1 00:00:00,090 --> 00:00:02,490 The following content is provided under a Creative 2 00:00:02,490 --> 00:00:04,059 Commons license. 3 00:00:04,059 --> 00:00:06,330 Your support will help MIT OpenCourseWare 4 00:00:06,330 --> 00:00:10,720 continue to offer high quality educational resources for free. 5 00:00:10,720 --> 00:00:13,350 To make a donation or view additional materials 6 00:00:13,350 --> 00:00:17,280 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,280 --> 00:00:18,480 at ocw.mit.edu. 8 00:00:27,687 --> 00:00:32,070 PROFESSOR: So we had a big lecture last time 9 00:00:32,070 --> 00:00:39,720 on perfect insurance and implications for targeting, 10 00:00:39,720 --> 00:00:44,290 and policy, and evaluations. 11 00:00:44,290 --> 00:00:46,420 There is a series of lectures now 12 00:00:46,420 --> 00:00:52,120 that have to do with working off of that basic risk sharing 13 00:00:52,120 --> 00:00:53,500 framework. 14 00:00:53,500 --> 00:00:56,770 Today we're going to talk about the implications for what we 15 00:00:56,770 --> 00:00:59,290 should see in rates of return. 16 00:00:59,290 --> 00:01:01,420 And then next class, we're going to talk 17 00:01:01,420 --> 00:01:09,460 about alternative models of what we might see in the consumption 18 00:01:09,460 --> 00:01:12,118 data. 19 00:01:12,118 --> 00:01:13,660 And then the lecture after that we're 20 00:01:13,660 --> 00:01:17,260 going to return to the perfect market model 21 00:01:17,260 --> 00:01:19,910 and think about labor supply. 22 00:01:19,910 --> 00:01:22,400 And then finally, we're going to get to explicit obstacles 23 00:01:22,400 --> 00:01:23,270 to trade. 24 00:01:23,270 --> 00:01:26,810 I must say that rather than put off the obstacles, 25 00:01:26,810 --> 00:01:29,630 we've been noting and even talking 26 00:01:29,630 --> 00:01:32,780 about alternative models along the way. 27 00:01:35,660 --> 00:01:37,490 Because these benchmarks are sometimes 28 00:01:37,490 --> 00:01:40,010 rejected and you're going to see that a bit today as well. 29 00:01:42,550 --> 00:01:47,940 So this perfect market standard within villages 30 00:01:47,940 --> 00:01:51,570 that has to do with relatives and friends 31 00:01:51,570 --> 00:01:54,210 interacting with each other has implications 32 00:01:54,210 --> 00:01:56,520 for how you adjust for risk. 33 00:01:56,520 --> 00:01:59,860 And we're going to do that with a vengeance. 34 00:01:59,860 --> 00:02:02,920 But it will turn out that it does-- 35 00:02:02,920 --> 00:02:05,530 that framework allows us to distinguish aggregate 36 00:02:05,530 --> 00:02:07,790 from idiosyncratic risk. 37 00:02:07,790 --> 00:02:11,020 And the idiosyncratic risk should not 38 00:02:11,020 --> 00:02:16,800 be showing up in rates of return, but it does at the end. 39 00:02:19,380 --> 00:02:22,050 And then I'll say a few words about what else 40 00:02:22,050 --> 00:02:24,930 we know about the tie data in terms 41 00:02:24,930 --> 00:02:28,440 of the decomposition of volatility 42 00:02:28,440 --> 00:02:31,710 linking back to a paper we saw the very 43 00:02:31,710 --> 00:02:39,560 first lecture on quantifying the growth rates by sector. 44 00:02:39,560 --> 00:02:42,220 But we're going to do it by wealth. 45 00:02:42,220 --> 00:02:45,490 At least I'll say a few words about it. 46 00:02:45,490 --> 00:02:51,360 And then I'm going to toward the end of the class sort of return 47 00:02:51,360 --> 00:02:53,880 to this idea that either things aren't 48 00:02:53,880 --> 00:02:57,080 perfect and/or people are making mistakes. 49 00:02:57,080 --> 00:03:02,700 And we'll do that in some unusual contexts, 50 00:03:02,700 --> 00:03:05,550 one that has to do with data from Sweden, 51 00:03:05,550 --> 00:03:07,860 an unusually rich database from Sweden, 52 00:03:07,860 --> 00:03:12,750 and another that has to do with the US airlines. 53 00:03:12,750 --> 00:03:14,850 But the basic frameworks that are getting 54 00:03:14,850 --> 00:03:18,330 used, whether in the developing context, or Sweden, 55 00:03:18,330 --> 00:03:22,030 or US airlines, are basically all the same. 56 00:03:22,030 --> 00:03:23,970 So there is a strong complementarity 57 00:03:23,970 --> 00:03:26,020 across these papers. 58 00:03:26,020 --> 00:03:31,800 This paper with Chris has been in the works for a while. 59 00:03:31,800 --> 00:03:36,370 But we are now able to use you know 13 years of monthly data. 60 00:03:36,370 --> 00:03:41,890 So we are doing better than before. 61 00:03:41,890 --> 00:03:46,230 So we want to talk about risk and return of productive assets 62 00:03:46,230 --> 00:03:47,520 in developing countries. 63 00:03:50,390 --> 00:03:53,300 We already looked at some of the slides showing 64 00:03:53,300 --> 00:03:57,530 how rates of return differ a lot across different households, 65 00:03:57,530 --> 00:04:01,750 differ in large part by wealth and how 66 00:04:01,750 --> 00:04:06,070 poor people have relatively high rates of return. 67 00:04:06,070 --> 00:04:07,090 And they're saving. 68 00:04:07,090 --> 00:04:11,050 And they're accumulating assets and so on. 69 00:04:15,560 --> 00:04:19,160 Another way people look at rates of return is to say, 70 00:04:19,160 --> 00:04:24,540 you know, well, some people are more talented than others. 71 00:04:24,540 --> 00:04:26,840 So if we look at rates of return, 72 00:04:26,840 --> 00:04:30,380 we get some notion of underlying productivity 73 00:04:30,380 --> 00:04:32,900 as in TFP and so on. 74 00:04:32,900 --> 00:04:35,960 We've had many lectures about TFP 75 00:04:35,960 --> 00:04:39,500 and coefficients in front multiplying 76 00:04:39,500 --> 00:04:42,890 in front of production functions and so on. 77 00:04:42,890 --> 00:04:44,750 But correct me if I'm wrong. 78 00:04:44,750 --> 00:04:50,390 Nowhere in any of that stuff did we ever adjust for risk. 79 00:04:50,390 --> 00:04:54,220 So what's the intuition for adjusting for risk? 80 00:04:54,220 --> 00:05:00,670 Well, if you want to look at compensating differentials, 81 00:05:00,670 --> 00:05:03,370 the higher the risk of a project, the higher the rate 82 00:05:03,370 --> 00:05:05,020 of return ought to be. 83 00:05:05,020 --> 00:05:08,300 Other things equal to compensate for that risk. 84 00:05:08,300 --> 00:05:11,440 You know, like junk bonds have higher yields 85 00:05:11,440 --> 00:05:14,360 and so on and so forth. 86 00:05:14,360 --> 00:05:16,720 So maybe these guys with seemingly very high rates 87 00:05:16,720 --> 00:05:21,370 of return actually are just doing risky things. 88 00:05:21,370 --> 00:05:24,720 And indeed, if enough of them do risky things and on average 89 00:05:24,720 --> 00:05:26,240 some of them succeed and maybe that 90 00:05:26,240 --> 00:05:27,960 would generate the high rate of return. 91 00:05:27,960 --> 00:05:32,655 So we really need to think about how to measure the risk. 92 00:05:37,620 --> 00:05:39,450 And we're going to rely on finance theory. 93 00:05:39,450 --> 00:05:46,080 But I'll be very careful to sort of build 94 00:05:46,080 --> 00:05:48,240 into it the economic models. 95 00:05:48,240 --> 00:05:52,110 You may learn a little bit of finance jargon along the way. 96 00:05:52,110 --> 00:05:54,180 But I'm not going to start with that. 97 00:05:54,180 --> 00:05:56,850 I'll get you up to speed. 98 00:05:56,850 --> 00:06:00,090 It's really not that hard when you look at the equations. 99 00:06:05,200 --> 00:06:08,030 OK, so what do we find? 100 00:06:13,220 --> 00:06:17,905 We do find that higher risk is associated 101 00:06:17,905 --> 00:06:19,030 with higher rate of return. 102 00:06:21,670 --> 00:06:24,070 But the risk that we're going to be concentrating on 103 00:06:24,070 --> 00:06:26,860 in the model is not idiosyncratic risk. 104 00:06:26,860 --> 00:06:31,110 It's village level risk. 105 00:06:31,110 --> 00:06:35,540 So when you think about households together pooling 106 00:06:35,540 --> 00:06:39,800 resources, as in a risk sharing syndicate, 107 00:06:39,800 --> 00:06:43,100 they would care about say aggregate consumption should 108 00:06:43,100 --> 00:06:45,440 move individual consumption. 109 00:06:45,440 --> 00:06:48,470 And idiosyncratic income shock should not 110 00:06:48,470 --> 00:06:51,270 have an influence on consumption. 111 00:06:51,270 --> 00:06:53,315 So when is something really valuable? 112 00:06:55,840 --> 00:06:57,650 A project is valuable when it has 113 00:06:57,650 --> 00:07:01,070 a return, which is negatively correlated with the village 114 00:07:01,070 --> 00:07:02,330 average return. 115 00:07:02,330 --> 00:07:05,930 So that the resources come in when you need it. 116 00:07:05,930 --> 00:07:09,890 So the quote market, the way the finance guys 117 00:07:09,890 --> 00:07:11,615 would use it, for us is the village. 118 00:07:17,410 --> 00:07:24,110 And indeed, the more a household has a return on its projects 119 00:07:24,110 --> 00:07:27,410 that are correlated with the village average return, 120 00:07:27,410 --> 00:07:31,850 the higher is going to be the measured expected or average 121 00:07:31,850 --> 00:07:33,505 return on that household's assets. 122 00:07:36,170 --> 00:07:40,140 And we have all kinds of ways of adjusting for human capital 123 00:07:40,140 --> 00:07:43,990 and so on, which I'll get into. 124 00:07:43,990 --> 00:07:45,790 As I said though, it does in the end 125 00:07:45,790 --> 00:07:48,940 leave some idiosyncratic risk. 126 00:07:48,940 --> 00:07:51,865 And that's also generating higher expected returns. 127 00:07:56,070 --> 00:08:00,260 Aggregate and idiosyncratic risk is negatively 128 00:08:00,260 --> 00:08:02,940 correlated with age. 129 00:08:02,940 --> 00:08:07,250 So the older a household head basically, 130 00:08:07,250 --> 00:08:12,130 the quote, less risky things that they're doing. 131 00:08:12,130 --> 00:08:15,020 But both in the idiosyncratic and aggregate sense 132 00:08:15,020 --> 00:08:19,300 they tend to do things which are less correlated with a village 133 00:08:19,300 --> 00:08:22,630 average. 134 00:08:22,630 --> 00:08:24,040 It's negative with wealth. 135 00:08:24,040 --> 00:08:32,260 Meaning the lower is wealth, the higher both the idiosyncratic 136 00:08:32,260 --> 00:08:33,460 and aggregate. 137 00:08:33,460 --> 00:08:36,970 So this gets us into poor people and how 138 00:08:36,970 --> 00:08:39,549 exposed are they to risk? 139 00:08:39,549 --> 00:08:43,610 We've seen a bit of that already in risk and return 140 00:08:43,610 --> 00:08:47,120 in village India that there are some landless laborers 141 00:08:47,120 --> 00:08:50,960 and labor income that tends to move consumption around more. 142 00:08:50,960 --> 00:08:54,950 This is a bit different way of measuring it in the sense 143 00:08:54,950 --> 00:08:58,160 that we're not going to look so much at the consumption data. 144 00:08:58,160 --> 00:09:01,760 We're going to assume everyone is in this risk sharing 145 00:09:01,760 --> 00:09:02,360 syndicate. 146 00:09:02,360 --> 00:09:04,040 But we turn around and see what is 147 00:09:04,040 --> 00:09:06,360 reflected in rates of return. 148 00:09:09,120 --> 00:09:11,580 And in particular, relatively poor people 149 00:09:11,580 --> 00:09:14,680 are more exposed to risk. 150 00:09:14,680 --> 00:09:16,950 But it's not just their own idiosyncratic risk. 151 00:09:16,950 --> 00:09:18,930 It's the aggregate risk. 152 00:09:31,540 --> 00:09:36,390 And there is a little bit of role for education. 153 00:09:36,390 --> 00:09:37,940 But it's kind of problematic. 154 00:09:37,940 --> 00:09:40,370 And there's some selection bias that I might 155 00:09:40,370 --> 00:09:41,600 talk about when we get there. 156 00:09:44,240 --> 00:09:48,080 And then this is maybe the punch line. 157 00:09:48,080 --> 00:09:50,700 If you want to think about talent, 158 00:09:50,700 --> 00:09:55,510 then you want to adjust for all sources of risk. 159 00:09:55,510 --> 00:09:58,200 And when we do that, we find who are seemingly 160 00:09:58,200 --> 00:10:01,260 the really productive people in the village. 161 00:10:01,260 --> 00:10:03,870 And all of a sudden, it's the higher wealth people 162 00:10:03,870 --> 00:10:07,440 who have the higher risk adjusted rate of return 163 00:10:07,440 --> 00:10:11,050 and female headed households. 164 00:10:11,050 --> 00:10:14,410 So relatively wealthy females actually 165 00:10:14,410 --> 00:10:17,690 dominate in terms of getting a higher rate of return. 166 00:10:17,690 --> 00:10:20,330 So we have a basic model. 167 00:10:20,330 --> 00:10:27,220 They're going to be j households and l production activities. 168 00:10:27,220 --> 00:10:32,290 Each activity utilizes capital as an input. 169 00:10:32,290 --> 00:10:36,700 And let's simplify and say all these technologies 170 00:10:36,700 --> 00:10:39,790 produce the same thing, consumption goods. 171 00:10:39,790 --> 00:10:43,960 And we'll simplify further and assume all the technologies are 172 00:10:43,960 --> 00:10:45,080 linear. 173 00:10:45,080 --> 00:10:45,785 Yeah, Matt. 174 00:10:45,785 --> 00:10:47,160 AUDIENCE: Can I just actually ask 175 00:10:47,160 --> 00:10:48,868 a couple of things about previous slides? 176 00:10:48,868 --> 00:10:53,400 So are we assuming there's no sharing between them? 177 00:10:57,450 --> 00:10:59,370 PROFESSOR: So we are again, going 178 00:10:59,370 --> 00:11:05,090 to take a stand on our baseline. 179 00:11:05,090 --> 00:11:07,180 And it's actually going to be all four 180 00:11:07,180 --> 00:11:10,630 villages in a province, not just a single village. 181 00:11:10,630 --> 00:11:13,370 But then we go back and check for villages individually. 182 00:11:13,370 --> 00:11:18,160 And we actually go back further and look one network at a time. 183 00:11:18,160 --> 00:11:19,960 The basic results don't change. 184 00:11:19,960 --> 00:11:21,360 AUDIENCE: OK. 185 00:11:21,360 --> 00:11:24,580 Another thing which I don't really understand 186 00:11:24,580 --> 00:11:28,850 is when we have this result that returns 187 00:11:28,850 --> 00:11:31,155 risk adjusted returns are lower for those 188 00:11:31,155 --> 00:11:33,430 with lower [INAUDIBLE]. 189 00:11:33,430 --> 00:11:36,410 How do we think about in terms of one story's 190 00:11:36,410 --> 00:11:38,370 that the people with low initial wealth, 191 00:11:38,370 --> 00:11:41,250 they're very productive people amongst them. 192 00:11:41,250 --> 00:11:44,680 But [INAUDIBLE] get sufficient size of their business. 193 00:11:44,680 --> 00:11:48,430 So their marginal returns might be really high. 194 00:11:48,430 --> 00:11:50,580 And the average returns as well, depending on-- 195 00:11:50,580 --> 00:11:52,080 PROFESSOR: Yeah, so this paper isn't 196 00:11:52,080 --> 00:11:53,288 going to help much with that. 197 00:11:53,288 --> 00:11:55,570 Because we're going to assume linear technologies. 198 00:11:55,570 --> 00:11:58,058 And margins are going to be equal to averages. 199 00:11:58,058 --> 00:11:58,600 AUDIENCE: OK. 200 00:12:04,840 --> 00:12:06,670 PROFESSOR: And more generally, you know, 201 00:12:06,670 --> 00:12:08,860 wealth is clearly an endogenous variable. 202 00:12:08,860 --> 00:12:12,710 So we're not saying high wealth is causing people to have-- 203 00:12:12,710 --> 00:12:15,010 I mean, it's more likely the other way around. 204 00:12:15,010 --> 00:12:17,530 But yeah, we've gone through a series of models 205 00:12:17,530 --> 00:12:20,080 where wealth helps overcome constraints. 206 00:12:20,080 --> 00:12:23,760 The first four lectures were like that. 207 00:12:23,760 --> 00:12:27,330 So in a way, this is another fact finding mission. 208 00:12:27,330 --> 00:12:29,040 But it's not just data summaries. 209 00:12:29,040 --> 00:12:32,220 It's looking at the data through the lens of the model. 210 00:12:32,220 --> 00:12:38,130 And you have to make some assumptions to do that. 211 00:12:38,130 --> 00:12:44,380 OK, so we have j production activities. 212 00:12:44,380 --> 00:12:46,030 We're going to start the economy off 213 00:12:46,030 --> 00:12:48,880 with some aggregate wealth, w. 214 00:12:48,880 --> 00:12:53,440 And those are basically the projects, the assets, 215 00:12:53,440 --> 00:12:56,970 or the trees if you like. 216 00:12:56,970 --> 00:12:58,980 And those projects are going to have 217 00:12:58,980 --> 00:13:02,160 rates of return, the fruit. 218 00:13:02,160 --> 00:13:04,110 So at the beginning of the period, 219 00:13:04,110 --> 00:13:07,470 the total sort of wealth available 220 00:13:07,470 --> 00:13:09,570 is the sum of the trees and the fruit. 221 00:13:09,570 --> 00:13:14,040 So this is a standard kind of solo reversible capital 222 00:13:14,040 --> 00:13:18,630 assumption that the assets can basically be sold. 223 00:13:18,630 --> 00:13:20,100 There's no irreversibility. 224 00:13:20,100 --> 00:13:22,800 You can convert them into consumption if you choose to. 225 00:13:26,060 --> 00:13:29,360 So we're going to have a social planner 226 00:13:29,360 --> 00:13:33,560 sort of directing the show, which 227 00:13:33,560 --> 00:13:38,330 is not to say this might not decentralize in some way. 228 00:13:38,330 --> 00:13:42,240 That said, I want to emphasize it's not 229 00:13:42,240 --> 00:13:47,130 like finance in the sense that people participate on the New 230 00:13:47,130 --> 00:13:49,440 York Stock Exchange or the financial markets, 231 00:13:49,440 --> 00:13:51,750 and they're buying and selling stocks. 232 00:13:51,750 --> 00:13:54,630 We don't even have the data of all these capital goods. 233 00:13:54,630 --> 00:13:57,850 That's not the mechanism. 234 00:13:57,850 --> 00:14:02,040 This planner's problem may be decentralized in some way. 235 00:14:02,040 --> 00:14:03,960 But it's just much more straightforward, 236 00:14:03,960 --> 00:14:05,910 just like when we did the risk sharing 237 00:14:05,910 --> 00:14:07,950 stuff not to necessarily be forced 238 00:14:07,950 --> 00:14:10,920 into some interpretation. 239 00:14:10,920 --> 00:14:13,860 We're just going to solve the planning problem directly. 240 00:14:13,860 --> 00:14:19,470 So somehow or other, a household is assigned. 241 00:14:19,470 --> 00:14:24,320 Household j is assigned capital and is operating project type 242 00:14:24,320 --> 00:14:25,360 i. 243 00:14:25,360 --> 00:14:28,340 And this is the net rate of return. 244 00:14:28,340 --> 00:14:31,780 Notice that we allow individuals to vary 245 00:14:31,780 --> 00:14:33,640 in their rates of return. 246 00:14:33,640 --> 00:14:35,860 The planner could take advantage if it 247 00:14:35,860 --> 00:14:38,740 knows that some people are better than other people 248 00:14:38,740 --> 00:14:39,620 at doing things. 249 00:14:39,620 --> 00:14:41,680 So we're not just getting rid of talent. 250 00:14:41,680 --> 00:14:47,600 We're embedding it at some level in these rates of return. 251 00:14:47,600 --> 00:14:57,203 And then they have basically the tree and the fruit. 252 00:14:57,203 --> 00:14:58,370 That's their starting point. 253 00:14:58,370 --> 00:15:01,730 And then they get taxes and transfers, these Taus. 254 00:15:01,730 --> 00:15:05,210 I mean, here it's written positive as if it's incoming 255 00:15:05,210 --> 00:15:08,180 and adds to the resources of the household. 256 00:15:08,180 --> 00:15:12,350 But in fact, like a risk sharing group 257 00:15:12,350 --> 00:15:18,480 you can give and get and contribute to the social fund. 258 00:15:18,480 --> 00:15:24,380 So the planning problem is to maximize discounted 259 00:15:24,380 --> 00:15:26,390 weighted expected utility. 260 00:15:26,390 --> 00:15:29,300 So these Lambda j weights are the pareto weights 261 00:15:29,300 --> 00:15:32,090 for households type j. 262 00:15:32,090 --> 00:15:35,780 They're not necessarily the same over all the households. 263 00:15:35,780 --> 00:15:39,860 And this whole term here is the utility function, 264 00:15:39,860 --> 00:15:46,660 which as noted, is just the return on the trees 265 00:15:46,660 --> 00:15:50,240 plus these transfers. 266 00:15:50,240 --> 00:15:58,240 And then discounted expected return for tomorrow 267 00:15:58,240 --> 00:15:59,900 I usually write as Beta. 268 00:15:59,900 --> 00:16:04,160 But anyway, it's an intertemporal discount rate. 269 00:16:04,160 --> 00:16:06,640 And so you have the value function today 270 00:16:06,640 --> 00:16:12,140 given wealth today and expected value of wealth tomorrow w 271 00:16:12,140 --> 00:16:13,550 prime. 272 00:16:13,550 --> 00:16:17,170 And wealth today can be allocated 273 00:16:17,170 --> 00:16:20,830 into basically consumption. 274 00:16:20,830 --> 00:16:23,770 So this is just summing over not only 275 00:16:23,770 --> 00:16:27,640 over all projects for household j, but all households j. 276 00:16:27,640 --> 00:16:31,270 So this is again, just consumption. 277 00:16:31,270 --> 00:16:35,620 So consumption plus capital allocated tomorrow 278 00:16:35,620 --> 00:16:41,380 equals total wealth, pretty standard kind of growth market 279 00:16:41,380 --> 00:16:42,442 structure. 280 00:16:46,380 --> 00:16:50,670 And what is total wealth of the economy? 281 00:16:50,670 --> 00:16:53,580 It's basically not only the fruit of the trees, 282 00:16:53,580 --> 00:16:54,990 but the trees themselves. 283 00:16:57,970 --> 00:17:00,470 So you can take this expression and put it on the right hand 284 00:17:00,470 --> 00:17:02,870 side if you want. 285 00:17:02,870 --> 00:17:04,609 Because they have pre-existing capital. 286 00:17:04,609 --> 00:17:06,710 They have the rate of return on that. 287 00:17:06,710 --> 00:17:08,540 You've got total resources available. 288 00:17:08,540 --> 00:17:10,940 You can allocate it to consumption 289 00:17:10,940 --> 00:17:14,950 or set some aside to continue the capital stock for tomorrow. 290 00:17:20,160 --> 00:17:22,380 And so we just substitute in the expressions 291 00:17:22,380 --> 00:17:31,330 for tomorrow's wealth and today's wealth for that matter. 292 00:17:31,330 --> 00:17:35,280 And then this odd looking thing here 293 00:17:35,280 --> 00:17:37,980 is just a substitution from the previous equation. 294 00:17:37,980 --> 00:17:41,640 But there's a common term on both sides. 295 00:17:41,640 --> 00:17:43,110 That's why it looks kind of weird. 296 00:17:43,110 --> 00:17:48,600 Because this is really 1 plus r times k over here. 297 00:17:48,600 --> 00:17:51,090 But there's also a 1 plus r times k here. 298 00:17:51,090 --> 00:17:53,580 And the rk things are canceling out. 299 00:17:53,580 --> 00:17:58,680 So this is just straightforward algebra. 300 00:17:58,680 --> 00:18:01,560 So we're going to maximize this thing 301 00:18:01,560 --> 00:18:06,120 by choosing the transfer as Tau j and the assignments 302 00:18:06,120 --> 00:18:07,560 of tomorrow's capital stock. 303 00:18:10,512 --> 00:18:12,972 AUDIENCE: Was there supposed to be uncertainty? 304 00:18:12,972 --> 00:18:15,440 It's just their return on capital? 305 00:18:15,440 --> 00:18:17,930 PROFESSOR: Yeah. 306 00:18:17,930 --> 00:18:21,226 Yeah, there's no preference shocks here. 307 00:18:21,226 --> 00:18:23,138 AUDIENCE: What's the process [INAUDIBLE]?? 308 00:18:23,138 --> 00:18:24,530 [INAUDIBLE] 309 00:18:24,530 --> 00:18:26,612 PROFESSOR: Don't have to specify yet. 310 00:18:26,612 --> 00:18:28,090 AUDIENCE: OK. 311 00:18:28,090 --> 00:18:30,290 PROFESSOR: That's probably a good thing. 312 00:18:30,290 --> 00:18:36,800 OK, so if you looked, we've actually seen this before. 313 00:18:36,800 --> 00:18:40,700 But it's explicit here again. 314 00:18:40,700 --> 00:18:43,970 Consumption and capital are interrelated through 315 00:18:43,970 --> 00:18:45,170 this resource constraint. 316 00:18:45,170 --> 00:18:48,890 So when you take a derivative to maximize with respect 317 00:18:48,890 --> 00:18:52,250 to the transfers, you'll pick up a derivative 318 00:18:52,250 --> 00:18:54,560 in the utility function. 319 00:18:54,560 --> 00:18:57,590 And the sum of total transfers is down here 320 00:18:57,590 --> 00:18:58,750 in the resource constraint. 321 00:18:58,750 --> 00:19:01,150 And there's a Lagrange multiplier in front of it, 322 00:19:01,150 --> 00:19:01,910 right? 323 00:19:01,910 --> 00:19:03,650 So you're going to get margin weighted, 324 00:19:03,650 --> 00:19:06,110 margin utility of consumption today 325 00:19:06,110 --> 00:19:08,265 equal to a Lagrange multiplier. 326 00:19:08,265 --> 00:19:09,890 And when you differentiate with respect 327 00:19:09,890 --> 00:19:15,120 to the choice of tomorrow's capital stock k prime, 328 00:19:15,120 --> 00:19:17,280 well, that's going to enter in tomorrow's value. 329 00:19:17,280 --> 00:19:20,940 So you'll have a derivative of the value function 330 00:19:20,940 --> 00:19:25,690 and then internally this sort of rate of return. 331 00:19:25,690 --> 00:19:32,540 And this prime thing is also entering into the same resource 332 00:19:32,540 --> 00:19:33,040 constraint. 333 00:19:33,040 --> 00:19:34,707 So you're going to get the same Lagrange 334 00:19:34,707 --> 00:19:39,140 multiplier as on consumption. 335 00:19:39,140 --> 00:19:43,480 So here is a summary of those words. 336 00:19:43,480 --> 00:19:46,060 Weighted margin utilities are equated 337 00:19:46,060 --> 00:19:50,290 across all the households to a common contemporaneous Lagrange 338 00:19:50,290 --> 00:19:52,030 multiplier. 339 00:19:52,030 --> 00:19:55,930 And then this is kind of a-- 340 00:19:55,930 --> 00:20:01,450 it's an exactly Euler equation for capital accumulation. 341 00:20:01,450 --> 00:20:04,510 This is the price of capital today. 342 00:20:04,510 --> 00:20:06,410 It's how much consumption you're giving up. 343 00:20:06,410 --> 00:20:09,340 And this is expected discounted value 344 00:20:09,340 --> 00:20:11,350 of having capital tomorrow. 345 00:20:11,350 --> 00:20:13,810 It's the derivative of the value function 346 00:20:13,810 --> 00:20:16,180 times the rate of return, depending 347 00:20:16,180 --> 00:20:19,450 on which project i and J is being chosen. 348 00:20:19,450 --> 00:20:25,550 Note that this is for every project, every capital stock 349 00:20:25,550 --> 00:20:28,220 of type i for household j. 350 00:20:31,426 --> 00:20:34,850 Now, so far I've talked about real assets. 351 00:20:34,850 --> 00:20:37,790 But it's not too hard. 352 00:20:37,790 --> 00:20:41,330 And we do actually allow external borrowing. 353 00:20:41,330 --> 00:20:45,710 You could imagine a village is able to borrow in land. 354 00:20:45,710 --> 00:20:48,590 Or the whole set of four villages 355 00:20:48,590 --> 00:20:52,260 have some relationship with the rest of the external economy. 356 00:20:52,260 --> 00:20:56,040 That still leaves this sub problem. 357 00:20:56,040 --> 00:20:59,030 I mean, throwing these things in might 358 00:20:59,030 --> 00:21:01,370 deliver some extra conditions that we're ignoring. 359 00:21:01,370 --> 00:21:03,787 But what we're doing is not inconsistent with having 360 00:21:03,787 --> 00:21:04,370 this equation. 361 00:21:07,880 --> 00:21:14,330 All right, so if you just take this one 362 00:21:14,330 --> 00:21:21,245 and divide both sides through by Mu, you get this. 363 00:21:27,410 --> 00:21:29,710 And then you take the expectation operator 364 00:21:29,710 --> 00:21:31,690 in front of everything, including Mu, 365 00:21:31,690 --> 00:21:36,470 even though it's not random from the point of day t. 366 00:21:36,470 --> 00:21:41,510 And then you can rewrite this guy here 367 00:21:41,510 --> 00:21:46,040 as something called m or m prime, since in effect it's 368 00:21:46,040 --> 00:21:47,840 for tomorrow. 369 00:21:47,840 --> 00:21:55,520 And this r prime ij is basically capital R is little r. 370 00:21:55,520 --> 00:21:58,040 One plus r is sort of the gross rate of return. 371 00:22:00,910 --> 00:22:05,550 So this is hopefully not mysterious. 372 00:22:05,550 --> 00:22:09,000 It's just basically a relabeling of variables. 373 00:22:09,000 --> 00:22:11,930 And it's like the Euler equation. 374 00:22:11,930 --> 00:22:14,720 But if you want to impress your friends 375 00:22:14,720 --> 00:22:17,510 and bewilder your enemies, you call this thing 376 00:22:17,510 --> 00:22:21,580 the stochastic discount factor. 377 00:22:21,580 --> 00:22:25,860 But all it is is the way society as a whole 378 00:22:25,860 --> 00:22:27,360 is discounting the future. 379 00:22:27,360 --> 00:22:33,310 It's tomorrow's sort of shadow price of resources relative 380 00:22:33,310 --> 00:22:35,040 to today's. 381 00:22:35,040 --> 00:22:37,800 So you're discounting tomorrow. 382 00:22:37,800 --> 00:22:39,960 And it's random. 383 00:22:39,960 --> 00:22:41,820 Because these rates of return are random. 384 00:22:41,820 --> 00:22:45,090 And so the amount of resources available in the economy 385 00:22:45,090 --> 00:22:46,290 is likely random. 386 00:22:46,290 --> 00:22:47,490 So it's stochastic. 387 00:22:53,160 --> 00:22:55,260 There's a danger in talking to someone 388 00:22:55,260 --> 00:22:57,060 about stochastic discount factors. 389 00:22:57,060 --> 00:23:00,980 Because the conversation will keep going. 390 00:23:00,980 --> 00:23:03,720 And you may learn more or get bewildered. 391 00:23:03,720 --> 00:23:07,230 But anyway, as promised, we'll keep track of this. 392 00:23:13,690 --> 00:23:18,540 So it's true for all households, all sectors. 393 00:23:18,540 --> 00:23:22,427 And the finance jargon is we just 394 00:23:22,427 --> 00:23:24,010 looked at something called the pricing 395 00:23:24,010 --> 00:23:27,850 equation in the consumption based asset pricing world. 396 00:23:27,850 --> 00:23:30,850 But for us it's just an Euler equation holding 397 00:23:30,850 --> 00:23:34,300 at say the village or let's call it township level. 398 00:23:38,600 --> 00:23:42,740 Another thing you may or may not know or remember from finance 399 00:23:42,740 --> 00:23:46,280 is you can take assets and bundle them. 400 00:23:46,280 --> 00:23:48,110 So you can have a particular asset 401 00:23:48,110 --> 00:23:51,410 held by a particular household, a project. 402 00:23:51,410 --> 00:23:54,650 Or you could take a collection of assets. 403 00:23:54,650 --> 00:23:58,670 That Euler equation has to hold for any asset individually 404 00:23:58,670 --> 00:24:00,320 and all assets collectively. 405 00:24:00,320 --> 00:24:03,890 You can bundle, package, rebundle anyway you want. 406 00:24:03,890 --> 00:24:07,140 And anything that's actually held-- 407 00:24:07,140 --> 00:24:12,960 by the way, there's sort of out of equilibrium projects 408 00:24:12,960 --> 00:24:14,850 we're not seeing. 409 00:24:14,850 --> 00:24:19,290 They wouldn't satisfy the Euler equation. 410 00:24:19,290 --> 00:24:22,170 They have a low rate of return relative to the other ones. 411 00:24:22,170 --> 00:24:24,060 So we're only seeing these equilibrium ones 412 00:24:24,060 --> 00:24:26,310 that the households actually hold. 413 00:24:26,310 --> 00:24:30,000 And of course, we're looking at the data at what they actually 414 00:24:30,000 --> 00:24:32,530 hold. 415 00:24:32,530 --> 00:24:35,630 I'm mentioning this bundling because-- 416 00:24:35,630 --> 00:24:38,070 and you'll see it again. 417 00:24:38,070 --> 00:24:41,790 But we might as well get our minds around it here. 418 00:24:41,790 --> 00:24:45,030 We are going to look at a household's rate of return. 419 00:24:45,030 --> 00:24:47,700 And typical households, as you know, you've already seen this, 420 00:24:47,700 --> 00:24:50,610 are doing more than one thing. 421 00:24:50,610 --> 00:24:54,240 Some of the incoming money is from labor supply. 422 00:24:54,240 --> 00:24:56,550 They have crops, maybe multiple crops. 423 00:24:56,550 --> 00:25:01,800 Some of them have both that and a business and so on. 424 00:25:01,800 --> 00:25:06,540 We try very hard to assign these assets individually 425 00:25:06,540 --> 00:25:08,340 to particular activities. 426 00:25:08,340 --> 00:25:09,660 But it's kind of treacherous. 427 00:25:09,660 --> 00:25:11,700 And we're likely to make mistakes. 428 00:25:11,700 --> 00:25:13,800 What do you do with a pickup truck for example? 429 00:25:13,800 --> 00:25:16,260 Is that just used in farming? 430 00:25:16,260 --> 00:25:17,860 Or they're going to the bank. 431 00:25:17,860 --> 00:25:20,070 They're taking the kids to school. 432 00:25:20,070 --> 00:25:22,770 And so rather than face all of that 433 00:25:22,770 --> 00:25:26,350 we just aggregate up over all the activities 434 00:25:26,350 --> 00:25:29,460 any particular household is doing and call that 435 00:25:29,460 --> 00:25:30,750 a collection of assets. 436 00:25:30,750 --> 00:25:34,460 And the Euler equation should apply. 437 00:25:34,460 --> 00:25:36,330 Now, remember a little bit of your sort 438 00:25:36,330 --> 00:25:44,670 of econometrics with means and variances or easy mistakes 439 00:25:44,670 --> 00:25:45,810 to make. 440 00:25:45,810 --> 00:25:48,000 The expectation of two random variables 441 00:25:48,000 --> 00:25:53,250 is not just the product of the expectations. 442 00:25:53,250 --> 00:25:56,540 You've got to adjust for the covariance, 443 00:25:56,540 --> 00:25:59,180 unless this happens to be zero. 444 00:25:59,180 --> 00:26:02,270 But this covariance is going to be crucial for us. 445 00:26:02,270 --> 00:26:07,700 Because you can see already it's the covariance between dare 446 00:26:07,700 --> 00:26:10,010 I say it, the stochastic discount factor, 447 00:26:10,010 --> 00:26:14,060 which reflects the community's relative valuation of resources 448 00:26:14,060 --> 00:26:20,390 and the particular return on project i held by household j. 449 00:26:20,390 --> 00:26:27,460 So since we already had this equal to 1 as the Euler 450 00:26:27,460 --> 00:26:30,820 equation, right? 451 00:26:30,820 --> 00:26:36,190 So now we just substitute this stuff into here. 452 00:26:36,190 --> 00:26:38,130 And we get this. 453 00:26:38,130 --> 00:26:42,690 And you could basically divide through by the expectation 454 00:26:42,690 --> 00:26:45,450 of m prime. 455 00:26:45,450 --> 00:26:49,470 You're going to get 1 over that here, get rid of it here. 456 00:26:49,470 --> 00:26:53,010 Get the covariance divided by it here. 457 00:26:53,010 --> 00:26:55,050 And then you divide and multiply, 458 00:26:55,050 --> 00:26:57,810 which doesn't do any harm, by the variance 459 00:26:57,810 --> 00:27:01,800 of m prime and rearrange terms. 460 00:27:01,800 --> 00:27:06,100 So you get this thing. 461 00:27:06,100 --> 00:27:08,180 So we're finally arriving at something 462 00:27:08,180 --> 00:27:14,520 close to what we want, which is the expected rate of return, 463 00:27:14,520 --> 00:27:15,980 which is going to be in the data, 464 00:27:15,980 --> 00:27:19,980 the average return for household j over all the time periods. 465 00:27:19,980 --> 00:27:20,480 Not quite. 466 00:27:23,520 --> 00:27:25,920 It sort of looks like a linear function, 467 00:27:25,920 --> 00:27:30,810 something with an intercept, and then Beta Lambda. 468 00:27:30,810 --> 00:27:36,030 Beta, and finance guys talk about betas all the time. 469 00:27:36,030 --> 00:27:40,530 Beta for us just means sort of the normalized covariance 470 00:27:40,530 --> 00:27:47,710 between the returns on ij and the stochastic discount 471 00:27:47,710 --> 00:27:51,030 factor, which I already pointed to above. 472 00:27:51,030 --> 00:27:53,080 It's normalized by the overall variance. 473 00:27:56,320 --> 00:27:58,060 So that's kind of the risk factor, 474 00:27:58,060 --> 00:28:00,810 or the quantity of risk. 475 00:28:00,810 --> 00:28:06,440 And this other thing could be called the price of risk. 476 00:28:06,440 --> 00:28:08,210 But it's nothing other than this. 477 00:28:08,210 --> 00:28:10,190 It's the variance divided by the mean. 478 00:28:14,920 --> 00:28:19,560 It almost looks like a coefficient of variation, 479 00:28:19,560 --> 00:28:23,669 like Sigma squared divided by Mu or something. 480 00:28:29,420 --> 00:28:30,800 And there's a name for it. 481 00:28:30,800 --> 00:28:35,280 And I'll tell you what it is in a second. 482 00:28:35,280 --> 00:28:38,000 All right, so this is what I said already. 483 00:28:38,000 --> 00:28:43,280 Quantities, prices-- oh, and one more thing. 484 00:28:43,280 --> 00:28:46,490 What was that intercept? 485 00:28:46,490 --> 00:28:49,460 Well basically, let's just define 486 00:28:49,460 --> 00:28:52,760 this thing, this Gamma, well, it was already 487 00:28:52,760 --> 00:28:56,420 defined to be 1 over the expectation of m prime. 488 00:28:56,420 --> 00:28:59,215 But let's call it the risk free return. 489 00:29:04,090 --> 00:29:07,470 First of all, why is there no risk? 490 00:29:07,470 --> 00:29:10,080 Because all the variability in the economy 491 00:29:10,080 --> 00:29:16,290 is in m prime or the one that we care about for that equation. 492 00:29:16,290 --> 00:29:18,250 And we've already taken the expectation. 493 00:29:18,250 --> 00:29:19,920 So there's nothing random left. 494 00:29:19,920 --> 00:29:21,910 So this is a number. 495 00:29:21,910 --> 00:29:25,360 It's not something stochastic. 496 00:29:25,360 --> 00:29:26,440 It should be obvious. 497 00:29:26,440 --> 00:29:30,220 But I always do it myself, which is take that to be an asset, 498 00:29:30,220 --> 00:29:33,940 plug that back into the asset Euler equation 499 00:29:33,940 --> 00:29:36,850 that we already have and thus convince yourself 500 00:29:36,850 --> 00:29:40,690 that that equation applies for the risk free return. 501 00:29:40,690 --> 00:29:45,610 And you'll get this right back again, OK? 502 00:29:49,560 --> 00:29:53,190 So anyway, the point is risk free because the covariance 503 00:29:53,190 --> 00:29:57,030 of this risk free rate with m prime is 0 by construction. 504 00:30:16,390 --> 00:30:21,660 So let's just look at this again. 505 00:30:21,660 --> 00:30:27,940 This is the rate of return of the mean, or average, rate 506 00:30:27,940 --> 00:30:30,940 of return on project ij. 507 00:30:30,940 --> 00:30:32,900 Subtract off the risk free rate. 508 00:30:32,900 --> 00:30:34,450 This is the return differential. 509 00:30:34,450 --> 00:30:37,540 This is how much the-- 510 00:30:37,540 --> 00:30:41,800 in finance, it would be like the junk bond premium 511 00:30:41,800 --> 00:30:43,120 over and above treasuries. 512 00:30:45,770 --> 00:30:50,490 And so that difference is sort of the premium 513 00:30:50,490 --> 00:30:55,050 that you get for holding a risky asset. 514 00:30:55,050 --> 00:30:59,790 And it's linearly related to the covariance 515 00:30:59,790 --> 00:31:01,280 of that asset with the market. 516 00:31:06,090 --> 00:31:08,400 So again, I'm going back and forth a bit more 517 00:31:08,400 --> 00:31:09,870 with this finance language. 518 00:31:09,870 --> 00:31:12,300 But it's just all right off the Euler equation. 519 00:31:12,300 --> 00:31:19,320 This is just standard sort of manipulation. 520 00:31:19,320 --> 00:31:24,750 So we can even make it more obvious 521 00:31:24,750 --> 00:31:28,800 if you're wondering what m prime really is. 522 00:31:28,800 --> 00:31:32,340 Let's go with quadratic utility. 523 00:31:32,340 --> 00:31:34,856 So this is the form of it. 524 00:31:34,856 --> 00:31:40,060 The community's value function as a function of wealth 525 00:31:40,060 --> 00:31:44,560 is just basically the squared of the difference between wealth 526 00:31:44,560 --> 00:31:51,680 and some subsistence level with a coefficient in front of it. 527 00:31:51,680 --> 00:31:54,230 So of course, if you take the derivative of it 528 00:31:54,230 --> 00:31:58,340 with respect to w the twos cancel out. 529 00:31:58,340 --> 00:32:01,640 And you get eta times this difference, which is linear, 530 00:32:01,640 --> 00:32:02,570 by the way. 531 00:32:02,570 --> 00:32:04,250 That's huge. 532 00:32:04,250 --> 00:32:09,350 So marginal value of wealth is linear in wealth. 533 00:32:09,350 --> 00:32:12,380 That's what you get at a quadratic. 534 00:32:12,380 --> 00:32:16,150 And then you just substitute our expression for w 535 00:32:16,150 --> 00:32:22,570 prime tomorrow into that expression 536 00:32:22,570 --> 00:32:25,770 and do a little relabeling. 537 00:32:25,770 --> 00:32:28,560 So all of a sudden, this looks like the return 538 00:32:28,560 --> 00:32:35,390 on the village average and the village average capital stock. 539 00:32:35,390 --> 00:32:37,460 OK, the village average capital stock 540 00:32:37,460 --> 00:32:40,580 is the sum of the capital stocks allocated 541 00:32:40,580 --> 00:32:43,040 over all the projects and all the households, 542 00:32:43,040 --> 00:32:47,120 as it should be to be in total, right? 543 00:32:47,120 --> 00:32:50,300 And then what is the rate of return on it? 544 00:32:50,300 --> 00:32:56,090 Well basically, it's like a capital weighted return. 545 00:32:56,090 --> 00:32:59,720 So the total return is coming from a bunch 546 00:32:59,720 --> 00:33:01,130 of individual projects. 547 00:33:01,130 --> 00:33:04,760 So you just take the return on all the individual projects 548 00:33:04,760 --> 00:33:07,130 but weight them by the capital being allocated 549 00:33:07,130 --> 00:33:09,680 to those projects and renormalize 550 00:33:09,680 --> 00:33:11,930 by the total capital stock. 551 00:33:11,930 --> 00:33:14,645 So it's a portfolio weighted return. 552 00:33:17,760 --> 00:33:19,800 That's just a definition. 553 00:33:19,800 --> 00:33:22,840 But of course, then it looks like this. 554 00:33:22,840 --> 00:33:26,440 And you take this up here and this here. 555 00:33:26,440 --> 00:33:28,513 And you realize that there's things canceling. 556 00:33:28,513 --> 00:33:30,430 And that's why it's really just equal to this. 557 00:33:36,270 --> 00:33:40,740 But we'll use this now. 558 00:33:40,740 --> 00:33:43,800 So m prime, which is the derivative tomorrow, 559 00:33:43,800 --> 00:33:47,430 is just this thing divided by Mu. 560 00:33:47,430 --> 00:33:50,010 Remember we have to take the current shadow price 561 00:33:50,010 --> 00:33:53,430 and divide through. 562 00:33:53,430 --> 00:33:56,190 And then this is all additive and linear. 563 00:34:04,420 --> 00:34:06,780 So we get this. 564 00:34:06,780 --> 00:34:12,460 And now, m prime here looks like this plus this. 565 00:34:12,460 --> 00:34:14,810 This looks like a constant term that doesn't 566 00:34:14,810 --> 00:34:17,750 depend on the rate of return. 567 00:34:17,750 --> 00:34:20,510 And this is a coefficient premultiplying 568 00:34:20,510 --> 00:34:21,989 the rate of return. 569 00:34:21,989 --> 00:34:29,020 So it's starting to look like a pretty convenient equation 570 00:34:29,020 --> 00:34:32,440 for the stochastic discount factor. 571 00:34:32,440 --> 00:34:36,474 It's linear, linear in the village rate of return. 572 00:34:40,480 --> 00:34:43,750 And again, we have this thing we already derived, 573 00:34:43,750 --> 00:34:48,230 which was a manipulation of the Euler equation. 574 00:34:48,230 --> 00:34:51,580 And everywhere you see m prime, you 575 00:34:51,580 --> 00:34:56,070 start substituting a minus brm prime. 576 00:34:56,070 --> 00:34:57,820 And then you got to remember certain rules 577 00:34:57,820 --> 00:35:02,680 about covariance operators and variance operators. 578 00:35:02,680 --> 00:35:06,430 Variance operators will square coefficients in front of them. 579 00:35:06,430 --> 00:35:12,770 Covariance operators will bring the coefficient outside. 580 00:35:12,770 --> 00:35:15,790 There's a lot of substitutions here. 581 00:35:15,790 --> 00:35:16,957 there's b's and b squares. 582 00:35:16,957 --> 00:35:18,790 And they're going to cancel with each other. 583 00:35:18,790 --> 00:35:20,082 And you end up with this thing. 584 00:35:22,660 --> 00:35:25,120 So this says the expected return, or sample 585 00:35:25,120 --> 00:35:35,360 average return, should just be the covariance 586 00:35:35,360 --> 00:35:38,390 of the return with the market with the village average 587 00:35:38,390 --> 00:35:40,210 aggregate. 588 00:35:40,210 --> 00:35:42,490 By the way, we know how to construct that. 589 00:35:42,490 --> 00:35:45,850 Because we have it in the data. 590 00:35:45,850 --> 00:35:50,790 And we have the variance as well. 591 00:35:50,790 --> 00:35:56,150 And then this is just the sort of coefficient 592 00:35:56,150 --> 00:35:57,350 that multiplies it. 593 00:36:02,230 --> 00:36:06,710 But that's what I was saying about that coefficient 594 00:36:06,710 --> 00:36:08,150 of variation. 595 00:36:08,150 --> 00:36:09,860 It's a variance divided by a mean. 596 00:36:14,040 --> 00:36:15,420 So where have we ended up? 597 00:36:17,950 --> 00:36:21,670 Well, with that quadratic we now have pretty much 598 00:36:21,670 --> 00:36:26,170 an exact expression that the expected rate of return 599 00:36:26,170 --> 00:36:29,170 on project i run by household j should just 600 00:36:29,170 --> 00:36:34,510 be a linear function with a common constant term that 601 00:36:34,510 --> 00:36:38,740 has nothing do with i and j and then 602 00:36:38,740 --> 00:36:43,060 the covariance of that household's 603 00:36:43,060 --> 00:36:47,780 return with the village average return, which is something 604 00:36:47,780 --> 00:36:49,460 we can compute. 605 00:36:49,460 --> 00:36:53,810 Because if you start thinking about this like a regression, 606 00:36:53,810 --> 00:36:55,940 we'll know this from the data. 607 00:36:55,940 --> 00:36:58,250 We'll know this from the data. 608 00:36:58,250 --> 00:37:00,140 I'll tell you how to get it in a minute. 609 00:37:00,140 --> 00:37:02,600 And we'll just estimate Lambda and Gamma. 610 00:37:02,600 --> 00:37:05,300 Well, not quite, Gamma we can do something special with. 611 00:37:05,300 --> 00:37:07,160 But that's the idea. 612 00:37:10,437 --> 00:37:11,520 So I've said this already. 613 00:37:11,520 --> 00:37:12,870 But it bears repeating. 614 00:37:15,720 --> 00:37:18,050 Our stuff looks a lot like this cap m. 615 00:37:18,050 --> 00:37:19,800 But the mechanism is very different. 616 00:37:19,800 --> 00:37:22,970 We do not have households trading assets 617 00:37:22,970 --> 00:37:26,480 that are priced in centralized markets. 618 00:37:26,480 --> 00:37:29,060 We're instead optimally allocating 619 00:37:29,060 --> 00:37:32,350 assets across households, but then 620 00:37:32,350 --> 00:37:37,360 not forcing them to eat the return stream. 621 00:37:37,360 --> 00:37:39,700 Instead, they enter into this risk syndicate 622 00:37:39,700 --> 00:37:44,920 as if a social planner were reallocating consumption. 623 00:37:44,920 --> 00:37:48,790 Whereas, in finance you kind of assume you're an investor. 624 00:37:48,790 --> 00:37:51,160 You could do means and variances and take some risks 625 00:37:51,160 --> 00:37:52,090 on your portfolio. 626 00:37:52,090 --> 00:37:56,590 And then you're going to eat it or at least dynamically 627 00:37:56,590 --> 00:37:59,745 optimize, eat some, save some for tomorrow. 628 00:37:59,745 --> 00:38:00,870 But this is very different. 629 00:38:00,870 --> 00:38:03,310 And it's key that they don't have 630 00:38:03,310 --> 00:38:06,550 to eat the returns off their capital stock 631 00:38:06,550 --> 00:38:09,280 or make their own independent savings decisions. 632 00:38:17,200 --> 00:38:22,460 And you've seen last time building up to this 633 00:38:22,460 --> 00:38:25,400 that households are sharing a lot of risk with each other. 634 00:38:25,400 --> 00:38:29,890 And these informal village money markets are quite active. 635 00:38:29,890 --> 00:38:31,840 We called them a money market last time. 636 00:38:31,840 --> 00:38:34,300 So we've already been using that language. 637 00:38:37,255 --> 00:38:38,630 That's what this slide is saying. 638 00:38:38,630 --> 00:38:41,120 That's just a reminder of what we talked about last time. 639 00:38:44,795 --> 00:38:45,970 So data, it's monthly. 640 00:38:48,738 --> 00:38:51,030 I don't know what they're called, four villages grouped 641 00:38:51,030 --> 00:38:53,390 together in a tombone. 642 00:38:53,390 --> 00:38:56,840 So we kind of started adopting this South Africa language. 643 00:38:56,840 --> 00:38:59,000 I don't know whether I like it. 644 00:38:59,000 --> 00:39:01,212 We're calling them townships. 645 00:39:01,212 --> 00:39:03,370 AUDIENCE: It has a slight connotation [INAUDIBLE].. 646 00:39:03,370 --> 00:39:04,135 PROFESSOR: Yeah. 647 00:39:04,135 --> 00:39:09,350 AUDIENCE: It's rural and maybe not the best place to be. 648 00:39:09,350 --> 00:39:10,330 PROFESSOR: Yeah. 649 00:39:10,330 --> 00:39:15,010 So tombone is Thai for the fact that we picked four at random 650 00:39:15,010 --> 00:39:17,320 in this geographic area. 651 00:39:17,320 --> 00:39:20,180 But no one knows what a tombone is. 652 00:39:20,180 --> 00:39:24,540 But clearly, townships distinguishes it from villages. 653 00:39:24,540 --> 00:39:27,870 It's four villages in the data anyway. 654 00:39:27,870 --> 00:39:31,980 You know all about where they're located. 655 00:39:31,980 --> 00:39:36,240 Reminder that we started in August of '98. 656 00:39:36,240 --> 00:39:40,630 We're going to ignore the first four months basically. 657 00:39:40,630 --> 00:39:48,990 And use the data from 1990 on, 1999. 658 00:39:48,990 --> 00:39:54,240 We're still out there at month 174. 659 00:39:54,240 --> 00:39:55,990 What we're going to use-- 660 00:39:55,990 --> 00:39:58,170 and Chris and I just basically redid 661 00:39:58,170 --> 00:40:02,350 this in the last few weeks-- 662 00:40:02,350 --> 00:40:08,340 we're going to use month five to 160 or basically 156 months, 663 00:40:08,340 --> 00:40:18,110 or 13 full years of the data at the monthly level for the 541 664 00:40:18,110 --> 00:40:24,050 households who are basically have not dropped 665 00:40:24,050 --> 00:40:26,180 out sort of a balanced panel. 666 00:40:29,720 --> 00:40:37,150 Now, about the townships, so what percentage of households 667 00:40:37,150 --> 00:40:40,930 have relatives living in the same village? 668 00:40:40,930 --> 00:40:46,530 It's a bit low into only half in [INAUDIBLE].. 669 00:40:46,530 --> 00:40:49,180 It's 3/4 in Logburi. 670 00:40:49,180 --> 00:40:52,300 And Buriram is already up to the 80s if not to the 90s. 671 00:40:52,300 --> 00:40:55,690 But if you go to the township level, 672 00:40:55,690 --> 00:41:00,540 then 87, really 88 is the lowest percent. 673 00:41:00,540 --> 00:41:03,480 In other words, almost every household 674 00:41:03,480 --> 00:41:05,280 has a relative if not in their own 675 00:41:05,280 --> 00:41:08,620 village then in a village nearby. 676 00:41:08,620 --> 00:41:11,740 So we stopped kind of looking at networks after this. 677 00:41:11,740 --> 00:41:16,620 And networks confuse people, rightly so. 678 00:41:16,620 --> 00:41:17,550 Because who's in it? 679 00:41:17,550 --> 00:41:18,520 And who isn't? 680 00:41:18,520 --> 00:41:20,560 And is there selection bias, and so on? 681 00:41:20,560 --> 00:41:22,860 So we just made it easy for ourselves 682 00:41:22,860 --> 00:41:25,740 and said, ah, they're all really related to each other anyway. 683 00:41:25,740 --> 00:41:28,630 So let's use the whole sample. 684 00:41:28,630 --> 00:41:30,570 But I'll show you what we go back and check. 685 00:41:34,470 --> 00:41:37,660 This looks like risk and return in village India. 686 00:41:37,660 --> 00:41:39,900 I mean, you can see the cultivation activities, 687 00:41:39,900 --> 00:41:46,140 livestock, fish, shrimp, wage earning, and so on. 688 00:41:46,140 --> 00:41:48,420 Wage earning is a bit heavier in the Northeast. 689 00:41:48,420 --> 00:41:52,350 And in [INAUDIBLE] only [INAUDIBLE] 690 00:41:52,350 --> 00:41:55,395 has fish and shrimp. 691 00:41:55,395 --> 00:41:57,270 It sounds like a restaurant. 692 00:41:57,270 --> 00:41:58,770 I know I've already told you though. 693 00:41:58,770 --> 00:42:02,400 That's what you're eating when you buy shrimp at Costco. 694 00:42:05,530 --> 00:42:09,070 And all the business, livestock is pretty heavy. 695 00:42:09,070 --> 00:42:14,710 And Logburi, also [INAUDIBLE],, those are the dairy cattle. 696 00:42:14,710 --> 00:42:18,460 So that's just a quick reminder of the "projects." 697 00:42:18,460 --> 00:42:23,560 My project is a cow, et cetera. 698 00:42:23,560 --> 00:42:24,893 It's a cash cow. 699 00:42:24,893 --> 00:42:25,560 That's terrible. 700 00:42:28,890 --> 00:42:33,770 And here is some just reminder of descriptive 701 00:42:33,770 --> 00:42:37,610 statistics, males, females, education levels. 702 00:42:37,610 --> 00:42:40,820 Some of this you've seen before, income levels, assets 703 00:42:40,820 --> 00:42:43,750 and liabilities, and so on. 704 00:42:47,468 --> 00:42:49,010 So we're going to use a total return. 705 00:42:49,010 --> 00:42:51,260 And we're going to include financial assets. 706 00:42:51,260 --> 00:42:54,620 We're not going to separate-- 707 00:42:54,620 --> 00:42:56,060 by the way, it's a bit problematic 708 00:42:56,060 --> 00:42:58,370 to know what to do with a savings account. 709 00:42:58,370 --> 00:43:00,650 It's a financial asset. 710 00:43:00,650 --> 00:43:03,530 But on the other hand, maybe like inventory, 711 00:43:03,530 --> 00:43:05,490 it's kind of contributing to the business. 712 00:43:05,490 --> 00:43:08,430 And if we didn't have it in there, then people would ask. 713 00:43:08,430 --> 00:43:10,290 So it didn't make much difference. 714 00:43:10,290 --> 00:43:12,890 So we put in all the financial assets. 715 00:43:12,890 --> 00:43:14,780 Actually, subtracted off the debts too. 716 00:43:17,300 --> 00:43:19,460 It doesn't really matter. 717 00:43:19,460 --> 00:43:21,800 If you want to think about this as real rates of return, 718 00:43:21,800 --> 00:43:29,740 you would not be misled in real projects, 719 00:43:29,740 --> 00:43:32,400 real people, real assets. 720 00:43:32,400 --> 00:43:36,680 OK, you know we constructed these financial accounts. 721 00:43:36,680 --> 00:43:38,030 This is problematic. 722 00:43:38,030 --> 00:43:43,910 We have to sort of subtract off the cost of labor. 723 00:43:43,910 --> 00:43:48,900 And when it's household labor, it's not priced. 724 00:43:48,900 --> 00:43:52,260 This is probably our single biggest problem. 725 00:43:52,260 --> 00:43:54,900 And when I show you residual rates of return in a minute, 726 00:43:54,900 --> 00:43:57,540 you'll see some of them are low. 727 00:43:57,540 --> 00:44:00,460 We probably subtracted off too much. 728 00:44:00,460 --> 00:44:01,810 But it's very hard to know. 729 00:44:01,810 --> 00:44:05,870 Because we try to grab instruments and adjust. 730 00:44:05,870 --> 00:44:11,400 But it's really kind of not terribly compelling. 731 00:44:11,400 --> 00:44:14,690 You'll see this again when we get to the labor paper. 732 00:44:14,690 --> 00:44:17,330 So we adjust the income. 733 00:44:17,330 --> 00:44:20,420 We divide by fixed assets. 734 00:44:20,420 --> 00:44:23,570 That, as you know, is rate of return on assets. 735 00:44:23,570 --> 00:44:24,970 We may get real. 736 00:44:24,970 --> 00:44:26,745 The data is nominal. 737 00:44:26,745 --> 00:44:28,370 It's all measured in Thai [INAUDIBLE].. 738 00:44:28,370 --> 00:44:35,160 So we deflate by Bank of Thailand regional price 739 00:44:35,160 --> 00:44:35,660 changes. 740 00:44:40,640 --> 00:44:48,690 This is the table of the rates of return mean standard 741 00:44:48,690 --> 00:44:50,880 deviation and the so-called-- 742 00:44:50,880 --> 00:44:52,230 so I forgot to say it. 743 00:44:52,230 --> 00:44:54,810 But that thing I kept saying was sort of 744 00:44:54,810 --> 00:44:57,780 like a coefficient of variation, that's 745 00:44:57,780 --> 00:45:01,510 like the inverse Sharpe ratio. 746 00:45:01,510 --> 00:45:03,590 So you can add that to your vocabulario. 747 00:45:07,300 --> 00:45:15,510 Now, each household has a sample average. 748 00:45:15,510 --> 00:45:18,570 So you're going to have a mean standard deviation, et cetera, 749 00:45:18,570 --> 00:45:21,990 those statistical moments for every single household. 750 00:45:21,990 --> 00:45:25,480 So you have a histogram in the population. 751 00:45:25,480 --> 00:45:28,290 So you can look at the median mean if you want, 752 00:45:28,290 --> 00:45:35,250 if it's not too confusing, or the 25th and 75th quartiles 753 00:45:35,250 --> 00:45:36,150 of rates of return. 754 00:45:48,410 --> 00:45:49,700 Some of them are high. 755 00:45:49,700 --> 00:45:52,310 Many of them are not that high. 756 00:45:56,200 --> 00:45:59,180 But in any event, these are not adjusted at all. 757 00:45:59,180 --> 00:46:00,895 They're just the crude rates of return. 758 00:46:04,460 --> 00:46:07,180 OK, so now we got to decide what to do with the risk free rate. 759 00:46:09,820 --> 00:46:13,340 Well, these are supposed to be real. 760 00:46:13,340 --> 00:46:15,190 So we're basically going to assume 761 00:46:15,190 --> 00:46:18,550 they have something like inventory that 762 00:46:18,550 --> 00:46:20,590 goes up with the price level. 763 00:46:20,590 --> 00:46:23,970 And there's nothing stochastic about it. 764 00:46:23,970 --> 00:46:26,415 So we're going to assume the real rate of return is zero. 765 00:46:30,150 --> 00:46:32,460 Now again, if we're guessing wrong about this, 766 00:46:32,460 --> 00:46:34,710 we're going to be guessing wrong about the intercepts. 767 00:46:34,710 --> 00:46:39,525 Because everything we do is subtracting off zero. 768 00:46:44,580 --> 00:46:45,930 But anyway, that's what we do. 769 00:46:48,540 --> 00:46:56,230 The market return is the average township rate of return. 770 00:46:56,230 --> 00:46:59,360 And again, that's just looking at the income 771 00:46:59,360 --> 00:47:05,480 over all the households divided by all the assets. 772 00:47:11,120 --> 00:47:12,770 We're about to run a regression though. 773 00:47:12,770 --> 00:47:17,177 So we will take out the household's own contribution 774 00:47:17,177 --> 00:47:18,135 to the village average. 775 00:47:18,135 --> 00:47:20,770 It's like a leave out mean. 776 00:47:20,770 --> 00:47:23,540 So we don't you know bias it in the obvious way. 777 00:47:23,540 --> 00:47:25,960 Yes? 778 00:47:25,960 --> 00:47:29,480 AUDIENCE: [INAUDIBLE] 779 00:47:29,480 --> 00:47:31,340 PROFESSOR: Depreciation is in here. 780 00:47:31,340 --> 00:47:37,622 Because depreciation is a cost that we're subtracting off 781 00:47:37,622 --> 00:47:38,705 in the financial accounts. 782 00:47:38,705 --> 00:47:40,705 AUDIENCE: So that's where it comes [INAUDIBLE]?? 783 00:47:40,705 --> 00:47:42,190 PROFESSOR: Uh-huh. 784 00:47:42,190 --> 00:47:47,800 So these numbers are basically coming off of the income 785 00:47:47,800 --> 00:47:49,120 as in the income statement. 786 00:47:49,120 --> 00:47:52,820 And the assets as in the balance sheet, 787 00:47:52,820 --> 00:47:54,400 which you've seen before. 788 00:47:54,400 --> 00:47:57,560 Although, it is true that we cover a lot of ground. 789 00:47:57,560 --> 00:48:00,240 So I'm happy to remind you. 790 00:48:03,180 --> 00:48:05,280 So how do we get the relationship 791 00:48:05,280 --> 00:48:08,130 of the household's rate of return to the village average? 792 00:48:08,130 --> 00:48:10,270 We run a regression. 793 00:48:10,270 --> 00:48:13,060 We run a regression of the household's, 794 00:48:13,060 --> 00:48:18,230 over all of its projects, household's return at day t. 795 00:48:18,230 --> 00:48:21,400 But there are lots of dates t with all those months-- 796 00:48:21,400 --> 00:48:23,260 more on that in a second-- 797 00:48:23,260 --> 00:48:27,450 regressed against the village return at day t. 798 00:48:27,450 --> 00:48:29,470 OK, so this beta is just literally 799 00:48:29,470 --> 00:48:33,950 the regression coefficient that we wanted conveniently. 800 00:48:33,950 --> 00:48:34,618 Yes? 801 00:48:34,618 --> 00:48:36,160 AUDIENCE: We are assuming [INAUDIBLE] 802 00:48:36,160 --> 00:48:40,790 is constant over time for each household? 803 00:48:40,790 --> 00:48:44,150 PROFESSOR: OK, so yeah, there's several adjustments. 804 00:48:44,150 --> 00:48:45,600 I think it's on the next page. 805 00:48:45,600 --> 00:48:48,770 But anyway, so actually, what we're going to do 806 00:48:48,770 --> 00:48:54,060 is do five year increments. 807 00:48:54,060 --> 00:48:56,580 You could just take one household 808 00:48:56,580 --> 00:49:01,970 over all the many years and months 809 00:49:01,970 --> 00:49:05,890 and ignore possible shifts in their portfolio. 810 00:49:05,890 --> 00:49:09,490 But like you're saying, that might be a bad idea. 811 00:49:09,490 --> 00:49:15,680 So we redid it as if the household 812 00:49:15,680 --> 00:49:18,260 had returns on a portfolio from year one 813 00:49:18,260 --> 00:49:21,920 through five then returns on a portfolio from year two 814 00:49:21,920 --> 00:49:24,290 through six, seven through eight, 815 00:49:24,290 --> 00:49:25,700 and so on all the way through. 816 00:49:25,700 --> 00:49:29,840 And it turns out that idea, as many others, 817 00:49:29,840 --> 00:49:31,995 come from the finance literature. 818 00:49:31,995 --> 00:49:33,120 So that's what we're doing. 819 00:49:35,730 --> 00:49:41,020 The other adjustment I should have mentioned earlier. 820 00:49:41,020 --> 00:49:42,750 And I didn't. 821 00:49:42,750 --> 00:49:46,350 But you remember when we use a quadratic utility 822 00:49:46,350 --> 00:49:49,710 it was a plus b times something, right? 823 00:49:49,710 --> 00:49:52,460 And there was no t on those things. 824 00:49:52,460 --> 00:49:56,850 So it was like the marginal utility of wealth 825 00:49:56,850 --> 00:49:58,230 just depends on wealth. 826 00:49:58,230 --> 00:50:00,040 And it doesn't depend on anything else. 827 00:50:00,040 --> 00:50:05,070 But in many intertemporal models, 828 00:50:05,070 --> 00:50:08,010 those things would be moving around. 829 00:50:08,010 --> 00:50:12,480 So I'll tell you about that adjustment too. 830 00:50:12,480 --> 00:50:14,350 We actually did it all the different ways. 831 00:50:20,130 --> 00:50:21,810 But these are the key steps. 832 00:50:21,810 --> 00:50:24,100 We run the regression, or regressions, 833 00:50:24,100 --> 00:50:25,200 for each household. 834 00:50:28,250 --> 00:50:35,590 And then we get the beta for each household j. 835 00:50:35,590 --> 00:50:41,440 And we get the average return, either over all the years 836 00:50:41,440 --> 00:50:43,610 or over these five year increments. 837 00:50:43,610 --> 00:50:48,350 And then we run this regression essentially 838 00:50:48,350 --> 00:50:51,410 with this already coming from a previous regression using 839 00:50:51,410 --> 00:50:52,400 the panel. 840 00:50:52,400 --> 00:50:54,660 This thing is just a cross-sectional regression. 841 00:50:54,660 --> 00:50:56,960 There's no time date here. 842 00:50:56,960 --> 00:50:59,070 This is the average return. 843 00:50:59,070 --> 00:51:01,340 This is the extent to which the village 844 00:51:01,340 --> 00:51:04,520 that household's returns are correlated with the village 845 00:51:04,520 --> 00:51:05,530 average. 846 00:51:08,530 --> 00:51:13,730 And we'll get expressions for lambda, alpha, and so on. 847 00:51:13,730 --> 00:51:16,370 And there are restrictions. 848 00:51:16,370 --> 00:51:20,310 Although, you no doubt can't remember seven 849 00:51:20,310 --> 00:51:23,630 and a half slides back that and this lambda 850 00:51:23,630 --> 00:51:26,150 ought to be equal to something like the expected market 851 00:51:26,150 --> 00:51:27,810 rate of return. 852 00:51:27,810 --> 00:51:30,390 Just take my word for it. 853 00:51:30,390 --> 00:51:31,830 We don't impose that restriction. 854 00:51:31,830 --> 00:51:41,500 So here's the first result. Beta is on the right hand side. 855 00:51:41,500 --> 00:51:45,070 And it's being regressed against the household's mean rate 856 00:51:45,070 --> 00:51:51,640 of return and three of the four provinces. 857 00:51:51,640 --> 00:51:55,747 It's quite positive and significant. 858 00:52:01,850 --> 00:52:04,490 These are the regression coefficients, the lambdas 859 00:52:04,490 --> 00:52:05,720 basically. 860 00:52:05,720 --> 00:52:08,830 And this is the estimated constant. 861 00:52:08,830 --> 00:52:10,870 And r squares. 862 00:52:10,870 --> 00:52:11,770 You know what it is. 863 00:52:11,770 --> 00:52:13,130 It's kind of worth noting. 864 00:52:13,130 --> 00:52:17,640 Buriram fails and has a very low r square. 865 00:52:17,640 --> 00:52:19,540 And Buriram is one of the places I've 866 00:52:19,540 --> 00:52:24,220 mentioned, where the farmland got plowed over with roads. 867 00:52:24,220 --> 00:52:26,650 And the town was being built up. 868 00:52:26,650 --> 00:52:30,870 So there arguably were a lot of changes in occupations. 869 00:52:30,870 --> 00:52:33,240 We'll try to fix that. 870 00:52:33,240 --> 00:52:35,400 Yes? 871 00:52:35,400 --> 00:52:37,500 AUDIENCE: Is this for one five year period? 872 00:52:37,500 --> 00:52:39,690 Or is this like an average of the-- 873 00:52:39,690 --> 00:52:45,420 PROFESSOR: This is actually, with treating each household 874 00:52:45,420 --> 00:52:46,825 multiple times. 875 00:52:46,825 --> 00:52:48,160 AUDIENCE: OK, so-- 876 00:52:48,160 --> 00:52:48,990 PROFESSOR: I think. 877 00:52:48,990 --> 00:52:49,770 Let me just see. 878 00:52:59,590 --> 00:53:03,027 AUDIENCE: [INAUDIBLE] it's like putting 20 years. 879 00:53:09,873 --> 00:53:11,040 PROFESSOR: No, it's not yet. 880 00:53:11,040 --> 00:53:12,900 AUDIENCE: So that's like the whole thing. 881 00:53:12,900 --> 00:53:14,405 PROFESSOR: This is the whole thing. 882 00:53:14,405 --> 00:53:17,690 AUDIENCE: So do we have to worry about [INAUDIBLE] issues 883 00:53:17,690 --> 00:53:19,976 or [INAUDIBLE] problems with us? 884 00:53:19,976 --> 00:53:23,174 Or is that not-- do I misunderstood how 885 00:53:23,174 --> 00:53:24,410 the regression [INAUDIBLE]? 886 00:53:24,410 --> 00:53:26,395 So is there some possibility that there's 887 00:53:26,395 --> 00:53:30,355 like going to be trends in the errors that are not picked up? 888 00:53:30,355 --> 00:53:31,840 Because you set the constant. 889 00:53:31,840 --> 00:53:34,970 [INAUDIBLE] So we don't have to worry too much about using 890 00:53:34,970 --> 00:53:35,835 the whole-- 891 00:53:35,835 --> 00:53:37,210 PROFESSOR: We worried quite a bit 892 00:53:37,210 --> 00:53:41,620 about potential econometric biases and so on and so forth. 893 00:53:41,620 --> 00:53:43,600 Then we went back and read the classics 894 00:53:43,600 --> 00:53:47,620 in finance, [INAUDIBLE],, French, all these guys. 895 00:53:47,620 --> 00:53:49,660 And we're doing what they're doing. 896 00:53:49,660 --> 00:53:52,470 So we felt better. 897 00:53:52,470 --> 00:53:56,880 [LAUGHTER] 898 00:53:56,880 --> 00:53:58,410 AUDIENCE: [INAUDIBLE] if we regress 899 00:53:58,410 --> 00:54:01,270 the errors on the [INAUDIBLE],, does it pause the test? 900 00:54:01,270 --> 00:54:02,730 Or is it-- 901 00:54:02,730 --> 00:54:03,960 PROFESSOR: Oh, we haven't-- 902 00:54:03,960 --> 00:54:09,420 yeah, I don't think we've looked for autocorrelation and stuff 903 00:54:09,420 --> 00:54:09,920 like that. 904 00:54:09,920 --> 00:54:12,000 AUDIENCE: [INAUDIBLE] we get hammered three hours 905 00:54:12,000 --> 00:54:13,083 and make that [INAUDIBLE]. 906 00:54:13,083 --> 00:54:15,642 That's what we're doing [INAUDIBLE].. 907 00:54:15,642 --> 00:54:17,190 PROFESSOR: The HH factor. 908 00:54:19,960 --> 00:54:21,630 OK, we'll check that. 909 00:54:21,630 --> 00:54:22,670 Yes? 910 00:54:22,670 --> 00:54:25,460 AUDIENCE: So do you think it's worse 911 00:54:25,460 --> 00:54:28,020 to joint tested r [INAUDIBLE] j for each household, 912 00:54:28,020 --> 00:54:30,303 like the finance guys? 913 00:54:30,303 --> 00:54:32,220 PROFESSOR: We're about to show you the alphas. 914 00:54:32,220 --> 00:54:32,762 AUDIENCE: OK. 915 00:54:32,762 --> 00:54:35,440 PROFESSOR: I haven't gotten there yet. 916 00:54:35,440 --> 00:54:37,510 We'll see when I get there whether you have 917 00:54:37,510 --> 00:54:38,710 something different in mind. 918 00:54:42,760 --> 00:54:50,580 Anyway, so if you want to visually see 919 00:54:50,580 --> 00:54:54,650 sort of a mean variance frontier, 920 00:54:54,650 --> 00:54:56,790 you the beta is down here. 921 00:54:56,790 --> 00:55:02,280 That's kind of the risk factor, if you believe this model. 922 00:55:02,280 --> 00:55:04,350 And the expected returns are here. 923 00:55:04,350 --> 00:55:08,660 And you can see a pretty close fit. 924 00:55:08,660 --> 00:55:14,390 Now, this I've shown to the finance guys 925 00:55:14,390 --> 00:55:15,500 at lunches and things. 926 00:55:15,500 --> 00:55:18,270 And they're like, wow. 927 00:55:18,270 --> 00:55:21,890 Because this is actually pretty good 928 00:55:21,890 --> 00:55:24,245 relative to New York financial markets. 929 00:55:27,920 --> 00:55:29,540 Oh, it's an easy target, OK. 930 00:55:33,820 --> 00:55:39,760 So so far we are showing that just to repeat, 931 00:55:39,760 --> 00:55:43,990 when someone has a higher return, it's partly not talent. 932 00:55:43,990 --> 00:55:49,740 It's just that it's correlated with the village average. 933 00:55:49,740 --> 00:55:54,560 And it's high because you need to adjust for the risk. 934 00:55:54,560 --> 00:55:56,900 Now, we can do this at the village level, in which case 935 00:55:56,900 --> 00:55:58,740 nine of the 16 villages we're going 936 00:55:58,740 --> 00:56:02,450 to have this positive correlation that the theory 937 00:56:02,450 --> 00:56:03,450 says ought to be there. 938 00:56:03,450 --> 00:56:10,170 And when we go to the network level, 939 00:56:10,170 --> 00:56:13,813 we have five out of nine networks. 940 00:56:13,813 --> 00:56:15,480 And I'll show you about the adjustments, 941 00:56:15,480 --> 00:56:18,780 remind you here's a kinship network. 942 00:56:18,780 --> 00:56:21,540 206 is married with 207 in some way. 943 00:56:21,540 --> 00:56:24,090 And 214 has all these. 944 00:56:24,090 --> 00:56:28,650 So can it literally connect the dots? 945 00:56:28,650 --> 00:56:31,320 Here's a big dynasty down here. 946 00:56:31,320 --> 00:56:34,840 Here's a little dynasty there, another little dynasty there. 947 00:56:34,840 --> 00:56:37,680 So we went through all the villages. 948 00:56:37,680 --> 00:56:40,710 And they had to have enough data to do this. 949 00:56:40,710 --> 00:56:48,200 So we ended up with networks. 950 00:56:48,200 --> 00:56:54,970 Now, some villages have more than one, et cetera. 951 00:56:54,970 --> 00:56:58,290 So of the nine with enough data, we're 952 00:56:58,290 --> 00:57:01,620 picking up the theory doing well here and not 953 00:57:01,620 --> 00:57:02,780 in some of the other ones. 954 00:57:02,780 --> 00:57:10,040 So as I said, we go micro, go macro, zooming in and out. 955 00:57:10,040 --> 00:57:15,940 There's a lot of explanation of the rate of return. 956 00:57:15,940 --> 00:57:18,310 That has to do with the village average. 957 00:57:18,310 --> 00:57:20,940 This is villages. 958 00:57:20,940 --> 00:57:29,540 OK, so this has to do with changing projects, basically. 959 00:57:29,540 --> 00:57:30,590 So it's what I said. 960 00:57:30,590 --> 00:57:35,720 We use these sort of five year intervals and redo it. 961 00:57:38,630 --> 00:57:42,880 And kind of reassuringly, Buriram pops back in there. 962 00:57:42,880 --> 00:57:44,690 Because Buriram was the place for sure 963 00:57:44,690 --> 00:57:48,440 that I know that they switched occupations quite a bit 964 00:57:48,440 --> 00:57:51,600 and moved from lower to higher rates of return. 965 00:57:51,600 --> 00:57:54,770 So it's kind of reassuring, given the previous work 966 00:57:54,770 --> 00:58:00,770 to see that this adjustment allows us to recover something. 967 00:58:00,770 --> 00:58:04,790 Although, the r square is nothing to brag about. 968 00:58:08,650 --> 00:58:13,570 Now, another hard thing, easy and hard at the same time, 969 00:58:13,570 --> 00:58:19,220 is human capital, not physical capital. 970 00:58:19,220 --> 00:58:22,070 So as you know, a lot of these households have laborers. 971 00:58:22,070 --> 00:58:24,020 They're earning wages. 972 00:58:24,020 --> 00:58:28,490 And you say, well, what's that the fruit of what tree is that? 973 00:58:28,490 --> 00:58:30,785 Well, the tree is human capital. 974 00:58:30,785 --> 00:58:34,070 Of course, you never really see that. 975 00:58:34,070 --> 00:58:37,030 You can write big H. And you have the notation for it. 976 00:58:37,030 --> 00:58:39,100 But what is it really? 977 00:58:39,100 --> 00:58:43,037 Unfortunately, we don't need the measure of their stock. 978 00:58:43,037 --> 00:58:44,620 All we need to do is measure the flow. 979 00:58:47,400 --> 00:58:49,950 So basically, it's not quite right. 980 00:58:49,950 --> 00:58:53,850 But largely, the return on human capital 981 00:58:53,850 --> 00:58:56,620 are the wages these households are earning. 982 00:58:56,620 --> 00:58:59,700 And we will now put that in the equation as well. 983 00:59:05,423 --> 00:59:07,673 AUDIENCE: Can I ask you a question about [INAUDIBLE]?? 984 00:59:07,673 --> 00:59:08,440 PROFESSOR: Yep. 985 00:59:08,440 --> 00:59:10,330 AUDIENCE: So the way I understand 986 00:59:10,330 --> 00:59:13,092 this is rather than something like skill and talent, 987 00:59:13,092 --> 00:59:14,800 you're saying people [INAUDIBLE] returns, 988 00:59:14,800 --> 00:59:17,000 because they're somewhere all along this return frontier. 989 00:59:17,000 --> 00:59:18,000 PROFESSOR: That's right. 990 00:59:18,000 --> 00:59:21,040 AUDIENCE: So once we think of this model, 991 00:59:21,040 --> 00:59:23,110 like how do we then respond to the big questions 992 00:59:23,110 --> 00:59:27,570 of the puzzles of heterogeneous returns? 993 00:59:27,570 --> 00:59:28,278 Do we know what-- 994 00:59:28,278 --> 00:59:29,737 PROFESSOR: Well, we don't know yet. 995 00:59:29,737 --> 00:59:30,610 I haven't shown you. 996 00:59:30,610 --> 00:59:33,100 Maybe there's no puzzle. 997 00:59:33,100 --> 00:59:34,240 That's the point. 998 00:59:34,240 --> 00:59:37,442 People aren't adjusting. 999 00:59:37,442 --> 00:59:39,330 AUDIENCE: But there's still-- 1000 00:59:39,330 --> 00:59:41,750 PROFESSOR: But anyway, not to keep you in suspense. 1001 00:59:41,750 --> 00:59:44,220 It is going to turn out that there is a residual. 1002 00:59:44,220 --> 00:59:46,440 And then we can see what it's related to. 1003 00:59:46,440 --> 00:59:50,220 And I actually said it's wealthy females who 1004 00:59:50,220 --> 00:59:54,484 have the high residual rate of return. 1005 00:59:54,484 --> 00:59:56,304 AUDIENCE: So essentially the question 1006 00:59:56,304 --> 00:59:59,202 is, given that they're on that [INAUDIBLE] regression line, 1007 00:59:59,202 --> 01:00:00,410 which ones are where and why? 1008 01:00:00,410 --> 01:00:03,500 And part of the answer might be explained by-- 1009 01:00:03,500 --> 01:00:05,920 PROFESSOR: Well, there is part of it 1010 01:00:05,920 --> 01:00:11,940 that we're not explaining, even in the definition of the model, 1011 01:00:11,940 --> 01:00:13,350 in the construction of the model, 1012 01:00:13,350 --> 01:00:16,670 and another part that's outside the model altogether. 1013 01:00:16,670 --> 01:00:19,890 What we're not doing very well is 1014 01:00:19,890 --> 01:00:22,620 why household j is running project i 1015 01:00:22,620 --> 01:00:24,240 and some other household is not. 1016 01:00:24,240 --> 01:00:27,330 We're just acting like the social planner knew 1017 01:00:27,330 --> 01:00:31,530 and efficiently allocated projects across households. 1018 01:00:31,530 --> 01:00:37,330 So that part is sort of related to the talent thing. 1019 01:00:37,330 --> 01:00:38,250 But we never see it. 1020 01:00:42,120 --> 01:00:45,360 We can only look at the residual return, 1021 01:00:45,360 --> 01:00:49,170 which actually ought to be zero if the model is true. 1022 01:00:53,210 --> 01:00:59,030 Anyway, so another adjustment that I've mentioned 1023 01:00:59,030 --> 01:01:02,150 is that a plus bw thing. 1024 01:01:02,150 --> 01:01:07,560 And you might want to have time subscript. 1025 01:01:07,560 --> 01:01:09,100 Sorry, I'm jumping ahead. 1026 01:01:09,100 --> 01:01:10,810 Here's the human capital thing. 1027 01:01:10,810 --> 01:01:15,840 So now the rate of return has two factors a la, basically, 1028 01:01:15,840 --> 01:01:18,600 [INAUDIBLE] type thing, OK? 1029 01:01:18,600 --> 01:01:20,308 One is the physical capital. 1030 01:01:20,308 --> 01:01:21,600 And the other is human capital. 1031 01:01:26,260 --> 01:01:31,420 And we can try to get both betas. 1032 01:01:31,420 --> 01:01:36,760 Another is this problem with the varying shadow prices. 1033 01:01:39,730 --> 01:01:43,990 Well, another way to say this mu, act like mu is a constant. 1034 01:01:43,990 --> 01:01:50,270 Mu t is the value of resources at day t. 1035 01:01:50,270 --> 01:01:52,880 In the derivation, it was always today versus tomorrow. 1036 01:01:52,880 --> 01:01:54,590 And it kind of got suppressed. 1037 01:01:54,590 --> 01:01:56,810 But suppose a village has a run of bad luck, 1038 01:01:56,810 --> 01:01:59,450 like [INAUDIBLE],, with those shrimp ponds going bad. 1039 01:01:59,450 --> 01:02:02,240 Then they have less and less income. 1040 01:02:02,240 --> 01:02:04,970 So you would think mu t is going up. 1041 01:02:04,970 --> 01:02:09,480 Because the marginal value, the shadow price is going up. 1042 01:02:09,480 --> 01:02:12,840 So we really do need to adjust for that. 1043 01:02:12,840 --> 01:02:15,970 But there again, there's a way to do it. 1044 01:02:15,970 --> 01:02:22,600 It turns out that time varying stochastic discount 1045 01:02:22,600 --> 01:02:27,900 factor is related to the consumption wealth ratio. 1046 01:02:27,900 --> 01:02:31,740 And in turn, the law consumption wealth ratio 1047 01:02:31,740 --> 01:02:37,840 depends on three factors, consumption, physical wealth, 1048 01:02:37,840 --> 01:02:41,135 and basically, labor earnings. 1049 01:02:45,760 --> 01:02:47,830 Rather than getting bogged down in the details, 1050 01:02:47,830 --> 01:02:50,470 I think intuitively you could just think, 1051 01:02:50,470 --> 01:02:52,400 well, you know, there's physical capital. 1052 01:02:52,400 --> 01:02:58,210 So basically, the consumption wealth ratio 1053 01:02:58,210 --> 01:03:02,500 is kind of picking up the degree to which they have wealth 1054 01:03:02,500 --> 01:03:04,760 today relative to consumption. 1055 01:03:04,760 --> 01:03:06,790 So that's kind of like an obvious argument 1056 01:03:06,790 --> 01:03:11,200 to have in today's shadow price. 1057 01:03:11,200 --> 01:03:13,280 And these things that determine the consumption 1058 01:03:13,280 --> 01:03:16,960 wealth, or the law consumption wealth ratio, kind of look 1059 01:03:16,960 --> 01:03:21,460 like the accounting variables that we've had before. 1060 01:03:21,460 --> 01:03:24,100 You know, how much you eating? 1061 01:03:24,100 --> 01:03:27,700 Again, how much is your physical capital today? 1062 01:03:27,700 --> 01:03:32,360 And then how much is your labor earnings? 1063 01:03:32,360 --> 01:03:34,780 So that's kind of the spirit of it. 1064 01:03:34,780 --> 01:03:40,280 Again, do our homework and we can find this exact derivation 1065 01:03:40,280 --> 01:03:41,360 in the literature. 1066 01:03:41,360 --> 01:03:44,360 So this consumption asset ratio just looks like this. 1067 01:03:47,490 --> 01:03:50,460 So we find that in the data by regressing it 1068 01:03:50,460 --> 01:03:53,550 on to the arguments that I just mentioned, 1069 01:03:53,550 --> 01:03:55,540 consumption and so on. 1070 01:03:55,540 --> 01:04:00,520 And then we substitute in that estimated value 1071 01:04:00,520 --> 01:04:06,100 into the regression that already was adjusted for human capital. 1072 01:04:06,100 --> 01:04:07,930 So now we just did a double adjustment. 1073 01:04:07,930 --> 01:04:11,470 We put human capital in the rate of return on human capital. 1074 01:04:11,470 --> 01:04:13,660 And now we have extra data terms that 1075 01:04:13,660 --> 01:04:19,090 have to do with the covariance of those physical and human 1076 01:04:19,090 --> 01:04:22,700 capital returns with this. 1077 01:04:22,700 --> 01:04:24,940 So basically, we're just interacting. 1078 01:04:24,940 --> 01:04:26,140 We have levels of things. 1079 01:04:26,140 --> 01:04:29,840 And then we're interacting it with the rates of return. 1080 01:04:29,840 --> 01:04:30,710 So we do that. 1081 01:04:30,710 --> 01:04:31,600 We end up with this. 1082 01:04:31,600 --> 01:04:33,100 It's a longer equation. 1083 01:04:33,100 --> 01:04:34,870 And we run it. 1084 01:04:34,870 --> 01:04:40,450 And we're still getting the beta on physical capital. 1085 01:04:40,450 --> 01:04:42,730 It's quite hardy. 1086 01:04:42,730 --> 01:04:43,495 It's quite robust. 1087 01:04:46,570 --> 01:04:51,610 Human capital is in there sometimes, sometimes not. 1088 01:04:51,610 --> 01:04:54,170 But at least putting it in doesn't harm this. 1089 01:04:54,170 --> 01:04:56,720 In other words, as I said, we do all the adjustments 1090 01:04:56,720 --> 01:04:57,350 that we can. 1091 01:04:57,350 --> 01:05:01,820 And we're still getting the basic result back out. 1092 01:05:05,520 --> 01:05:08,760 Now, you want to know about risk? 1093 01:05:08,760 --> 01:05:12,490 Well, this is the equation that we're running. 1094 01:05:12,490 --> 01:05:15,380 So you can do a decomposition of variance. 1095 01:05:15,380 --> 01:05:18,880 The total variance in returns is just the variance 1096 01:05:18,880 --> 01:05:23,260 having to do with the regression times the variant, 1097 01:05:23,260 --> 01:05:24,640 or basically, this thing. 1098 01:05:24,640 --> 01:05:27,070 This is the contribution of market risk 1099 01:05:27,070 --> 01:05:30,460 to the variance of household j. 1100 01:05:30,460 --> 01:05:36,620 And there's a residual here that we were just chatting about. 1101 01:05:36,620 --> 01:05:39,980 So we estimate its variance. 1102 01:05:39,980 --> 01:05:43,280 And so that's the contribution of idiosyncratic risk 1103 01:05:43,280 --> 01:05:45,245 to the overall variance. 1104 01:05:45,245 --> 01:05:48,530 So now, we have this measure, finally. 1105 01:05:48,530 --> 01:05:52,100 But note that it didn't just come from using the data. 1106 01:05:52,100 --> 01:05:54,590 We used the structure of the model to back it out. 1107 01:06:01,600 --> 01:06:09,180 And that idiosyncratic part is large, at least half 1108 01:06:09,180 --> 01:06:11,590 and in many instances. 1109 01:06:11,590 --> 01:06:14,200 Substantially more than half of the risk 1110 01:06:14,200 --> 01:06:17,110 is due to the idiosyncratic component, rather than 1111 01:06:17,110 --> 01:06:17,970 the aggregate. 1112 01:06:17,970 --> 01:06:20,360 Now, one word of caution. 1113 01:06:20,360 --> 01:06:23,230 We still haven't rejected the model. 1114 01:06:23,230 --> 01:06:27,490 No one in finance says there aren't idiosyncratic returns. 1115 01:06:27,490 --> 01:06:29,800 The question is whether they're priced. 1116 01:06:29,800 --> 01:06:33,850 If you believe in the capital asset model or the consumption 1117 01:06:33,850 --> 01:06:38,350 based risk sharing model, then idiosyncratic returns 1118 01:06:38,350 --> 01:06:38,860 can exist. 1119 01:06:38,860 --> 01:06:40,120 But they're completely pooled. 1120 01:06:43,070 --> 01:06:45,710 So this per se does not reject the model. 1121 01:06:45,710 --> 01:06:51,500 But when we now stick the variance, 1122 01:06:51,500 --> 01:06:57,060 sigma j, into the benchmark model. 1123 01:06:57,060 --> 01:07:02,210 And we're still doing OK with aggregate risk. 1124 01:07:02,210 --> 01:07:04,110 But here's the rejection, if you like. 1125 01:07:04,110 --> 01:07:07,260 The idiosyncratic risk is positively 1126 01:07:07,260 --> 01:07:09,590 associated with expected rate of return 1127 01:07:09,590 --> 01:07:12,370 and for all the households. 1128 01:07:12,370 --> 01:07:19,450 Now, this is the if you like, the disappointing part, 1129 01:07:19,450 --> 01:07:22,390 or the tension, which is you go to all 1130 01:07:22,390 --> 01:07:25,030 this work with a benchmark. 1131 01:07:25,030 --> 01:07:26,710 And it seems to be doing really well. 1132 01:07:26,710 --> 01:07:32,380 But there are features of the data against which 1133 01:07:32,380 --> 01:07:33,400 it's not doing well. 1134 01:07:37,090 --> 01:07:41,620 So it's clear that it's not an entirely perfect markets 1135 01:07:41,620 --> 01:07:44,860 world from the point of view of the rate of return 1136 01:07:44,860 --> 01:07:47,470 of these assets. 1137 01:07:47,470 --> 01:07:49,570 But is the glass half empty or half full? 1138 01:07:49,570 --> 01:07:53,080 Because it's also true that a substantial amount 1139 01:07:53,080 --> 01:07:55,600 of the rates of return had to do with market risk. 1140 01:07:55,600 --> 01:07:58,590 And most development researchers would 1141 01:07:58,590 --> 01:08:00,030 have ignored that market part. 1142 01:08:00,030 --> 01:08:02,820 I think it's fair to say, even though it's 1143 01:08:02,820 --> 01:08:05,160 kind of a natural corollary to risk sharing. 1144 01:08:19,540 --> 01:08:21,099 So let's go back to these alphas. 1145 01:08:26,029 --> 01:08:29,290 So Jensen talks about having portfolio managers who 1146 01:08:29,290 --> 01:08:32,630 are somehow smarter or better than others. 1147 01:08:32,630 --> 01:08:34,665 And they have abnormal returns. 1148 01:08:34,665 --> 01:08:35,540 I mean, I don't know. 1149 01:08:35,540 --> 01:08:37,359 This is kind of hard for economists. 1150 01:08:37,359 --> 01:08:42,380 It's like, well, if you do so well, why don't everyone 1151 01:08:42,380 --> 01:08:43,580 just go in there? 1152 01:08:43,580 --> 01:08:46,590 Like, I never make money. 1153 01:08:46,590 --> 01:08:47,960 I don't trust my instincts. 1154 01:08:47,960 --> 01:08:54,890 But I'll tell you story about Walmart. 1155 01:08:54,890 --> 01:08:59,330 So one of my colleagues who was at Chicago, a sociologist, 1156 01:08:59,330 --> 01:09:00,450 was in Arkansas. 1157 01:09:00,450 --> 01:09:06,420 And he saw this big square flat building in northern Arkansas. 1158 01:09:06,420 --> 01:09:09,029 And he sort of checked it out and said, 1159 01:09:09,029 --> 01:09:11,470 well, this is a really novel way of doing business. 1160 01:09:11,470 --> 01:09:14,175 Well, it turned out to be practically the first branch 1161 01:09:14,175 --> 01:09:14,675 of Walmart. 1162 01:09:14,675 --> 01:09:15,769 And he bought stock. 1163 01:09:18,290 --> 01:09:22,069 He did quite well obviously. 1164 01:09:22,069 --> 01:09:24,952 Anyway, so maybe some portfolio managers 1165 01:09:24,952 --> 01:09:25,910 are better than others. 1166 01:09:25,910 --> 01:09:30,300 Maybe some households are somehow better than others. 1167 01:09:30,300 --> 01:09:39,080 And we've now got a way of adjusting for all those risk 1168 01:09:39,080 --> 01:09:44,270 factors, both the idiosyncratic and the aggregate. 1169 01:09:44,270 --> 01:09:46,970 By the way, you will be relieved a bit 1170 01:09:46,970 --> 01:09:49,910 maybe to know that when we rank order 1171 01:09:49,910 --> 01:09:52,490 the households by the unadjusted rates of return 1172 01:09:52,490 --> 01:09:54,680 and the risk adjusted rates of return, 1173 01:09:54,680 --> 01:09:58,280 the ordering is largely preserved. 1174 01:09:58,280 --> 01:10:00,590 But the orders of magnitude are not. 1175 01:10:00,590 --> 01:10:03,140 The second point is it's not just completely 1176 01:10:03,140 --> 01:10:06,920 downshifting the distribution after you subtract stuff off. 1177 01:10:06,920 --> 01:10:08,180 The tails come in. 1178 01:10:08,180 --> 01:10:10,760 So it has a different level of skewness. 1179 01:10:10,760 --> 01:10:14,840 So it's kind of a serious filter on the data. 1180 01:10:14,840 --> 01:10:19,820 But some of the earlier results that poor households 1181 01:10:19,820 --> 01:10:22,775 have high rates of return and reinvest in their own projects, 1182 01:10:22,775 --> 01:10:23,900 we're going to rerun those. 1183 01:10:23,900 --> 01:10:28,130 But we're pretty confident those kind of results don't go away. 1184 01:10:28,130 --> 01:10:30,665 And I haven't misled you in the earlier lectures. 1185 01:10:33,720 --> 01:10:39,690 So finally, here is running these regressions, where 1186 01:10:39,690 --> 01:10:43,950 we have aggregate risk, also allow idiosyncratic 1187 01:10:43,950 --> 01:10:51,120 risk, where we have the betas on aggregate physical capital 1188 01:10:51,120 --> 01:10:53,560 and the coefficients on sigma. 1189 01:10:53,560 --> 01:11:04,050 So the first two slides I said households who are older 1190 01:11:04,050 --> 01:11:06,420 take on less risk, which means basically, 1191 01:11:06,420 --> 01:11:08,550 both the idiosyncratic and aggregate risk 1192 01:11:08,550 --> 01:11:11,050 factors are negative. 1193 01:11:11,050 --> 01:11:15,990 You might be willing to tell a demographic story for that. 1194 01:11:15,990 --> 01:11:18,130 We don't really have it embedded in the model. 1195 01:11:18,130 --> 01:11:23,750 It's more like a residual or behavioral thing at this point. 1196 01:11:23,750 --> 01:11:27,740 Because these residuals aren't supposed to be there. 1197 01:11:27,740 --> 01:11:32,950 And here is basically the wealth again, negative. 1198 01:11:32,950 --> 01:11:40,450 So poor people have higher correlation of their activities 1199 01:11:40,450 --> 01:11:42,650 with a village average. 1200 01:11:42,650 --> 01:11:45,215 And the residual have a higher residual variance. 1201 01:11:47,765 --> 01:11:49,990 I'm going to come back to that. 1202 01:11:49,990 --> 01:11:52,350 Poor people seem to be exposed to a lot of risk. 1203 01:11:57,870 --> 01:12:04,470 However, if you take out both sources of risk and regress 1204 01:12:04,470 --> 01:12:07,260 on demographics and all these things, 1205 01:12:07,260 --> 01:12:10,050 wealth finally goes positive. 1206 01:12:10,050 --> 01:12:17,970 And also, this is a dummy for male, so to speak, is negative. 1207 01:12:17,970 --> 01:12:22,590 So that the female headed households and the high wealth 1208 01:12:22,590 --> 01:12:25,950 households are the households with the highest sort 1209 01:12:25,950 --> 01:12:27,380 of residual rates of return. 1210 01:12:33,300 --> 01:12:40,350 OK, so now what I don't have in front of me unfortunately, 1211 01:12:40,350 --> 01:12:42,750 we didn't quite get close enough. 1212 01:12:42,750 --> 01:12:45,960 But you may remember that QJE paper from lecture one 1213 01:12:45,960 --> 01:12:50,250 on volatility, growth, finance, what's related? 1214 01:12:50,250 --> 01:12:52,860 And we said, well, we've got to look at sectors. 1215 01:12:52,860 --> 01:12:55,710 We've got to figure out how much each sector is contributing 1216 01:12:55,710 --> 01:12:59,280 to overall change in value added. 1217 01:12:59,280 --> 01:13:01,460 And there was some really cool decomposition. 1218 01:13:01,460 --> 01:13:05,650 So we're running that on these Thai data. 1219 01:13:05,650 --> 01:13:12,430 So we can see at the level of income 1220 01:13:12,430 --> 01:13:14,420 how diversified are these households? 1221 01:13:14,420 --> 01:13:20,390 It's similar, but not identical to this CAPM type approach. 1222 01:13:20,390 --> 01:13:22,930 And so far at least, we're getting the same answer, 1223 01:13:22,930 --> 01:13:28,330 that it's the relatively poor households who are specialized. 1224 01:13:28,330 --> 01:13:30,090 And the things they specialize in 1225 01:13:30,090 --> 01:13:38,300 have high volatility, and so on. 1226 01:13:38,300 --> 01:13:41,360 So poor people seem to be exposed to risk 1227 01:13:41,360 --> 01:13:42,740 at least on the income side. 1228 01:13:47,220 --> 01:13:57,560 So here's moving to Sweden, more sort of standard asset 1229 01:13:57,560 --> 01:14:02,310 stuff, which John Campbell and co-authors 1230 01:14:02,310 --> 01:14:05,580 have done called Down or Out. 1231 01:14:05,580 --> 01:14:11,780 And what they're trying to do is very similar. 1232 01:14:11,780 --> 01:14:15,170 They're trying to look at household management 1233 01:14:15,170 --> 01:14:18,890 of financial affairs using measurement 1234 01:14:18,890 --> 01:14:22,760 in this amazing Swedish data. 1235 01:14:22,760 --> 01:14:25,580 Sweden is a socialist country largely. 1236 01:14:25,580 --> 01:14:27,080 And they measure everything. 1237 01:14:27,080 --> 01:14:31,160 And everyone has a common ID, and your whole portfolio, 1238 01:14:31,160 --> 01:14:32,810 labor supply, everything. 1239 01:14:35,790 --> 01:14:38,720 So I've been collaborating a little bit 1240 01:14:38,720 --> 01:14:45,190 with a Riksbank largely influenced by this paper. 1241 01:14:45,190 --> 01:14:48,550 Now unfortunately, it takes us away from development. 1242 01:14:48,550 --> 01:14:49,690 That's not my point. 1243 01:14:49,690 --> 01:14:51,680 My point is the commonality. 1244 01:14:51,680 --> 01:14:53,680 They're going to look at mean variance frontiers 1245 01:14:53,680 --> 01:14:56,080 and see what households are doing. 1246 01:14:56,080 --> 01:14:59,770 In particular, what are the poor people doing or the rich ones? 1247 01:15:03,080 --> 01:15:04,790 The focus is a bit different, which is 1248 01:15:04,790 --> 01:15:07,560 households can make mistakes. 1249 01:15:07,560 --> 01:15:13,400 In other words, let's just assume the model is right. 1250 01:15:13,400 --> 01:15:15,680 And the mean variance frontier is 1251 01:15:15,680 --> 01:15:19,460 what it is and then see households in the interior who 1252 01:15:19,460 --> 01:15:21,538 could get less variance or a higher mean 1253 01:15:21,538 --> 01:15:22,955 if they only move to the frontier. 1254 01:15:25,560 --> 01:15:27,450 And then they look by characteristics, 1255 01:15:27,450 --> 01:15:29,340 like education, wealth, and so on 1256 01:15:29,340 --> 01:15:35,130 to see who is under diversified-- 1257 01:15:35,130 --> 01:15:37,480 those are the down people-- 1258 01:15:37,480 --> 01:15:40,360 and who's not participating as in the stock market. 1259 01:15:40,360 --> 01:15:42,840 Those are the out people. 1260 01:15:42,840 --> 01:15:47,190 And hence the title, very clever, Down and Out. 1261 01:15:47,190 --> 01:15:51,820 And they measure the welfare costs of those deviations. 1262 01:15:51,820 --> 01:15:53,450 As I said, they have amazing data. 1263 01:15:53,450 --> 01:15:59,440 And here you can see sort of how households manage their growth 1264 01:15:59,440 --> 01:16:01,720 wealth in Sweden. 1265 01:16:01,720 --> 01:16:03,160 This is the cash. 1266 01:16:03,160 --> 01:16:03,910 Oh, look at that. 1267 01:16:03,910 --> 01:16:07,780 Poor people have a lot of cash. 1268 01:16:07,780 --> 01:16:10,000 I think cash just doesn't mean Swedish krona. 1269 01:16:10,000 --> 01:16:13,035 I think it also means bank accounts. 1270 01:16:17,480 --> 01:16:19,980 But stocks, poor people don't hold stocks. 1271 01:16:23,200 --> 01:16:26,350 Mutual fund has this funny hunch-- now, 1272 01:16:26,350 --> 01:16:29,860 it's interesting that this is real estate. 1273 01:16:29,860 --> 01:16:33,430 So this is both financial as well as real. 1274 01:16:33,430 --> 01:16:37,340 And on a household side, there are some businesses here 1275 01:16:37,340 --> 01:16:37,840 actually. 1276 01:16:37,840 --> 01:16:43,520 But most of these households are salary employees. 1277 01:16:43,520 --> 01:16:45,660 But they can hold durable goods in housing. 1278 01:16:45,660 --> 01:16:50,750 If you take the physical housing wealth out of it, 1279 01:16:50,750 --> 01:16:52,895 then the cash thing is still going down. 1280 01:16:56,290 --> 01:16:59,410 The mutual funds is largely flat, except at the very low 1281 01:16:59,410 --> 01:17:00,160 and the high end. 1282 01:17:00,160 --> 01:17:02,380 And then you see this stock. 1283 01:17:05,350 --> 01:17:08,880 It's the 90 percentile up are the people who 1284 01:17:08,880 --> 01:17:13,690 have reasonably substantial holdings in the stocks. 1285 01:17:13,690 --> 01:17:17,650 I ask myself these questions a lot in Thailand. 1286 01:17:17,650 --> 01:17:21,960 Sort of maybe they shouldn't be investing 1287 01:17:21,960 --> 01:17:22,890 in their own projects. 1288 01:17:22,890 --> 01:17:27,510 Maybe they should be investing in Bangkok money market 1289 01:17:27,510 --> 01:17:31,520 funds, safe funds. 1290 01:17:31,520 --> 01:17:33,950 We should be sort of looking at the whole mean variance 1291 01:17:33,950 --> 01:17:36,100 frontier for these. 1292 01:17:36,100 --> 01:17:37,420 And we are asking them now. 1293 01:17:37,420 --> 01:17:38,605 We're actively involved. 1294 01:17:38,605 --> 01:17:41,150 I was on the phone again last night. 1295 01:17:41,150 --> 01:17:45,800 We're about to be asking them a bunch of questions about, 1296 01:17:45,800 --> 01:17:47,370 are they aware of other assets? 1297 01:17:50,150 --> 01:17:53,540 But in Sweden the point that Campbell is going to make 1298 01:17:53,540 --> 01:18:02,180 is you've got those categories. 1299 01:18:02,180 --> 01:18:06,050 And households can make mistakes by picking volatile assets, 1300 01:18:06,050 --> 01:18:09,380 holding a concentrated portfolio, picking correlated. 1301 01:18:09,380 --> 01:18:11,930 See the parallel here with what I was saying 1302 01:18:11,930 --> 01:18:17,630 happens in the Thai villages in terms of relatively poor people 1303 01:18:17,630 --> 01:18:19,910 not being diversified and for some reason 1304 01:18:19,910 --> 01:18:20,960 doing riskier things. 1305 01:18:24,400 --> 01:18:26,080 Or if you go in the stock market, 1306 01:18:26,080 --> 01:18:28,035 you could pick your own stocks. 1307 01:18:28,035 --> 01:18:30,400 It's not a particularly clever thing to do. 1308 01:18:34,210 --> 01:18:36,280 And this is the picture that makes the paper. 1309 01:18:40,570 --> 01:18:42,960 So here's the sort of mean variance 1310 01:18:42,960 --> 01:18:46,140 frontier, standard deviation in means. 1311 01:18:46,140 --> 01:18:49,630 Here's where they ought to be. 1312 01:18:49,630 --> 01:18:52,210 Adjusting or not for international asset holdings, 1313 01:18:52,210 --> 01:18:52,840 that's another. 1314 01:18:52,840 --> 01:18:54,790 They do both. 1315 01:18:54,790 --> 01:19:01,880 But they're basically saying, small guys in some sense 1316 01:19:01,880 --> 01:19:03,950 are unsophisticated and cautious. 1317 01:19:03,950 --> 01:19:05,720 They're pretty far off the frontier. 1318 01:19:05,720 --> 01:19:09,320 But they don't have kind of a lot to lose. 1319 01:19:09,320 --> 01:19:17,390 And these richer guys up here, they're more sophisticated. 1320 01:19:17,390 --> 01:19:20,840 Their line is quote unquote above this brown one. 1321 01:19:20,840 --> 01:19:22,190 But their gap is huge. 1322 01:19:22,190 --> 01:19:25,330 So I'll spare you the details. 1323 01:19:25,330 --> 01:19:27,350 They're actually measuring the welfare loss. 1324 01:19:27,350 --> 01:19:30,050 And some of these richer households are-- 1325 01:19:30,050 --> 01:19:33,410 because they are not diversifying-- actually 1326 01:19:33,410 --> 01:19:36,740 have fairly substantial welfare losses. 1327 01:19:36,740 --> 01:19:42,020 Now, John goes behavioral in this and maybe rightly so. 1328 01:19:42,020 --> 01:19:47,270 He's saying should we really be telling households in Brazil 1329 01:19:47,270 --> 01:19:50,450 about investing in whatever is [INAUDIBLE].. 1330 01:19:50,450 --> 01:19:53,480 I can't remember the acronym. 1331 01:19:53,480 --> 01:19:55,010 Or are they going to make mistakes 1332 01:19:55,010 --> 01:19:57,500 and they're better off not knowing? 1333 01:19:57,500 --> 01:19:58,430 There was a question. 1334 01:19:58,430 --> 01:20:00,430 AUDIENCE: This is already answered by the model, 1335 01:20:00,430 --> 01:20:02,830 but this is welfare. 1336 01:20:02,830 --> 01:20:05,510 This takes into account the marginal utility of wealth. 1337 01:20:05,510 --> 01:20:07,790 PROFESSOR: Yeah, actually, I'm sparing you a lot. 1338 01:20:07,790 --> 01:20:08,570 Oh, I should say. 1339 01:20:08,570 --> 01:20:10,617 This is on the reading list. 1340 01:20:10,617 --> 01:20:12,200 But I knew I wasn't going to have time 1341 01:20:12,200 --> 01:20:13,820 to cover it in much detail. 1342 01:20:13,820 --> 01:20:16,070 So I picked like six slides. 1343 01:20:16,070 --> 01:20:19,160 But I'll post the whole paper. 1344 01:20:19,160 --> 01:20:21,200 If you're interested, you don't necessarily 1345 01:20:21,200 --> 01:20:23,975 want to or have time to read the whole paper. 1346 01:20:23,975 --> 01:20:25,850 You might as well look at these lecture notes 1347 01:20:25,850 --> 01:20:28,110 that I created previously. 1348 01:20:28,110 --> 01:20:32,200 And the same thing for this paper, 1349 01:20:32,200 --> 01:20:36,220 which is [INAUDIBLE] with [INAUDIBLE],, Dynamic Risk 1350 01:20:36,220 --> 01:20:36,720 Management. 1351 01:20:36,720 --> 01:20:38,160 I've only got a few slides. 1352 01:20:38,160 --> 01:20:40,630 I think I'm going to jump and show you something. 1353 01:20:43,210 --> 01:20:44,190 Fly Southwest. 1354 01:20:46,790 --> 01:20:48,630 So this guy's loading that airplane 1355 01:20:48,630 --> 01:20:51,720 that capital stock up with this variable input, the fuel. 1356 01:20:54,760 --> 01:20:58,290 They buy forward positions. 1357 01:20:58,290 --> 01:21:02,480 Because the price of gasoline moves around a lot. 1358 01:21:02,480 --> 01:21:06,710 So they basically buy forward, OK? 1359 01:21:06,710 --> 01:21:11,640 They commit now to buy gasoline at a pegged future price. 1360 01:21:11,640 --> 01:21:14,150 Now, what happens if the spot price is lower than that? 1361 01:21:14,150 --> 01:21:16,010 It's like, oh, darn. 1362 01:21:16,010 --> 01:21:17,870 We should've waited. 1363 01:21:17,870 --> 01:21:19,910 Actually, you could renege on that contract. 1364 01:21:22,680 --> 01:21:24,690 And so what do they do with those things? 1365 01:21:24,690 --> 01:21:30,950 You've got to post collateral against these forward gasoline 1366 01:21:30,950 --> 01:21:31,450 hedges. 1367 01:21:34,190 --> 01:21:36,210 Where are we going with this? 1368 01:21:36,210 --> 01:21:40,490 We're going to get to sort of thinking about something 1369 01:21:40,490 --> 01:21:47,100 that Chris [INAUDIBLE] was doing in Ghana, which is, 1370 01:21:47,100 --> 01:21:55,370 do you want to use your scarce collateral to borrow and get 1371 01:21:55,370 --> 01:22:00,290 more aircraft with potentially high rate of return? 1372 01:22:00,290 --> 01:22:02,480 Or do you want to use your scarce collateral 1373 01:22:02,480 --> 01:22:05,750 and tie it up hedging against future states 1374 01:22:05,750 --> 01:22:08,260 of the world s prime? 1375 01:22:08,260 --> 01:22:13,260 And this paper is about how in practice this may not happen. 1376 01:22:13,260 --> 01:22:15,280 Now, when does it happen? 1377 01:22:19,900 --> 01:22:21,690 Where is it? 1378 01:22:21,690 --> 01:22:26,320 It happens when the airline isn't doing very well. 1379 01:22:26,320 --> 01:22:32,110 So if you think about relatively poor households, it's like, oh, 1380 01:22:32,110 --> 01:22:32,980 they're behavioral. 1381 01:22:32,980 --> 01:22:35,270 They're not buying insurance. 1382 01:22:35,270 --> 01:22:36,450 What's wrong with them? 1383 01:22:36,450 --> 01:22:37,330 They need it most. 1384 01:22:37,330 --> 01:22:40,260 They've got the most marginal value. 1385 01:22:40,260 --> 01:22:42,340 Well, no, not necessarily. 1386 01:22:42,340 --> 01:22:45,320 They may have better use for their existing wealth. 1387 01:22:45,320 --> 01:22:49,810 So we're getting again, very explicitly now into obstacles. 1388 01:22:49,810 --> 01:22:53,050 So when you start writing down models with obstacles 1389 01:22:53,050 --> 01:22:56,230 and barriers to trade, you can get 1390 01:22:56,230 --> 01:23:00,040 at this issue about borrowing to finance 1391 01:23:00,040 --> 01:23:02,110 projects versus borrowing. 1392 01:23:02,110 --> 01:23:05,620 So maybe it's still possible that those relatively poor 1393 01:23:05,620 --> 01:23:07,810 people who seem to be doing really risky things 1394 01:23:07,810 --> 01:23:09,940 and aren't hedged against it, maybe 1395 01:23:09,940 --> 01:23:12,840 there's a reason for that.