 00:59:36.280 --> 00:59:40.870 align:middle line:84% which is, a household experiences expenses associated 00:59:40.870 --> 00:59:44.620 align:middle line:84% with the illness, even if it's not a working member. 00:59:44.620 --> 00:59:47.050 align:middle line:84% How do they cover those expenses? 00:59:47.050 --> 00:59:48.370 align:middle line:90% They try to cut back. 00:59:48.370 --> 00:59:50.050 align:middle line:90% They cut back on spending. 00:59:50.050 --> 00:59:53.890 align:middle line:84% In these village economies, businesses are connected. 00:59:53.890 --> 00:59:56.170 align:middle line:84% They're buying and selling inputs from one another, 00:59:56.170 --> 00:59:57.650 align:middle line:90% and selling output. 00:59:57.650 --> 01:00:00.580 align:middle line:84% So if they have to cut back and they don't have the revenue 01:00:00.580 --> 01:00:04.060 align:middle line:84% that they had before, the people who had been buying 01:00:04.060 --> 01:00:08.410 align:middle line:84% had been selling to them no longer have the sales. 01:00:08.410 --> 01:00:11.500 align:middle line:84% Just like one business is connected to another, 01:00:11.500 --> 01:00:13.690 align:middle line:84% they all go down the supply chain, 01:00:13.690 --> 01:00:15.350 align:middle line:90% because they're connected. 01:00:15.350 --> 01:00:19.270 align:middle line:84% We had a lecture at the end on interconnections 01:00:19.270 --> 01:00:20.110 align:middle line:90% among households. 01:00:20.110 --> 01:00:21.230 align:middle line:90% We did Leontief. 01:00:21.230 --> 01:00:23.170 align:middle line:90% We did the input output matrix. 01:00:23.170 --> 01:00:26.710 align:middle line:84% I showed you Fukujima and Shima, and the effect 01:00:26.710 --> 01:00:27.970 align:middle line:90% of the earthquake there. 01:00:27.970 --> 01:00:30.940 align:middle line:84% And those were all supply chains. 01:00:30.940 --> 01:00:33.160 align:middle line:84% One sector is connected to another. 01:00:33.160 --> 01:00:34.870 align:middle line:90% One firm's connected to another. 01:00:34.870 --> 01:00:37.120 align:middle line:84% These Thai households are connected to another. 01:00:37.120 --> 01:00:39.260 align:middle line:90% And the point of this-- 01:00:39.260 --> 01:00:42.250 align:middle line:84% I guess I haven't said that-- is, yet, the closer they 01:00:42.250 --> 01:00:45.640 align:middle line:84% are to the adversely impacted household, 01:00:45.640 --> 01:00:47.177 align:middle line:90% the more they suffer. 01:00:47.177 --> 01:00:48.760 align:middle line:84% So you think networks are good things. 01:00:48.760 --> 01:00:50.230 align:middle line:84% Networks are a good thing when it 01:00:50.230 --> 01:00:52.150 align:middle line:90% comes to financial gift giving. 01:00:52.150 --> 01:00:55.360 align:middle line:84% But if gift giving doesn't cover the adverse shock, 01:00:55.360 --> 01:00:57.400 align:middle line:84% we're actually getting an amplification 01:00:57.400 --> 01:00:59.110 align:middle line:84% in this economy that's showing up 01:00:59.110 --> 01:01:03.310 align:middle line:84% in terms of lost wages and less production, and less sales. 01:01:03.310 --> 01:01:06.520 align:middle line:84% And finally, this distinction, which I've 01:01:06.520 --> 01:01:10.090 align:middle line:84% been pushing today, about aggregate and idiosyncratic 01:01:10.090 --> 01:01:11.470 align:middle line:90% shocks-- 01:01:11.470 --> 01:01:14.020 align:middle line:84% go to one of the areas, Chachoengsao, 01:01:14.020 --> 01:01:17.440 align:middle line:84% where they have fish ponds, shrimp ponds in particular. 01:01:17.440 --> 01:01:20.830 align:middle line:90% And it's pretty polluted. 01:01:20.830 --> 01:01:24.850 align:middle line:84% And they didn't have green agriculture, so to speak. 01:01:24.850 --> 01:01:27.850 align:middle line:84% And the EU put a ban on the shrimp. 01:01:27.850 --> 01:01:29.750 align:middle line:84% By the way, if you go to Walmart-- 01:01:29.750 --> 01:01:30.580 align:middle line:90% you say, villages? 01:01:30.580 --> 01:01:31.120 align:middle line:90% Who cares? 01:01:31.120 --> 01:01:34.480 align:middle line:84% Well anyway, they produce the shrimp that you buy in Walmart. 01:01:34.480 --> 01:01:38.350 align:middle line:84% But the EU put a ban on the shrimp, 01:01:38.350 --> 01:01:40.960 align:middle line:84% because they say it wasn't clean, which it wasn't. 01:01:40.960 --> 01:01:44.020 align:middle line:84% Now, the point is, most but not all households 01:01:44.020 --> 01:01:46.300 align:middle line:90% are doing those shrimp ponds. 01:01:46.300 --> 01:01:49.340 align:middle line:84% And the ban is like an aggregate shock. 01:01:49.340 --> 01:01:52.520 align:middle line:84% So we can compare the aggregate shock, 01:01:52.520 --> 01:01:56.320 align:middle line:84% which is most of the households, to the idiosyncratic illness 01:01:56.320 --> 01:01:56.890 align:middle line:90% shocks. 01:01:56.890 --> 01:02:00.070 align:middle line:84% And you can see that although gifts go up-- 01:02:00.070 --> 01:02:01.510 align:middle line:90% I already showed you that-- 01:02:01.510 --> 01:02:04.900 align:middle line:84% for the idiosyncratic shocks, including in this village, 01:02:04.900 --> 01:02:06.662 align:middle line:84% there's not that clear picture when 01:02:06.662 --> 01:02:07.870 align:middle line:90% it comes to the shrimp shock. 01:02:07.870 --> 01:02:11.380 align:middle line:84% Because it's an aggregate shock, there's not a lot of ways-- 01:02:11.380 --> 01:02:14.180 align:middle line:84% excuse me-- to reallocate that risk. 01:02:14.180 --> 01:02:16.750 align:middle line:84% And this is the associated decline 01:02:16.750 --> 01:02:20.904 align:middle line:84% in employment, which is bigger under the aggregate shock. 01:02:20.904 --> 01:02:22.600 align:middle line:90% OK, questions? 01:02:22.600 --> 01:02:25.500 align:middle line:90% 01:02:25.500 --> 01:02:26.340 align:middle line:90% OK. 01:02:26.340 --> 01:02:28.410 align:middle line:90% That's what I have for today. 01:02:28.410 --> 01:02:31.240 align:middle line:90% And we'll continue on Thursday. 01:02:31.240 --> 01:02:33.000 align:middle line:90% Thank you for coming today. 01:02:33.000 --> 01:02:34.970 align:middle line:90% Talk to you soon. 01:02:34.970 --> 01:02:45.000 align:middle line:90%