1 00:00:00,000 --> 00:00:02,435 [SQUEAKING] 2 00:00:02,435 --> 00:00:04,383 [RUSTLING] 3 00:00:04,383 --> 00:00:06,818 [CLICKING] 4 00:00:11,055 --> 00:00:12,180 FRANK SCHILBACH: All right. 5 00:00:12,180 --> 00:00:16,088 Welcome to lectures seven and eight. 6 00:00:16,088 --> 00:00:17,880 We're going to talk about risk preferences. 7 00:00:17,880 --> 00:00:18,830 Hello? 8 00:00:18,830 --> 00:00:21,190 We're going to talk about risk preferences. 9 00:00:21,190 --> 00:00:23,010 In particular, sort from the perspective 10 00:00:23,010 --> 00:00:25,440 of expected utility, which is sort of the classical way 11 00:00:25,440 --> 00:00:27,270 of economics to view this. 12 00:00:27,270 --> 00:00:32,475 This is going to take one and 1/2, perhaps two lectures. 13 00:00:32,475 --> 00:00:34,350 Broadly speaking, we're going to look at what 14 00:00:34,350 --> 00:00:35,820 does economics usually assume. 15 00:00:35,820 --> 00:00:38,340 How does economics think about risk preferences, 16 00:00:38,340 --> 00:00:42,280 about choices involving risk? 17 00:00:42,280 --> 00:00:45,900 How do we think about sort of measuring risk preferences? 18 00:00:45,900 --> 00:00:48,330 What are some of the implications and what are some 19 00:00:48,330 --> 00:00:50,700 of the limits of risk preferences in terms of what we 20 00:00:50,700 --> 00:00:53,760 can explain and what we cannot explain? 21 00:00:53,760 --> 00:00:56,280 And then in the following lectures 22 00:00:56,280 --> 00:00:59,280 we're going to have an alternative model of reference 23 00:00:59,280 --> 00:01:01,792 dependence preferences where essentially you're 24 00:01:01,792 --> 00:01:03,750 going to relax or change some of the underlying 25 00:01:03,750 --> 00:01:10,770 assumptions on how to measure preferences related to risk. 26 00:01:10,770 --> 00:01:14,170 Problem set two will be posted soon-- later this week. 27 00:01:14,170 --> 00:01:16,380 I'm sure you can't wait for this. 28 00:01:16,380 --> 00:01:22,183 A reminder, late submissions will not be accepted. 29 00:01:22,183 --> 00:01:23,850 This is always like a commitment problem 30 00:01:23,850 --> 00:01:26,370 because people come up with all sorts of good excuses 31 00:01:26,370 --> 00:01:29,058 why they submitted the problem set late 32 00:01:29,058 --> 00:01:30,600 and then I kind of feel bad about it. 33 00:01:30,600 --> 00:01:33,030 So I'm here with committing to not accepting 34 00:01:33,030 --> 00:01:34,530 any late submissions for whatever 35 00:01:34,530 --> 00:01:37,200 reasons unless you have sort of a medical excuse 36 00:01:37,200 --> 00:01:41,730 or sort of an excuse notice. 37 00:01:41,730 --> 00:01:44,460 So no my PDF was corrupted and all sorts 38 00:01:44,460 --> 00:01:45,780 of other good reasons. 39 00:01:45,780 --> 00:01:48,060 I was a student once as well and I know 40 00:01:48,060 --> 00:01:51,060 students are very creative. 41 00:01:51,060 --> 00:01:54,330 We will post previous problems sets, midterms, and finals 42 00:01:54,330 --> 00:01:55,530 for you to practice overall. 43 00:01:55,530 --> 00:01:57,510 I think of the problem sets less of a way 44 00:01:57,510 --> 00:02:01,650 for testing you or testing sort of whether you can do it 45 00:02:01,650 --> 00:02:04,050 or not, but rather as a way for you to practice things, 46 00:02:04,050 --> 00:02:07,388 whether you have understood the materials in parts 47 00:02:07,388 --> 00:02:08,430 of the past problem sets. 48 00:02:08,430 --> 00:02:11,700 And midterms and finals will sort of help you with that. 49 00:02:11,700 --> 00:02:14,160 As usual, please ask questions on Piazza 50 00:02:14,160 --> 00:02:16,630 or come to office hours. 51 00:02:16,630 --> 00:02:18,180 So what we're going to talk about 52 00:02:18,180 --> 00:02:20,160 is, broadly speaking risk aversion. 53 00:02:20,160 --> 00:02:24,520 How do economists think about choices involving risk? 54 00:02:24,520 --> 00:02:28,350 Then again, I sort of outline sort of the very simple 55 00:02:28,350 --> 00:02:31,650 or the basic model of-- 56 00:02:31,650 --> 00:02:33,420 main workhorse model of economics-- 57 00:02:33,420 --> 00:02:35,378 is to think about choices involving risk, which 58 00:02:35,378 --> 00:02:37,100 is the expected utility model. 59 00:02:37,100 --> 00:02:38,885 We're going to then think about how do we 60 00:02:38,885 --> 00:02:41,010 measure risk preferences, the underlying preference 61 00:02:41,010 --> 00:02:45,600 parameters that sort of are embedded in this model. 62 00:02:45,600 --> 00:02:48,780 We're going to lead then to some absurd implications 63 00:02:48,780 --> 00:02:49,720 in particular. 64 00:02:49,720 --> 00:02:52,680 So discrepancy-- how people tend to think about small scale 65 00:02:52,680 --> 00:02:54,540 and large scale risk aversion. 66 00:02:54,540 --> 00:02:56,820 What I mean by that-- essentially small gambles that 67 00:02:56,820 --> 00:03:00,300 involve a few dollars versus really large scale choices 68 00:03:00,300 --> 00:03:02,430 that involve thousands of dollars. 69 00:03:02,430 --> 00:03:05,760 And what I'm going to show you, very similar to some degree 70 00:03:05,760 --> 00:03:10,860 to how we think about time preferences where the typical 71 00:03:10,860 --> 00:03:15,330 exponential discounting model cannot explain both short run 72 00:03:15,330 --> 00:03:17,848 and long run time preference decisions that people make. 73 00:03:17,848 --> 00:03:19,390 That's just a sort of a calibration-- 74 00:03:19,390 --> 00:03:20,760 really very hard to do. 75 00:03:20,760 --> 00:03:22,680 Similarly, the expected utility model 76 00:03:22,680 --> 00:03:27,270 has problems with reconciling small scale and large scale 77 00:03:27,270 --> 00:03:29,273 choices that people make. 78 00:03:29,273 --> 00:03:30,690 I'll tell you that in more detail. 79 00:03:30,690 --> 00:03:33,000 But in short, the summary is if people 80 00:03:33,000 --> 00:03:36,960 are risk averse when it comes to small gambles, that implies 81 00:03:36,960 --> 00:03:39,210 that they're absurdly risk averse coming 82 00:03:39,210 --> 00:03:42,220 from large gambles if you sort of take that model seriously. 83 00:03:42,220 --> 00:03:46,150 And so that's kind of like not really true in reality. 84 00:03:46,150 --> 00:03:47,670 And so then we sort think about how 85 00:03:47,670 --> 00:03:49,960 to relax those kinds of assumptions. 86 00:03:49,960 --> 00:03:50,460 OK. 87 00:03:50,460 --> 00:03:53,850 So first let's think about what kinds of choices and decisions 88 00:03:53,850 --> 00:03:56,070 do in fact involve risk and uncertainty. 89 00:03:56,070 --> 00:04:00,930 What examples do we have in your life? 90 00:04:00,930 --> 00:04:05,980 What is risky or what would involve uncertainty? 91 00:04:05,980 --> 00:04:06,480 Yes? 92 00:04:06,480 --> 00:04:08,452 AUDIENCE: Whether or not [INAUDIBLE].. 93 00:04:11,382 --> 00:04:12,340 FRANK SCHILBACH: Right. 94 00:04:12,340 --> 00:04:13,930 Whether or not to get education. 95 00:04:13,930 --> 00:04:15,880 Whether or not to study and so on. 96 00:04:15,880 --> 00:04:17,680 Because the reward often is like uncertain. 97 00:04:17,680 --> 00:04:17,860 Right? 98 00:04:17,860 --> 00:04:18,579 You might get a job. 99 00:04:18,579 --> 00:04:19,540 You might not get a job. 100 00:04:19,540 --> 00:04:21,040 You might do really well in college. 101 00:04:21,040 --> 00:04:22,130 You might not. 102 00:04:22,130 --> 00:04:23,090 And so on and so forth. 103 00:04:23,090 --> 00:04:26,870 So the costs-- you might like it, you might not like it, 104 00:04:26,870 --> 00:04:27,370 and so on. 105 00:04:27,370 --> 00:04:28,840 It's not clear. 106 00:04:28,840 --> 00:04:30,640 So the costs and benefits are uncertain. 107 00:04:30,640 --> 00:04:32,240 There might be a recession when you graduate. 108 00:04:32,240 --> 00:04:33,198 And so on and so forth. 109 00:04:33,198 --> 00:04:36,489 So the returns and costs are both uncertain. 110 00:04:40,380 --> 00:04:40,880 Yes? 111 00:04:40,880 --> 00:04:42,358 AUDIENCE: Making large purchases, 112 00:04:42,358 --> 00:04:44,230 like buying [INAUDIBLE]. 113 00:04:44,230 --> 00:04:46,110 Because you don't know [INAUDIBLE].. 114 00:04:46,110 --> 00:04:47,450 FRANK SCHILBACH: Yeah, exactly. 115 00:04:47,450 --> 00:04:50,400 You might buy a house or you might 116 00:04:50,400 --> 00:04:53,582 think about buying or renting more broadly. 117 00:04:53,582 --> 00:04:55,290 And there it depends a lot on essentially 118 00:04:55,290 --> 00:04:56,915 what's happening to the housing market. 119 00:04:56,915 --> 00:04:59,070 If the housing market goes up or down, 120 00:04:59,070 --> 00:05:01,930 the choice to buy a house versus renting is very different. 121 00:05:01,930 --> 00:05:02,430 Right? 122 00:05:02,430 --> 00:05:04,305 So if the housing market goes up, most likely 123 00:05:04,305 --> 00:05:05,638 you should probably buy a house. 124 00:05:05,638 --> 00:05:07,650 If the housing market actually happens to tank, 125 00:05:07,650 --> 00:05:10,050 the [INAUDIBLE] [? at ?] [? least ?] it's a bad idea 126 00:05:10,050 --> 00:05:11,430 to do so. 127 00:05:11,430 --> 00:05:12,570 Yes? 128 00:05:12,570 --> 00:05:14,972 AUDIENCE: [INAUDIBLE] [? renters ?] insurance. 129 00:05:14,972 --> 00:05:15,930 FRANK SCHILBACH: Right. 130 00:05:15,930 --> 00:05:18,210 So the two choices that we have so far 131 00:05:18,210 --> 00:05:19,740 were essentially choices involving 132 00:05:19,740 --> 00:05:21,210 risk where you sort of essentially 133 00:05:21,210 --> 00:05:23,370 decide to do something where the outcomes are 134 00:05:23,370 --> 00:05:25,105 uncertain or risky in some way. 135 00:05:25,105 --> 00:05:26,730 Now, what you're saying, in some sense, 136 00:05:26,730 --> 00:05:28,770 is like, a bunch of other choices, 137 00:05:28,770 --> 00:05:31,830 potentially, are risk mitigation strategies. 138 00:05:31,830 --> 00:05:35,040 So you have, essentially, certain risk in your life. 139 00:05:35,040 --> 00:05:36,840 And you have choices where you could say, 140 00:05:36,840 --> 00:05:37,890 I could buy insurance. 141 00:05:37,890 --> 00:05:41,460 Or I could sort make other choices that mitigate or reduce 142 00:05:41,460 --> 00:05:43,470 the risk that I'm exposed to. 143 00:05:43,470 --> 00:05:45,480 And one sort of canonical example of that 144 00:05:45,480 --> 00:05:49,260 is purchasing any type of insurance 145 00:05:49,260 --> 00:05:51,720 but, in particular, renter's insurance, as you mentioned. 146 00:05:51,720 --> 00:05:53,460 Yes. 147 00:05:53,460 --> 00:05:54,231 Yeah? 148 00:05:54,231 --> 00:05:57,320 AUDIENCE: For farmers, the crop they choose to grow. 149 00:05:57,320 --> 00:06:00,390 FRANK SCHILBACH: Yes, so essentially, call that-- 150 00:06:00,390 --> 00:06:03,210 in development in particular, or development economics 151 00:06:03,210 --> 00:06:06,660 in particular, there's lots of issues of production choices 152 00:06:06,660 --> 00:06:08,280 that people make. 153 00:06:08,280 --> 00:06:10,680 This could be like what crops to grow, whether you should 154 00:06:10,680 --> 00:06:13,800 buy a machine, whether you should start a business, 155 00:06:13,800 --> 00:06:14,300 and so on. 156 00:06:14,300 --> 00:06:16,440 So there's all sorts of choices in terms 157 00:06:16,440 --> 00:06:21,360 of what business to go into, what kinds of specifics, 158 00:06:21,360 --> 00:06:23,610 what product to sell if you have a business. 159 00:06:23,610 --> 00:06:27,480 And in the farmer case, what crops should you grow? 160 00:06:27,480 --> 00:06:28,860 Should you buy fertilizer? 161 00:06:28,860 --> 00:06:32,700 Should you use other inputs and so on and so forth. 162 00:06:32,700 --> 00:06:34,080 Should you do [INAUDIBLE] there's 163 00:06:34,080 --> 00:06:36,163 a bunch of different other-- should you intercrop? 164 00:06:36,163 --> 00:06:38,070 There's a bunch of different other choices 165 00:06:38,070 --> 00:06:41,970 that you could make that essentially involve risks, 166 00:06:41,970 --> 00:06:44,022 because the outcome, essentially, is uncertain, 167 00:06:44,022 --> 00:06:46,230 because essentially, the season might be good or bad. 168 00:06:46,230 --> 00:06:48,490 In the farmer's case, if you, for example, 169 00:06:48,490 --> 00:06:50,190 purchase fertilizer or a certain-- 170 00:06:50,190 --> 00:06:54,815 for example, you could purchase or use drought-resistant crops. 171 00:06:54,815 --> 00:06:56,190 Of course, if there's no drought, 172 00:06:56,190 --> 00:06:57,690 then that's not really that helpful. 173 00:06:57,690 --> 00:07:02,440 But if there's a drought, that's really high return to do. 174 00:07:02,440 --> 00:07:02,950 Yes? 175 00:07:02,950 --> 00:07:03,450 Yes? 176 00:07:03,450 --> 00:07:05,812 AUDIENCE: Creating an investment portfolio. 177 00:07:05,812 --> 00:07:07,020 FRANK SCHILBACH: Creating a-- 178 00:07:07,020 --> 00:07:08,790 AUDIENCE: Investment portfolio. 179 00:07:08,790 --> 00:07:11,280 FRANK SCHILBACH: Yeah, so investing your money 180 00:07:11,280 --> 00:07:16,050 into a different-- in the stock market or in other sort 181 00:07:16,050 --> 00:07:17,940 of bonds or the like-- 182 00:07:17,940 --> 00:07:20,080 how should you invest the money? 183 00:07:20,080 --> 00:07:22,920 That's kind of related, to some degree, 184 00:07:22,920 --> 00:07:25,500 to the renting versus buying a house. 185 00:07:25,500 --> 00:07:28,680 You can think of buying as a house as one asset, one 186 00:07:28,680 --> 00:07:31,680 potential very sort of illiquid asset that you could buy. 187 00:07:31,680 --> 00:07:33,157 Similarly, you could buy stocks. 188 00:07:33,157 --> 00:07:33,990 You could buy bonds. 189 00:07:33,990 --> 00:07:36,630 You could keep just cash and so on. 190 00:07:36,630 --> 00:07:38,370 And there, that very much depends on, 191 00:07:38,370 --> 00:07:41,112 the return depends on things that 192 00:07:41,112 --> 00:07:43,070 are out of your hand, which essentially is just 193 00:07:43,070 --> 00:07:45,420 what the stock market might do. 194 00:07:45,420 --> 00:07:48,330 So I think once you think about choices 195 00:07:48,330 --> 00:07:51,150 involving risks, essentially almost any choice 196 00:07:51,150 --> 00:07:56,430 in your life actually is risky to some degree or uncertain, 197 00:07:56,430 --> 00:07:59,730 ranging from going to college, doing problem sets, 198 00:07:59,730 --> 00:08:00,810 studying for exams. 199 00:08:00,810 --> 00:08:02,190 Which exams should you study for? 200 00:08:02,190 --> 00:08:04,200 Which questions are people going to ask? 201 00:08:04,200 --> 00:08:09,210 Health decisions-- should you invest in your health or not? 202 00:08:09,210 --> 00:08:11,910 For a lot of diseases that people might get, 203 00:08:11,910 --> 00:08:13,240 it's often very uncertain. 204 00:08:13,240 --> 00:08:18,000 So even if you're smoking a lot, not every smoker 205 00:08:18,000 --> 00:08:19,245 falls sick or the like. 206 00:08:19,245 --> 00:08:23,880 No, just the risk of cancer and other diseases increases. 207 00:08:23,880 --> 00:08:27,240 That sort of financial investments, 208 00:08:27,240 --> 00:08:29,567 dating choices, and so on and so forth-- 209 00:08:29,567 --> 00:08:31,650 even friendship choices are, in some sense, risky. 210 00:08:31,650 --> 00:08:33,150 If you want, riding a bicycle-- 211 00:08:33,150 --> 00:08:35,490 that's very sort of small choices-- 212 00:08:35,490 --> 00:08:37,039 wearing a helmet versus not. 213 00:08:37,039 --> 00:08:38,789 Essentially, almost anything in your life, 214 00:08:38,789 --> 00:08:40,706 if you think about what are the outcomes, what 215 00:08:40,706 --> 00:08:42,690 are the different choices that you have, 216 00:08:42,690 --> 00:08:46,020 and what are the outcomes associated with those choices, 217 00:08:46,020 --> 00:08:49,668 almost all of those choices are associated with uncertainty 218 00:08:49,668 --> 00:08:51,210 and a sense of you're not quite sure. 219 00:08:51,210 --> 00:08:53,550 Is the return going to be high or low? 220 00:08:53,550 --> 00:08:56,110 Then as I said before, in addition to that, 221 00:08:56,110 --> 00:08:59,535 there's sort of risk mitigating strategies and a sense of you 222 00:08:59,535 --> 00:09:01,560 have a lot of choices in a lot of issues 223 00:09:01,560 --> 00:09:03,210 that are associated with risk. 224 00:09:03,210 --> 00:09:05,700 And now you can choose to reduce your exposure 225 00:09:05,700 --> 00:09:08,670 to risk by purchasing insurance or, for example, also 226 00:09:08,670 --> 00:09:11,760 by avoiding certain behaviors, right? 227 00:09:11,760 --> 00:09:14,730 So if you're worried about being robbed, for example, 228 00:09:14,730 --> 00:09:18,690 in a certain part of town, you might 229 00:09:18,690 --> 00:09:20,850 choose to go through that part of town. 230 00:09:20,850 --> 00:09:22,530 And that's a risky thing to do. 231 00:09:22,530 --> 00:09:25,002 Or you can have risk mitigating strategies where you just 232 00:09:25,002 --> 00:09:27,210 don't leave your house, or just go in different ways, 233 00:09:27,210 --> 00:09:29,700 or just never go into certain areas, which essentially 234 00:09:29,700 --> 00:09:32,040 are ways to protect you, to reduce your risk 235 00:09:32,040 --> 00:09:35,040 exposure overall. 236 00:09:35,040 --> 00:09:36,312 Any questions? 237 00:09:40,470 --> 00:09:44,180 OK, so now let me sort of just tell you 238 00:09:44,180 --> 00:09:47,120 three broad, stylized facts that we're going to try and explain 239 00:09:47,120 --> 00:09:48,530 or try to tackle. 240 00:09:48,530 --> 00:09:51,480 And that's kind of what economics is trying to do. 241 00:09:51,480 --> 00:09:53,923 So the first question is-- 242 00:09:53,923 --> 00:09:55,340 the first thing that comes to mind 243 00:09:55,340 --> 00:09:57,950 when you think about economics and modeling choices 244 00:09:57,950 --> 00:10:00,350 involving risk is risk aversion. 245 00:10:00,350 --> 00:10:01,850 How do we think about risk aversion? 246 00:10:01,850 --> 00:10:02,900 Or what is risk aversion? 247 00:10:05,450 --> 00:10:06,950 Why are people averse to risk? 248 00:10:06,950 --> 00:10:08,600 Yeah. 249 00:10:08,600 --> 00:10:10,502 AUDIENCE: Risk aversion is the tendency 250 00:10:10,502 --> 00:10:14,394 to avoid bets that are more risky, even though they 251 00:10:14,394 --> 00:10:17,874 will still ostensibly benefit you the same. 252 00:10:17,874 --> 00:10:18,890 FRANK SCHILBACH: Mhm. 253 00:10:18,890 --> 00:10:22,700 So one-- you said, essentially, if there are certain bets that 254 00:10:22,700 --> 00:10:26,660 involve risk, where the expected values or an expectation 255 00:10:26,660 --> 00:10:29,420 you're going to do pretty well-- perhaps better than some safe 256 00:10:29,420 --> 00:10:30,350 outcomes-- 257 00:10:30,350 --> 00:10:33,830 people tend to avoid those kinds of bets. 258 00:10:33,830 --> 00:10:36,420 And that we might call risk aversion. 259 00:10:36,420 --> 00:10:38,510 So that's exactly right. 260 00:10:38,510 --> 00:10:40,342 But now, why are people doing that? 261 00:10:40,342 --> 00:10:42,050 What are the underlying reasons for that? 262 00:10:46,690 --> 00:10:48,850 Yes. 263 00:10:48,850 --> 00:10:50,860 AUDIENCE: Potentially involved is 264 00:10:50,860 --> 00:10:55,500 loss aversion, which in the readings, 265 00:10:55,500 --> 00:10:59,200 I believe, some studies by [INAUDIBLE] 266 00:10:59,200 --> 00:11:03,100 and others mentioned that, showed that we had aversions 267 00:11:03,100 --> 00:11:07,305 specifically to losing money or utility 268 00:11:07,305 --> 00:11:10,020 rather than risk in and of itself. 269 00:11:10,020 --> 00:11:11,162 But that might be wrong. 270 00:11:11,162 --> 00:11:12,120 FRANK SCHILBACH: Right. 271 00:11:12,120 --> 00:11:13,740 So one part would be to say, people 272 00:11:13,740 --> 00:11:17,670 might sort of lose or gain money in certain gambles. 273 00:11:17,670 --> 00:11:19,710 And what you're saying is, essentially, people 274 00:11:19,710 --> 00:11:23,820 might not treat the losses the same as they treat the gains. 275 00:11:23,820 --> 00:11:27,090 And then you might sort of decline certain gambles 276 00:11:27,090 --> 00:11:28,350 or certain risks. 277 00:11:28,350 --> 00:11:31,770 You're just worried about losing out, and you put a lot of value 278 00:11:31,770 --> 00:11:32,455 on that. 279 00:11:32,455 --> 00:11:33,330 That's exactly right. 280 00:11:33,330 --> 00:11:37,733 We're going to talk about this next week in a lot more detail. 281 00:11:37,733 --> 00:11:39,900 But what are some other reasons why people might not 282 00:11:39,900 --> 00:11:42,810 want to engage in risk? 283 00:11:42,810 --> 00:11:43,360 Yes. 284 00:11:43,360 --> 00:11:45,420 AUDIENCE: I'd rather be definitely OK than either 285 00:11:45,420 --> 00:11:47,712 [? to ?] [? the ?] [? point ?] between super successful 286 00:11:47,712 --> 00:11:48,624 or die. 287 00:11:48,624 --> 00:11:49,499 FRANK SCHILBACH: Mhm. 288 00:11:49,499 --> 00:11:50,515 And why is that? 289 00:11:50,515 --> 00:11:52,640 AUDIENCE: [INAUDIBLE] diminishing marginal utility, 290 00:11:52,640 --> 00:11:53,040 [? maybe. ?] 291 00:11:53,040 --> 00:11:53,250 FRANK SCHILBACH: Right. 292 00:11:53,250 --> 00:11:54,840 So one part is-- and that's exactly how 293 00:11:54,840 --> 00:11:57,450 economists think about this-- is diminishing marginal utility. 294 00:11:57,450 --> 00:12:00,480 That's to say, if you're really poor, 295 00:12:00,480 --> 00:12:02,580 getting your first dollar has really high value 296 00:12:02,580 --> 00:12:04,423 to you-- the reason being that now, 297 00:12:04,423 --> 00:12:06,090 essentially, otherwise you would starve, 298 00:12:06,090 --> 00:12:07,680 or you can't eat and so on. 299 00:12:07,680 --> 00:12:11,130 The value of whatever you purchase with that dollar 300 00:12:11,130 --> 00:12:14,340 is really high, because you just have nothing otherwise. 301 00:12:14,340 --> 00:12:16,260 Now, if I give you a million dollars and then 302 00:12:16,260 --> 00:12:18,540 another dollar, then essentially the additional dollar 303 00:12:18,540 --> 00:12:19,915 that I give you after the million 304 00:12:19,915 --> 00:12:21,510 is just not doing very much. 305 00:12:21,510 --> 00:12:24,630 So the marginal utility of that dollar is low. 306 00:12:24,630 --> 00:12:27,253 And that's sort of diminishing marginal utility of wealth. 307 00:12:27,253 --> 00:12:29,170 That's exactly how economists talk about this. 308 00:12:29,170 --> 00:12:33,450 We're going to get back to that in a lot of detail. 309 00:12:33,450 --> 00:12:34,440 Yeah? 310 00:12:34,440 --> 00:12:36,232 AUDIENCE: I think if you look a little more 311 00:12:36,232 --> 00:12:40,380 at extreme examples, [INAUDIBLE] if I lose so much money, 312 00:12:40,380 --> 00:12:42,645 I won't be able to afford my expenses or something. 313 00:12:42,645 --> 00:12:44,770 So it doesn't matter what is [? created ?] [? by ?] 314 00:12:44,770 --> 00:12:50,842 [INAUDIBLE] lose a lot [INAUDIBLE] 315 00:12:50,842 --> 00:12:51,800 FRANK SCHILBACH: Right. 316 00:12:51,800 --> 00:12:54,590 So there might be sort of certain minimum standards, 317 00:12:54,590 --> 00:12:57,565 in some sense, that people have over their outcomes. 318 00:12:57,565 --> 00:13:00,050 Or you say, for example, you really 319 00:13:00,050 --> 00:13:03,140 want to have a place to sleep or you want to have some meal. 320 00:13:03,140 --> 00:13:05,840 And essentially, if you're below that threshold, 321 00:13:05,840 --> 00:13:10,100 essentially your marginal utility anywhere below that 322 00:13:10,100 --> 00:13:11,870 is really high, because you really want 323 00:13:11,870 --> 00:13:13,140 to get over that threshold. 324 00:13:13,140 --> 00:13:19,730 And so you might avoid certain choices or investments 325 00:13:19,730 --> 00:13:20,570 or the like. 326 00:13:20,570 --> 00:13:22,760 If there's even a small chance of getting 327 00:13:22,760 --> 00:13:26,520 below your threshold, you might be really averse to that. 328 00:13:26,520 --> 00:13:28,730 But what are some more perhaps psychological reasons 329 00:13:28,730 --> 00:13:30,540 why people don't like risks? 330 00:13:30,540 --> 00:13:31,040 Yeah? 331 00:13:31,040 --> 00:13:42,350 AUDIENCE: [INAUDIBLE] [? potential ?] [INAUDIBLE] 332 00:13:42,350 --> 00:13:43,403 FRANK SCHILBACH: Mhm. 333 00:13:43,403 --> 00:13:44,070 So that's right. 334 00:13:44,070 --> 00:13:44,720 That's what people do. 335 00:13:44,720 --> 00:13:46,230 We're going to also talk about that. 336 00:13:46,230 --> 00:13:49,430 But why do people not like the risk? 337 00:13:49,430 --> 00:13:51,740 Or some people like, actually, risk. 338 00:13:51,740 --> 00:13:55,640 But what is the issue about having a lot of exposure? 339 00:13:55,640 --> 00:13:59,380 Why do people purchase insurance, for example? 340 00:13:59,380 --> 00:14:00,250 Yes? 341 00:14:00,250 --> 00:14:02,618 AUDIENCE: Some amount of uncertainty [INAUDIBLE] 342 00:14:02,618 --> 00:14:04,660 [? risk ?] [? aversion, ?] [INAUDIBLE] the higher 343 00:14:04,660 --> 00:14:07,422 the uncertainty of the outcome, [INAUDIBLE] 344 00:14:07,422 --> 00:14:08,380 FRANK SCHILBACH: Right. 345 00:14:08,380 --> 00:14:10,280 So there's one part that's what you said, 346 00:14:10,280 --> 00:14:12,340 which is there's diminishing marginal utility of wealth. 347 00:14:12,340 --> 00:14:13,900 And this is exactly how we're going to model this 348 00:14:13,900 --> 00:14:15,670 and how economists think about this. 349 00:14:15,670 --> 00:14:17,300 However, there's other things involved, 350 00:14:17,300 --> 00:14:19,480 which is just things like anxiety or uncertainty. 351 00:14:19,480 --> 00:14:21,250 People might just not-- 352 00:14:21,250 --> 00:14:23,080 suppose a storm is coming up. 353 00:14:23,080 --> 00:14:24,340 I might purchase insurance. 354 00:14:24,340 --> 00:14:26,710 And if I purchase insurance, like flood insurance, 355 00:14:26,710 --> 00:14:29,980 or the like for a house, I might just feel much-- 356 00:14:29,980 --> 00:14:32,230 I might sleep better at night and so on and so forth. 357 00:14:32,230 --> 00:14:35,397 I might just feel better about concerns-- 358 00:14:35,397 --> 00:14:36,980 or like health insurance, for example, 359 00:14:36,980 --> 00:14:40,360 might lower anxiety and so on, because people are just 360 00:14:40,360 --> 00:14:42,670 not worried constantly about like falling 361 00:14:42,670 --> 00:14:45,070 ill or like disasters happening. 362 00:14:45,070 --> 00:14:47,830 And that's beyond potentially any 363 00:14:47,830 --> 00:14:50,710 diminishing marginal utility of wealth. 364 00:14:50,710 --> 00:14:54,940 That sort of anxiety, stress, worries, and so on. 365 00:14:54,940 --> 00:14:56,804 Any other reasons? 366 00:14:56,804 --> 00:14:58,070 Yeah? 367 00:14:58,070 --> 00:15:00,473 AUDIENCE: I think even beyond people wanting to not be 368 00:15:00,473 --> 00:15:02,390 stressed and anxious, there's also the element 369 00:15:02,390 --> 00:15:05,690 of, if you're buying insurance to smooth your consumption 370 00:15:05,690 --> 00:15:08,090 between different states of the world, 371 00:15:08,090 --> 00:15:12,840 it makes it a lot easier to plan for states after [INAUDIBLE] If 372 00:15:12,840 --> 00:15:13,340 you're-- 373 00:15:13,340 --> 00:15:13,700 FRANK SCHILBACH: Well, that's interesting. 374 00:15:13,700 --> 00:15:15,225 AUDIENCE: [INAUDIBLE] 375 00:15:15,225 --> 00:15:16,100 FRANK SCHILBACH: Yes. 376 00:15:16,100 --> 00:15:16,975 That's exactly right. 377 00:15:16,975 --> 00:15:19,152 So in some sense, if you have insurance, 378 00:15:19,152 --> 00:15:21,110 if you reduce risks in the states of the world, 379 00:15:21,110 --> 00:15:23,240 you can sort of, essentially, exclude a bunch 380 00:15:23,240 --> 00:15:24,365 of bad states of the world. 381 00:15:24,365 --> 00:15:26,282 For example, suppose you buy health insurance, 382 00:15:26,282 --> 00:15:28,190 suppose you have flood insurance, and so on. 383 00:15:28,190 --> 00:15:29,780 A lot of bad things that might happen you 384 00:15:29,780 --> 00:15:30,720 might be able to deal with. 385 00:15:30,720 --> 00:15:32,240 And you don't have to necessarily 386 00:15:32,240 --> 00:15:34,880 have a contingency plan of what if I fall sick 387 00:15:34,880 --> 00:15:37,220 and then go bankrupt, and all sorts of other bad things 388 00:15:37,220 --> 00:15:37,940 happen. 389 00:15:37,940 --> 00:15:39,710 Or what if I-- 390 00:15:39,710 --> 00:15:40,712 there's flood insurance. 391 00:15:40,712 --> 00:15:42,170 I can't pay the bills and then have 392 00:15:42,170 --> 00:15:44,010 to leave my house and so on. 393 00:15:44,010 --> 00:15:45,920 So essentially, it makes planning easier, 394 00:15:45,920 --> 00:15:48,282 in part because it's just sort of easier in the mind. 395 00:15:48,282 --> 00:15:49,490 People feel more comfortable. 396 00:15:49,490 --> 00:15:52,670 And part-- it's actually computational or just easier 397 00:15:52,670 --> 00:15:53,420 to do. 398 00:15:53,420 --> 00:15:55,178 So I added some reasons here. 399 00:15:55,178 --> 00:15:56,720 There's a bunch of different reasons. 400 00:15:56,720 --> 00:15:59,840 I think it's important to understand that economists have 401 00:15:59,840 --> 00:16:03,740 modeled risk aversion as diminishing 402 00:16:03,740 --> 00:16:05,010 marginal utility of wealth. 403 00:16:05,010 --> 00:16:07,310 That's a very simple way of doing this. 404 00:16:07,310 --> 00:16:10,950 It captures a lot of things, but perhaps not all of them. 405 00:16:10,950 --> 00:16:13,820 And so here's some reasons that I mentioned. 406 00:16:13,820 --> 00:16:15,400 Sort of contingent planning becomes 407 00:16:15,400 --> 00:16:16,400 harder if you have risk. 408 00:16:16,400 --> 00:16:18,530 That's what Maya just said. 409 00:16:18,530 --> 00:16:22,220 People are worried or stressed or anxious when 410 00:16:22,220 --> 00:16:24,710 they have lots of uncertainty. 411 00:16:24,710 --> 00:16:27,160 People might feel regret over missed opportunity. 412 00:16:27,160 --> 00:16:30,620 That's like, if I offer you some insurance right now, 413 00:16:30,620 --> 00:16:34,340 and you might say, well, it's actually unlikely 414 00:16:34,340 --> 00:16:36,363 that anything bad happens. 415 00:16:36,363 --> 00:16:38,030 But in case something really bad happens 416 00:16:38,030 --> 00:16:40,340 and you had the chance to actually avoid it, then 417 00:16:40,340 --> 00:16:43,310 you might feel particularly bad not just because the outcome is 418 00:16:43,310 --> 00:16:45,230 bad, but because it offered it to you 419 00:16:45,230 --> 00:16:47,930 and you didn't accept it. 420 00:16:47,930 --> 00:16:51,270 There's sort of disappointment relative to expectations. 421 00:16:51,270 --> 00:16:54,410 This is essentially getting into territory of losses and gains. 422 00:16:54,410 --> 00:16:56,000 When people have certain expectations, 423 00:16:56,000 --> 00:16:58,640 they have an expectation to have a certain income and the like. 424 00:16:58,640 --> 00:17:01,670 Now, if bad stuff happens, they fall below those expectations 425 00:17:01,670 --> 00:17:03,860 and perceive those outcomes then as losses 426 00:17:03,860 --> 00:17:08,508 compared to the status quo or the expectations that they had. 427 00:17:08,508 --> 00:17:10,550 Again, economists think about this as diminishing 428 00:17:10,550 --> 00:17:12,109 marginal utility of wealth. 429 00:17:12,109 --> 00:17:15,230 That's a very simple way of modeling this. 430 00:17:15,230 --> 00:17:18,140 And we're going to see kind of what the limitations of those 431 00:17:18,140 --> 00:17:18,770 are. 432 00:17:18,770 --> 00:17:20,270 Now, I'm going to show you the three 433 00:17:20,270 --> 00:17:22,190 stylized facts about the world. 434 00:17:22,190 --> 00:17:23,690 And then we're going to discuss kind 435 00:17:23,690 --> 00:17:25,220 of how to perhaps model that. 436 00:17:25,220 --> 00:17:27,230 So the first one is essentially very simple. 437 00:17:27,230 --> 00:17:31,280 People are risk averse in various ways. 438 00:17:31,280 --> 00:17:34,160 And one sort of basic fact is that lots of people 439 00:17:34,160 --> 00:17:34,970 buy insurance. 440 00:17:34,970 --> 00:17:37,310 People are willing to pay to purchase insurance that 441 00:17:37,310 --> 00:17:41,030 gives you essentially money or an expectation less money 442 00:17:41,030 --> 00:17:42,560 than you pay, right? 443 00:17:42,560 --> 00:17:44,780 So fair insurance, as economists would 444 00:17:44,780 --> 00:17:46,980 model is or think about it, is to say 445 00:17:46,980 --> 00:17:49,340 if I purchase insurance that pays you the expected 446 00:17:49,340 --> 00:17:51,360 value of the insurance. 447 00:17:51,360 --> 00:17:53,390 So if I pay a premium for an insurance, 448 00:17:53,390 --> 00:17:55,550 there's a probability of something bad happening 449 00:17:55,550 --> 00:17:59,480 and then sort of a loss or some insurance payment that I get 450 00:17:59,480 --> 00:18:01,340 in case something bad happens. 451 00:18:01,340 --> 00:18:04,100 Fair insurance would be the premium is essentially, 452 00:18:04,100 --> 00:18:11,343 in expectation, the same as the expectation of the loss, which 453 00:18:11,343 --> 00:18:13,010 is the probability of the loss occurring 454 00:18:13,010 --> 00:18:15,330 and the actual payment that I get from the insurance. 455 00:18:15,330 --> 00:18:17,580 Of course, the insurance industry wants to make money. 456 00:18:17,580 --> 00:18:20,750 So the insurance industry will not offer fair insurance, 457 00:18:20,750 --> 00:18:22,370 but less than fair insurance. 458 00:18:22,370 --> 00:18:25,290 Essentially, there's a price for purchasing insurance. 459 00:18:25,290 --> 00:18:27,290 Lots of people are willing to pay for insurance. 460 00:18:27,290 --> 00:18:29,330 People are willing to pay money to get insurance 461 00:18:29,330 --> 00:18:31,130 to reduce the risk or the exposure 462 00:18:31,130 --> 00:18:32,690 to risks that they have. 463 00:18:32,690 --> 00:18:35,060 There's social security in various ways 464 00:18:35,060 --> 00:18:37,370 where essentially people sort of insure themselves 465 00:18:37,370 --> 00:18:41,330 or society insures them for old age or not being able to take 466 00:18:41,330 --> 00:18:42,200 care of themselves. 467 00:18:42,200 --> 00:18:43,760 You could argue that's perhaps also 468 00:18:43,760 --> 00:18:47,325 due to present bias or other paternalistic reasons. 469 00:18:47,325 --> 00:18:48,950 But surely like society, in some sense, 470 00:18:48,950 --> 00:18:51,230 is helping people insure themselves 471 00:18:51,230 --> 00:18:56,240 against potential states of the world where 472 00:18:56,240 --> 00:18:57,830 they might be in need. 473 00:18:57,830 --> 00:19:00,270 There's very sort of other-- 474 00:19:00,270 --> 00:19:02,210 sorry-- institutions, including sort 475 00:19:02,210 --> 00:19:05,000 of extended families, informal insurance in developing 476 00:19:05,000 --> 00:19:07,830 countries, sharecropping, and so on and so forth. 477 00:19:07,830 --> 00:19:08,938 What's sharecropping? 478 00:19:12,010 --> 00:19:12,510 Yes. 479 00:19:12,510 --> 00:19:17,400 AUDIENCE: When you go multiple crops at the same time. 480 00:19:17,400 --> 00:19:18,370 FRANK SCHILBACH: No. 481 00:19:18,370 --> 00:19:21,150 That's intercropping or the like, 482 00:19:21,150 --> 00:19:23,270 but there might be referred to that as well. 483 00:19:23,270 --> 00:19:23,770 Yeah. 484 00:19:23,770 --> 00:19:27,913 AUDIENCE: It's when the person rents out their land for you 485 00:19:27,913 --> 00:19:33,048 work on and you get all the benefits from the land, 486 00:19:33,048 --> 00:19:36,017 but [? they ?] [INAUDIBLE] [? rent ?] [INAUDIBLE].. 487 00:19:36,017 --> 00:19:37,350 FRANK SCHILBACH: Right, exactly. 488 00:19:37,350 --> 00:19:40,020 So it's essentially these kinds of arrangement, which 489 00:19:40,020 --> 00:19:42,270 are often somebody has land. 490 00:19:42,270 --> 00:19:43,860 Somebody rents out the land. 491 00:19:43,860 --> 00:19:47,820 And then you have to pay them something back 492 00:19:47,820 --> 00:19:49,920 and then can keep some of the output and so on. 493 00:19:49,920 --> 00:19:51,900 And often that's essentially some way 494 00:19:51,900 --> 00:19:53,725 essentially reducing risk. 495 00:19:53,725 --> 00:19:55,350 So there's various sort of institution. 496 00:19:55,350 --> 00:19:57,902 But broadly speaking, we think, in many situations, 497 00:19:57,902 --> 00:19:58,860 people don't like risk. 498 00:19:58,860 --> 00:20:02,940 And they look for ways to reduce the exposure to risks. 499 00:20:02,940 --> 00:20:05,520 There's also these informal insurance arrangements, 500 00:20:05,520 --> 00:20:08,615 which are things like people get together. 501 00:20:08,615 --> 00:20:09,990 And they sort of help each other. 502 00:20:09,990 --> 00:20:13,170 Whenever something bad happens, one person 503 00:20:13,170 --> 00:20:15,990 is then being helped by everybody else. 504 00:20:15,990 --> 00:20:19,260 And that's sort of replacing some sort of formula 505 00:20:19,260 --> 00:20:21,600 for insurance schemes and particularly 506 00:20:21,600 --> 00:20:23,220 in developing countries. 507 00:20:23,220 --> 00:20:26,220 Second, risk reduction has its price. 508 00:20:26,220 --> 00:20:29,550 That is to say people are willing to take on risk 509 00:20:29,550 --> 00:20:31,518 if the return is high enough. 510 00:20:31,518 --> 00:20:33,060 So another way to put this is, if you 511 00:20:33,060 --> 00:20:36,150 want to purchase insurance, usually you have to pay for it. 512 00:20:36,150 --> 00:20:38,190 The insurance industry makes a lot of money. 513 00:20:38,190 --> 00:20:43,830 Put differently, people are willing to take on some risk 514 00:20:43,830 --> 00:20:45,075 if things get cheaper, right? 515 00:20:45,075 --> 00:20:46,950 For example, if you think about buying a car, 516 00:20:46,950 --> 00:20:48,825 you could buy a super safe car with all sorts 517 00:20:48,825 --> 00:20:49,860 of safety features. 518 00:20:49,860 --> 00:20:50,970 Not everybody does that. 519 00:20:50,970 --> 00:20:54,510 The reason is because cheaper cars are less safe. 520 00:20:54,510 --> 00:20:55,710 Cars are cheaper. 521 00:20:55,710 --> 00:20:57,210 So you're might just sort of willing 522 00:20:57,210 --> 00:21:00,790 to take on some risk in some situations for some price, 523 00:21:00,790 --> 00:21:01,290 right? 524 00:21:01,290 --> 00:21:03,690 When you think about starting a restaurant, 525 00:21:03,690 --> 00:21:06,952 restaurants essentially fail all the time. 526 00:21:06,952 --> 00:21:08,910 Yet people are always sort of willing to do it. 527 00:21:08,910 --> 00:21:12,060 Presumably, the reason is because if you actually 528 00:21:12,060 --> 00:21:14,200 succeed, you're going to make quite a bit of money. 529 00:21:14,200 --> 00:21:16,020 So if there's a high expected return, 530 00:21:16,020 --> 00:21:18,810 people are willing to take on some risk. 531 00:21:18,810 --> 00:21:20,740 People put in money into the stock market, 532 00:21:20,740 --> 00:21:22,670 so they increase their risk exposure. 533 00:21:22,670 --> 00:21:25,170 The reason why they do that is because, in expectation, they 534 00:21:25,170 --> 00:21:27,940 make quite a bit of money. 535 00:21:27,940 --> 00:21:31,298 But of course, that often entails risk. 536 00:21:31,298 --> 00:21:33,840 So one way to think about the entire sort of finance industry 537 00:21:33,840 --> 00:21:35,280 is risk intermediation. 538 00:21:35,280 --> 00:21:36,960 Essentially, there are some businesses 539 00:21:36,960 --> 00:21:38,590 that have a lot of risk. 540 00:21:38,590 --> 00:21:42,630 And that risk is sort of offloaded to investors. 541 00:21:42,630 --> 00:21:44,370 And the investors accept that risk. 542 00:21:44,370 --> 00:21:46,170 They say, I'm willing to take on that risk, 543 00:21:46,170 --> 00:21:48,730 but only for a good return. 544 00:21:48,730 --> 00:21:50,940 So I'm not going to take on risk from you 545 00:21:50,940 --> 00:21:52,980 if I'm not, in expectation, making money. 546 00:21:52,980 --> 00:21:55,290 But often, essentially, there's a trade off between. 547 00:21:55,290 --> 00:21:57,120 And this is-- well, if you've taken finance classes and so 548 00:21:57,120 --> 00:21:58,380 on, that's kind of obvious. 549 00:21:58,380 --> 00:22:01,440 There's a trade between risk and expected return. 550 00:22:04,187 --> 00:22:05,770 In what situations are people actually 551 00:22:05,770 --> 00:22:10,390 willing to take on risk for its own sake or just-- 552 00:22:10,390 --> 00:22:11,950 so I told you people are risk averse. 553 00:22:11,950 --> 00:22:14,390 And that's true in most situations. 554 00:22:14,390 --> 00:22:16,700 But where are people actually willing to take on risks? 555 00:22:16,700 --> 00:22:17,020 Yes. 556 00:22:17,020 --> 00:22:18,346 AUDIENCE: [INAUDIBLE] casino? 557 00:22:18,346 --> 00:22:19,304 FRANK SCHILBACH: Right. 558 00:22:19,304 --> 00:22:21,280 Lots of people actually go to casinos. 559 00:22:21,280 --> 00:22:26,690 And here, the expected return is actually a negative. 560 00:22:26,690 --> 00:22:28,690 You know, you're going to lose money on average. 561 00:22:28,690 --> 00:22:32,860 Unless you're sort of a smart MIT student who can count cards 562 00:22:32,860 --> 00:22:34,570 in poker or something, you're going 563 00:22:34,570 --> 00:22:35,980 to lose money essentially. 564 00:22:35,980 --> 00:22:39,670 So there must be some form of some preference or some desire 565 00:22:39,670 --> 00:22:43,132 to take on risk in some situations because you cannot 566 00:22:43,132 --> 00:22:45,340 just-- this is not like investing in the stock market 567 00:22:45,340 --> 00:22:47,260 where, on average, you're going to get money. 568 00:22:47,260 --> 00:22:49,420 If you go to the casino, on average 569 00:22:49,420 --> 00:22:50,660 you're going to lose money. 570 00:22:50,660 --> 00:22:52,820 Now, you could say it's so much fun and so on. 571 00:22:52,820 --> 00:22:54,070 There could also be addiction. 572 00:22:54,070 --> 00:22:56,290 There could be also self-control issues and so on. 573 00:22:56,290 --> 00:22:58,373 Or there could be something about people's beliefs 574 00:22:58,373 --> 00:23:00,413 or preferences that induce them to take on risk. 575 00:23:00,413 --> 00:23:02,830 But notice that's different from what we discussed before. 576 00:23:02,830 --> 00:23:05,500 That's not really consistent with risk aversion 577 00:23:05,500 --> 00:23:08,560 because people choose to increase the risk that they're 578 00:23:08,560 --> 00:23:09,790 exposed to. 579 00:23:09,790 --> 00:23:12,025 Any other-- yeah. 580 00:23:12,025 --> 00:23:13,818 AUDIENCE: Buying lottery tickets. 581 00:23:13,818 --> 00:23:14,860 FRANK SCHILBACH: Exactly. 582 00:23:14,860 --> 00:23:19,810 People are buying lots of lottery tickets. 583 00:23:19,810 --> 00:23:22,120 Similar, they're doing lots of sports betting. 584 00:23:22,120 --> 00:23:24,970 And again, what you're doing here is, to be very clear, 585 00:23:24,970 --> 00:23:26,560 on average you're going to lose money 586 00:23:26,560 --> 00:23:30,010 and that you're going to increase risk or the exposure 587 00:23:30,010 --> 00:23:30,790 to risk. 588 00:23:30,790 --> 00:23:33,147 And there's some questions on why people are doing this. 589 00:23:33,147 --> 00:23:34,480 We're going to get back to this. 590 00:23:34,480 --> 00:23:36,188 We're going to not talk about this today, 591 00:23:36,188 --> 00:23:37,570 but I sort of want to flag that. 592 00:23:37,570 --> 00:23:39,400 While people are risk averse in many, 593 00:23:39,400 --> 00:23:42,610 in almost, nearly all situations of the world 594 00:23:42,610 --> 00:23:44,330 of important choices that you encounter, 595 00:23:44,330 --> 00:23:47,650 there are some choices where people are, in fact, exposing 596 00:23:47,650 --> 00:23:52,090 themselves to risk in addition to exposure to risks 597 00:23:52,090 --> 00:23:55,680 that actually has high expected value. 598 00:23:55,680 --> 00:23:56,770 Any questions on this? 599 00:24:02,960 --> 00:24:03,610 OK. 600 00:24:03,610 --> 00:24:05,960 So now, we're going to talk about the expected utility 601 00:24:05,960 --> 00:24:10,400 and sort of how do economists think about how should we 602 00:24:10,400 --> 00:24:10,900 behave. 603 00:24:10,900 --> 00:24:13,150 And that's a normative model, how the economists think 604 00:24:13,150 --> 00:24:16,090 about how people should behave when it comes 605 00:24:16,090 --> 00:24:20,080 to choices involving risk. 606 00:24:20,080 --> 00:24:25,190 So what is expected utility? 607 00:24:25,190 --> 00:24:26,630 What does the model assume? 608 00:24:26,630 --> 00:24:28,040 Or what is it about? 609 00:24:32,750 --> 00:24:33,320 Yeah. 610 00:24:33,320 --> 00:24:35,830 AUDIENCE: It's the utility of each state 611 00:24:35,830 --> 00:24:38,280 of the world multiplied by the probability of that state 612 00:24:38,280 --> 00:24:39,647 of the word occurring. 613 00:24:39,647 --> 00:24:40,980 FRANK SCHILBACH: Right, exactly. 614 00:24:40,980 --> 00:24:42,610 So the assumption here is there's 615 00:24:42,610 --> 00:24:43,860 different states of the world. 616 00:24:43,860 --> 00:24:45,980 There's good things and bad things may happen. 617 00:24:45,980 --> 00:24:47,680 You might get a job. 618 00:24:47,680 --> 00:24:48,680 You might not get a job. 619 00:24:48,680 --> 00:24:51,120 You might get a good grade, bad grade, and so on. 620 00:24:51,120 --> 00:24:53,390 You can sort of partition the world or anything 621 00:24:53,390 --> 00:24:54,890 that's going to happen in the future 622 00:24:54,890 --> 00:24:56,360 into different states of the world. 623 00:24:56,360 --> 00:25:00,770 We can associate a utility, so an outcome, 624 00:25:00,770 --> 00:25:03,680 and an associated utility with that state of the world, right? 625 00:25:03,680 --> 00:25:06,060 If you get a good job, you get a high income. 626 00:25:06,060 --> 00:25:07,550 And if you don't get a job, you get 627 00:25:07,550 --> 00:25:09,230 a low income or whatever or unemployment 628 00:25:09,230 --> 00:25:10,890 insurance or whatever. 629 00:25:10,890 --> 00:25:14,690 And there are certain utilities associated with these outcomes. 630 00:25:14,690 --> 00:25:16,555 Expected utility, now, is essentially 631 00:25:16,555 --> 00:25:18,680 say, OK, now for each of these states of the world, 632 00:25:18,680 --> 00:25:21,110 there's a probability of the state of the world happening. 633 00:25:21,110 --> 00:25:23,330 And I'm going to use essentially the weighted average, which 634 00:25:23,330 --> 00:25:25,705 essentially is weighting each state with their associated 635 00:25:25,705 --> 00:25:29,510 probability and then using the associated 636 00:25:29,510 --> 00:25:30,890 utilities for each state. 637 00:25:30,890 --> 00:25:33,080 And the expectations of those utilities 638 00:25:33,080 --> 00:25:35,193 is what's expected utility. 639 00:25:35,193 --> 00:25:36,360 And that's very complicated. 640 00:25:36,360 --> 00:25:38,443 I'm going to sort of get [? to where ?] [? that ?] 641 00:25:38,443 --> 00:25:40,947 [? is ?] said in more words than necessary. 642 00:25:40,947 --> 00:25:42,280 Let me sort of get back to this. 643 00:25:42,280 --> 00:25:47,980 So first, the thing about expected monetary value-- 644 00:25:47,980 --> 00:25:49,453 so suppose there's a gamble. 645 00:25:49,453 --> 00:25:50,870 And this is not a very simplified. 646 00:25:50,870 --> 00:25:51,578 There's a gamble. 647 00:25:51,578 --> 00:25:53,690 I'll call it G over two states of the world. 648 00:25:53,690 --> 00:25:57,380 State 1 occurs with probability p and yields monetary payoff x. 649 00:25:57,380 --> 00:25:59,810 State 2 occurs with probability 1 minus p 650 00:25:59,810 --> 00:26:02,120 and yields monetary payoff y. 651 00:26:02,120 --> 00:26:04,700 Now, the expected monetary value-- 652 00:26:04,700 --> 00:26:06,230 now, this is not expected utility. 653 00:26:06,230 --> 00:26:07,710 This expected monetary value. 654 00:26:07,710 --> 00:26:10,640 This is how much money you get in expectation-- is essentially 655 00:26:10,640 --> 00:26:12,920 just the weighted average of those two things sort of 656 00:26:12,920 --> 00:26:14,870 weighted by the probabilities. 657 00:26:14,870 --> 00:26:17,138 So that's p times x plus 1 minus p times y. 658 00:26:17,138 --> 00:26:19,430 That's just the expected value of how much money you're 659 00:26:19,430 --> 00:26:21,470 going to get from this gamble. 660 00:26:21,470 --> 00:26:24,590 Now, this is just a definition of fair gamble. 661 00:26:24,590 --> 00:26:26,570 And this is what economists tend to use a lot. 662 00:26:26,570 --> 00:26:29,900 A fair gamble is one with a price 663 00:26:29,900 --> 00:26:33,160 equal to its expected monetary value, right? 664 00:26:33,160 --> 00:26:37,670 So if I ask you would you like to take this gamble, 665 00:26:37,670 --> 00:26:39,813 you're going to ask kind of, is this a fair gamble? 666 00:26:39,813 --> 00:26:41,480 Essentially, that's just asking about is 667 00:26:41,480 --> 00:26:45,290 it paying the expected value of this in terms of money. 668 00:26:45,290 --> 00:26:49,880 I put monetary in parentheses because I could also provide 669 00:26:49,880 --> 00:26:51,650 you a fair gamble of apples. 670 00:26:51,650 --> 00:26:54,890 And then it would just be the expected value of apples. 671 00:26:54,890 --> 00:26:58,460 That would be also a fair gamble potentially. 672 00:26:58,460 --> 00:27:01,070 Now, what's the expected utility of this gamble? 673 00:27:01,070 --> 00:27:03,020 Well, now, you need to have a utility function 674 00:27:03,020 --> 00:27:04,650 for each of these outcomes. 675 00:27:04,650 --> 00:27:06,920 So if my utility function is u of x, 676 00:27:06,920 --> 00:27:11,060 this kind of how much utility I get in the state of actually 677 00:27:11,060 --> 00:27:13,220 getting x or y. 678 00:27:13,220 --> 00:27:16,343 So-called xi is where i is the state of the world. 679 00:27:16,343 --> 00:27:18,260 So essentially, now, it's the weighted average 680 00:27:18,260 --> 00:27:23,180 of p i times u of xi, so in this case, p times u of x 681 00:27:23,180 --> 00:27:26,540 plus y minus p times u of y. 682 00:27:26,540 --> 00:27:28,010 Any questions on this so far? 683 00:27:36,240 --> 00:27:39,180 And so when you now think about evaluating gambles 684 00:27:39,180 --> 00:27:42,420 using an expected utility, if your utility function 685 00:27:42,420 --> 00:27:47,197 is linear, then you're going to essentially decide 686 00:27:47,197 --> 00:27:49,530 the same way as if you were just evaluating the expected 687 00:27:49,530 --> 00:27:52,980 monetary value, right? 688 00:27:52,980 --> 00:27:55,590 And if not, if the utility function is concave and convex, 689 00:27:55,590 --> 00:27:59,070 then essentially people are potentially risk averse. 690 00:27:59,070 --> 00:28:03,270 So how economists think about expected monetary value 691 00:28:03,270 --> 00:28:05,430 is the history of that used to be, 692 00:28:05,430 --> 00:28:07,800 the first theory that people wrote down was, 693 00:28:07,800 --> 00:28:10,350 this was a model how people thought people should behave. 694 00:28:10,350 --> 00:28:12,808 There was a normative model that people wrote at some point 695 00:28:12,808 --> 00:28:16,800 and said, rational people should essentially 696 00:28:16,800 --> 00:28:19,530 maximize monetary payouts, which is 697 00:28:19,530 --> 00:28:24,600 say, if the expected monetary value of a certain gamble 698 00:28:24,600 --> 00:28:25,980 is high, you should accept it. 699 00:28:25,980 --> 00:28:27,790 Or if it's higher than its price, 700 00:28:27,790 --> 00:28:29,760 then you should accept it, otherwise not. 701 00:28:29,760 --> 00:28:31,920 Now, it turns out that, in practice, that's 702 00:28:31,920 --> 00:28:33,180 not descriptively accurate. 703 00:28:33,180 --> 00:28:35,370 That's just not how people behave on the world. 704 00:28:35,370 --> 00:28:37,350 And in fact, and the reason being that people 705 00:28:37,350 --> 00:28:39,210 are risk averse in most situations. 706 00:28:42,390 --> 00:28:44,790 When using, now, the expected monetary value, essentially 707 00:28:44,790 --> 00:28:46,540 they use the expected money value 708 00:28:46,540 --> 00:28:48,790 as a definition for risk neutrality. 709 00:28:48,790 --> 00:28:50,790 If somebody is risk neutral, if somebody doesn't 710 00:28:50,790 --> 00:28:53,100 care at all about risk in some situation, 711 00:28:53,100 --> 00:28:55,650 that person essentially just is maximizing the expected 712 00:28:55,650 --> 00:28:57,685 monetary value, right? 713 00:28:57,685 --> 00:28:59,060 So a decision maker is-- and this 714 00:28:59,060 --> 00:29:01,620 is a definition-- is risk neutral if, for any lottery G, 715 00:29:01,620 --> 00:29:03,720 she is indifferent between G and getting 716 00:29:03,720 --> 00:29:07,140 the expected monetary value G for sure. 717 00:29:07,140 --> 00:29:09,660 And so the decision maker is risk neutral if the utility 718 00:29:09,660 --> 00:29:12,868 function is linear, OK? 719 00:29:12,868 --> 00:29:14,910 Essentially, the more money you get, then there's 720 00:29:14,910 --> 00:29:18,630 no diminishing marginal utility of money. 721 00:29:18,630 --> 00:29:22,480 Now, what's risk aversion then? 722 00:29:22,480 --> 00:29:25,980 A decision maker is risk averse if, for any lottery G, 723 00:29:25,980 --> 00:29:30,810 she prefers getting the expected monetary value G for sure 724 00:29:30,810 --> 00:29:33,480 rather than taking G. And the person 725 00:29:33,480 --> 00:29:35,940 is risk loving if the person rather 726 00:29:35,940 --> 00:29:37,650 has the lottery than the expected 727 00:29:37,650 --> 00:29:41,587 monetary value for sure. 728 00:29:41,587 --> 00:29:42,670 These are just definition. 729 00:29:42,670 --> 00:29:44,440 That's just the way how economists think about risk. 730 00:29:44,440 --> 00:29:45,940 That's just definition, defining how 731 00:29:45,940 --> 00:29:50,160 we think about risk aversion and risk lovingness if you want. 732 00:29:50,160 --> 00:29:53,700 Now, let me give you just a very simple example. 733 00:29:53,700 --> 00:29:58,140 Suppose a person with wealth, $10,000 is offered a gamble. 734 00:29:58,140 --> 00:30:01,290 The gamble is you can gain $500 with a 50% chance 735 00:30:01,290 --> 00:30:03,750 and lose $400 with a 50% chance. 736 00:30:03,750 --> 00:30:06,963 Will you accept this gamble? 737 00:30:06,963 --> 00:30:07,880 How do we do this now? 738 00:30:14,710 --> 00:30:18,980 Suppose I'm just maximizing the expected monetary value. 739 00:30:18,980 --> 00:30:20,860 What am I going to do? 740 00:30:20,860 --> 00:30:21,646 Yeah. 741 00:30:21,646 --> 00:30:24,612 AUDIENCE: You take [INAUDIBLE] something [INAUDIBLE]?? 742 00:30:24,612 --> 00:30:25,570 FRANK SCHILBACH: Right. 743 00:30:25,570 --> 00:30:27,070 So what I'm going to do is I'm going 744 00:30:27,070 --> 00:30:29,950 to just look at what's my expected monetary value 745 00:30:29,950 --> 00:30:32,650 of accepting your lottery, which is 746 00:30:32,650 --> 00:30:37,960 0.5, which is the probability of a loss times 9,600. 747 00:30:37,960 --> 00:30:42,010 This is 10,000 minus the 400 that I lose plus 0.5 times 748 00:30:42,010 --> 00:30:46,510 10,000 plus 500, which gives me 10,050. 749 00:30:46,510 --> 00:30:49,150 If I reject the lottery, I'm just where I am before. 750 00:30:49,150 --> 00:30:51,160 Now, the risk neutral decision maker 751 00:30:51,160 --> 00:30:54,520 will reject the gamble, in fact, irrespective 752 00:30:54,520 --> 00:30:55,540 of the initial wealth. 753 00:30:55,540 --> 00:30:57,370 Because, essentially, everything is linear, 754 00:30:57,370 --> 00:30:58,790 so you just drop out the wealth. 755 00:30:58,790 --> 00:31:01,270 You can just look at what's the expected value regardless 756 00:31:01,270 --> 00:31:02,890 of how much money the person has. 757 00:31:02,890 --> 00:31:03,920 AUDIENCE: So you mean [INAUDIBLE] [? accepting ?] 758 00:31:03,920 --> 00:31:05,102 [INAUDIBLE]? 759 00:31:07,603 --> 00:31:08,770 FRANK SCHILBACH: Yes, sorry. 760 00:31:08,770 --> 00:31:11,600 That's a typo. 761 00:31:11,600 --> 00:31:12,310 Yes, sorry. 762 00:31:12,310 --> 00:31:12,920 That's a typo. 763 00:31:12,920 --> 00:31:14,700 Yes, thank you. 764 00:31:14,700 --> 00:31:15,200 Yeah. 765 00:31:15,200 --> 00:31:16,990 So exactly, the expected monetary value 766 00:31:16,990 --> 00:31:21,280 is higher than the status quo, so you accept the gamble. 767 00:31:21,280 --> 00:31:24,500 And that doesn't depend on the initial wealth. 768 00:31:24,500 --> 00:31:25,400 OK. 769 00:31:25,400 --> 00:31:27,690 So now, what's the expected utility maximizer do? 770 00:31:27,690 --> 00:31:30,470 And how does an expected utility maximizer think about this? 771 00:31:40,460 --> 00:31:41,788 Yes? 772 00:31:41,788 --> 00:31:43,580 AUDIENCE: In their calculation, rather than 773 00:31:43,580 --> 00:31:47,510 weighting the 9,600 and the 10,500, 774 00:31:47,510 --> 00:31:49,448 they'll weight the utility value. 775 00:31:49,448 --> 00:31:50,490 FRANK SCHILBACH: Exactly. 776 00:31:50,490 --> 00:31:52,130 So now, we need the utility function. 777 00:31:52,130 --> 00:31:56,330 What's the utility of 9,600, the utility of 10,500, 778 00:31:56,330 --> 00:31:58,100 and the utility of 10,000? 779 00:31:58,100 --> 00:32:01,760 Now, will she accept the gamble? 780 00:32:01,760 --> 00:32:03,200 Well, now, it depends essentially 781 00:32:03,200 --> 00:32:04,770 on the utility function. 782 00:32:04,770 --> 00:32:07,190 What's the shape of that utility function look like? 783 00:32:07,190 --> 00:32:08,960 In particular, it depends on the concavity 784 00:32:08,960 --> 00:32:10,590 of the utility function. 785 00:32:10,590 --> 00:32:13,020 So what do I mean by the concavity of the utility 786 00:32:13,020 --> 00:32:13,520 function? 787 00:32:13,520 --> 00:32:15,220 This is concave function. 788 00:32:15,220 --> 00:32:16,670 What do I mean by that? 789 00:32:19,350 --> 00:32:20,850 What's the definition? 790 00:32:20,850 --> 00:32:21,647 Yes. 791 00:32:21,647 --> 00:32:22,712 AUDIENCE: [INAUDIBLE] 792 00:32:22,712 --> 00:32:23,670 FRANK SCHILBACH: Right. 793 00:32:23,670 --> 00:32:25,878 So one definition is a second derivative is negative. 794 00:32:25,878 --> 00:32:26,820 That's exactly right. 795 00:32:26,820 --> 00:32:30,150 That's true if the function is twice differentiable. 796 00:32:30,150 --> 00:32:31,860 We have a slightly different definition 797 00:32:31,860 --> 00:32:33,930 that's slightly more general because it doesn't 798 00:32:33,930 --> 00:32:36,150 depend on differentiability. 799 00:32:36,150 --> 00:32:39,120 But essentially, it's to say it's the following definition, 800 00:32:39,120 --> 00:32:42,000 if the utility of a convex combination of two outcomes-- 801 00:32:42,000 --> 00:32:43,920 I'm going to tell you about this in a second-- 802 00:32:43,920 --> 00:32:47,940 is larger than the convex combination of the utility 803 00:32:47,940 --> 00:32:49,930 of those outcomes. 804 00:32:49,930 --> 00:32:50,950 What do I mean by that? 805 00:32:50,950 --> 00:32:54,000 Suppose you have an outcome x and a utility associated 806 00:32:54,000 --> 00:32:56,100 with that that's u of x. 807 00:32:56,100 --> 00:32:58,290 Suppose you have an outcome y and a utility 808 00:32:58,290 --> 00:33:01,630 of u of y associated with that. 809 00:33:01,630 --> 00:33:04,090 And now, suppose you have a convex combination of x and y, 810 00:33:04,090 --> 00:33:09,090 which is just p is a probability of p times x 811 00:33:09,090 --> 00:33:10,980 plus 1 minus p times y. 812 00:33:10,980 --> 00:33:12,690 That's in the middle of x and y. 813 00:33:12,690 --> 00:33:17,790 So I take a weighted average of x and y that adds up to 1. 814 00:33:17,790 --> 00:33:22,020 Now, if I have the utility associated with that convex 815 00:33:22,020 --> 00:33:27,370 combination, that's u of px plus 1 minus p times y. 816 00:33:27,370 --> 00:33:30,040 That's just the utility associated with that. 817 00:33:30,040 --> 00:33:33,390 Now, if I draw a line between those two graphs 818 00:33:33,390 --> 00:33:37,110 and look at what's the convex combination of p, 819 00:33:37,110 --> 00:33:40,435 so what's p of u of x plus 1 minus p of u of y? 820 00:33:40,435 --> 00:33:42,060 That's essentially the weighted average 821 00:33:42,060 --> 00:33:45,330 of the utilities associated with x and y. 822 00:33:45,330 --> 00:33:48,480 Now, the question is, is the average 823 00:33:48,480 --> 00:33:50,200 of the utility of the average higher 824 00:33:50,200 --> 00:33:53,218 or lower than the average of the utilities? 825 00:33:53,218 --> 00:33:55,510 Can somebody explain this in words of what I just said? 826 00:33:55,510 --> 00:33:56,680 Or what do I mean? 827 00:33:56,680 --> 00:33:58,000 Can somebody repeat this? 828 00:34:08,690 --> 00:34:09,190 Yes? 829 00:34:09,190 --> 00:34:11,496 AUDIENCE: I mean, technically, we're just trying to see if you 830 00:34:11,496 --> 00:34:13,579 take two points in the [INAUDIBLE] and draw a line 831 00:34:13,579 --> 00:34:16,302 between them, would the line be [? below ?] [? the curve? ?] 832 00:34:16,302 --> 00:34:17,260 FRANK SCHILBACH: Right. 833 00:34:17,260 --> 00:34:19,090 Is the line above or below the curve? 834 00:34:19,090 --> 00:34:21,460 In this case, the line is below the curve. 835 00:34:21,460 --> 00:34:23,860 Now, what that means is, if I give you two outcomes 836 00:34:23,860 --> 00:34:25,600 and I say, would you rather have-- 837 00:34:25,600 --> 00:34:27,610 you could have x and y, or would you rather 838 00:34:27,610 --> 00:34:30,940 have the some weighted average of x and y? 839 00:34:30,940 --> 00:34:34,120 Now, the question is, what's the utility associated 840 00:34:34,120 --> 00:34:36,275 with this average of x and y? 841 00:34:36,275 --> 00:34:38,650 That's the thing that you see here on the left upper side 842 00:34:38,650 --> 00:34:42,219 is u of p of x plus 1 minus p times y. 843 00:34:42,219 --> 00:34:45,699 That's essentially the utility of the weighted average. 844 00:34:45,699 --> 00:34:48,538 Is that larger or smaller than the weighted average 845 00:34:48,538 --> 00:34:50,830 of the utility, which is the thing that I show you here 846 00:34:50,830 --> 00:34:51,667 below? 847 00:34:51,667 --> 00:34:53,500 And what you see is, in this case-- and this 848 00:34:53,500 --> 00:34:55,540 is because the line is exactly as I say-- it's 849 00:34:55,540 --> 00:34:56,830 below the utility function. 850 00:34:56,830 --> 00:34:59,050 If the line is below the utility function, that 851 00:34:59,050 --> 00:35:02,560 means essentially that the utility of the weighted average 852 00:35:02,560 --> 00:35:06,220 is higher than the weighted average of the utilities, which 853 00:35:06,220 --> 00:35:09,130 means essentially the function is concave. 854 00:35:09,130 --> 00:35:11,950 And that means essentially that the person 855 00:35:11,950 --> 00:35:13,720 is risk averse, as we call it. 856 00:35:13,720 --> 00:35:17,020 You'd rather have the average than the spread of the two 857 00:35:17,020 --> 00:35:19,370 outcomes. 858 00:35:19,370 --> 00:35:21,365 Any questions on this or comments? 859 00:35:27,650 --> 00:35:28,150 OK. 860 00:35:28,150 --> 00:35:29,700 So you can look at this in detail 861 00:35:29,700 --> 00:35:34,530 but essentially it's a simple definition. 862 00:35:34,530 --> 00:35:37,560 So now, expected utility says essentially the following. 863 00:35:37,560 --> 00:35:40,350 It says a risk averse person rejects all fair gambles. 864 00:35:40,350 --> 00:35:42,650 And again, fair gambles are gambles that pay you 865 00:35:42,650 --> 00:35:44,552 the expected monetary value. 866 00:35:44,552 --> 00:35:46,010 And the reason why that person does 867 00:35:46,010 --> 00:35:48,890 that is because the expected utility 868 00:35:48,890 --> 00:35:53,840 is lower than the utility of the expected monetary value. 869 00:35:53,840 --> 00:35:56,180 Essentially, as you just said, it's 870 00:35:56,180 --> 00:36:00,020 because the straight line is below the utility function. 871 00:36:00,020 --> 00:36:02,510 And that's essentially exactly the same definition here. 872 00:36:02,510 --> 00:36:05,690 Therefore, a risk averse person who 873 00:36:05,690 --> 00:36:10,190 has a concave utility function rejects all fair gambles. 874 00:36:10,190 --> 00:36:13,380 Now, what does expected utility theory then say? 875 00:36:13,380 --> 00:36:17,370 Well, it says risky options are valued by doing three things. 876 00:36:17,370 --> 00:36:20,657 One is you have to define utility over final outcomes. 877 00:36:20,657 --> 00:36:23,240 And this is sort of getting back what you were saying earlier. 878 00:36:23,240 --> 00:36:26,587 People might be worried about losses or gains or the like. 879 00:36:26,587 --> 00:36:27,920 We're assuming all of this away. 880 00:36:27,920 --> 00:36:31,400 We're just saying, their final outcomes-- how much money you 881 00:36:31,400 --> 00:36:34,940 have, what grades you have, how many kids you have, 882 00:36:34,940 --> 00:36:37,160 and so on, these are final outcomes, 883 00:36:37,160 --> 00:36:41,990 things that sort of where an absolute value is defined. 884 00:36:41,990 --> 00:36:44,900 There's a utility associated with those outcomes. 885 00:36:44,900 --> 00:36:46,910 It's not about you expected more money 886 00:36:46,910 --> 00:36:48,200 or less money or the like. 887 00:36:48,200 --> 00:36:49,718 That's completely irrelevant. 888 00:36:49,718 --> 00:36:51,260 We're just looking at final outcomes. 889 00:36:51,260 --> 00:36:53,177 How much money do you end up actually getting? 890 00:36:53,177 --> 00:36:55,575 And we're associating some utility with that. 891 00:36:55,575 --> 00:36:57,200 That's assumption number one, or that's 892 00:36:57,200 --> 00:36:59,090 the first thing one does. 893 00:36:59,090 --> 00:37:02,300 Second is you weight these utilities for each outcomes 894 00:37:02,300 --> 00:37:03,388 by its probability. 895 00:37:03,388 --> 00:37:05,180 Essentially, we know what the probabilities 896 00:37:05,180 --> 00:37:06,750 are for each of those outcomes. 897 00:37:06,750 --> 00:37:10,220 We're going to take the weighted average of these utilities. 898 00:37:10,220 --> 00:37:13,580 And then we sort of adding them up. 899 00:37:13,580 --> 00:37:16,190 And then by adding them up, essentially we 900 00:37:16,190 --> 00:37:17,960 can evaluate all sorts of lotteries. 901 00:37:17,960 --> 00:37:20,600 And then we just compare those lotteries 902 00:37:20,600 --> 00:37:22,310 either with some fixed amount of money 903 00:37:22,310 --> 00:37:26,330 or some other lotteries, the outcomes that we might get. 904 00:37:26,330 --> 00:37:28,857 Now, there's two key implicit assumptions 905 00:37:28,857 --> 00:37:29,940 that are really important. 906 00:37:29,940 --> 00:37:32,070 One is only final outcomes matter. 907 00:37:32,070 --> 00:37:34,100 It doesn't matter what you expected in advance. 908 00:37:34,100 --> 00:37:36,142 It doesn't matter what you thought you might get. 909 00:37:36,142 --> 00:37:38,250 And it doesn't matter what you had yesterday. 910 00:37:38,250 --> 00:37:39,667 All of these things are completely 911 00:37:39,667 --> 00:37:42,170 irrelevant in the simplest form of expected utility 912 00:37:42,170 --> 00:37:44,420 unless you sort of have information or the like. 913 00:37:44,420 --> 00:37:46,310 Only final outcomes matter. 914 00:37:46,310 --> 00:37:48,530 And then there is linearity and probabilities. 915 00:37:48,530 --> 00:37:51,920 That's to say we put weight on the different types of states 916 00:37:51,920 --> 00:37:56,360 of the world relative to what the probability of those states 917 00:37:56,360 --> 00:37:57,410 are. 918 00:37:57,410 --> 00:38:00,320 So it cannot be that, if something is twice as likely, 919 00:38:00,320 --> 00:38:02,480 you should put twice as much weight on that 920 00:38:02,480 --> 00:38:04,400 in your evaluation of the outcomes. 921 00:38:04,400 --> 00:38:08,000 It cannot be that this is non-linear in certain ways. 922 00:38:08,000 --> 00:38:11,560 There's linearity in probabilities. 923 00:38:11,560 --> 00:38:12,580 Any questions on this? 924 00:38:22,730 --> 00:38:25,670 So now, let me get back to what I said previously. 925 00:38:25,670 --> 00:38:27,352 What are we assuming away here? 926 00:38:27,352 --> 00:38:29,060 What are the things that are not in here? 927 00:38:48,370 --> 00:38:48,870 Yeah. 928 00:38:48,870 --> 00:38:51,698 AUDIENCE: [INAUDIBLE] 929 00:38:51,698 --> 00:38:52,740 FRANK SCHILBACH: Exactly. 930 00:38:52,740 --> 00:38:57,010 So essentially, all the other things that we said previously 931 00:38:57,010 --> 00:38:58,740 we are assuming away, for example, things 932 00:38:58,740 --> 00:39:01,680 like anxiety over certain outcomes, worries, stress, 933 00:39:01,680 --> 00:39:02,730 and so on. 934 00:39:02,730 --> 00:39:05,976 I'm also assuming away regret. 935 00:39:05,976 --> 00:39:08,035 I'm assuming away the gains and losses. 936 00:39:08,035 --> 00:39:09,660 So essentially, anything we said before 937 00:39:09,660 --> 00:39:11,190 is essentially just stripped away 938 00:39:11,190 --> 00:39:13,470 and simplified in some sense and saying, 939 00:39:13,470 --> 00:39:15,840 we can explain a lot of behaviors just using 940 00:39:15,840 --> 00:39:18,180 the concavity of the utility function. 941 00:39:18,180 --> 00:39:19,758 Now, I have one example for you. 942 00:39:19,758 --> 00:39:21,300 And I think, I encourage, you sort of 943 00:39:21,300 --> 00:39:23,190 for any of these kinds of assumptions or kind 944 00:39:23,190 --> 00:39:26,288 of functions or things that you see in economics, 945 00:39:26,288 --> 00:39:28,080 it's worth sort of looking out in the world 946 00:39:28,080 --> 00:39:30,960 what people are actually doing and trying to see 947 00:39:30,960 --> 00:39:33,408 is that actually compatible with people, with behavior 948 00:39:33,408 --> 00:39:34,450 that we see in the world. 949 00:39:34,450 --> 00:39:36,460 And here's sort of one example. 950 00:39:36,460 --> 00:39:39,780 So I actually don't think this is irrational behavior. 951 00:39:39,780 --> 00:39:43,170 And that's actually a good example of so 952 00:39:43,170 --> 00:39:46,540 what we might confuse with irrational behaviors. 953 00:39:46,540 --> 00:39:51,028 So I guess what we see is that expected utility has 954 00:39:51,028 --> 00:39:53,070 a lot of trouble explaining this behavior, right? 955 00:39:53,070 --> 00:39:55,770 Because essentially, you spent like $5 on those lotteries. 956 00:39:55,770 --> 00:39:57,330 I'm offering you $10. 957 00:39:57,330 --> 00:39:59,310 So you get twice as many tickets. 958 00:39:59,310 --> 00:40:01,570 So your probability of winning will be twice as high. 959 00:40:01,570 --> 00:40:04,200 Presumably, you prefer winning or losing. 960 00:40:04,200 --> 00:40:06,003 So, therefore, you should obviously 961 00:40:06,003 --> 00:40:07,920 take that deal unless there's some transaction 962 00:40:07,920 --> 00:40:09,180 costs and the like. 963 00:40:09,180 --> 00:40:10,950 People are not doing that. 964 00:40:10,950 --> 00:40:14,010 The main reason that's mentioned here is regret. 965 00:40:14,010 --> 00:40:16,140 Now, what the person was saying here 966 00:40:16,140 --> 00:40:18,450 is these are perhaps irrational decisions. 967 00:40:18,450 --> 00:40:19,950 I actually don't think that's right. 968 00:40:19,950 --> 00:40:22,770 Essentially, it's just we cannot rationalize the decision that 969 00:40:22,770 --> 00:40:26,670 we see with expected utility in the sense that it looks like 970 00:40:26,670 --> 00:40:28,590 the person behaves in irrational ways, 971 00:40:28,590 --> 00:40:31,140 but the person may just have regret aversion, 972 00:40:31,140 --> 00:40:33,780 something that essentially is not in the utility function. 973 00:40:33,780 --> 00:40:35,880 We sort of modeled it in the wrong way. 974 00:40:35,880 --> 00:40:37,650 And sort of, by not capturing this, 975 00:40:37,650 --> 00:40:39,670 we might miss certain behaviors. 976 00:40:39,670 --> 00:40:42,090 Now, we're going to talk a lot about-- not about lotteries 977 00:40:42,090 --> 00:40:42,450 right now. 978 00:40:42,450 --> 00:40:44,658 We're going to get back to this a little bit in terms 979 00:40:44,658 --> 00:40:47,047 of why people engage in risk. 980 00:40:47,047 --> 00:40:49,380 But I just want to be clear on what we're assuming here. 981 00:40:49,380 --> 00:40:50,838 We're assuming a lot of stuff away, 982 00:40:50,838 --> 00:40:54,600 and I want you to be aware of that. 983 00:40:54,600 --> 00:40:57,420 There's another question which actually 984 00:40:57,420 --> 00:41:01,762 the question or the video did not sort of try to tackle, 985 00:41:01,762 --> 00:41:03,720 which is why are people playing these lotteries 986 00:41:03,720 --> 00:41:05,070 in the first place. 987 00:41:05,070 --> 00:41:07,210 Why engage in the lotteries in the first place? 988 00:41:07,210 --> 00:41:09,815 In some sense, that wasn't clear either. 989 00:41:09,815 --> 00:41:11,440 Again, we're going to get back to that. 990 00:41:11,440 --> 00:41:13,977 But the point of the video was to show you 991 00:41:13,977 --> 00:41:16,560 that, in some sense, these are a bunch of assumptions that are 992 00:41:16,560 --> 00:41:18,205 in the expected utility model. 993 00:41:18,205 --> 00:41:19,830 Not all of these assumptions are right. 994 00:41:19,830 --> 00:41:23,028 And you know, we want to be sort of aware of that. 995 00:41:23,028 --> 00:41:25,320 But let me sort of just summarize what I just told you. 996 00:41:25,320 --> 00:41:29,650 And this, in some sense, is recap of 14.01 if you want, 997 00:41:29,650 --> 00:41:32,310 which I think in part you also discussed in recitation. 998 00:41:32,310 --> 00:41:34,470 Or there's like a handout from 14.01 999 00:41:34,470 --> 00:41:37,620 that you can look at to study it in more details. 1000 00:41:37,620 --> 00:41:39,330 So many important economic choices 1001 00:41:39,330 --> 00:41:43,530 involve risk and people are risk averse in many contexts. 1002 00:41:43,530 --> 00:41:47,160 The expected utility model is a workhorse model 1003 00:41:47,160 --> 00:41:50,120 of the economics for studying risk. 1004 00:41:50,120 --> 00:41:51,870 And the way it's done is, essentially, one 1005 00:41:51,870 --> 00:41:54,540 takes the weighted average of utilities from final outcomes. 1006 00:41:54,540 --> 00:41:57,270 That's what matters for assessing outcomes. 1007 00:41:57,270 --> 00:41:58,033 OK. 1008 00:41:58,033 --> 00:41:59,700 And so, now, we're going to see, OK, now 1009 00:41:59,700 --> 00:42:01,560 taking that model very seriously, what 1010 00:42:01,560 --> 00:42:02,430 can be explained? 1011 00:42:02,430 --> 00:42:06,900 And what are perhaps the limits of doing so? 1012 00:42:06,900 --> 00:42:09,210 And sort of risk aversion comes solely 1013 00:42:09,210 --> 00:42:13,270 and exclusively from the concavity of the utility 1014 00:42:13,270 --> 00:42:13,770 function. 1015 00:42:13,770 --> 00:42:16,680 There's no other reasons to avoid risk. 1016 00:42:16,680 --> 00:42:20,160 Then essentially your utility function is concave. 1017 00:42:20,160 --> 00:42:20,760 OK. 1018 00:42:20,760 --> 00:42:22,110 So now, how do we measure risk? 1019 00:42:22,110 --> 00:42:23,910 And that's, again, sort of definitions 1020 00:42:23,910 --> 00:42:25,512 that economists use. 1021 00:42:25,512 --> 00:42:26,970 When you think about risk aversion, 1022 00:42:26,970 --> 00:42:27,870 how do you measure this? 1023 00:42:27,870 --> 00:42:30,120 Well, you measure it essentially through the concavity 1024 00:42:30,120 --> 00:42:32,802 of the utility function, which is, as you were saying earlier, 1025 00:42:32,802 --> 00:42:35,010 it's coming from the second derivative of the utility 1026 00:42:35,010 --> 00:42:35,820 function. 1027 00:42:35,820 --> 00:42:38,340 There's two main measures that economists use. 1028 00:42:38,340 --> 00:42:40,860 There's sort of the absolute or the coefficient 1029 00:42:40,860 --> 00:42:43,830 of absolute risk aversion. 1030 00:42:43,830 --> 00:42:45,570 We call that r. 1031 00:42:45,570 --> 00:42:48,805 It's essentially taking the second derivative, 1032 00:42:48,805 --> 00:42:49,930 which tends to be negative. 1033 00:42:49,930 --> 00:42:52,770 So we take the negative of that. 1034 00:42:52,770 --> 00:42:54,720 We scale it by the first derivative. 1035 00:42:54,720 --> 00:42:58,250 That's essentially to make it insensitive to 1036 00:42:58,250 --> 00:43:01,440 if you multiply the utility function by a constant. 1037 00:43:01,440 --> 00:43:04,040 Presumably, that doesn't change anything to your choices. 1038 00:43:04,040 --> 00:43:06,490 So you risk aversion should not change. 1039 00:43:06,490 --> 00:43:09,900 And, therefore, we sort of have to normalize 1040 00:43:09,900 --> 00:43:12,920 or we divide by the first derivative. 1041 00:43:12,920 --> 00:43:15,780 A second version of that, or an alternative version, 1042 00:43:15,780 --> 00:43:19,440 is the coefficient of relative risk aversion, 1043 00:43:19,440 --> 00:43:22,620 which essentially is-- 1044 00:43:22,620 --> 00:43:23,790 we call it-- gamma. 1045 00:43:23,790 --> 00:43:27,900 Gamma is x, the wealth outcome that we 1046 00:43:27,900 --> 00:43:32,040 look at times r times the coefficient of absolute risk 1047 00:43:32,040 --> 00:43:32,850 aversion. 1048 00:43:32,850 --> 00:43:37,980 It's the elasticity of the slope of the utility function, which 1049 00:43:37,980 --> 00:43:39,150 I've written out here. 1050 00:43:39,150 --> 00:43:41,040 And sort of one very nice property of this-- 1051 00:43:41,040 --> 00:43:42,580 and again, that's a definition. 1052 00:43:42,580 --> 00:43:43,740 There's not much to argue with this. 1053 00:43:43,740 --> 00:43:45,448 This is just how economists measure this. 1054 00:43:45,448 --> 00:43:47,320 One nice property of this is, if you 1055 00:43:47,320 --> 00:43:49,900 look at portfolio models or the like, 1056 00:43:49,900 --> 00:43:53,920 one implications of constant relative risk aversion, which 1057 00:43:53,920 --> 00:43:56,140 I'm going to show you a function of in a bit, 1058 00:43:56,140 --> 00:43:59,008 is that people with constant relative risk aversion 1059 00:43:59,008 --> 00:44:01,300 invest a constant share of their wealth in risky assets 1060 00:44:01,300 --> 00:44:03,490 regardless of their level of wealth. 1061 00:44:03,490 --> 00:44:08,560 That's a main sort of result from a finance or portfolio 1062 00:44:08,560 --> 00:44:09,880 models. 1063 00:44:09,880 --> 00:44:11,958 In some sense, that's sort of irrelevant for you. 1064 00:44:11,958 --> 00:44:13,750 These are just definitions in the sense of, 1065 00:44:13,750 --> 00:44:15,640 if you wanted to measure risk aversion, 1066 00:44:15,640 --> 00:44:20,400 this is what economists have used mostly, OK? 1067 00:44:24,370 --> 00:44:26,680 Now, if I give you this definition, 1068 00:44:26,680 --> 00:44:28,210 how would you actually measure this? 1069 00:44:28,210 --> 00:44:30,310 If you wanted to know my risk aversion, 1070 00:44:30,310 --> 00:44:33,590 how would you do that? 1071 00:44:33,590 --> 00:44:37,390 And so let me give you actually a utility function here. 1072 00:44:37,390 --> 00:44:40,600 So let me give you actually two utility functions. 1073 00:44:40,600 --> 00:44:42,430 Here's just examples of one example 1074 00:44:42,430 --> 00:44:46,570 of the constant absolute risk aversion function 1075 00:44:46,570 --> 00:44:48,130 that you see here. 1076 00:44:48,130 --> 00:44:50,920 Or a Constant Relative Risk Aversion, CRRA, this 1077 00:44:50,920 --> 00:44:52,398 is what we mostly use. 1078 00:44:52,398 --> 00:44:54,190 So that's just the definition of a function 1079 00:44:54,190 --> 00:44:56,750 that has the property that it has constant relative risk 1080 00:44:56,750 --> 00:44:57,250 aversion. 1081 00:44:57,250 --> 00:44:59,500 You can sort of verify that. 1082 00:44:59,500 --> 00:45:02,560 We're going to focus here on CRRA functions, which are sort 1083 00:45:02,560 --> 00:45:04,760 of what economists mostly use. 1084 00:45:04,760 --> 00:45:07,150 So now, if I told you this is my utility function, 1085 00:45:07,150 --> 00:45:08,960 my totally function looks like this, 1086 00:45:08,960 --> 00:45:13,150 now how would you estimate my risk aversion? 1087 00:45:19,100 --> 00:45:21,728 AUDIENCE: [? I ?] can give you two gambles and then 1088 00:45:21,728 --> 00:45:23,372 [INAUDIBLE]? 1089 00:45:23,372 --> 00:45:24,330 FRANK SCHILBACH: Right. 1090 00:45:24,330 --> 00:45:27,120 So could you give me essentially choices 1091 00:45:27,120 --> 00:45:30,660 of outcomes that have essentially some uncertainty 1092 00:45:30,660 --> 00:45:32,610 or different risk involved. 1093 00:45:32,610 --> 00:45:36,870 And then I'll give you the choices. 1094 00:45:36,870 --> 00:45:38,590 If I say I prefer one over the other, 1095 00:45:38,590 --> 00:45:39,840 can you tell what my gamma is? 1096 00:45:45,456 --> 00:45:46,357 AUDIENCE: No. 1097 00:45:46,357 --> 00:45:47,940 FRANK SCHILBACH: What can you tell me? 1098 00:45:47,940 --> 00:45:48,780 Or what can you say? 1099 00:46:02,145 --> 00:46:05,210 AUDIENCE: I guess you can say the [? extent, ?] 1100 00:46:05,210 --> 00:46:07,370 but maybe not [INAUDIBLE] value [INAUDIBLE].. 1101 00:46:07,370 --> 00:46:07,640 FRANK SCHILBACH: Yeah. 1102 00:46:07,640 --> 00:46:09,270 You can put some bounds on it, right? 1103 00:46:09,270 --> 00:46:10,620 So I'm going to show you this in a second. 1104 00:46:10,620 --> 00:46:12,080 But essentially, if I say I prefer 1105 00:46:12,080 --> 00:46:13,740 one option over the other, you're 1106 00:46:13,740 --> 00:46:15,740 going to have gamma on the left-hand side, gamma 1107 00:46:15,740 --> 00:46:18,407 on the right-hand side, and give you some equations, essentially 1108 00:46:18,407 --> 00:46:19,400 some inequality. 1109 00:46:19,400 --> 00:46:22,425 And then if you solve that equation, 1110 00:46:22,425 --> 00:46:24,050 you're going to get some bound on gamma 1111 00:46:24,050 --> 00:46:27,350 that sort of essentially tells you below or above. 1112 00:46:27,350 --> 00:46:29,990 Or my risk aversion must be below or above 1113 00:46:29,990 --> 00:46:32,210 a certain number. 1114 00:46:32,210 --> 00:46:33,190 What else could we do? 1115 00:46:41,730 --> 00:46:42,230 Yes? 1116 00:46:42,230 --> 00:46:44,200 AUDIENCE: [? Ask ?] [? them ?] [? when they're ?] [INAUDIBLE]?? 1117 00:46:44,200 --> 00:46:44,740 FRANK SCHILBACH: Exactly. 1118 00:46:44,740 --> 00:46:46,810 And that's what's called the certainty 1119 00:46:46,810 --> 00:46:50,680 or-- so the simplest way of doing that is to say, here's 1120 00:46:50,680 --> 00:46:53,650 a lottery between some gains or losses 1121 00:46:53,650 --> 00:46:55,510 or two gains with certain probabilities. 1122 00:46:55,510 --> 00:46:56,835 There's some risk involved. 1123 00:46:56,835 --> 00:46:58,210 And then we could ask you, what's 1124 00:46:58,210 --> 00:47:01,360 the amount that makes you indifferent between receiving 1125 00:47:01,360 --> 00:47:05,167 that amount for sure and the gamble that I'm offering you? 1126 00:47:05,167 --> 00:47:07,000 Now, that's called the certainty equivalent. 1127 00:47:07,000 --> 00:47:08,800 Essentially, it's the amount of money, 1128 00:47:08,800 --> 00:47:12,460 if I have a certain gamble, what's the amount of money 1129 00:47:12,460 --> 00:47:15,070 that, if you get it for sure, makes you exactly 1130 00:47:15,070 --> 00:47:18,160 indifferent between that amount of money for sure 1131 00:47:18,160 --> 00:47:20,890 and the gamble, which is uncertain, right? 1132 00:47:20,890 --> 00:47:23,080 So if we then had the certainty equivalent, 1133 00:47:23,080 --> 00:47:24,910 now you could essentially just back out 1134 00:47:24,910 --> 00:47:29,020 what my gamma is by just solving for gamma that's there. 1135 00:47:29,020 --> 00:47:31,750 Let me actually show you that. 1136 00:47:31,750 --> 00:47:33,413 There's another thing that we could do. 1137 00:47:33,413 --> 00:47:34,330 What else could we do? 1138 00:47:34,330 --> 00:47:37,090 So we said, OK, if you gamble, choices 1139 00:47:37,090 --> 00:47:39,310 between different gambles, I could ask you 1140 00:47:39,310 --> 00:47:40,720 for certainty equivalent. 1141 00:47:40,720 --> 00:47:43,030 Now, these are all kind of lab ways of doing this. 1142 00:47:43,030 --> 00:47:44,530 But if you looked in the real world, 1143 00:47:44,530 --> 00:47:46,180 if you try to sort of figure out in the real world 1144 00:47:46,180 --> 00:47:47,638 how are people making these choices 1145 00:47:47,638 --> 00:47:49,990 or choices in the world, what kinds of choices could 1146 00:47:49,990 --> 00:47:52,960 you observe to figure out what people's gamma is? 1147 00:47:52,960 --> 00:47:54,460 Yes. 1148 00:47:54,460 --> 00:47:56,627 AUDIENCE: Could you sell them insurance or an option 1149 00:47:56,627 --> 00:47:58,752 to mitigate their risk and figure out how much they 1150 00:47:58,752 --> 00:47:59,780 value that mitigation? 1151 00:47:59,780 --> 00:48:00,310 FRANK SCHILBACH: Exactly. 1152 00:48:00,310 --> 00:48:01,000 That's exactly right. 1153 00:48:01,000 --> 00:48:02,917 And that's exactly what we're going to discuss 1154 00:48:02,917 --> 00:48:04,990 and what people have done. 1155 00:48:04,990 --> 00:48:08,200 Now, it's a little bit tricky that in usually cases, 1156 00:48:08,200 --> 00:48:11,410 if I just ask you what insurance have you chosen, 1157 00:48:11,410 --> 00:48:14,110 it's a little tricky to figure out what your gamma actually 1158 00:48:14,110 --> 00:48:17,050 is because I don't know what options you had, right? 1159 00:48:17,050 --> 00:48:20,290 So what I need is essentially a choice set between-- 1160 00:48:20,290 --> 00:48:21,810 suppose I'm selling you insurance. 1161 00:48:21,810 --> 00:48:23,560 In particular, what I'm going to show you, 1162 00:48:23,560 --> 00:48:25,985 I think, next time is Justin Sydnor's paper, 1163 00:48:25,985 --> 00:48:27,610 where people can choose between-- these 1164 00:48:27,610 --> 00:48:30,910 are customers in a certain home insurance where 1165 00:48:30,910 --> 00:48:33,978 people have choices between different deductibles, right? 1166 00:48:33,978 --> 00:48:36,520 And now, I can essentially say, if I choose a high deductible 1167 00:48:36,520 --> 00:48:38,260 versus a low deductible, essentially 1168 00:48:38,260 --> 00:48:41,140 it's implicitly you're choosing the risk exposure 1169 00:48:41,140 --> 00:48:42,910 that you have for price. 1170 00:48:42,910 --> 00:48:46,338 So in Sydnor's case, there's four different options 1171 00:48:46,338 --> 00:48:47,380 that people offer to him. 1172 00:48:47,380 --> 00:48:49,578 That was essentially both the choice set, 1173 00:48:49,578 --> 00:48:52,120 like what are the choices that people offered-- in this case, 1174 00:48:52,120 --> 00:48:54,310 I guess they're often offered four choices-- 1175 00:48:54,310 --> 00:48:57,640 and then the actual choice that they made. 1176 00:48:57,640 --> 00:48:59,660 Again, that's not going to give you 1177 00:48:59,660 --> 00:49:02,920 an exact gamma in terms of pinning it down exactly what it 1178 00:49:02,920 --> 00:49:05,290 is because there's four different inequalities that you 1179 00:49:05,290 --> 00:49:06,880 get from these choices. 1180 00:49:06,880 --> 00:49:09,100 But you can actually bound, as it turns out, 1181 00:49:09,100 --> 00:49:12,490 people's risk aversion pretty well using 1182 00:49:12,490 --> 00:49:14,930 those kinds of choices. 1183 00:49:14,930 --> 00:49:15,430 Exactly. 1184 00:49:15,430 --> 00:49:18,040 So that's what we have here is certain equivalence, choices 1185 00:49:18,040 --> 00:49:20,330 from gambles, and insurance choices. 1186 00:49:20,330 --> 00:49:23,650 So let's start with certainty equivalent. 1187 00:49:23,650 --> 00:49:29,350 So suppose your wealth equals either to $50,000 to $100,000 1188 00:49:29,350 --> 00:49:31,660 each with probability 50%. 1189 00:49:31,660 --> 00:49:34,837 Suppose that's essentially there's 1190 00:49:34,837 --> 00:49:35,920 lots of risk in your life. 1191 00:49:35,920 --> 00:49:38,890 Either it's 50,000, 100,000, starting 1192 00:49:38,890 --> 00:49:40,570 tomorrow you're going to find out 1193 00:49:40,570 --> 00:49:42,250 the chance of that is 50% each. 1194 00:49:42,250 --> 00:49:43,750 Now, of course, that's hypothetical, 1195 00:49:43,750 --> 00:49:46,330 but let's suppose that for a second. 1196 00:49:46,330 --> 00:49:49,970 You're expected wealth then, of course, is 75,000. 1197 00:49:49,970 --> 00:49:52,660 Now, what guaranteed amount, the certainty equivalent, 1198 00:49:52,660 --> 00:49:56,000 of the WCE do you find equally desirable? 1199 00:49:56,000 --> 00:49:57,850 If I could make all of your risk go away 1200 00:49:57,850 --> 00:49:59,642 and just say I'm giving you a fixed amount, 1201 00:49:59,642 --> 00:50:01,730 what amount would you choose? 1202 00:50:01,730 --> 00:50:11,070 Now, when you do that, essentially, 1203 00:50:11,070 --> 00:50:14,517 if you give me an amount W, a certain equivalent, 1204 00:50:14,517 --> 00:50:16,350 that gives me essentially an equation, which 1205 00:50:16,350 --> 00:50:18,270 is the utility from the certainty equivalent, 1206 00:50:18,270 --> 00:50:22,380 by definition, since you just told me that, 1207 00:50:22,380 --> 00:50:24,420 must be the same as the weighted average 1208 00:50:24,420 --> 00:50:26,315 of the utility of 50,000 and the ultimately 1209 00:50:26,315 --> 00:50:30,420 of 100,000 with probability 50% each, right? 1210 00:50:30,420 --> 00:50:32,940 And once you do that, now you get essentially some nonlinear 1211 00:50:32,940 --> 00:50:37,230 equation that depends on gamma that you can solve. 1212 00:50:37,230 --> 00:50:42,060 Perhaps not in closed form, but you can essentially 1213 00:50:42,060 --> 00:50:47,660 figure out what the answer is in Mathematica or the like, OK? 1214 00:50:47,660 --> 00:50:53,990 Now, as it turns out, now you can solve for this. 1215 00:50:53,990 --> 00:50:57,310 And the implied values of gamma I've written down for here. 1216 00:50:57,310 --> 00:51:02,765 So if you tell me here 70,000, gamma is 1. 1217 00:51:02,765 --> 00:51:04,920 If you tell me 66,000, it's 2. 1218 00:51:04,920 --> 00:51:06,190 58,000, it's 5. 1219 00:51:06,190 --> 00:51:08,330 53,000, it's 10. 1220 00:51:08,330 --> 00:51:13,040 51,000, it's 30. 1221 00:51:13,040 --> 00:51:15,020 Who would say anything below 10? 1222 00:51:24,810 --> 00:51:27,508 Yes, no? 1223 00:51:27,508 --> 00:51:28,300 What would you say? 1224 00:51:28,300 --> 00:51:30,430 AUDIENCE: By below, you mean less than 10? 1225 00:51:30,430 --> 00:51:32,728 FRANK SCHILBACH: So value of gamma less than 10, yes. 1226 00:51:32,728 --> 00:51:33,770 AUDIENCE: Yeah, for sure. 1227 00:51:33,770 --> 00:51:35,062 FRANK SCHILBACH: Yes, for sure. 1228 00:51:35,062 --> 00:51:38,140 That seems very reasonable. 1229 00:51:38,140 --> 00:51:43,450 If you think about value of 30, if you had a value of 30, 1230 00:51:43,450 --> 00:51:46,073 you probably would not leave the house ever in some sense. 1231 00:51:46,073 --> 00:51:47,740 You would not come to class or something 1232 00:51:47,740 --> 00:51:49,780 because you're worried about some stuff falling 1233 00:51:49,780 --> 00:51:51,610 on your head or the like. 1234 00:51:51,610 --> 00:51:55,150 Because, again, let me show you what the lottery was. 1235 00:51:55,150 --> 00:52:00,340 The lottery was between 50,000 100,000 with 50% chance. 1236 00:52:00,340 --> 00:52:02,290 If you tell me you're indifferent between that 1237 00:52:02,290 --> 00:52:05,170 and 51,000 for sure, you're essentially 1238 00:52:05,170 --> 00:52:09,730 valuing this small increment coming from 50,000 to 51,209. 1239 00:52:09,730 --> 00:52:12,790 That's $1,209. 1240 00:52:12,790 --> 00:52:17,260 You value that a lot compared to the 50% chance 1241 00:52:17,260 --> 00:52:21,310 of actually getting $100,000. 1242 00:52:21,310 --> 00:52:24,580 So we sort of think that, when looking at these large scale 1243 00:52:24,580 --> 00:52:26,710 choices, economists often assume, I think, 1244 00:52:26,710 --> 00:52:30,880 that people's gamma is somewhere between 0 and 2, OK? 1245 00:52:30,880 --> 00:52:33,370 So somewhere maybe 70,000, maybe even 1246 00:52:33,370 --> 00:52:35,737 lower than that, maybe 66,000, these 1247 00:52:35,737 --> 00:52:38,320 are sort of reasonable choices that we think people are making 1248 00:52:38,320 --> 00:52:41,920 or you see people making in their lives. 1249 00:52:41,920 --> 00:52:44,695 Anything above that seems like it's just not right 1250 00:52:44,695 --> 00:52:46,570 because, in some sense, that's not how people 1251 00:52:46,570 --> 00:52:48,010 behave in the real world. 1252 00:52:48,010 --> 00:52:50,950 People are comfortable with at least some risk in their life 1253 00:52:50,950 --> 00:52:52,430 when you look at them. 1254 00:52:52,430 --> 00:52:55,030 So the broad lesson is that choices involving large scale 1255 00:52:55,030 --> 00:53:01,930 risk suggests that gamma can't be too large, OK? 1256 00:53:04,860 --> 00:53:06,030 Now, second we can say-- 1257 00:53:06,030 --> 00:53:08,388 OK, so those are large scale choices. 1258 00:53:08,388 --> 00:53:10,680 Now, we're going to look at sort of small scale choices 1259 00:53:10,680 --> 00:53:15,450 using small gambles as [? Deckson ?] was just 1260 00:53:15,450 --> 00:53:16,500 alluding to. 1261 00:53:16,500 --> 00:53:19,890 So here's a choice involving a small scale gamble. 1262 00:53:19,890 --> 00:53:26,280 What if you had a 50-50 bet to win $11 and lose $10? 1263 00:53:26,280 --> 00:53:27,420 Who would take that bet? 1264 00:53:33,900 --> 00:53:36,580 Who would not take it? 1265 00:53:36,580 --> 00:53:37,210 OK. 1266 00:53:37,210 --> 00:53:41,860 So suppose you know there's a question kind of like, follow 1267 00:53:41,860 --> 00:53:46,210 those questions, now, since your utility is not 1268 00:53:46,210 --> 00:53:48,940 necessarily linear, we need to know what your wealth is. 1269 00:53:48,940 --> 00:53:50,650 Suppose it's 20,000, but you can choose 1270 00:53:50,650 --> 00:53:52,120 all sorts of other numbers. 1271 00:53:52,120 --> 00:53:54,920 And you turn down a 50-50 bet to win-- 1272 00:53:54,920 --> 00:53:56,930 this is 110 and lose 100. 1273 00:53:56,930 --> 00:53:59,170 You could do this for 11 and 10 as well. 1274 00:53:59,170 --> 00:54:02,410 What can we learn now about your gamma? 1275 00:54:02,410 --> 00:54:04,150 And this is what I was saying earlier. 1276 00:54:04,150 --> 00:54:06,370 Now, it's essentially, if you turn down this bet, 1277 00:54:06,370 --> 00:54:09,700 it must be that having 20,000, which is the status quo if you 1278 00:54:09,700 --> 00:54:11,770 turn down the bet, the utility of that 1279 00:54:11,770 --> 00:54:19,810 is larger than 50% of 20,000 plus 110 plus 0.5 times 1280 00:54:19,810 --> 00:54:21,880 the utility of 20,000 minus 100. 1281 00:54:21,880 --> 00:54:25,690 And again, I can sort of then plug in the utility function 1282 00:54:25,690 --> 00:54:28,240 and essentially solve for gamma. 1283 00:54:28,240 --> 00:54:31,330 Now, if you solve for gamma-- 1284 00:54:31,330 --> 00:54:34,330 and some of the next problem set is 1285 00:54:34,330 --> 00:54:36,640 doing some of that-- is essentially 1286 00:54:36,640 --> 00:54:41,980 rejecting this bet is implying that gamma is larger than 18. 1287 00:54:41,980 --> 00:54:44,260 Now, 18 is actually not that large. 1288 00:54:44,260 --> 00:54:46,660 But surely, 18 is larger than 2. 1289 00:54:46,660 --> 00:54:48,910 And we just sort of agreed earlier on 1290 00:54:48,910 --> 00:54:51,520 that gamma should be somewhere below 10, 1291 00:54:51,520 --> 00:54:55,120 presumably somewhere around 2 or maybe 1. 1292 00:54:55,120 --> 00:54:57,580 So what we get here now is, when you look at large scale 1293 00:54:57,580 --> 00:55:00,040 choices, it looks like people's gamma is 1294 00:55:00,040 --> 00:55:04,390 somewhere between 0 and 2, perhaps below 5 or something, 1295 00:55:04,390 --> 00:55:06,010 but surely not above 10. 1296 00:55:06,010 --> 00:55:08,290 When you look at small scale choices that 1297 00:55:08,290 --> 00:55:10,100 seem pretty reasonable-- and many of you 1298 00:55:10,100 --> 00:55:14,017 seem to agree that you might not want to take certain bets. 1299 00:55:14,017 --> 00:55:15,850 Maybe you're credit constrained or the like. 1300 00:55:15,850 --> 00:55:20,000 But in any case, it looks like people's gamma is really large. 1301 00:55:20,000 --> 00:55:20,500 OK. 1302 00:55:20,500 --> 00:55:22,125 And so, now, the question is, how do we 1303 00:55:22,125 --> 00:55:23,290 sort of reconcile this? 1304 00:55:23,290 --> 00:55:27,790 How do we put these things together? 1305 00:55:27,790 --> 00:55:31,900 Now, Matthew Rabin has written a paper of this and sort of says, 1306 00:55:31,900 --> 00:55:35,200 this is not just sort of an intuitive argument. 1307 00:55:35,200 --> 00:55:38,050 This is a paper in Econometrica from 2000. 1308 00:55:38,050 --> 00:55:41,710 But in fact, he sort of proves that, when 1309 00:55:41,710 --> 00:55:44,920 people reject small scale gambles, that just 1310 00:55:44,920 --> 00:55:48,640 sort of implies crazy stuff for large scale choices, 1311 00:55:48,640 --> 00:55:51,760 essentially stuff that just seems completely implausible. 1312 00:55:51,760 --> 00:55:53,980 And essentially, he, under minimal assumptions, 1313 00:55:53,980 --> 00:55:58,700 proves that this doesn't make a lot of sense. 1314 00:55:58,700 --> 00:56:01,870 Now, what do I mean by this is and what do we learn from this 1315 00:56:01,870 --> 00:56:04,210 is that essentially the marginal utility of money 1316 00:56:04,210 --> 00:56:08,890 must decrease extremely rapidly if you sort of take 1317 00:56:08,890 --> 00:56:11,500 this model seriously. 1318 00:56:11,500 --> 00:56:13,990 He does this under new assumptions about the utility 1319 00:56:13,990 --> 00:56:14,490 function. 1320 00:56:14,490 --> 00:56:16,115 So it's not just something special case 1321 00:56:16,115 --> 00:56:17,830 that he sort of doctored together 1322 00:56:17,830 --> 00:56:20,560 with some special assumptions of the utility function. 1323 00:56:20,560 --> 00:56:22,570 The only thing, in fact, that he's assuming 1324 00:56:22,570 --> 00:56:28,580 is that the utility function is weakly concave. 1325 00:56:28,580 --> 00:56:29,080 OK. 1326 00:56:29,080 --> 00:56:33,880 And so here's the example that was also in your reading. 1327 00:56:33,880 --> 00:56:37,180 Suppose there's Johnny, who is a risk averse expected 1328 00:56:37,180 --> 00:56:39,340 utility maximizer where the utility 1329 00:56:39,340 --> 00:56:41,380 function or the second derivative 1330 00:56:41,380 --> 00:56:43,960 is smaller or equal than 0, meaning 1331 00:56:43,960 --> 00:56:48,070 that essentially his utility function is weakly concave. 1332 00:56:48,070 --> 00:56:52,960 Suppose that person turns down a 50-50 gamble of losing $10 1333 00:56:52,960 --> 00:56:55,833 and gaining $11 for any level of wealth. 1334 00:56:55,833 --> 00:56:58,000 That assumption at the end, for any level of wealth, 1335 00:56:58,000 --> 00:57:00,800 is kind of important, but actually not that important. 1336 00:57:00,800 --> 00:57:03,430 You can sort of relax that as well. 1337 00:57:03,430 --> 00:57:06,430 For our purposes, we can sort of mostly ignore it. 1338 00:57:06,430 --> 00:57:08,710 Now, what's the biggest Y such that we 1339 00:57:08,710 --> 00:57:14,590 know Johnny will turn down a 50-50, lose 100, win Y bet? 1340 00:57:14,590 --> 00:57:16,210 So here are the answers. 1341 00:57:16,210 --> 00:57:20,372 And what's the correct answer? 1342 00:57:20,372 --> 00:57:22,300 AUDIENCE: G. 1343 00:57:22,300 --> 00:57:25,570 FRANK SCHILBACH: G. And why is that? 1344 00:57:25,570 --> 00:57:30,350 Or can somebody explain what's going on? 1345 00:57:34,970 --> 00:57:35,470 Yes. 1346 00:57:39,710 --> 00:57:41,710 AUDIENCE: Is it because he will reject 1347 00:57:41,710 --> 00:57:43,290 this bet for any level of wealth, 1348 00:57:43,290 --> 00:57:48,260 so that kind of implies that he's not 1349 00:57:48,260 --> 00:57:50,413 able to accept any level of risk? 1350 00:57:50,413 --> 00:57:51,580 FRANK SCHILBACH: No, no, no. 1351 00:57:51,580 --> 00:57:54,130 I think that's just because, for the iteration forward 1352 00:57:54,130 --> 00:57:57,010 in the proof of the thing, he needs 1353 00:57:57,010 --> 00:57:59,420 to sort make that argument. 1354 00:57:59,420 --> 00:58:01,400 But in fact, that's not essential. 1355 00:58:01,400 --> 00:58:03,130 There's some restrictions to that. 1356 00:58:03,130 --> 00:58:05,620 You can prove the same thing maybe not as 1357 00:58:05,620 --> 00:58:07,838 stark in terms of a result, but this is just 1358 00:58:07,838 --> 00:58:09,130 because he's iterating forward. 1359 00:58:09,130 --> 00:58:10,713 He needs to sort of prove the sequence 1360 00:58:10,713 --> 00:58:13,350 of utilities that derives. 1361 00:58:13,350 --> 00:58:15,100 But it's actually not necessarily central. 1362 00:58:21,000 --> 00:58:21,870 Yes. 1363 00:58:21,870 --> 00:58:26,073 AUDIENCE: I think the paper argued that Johnny [INAUDIBLE] 1364 00:58:26,073 --> 00:58:30,248 implied that the [INAUDIBLE] [? utility ?] [INAUDIBLE] very 1365 00:58:30,248 --> 00:58:32,658 [? rapidly decreasing, ?] [? which means that ?] between 1366 00:58:32,658 --> 00:58:36,915 that he will [INAUDIBLE]. 1367 00:58:36,915 --> 00:58:37,790 FRANK SCHILBACH: Yes. 1368 00:58:37,790 --> 00:58:39,470 So what's happening here is that-- 1369 00:58:41,990 --> 00:58:43,910 so let's sort of start very simply. 1370 00:58:43,910 --> 00:58:47,260 Let's start with Johnny's first choice 1371 00:58:47,260 --> 00:58:51,280 that says he rejects the bet, which means essentially 1372 00:58:51,280 --> 00:58:53,800 on the right-hand side is utility of status quo, 1373 00:58:53,800 --> 00:58:55,840 essentially just utility if w. 1374 00:58:55,840 --> 00:58:58,735 On the left-hand side is 50% chance of winning $11 1375 00:58:58,735 --> 00:59:02,020 and 50% chance of losing $10. 1376 00:59:02,020 --> 00:59:04,660 Now, you can sort of multiply this 1377 00:59:04,660 --> 00:59:08,860 by 2 and rearrange, which gives you the second line. 1378 00:59:08,860 --> 00:59:11,800 Essentially, that says that the increase in utility going 1379 00:59:11,800 --> 00:59:17,110 from w to w plus 11 is smaller than the increase in utility 1380 00:59:17,110 --> 00:59:22,280 going from w minus 10 to w. 1381 00:59:22,280 --> 00:59:25,390 OK, that's just the left-hand side and the right-hand side. 1382 00:59:25,390 --> 00:59:28,550 I'm just rearranging terms. 1383 00:59:28,550 --> 00:59:30,490 So what that means is that, again, 1384 00:59:30,490 --> 00:59:31,990 like on the left-hand side, how much 1385 00:59:31,990 --> 00:59:36,520 does the utility increase if I go from w to w plus 11? 1386 00:59:36,520 --> 00:59:39,880 Essentially, if I add $11 from coming from w, 1387 00:59:39,880 --> 00:59:45,670 that utility that he values by at most 10/11-- so each dollar 1388 00:59:45,670 --> 00:59:47,620 that he gets on the left-hand side 1389 00:59:47,620 --> 00:59:51,400 is valued at most 10/11 as much as the dollars between w 1390 00:59:51,400 --> 00:59:54,010 minus 10 and w, right? 1391 00:59:54,010 --> 00:59:57,558 So if you have $10 on the right, $11 on the left, 1392 00:59:57,558 --> 01:00:00,100 you prefer the right-hand side over the left-hand side, which 1393 01:00:00,100 --> 01:00:04,480 means each dollar must be valued more on the right-hand side. 1394 01:00:04,480 --> 01:00:06,770 Put differently, the dollars on the left-hand side, 1395 01:00:06,770 --> 01:00:10,850 that value is 10/11 of the dollars on the right-hand side, 1396 01:00:10,850 --> 01:00:11,960 OK? 1397 01:00:11,960 --> 01:00:14,720 So just to repeat again, on the right-hand side, 1398 01:00:14,720 --> 01:00:16,250 we're adding $10. 1399 01:00:16,250 --> 01:00:19,640 On the left-hand side, we are adding $11 1400 01:00:19,640 --> 01:00:22,830 or subtracting-- we're adding $11 on left-hand side 1401 01:00:22,830 --> 01:00:25,520 and we're subtracting $10 and the right-hand side. 1402 01:00:25,520 --> 01:00:28,670 Now, since you prefer the thing or the thing 1403 01:00:28,670 --> 01:00:30,260 on the right-hand side is larger, 1404 01:00:30,260 --> 01:00:32,600 that must mean that each dollar on the right-hand side 1405 01:00:32,600 --> 01:00:33,680 is worth more. 1406 01:00:33,680 --> 01:00:37,202 It's 11/10 compared to the dollars on the left-hand side. 1407 01:00:37,202 --> 01:00:39,410 Or put differently, each dollar on the left-hand side 1408 01:00:39,410 --> 01:00:43,500 has value 10/11 of each dollar on the right-hand side. 1409 01:00:43,500 --> 01:00:45,000 You can sort think about this a bit. 1410 01:00:45,000 --> 01:00:47,440 But trust me, that is correct. 1411 01:00:47,440 --> 01:00:50,280 Now, there's diminishing marginal utility. 1412 01:00:50,280 --> 01:00:52,050 Essentially, concavity sort of says 1413 01:00:52,050 --> 01:00:55,140 that the marginal dollar at w minus 10 1414 01:00:55,140 --> 01:00:58,330 is at least as valuable as the marginal dollar at w. 1415 01:00:58,330 --> 01:01:02,910 That's essentially just simple assumption of concavity, 1416 01:01:02,910 --> 01:01:06,430 essentially just saying, there's diminishing marginal utility. 1417 01:01:06,430 --> 01:01:09,360 So the lower the amount of wealth that you have, 1418 01:01:09,360 --> 01:01:13,470 the weakly larger the marginal utility is. 1419 01:01:13,470 --> 01:01:16,050 So the marginal utility at w minus 10 1420 01:01:16,050 --> 01:01:19,710 is at least as large as the marginal utility at w. 1421 01:01:19,710 --> 01:01:21,570 And that marginal utility for dollar 1422 01:01:21,570 --> 01:01:26,850 is at least as valuable as the marginal utility at w plus 11. 1423 01:01:26,850 --> 01:01:29,400 Now, sort of taken together, that means 1424 01:01:29,400 --> 01:01:34,470 that Johnny values $1 at w plus 11 by, at most, 10/11 as 1425 01:01:34,470 --> 01:01:39,000 much as he values the dollars at w minus 10. 1426 01:01:39,000 --> 01:01:41,670 What does that mean is that if you go from minus 10 1427 01:01:41,670 --> 01:01:46,650 to a plus 11 essentially the marginal dollar that you get 1428 01:01:46,650 --> 01:01:51,420 is worth 10 11th as much for every $21 1429 01:01:51,420 --> 01:01:53,880 that he increases his Wilson. 1430 01:01:58,210 --> 01:02:04,540 So I think, given some of the confused faces I see, 1431 01:02:04,540 --> 01:02:06,940 we might do some of this in recitation. 1432 01:02:06,940 --> 01:02:10,150 But this is essentially simple algebra and using 1433 01:02:10,150 --> 01:02:13,730 the minimal assumptions that I made. 1434 01:02:13,730 --> 01:02:15,190 Now, you can do the same thing as 1435 01:02:15,190 --> 01:02:17,203 like if the person were $21 richer. 1436 01:02:17,203 --> 01:02:19,120 So essentially, now, I'm doing the same thing, 1437 01:02:19,120 --> 01:02:22,330 just adding $21 on each side. 1438 01:02:22,330 --> 01:02:24,070 I'm doing the exact same thing. 1439 01:02:24,070 --> 01:02:28,420 And I'm going to get essentially the exact same thing. 1440 01:02:28,420 --> 01:02:32,890 It's essentially saying that he values each dollar that he gets 1441 01:02:32,890 --> 01:02:38,110 at w plus $32 by, at most, 10/11 to the power of 2 5/6 as much 1442 01:02:38,110 --> 01:02:40,928 as he values the dollars at w minus 10. 1443 01:02:40,928 --> 01:02:43,220 So what I'm essentially doing is I'm iterating forward. 1444 01:02:43,220 --> 01:02:45,940 So I know the utility function is concave by sort 1445 01:02:45,940 --> 01:02:47,020 of your first choice. 1446 01:02:47,020 --> 01:02:49,030 I know that essentially [INAUDIBLE] utility 1447 01:02:49,030 --> 01:02:51,982 is declining going on one side. 1448 01:02:51,982 --> 01:02:54,190 So now, essentially taking this forward-- essentially 1449 01:02:54,190 --> 01:02:59,080 saying, well, for every $21, you value each dollar by 10/11 1450 01:02:59,080 --> 01:02:59,860 as much. 1451 01:02:59,860 --> 01:03:01,360 So now, I'm saying, well, if you had 1452 01:03:01,360 --> 01:03:07,090 $21 plus $21 is $42 plus $29 is $63, 1453 01:03:07,090 --> 01:03:09,620 your marginal utility must be really declining very, 1454 01:03:09,620 --> 01:03:11,060 very rapidly. 1455 01:03:11,060 --> 01:03:14,380 So once you have a lot more money, then essentially you 1456 01:03:14,380 --> 01:03:17,500 just don't care at all about any marginal dollar that you get. 1457 01:03:17,500 --> 01:03:21,640 So you can do this by if the person was $42 richer. 1458 01:03:21,640 --> 01:03:24,470 Essentially, you'd care about each dollar 5/6 as much. 1459 01:03:24,470 --> 01:03:27,830 If it's $420, you care about it 3/20 as much. 1460 01:03:27,830 --> 01:03:30,580 And if you were $840 richer, you care about it 1461 01:03:30,580 --> 01:03:32,480 only 2/100 as much. 1462 01:03:32,480 --> 01:03:34,480 Essentially, that's to say-- and this is exactly 1463 01:03:34,480 --> 01:03:36,188 as you were saying-- the marginal utility 1464 01:03:36,188 --> 01:03:38,950 plummets for substantial changes in lifetime wealth. 1465 01:03:38,950 --> 01:03:42,430 So you care less than 2% about an additional dollar 1466 01:03:42,430 --> 01:03:48,250 when you are $900 richer than you are right now. 1467 01:03:48,250 --> 01:03:51,730 That doesn't feel right, but essentially it's 1468 01:03:51,730 --> 01:03:55,840 a simple implication of what was just assumed. 1469 01:03:55,840 --> 01:03:56,890 There's no magic here. 1470 01:03:56,890 --> 01:03:59,830 This is very simple algebra and using 1471 01:03:59,830 --> 01:04:01,930 very simple minor assumptions. 1472 01:04:01,930 --> 01:04:04,660 But essentially, it's saying, if this person rejects this gamble 1473 01:04:04,660 --> 01:04:07,570 as we just had, it follows-- 1474 01:04:07,570 --> 01:04:10,090 and there's sort of complicated proofs in the paper. 1475 01:04:10,090 --> 01:04:11,800 But it follows that, essentially, 1476 01:04:11,800 --> 01:04:17,080 the additional for, if you give the person $900 more, 1477 01:04:17,080 --> 01:04:19,630 the person values each dollar only 2% 1478 01:04:19,630 --> 01:04:24,370 as much as when the person is $900 richer. 1479 01:04:24,370 --> 01:04:27,130 And so then you look at these consequences. 1480 01:04:27,130 --> 01:04:29,140 And you can read this in the Rabin and Thaler 1481 01:04:29,140 --> 01:04:32,560 paper or the original Rabin paper if you like. 1482 01:04:32,560 --> 01:04:35,943 Essentially, you get these absurd conclusions. 1483 01:04:35,943 --> 01:04:37,360 If you look at the left-hand side, 1484 01:04:37,360 --> 01:04:40,150 these are sort of like if an expected utility maximizer 1485 01:04:40,150 --> 01:04:42,010 always turns down certain bets. 1486 01:04:42,010 --> 01:04:43,840 On the left-hand side, it follows 1487 01:04:43,840 --> 01:04:47,770 that he also turns on the bets on the right-hand side. 1488 01:04:47,770 --> 01:04:51,890 And we think, you know, for example, 1489 01:04:51,890 --> 01:04:54,820 if I told you losing $10 or gaining 1490 01:04:54,820 --> 01:04:57,280 $11, that seems like a reasonable thing 1491 01:04:57,280 --> 01:04:58,330 to reject perhaps. 1492 01:04:58,330 --> 01:05:00,520 That seems like a thing that one might do. 1493 01:05:00,520 --> 01:05:03,500 At least, you guys were saying that you might do that. 1494 01:05:03,500 --> 01:05:05,080 Well, if that's the case, then you 1495 01:05:05,080 --> 01:05:11,620 should also accept or reject the gamble of losing $100 1496 01:05:11,620 --> 01:05:14,080 and gaining infinite amount of dollars. 1497 01:05:14,080 --> 01:05:17,170 And that seems obviously absurd. 1498 01:05:17,170 --> 01:05:22,030 And so that can't be really true. 1499 01:05:22,030 --> 01:05:25,300 Now, what's going on here essentially 1500 01:05:25,300 --> 01:05:28,540 is to say is that the utility function, as it 1501 01:05:28,540 --> 01:05:32,200 is an expected utility, has trouble reconciling 1502 01:05:32,200 --> 01:05:35,650 people's small scale choices and large scale choices. 1503 01:05:35,650 --> 01:05:37,690 And it's similar to what we talked about, 1504 01:05:37,690 --> 01:05:39,370 like exponential discounting. 1505 01:05:39,370 --> 01:05:41,410 We only have one parameter here, which 1506 01:05:41,410 --> 01:05:44,350 is gamma for both gains and losses 1507 01:05:44,350 --> 01:05:46,150 and for all sorts of scales. 1508 01:05:46,150 --> 01:05:49,570 And that parameter is just not able to fit people's choices 1509 01:05:49,570 --> 01:05:50,560 in sensible ways. 1510 01:05:50,560 --> 01:05:52,810 It seems to be people have small scale risk 1511 01:05:52,810 --> 01:05:54,410 aversion in some sense. 1512 01:05:54,410 --> 01:05:58,540 And it seems to be people are not incredibly risk averse 1513 01:05:58,540 --> 01:06:00,490 for large amounts of money. 1514 01:06:00,490 --> 01:06:04,180 And so, now, the expected utility model cannot match both 1515 01:06:04,180 --> 01:06:06,430 of those things. 1516 01:06:06,430 --> 01:06:11,050 That's essentially what the Rabin paper does. 1517 01:06:11,050 --> 01:06:16,270 We'll talk about this in some slower reform in recitation 1518 01:06:16,270 --> 01:06:17,680 to sort of go over this. 1519 01:06:17,680 --> 01:06:19,690 But in some sense, the important part here 1520 01:06:19,690 --> 01:06:21,550 is to understand the intuition. 1521 01:06:21,550 --> 01:06:24,310 And intuition, essentially, is that, if there's 1522 01:06:24,310 --> 01:06:28,270 curvature over very small scales or over very small stakes, 1523 01:06:28,270 --> 01:06:30,940 it must be there's lots of curvature going forward 1524 01:06:30,940 --> 01:06:32,200 over large scales. 1525 01:06:32,200 --> 01:06:34,130 And that's just not plausible. 1526 01:06:34,130 --> 01:06:36,130 Because, essentially, then people would just not 1527 01:06:36,130 --> 01:06:39,400 value really, really large amounts. 1528 01:06:39,400 --> 01:06:44,380 And we know that people do value money at least to some extent. 1529 01:06:44,380 --> 01:06:47,200 Any questions on this overall? 1530 01:06:52,470 --> 01:06:53,752 Yeah. 1531 01:06:53,752 --> 01:06:57,810 AUDIENCE: [INAUDIBLE] I guess [INAUDIBLE] [? mimicked ?] 1532 01:06:57,810 --> 01:06:59,850 the [INAUDIBLE]. 1533 01:06:59,850 --> 01:07:02,783 I guess, does the [INAUDIBLE] hyperbolic model essentially 1534 01:07:02,783 --> 01:07:05,800 almost [? work ?] [? here ?] where [INAUDIBLE] 1535 01:07:05,800 --> 01:07:11,420 to [INAUDIBLE] singular [INAUDIBLE] if someone tried 1536 01:07:11,420 --> 01:07:15,210 to do the long-term, short-term thing, [INAUDIBLE].. 1537 01:07:15,210 --> 01:07:16,560 FRANK SCHILBACH: Yeah. 1538 01:07:16,560 --> 01:07:18,690 So what we're going to do is-- so notice 1539 01:07:18,690 --> 01:07:20,970 that, here, he was not assuming anything 1540 01:07:20,970 --> 01:07:22,380 about the utility function. 1541 01:07:22,380 --> 01:07:25,860 The only thing he was assuming, or Rabin was assuming here, 1542 01:07:25,860 --> 01:07:30,480 is that the person is expected utility maximizer 1543 01:07:30,480 --> 01:07:33,240 and that the utility function is weakly, not even 1544 01:07:33,240 --> 01:07:35,370 strictly, concave. 1545 01:07:35,370 --> 01:07:38,820 Now, what that means is you can't sort of just 1546 01:07:38,820 --> 01:07:41,130 change the functional form. 1547 01:07:41,130 --> 01:07:45,280 This is a general proof for any utility function that you use. 1548 01:07:45,280 --> 01:07:47,350 So what you have to do now is either sort of say, 1549 01:07:47,350 --> 01:07:49,770 well, there's some other assumptions 1550 01:07:49,770 --> 01:07:54,690 wrong about expected utility in terms of weighting 1551 01:07:54,690 --> 01:07:59,760 the probabilities or stuff like that that essentially 1552 01:07:59,760 --> 01:08:00,885 can explain the phenomenon. 1553 01:08:00,885 --> 01:08:04,120 It could be something about [INAUDIBLE] aversion and so on. 1554 01:08:04,120 --> 01:08:05,532 These seem kind of unlikely. 1555 01:08:05,532 --> 01:08:06,990 The most likely thing-- and this is 1556 01:08:06,990 --> 01:08:08,782 what I'm going to talk about next week-- is 1557 01:08:08,782 --> 01:08:12,480 Kahneman-Tversky's sort of loss aversion framework where you 1558 01:08:12,480 --> 01:08:16,649 say, if you put different weight on gains versus losses, 1559 01:08:16,649 --> 01:08:19,229 then essentially you have two parameters. 1560 01:08:19,229 --> 01:08:22,830 You have one parameter about your risk aversion over gains. 1561 01:08:22,830 --> 01:08:26,430 And you have a parameter that's steers kind of how you feel 1562 01:08:26,430 --> 01:08:28,529 about losses compared to gains. 1563 01:08:28,529 --> 01:08:31,140 So once you do that, then you have another degree of freedom. 1564 01:08:31,140 --> 01:08:34,950 And you can explain a lot of [? favors ?] potentially. 1565 01:08:34,950 --> 01:08:37,152 But that's kind of the equivalent of that exactly. 1566 01:08:37,152 --> 01:08:38,819 But the difference here is that it's not 1567 01:08:38,819 --> 01:08:41,236 coming through the utility function, the reason 1568 01:08:41,236 --> 01:08:43,319 being that the problem is actually not the utility 1569 01:08:43,319 --> 01:08:43,819 function. 1570 01:08:43,819 --> 01:08:46,830 Because as I said, there's actually no assumption here 1571 01:08:46,830 --> 01:08:49,080 that can even be changed because it's 1572 01:08:49,080 --> 01:08:51,510 very general for any function that you assume, 1573 01:08:51,510 --> 01:08:54,680 be it any of the ones that I just showed you previously. 1574 01:08:58,680 --> 01:08:59,180 OK. 1575 01:09:03,870 --> 01:09:05,743 So then the last choice-- 1576 01:09:05,743 --> 01:09:08,160 [INAUDIBLE] doing we'll get started on this and then going 1577 01:09:08,160 --> 01:09:09,450 to finish next time-- 1578 01:09:09,450 --> 01:09:11,100 is, as your classmate was saying, 1579 01:09:11,100 --> 01:09:12,450 about insurance choices. 1580 01:09:12,450 --> 01:09:14,050 So how do we do that? 1581 01:09:14,050 --> 01:09:16,649 So this is a very nice paper by Justin Sydnor, 1582 01:09:16,649 --> 01:09:19,920 who's using sort of real world insurance choices. 1583 01:09:19,920 --> 01:09:23,288 And what's very nice about it is that you might not say, well, 1584 01:09:23,288 --> 01:09:25,080 I might sort of say, well, college students 1585 01:09:25,080 --> 01:09:27,990 and lab choices gives you funky answers. 1586 01:09:27,990 --> 01:09:29,760 And you might not sort of believe 1587 01:09:29,760 --> 01:09:32,529 that this is really predictive of anything in the real world. 1588 01:09:32,529 --> 01:09:34,439 So we really want real world choices 1589 01:09:34,439 --> 01:09:37,410 that people make in their lives. 1590 01:09:37,410 --> 01:09:40,260 And sort of you might also worry about demand effects 1591 01:09:40,260 --> 01:09:42,240 and about sort of people behaving a little bit 1592 01:09:42,240 --> 01:09:43,630 funny in experiment. 1593 01:09:43,630 --> 01:09:46,020 So let's find real world choices that people have made 1594 01:09:46,020 --> 01:09:46,770 and try to see. 1595 01:09:46,770 --> 01:09:49,569 Maybe we can estimate gamma using that. 1596 01:09:49,569 --> 01:09:54,029 And so what Justin Sydnor has is data from a large home 1597 01:09:54,029 --> 01:09:56,250 insurance provider. 1598 01:09:56,250 --> 01:09:58,625 He has a bunch of standard policies. 1599 01:09:58,625 --> 01:10:00,000 There's a random sample of those. 1600 01:10:00,000 --> 01:10:03,150 So there are 50,000 standard policies. 1601 01:10:03,150 --> 01:10:06,900 What he has, importantly, he has both the options 1602 01:10:06,900 --> 01:10:09,390 that people had-- so what is your choice set? 1603 01:10:09,390 --> 01:10:11,490 Here's four different choices for each person. 1604 01:10:11,490 --> 01:10:14,790 And he has then the choices that people made. 1605 01:10:14,790 --> 01:10:17,550 Plus, he has claims that people made after that. 1606 01:10:17,550 --> 01:10:19,035 He has all the new customers, which 1607 01:10:19,035 --> 01:10:20,660 matters a little bit because, you know, 1608 01:10:20,660 --> 01:10:22,440 you might say new customers are confused. 1609 01:10:22,440 --> 01:10:24,900 Maybe the old ones are the ones that are right. 1610 01:10:24,900 --> 01:10:28,527 Now, the key part here is the deductible 1611 01:10:28,527 --> 01:10:29,610 that people were choosing. 1612 01:10:29,610 --> 01:10:31,030 What is a deductible? 1613 01:10:37,400 --> 01:10:38,208 Yes. 1614 01:10:38,208 --> 01:10:40,000 AUDIENCE: How much you'll pay out of pocket 1615 01:10:40,000 --> 01:10:41,598 before the insurance kicks in? 1616 01:10:41,598 --> 01:10:42,640 FRANK SCHILBACH: Exactly. 1617 01:10:42,640 --> 01:10:45,620 So this is expenses paid out of pocket 1618 01:10:45,620 --> 01:10:48,980 before the insurer starts paying any expenses. 1619 01:10:48,980 --> 01:10:52,430 That would be like, if you had some damage to your house 1620 01:10:52,430 --> 01:10:56,330 for some small amount, you would have to pay that for yourself. 1621 01:10:56,330 --> 01:10:58,065 If you have some large amount of damage, 1622 01:10:58,065 --> 01:10:59,690 you have to still pay the small amount. 1623 01:10:59,690 --> 01:11:02,360 And then the insurer would pay the rest. 1624 01:11:02,360 --> 01:11:05,458 And that's usually used to deter a large number of claims 1625 01:11:05,458 --> 01:11:07,250 because you know the insurance company just 1626 01:11:07,250 --> 01:11:09,860 doesn't want to pay for every $50 of damage 1627 01:11:09,860 --> 01:11:10,930 that you might have. 1628 01:11:10,930 --> 01:11:12,680 Because that's just really costly for them 1629 01:11:12,680 --> 01:11:15,720 to do for administrative costs. 1630 01:11:15,720 --> 01:11:20,370 Now, what Sydnor has is choices over menus of four deductibles. 1631 01:11:20,370 --> 01:11:25,070 And again, as I said, he has both individual choice set 1632 01:11:25,070 --> 01:11:26,967 and their preferred options. 1633 01:11:26,967 --> 01:11:28,550 If you only had the preferred options, 1634 01:11:28,550 --> 01:11:32,330 it would be very hard to figure out kind of what actually-- 1635 01:11:32,330 --> 01:11:36,560 because you then can't really say what's the counterfactual. 1636 01:11:36,560 --> 01:11:39,180 You don't essentially what else he could have chosen 1637 01:11:39,180 --> 01:11:41,610 or he or she should have chosen. 1638 01:11:41,610 --> 01:11:43,482 So you kind of want to different options 1639 01:11:43,482 --> 01:11:44,690 and then sort of the outcome. 1640 01:11:44,690 --> 01:11:47,090 And then say, OK, since you had these different options 1641 01:11:47,090 --> 01:11:49,980 available, it must be that you preferred one or the other. 1642 01:11:49,980 --> 01:11:53,370 It must be that you're risk averse or not. 1643 01:11:53,370 --> 01:11:56,540 So here's kind of what these data look like. 1644 01:11:56,540 --> 01:11:59,010 The sample data are deductibles. 1645 01:11:59,010 --> 01:11:59,510 OK. 1646 01:11:59,510 --> 01:12:01,220 This is, again, the amount that you 1647 01:12:01,220 --> 01:12:04,310 have to pay out of pocket until the insurer sort of kicks 1648 01:12:04,310 --> 01:12:05,720 in and pays for you. 1649 01:12:05,720 --> 01:12:08,060 There is the premium, which is how much you 1650 01:12:08,060 --> 01:12:09,920 have to pay every year anyway regardless 1651 01:12:09,920 --> 01:12:12,910 of what anything would happen. 1652 01:12:12,910 --> 01:12:17,150 There's sort of, relative to the $1,000 policy, kind of what's 1653 01:12:17,150 --> 01:12:17,990 the premium. 1654 01:12:17,990 --> 01:12:20,420 That's to say how much more money you have 1655 01:12:20,420 --> 01:12:22,340 to pay for a certain premium. 1656 01:12:22,340 --> 01:12:26,900 So for example, choice one has a premium of $504. 1657 01:12:26,900 --> 01:12:31,400 Choice two has a premium of $588. 1658 01:12:31,400 --> 01:12:34,490 So that's $84 higher. 1659 01:12:34,490 --> 01:12:38,570 You pay essentially $84 in premium every year 1660 01:12:38,570 --> 01:12:43,080 to reduce your deductible from $1,000 to $500. 1661 01:12:43,080 --> 01:12:43,580 OK. 1662 01:12:43,580 --> 01:12:45,080 So what you can do, essentially, you 1663 01:12:45,080 --> 01:12:47,900 can reduce your deductible at a price. 1664 01:12:47,900 --> 01:12:51,350 The price relative to the $1,000 policy is in the third column. 1665 01:12:51,350 --> 01:12:53,970 And you see the deductible on the left-hand side. 1666 01:12:53,970 --> 01:12:56,120 So this person is like policyholder-- 1667 01:12:56,120 --> 01:12:57,130 yeah. 1668 01:12:57,130 --> 01:12:59,030 AUDIENCE: If you're comparing their choices, 1669 01:12:59,030 --> 01:13:02,060 couldn't it be that they're just a more risky person and not 1670 01:13:02,060 --> 01:13:04,658 necessarily risk averse? 1671 01:13:04,658 --> 01:13:05,700 FRANK SCHILBACH: Correct. 1672 01:13:05,700 --> 01:13:07,130 So that's exactly right. 1673 01:13:07,130 --> 01:13:10,273 So there's sort of unobservable risk that people might have. 1674 01:13:10,273 --> 01:13:11,190 I'll get back to that. 1675 01:13:11,190 --> 01:13:15,410 But essentially, what you see is that a lot of people 1676 01:13:15,410 --> 01:13:16,940 make very similar choices. 1677 01:13:16,940 --> 01:13:19,910 Then on average, people's risk is relatively low. 1678 01:13:19,910 --> 01:13:21,410 So what you're saying-- essentially, 1679 01:13:21,410 --> 01:13:22,730 I need to know your claim rate. 1680 01:13:22,730 --> 01:13:25,147 I need to know kind of what's your probability of actually 1681 01:13:25,147 --> 01:13:26,510 having any damages. 1682 01:13:26,510 --> 01:13:28,520 And it turns out claim rates are extremely 1683 01:13:28,520 --> 01:13:31,070 low in the sample, the order of magnitude something 1684 01:13:31,070 --> 01:13:32,330 like below 5%. 1685 01:13:32,330 --> 01:13:34,320 Or I think it's even lower. 1686 01:13:34,320 --> 01:13:37,460 So it cannot be that everybody is a high risk person. 1687 01:13:37,460 --> 01:13:39,830 It can be potentially that everybody thinks 1688 01:13:39,830 --> 01:13:41,270 they're a high risk person. 1689 01:13:41,270 --> 01:13:45,990 But, you know, then there's a different mistake going on. 1690 01:13:45,990 --> 01:13:47,600 So what he's assuming, essentially, 1691 01:13:47,600 --> 01:13:51,800 is, on average, it must be that there's some high risk people 1692 01:13:51,800 --> 01:13:53,070 and some low risk people. 1693 01:13:53,070 --> 01:13:55,403 But essentially, he's sort of kind of assuming this away 1694 01:13:55,403 --> 01:13:57,560 and sort of saying, look, on average claim rates 1695 01:13:57,560 --> 01:13:58,590 are really low. 1696 01:13:58,590 --> 01:14:03,890 It could be that there is some fraction of really high risk 1697 01:14:03,890 --> 01:14:04,610 people. 1698 01:14:04,610 --> 01:14:07,340 But by definition, since they're only 1699 01:14:07,340 --> 01:14:09,830 something like 5% of claim rates, 1700 01:14:09,830 --> 01:14:11,420 it can't be that there's everybody 1701 01:14:11,420 --> 01:14:14,330 is a high risk person. 1702 01:14:14,330 --> 01:14:18,230 So it must be that there's some people who behave as if they're 1703 01:14:18,230 --> 01:14:21,050 either really risk averse or as if they think they're really 1704 01:14:21,050 --> 01:14:22,040 high risk people. 1705 01:14:22,040 --> 01:14:24,680 And this is kind of where the old and new customers are 1706 01:14:24,680 --> 01:14:25,250 helpful for. 1707 01:14:25,250 --> 01:14:28,220 Because there are some customers who have been at this company 1708 01:14:28,220 --> 01:14:29,962 for, like, 10, 15 years. 1709 01:14:29,962 --> 01:14:31,670 And sort of, there, you know, you kind of 1710 01:14:31,670 --> 01:14:35,660 should know what kind of risk person you are perhaps. 1711 01:14:35,660 --> 01:14:37,410 But that's a great question. 1712 01:14:37,410 --> 01:14:39,590 I'll actually get back to that. 1713 01:14:39,590 --> 01:14:43,610 OK, so policy holder one, their home was built in 1966. 1714 01:14:43,610 --> 01:14:45,850 He had an insured value of 180,000. 1715 01:14:45,850 --> 01:14:48,380 The menu available for this policy in the same year 1716 01:14:48,380 --> 01:14:50,138 was the following. 1717 01:14:50,138 --> 01:14:52,430 And then he has also the choice on the right-hand side. 1718 01:14:52,430 --> 01:14:54,740 You see the policies that are chosen. 1719 01:14:54,740 --> 01:15:00,160 So that person chose, for example, a deductible of $200 1720 01:15:00,160 --> 01:15:05,120 and for a price of $157 relative to paying 1721 01:15:05,120 --> 01:15:07,790 the $1,000 deductible. 1722 01:15:07,790 --> 01:15:14,390 Policyholder two, similarly, sort of chose the first option. 1723 01:15:14,390 --> 01:15:16,640 Notice that the price has changed a little bit in part 1724 01:15:16,640 --> 01:15:18,230 because the company has sort of taken 1725 01:15:18,230 --> 01:15:21,680 into account some covariates and some risk in some ways already. 1726 01:15:21,680 --> 01:15:23,960 So the company is kind of pricing specifically 1727 01:15:23,960 --> 01:15:26,390 depending on what your home value is and maybe the area 1728 01:15:26,390 --> 01:15:27,660 and so on and so forth. 1729 01:15:27,660 --> 01:15:29,510 But since Sydnor has all that information, 1730 01:15:29,510 --> 01:15:32,370 he can sort of just take that into account. 1731 01:15:32,370 --> 01:15:35,970 Now, what can we now say about risk aversion? 1732 01:15:35,970 --> 01:15:38,460 How can we now sort of estimate risk 1733 01:15:38,460 --> 01:15:40,830 aversion using these choices? 1734 01:15:51,150 --> 01:15:51,650 Yes. 1735 01:15:51,650 --> 01:15:53,108 AUDIENCE: If you know your house is 1736 01:15:53,108 --> 01:15:58,152 [INAUDIBLE] and your [INAUDIBLE] problems [INAUDIBLE] 1737 01:15:58,152 --> 01:16:01,140 so then you don't have to pay [INAUDIBLE].. 1738 01:16:03,595 --> 01:16:04,470 FRANK SCHILBACH: Yes. 1739 01:16:04,470 --> 01:16:05,910 So what you need to know is essentially 1740 01:16:05,910 --> 01:16:06,840 a number of different things. 1741 01:16:06,840 --> 01:16:08,757 You need to know the deductibles, the premiums 1742 01:16:08,757 --> 01:16:11,090 for each option, the claim probabilities, and the wealth 1743 01:16:11,090 --> 01:16:11,850 levels. 1744 01:16:11,850 --> 01:16:13,540 I'll talk about this in more detail. 1745 01:16:13,540 --> 01:16:17,220 But essentially, what you can do is, for each of these options, 1746 01:16:17,220 --> 01:16:21,030 you can write down an indirect utility of wealth function. 1747 01:16:21,030 --> 01:16:23,160 You essentially can write down what's the expected 1748 01:16:23,160 --> 01:16:25,660 utility of that option. 1749 01:16:25,660 --> 01:16:30,760 And then you can essentially just put bounds essentially 1750 01:16:30,760 --> 01:16:34,000 on if you preferred option one or option two. 1751 01:16:34,000 --> 01:16:36,910 That tells me something about your gamma. 1752 01:16:36,910 --> 01:16:39,850 And so what Sydnor then does is essentially estimate gamma 1753 01:16:39,850 --> 01:16:41,980 using those different choices. 1754 01:16:41,980 --> 01:16:43,810 I'm going to go over that in a lot more 1755 01:16:43,810 --> 01:16:48,090 detail and slower next time.