WEBVTT 00:00:00.000 --> 00:00:02.435 [SQUEAKING] 00:00:02.435 --> 00:00:04.383 [RUSTLING] 00:00:04.383 --> 00:00:06.818 [CLICKING] 00:00:11.055 --> 00:00:12.180 FRANK SCHILBACH: All right. 00:00:12.180 --> 00:00:16.088 Welcome to lectures seven and eight. 00:00:16.088 --> 00:00:17.880 We're going to talk about risk preferences. 00:00:17.880 --> 00:00:18.830 Hello? 00:00:18.830 --> 00:00:21.190 We're going to talk about risk preferences. 00:00:21.190 --> 00:00:23.010 In particular, sort from the perspective 00:00:23.010 --> 00:00:25.440 of expected utility, which is sort of the classical way 00:00:25.440 --> 00:00:27.270 of economics to view this. 00:00:27.270 --> 00:00:32.475 This is going to take one and 1/2, perhaps two lectures. 00:00:32.475 --> 00:00:34.350 Broadly speaking, we're going to look at what 00:00:34.350 --> 00:00:35.820 does economics usually assume. 00:00:35.820 --> 00:00:38.340 How does economics think about risk preferences, 00:00:38.340 --> 00:00:42.280 about choices involving risk? 00:00:42.280 --> 00:00:45.900 How do we think about sort of measuring risk preferences? 00:00:45.900 --> 00:00:48.330 What are some of the implications and what are some 00:00:48.330 --> 00:00:50.700 of the limits of risk preferences in terms of what we 00:00:50.700 --> 00:00:53.760 can explain and what we cannot explain? 00:00:53.760 --> 00:00:56.280 And then in the following lectures 00:00:56.280 --> 00:00:59.280 we're going to have an alternative model of reference 00:00:59.280 --> 00:01:01.792 dependence preferences where essentially you're 00:01:01.792 --> 00:01:03.750 going to relax or change some of the underlying 00:01:03.750 --> 00:01:10.770 assumptions on how to measure preferences related to risk. 00:01:10.770 --> 00:01:14.170 Problem set two will be posted soon-- later this week. 00:01:14.170 --> 00:01:16.380 I'm sure you can't wait for this. 00:01:16.380 --> 00:01:22.183 A reminder, late submissions will not be accepted. 00:01:22.183 --> 00:01:23.850 This is always like a commitment problem 00:01:23.850 --> 00:01:26.370 because people come up with all sorts of good excuses 00:01:26.370 --> 00:01:29.058 why they submitted the problem set late 00:01:29.058 --> 00:01:30.600 and then I kind of feel bad about it. 00:01:30.600 --> 00:01:33.030 So I'm here with committing to not accepting 00:01:33.030 --> 00:01:34.530 any late submissions for whatever 00:01:34.530 --> 00:01:37.200 reasons unless you have sort of a medical excuse 00:01:37.200 --> 00:01:41.730 or sort of an excuse notice. 00:01:41.730 --> 00:01:44.460 So no my PDF was corrupted and all sorts 00:01:44.460 --> 00:01:45.780 of other good reasons. 00:01:45.780 --> 00:01:48.060 I was a student once as well and I know 00:01:48.060 --> 00:01:51.060 students are very creative. 00:01:51.060 --> 00:01:54.330 We will post previous problems sets, midterms, and finals 00:01:54.330 --> 00:01:55.530 for you to practice overall. 00:01:55.530 --> 00:01:57.510 I think of the problem sets less of a way 00:01:57.510 --> 00:02:01.650 for testing you or testing sort of whether you can do it 00:02:01.650 --> 00:02:04.050 or not, but rather as a way for you to practice things, 00:02:04.050 --> 00:02:07.388 whether you have understood the materials in parts 00:02:07.388 --> 00:02:08.430 of the past problem sets. 00:02:08.430 --> 00:02:11.700 And midterms and finals will sort of help you with that. 00:02:11.700 --> 00:02:14.160 As usual, please ask questions on Piazza 00:02:14.160 --> 00:02:16.630 or come to office hours. 00:02:16.630 --> 00:02:18.180 So what we're going to talk about 00:02:18.180 --> 00:02:20.160 is, broadly speaking risk aversion. 00:02:20.160 --> 00:02:24.520 How do economists think about choices involving risk? 00:02:24.520 --> 00:02:28.350 Then again, I sort of outline sort of the very simple 00:02:28.350 --> 00:02:31.650 or the basic model of-- 00:02:31.650 --> 00:02:33.420 main workhorse model of economics-- 00:02:33.420 --> 00:02:35.378 is to think about choices involving risk, which 00:02:35.378 --> 00:02:37.100 is the expected utility model. 00:02:37.100 --> 00:02:38.885 We're going to then think about how do we 00:02:38.885 --> 00:02:41.010 measure risk preferences, the underlying preference 00:02:41.010 --> 00:02:45.600 parameters that sort of are embedded in this model. 00:02:45.600 --> 00:02:48.780 We're going to lead then to some absurd implications 00:02:48.780 --> 00:02:49.720 in particular. 00:02:49.720 --> 00:02:52.680 So discrepancy-- how people tend to think about small scale 00:02:52.680 --> 00:02:54.540 and large scale risk aversion. 00:02:54.540 --> 00:02:56.820 What I mean by that-- essentially small gambles that 00:02:56.820 --> 00:03:00.300 involve a few dollars versus really large scale choices 00:03:00.300 --> 00:03:02.430 that involve thousands of dollars. 00:03:02.430 --> 00:03:05.760 And what I'm going to show you, very similar to some degree 00:03:05.760 --> 00:03:10.860 to how we think about time preferences where the typical 00:03:10.860 --> 00:03:15.330 exponential discounting model cannot explain both short run 00:03:15.330 --> 00:03:17.848 and long run time preference decisions that people make. 00:03:17.848 --> 00:03:19.390 That's just a sort of a calibration-- 00:03:19.390 --> 00:03:20.760 really very hard to do. 00:03:20.760 --> 00:03:22.680 Similarly, the expected utility model 00:03:22.680 --> 00:03:27.270 has problems with reconciling small scale and large scale 00:03:27.270 --> 00:03:29.273 choices that people make. 00:03:29.273 --> 00:03:30.690 I'll tell you that in more detail. 00:03:30.690 --> 00:03:33.000 But in short, the summary is if people 00:03:33.000 --> 00:03:36.960 are risk averse when it comes to small gambles, that implies 00:03:36.960 --> 00:03:39.210 that they're absurdly risk averse coming 00:03:39.210 --> 00:03:42.220 from large gambles if you sort of take that model seriously. 00:03:42.220 --> 00:03:46.150 And so that's kind of like not really true in reality. 00:03:46.150 --> 00:03:47.670 And so then we sort think about how 00:03:47.670 --> 00:03:49.960 to relax those kinds of assumptions. 00:03:49.960 --> 00:03:50.460 OK. 00:03:50.460 --> 00:03:53.850 So first let's think about what kinds of choices and decisions 00:03:53.850 --> 00:03:56.070 do in fact involve risk and uncertainty. 00:03:56.070 --> 00:04:00.930 What examples do we have in your life? 00:04:00.930 --> 00:04:05.980 What is risky or what would involve uncertainty? 00:04:05.980 --> 00:04:06.480 Yes? 00:04:06.480 --> 00:04:08.452 AUDIENCE: Whether or not [INAUDIBLE].. 00:04:11.382 --> 00:04:12.340 FRANK SCHILBACH: Right. 00:04:12.340 --> 00:04:13.930 Whether or not to get education. 00:04:13.930 --> 00:04:15.880 Whether or not to study and so on. 00:04:15.880 --> 00:04:17.680 Because the reward often is like uncertain. 00:04:17.680 --> 00:04:17.860 Right? 00:04:17.860 --> 00:04:18.579 You might get a job. 00:04:18.579 --> 00:04:19.540 You might not get a job. 00:04:19.540 --> 00:04:21.040 You might do really well in college. 00:04:21.040 --> 00:04:22.130 You might not. 00:04:22.130 --> 00:04:23.090 And so on and so forth. 00:04:23.090 --> 00:04:26.870 So the costs-- you might like it, you might not like it, 00:04:26.870 --> 00:04:27.370 and so on. 00:04:27.370 --> 00:04:28.840 It's not clear. 00:04:28.840 --> 00:04:30.640 So the costs and benefits are uncertain. 00:04:30.640 --> 00:04:32.240 There might be a recession when you graduate. 00:04:32.240 --> 00:04:33.198 And so on and so forth. 00:04:33.198 --> 00:04:36.489 So the returns and costs are both uncertain. 00:04:40.380 --> 00:04:40.880 Yes? 00:04:40.880 --> 00:04:42.358 AUDIENCE: Making large purchases, 00:04:42.358 --> 00:04:44.230 like buying [INAUDIBLE]. 00:04:44.230 --> 00:04:46.110 Because you don't know [INAUDIBLE].. 00:04:46.110 --> 00:04:47.450 FRANK SCHILBACH: Yeah, exactly. 00:04:47.450 --> 00:04:50.400 You might buy a house or you might 00:04:50.400 --> 00:04:53.582 think about buying or renting more broadly. 00:04:53.582 --> 00:04:55.290 And there it depends a lot on essentially 00:04:55.290 --> 00:04:56.915 what's happening to the housing market. 00:04:56.915 --> 00:04:59.070 If the housing market goes up or down, 00:04:59.070 --> 00:05:01.930 the choice to buy a house versus renting is very different. 00:05:01.930 --> 00:05:02.430 Right? 00:05:02.430 --> 00:05:04.305 So if the housing market goes up, most likely 00:05:04.305 --> 00:05:05.638 you should probably buy a house. 00:05:05.638 --> 00:05:07.650 If the housing market actually happens to tank, 00:05:07.650 --> 00:05:10.050 the [INAUDIBLE] [? at ?] [? least ?] it's a bad idea 00:05:10.050 --> 00:05:11.430 to do so. 00:05:11.430 --> 00:05:12.570 Yes? 00:05:12.570 --> 00:05:14.972 AUDIENCE: [INAUDIBLE] [? renters ?] insurance. 00:05:14.972 --> 00:05:15.930 FRANK SCHILBACH: Right. 00:05:15.930 --> 00:05:18.210 So the two choices that we have so far 00:05:18.210 --> 00:05:19.740 were essentially choices involving 00:05:19.740 --> 00:05:21.210 risk where you sort of essentially 00:05:21.210 --> 00:05:23.370 decide to do something where the outcomes are 00:05:23.370 --> 00:05:25.105 uncertain or risky in some way. 00:05:25.105 --> 00:05:26.730 Now, what you're saying, in some sense, 00:05:26.730 --> 00:05:28.770 is like, a bunch of other choices, 00:05:28.770 --> 00:05:31.830 potentially, are risk mitigation strategies. 00:05:31.830 --> 00:05:35.040 So you have, essentially, certain risk in your life. 00:05:35.040 --> 00:05:36.840 And you have choices where you could say, 00:05:36.840 --> 00:05:37.890 I could buy insurance. 00:05:37.890 --> 00:05:41.460 Or I could sort make other choices that mitigate or reduce 00:05:41.460 --> 00:05:43.470 the risk that I'm exposed to. 00:05:43.470 --> 00:05:45.480 And one sort of canonical example of that 00:05:45.480 --> 00:05:49.260 is purchasing any type of insurance 00:05:49.260 --> 00:05:51.720 but, in particular, renter's insurance, as you mentioned. 00:05:51.720 --> 00:05:53.460 Yes. 00:05:53.460 --> 00:05:54.231 Yeah? 00:05:54.231 --> 00:05:57.320 AUDIENCE: For farmers, the crop they choose to grow. 00:05:57.320 --> 00:06:00.390 FRANK SCHILBACH: Yes, so essentially, call that-- 00:06:00.390 --> 00:06:03.210 in development in particular, or development economics 00:06:03.210 --> 00:06:06.660 in particular, there's lots of issues of production choices 00:06:06.660 --> 00:06:08.280 that people make. 00:06:08.280 --> 00:06:10.680 This could be like what crops to grow, whether you should 00:06:10.680 --> 00:06:13.800 buy a machine, whether you should start a business, 00:06:13.800 --> 00:06:14.300 and so on. 00:06:14.300 --> 00:06:16.440 So there's all sorts of choices in terms 00:06:16.440 --> 00:06:21.360 of what business to go into, what kinds of specifics, 00:06:21.360 --> 00:06:23.610 what product to sell if you have a business. 00:06:23.610 --> 00:06:27.480 And in the farmer case, what crops should you grow? 00:06:27.480 --> 00:06:28.860 Should you buy fertilizer? 00:06:28.860 --> 00:06:32.700 Should you use other inputs and so on and so forth. 00:06:32.700 --> 00:06:34.080 Should you do [INAUDIBLE] there's 00:06:34.080 --> 00:06:36.163 a bunch of different other-- should you intercrop? 00:06:36.163 --> 00:06:38.070 There's a bunch of different other choices 00:06:38.070 --> 00:06:41.970 that you could make that essentially involve risks, 00:06:41.970 --> 00:06:44.022 because the outcome, essentially, is uncertain, 00:06:44.022 --> 00:06:46.230 because essentially, the season might be good or bad. 00:06:46.230 --> 00:06:48.490 In the farmer's case, if you, for example, 00:06:48.490 --> 00:06:50.190 purchase fertilizer or a certain-- 00:06:50.190 --> 00:06:54.815 for example, you could purchase or use drought-resistant crops. 00:06:54.815 --> 00:06:56.190 Of course, if there's no drought, 00:06:56.190 --> 00:06:57.690 then that's not really that helpful. 00:06:57.690 --> 00:07:02.440 But if there's a drought, that's really high return to do. 00:07:02.440 --> 00:07:02.950 Yes? 00:07:02.950 --> 00:07:03.450 Yes? 00:07:03.450 --> 00:07:05.812 AUDIENCE: Creating an investment portfolio. 00:07:05.812 --> 00:07:07.020 FRANK SCHILBACH: Creating a-- 00:07:07.020 --> 00:07:08.790 AUDIENCE: Investment portfolio. 00:07:08.790 --> 00:07:11.280 FRANK SCHILBACH: Yeah, so investing your money 00:07:11.280 --> 00:07:16.050 into a different-- in the stock market or in other sort 00:07:16.050 --> 00:07:17.940 of bonds or the like-- 00:07:17.940 --> 00:07:20.080 how should you invest the money? 00:07:20.080 --> 00:07:22.920 That's kind of related, to some degree, 00:07:22.920 --> 00:07:25.500 to the renting versus buying a house. 00:07:25.500 --> 00:07:28.680 You can think of buying as a house as one asset, one 00:07:28.680 --> 00:07:31.680 potential very sort of illiquid asset that you could buy. 00:07:31.680 --> 00:07:33.157 Similarly, you could buy stocks. 00:07:33.157 --> 00:07:33.990 You could buy bonds. 00:07:33.990 --> 00:07:36.630 You could keep just cash and so on. 00:07:36.630 --> 00:07:38.370 And there, that very much depends on, 00:07:38.370 --> 00:07:41.112 the return depends on things that 00:07:41.112 --> 00:07:43.070 are out of your hand, which essentially is just 00:07:43.070 --> 00:07:45.420 what the stock market might do. 00:07:45.420 --> 00:07:48.330 So I think once you think about choices 00:07:48.330 --> 00:07:51.150 involving risks, essentially almost any choice 00:07:51.150 --> 00:07:56.430 in your life actually is risky to some degree or uncertain, 00:07:56.430 --> 00:07:59.730 ranging from going to college, doing problem sets, 00:07:59.730 --> 00:08:00.810 studying for exams. 00:08:00.810 --> 00:08:02.190 Which exams should you study for? 00:08:02.190 --> 00:08:04.200 Which questions are people going to ask? 00:08:04.200 --> 00:08:09.210 Health decisions-- should you invest in your health or not? 00:08:09.210 --> 00:08:11.910 For a lot of diseases that people might get, 00:08:11.910 --> 00:08:13.240 it's often very uncertain. 00:08:13.240 --> 00:08:18.000 So even if you're smoking a lot, not every smoker 00:08:18.000 --> 00:08:19.245 falls sick or the like. 00:08:19.245 --> 00:08:23.880 No, just the risk of cancer and other diseases increases. 00:08:23.880 --> 00:08:27.240 That sort of financial investments, 00:08:27.240 --> 00:08:29.567 dating choices, and so on and so forth-- 00:08:29.567 --> 00:08:31.650 even friendship choices are, in some sense, risky. 00:08:31.650 --> 00:08:33.150 If you want, riding a bicycle-- 00:08:33.150 --> 00:08:35.490 that's very sort of small choices-- 00:08:35.490 --> 00:08:37.039 wearing a helmet versus not. 00:08:37.039 --> 00:08:38.789 Essentially, almost anything in your life, 00:08:38.789 --> 00:08:40.706 if you think about what are the outcomes, what 00:08:40.706 --> 00:08:42.690 are the different choices that you have, 00:08:42.690 --> 00:08:46.020 and what are the outcomes associated with those choices, 00:08:46.020 --> 00:08:49.668 almost all of those choices are associated with uncertainty 00:08:49.668 --> 00:08:51.210 and a sense of you're not quite sure. 00:08:51.210 --> 00:08:53.550 Is the return going to be high or low? 00:08:53.550 --> 00:08:56.110 Then as I said before, in addition to that, 00:08:56.110 --> 00:08:59.535 there's sort of risk mitigating strategies and a sense of you 00:08:59.535 --> 00:09:01.560 have a lot of choices in a lot of issues 00:09:01.560 --> 00:09:03.210 that are associated with risk. 00:09:03.210 --> 00:09:05.700 And now you can choose to reduce your exposure 00:09:05.700 --> 00:09:08.670 to risk by purchasing insurance or, for example, also 00:09:08.670 --> 00:09:11.760 by avoiding certain behaviors, right? 00:09:11.760 --> 00:09:14.730 So if you're worried about being robbed, for example, 00:09:14.730 --> 00:09:18.690 in a certain part of town, you might 00:09:18.690 --> 00:09:20.850 choose to go through that part of town. 00:09:20.850 --> 00:09:22.530 And that's a risky thing to do. 00:09:22.530 --> 00:09:25.002 Or you can have risk mitigating strategies where you just 00:09:25.002 --> 00:09:27.210 don't leave your house, or just go in different ways, 00:09:27.210 --> 00:09:29.700 or just never go into certain areas, which essentially 00:09:29.700 --> 00:09:32.040 are ways to protect you, to reduce your risk 00:09:32.040 --> 00:09:35.040 exposure overall. 00:09:35.040 --> 00:09:36.312 Any questions? 00:09:40.470 --> 00:09:44.180 OK, so now let me sort of just tell you 00:09:44.180 --> 00:09:47.120 three broad, stylized facts that we're going to try and explain 00:09:47.120 --> 00:09:48.530 or try to tackle. 00:09:48.530 --> 00:09:51.480 And that's kind of what economics is trying to do. 00:09:51.480 --> 00:09:53.923 So the first question is-- 00:09:53.923 --> 00:09:55.340 the first thing that comes to mind 00:09:55.340 --> 00:09:57.950 when you think about economics and modeling choices 00:09:57.950 --> 00:10:00.350 involving risk is risk aversion. 00:10:00.350 --> 00:10:01.850 How do we think about risk aversion? 00:10:01.850 --> 00:10:02.900 Or what is risk aversion? 00:10:05.450 --> 00:10:06.950 Why are people averse to risk? 00:10:06.950 --> 00:10:08.600 Yeah. 00:10:08.600 --> 00:10:10.502 AUDIENCE: Risk aversion is the tendency 00:10:10.502 --> 00:10:14.394 to avoid bets that are more risky, even though they 00:10:14.394 --> 00:10:17.874 will still ostensibly benefit you the same. 00:10:17.874 --> 00:10:18.890 FRANK SCHILBACH: Mhm. 00:10:18.890 --> 00:10:22.700 So one-- you said, essentially, if there are certain bets that 00:10:22.700 --> 00:10:26.660 involve risk, where the expected values or an expectation 00:10:26.660 --> 00:10:29.420 you're going to do pretty well-- perhaps better than some safe 00:10:29.420 --> 00:10:30.350 outcomes-- 00:10:30.350 --> 00:10:33.830 people tend to avoid those kinds of bets. 00:10:33.830 --> 00:10:36.420 And that we might call risk aversion. 00:10:36.420 --> 00:10:38.510 So that's exactly right. 00:10:38.510 --> 00:10:40.342 But now, why are people doing that? 00:10:40.342 --> 00:10:42.050 What are the underlying reasons for that? 00:10:46.690 --> 00:10:48.850 Yes. 00:10:48.850 --> 00:10:50.860 AUDIENCE: Potentially involved is 00:10:50.860 --> 00:10:55.500 loss aversion, which in the readings, 00:10:55.500 --> 00:10:59.200 I believe, some studies by [INAUDIBLE] 00:10:59.200 --> 00:11:03.100 and others mentioned that, showed that we had aversions 00:11:03.100 --> 00:11:07.305 specifically to losing money or utility 00:11:07.305 --> 00:11:10.020 rather than risk in and of itself. 00:11:10.020 --> 00:11:11.162 But that might be wrong. 00:11:11.162 --> 00:11:12.120 FRANK SCHILBACH: Right. 00:11:12.120 --> 00:11:13.740 So one part would be to say, people 00:11:13.740 --> 00:11:17.670 might sort of lose or gain money in certain gambles. 00:11:17.670 --> 00:11:19.710 And what you're saying is, essentially, people 00:11:19.710 --> 00:11:23.820 might not treat the losses the same as they treat the gains. 00:11:23.820 --> 00:11:27.090 And then you might sort of decline certain gambles 00:11:27.090 --> 00:11:28.350 or certain risks. 00:11:28.350 --> 00:11:31.770 You're just worried about losing out, and you put a lot of value 00:11:31.770 --> 00:11:32.455 on that. 00:11:32.455 --> 00:11:33.330 That's exactly right. 00:11:33.330 --> 00:11:37.733 We're going to talk about this next week in a lot more detail. 00:11:37.733 --> 00:11:39.900 But what are some other reasons why people might not 00:11:39.900 --> 00:11:42.810 want to engage in risk? 00:11:42.810 --> 00:11:43.360 Yes. 00:11:43.360 --> 00:11:45.420 AUDIENCE: I'd rather be definitely OK than either 00:11:45.420 --> 00:11:47.712 [? to ?] [? the ?] [? point ?] between super successful 00:11:47.712 --> 00:11:48.624 or die. 00:11:48.624 --> 00:11:49.499 FRANK SCHILBACH: Mhm. 00:11:49.499 --> 00:11:50.515 And why is that? 00:11:50.515 --> 00:11:52.640 AUDIENCE: [INAUDIBLE] diminishing marginal utility, 00:11:52.640 --> 00:11:53.040 [? maybe. ?] 00:11:53.040 --> 00:11:53.250 FRANK SCHILBACH: Right. 00:11:53.250 --> 00:11:54.840 So one part is-- and that's exactly how 00:11:54.840 --> 00:11:57.450 economists think about this-- is diminishing marginal utility. 00:11:57.450 --> 00:12:00.480 That's to say, if you're really poor, 00:12:00.480 --> 00:12:02.580 getting your first dollar has really high value 00:12:02.580 --> 00:12:04.423 to you-- the reason being that now, 00:12:04.423 --> 00:12:06.090 essentially, otherwise you would starve, 00:12:06.090 --> 00:12:07.680 or you can't eat and so on. 00:12:07.680 --> 00:12:11.130 The value of whatever you purchase with that dollar 00:12:11.130 --> 00:12:14.340 is really high, because you just have nothing otherwise. 00:12:14.340 --> 00:12:16.260 Now, if I give you a million dollars and then 00:12:16.260 --> 00:12:18.540 another dollar, then essentially the additional dollar 00:12:18.540 --> 00:12:19.915 that I give you after the million 00:12:19.915 --> 00:12:21.510 is just not doing very much. 00:12:21.510 --> 00:12:24.630 So the marginal utility of that dollar is low. 00:12:24.630 --> 00:12:27.253 And that's sort of diminishing marginal utility of wealth. 00:12:27.253 --> 00:12:29.170 That's exactly how economists talk about this. 00:12:29.170 --> 00:12:33.450 We're going to get back to that in a lot of detail. 00:12:33.450 --> 00:12:34.440 Yeah? 00:12:34.440 --> 00:12:36.232 AUDIENCE: I think if you look a little more 00:12:36.232 --> 00:12:40.380 at extreme examples, [INAUDIBLE] if I lose so much money, 00:12:40.380 --> 00:12:42.645 I won't be able to afford my expenses or something. 00:12:42.645 --> 00:12:44.770 So it doesn't matter what is [? created ?] [? by ?] 00:12:44.770 --> 00:12:50.842 [INAUDIBLE] lose a lot [INAUDIBLE] 00:12:50.842 --> 00:12:51.800 FRANK SCHILBACH: Right. 00:12:51.800 --> 00:12:54.590 So there might be sort of certain minimum standards, 00:12:54.590 --> 00:12:57.565 in some sense, that people have over their outcomes. 00:12:57.565 --> 00:13:00.050 Or you say, for example, you really 00:13:00.050 --> 00:13:03.140 want to have a place to sleep or you want to have some meal. 00:13:03.140 --> 00:13:05.840 And essentially, if you're below that threshold, 00:13:05.840 --> 00:13:10.100 essentially your marginal utility anywhere below that 00:13:10.100 --> 00:13:11.870 is really high, because you really want 00:13:11.870 --> 00:13:13.140 to get over that threshold. 00:13:13.140 --> 00:13:19.730 And so you might avoid certain choices or investments 00:13:19.730 --> 00:13:20.570 or the like. 00:13:20.570 --> 00:13:22.760 If there's even a small chance of getting 00:13:22.760 --> 00:13:26.520 below your threshold, you might be really averse to that. 00:13:26.520 --> 00:13:28.730 But what are some more perhaps psychological reasons 00:13:28.730 --> 00:13:30.540 why people don't like risks? 00:13:30.540 --> 00:13:31.040 Yeah? 00:13:31.040 --> 00:13:42.350 AUDIENCE: [INAUDIBLE] [? potential ?] [INAUDIBLE] 00:13:42.350 --> 00:13:43.403 FRANK SCHILBACH: Mhm. 00:13:43.403 --> 00:13:44.070 So that's right. 00:13:44.070 --> 00:13:44.720 That's what people do. 00:13:44.720 --> 00:13:46.230 We're going to also talk about that. 00:13:46.230 --> 00:13:49.430 But why do people not like the risk? 00:13:49.430 --> 00:13:51.740 Or some people like, actually, risk. 00:13:51.740 --> 00:13:55.640 But what is the issue about having a lot of exposure? 00:13:55.640 --> 00:13:59.380 Why do people purchase insurance, for example? 00:13:59.380 --> 00:14:00.250 Yes? 00:14:00.250 --> 00:14:02.618 AUDIENCE: Some amount of uncertainty [INAUDIBLE] 00:14:02.618 --> 00:14:04.660 [? risk ?] [? aversion, ?] [INAUDIBLE] the higher 00:14:04.660 --> 00:14:07.422 the uncertainty of the outcome, [INAUDIBLE] 00:14:07.422 --> 00:14:08.380 FRANK SCHILBACH: Right. 00:14:08.380 --> 00:14:10.280 So there's one part that's what you said, 00:14:10.280 --> 00:14:12.340 which is there's diminishing marginal utility of wealth. 00:14:12.340 --> 00:14:13.900 And this is exactly how we're going to model this 00:14:13.900 --> 00:14:15.670 and how economists think about this. 00:14:15.670 --> 00:14:17.300 However, there's other things involved, 00:14:17.300 --> 00:14:19.480 which is just things like anxiety or uncertainty. 00:14:19.480 --> 00:14:21.250 People might just not-- 00:14:21.250 --> 00:14:23.080 suppose a storm is coming up. 00:14:23.080 --> 00:14:24.340 I might purchase insurance. 00:14:24.340 --> 00:14:26.710 And if I purchase insurance, like flood insurance, 00:14:26.710 --> 00:14:29.980 or the like for a house, I might just feel much-- 00:14:29.980 --> 00:14:32.230 I might sleep better at night and so on and so forth. 00:14:32.230 --> 00:14:35.397 I might just feel better about concerns-- 00:14:35.397 --> 00:14:36.980 or like health insurance, for example, 00:14:36.980 --> 00:14:40.360 might lower anxiety and so on, because people are just 00:14:40.360 --> 00:14:42.670 not worried constantly about like falling 00:14:42.670 --> 00:14:45.070 ill or like disasters happening. 00:14:45.070 --> 00:14:47.830 And that's beyond potentially any 00:14:47.830 --> 00:14:50.710 diminishing marginal utility of wealth. 00:14:50.710 --> 00:14:54.940 That sort of anxiety, stress, worries, and so on. 00:14:54.940 --> 00:14:56.804 Any other reasons? 00:14:56.804 --> 00:14:58.070 Yeah? 00:14:58.070 --> 00:15:00.473 AUDIENCE: I think even beyond people wanting to not be 00:15:00.473 --> 00:15:02.390 stressed and anxious, there's also the element 00:15:02.390 --> 00:15:05.690 of, if you're buying insurance to smooth your consumption 00:15:05.690 --> 00:15:08.090 between different states of the world, 00:15:08.090 --> 00:15:12.840 it makes it a lot easier to plan for states after [INAUDIBLE] If 00:15:12.840 --> 00:15:13.340 you're-- 00:15:13.340 --> 00:15:13.700 FRANK SCHILBACH: Well, that's interesting. 00:15:13.700 --> 00:15:15.225 AUDIENCE: [INAUDIBLE] 00:15:15.225 --> 00:15:16.100 FRANK SCHILBACH: Yes. 00:15:16.100 --> 00:15:16.975 That's exactly right. 00:15:16.975 --> 00:15:19.152 So in some sense, if you have insurance, 00:15:19.152 --> 00:15:21.110 if you reduce risks in the states of the world, 00:15:21.110 --> 00:15:23.240 you can sort of, essentially, exclude a bunch 00:15:23.240 --> 00:15:24.365 of bad states of the world. 00:15:24.365 --> 00:15:26.282 For example, suppose you buy health insurance, 00:15:26.282 --> 00:15:28.190 suppose you have flood insurance, and so on. 00:15:28.190 --> 00:15:29.780 A lot of bad things that might happen you 00:15:29.780 --> 00:15:30.720 might be able to deal with. 00:15:30.720 --> 00:15:32.240 And you don't have to necessarily 00:15:32.240 --> 00:15:34.880 have a contingency plan of what if I fall sick 00:15:34.880 --> 00:15:37.220 and then go bankrupt, and all sorts of other bad things 00:15:37.220 --> 00:15:37.940 happen. 00:15:37.940 --> 00:15:39.710 Or what if I-- 00:15:39.710 --> 00:15:40.712 there's flood insurance. 00:15:40.712 --> 00:15:42.170 I can't pay the bills and then have 00:15:42.170 --> 00:15:44.010 to leave my house and so on. 00:15:44.010 --> 00:15:45.920 So essentially, it makes planning easier, 00:15:45.920 --> 00:15:48.282 in part because it's just sort of easier in the mind. 00:15:48.282 --> 00:15:49.490 People feel more comfortable. 00:15:49.490 --> 00:15:52.670 And part-- it's actually computational or just easier 00:15:52.670 --> 00:15:53.420 to do. 00:15:53.420 --> 00:15:55.178 So I added some reasons here. 00:15:55.178 --> 00:15:56.720 There's a bunch of different reasons. 00:15:56.720 --> 00:15:59.840 I think it's important to understand that economists have 00:15:59.840 --> 00:16:03.740 modeled risk aversion as diminishing 00:16:03.740 --> 00:16:05.010 marginal utility of wealth. 00:16:05.010 --> 00:16:07.310 That's a very simple way of doing this. 00:16:07.310 --> 00:16:10.950 It captures a lot of things, but perhaps not all of them. 00:16:10.950 --> 00:16:13.820 And so here's some reasons that I mentioned. 00:16:13.820 --> 00:16:15.400 Sort of contingent planning becomes 00:16:15.400 --> 00:16:16.400 harder if you have risk. 00:16:16.400 --> 00:16:18.530 That's what Maya just said. 00:16:18.530 --> 00:16:22.220 People are worried or stressed or anxious when 00:16:22.220 --> 00:16:24.710 they have lots of uncertainty. 00:16:24.710 --> 00:16:27.160 People might feel regret over missed opportunity. 00:16:27.160 --> 00:16:30.620 That's like, if I offer you some insurance right now, 00:16:30.620 --> 00:16:34.340 and you might say, well, it's actually unlikely 00:16:34.340 --> 00:16:36.363 that anything bad happens. 00:16:36.363 --> 00:16:38.030 But in case something really bad happens 00:16:38.030 --> 00:16:40.340 and you had the chance to actually avoid it, then 00:16:40.340 --> 00:16:43.310 you might feel particularly bad not just because the outcome is 00:16:43.310 --> 00:16:45.230 bad, but because it offered it to you 00:16:45.230 --> 00:16:47.930 and you didn't accept it. 00:16:47.930 --> 00:16:51.270 There's sort of disappointment relative to expectations. 00:16:51.270 --> 00:16:54.410 This is essentially getting into territory of losses and gains. 00:16:54.410 --> 00:16:56.000 When people have certain expectations, 00:16:56.000 --> 00:16:58.640 they have an expectation to have a certain income and the like. 00:16:58.640 --> 00:17:01.670 Now, if bad stuff happens, they fall below those expectations 00:17:01.670 --> 00:17:03.860 and perceive those outcomes then as losses 00:17:03.860 --> 00:17:08.508 compared to the status quo or the expectations that they had. 00:17:08.508 --> 00:17:10.550 Again, economists think about this as diminishing 00:17:10.550 --> 00:17:12.109 marginal utility of wealth. 00:17:12.109 --> 00:17:15.230 That's a very simple way of modeling this. 00:17:15.230 --> 00:17:18.140 And we're going to see kind of what the limitations of those 00:17:18.140 --> 00:17:18.770 are. 00:17:18.770 --> 00:17:20.270 Now, I'm going to show you the three 00:17:20.270 --> 00:17:22.190 stylized facts about the world. 00:17:22.190 --> 00:17:23.690 And then we're going to discuss kind 00:17:23.690 --> 00:17:25.220 of how to perhaps model that. 00:17:25.220 --> 00:17:27.230 So the first one is essentially very simple. 00:17:27.230 --> 00:17:31.280 People are risk averse in various ways. 00:17:31.280 --> 00:17:34.160 And one sort of basic fact is that lots of people 00:17:34.160 --> 00:17:34.970 buy insurance. 00:17:34.970 --> 00:17:37.310 People are willing to pay to purchase insurance that 00:17:37.310 --> 00:17:41.030 gives you essentially money or an expectation less money 00:17:41.030 --> 00:17:42.560 than you pay, right? 00:17:42.560 --> 00:17:44.780 So fair insurance, as economists would 00:17:44.780 --> 00:17:46.980 model is or think about it, is to say 00:17:46.980 --> 00:17:49.340 if I purchase insurance that pays you the expected 00:17:49.340 --> 00:17:51.360 value of the insurance. 00:17:51.360 --> 00:17:53.390 So if I pay a premium for an insurance, 00:17:53.390 --> 00:17:55.550 there's a probability of something bad happening 00:17:55.550 --> 00:17:59.480 and then sort of a loss or some insurance payment that I get 00:17:59.480 --> 00:18:01.340 in case something bad happens. 00:18:01.340 --> 00:18:04.100 Fair insurance would be the premium is essentially, 00:18:04.100 --> 00:18:11.343 in expectation, the same as the expectation of the loss, which 00:18:11.343 --> 00:18:13.010 is the probability of the loss occurring 00:18:13.010 --> 00:18:15.330 and the actual payment that I get from the insurance. 00:18:15.330 --> 00:18:17.580 Of course, the insurance industry wants to make money. 00:18:17.580 --> 00:18:20.750 So the insurance industry will not offer fair insurance, 00:18:20.750 --> 00:18:22.370 but less than fair insurance. 00:18:22.370 --> 00:18:25.290 Essentially, there's a price for purchasing insurance. 00:18:25.290 --> 00:18:27.290 Lots of people are willing to pay for insurance. 00:18:27.290 --> 00:18:29.330 People are willing to pay money to get insurance 00:18:29.330 --> 00:18:31.130 to reduce the risk or the exposure 00:18:31.130 --> 00:18:32.690 to risks that they have. 00:18:32.690 --> 00:18:35.060 There's social security in various ways 00:18:35.060 --> 00:18:37.370 where essentially people sort of insure themselves 00:18:37.370 --> 00:18:41.330 or society insures them for old age or not being able to take 00:18:41.330 --> 00:18:42.200 care of themselves. 00:18:42.200 --> 00:18:43.760 You could argue that's perhaps also 00:18:43.760 --> 00:18:47.325 due to present bias or other paternalistic reasons. 00:18:47.325 --> 00:18:48.950 But surely like society, in some sense, 00:18:48.950 --> 00:18:51.230 is helping people insure themselves 00:18:51.230 --> 00:18:56.240 against potential states of the world where 00:18:56.240 --> 00:18:57.830 they might be in need. 00:18:57.830 --> 00:19:00.270 There's very sort of other-- 00:19:00.270 --> 00:19:02.210 sorry-- institutions, including sort 00:19:02.210 --> 00:19:05.000 of extended families, informal insurance in developing 00:19:05.000 --> 00:19:07.830 countries, sharecropping, and so on and so forth. 00:19:07.830 --> 00:19:08.938 What's sharecropping? 00:19:12.010 --> 00:19:12.510 Yes. 00:19:12.510 --> 00:19:17.400 AUDIENCE: When you go multiple crops at the same time. 00:19:17.400 --> 00:19:18.370 FRANK SCHILBACH: No. 00:19:18.370 --> 00:19:21.150 That's intercropping or the like, 00:19:21.150 --> 00:19:23.270 but there might be referred to that as well. 00:19:23.270 --> 00:19:23.770 Yeah. 00:19:23.770 --> 00:19:27.913 AUDIENCE: It's when the person rents out their land for you 00:19:27.913 --> 00:19:33.048 work on and you get all the benefits from the land, 00:19:33.048 --> 00:19:36.017 but [? they ?] [INAUDIBLE] [? rent ?] [INAUDIBLE].. 00:19:36.017 --> 00:19:37.350 FRANK SCHILBACH: Right, exactly. 00:19:37.350 --> 00:19:40.020 So it's essentially these kinds of arrangement, which 00:19:40.020 --> 00:19:42.270 are often somebody has land. 00:19:42.270 --> 00:19:43.860 Somebody rents out the land. 00:19:43.860 --> 00:19:47.820 And then you have to pay them something back 00:19:47.820 --> 00:19:49.920 and then can keep some of the output and so on. 00:19:49.920 --> 00:19:51.900 And often that's essentially some way 00:19:51.900 --> 00:19:53.725 essentially reducing risk. 00:19:53.725 --> 00:19:55.350 So there's various sort of institution. 00:19:55.350 --> 00:19:57.902 But broadly speaking, we think, in many situations, 00:19:57.902 --> 00:19:58.860 people don't like risk. 00:19:58.860 --> 00:20:02.940 And they look for ways to reduce the exposure to risks. 00:20:02.940 --> 00:20:05.520 There's also these informal insurance arrangements, 00:20:05.520 --> 00:20:08.615 which are things like people get together. 00:20:08.615 --> 00:20:09.990 And they sort of help each other. 00:20:09.990 --> 00:20:13.170 Whenever something bad happens, one person 00:20:13.170 --> 00:20:15.990 is then being helped by everybody else. 00:20:15.990 --> 00:20:19.260 And that's sort of replacing some sort of formula 00:20:19.260 --> 00:20:21.600 for insurance schemes and particularly 00:20:21.600 --> 00:20:23.220 in developing countries. 00:20:23.220 --> 00:20:26.220 Second, risk reduction has its price. 00:20:26.220 --> 00:20:29.550 That is to say people are willing to take on risk 00:20:29.550 --> 00:20:31.518 if the return is high enough. 00:20:31.518 --> 00:20:33.060 So another way to put this is, if you 00:20:33.060 --> 00:20:36.150 want to purchase insurance, usually you have to pay for it. 00:20:36.150 --> 00:20:38.190 The insurance industry makes a lot of money. 00:20:38.190 --> 00:20:43.830 Put differently, people are willing to take on some risk 00:20:43.830 --> 00:20:45.075 if things get cheaper, right? 00:20:45.075 --> 00:20:46.950 For example, if you think about buying a car, 00:20:46.950 --> 00:20:48.825 you could buy a super safe car with all sorts 00:20:48.825 --> 00:20:49.860 of safety features. 00:20:49.860 --> 00:20:50.970 Not everybody does that. 00:20:50.970 --> 00:20:54.510 The reason is because cheaper cars are less safe. 00:20:54.510 --> 00:20:55.710 Cars are cheaper. 00:20:55.710 --> 00:20:57.210 So you're might just sort of willing 00:20:57.210 --> 00:21:00.790 to take on some risk in some situations for some price, 00:21:00.790 --> 00:21:01.290 right? 00:21:01.290 --> 00:21:03.690 When you think about starting a restaurant, 00:21:03.690 --> 00:21:06.952 restaurants essentially fail all the time. 00:21:06.952 --> 00:21:08.910 Yet people are always sort of willing to do it. 00:21:08.910 --> 00:21:12.060 Presumably, the reason is because if you actually 00:21:12.060 --> 00:21:14.200 succeed, you're going to make quite a bit of money. 00:21:14.200 --> 00:21:16.020 So if there's a high expected return, 00:21:16.020 --> 00:21:18.810 people are willing to take on some risk. 00:21:18.810 --> 00:21:20.740 People put in money into the stock market, 00:21:20.740 --> 00:21:22.670 so they increase their risk exposure. 00:21:22.670 --> 00:21:25.170 The reason why they do that is because, in expectation, they 00:21:25.170 --> 00:21:27.940 make quite a bit of money. 00:21:27.940 --> 00:21:31.298 But of course, that often entails risk. 00:21:31.298 --> 00:21:33.840 So one way to think about the entire sort of finance industry 00:21:33.840 --> 00:21:35.280 is risk intermediation. 00:21:35.280 --> 00:21:36.960 Essentially, there are some businesses 00:21:36.960 --> 00:21:38.590 that have a lot of risk. 00:21:38.590 --> 00:21:42.630 And that risk is sort of offloaded to investors. 00:21:42.630 --> 00:21:44.370 And the investors accept that risk. 00:21:44.370 --> 00:21:46.170 They say, I'm willing to take on that risk, 00:21:46.170 --> 00:21:48.730 but only for a good return. 00:21:48.730 --> 00:21:50.940 So I'm not going to take on risk from you 00:21:50.940 --> 00:21:52.980 if I'm not, in expectation, making money. 00:21:52.980 --> 00:21:55.290 But often, essentially, there's a trade off between. 00:21:55.290 --> 00:21:57.120 And this is-- well, if you've taken finance classes and so 00:21:57.120 --> 00:21:58.380 on, that's kind of obvious. 00:21:58.380 --> 00:22:01.440 There's a trade between risk and expected return. 00:22:04.187 --> 00:22:05.770 In what situations are people actually 00:22:05.770 --> 00:22:10.390 willing to take on risk for its own sake or just-- 00:22:10.390 --> 00:22:11.950 so I told you people are risk averse. 00:22:11.950 --> 00:22:14.390 And that's true in most situations. 00:22:14.390 --> 00:22:16.700 But where are people actually willing to take on risks? 00:22:16.700 --> 00:22:17.020 Yes. 00:22:17.020 --> 00:22:18.346 AUDIENCE: [INAUDIBLE] casino? 00:22:18.346 --> 00:22:19.304 FRANK SCHILBACH: Right. 00:22:19.304 --> 00:22:21.280 Lots of people actually go to casinos. 00:22:21.280 --> 00:22:26.690 And here, the expected return is actually a negative. 00:22:26.690 --> 00:22:28.690 You know, you're going to lose money on average. 00:22:28.690 --> 00:22:32.860 Unless you're sort of a smart MIT student who can count cards 00:22:32.860 --> 00:22:34.570 in poker or something, you're going 00:22:34.570 --> 00:22:35.980 to lose money essentially. 00:22:35.980 --> 00:22:39.670 So there must be some form of some preference or some desire 00:22:39.670 --> 00:22:43.132 to take on risk in some situations because you cannot 00:22:43.132 --> 00:22:45.340 just-- this is not like investing in the stock market 00:22:45.340 --> 00:22:47.260 where, on average, you're going to get money. 00:22:47.260 --> 00:22:49.420 If you go to the casino, on average 00:22:49.420 --> 00:22:50.660 you're going to lose money. 00:22:50.660 --> 00:22:52.820 Now, you could say it's so much fun and so on. 00:22:52.820 --> 00:22:54.070 There could also be addiction. 00:22:54.070 --> 00:22:56.290 There could be also self-control issues and so on. 00:22:56.290 --> 00:22:58.373 Or there could be something about people's beliefs 00:22:58.373 --> 00:23:00.413 or preferences that induce them to take on risk. 00:23:00.413 --> 00:23:02.830 But notice that's different from what we discussed before. 00:23:02.830 --> 00:23:05.500 That's not really consistent with risk aversion 00:23:05.500 --> 00:23:08.560 because people choose to increase the risk that they're 00:23:08.560 --> 00:23:09.790 exposed to. 00:23:09.790 --> 00:23:12.025 Any other-- yeah. 00:23:12.025 --> 00:23:13.818 AUDIENCE: Buying lottery tickets. 00:23:13.818 --> 00:23:14.860 FRANK SCHILBACH: Exactly. 00:23:14.860 --> 00:23:19.810 People are buying lots of lottery tickets. 00:23:19.810 --> 00:23:22.120 Similar, they're doing lots of sports betting. 00:23:22.120 --> 00:23:24.970 And again, what you're doing here is, to be very clear, 00:23:24.970 --> 00:23:26.560 on average you're going to lose money 00:23:26.560 --> 00:23:30.010 and that you're going to increase risk or the exposure 00:23:30.010 --> 00:23:30.790 to risk. 00:23:30.790 --> 00:23:33.147 And there's some questions on why people are doing this. 00:23:33.147 --> 00:23:34.480 We're going to get back to this. 00:23:34.480 --> 00:23:36.188 We're going to not talk about this today, 00:23:36.188 --> 00:23:37.570 but I sort of want to flag that. 00:23:37.570 --> 00:23:39.400 While people are risk averse in many, 00:23:39.400 --> 00:23:42.610 in almost, nearly all situations of the world 00:23:42.610 --> 00:23:44.330 of important choices that you encounter, 00:23:44.330 --> 00:23:47.650 there are some choices where people are, in fact, exposing 00:23:47.650 --> 00:23:52.090 themselves to risk in addition to exposure to risks 00:23:52.090 --> 00:23:55.680 that actually has high expected value. 00:23:55.680 --> 00:23:56.770 Any questions on this? 00:24:02.960 --> 00:24:03.610 OK. 00:24:03.610 --> 00:24:05.960 So now, we're going to talk about the expected utility 00:24:05.960 --> 00:24:10.400 and sort of how do economists think about how should we 00:24:10.400 --> 00:24:10.900 behave. 00:24:10.900 --> 00:24:13.150 And that's a normative model, how the economists think 00:24:13.150 --> 00:24:16.090 about how people should behave when it comes 00:24:16.090 --> 00:24:20.080 to choices involving risk. 00:24:20.080 --> 00:24:25.190 So what is expected utility? 00:24:25.190 --> 00:24:26.630 What does the model assume? 00:24:26.630 --> 00:24:28.040 Or what is it about? 00:24:32.750 --> 00:24:33.320 Yeah. 00:24:33.320 --> 00:24:35.830 AUDIENCE: It's the utility of each state 00:24:35.830 --> 00:24:38.280 of the world multiplied by the probability of that state 00:24:38.280 --> 00:24:39.647 of the word occurring. 00:24:39.647 --> 00:24:40.980 FRANK SCHILBACH: Right, exactly. 00:24:40.980 --> 00:24:42.610 So the assumption here is there's 00:24:42.610 --> 00:24:43.860 different states of the world. 00:24:43.860 --> 00:24:45.980 There's good things and bad things may happen. 00:24:45.980 --> 00:24:47.680 You might get a job. 00:24:47.680 --> 00:24:48.680 You might not get a job. 00:24:48.680 --> 00:24:51.120 You might get a good grade, bad grade, and so on. 00:24:51.120 --> 00:24:53.390 You can sort of partition the world or anything 00:24:53.390 --> 00:24:54.890 that's going to happen in the future 00:24:54.890 --> 00:24:56.360 into different states of the world. 00:24:56.360 --> 00:25:00.770 We can associate a utility, so an outcome, 00:25:00.770 --> 00:25:03.680 and an associated utility with that state of the world, right? 00:25:03.680 --> 00:25:06.060 If you get a good job, you get a high income. 00:25:06.060 --> 00:25:07.550 And if you don't get a job, you get 00:25:07.550 --> 00:25:09.230 a low income or whatever or unemployment 00:25:09.230 --> 00:25:10.890 insurance or whatever. 00:25:10.890 --> 00:25:14.690 And there are certain utilities associated with these outcomes. 00:25:14.690 --> 00:25:16.555 Expected utility, now, is essentially 00:25:16.555 --> 00:25:18.680 say, OK, now for each of these states of the world, 00:25:18.680 --> 00:25:21.110 there's a probability of the state of the world happening. 00:25:21.110 --> 00:25:23.330 And I'm going to use essentially the weighted average, which 00:25:23.330 --> 00:25:25.705 essentially is weighting each state with their associated 00:25:25.705 --> 00:25:29.510 probability and then using the associated 00:25:29.510 --> 00:25:30.890 utilities for each state. 00:25:30.890 --> 00:25:33.080 And the expectations of those utilities 00:25:33.080 --> 00:25:35.193 is what's expected utility. 00:25:35.193 --> 00:25:36.360 And that's very complicated. 00:25:36.360 --> 00:25:38.443 I'm going to sort of get [? to where ?] [? that ?] 00:25:38.443 --> 00:25:40.947 [? is ?] said in more words than necessary. 00:25:40.947 --> 00:25:42.280 Let me sort of get back to this. 00:25:42.280 --> 00:25:47.980 So first, the thing about expected monetary value-- 00:25:47.980 --> 00:25:49.453 so suppose there's a gamble. 00:25:49.453 --> 00:25:50.870 And this is not a very simplified. 00:25:50.870 --> 00:25:51.578 There's a gamble. 00:25:51.578 --> 00:25:53.690 I'll call it G over two states of the world. 00:25:53.690 --> 00:25:57.380 State 1 occurs with probability p and yields monetary payoff x. 00:25:57.380 --> 00:25:59.810 State 2 occurs with probability 1 minus p 00:25:59.810 --> 00:26:02.120 and yields monetary payoff y. 00:26:02.120 --> 00:26:04.700 Now, the expected monetary value-- 00:26:04.700 --> 00:26:06.230 now, this is not expected utility. 00:26:06.230 --> 00:26:07.710 This expected monetary value. 00:26:07.710 --> 00:26:10.640 This is how much money you get in expectation-- is essentially 00:26:10.640 --> 00:26:12.920 just the weighted average of those two things sort of 00:26:12.920 --> 00:26:14.870 weighted by the probabilities. 00:26:14.870 --> 00:26:17.138 So that's p times x plus 1 minus p times y. 00:26:17.138 --> 00:26:19.430 That's just the expected value of how much money you're 00:26:19.430 --> 00:26:21.470 going to get from this gamble. 00:26:21.470 --> 00:26:24.590 Now, this is just a definition of fair gamble. 00:26:24.590 --> 00:26:26.570 And this is what economists tend to use a lot. 00:26:26.570 --> 00:26:29.900 A fair gamble is one with a price 00:26:29.900 --> 00:26:33.160 equal to its expected monetary value, right? 00:26:33.160 --> 00:26:37.670 So if I ask you would you like to take this gamble, 00:26:37.670 --> 00:26:39.813 you're going to ask kind of, is this a fair gamble? 00:26:39.813 --> 00:26:41.480 Essentially, that's just asking about is 00:26:41.480 --> 00:26:45.290 it paying the expected value of this in terms of money. 00:26:45.290 --> 00:26:49.880 I put monetary in parentheses because I could also provide 00:26:49.880 --> 00:26:51.650 you a fair gamble of apples. 00:26:51.650 --> 00:26:54.890 And then it would just be the expected value of apples. 00:26:54.890 --> 00:26:58.460 That would be also a fair gamble potentially. 00:26:58.460 --> 00:27:01.070 Now, what's the expected utility of this gamble? 00:27:01.070 --> 00:27:03.020 Well, now, you need to have a utility function 00:27:03.020 --> 00:27:04.650 for each of these outcomes. 00:27:04.650 --> 00:27:06.920 So if my utility function is u of x, 00:27:06.920 --> 00:27:11.060 this kind of how much utility I get in the state of actually 00:27:11.060 --> 00:27:13.220 getting x or y. 00:27:13.220 --> 00:27:16.343 So-called xi is where i is the state of the world. 00:27:16.343 --> 00:27:18.260 So essentially, now, it's the weighted average 00:27:18.260 --> 00:27:23.180 of p i times u of xi, so in this case, p times u of x 00:27:23.180 --> 00:27:26.540 plus y minus p times u of y. 00:27:26.540 --> 00:27:28.010 Any questions on this so far? 00:27:36.240 --> 00:27:39.180 And so when you now think about evaluating gambles 00:27:39.180 --> 00:27:42.420 using an expected utility, if your utility function 00:27:42.420 --> 00:27:47.197 is linear, then you're going to essentially decide 00:27:47.197 --> 00:27:49.530 the same way as if you were just evaluating the expected 00:27:49.530 --> 00:27:52.980 monetary value, right? 00:27:52.980 --> 00:27:55.590 And if not, if the utility function is concave and convex, 00:27:55.590 --> 00:27:59.070 then essentially people are potentially risk averse. 00:27:59.070 --> 00:28:03.270 So how economists think about expected monetary value 00:28:03.270 --> 00:28:05.430 is the history of that used to be, 00:28:05.430 --> 00:28:07.800 the first theory that people wrote down was, 00:28:07.800 --> 00:28:10.350 this was a model how people thought people should behave. 00:28:10.350 --> 00:28:12.808 There was a normative model that people wrote at some point 00:28:12.808 --> 00:28:16.800 and said, rational people should essentially 00:28:16.800 --> 00:28:19.530 maximize monetary payouts, which is 00:28:19.530 --> 00:28:24.600 say, if the expected monetary value of a certain gamble 00:28:24.600 --> 00:28:25.980 is high, you should accept it. 00:28:25.980 --> 00:28:27.790 Or if it's higher than its price, 00:28:27.790 --> 00:28:29.760 then you should accept it, otherwise not. 00:28:29.760 --> 00:28:31.920 Now, it turns out that, in practice, that's 00:28:31.920 --> 00:28:33.180 not descriptively accurate. 00:28:33.180 --> 00:28:35.370 That's just not how people behave on the world. 00:28:35.370 --> 00:28:37.350 And in fact, and the reason being that people 00:28:37.350 --> 00:28:39.210 are risk averse in most situations. 00:28:42.390 --> 00:28:44.790 When using, now, the expected monetary value, essentially 00:28:44.790 --> 00:28:46.540 they use the expected money value 00:28:46.540 --> 00:28:48.790 as a definition for risk neutrality. 00:28:48.790 --> 00:28:50.790 If somebody is risk neutral, if somebody doesn't 00:28:50.790 --> 00:28:53.100 care at all about risk in some situation, 00:28:53.100 --> 00:28:55.650 that person essentially just is maximizing the expected 00:28:55.650 --> 00:28:57.685 monetary value, right? 00:28:57.685 --> 00:28:59.060 So a decision maker is-- and this 00:28:59.060 --> 00:29:01.620 is a definition-- is risk neutral if, for any lottery G, 00:29:01.620 --> 00:29:03.720 she is indifferent between G and getting 00:29:03.720 --> 00:29:07.140 the expected monetary value G for sure. 00:29:07.140 --> 00:29:09.660 And so the decision maker is risk neutral if the utility 00:29:09.660 --> 00:29:12.868 function is linear, OK? 00:29:12.868 --> 00:29:14.910 Essentially, the more money you get, then there's 00:29:14.910 --> 00:29:18.630 no diminishing marginal utility of money. 00:29:18.630 --> 00:29:22.480 Now, what's risk aversion then? 00:29:22.480 --> 00:29:25.980 A decision maker is risk averse if, for any lottery G, 00:29:25.980 --> 00:29:30.810 she prefers getting the expected monetary value G for sure 00:29:30.810 --> 00:29:33.480 rather than taking G. And the person 00:29:33.480 --> 00:29:35.940 is risk loving if the person rather 00:29:35.940 --> 00:29:37.650 has the lottery than the expected 00:29:37.650 --> 00:29:41.587 monetary value for sure. 00:29:41.587 --> 00:29:42.670 These are just definition. 00:29:42.670 --> 00:29:44.440 That's just the way how economists think about risk. 00:29:44.440 --> 00:29:45.940 That's just definition, defining how 00:29:45.940 --> 00:29:50.160 we think about risk aversion and risk lovingness if you want. 00:29:50.160 --> 00:29:53.700 Now, let me give you just a very simple example. 00:29:53.700 --> 00:29:58.140 Suppose a person with wealth, $10,000 is offered a gamble. 00:29:58.140 --> 00:30:01.290 The gamble is you can gain $500 with a 50% chance 00:30:01.290 --> 00:30:03.750 and lose $400 with a 50% chance. 00:30:03.750 --> 00:30:06.963 Will you accept this gamble? 00:30:06.963 --> 00:30:07.880 How do we do this now? 00:30:14.710 --> 00:30:18.980 Suppose I'm just maximizing the expected monetary value. 00:30:18.980 --> 00:30:20.860 What am I going to do? 00:30:20.860 --> 00:30:21.646 Yeah. 00:30:21.646 --> 00:30:24.612 AUDIENCE: You take [INAUDIBLE] something [INAUDIBLE]?? 00:30:24.612 --> 00:30:25.570 FRANK SCHILBACH: Right. 00:30:25.570 --> 00:30:27.070 So what I'm going to do is I'm going 00:30:27.070 --> 00:30:29.950 to just look at what's my expected monetary value 00:30:29.950 --> 00:30:32.650 of accepting your lottery, which is 00:30:32.650 --> 00:30:37.960 0.5, which is the probability of a loss times 9,600. 00:30:37.960 --> 00:30:42.010 This is 10,000 minus the 400 that I lose plus 0.5 times 00:30:42.010 --> 00:30:46.510 10,000 plus 500, which gives me 10,050. 00:30:46.510 --> 00:30:49.150 If I reject the lottery, I'm just where I am before. 00:30:49.150 --> 00:30:51.160 Now, the risk neutral decision maker 00:30:51.160 --> 00:30:54.520 will reject the gamble, in fact, irrespective 00:30:54.520 --> 00:30:55.540 of the initial wealth. 00:30:55.540 --> 00:30:57.370 Because, essentially, everything is linear, 00:30:57.370 --> 00:30:58.790 so you just drop out the wealth. 00:30:58.790 --> 00:31:01.270 You can just look at what's the expected value regardless 00:31:01.270 --> 00:31:02.890 of how much money the person has. 00:31:02.890 --> 00:31:03.920 AUDIENCE: So you mean [INAUDIBLE] [? accepting ?] 00:31:03.920 --> 00:31:05.102 [INAUDIBLE]? 00:31:07.603 --> 00:31:08.770 FRANK SCHILBACH: Yes, sorry. 00:31:08.770 --> 00:31:11.600 That's a typo. 00:31:11.600 --> 00:31:12.310 Yes, sorry. 00:31:12.310 --> 00:31:12.920 That's a typo. 00:31:12.920 --> 00:31:14.700 Yes, thank you. 00:31:14.700 --> 00:31:15.200 Yeah. 00:31:15.200 --> 00:31:16.990 So exactly, the expected monetary value 00:31:16.990 --> 00:31:21.280 is higher than the status quo, so you accept the gamble. 00:31:21.280 --> 00:31:24.500 And that doesn't depend on the initial wealth. 00:31:24.500 --> 00:31:25.400 OK. 00:31:25.400 --> 00:31:27.690 So now, what's the expected utility maximizer do? 00:31:27.690 --> 00:31:30.470 And how does an expected utility maximizer think about this? 00:31:40.460 --> 00:31:41.788 Yes? 00:31:41.788 --> 00:31:43.580 AUDIENCE: In their calculation, rather than 00:31:43.580 --> 00:31:47.510 weighting the 9,600 and the 10,500, 00:31:47.510 --> 00:31:49.448 they'll weight the utility value. 00:31:49.448 --> 00:31:50.490 FRANK SCHILBACH: Exactly. 00:31:50.490 --> 00:31:52.130 So now, we need the utility function. 00:31:52.130 --> 00:31:56.330 What's the utility of 9,600, the utility of 10,500, 00:31:56.330 --> 00:31:58.100 and the utility of 10,000? 00:31:58.100 --> 00:32:01.760 Now, will she accept the gamble? 00:32:01.760 --> 00:32:03.200 Well, now, it depends essentially 00:32:03.200 --> 00:32:04.770 on the utility function. 00:32:04.770 --> 00:32:07.190 What's the shape of that utility function look like? 00:32:07.190 --> 00:32:08.960 In particular, it depends on the concavity 00:32:08.960 --> 00:32:10.590 of the utility function. 00:32:10.590 --> 00:32:13.020 So what do I mean by the concavity of the utility 00:32:13.020 --> 00:32:13.520 function? 00:32:13.520 --> 00:32:15.220 This is concave function. 00:32:15.220 --> 00:32:16.670 What do I mean by that? 00:32:19.350 --> 00:32:20.850 What's the definition? 00:32:20.850 --> 00:32:21.647 Yes. 00:32:21.647 --> 00:32:22.712 AUDIENCE: [INAUDIBLE] 00:32:22.712 --> 00:32:23.670 FRANK SCHILBACH: Right. 00:32:23.670 --> 00:32:25.878 So one definition is a second derivative is negative. 00:32:25.878 --> 00:32:26.820 That's exactly right. 00:32:26.820 --> 00:32:30.150 That's true if the function is twice differentiable. 00:32:30.150 --> 00:32:31.860 We have a slightly different definition 00:32:31.860 --> 00:32:33.930 that's slightly more general because it doesn't 00:32:33.930 --> 00:32:36.150 depend on differentiability. 00:32:36.150 --> 00:32:39.120 But essentially, it's to say it's the following definition, 00:32:39.120 --> 00:32:42.000 if the utility of a convex combination of two outcomes-- 00:32:42.000 --> 00:32:43.920 I'm going to tell you about this in a second-- 00:32:43.920 --> 00:32:47.940 is larger than the convex combination of the utility 00:32:47.940 --> 00:32:49.930 of those outcomes. 00:32:49.930 --> 00:32:50.950 What do I mean by that? 00:32:50.950 --> 00:32:54.000 Suppose you have an outcome x and a utility associated 00:32:54.000 --> 00:32:56.100 with that that's u of x. 00:32:56.100 --> 00:32:58.290 Suppose you have an outcome y and a utility 00:32:58.290 --> 00:33:01.630 of u of y associated with that. 00:33:01.630 --> 00:33:04.090 And now, suppose you have a convex combination of x and y, 00:33:04.090 --> 00:33:09.090 which is just p is a probability of p times x 00:33:09.090 --> 00:33:10.980 plus 1 minus p times y. 00:33:10.980 --> 00:33:12.690 That's in the middle of x and y. 00:33:12.690 --> 00:33:17.790 So I take a weighted average of x and y that adds up to 1. 00:33:17.790 --> 00:33:22.020 Now, if I have the utility associated with that convex 00:33:22.020 --> 00:33:27.370 combination, that's u of px plus 1 minus p times y. 00:33:27.370 --> 00:33:30.040 That's just the utility associated with that. 00:33:30.040 --> 00:33:33.390 Now, if I draw a line between those two graphs 00:33:33.390 --> 00:33:37.110 and look at what's the convex combination of p, 00:33:37.110 --> 00:33:40.435 so what's p of u of x plus 1 minus p of u of y? 00:33:40.435 --> 00:33:42.060 That's essentially the weighted average 00:33:42.060 --> 00:33:45.330 of the utilities associated with x and y. 00:33:45.330 --> 00:33:48.480 Now, the question is, is the average 00:33:48.480 --> 00:33:50.200 of the utility of the average higher 00:33:50.200 --> 00:33:53.218 or lower than the average of the utilities? 00:33:53.218 --> 00:33:55.510 Can somebody explain this in words of what I just said? 00:33:55.510 --> 00:33:56.680 Or what do I mean? 00:33:56.680 --> 00:33:58.000 Can somebody repeat this? 00:34:08.690 --> 00:34:09.190 Yes? 00:34:09.190 --> 00:34:11.496 AUDIENCE: I mean, technically, we're just trying to see if you 00:34:11.496 --> 00:34:13.579 take two points in the [INAUDIBLE] and draw a line 00:34:13.579 --> 00:34:16.302 between them, would the line be [? below ?] [? the curve? ?] 00:34:16.302 --> 00:34:17.260 FRANK SCHILBACH: Right. 00:34:17.260 --> 00:34:19.090 Is the line above or below the curve? 00:34:19.090 --> 00:34:21.460 In this case, the line is below the curve. 00:34:21.460 --> 00:34:23.860 Now, what that means is, if I give you two outcomes 00:34:23.860 --> 00:34:25.600 and I say, would you rather have-- 00:34:25.600 --> 00:34:27.610 you could have x and y, or would you rather 00:34:27.610 --> 00:34:30.940 have the some weighted average of x and y? 00:34:30.940 --> 00:34:34.120 Now, the question is, what's the utility associated 00:34:34.120 --> 00:34:36.275 with this average of x and y? 00:34:36.275 --> 00:34:38.650 That's the thing that you see here on the left upper side 00:34:38.650 --> 00:34:42.219 is u of p of x plus 1 minus p times y. 00:34:42.219 --> 00:34:45.699 That's essentially the utility of the weighted average. 00:34:45.699 --> 00:34:48.538 Is that larger or smaller than the weighted average 00:34:48.538 --> 00:34:50.830 of the utility, which is the thing that I show you here 00:34:50.830 --> 00:34:51.667 below? 00:34:51.667 --> 00:34:53.500 And what you see is, in this case-- and this 00:34:53.500 --> 00:34:55.540 is because the line is exactly as I say-- it's 00:34:55.540 --> 00:34:56.830 below the utility function. 00:34:56.830 --> 00:34:59.050 If the line is below the utility function, that 00:34:59.050 --> 00:35:02.560 means essentially that the utility of the weighted average 00:35:02.560 --> 00:35:06.220 is higher than the weighted average of the utilities, which 00:35:06.220 --> 00:35:09.130 means essentially the function is concave. 00:35:09.130 --> 00:35:11.950 And that means essentially that the person 00:35:11.950 --> 00:35:13.720 is risk averse, as we call it. 00:35:13.720 --> 00:35:17.020 You'd rather have the average than the spread of the two 00:35:17.020 --> 00:35:19.370 outcomes. 00:35:19.370 --> 00:35:21.365 Any questions on this or comments? 00:35:27.650 --> 00:35:28.150 OK. 00:35:28.150 --> 00:35:29.700 So you can look at this in detail 00:35:29.700 --> 00:35:34.530 but essentially it's a simple definition. 00:35:34.530 --> 00:35:37.560 So now, expected utility says essentially the following. 00:35:37.560 --> 00:35:40.350 It says a risk averse person rejects all fair gambles. 00:35:40.350 --> 00:35:42.650 And again, fair gambles are gambles that pay you 00:35:42.650 --> 00:35:44.552 the expected monetary value. 00:35:44.552 --> 00:35:46.010 And the reason why that person does 00:35:46.010 --> 00:35:48.890 that is because the expected utility 00:35:48.890 --> 00:35:53.840 is lower than the utility of the expected monetary value. 00:35:53.840 --> 00:35:56.180 Essentially, as you just said, it's 00:35:56.180 --> 00:36:00.020 because the straight line is below the utility function. 00:36:00.020 --> 00:36:02.510 And that's essentially exactly the same definition here. 00:36:02.510 --> 00:36:05.690 Therefore, a risk averse person who 00:36:05.690 --> 00:36:10.190 has a concave utility function rejects all fair gambles. 00:36:10.190 --> 00:36:13.380 Now, what does expected utility theory then say? 00:36:13.380 --> 00:36:17.370 Well, it says risky options are valued by doing three things. 00:36:17.370 --> 00:36:20.657 One is you have to define utility over final outcomes. 00:36:20.657 --> 00:36:23.240 And this is sort of getting back what you were saying earlier. 00:36:23.240 --> 00:36:26.587 People might be worried about losses or gains or the like. 00:36:26.587 --> 00:36:27.920 We're assuming all of this away. 00:36:27.920 --> 00:36:31.400 We're just saying, their final outcomes-- how much money you 00:36:31.400 --> 00:36:34.940 have, what grades you have, how many kids you have, 00:36:34.940 --> 00:36:37.160 and so on, these are final outcomes, 00:36:37.160 --> 00:36:41.990 things that sort of where an absolute value is defined. 00:36:41.990 --> 00:36:44.900 There's a utility associated with those outcomes. 00:36:44.900 --> 00:36:46.910 It's not about you expected more money 00:36:46.910 --> 00:36:48.200 or less money or the like. 00:36:48.200 --> 00:36:49.718 That's completely irrelevant. 00:36:49.718 --> 00:36:51.260 We're just looking at final outcomes. 00:36:51.260 --> 00:36:53.177 How much money do you end up actually getting? 00:36:53.177 --> 00:36:55.575 And we're associating some utility with that. 00:36:55.575 --> 00:36:57.200 That's assumption number one, or that's 00:36:57.200 --> 00:36:59.090 the first thing one does. 00:36:59.090 --> 00:37:02.300 Second is you weight these utilities for each outcomes 00:37:02.300 --> 00:37:03.388 by its probability. 00:37:03.388 --> 00:37:05.180 Essentially, we know what the probabilities 00:37:05.180 --> 00:37:06.750 are for each of those outcomes. 00:37:06.750 --> 00:37:10.220 We're going to take the weighted average of these utilities. 00:37:10.220 --> 00:37:13.580 And then we sort of adding them up. 00:37:13.580 --> 00:37:16.190 And then by adding them up, essentially we 00:37:16.190 --> 00:37:17.960 can evaluate all sorts of lotteries. 00:37:17.960 --> 00:37:20.600 And then we just compare those lotteries 00:37:20.600 --> 00:37:22.310 either with some fixed amount of money 00:37:22.310 --> 00:37:26.330 or some other lotteries, the outcomes that we might get. 00:37:26.330 --> 00:37:28.857 Now, there's two key implicit assumptions 00:37:28.857 --> 00:37:29.940 that are really important. 00:37:29.940 --> 00:37:32.070 One is only final outcomes matter. 00:37:32.070 --> 00:37:34.100 It doesn't matter what you expected in advance. 00:37:34.100 --> 00:37:36.142 It doesn't matter what you thought you might get. 00:37:36.142 --> 00:37:38.250 And it doesn't matter what you had yesterday. 00:37:38.250 --> 00:37:39.667 All of these things are completely 00:37:39.667 --> 00:37:42.170 irrelevant in the simplest form of expected utility 00:37:42.170 --> 00:37:44.420 unless you sort of have information or the like. 00:37:44.420 --> 00:37:46.310 Only final outcomes matter. 00:37:46.310 --> 00:37:48.530 And then there is linearity and probabilities. 00:37:48.530 --> 00:37:51.920 That's to say we put weight on the different types of states 00:37:51.920 --> 00:37:56.360 of the world relative to what the probability of those states 00:37:56.360 --> 00:37:57.410 are. 00:37:57.410 --> 00:38:00.320 So it cannot be that, if something is twice as likely, 00:38:00.320 --> 00:38:02.480 you should put twice as much weight on that 00:38:02.480 --> 00:38:04.400 in your evaluation of the outcomes. 00:38:04.400 --> 00:38:08.000 It cannot be that this is non-linear in certain ways. 00:38:08.000 --> 00:38:11.560 There's linearity in probabilities. 00:38:11.560 --> 00:38:12.580 Any questions on this? 00:38:22.730 --> 00:38:25.670 So now, let me get back to what I said previously. 00:38:25.670 --> 00:38:27.352 What are we assuming away here? 00:38:27.352 --> 00:38:29.060 What are the things that are not in here? 00:38:48.370 --> 00:38:48.870 Yeah. 00:38:48.870 --> 00:38:51.698 AUDIENCE: [INAUDIBLE] 00:38:51.698 --> 00:38:52.740 FRANK SCHILBACH: Exactly. 00:38:52.740 --> 00:38:57.010 So essentially, all the other things that we said previously 00:38:57.010 --> 00:38:58.740 we are assuming away, for example, things 00:38:58.740 --> 00:39:01.680 like anxiety over certain outcomes, worries, stress, 00:39:01.680 --> 00:39:02.730 and so on. 00:39:02.730 --> 00:39:05.976 I'm also assuming away regret. 00:39:05.976 --> 00:39:08.035 I'm assuming away the gains and losses. 00:39:08.035 --> 00:39:09.660 So essentially, anything we said before 00:39:09.660 --> 00:39:11.190 is essentially just stripped away 00:39:11.190 --> 00:39:13.470 and simplified in some sense and saying, 00:39:13.470 --> 00:39:15.840 we can explain a lot of behaviors just using 00:39:15.840 --> 00:39:18.180 the concavity of the utility function. 00:39:18.180 --> 00:39:19.758 Now, I have one example for you. 00:39:19.758 --> 00:39:21.300 And I think, I encourage, you sort of 00:39:21.300 --> 00:39:23.190 for any of these kinds of assumptions or kind 00:39:23.190 --> 00:39:26.288 of functions or things that you see in economics, 00:39:26.288 --> 00:39:28.080 it's worth sort of looking out in the world 00:39:28.080 --> 00:39:30.960 what people are actually doing and trying to see 00:39:30.960 --> 00:39:33.408 is that actually compatible with people, with behavior 00:39:33.408 --> 00:39:34.450 that we see in the world. 00:39:34.450 --> 00:39:36.460 And here's sort of one example. 00:39:36.460 --> 00:39:39.780 So I actually don't think this is irrational behavior. 00:39:39.780 --> 00:39:43.170 And that's actually a good example of so 00:39:43.170 --> 00:39:46.540 what we might confuse with irrational behaviors. 00:39:46.540 --> 00:39:51.028 So I guess what we see is that expected utility has 00:39:51.028 --> 00:39:53.070 a lot of trouble explaining this behavior, right? 00:39:53.070 --> 00:39:55.770 Because essentially, you spent like $5 on those lotteries. 00:39:55.770 --> 00:39:57.330 I'm offering you $10. 00:39:57.330 --> 00:39:59.310 So you get twice as many tickets. 00:39:59.310 --> 00:40:01.570 So your probability of winning will be twice as high. 00:40:01.570 --> 00:40:04.200 Presumably, you prefer winning or losing. 00:40:04.200 --> 00:40:06.003 So, therefore, you should obviously 00:40:06.003 --> 00:40:07.920 take that deal unless there's some transaction 00:40:07.920 --> 00:40:09.180 costs and the like. 00:40:09.180 --> 00:40:10.950 People are not doing that. 00:40:10.950 --> 00:40:14.010 The main reason that's mentioned here is regret. 00:40:14.010 --> 00:40:16.140 Now, what the person was saying here 00:40:16.140 --> 00:40:18.450 is these are perhaps irrational decisions. 00:40:18.450 --> 00:40:19.950 I actually don't think that's right. 00:40:19.950 --> 00:40:22.770 Essentially, it's just we cannot rationalize the decision that 00:40:22.770 --> 00:40:26.670 we see with expected utility in the sense that it looks like 00:40:26.670 --> 00:40:28.590 the person behaves in irrational ways, 00:40:28.590 --> 00:40:31.140 but the person may just have regret aversion, 00:40:31.140 --> 00:40:33.780 something that essentially is not in the utility function. 00:40:33.780 --> 00:40:35.880 We sort of modeled it in the wrong way. 00:40:35.880 --> 00:40:37.650 And sort of, by not capturing this, 00:40:37.650 --> 00:40:39.670 we might miss certain behaviors. 00:40:39.670 --> 00:40:42.090 Now, we're going to talk a lot about-- not about lotteries 00:40:42.090 --> 00:40:42.450 right now. 00:40:42.450 --> 00:40:44.658 We're going to get back to this a little bit in terms 00:40:44.658 --> 00:40:47.047 of why people engage in risk. 00:40:47.047 --> 00:40:49.380 But I just want to be clear on what we're assuming here. 00:40:49.380 --> 00:40:50.838 We're assuming a lot of stuff away, 00:40:50.838 --> 00:40:54.600 and I want you to be aware of that. 00:40:54.600 --> 00:40:57.420 There's another question which actually 00:40:57.420 --> 00:41:01.762 the question or the video did not sort of try to tackle, 00:41:01.762 --> 00:41:03.720 which is why are people playing these lotteries 00:41:03.720 --> 00:41:05.070 in the first place. 00:41:05.070 --> 00:41:07.210 Why engage in the lotteries in the first place? 00:41:07.210 --> 00:41:09.815 In some sense, that wasn't clear either. 00:41:09.815 --> 00:41:11.440 Again, we're going to get back to that. 00:41:11.440 --> 00:41:13.977 But the point of the video was to show you 00:41:13.977 --> 00:41:16.560 that, in some sense, these are a bunch of assumptions that are 00:41:16.560 --> 00:41:18.205 in the expected utility model. 00:41:18.205 --> 00:41:19.830 Not all of these assumptions are right. 00:41:19.830 --> 00:41:23.028 And you know, we want to be sort of aware of that. 00:41:23.028 --> 00:41:25.320 But let me sort of just summarize what I just told you. 00:41:25.320 --> 00:41:29.650 And this, in some sense, is recap of 14.01 if you want, 00:41:29.650 --> 00:41:32.310 which I think in part you also discussed in recitation. 00:41:32.310 --> 00:41:34.470 Or there's like a handout from 14.01 00:41:34.470 --> 00:41:37.620 that you can look at to study it in more details. 00:41:37.620 --> 00:41:39.330 So many important economic choices 00:41:39.330 --> 00:41:43.530 involve risk and people are risk averse in many contexts. 00:41:43.530 --> 00:41:47.160 The expected utility model is a workhorse model 00:41:47.160 --> 00:41:50.120 of the economics for studying risk. 00:41:50.120 --> 00:41:51.870 And the way it's done is, essentially, one 00:41:51.870 --> 00:41:54.540 takes the weighted average of utilities from final outcomes. 00:41:54.540 --> 00:41:57.270 That's what matters for assessing outcomes. 00:41:57.270 --> 00:41:58.033 OK. 00:41:58.033 --> 00:41:59.700 And so, now, we're going to see, OK, now 00:41:59.700 --> 00:42:01.560 taking that model very seriously, what 00:42:01.560 --> 00:42:02.430 can be explained? 00:42:02.430 --> 00:42:06.900 And what are perhaps the limits of doing so? 00:42:06.900 --> 00:42:09.210 And sort of risk aversion comes solely 00:42:09.210 --> 00:42:13.270 and exclusively from the concavity of the utility 00:42:13.270 --> 00:42:13.770 function. 00:42:13.770 --> 00:42:16.680 There's no other reasons to avoid risk. 00:42:16.680 --> 00:42:20.160 Then essentially your utility function is concave. 00:42:20.160 --> 00:42:20.760 OK. 00:42:20.760 --> 00:42:22.110 So now, how do we measure risk? 00:42:22.110 --> 00:42:23.910 And that's, again, sort of definitions 00:42:23.910 --> 00:42:25.512 that economists use. 00:42:25.512 --> 00:42:26.970 When you think about risk aversion, 00:42:26.970 --> 00:42:27.870 how do you measure this? 00:42:27.870 --> 00:42:30.120 Well, you measure it essentially through the concavity 00:42:30.120 --> 00:42:32.802 of the utility function, which is, as you were saying earlier, 00:42:32.802 --> 00:42:35.010 it's coming from the second derivative of the utility 00:42:35.010 --> 00:42:35.820 function. 00:42:35.820 --> 00:42:38.340 There's two main measures that economists use. 00:42:38.340 --> 00:42:40.860 There's sort of the absolute or the coefficient 00:42:40.860 --> 00:42:43.830 of absolute risk aversion. 00:42:43.830 --> 00:42:45.570 We call that r. 00:42:45.570 --> 00:42:48.805 It's essentially taking the second derivative, 00:42:48.805 --> 00:42:49.930 which tends to be negative. 00:42:49.930 --> 00:42:52.770 So we take the negative of that. 00:42:52.770 --> 00:42:54.720 We scale it by the first derivative. 00:42:54.720 --> 00:42:58.250 That's essentially to make it insensitive to 00:42:58.250 --> 00:43:01.440 if you multiply the utility function by a constant. 00:43:01.440 --> 00:43:04.040 Presumably, that doesn't change anything to your choices. 00:43:04.040 --> 00:43:06.490 So you risk aversion should not change. 00:43:06.490 --> 00:43:09.900 And, therefore, we sort of have to normalize 00:43:09.900 --> 00:43:12.920 or we divide by the first derivative. 00:43:12.920 --> 00:43:15.780 A second version of that, or an alternative version, 00:43:15.780 --> 00:43:19.440 is the coefficient of relative risk aversion, 00:43:19.440 --> 00:43:22.620 which essentially is-- 00:43:22.620 --> 00:43:23.790 we call it-- gamma. 00:43:23.790 --> 00:43:27.900 Gamma is x, the wealth outcome that we 00:43:27.900 --> 00:43:32.040 look at times r times the coefficient of absolute risk 00:43:32.040 --> 00:43:32.850 aversion. 00:43:32.850 --> 00:43:37.980 It's the elasticity of the slope of the utility function, which 00:43:37.980 --> 00:43:39.150 I've written out here. 00:43:39.150 --> 00:43:41.040 And sort of one very nice property of this-- 00:43:41.040 --> 00:43:42.580 and again, that's a definition. 00:43:42.580 --> 00:43:43.740 There's not much to argue with this. 00:43:43.740 --> 00:43:45.448 This is just how economists measure this. 00:43:45.448 --> 00:43:47.320 One nice property of this is, if you 00:43:47.320 --> 00:43:49.900 look at portfolio models or the like, 00:43:49.900 --> 00:43:53.920 one implications of constant relative risk aversion, which 00:43:53.920 --> 00:43:56.140 I'm going to show you a function of in a bit, 00:43:56.140 --> 00:43:59.008 is that people with constant relative risk aversion 00:43:59.008 --> 00:44:01.300 invest a constant share of their wealth in risky assets 00:44:01.300 --> 00:44:03.490 regardless of their level of wealth. 00:44:03.490 --> 00:44:08.560 That's a main sort of result from a finance or portfolio 00:44:08.560 --> 00:44:09.880 models. 00:44:09.880 --> 00:44:11.958 In some sense, that's sort of irrelevant for you. 00:44:11.958 --> 00:44:13.750 These are just definitions in the sense of, 00:44:13.750 --> 00:44:15.640 if you wanted to measure risk aversion, 00:44:15.640 --> 00:44:20.400 this is what economists have used mostly, OK? 00:44:24.370 --> 00:44:26.680 Now, if I give you this definition, 00:44:26.680 --> 00:44:28.210 how would you actually measure this? 00:44:28.210 --> 00:44:30.310 If you wanted to know my risk aversion, 00:44:30.310 --> 00:44:33.590 how would you do that? 00:44:33.590 --> 00:44:37.390 And so let me give you actually a utility function here. 00:44:37.390 --> 00:44:40.600 So let me give you actually two utility functions. 00:44:40.600 --> 00:44:42.430 Here's just examples of one example 00:44:42.430 --> 00:44:46.570 of the constant absolute risk aversion function 00:44:46.570 --> 00:44:48.130 that you see here. 00:44:48.130 --> 00:44:50.920 Or a Constant Relative Risk Aversion, CRRA, this 00:44:50.920 --> 00:44:52.398 is what we mostly use. 00:44:52.398 --> 00:44:54.190 So that's just the definition of a function 00:44:54.190 --> 00:44:56.750 that has the property that it has constant relative risk 00:44:56.750 --> 00:44:57.250 aversion. 00:44:57.250 --> 00:44:59.500 You can sort of verify that. 00:44:59.500 --> 00:45:02.560 We're going to focus here on CRRA functions, which are sort 00:45:02.560 --> 00:45:04.760 of what economists mostly use. 00:45:04.760 --> 00:45:07.150 So now, if I told you this is my utility function, 00:45:07.150 --> 00:45:08.960 my totally function looks like this, 00:45:08.960 --> 00:45:13.150 now how would you estimate my risk aversion? 00:45:19.100 --> 00:45:21.728 AUDIENCE: [? I ?] can give you two gambles and then 00:45:21.728 --> 00:45:23.372 [INAUDIBLE]? 00:45:23.372 --> 00:45:24.330 FRANK SCHILBACH: Right. 00:45:24.330 --> 00:45:27.120 So could you give me essentially choices 00:45:27.120 --> 00:45:30.660 of outcomes that have essentially some uncertainty 00:45:30.660 --> 00:45:32.610 or different risk involved. 00:45:32.610 --> 00:45:36.870 And then I'll give you the choices. 00:45:36.870 --> 00:45:38.590 If I say I prefer one over the other, 00:45:38.590 --> 00:45:39.840 can you tell what my gamma is? 00:45:45.456 --> 00:45:46.357 AUDIENCE: No. 00:45:46.357 --> 00:45:47.940 FRANK SCHILBACH: What can you tell me? 00:45:47.940 --> 00:45:48.780 Or what can you say? 00:46:02.145 --> 00:46:05.210 AUDIENCE: I guess you can say the [? extent, ?] 00:46:05.210 --> 00:46:07.370 but maybe not [INAUDIBLE] value [INAUDIBLE].. 00:46:07.370 --> 00:46:07.640 FRANK SCHILBACH: Yeah. 00:46:07.640 --> 00:46:09.270 You can put some bounds on it, right? 00:46:09.270 --> 00:46:10.620 So I'm going to show you this in a second. 00:46:10.620 --> 00:46:12.080 But essentially, if I say I prefer 00:46:12.080 --> 00:46:13.740 one option over the other, you're 00:46:13.740 --> 00:46:15.740 going to have gamma on the left-hand side, gamma 00:46:15.740 --> 00:46:18.407 on the right-hand side, and give you some equations, essentially 00:46:18.407 --> 00:46:19.400 some inequality. 00:46:19.400 --> 00:46:22.425 And then if you solve that equation, 00:46:22.425 --> 00:46:24.050 you're going to get some bound on gamma 00:46:24.050 --> 00:46:27.350 that sort of essentially tells you below or above. 00:46:27.350 --> 00:46:29.990 Or my risk aversion must be below or above 00:46:29.990 --> 00:46:32.210 a certain number. 00:46:32.210 --> 00:46:33.190 What else could we do? 00:46:41.730 --> 00:46:42.230 Yes? 00:46:42.230 --> 00:46:44.200 AUDIENCE: [? Ask ?] [? them ?] [? when they're ?] [INAUDIBLE]?? 00:46:44.200 --> 00:46:44.740 FRANK SCHILBACH: Exactly. 00:46:44.740 --> 00:46:46.810 And that's what's called the certainty 00:46:46.810 --> 00:46:50.680 or-- so the simplest way of doing that is to say, here's 00:46:50.680 --> 00:46:53.650 a lottery between some gains or losses 00:46:53.650 --> 00:46:55.510 or two gains with certain probabilities. 00:46:55.510 --> 00:46:56.835 There's some risk involved. 00:46:56.835 --> 00:46:58.210 And then we could ask you, what's 00:46:58.210 --> 00:47:01.360 the amount that makes you indifferent between receiving 00:47:01.360 --> 00:47:05.167 that amount for sure and the gamble that I'm offering you? 00:47:05.167 --> 00:47:07.000 Now, that's called the certainty equivalent. 00:47:07.000 --> 00:47:08.800 Essentially, it's the amount of money, 00:47:08.800 --> 00:47:12.460 if I have a certain gamble, what's the amount of money 00:47:12.460 --> 00:47:15.070 that, if you get it for sure, makes you exactly 00:47:15.070 --> 00:47:18.160 indifferent between that amount of money for sure 00:47:18.160 --> 00:47:20.890 and the gamble, which is uncertain, right? 00:47:20.890 --> 00:47:23.080 So if we then had the certainty equivalent, 00:47:23.080 --> 00:47:24.910 now you could essentially just back out 00:47:24.910 --> 00:47:29.020 what my gamma is by just solving for gamma that's there. 00:47:29.020 --> 00:47:31.750 Let me actually show you that. 00:47:31.750 --> 00:47:33.413 There's another thing that we could do. 00:47:33.413 --> 00:47:34.330 What else could we do? 00:47:34.330 --> 00:47:37.090 So we said, OK, if you gamble, choices 00:47:37.090 --> 00:47:39.310 between different gambles, I could ask you 00:47:39.310 --> 00:47:40.720 for certainty equivalent. 00:47:40.720 --> 00:47:43.030 Now, these are all kind of lab ways of doing this. 00:47:43.030 --> 00:47:44.530 But if you looked in the real world, 00:47:44.530 --> 00:47:46.180 if you try to sort of figure out in the real world 00:47:46.180 --> 00:47:47.638 how are people making these choices 00:47:47.638 --> 00:47:49.990 or choices in the world, what kinds of choices could 00:47:49.990 --> 00:47:52.960 you observe to figure out what people's gamma is? 00:47:52.960 --> 00:47:54.460 Yes. 00:47:54.460 --> 00:47:56.627 AUDIENCE: Could you sell them insurance or an option 00:47:56.627 --> 00:47:58.752 to mitigate their risk and figure out how much they 00:47:58.752 --> 00:47:59.780 value that mitigation? 00:47:59.780 --> 00:48:00.310 FRANK SCHILBACH: Exactly. 00:48:00.310 --> 00:48:01.000 That's exactly right. 00:48:01.000 --> 00:48:02.917 And that's exactly what we're going to discuss 00:48:02.917 --> 00:48:04.990 and what people have done. 00:48:04.990 --> 00:48:08.200 Now, it's a little bit tricky that in usually cases, 00:48:08.200 --> 00:48:11.410 if I just ask you what insurance have you chosen, 00:48:11.410 --> 00:48:14.110 it's a little tricky to figure out what your gamma actually 00:48:14.110 --> 00:48:17.050 is because I don't know what options you had, right? 00:48:17.050 --> 00:48:20.290 So what I need is essentially a choice set between-- 00:48:20.290 --> 00:48:21.810 suppose I'm selling you insurance. 00:48:21.810 --> 00:48:23.560 In particular, what I'm going to show you, 00:48:23.560 --> 00:48:25.985 I think, next time is Justin Sydnor's paper, 00:48:25.985 --> 00:48:27.610 where people can choose between-- these 00:48:27.610 --> 00:48:30.910 are customers in a certain home insurance where 00:48:30.910 --> 00:48:33.978 people have choices between different deductibles, right? 00:48:33.978 --> 00:48:36.520 And now, I can essentially say, if I choose a high deductible 00:48:36.520 --> 00:48:38.260 versus a low deductible, essentially 00:48:38.260 --> 00:48:41.140 it's implicitly you're choosing the risk exposure 00:48:41.140 --> 00:48:42.910 that you have for price. 00:48:42.910 --> 00:48:46.338 So in Sydnor's case, there's four different options 00:48:46.338 --> 00:48:47.380 that people offer to him. 00:48:47.380 --> 00:48:49.578 That was essentially both the choice set, 00:48:49.578 --> 00:48:52.120 like what are the choices that people offered-- in this case, 00:48:52.120 --> 00:48:54.310 I guess they're often offered four choices-- 00:48:54.310 --> 00:48:57.640 and then the actual choice that they made. 00:48:57.640 --> 00:48:59.660 Again, that's not going to give you 00:48:59.660 --> 00:49:02.920 an exact gamma in terms of pinning it down exactly what it 00:49:02.920 --> 00:49:05.290 is because there's four different inequalities that you 00:49:05.290 --> 00:49:06.880 get from these choices. 00:49:06.880 --> 00:49:09.100 But you can actually bound, as it turns out, 00:49:09.100 --> 00:49:12.490 people's risk aversion pretty well using 00:49:12.490 --> 00:49:14.930 those kinds of choices. 00:49:14.930 --> 00:49:15.430 Exactly. 00:49:15.430 --> 00:49:18.040 So that's what we have here is certain equivalence, choices 00:49:18.040 --> 00:49:20.330 from gambles, and insurance choices. 00:49:20.330 --> 00:49:23.650 So let's start with certainty equivalent. 00:49:23.650 --> 00:49:29.350 So suppose your wealth equals either to $50,000 to $100,000 00:49:29.350 --> 00:49:31.660 each with probability 50%. 00:49:31.660 --> 00:49:34.837 Suppose that's essentially there's 00:49:34.837 --> 00:49:35.920 lots of risk in your life. 00:49:35.920 --> 00:49:38.890 Either it's 50,000, 100,000, starting 00:49:38.890 --> 00:49:40.570 tomorrow you're going to find out 00:49:40.570 --> 00:49:42.250 the chance of that is 50% each. 00:49:42.250 --> 00:49:43.750 Now, of course, that's hypothetical, 00:49:43.750 --> 00:49:46.330 but let's suppose that for a second. 00:49:46.330 --> 00:49:49.970 You're expected wealth then, of course, is 75,000. 00:49:49.970 --> 00:49:52.660 Now, what guaranteed amount, the certainty equivalent, 00:49:52.660 --> 00:49:56.000 of the WCE do you find equally desirable? 00:49:56.000 --> 00:49:57.850 If I could make all of your risk go away 00:49:57.850 --> 00:49:59.642 and just say I'm giving you a fixed amount, 00:49:59.642 --> 00:50:01.730 what amount would you choose? 00:50:01.730 --> 00:50:11.070 Now, when you do that, essentially, 00:50:11.070 --> 00:50:14.517 if you give me an amount W, a certain equivalent, 00:50:14.517 --> 00:50:16.350 that gives me essentially an equation, which 00:50:16.350 --> 00:50:18.270 is the utility from the certainty equivalent, 00:50:18.270 --> 00:50:22.380 by definition, since you just told me that, 00:50:22.380 --> 00:50:24.420 must be the same as the weighted average 00:50:24.420 --> 00:50:26.315 of the utility of 50,000 and the ultimately 00:50:26.315 --> 00:50:30.420 of 100,000 with probability 50% each, right? 00:50:30.420 --> 00:50:32.940 And once you do that, now you get essentially some nonlinear 00:50:32.940 --> 00:50:37.230 equation that depends on gamma that you can solve. 00:50:37.230 --> 00:50:42.060 Perhaps not in closed form, but you can essentially 00:50:42.060 --> 00:50:47.660 figure out what the answer is in Mathematica or the like, OK? 00:50:47.660 --> 00:50:53.990 Now, as it turns out, now you can solve for this. 00:50:53.990 --> 00:50:57.310 And the implied values of gamma I've written down for here. 00:50:57.310 --> 00:51:02.765 So if you tell me here 70,000, gamma is 1. 00:51:02.765 --> 00:51:04.920 If you tell me 66,000, it's 2. 00:51:04.920 --> 00:51:06.190 58,000, it's 5. 00:51:06.190 --> 00:51:08.330 53,000, it's 10. 00:51:08.330 --> 00:51:13.040 51,000, it's 30. 00:51:13.040 --> 00:51:15.020 Who would say anything below 10? 00:51:24.810 --> 00:51:27.508 Yes, no? 00:51:27.508 --> 00:51:28.300 What would you say? 00:51:28.300 --> 00:51:30.430 AUDIENCE: By below, you mean less than 10? 00:51:30.430 --> 00:51:32.728 FRANK SCHILBACH: So value of gamma less than 10, yes. 00:51:32.728 --> 00:51:33.770 AUDIENCE: Yeah, for sure. 00:51:33.770 --> 00:51:35.062 FRANK SCHILBACH: Yes, for sure. 00:51:35.062 --> 00:51:38.140 That seems very reasonable. 00:51:38.140 --> 00:51:43.450 If you think about value of 30, if you had a value of 30, 00:51:43.450 --> 00:51:46.073 you probably would not leave the house ever in some sense. 00:51:46.073 --> 00:51:47.740 You would not come to class or something 00:51:47.740 --> 00:51:49.780 because you're worried about some stuff falling 00:51:49.780 --> 00:51:51.610 on your head or the like. 00:51:51.610 --> 00:51:55.150 Because, again, let me show you what the lottery was. 00:51:55.150 --> 00:52:00.340 The lottery was between 50,000 100,000 with 50% chance. 00:52:00.340 --> 00:52:02.290 If you tell me you're indifferent between that 00:52:02.290 --> 00:52:05.170 and 51,000 for sure, you're essentially 00:52:05.170 --> 00:52:09.730 valuing this small increment coming from 50,000 to 51,209. 00:52:09.730 --> 00:52:12.790 That's $1,209. 00:52:12.790 --> 00:52:17.260 You value that a lot compared to the 50% chance 00:52:17.260 --> 00:52:21.310 of actually getting $100,000. 00:52:21.310 --> 00:52:24.580 So we sort of think that, when looking at these large scale 00:52:24.580 --> 00:52:26.710 choices, economists often assume, I think, 00:52:26.710 --> 00:52:30.880 that people's gamma is somewhere between 0 and 2, OK? 00:52:30.880 --> 00:52:33.370 So somewhere maybe 70,000, maybe even 00:52:33.370 --> 00:52:35.737 lower than that, maybe 66,000, these 00:52:35.737 --> 00:52:38.320 are sort of reasonable choices that we think people are making 00:52:38.320 --> 00:52:41.920 or you see people making in their lives. 00:52:41.920 --> 00:52:44.695 Anything above that seems like it's just not right 00:52:44.695 --> 00:52:46.570 because, in some sense, that's not how people 00:52:46.570 --> 00:52:48.010 behave in the real world. 00:52:48.010 --> 00:52:50.950 People are comfortable with at least some risk in their life 00:52:50.950 --> 00:52:52.430 when you look at them. 00:52:52.430 --> 00:52:55.030 So the broad lesson is that choices involving large scale 00:52:55.030 --> 00:53:01.930 risk suggests that gamma can't be too large, OK? 00:53:04.860 --> 00:53:06.030 Now, second we can say-- 00:53:06.030 --> 00:53:08.388 OK, so those are large scale choices. 00:53:08.388 --> 00:53:10.680 Now, we're going to look at sort of small scale choices 00:53:10.680 --> 00:53:15.450 using small gambles as [? Deckson ?] was just 00:53:15.450 --> 00:53:16.500 alluding to. 00:53:16.500 --> 00:53:19.890 So here's a choice involving a small scale gamble. 00:53:19.890 --> 00:53:26.280 What if you had a 50-50 bet to win $11 and lose $10? 00:53:26.280 --> 00:53:27.420 Who would take that bet? 00:53:33.900 --> 00:53:36.580 Who would not take it? 00:53:36.580 --> 00:53:37.210 OK. 00:53:37.210 --> 00:53:41.860 So suppose you know there's a question kind of like, follow 00:53:41.860 --> 00:53:46.210 those questions, now, since your utility is not 00:53:46.210 --> 00:53:48.940 necessarily linear, we need to know what your wealth is. 00:53:48.940 --> 00:53:50.650 Suppose it's 20,000, but you can choose 00:53:50.650 --> 00:53:52.120 all sorts of other numbers. 00:53:52.120 --> 00:53:54.920 And you turn down a 50-50 bet to win-- 00:53:54.920 --> 00:53:56.930 this is 110 and lose 100. 00:53:56.930 --> 00:53:59.170 You could do this for 11 and 10 as well. 00:53:59.170 --> 00:54:02.410 What can we learn now about your gamma? 00:54:02.410 --> 00:54:04.150 And this is what I was saying earlier. 00:54:04.150 --> 00:54:06.370 Now, it's essentially, if you turn down this bet, 00:54:06.370 --> 00:54:09.700 it must be that having 20,000, which is the status quo if you 00:54:09.700 --> 00:54:11.770 turn down the bet, the utility of that 00:54:11.770 --> 00:54:19.810 is larger than 50% of 20,000 plus 110 plus 0.5 times 00:54:19.810 --> 00:54:21.880 the utility of 20,000 minus 100. 00:54:21.880 --> 00:54:25.690 And again, I can sort of then plug in the utility function 00:54:25.690 --> 00:54:28.240 and essentially solve for gamma. 00:54:28.240 --> 00:54:31.330 Now, if you solve for gamma-- 00:54:31.330 --> 00:54:34.330 and some of the next problem set is 00:54:34.330 --> 00:54:36.640 doing some of that-- is essentially 00:54:36.640 --> 00:54:41.980 rejecting this bet is implying that gamma is larger than 18. 00:54:41.980 --> 00:54:44.260 Now, 18 is actually not that large. 00:54:44.260 --> 00:54:46.660 But surely, 18 is larger than 2. 00:54:46.660 --> 00:54:48.910 And we just sort of agreed earlier on 00:54:48.910 --> 00:54:51.520 that gamma should be somewhere below 10, 00:54:51.520 --> 00:54:55.120 presumably somewhere around 2 or maybe 1. 00:54:55.120 --> 00:54:57.580 So what we get here now is, when you look at large scale 00:54:57.580 --> 00:55:00.040 choices, it looks like people's gamma is 00:55:00.040 --> 00:55:04.390 somewhere between 0 and 2, perhaps below 5 or something, 00:55:04.390 --> 00:55:06.010 but surely not above 10. 00:55:06.010 --> 00:55:08.290 When you look at small scale choices that 00:55:08.290 --> 00:55:10.100 seem pretty reasonable-- and many of you 00:55:10.100 --> 00:55:14.017 seem to agree that you might not want to take certain bets. 00:55:14.017 --> 00:55:15.850 Maybe you're credit constrained or the like. 00:55:15.850 --> 00:55:20.000 But in any case, it looks like people's gamma is really large. 00:55:20.000 --> 00:55:20.500 OK. 00:55:20.500 --> 00:55:22.125 And so, now, the question is, how do we 00:55:22.125 --> 00:55:23.290 sort of reconcile this? 00:55:23.290 --> 00:55:27.790 How do we put these things together? 00:55:27.790 --> 00:55:31.900 Now, Matthew Rabin has written a paper of this and sort of says, 00:55:31.900 --> 00:55:35.200 this is not just sort of an intuitive argument. 00:55:35.200 --> 00:55:38.050 This is a paper in Econometrica from 2000. 00:55:38.050 --> 00:55:41.710 But in fact, he sort of proves that, when 00:55:41.710 --> 00:55:44.920 people reject small scale gambles, that just 00:55:44.920 --> 00:55:48.640 sort of implies crazy stuff for large scale choices, 00:55:48.640 --> 00:55:51.760 essentially stuff that just seems completely implausible. 00:55:51.760 --> 00:55:53.980 And essentially, he, under minimal assumptions, 00:55:53.980 --> 00:55:58.700 proves that this doesn't make a lot of sense. 00:55:58.700 --> 00:56:01.870 Now, what do I mean by this is and what do we learn from this 00:56:01.870 --> 00:56:04.210 is that essentially the marginal utility of money 00:56:04.210 --> 00:56:08.890 must decrease extremely rapidly if you sort of take 00:56:08.890 --> 00:56:11.500 this model seriously. 00:56:11.500 --> 00:56:13.990 He does this under new assumptions about the utility 00:56:13.990 --> 00:56:14.490 function. 00:56:14.490 --> 00:56:16.115 So it's not just something special case 00:56:16.115 --> 00:56:17.830 that he sort of doctored together 00:56:17.830 --> 00:56:20.560 with some special assumptions of the utility function. 00:56:20.560 --> 00:56:22.570 The only thing, in fact, that he's assuming 00:56:22.570 --> 00:56:28.580 is that the utility function is weakly concave. 00:56:28.580 --> 00:56:29.080 OK. 00:56:29.080 --> 00:56:33.880 And so here's the example that was also in your reading. 00:56:33.880 --> 00:56:37.180 Suppose there's Johnny, who is a risk averse expected 00:56:37.180 --> 00:56:39.340 utility maximizer where the utility 00:56:39.340 --> 00:56:41.380 function or the second derivative 00:56:41.380 --> 00:56:43.960 is smaller or equal than 0, meaning 00:56:43.960 --> 00:56:48.070 that essentially his utility function is weakly concave. 00:56:48.070 --> 00:56:52.960 Suppose that person turns down a 50-50 gamble of losing $10 00:56:52.960 --> 00:56:55.833 and gaining $11 for any level of wealth. 00:56:55.833 --> 00:56:58.000 That assumption at the end, for any level of wealth, 00:56:58.000 --> 00:57:00.800 is kind of important, but actually not that important. 00:57:00.800 --> 00:57:03.430 You can sort of relax that as well. 00:57:03.430 --> 00:57:06.430 For our purposes, we can sort of mostly ignore it. 00:57:06.430 --> 00:57:08.710 Now, what's the biggest Y such that we 00:57:08.710 --> 00:57:14.590 know Johnny will turn down a 50-50, lose 100, win Y bet? 00:57:14.590 --> 00:57:16.210 So here are the answers. 00:57:16.210 --> 00:57:20.372 And what's the correct answer? 00:57:20.372 --> 00:57:22.300 AUDIENCE: G. 00:57:22.300 --> 00:57:25.570 FRANK SCHILBACH: G. And why is that? 00:57:25.570 --> 00:57:30.350 Or can somebody explain what's going on? 00:57:34.970 --> 00:57:35.470 Yes. 00:57:39.710 --> 00:57:41.710 AUDIENCE: Is it because he will reject 00:57:41.710 --> 00:57:43.290 this bet for any level of wealth, 00:57:43.290 --> 00:57:48.260 so that kind of implies that he's not 00:57:48.260 --> 00:57:50.413 able to accept any level of risk? 00:57:50.413 --> 00:57:51.580 FRANK SCHILBACH: No, no, no. 00:57:51.580 --> 00:57:54.130 I think that's just because, for the iteration forward 00:57:54.130 --> 00:57:57.010 in the proof of the thing, he needs 00:57:57.010 --> 00:57:59.420 to sort make that argument. 00:57:59.420 --> 00:58:01.400 But in fact, that's not essential. 00:58:01.400 --> 00:58:03.130 There's some restrictions to that. 00:58:03.130 --> 00:58:05.620 You can prove the same thing maybe not as 00:58:05.620 --> 00:58:07.838 stark in terms of a result, but this is just 00:58:07.838 --> 00:58:09.130 because he's iterating forward. 00:58:09.130 --> 00:58:10.713 He needs to sort of prove the sequence 00:58:10.713 --> 00:58:13.350 of utilities that derives. 00:58:13.350 --> 00:58:15.100 But it's actually not necessarily central. 00:58:21.000 --> 00:58:21.870 Yes. 00:58:21.870 --> 00:58:26.073 AUDIENCE: I think the paper argued that Johnny [INAUDIBLE] 00:58:26.073 --> 00:58:30.248 implied that the [INAUDIBLE] [? utility ?] [INAUDIBLE] very 00:58:30.248 --> 00:58:32.658 [? rapidly decreasing, ?] [? which means that ?] between 00:58:32.658 --> 00:58:36.915 that he will [INAUDIBLE]. 00:58:36.915 --> 00:58:37.790 FRANK SCHILBACH: Yes. 00:58:37.790 --> 00:58:39.470 So what's happening here is that-- 00:58:41.990 --> 00:58:43.910 so let's sort of start very simply. 00:58:43.910 --> 00:58:47.260 Let's start with Johnny's first choice 00:58:47.260 --> 00:58:51.280 that says he rejects the bet, which means essentially 00:58:51.280 --> 00:58:53.800 on the right-hand side is utility of status quo, 00:58:53.800 --> 00:58:55.840 essentially just utility if w. 00:58:55.840 --> 00:58:58.735 On the left-hand side is 50% chance of winning $11 00:58:58.735 --> 00:59:02.020 and 50% chance of losing $10. 00:59:02.020 --> 00:59:04.660 Now, you can sort of multiply this 00:59:04.660 --> 00:59:08.860 by 2 and rearrange, which gives you the second line. 00:59:08.860 --> 00:59:11.800 Essentially, that says that the increase in utility going 00:59:11.800 --> 00:59:17.110 from w to w plus 11 is smaller than the increase in utility 00:59:17.110 --> 00:59:22.280 going from w minus 10 to w. 00:59:22.280 --> 00:59:25.390 OK, that's just the left-hand side and the right-hand side. 00:59:25.390 --> 00:59:28.550 I'm just rearranging terms. 00:59:28.550 --> 00:59:30.490 So what that means is that, again, 00:59:30.490 --> 00:59:31.990 like on the left-hand side, how much 00:59:31.990 --> 00:59:36.520 does the utility increase if I go from w to w plus 11? 00:59:36.520 --> 00:59:39.880 Essentially, if I add $11 from coming from w, 00:59:39.880 --> 00:59:45.670 that utility that he values by at most 10/11-- so each dollar 00:59:45.670 --> 00:59:47.620 that he gets on the left-hand side 00:59:47.620 --> 00:59:51.400 is valued at most 10/11 as much as the dollars between w 00:59:51.400 --> 00:59:54.010 minus 10 and w, right? 00:59:54.010 --> 00:59:57.558 So if you have $10 on the right, $11 on the left, 00:59:57.558 --> 01:00:00.100 you prefer the right-hand side over the left-hand side, which 01:00:00.100 --> 01:00:04.480 means each dollar must be valued more on the right-hand side. 01:00:04.480 --> 01:00:06.770 Put differently, the dollars on the left-hand side, 01:00:06.770 --> 01:00:10.850 that value is 10/11 of the dollars on the right-hand side, 01:00:10.850 --> 01:00:11.960 OK? 01:00:11.960 --> 01:00:14.720 So just to repeat again, on the right-hand side, 01:00:14.720 --> 01:00:16.250 we're adding $10. 01:00:16.250 --> 01:00:19.640 On the left-hand side, we are adding $11 01:00:19.640 --> 01:00:22.830 or subtracting-- we're adding $11 on left-hand side 01:00:22.830 --> 01:00:25.520 and we're subtracting $10 and the right-hand side. 01:00:25.520 --> 01:00:28.670 Now, since you prefer the thing or the thing 01:00:28.670 --> 01:00:30.260 on the right-hand side is larger, 01:00:30.260 --> 01:00:32.600 that must mean that each dollar on the right-hand side 01:00:32.600 --> 01:00:33.680 is worth more. 01:00:33.680 --> 01:00:37.202 It's 11/10 compared to the dollars on the left-hand side. 01:00:37.202 --> 01:00:39.410 Or put differently, each dollar on the left-hand side 01:00:39.410 --> 01:00:43.500 has value 10/11 of each dollar on the right-hand side. 01:00:43.500 --> 01:00:45.000 You can sort think about this a bit. 01:00:45.000 --> 01:00:47.440 But trust me, that is correct. 01:00:47.440 --> 01:00:50.280 Now, there's diminishing marginal utility. 01:00:50.280 --> 01:00:52.050 Essentially, concavity sort of says 01:00:52.050 --> 01:00:55.140 that the marginal dollar at w minus 10 01:00:55.140 --> 01:00:58.330 is at least as valuable as the marginal dollar at w. 01:00:58.330 --> 01:01:02.910 That's essentially just simple assumption of concavity, 01:01:02.910 --> 01:01:06.430 essentially just saying, there's diminishing marginal utility. 01:01:06.430 --> 01:01:09.360 So the lower the amount of wealth that you have, 01:01:09.360 --> 01:01:13.470 the weakly larger the marginal utility is. 01:01:13.470 --> 01:01:16.050 So the marginal utility at w minus 10 01:01:16.050 --> 01:01:19.710 is at least as large as the marginal utility at w. 01:01:19.710 --> 01:01:21.570 And that marginal utility for dollar 01:01:21.570 --> 01:01:26.850 is at least as valuable as the marginal utility at w plus 11. 01:01:26.850 --> 01:01:29.400 Now, sort of taken together, that means 01:01:29.400 --> 01:01:34.470 that Johnny values $1 at w plus 11 by, at most, 10/11 as 01:01:34.470 --> 01:01:39.000 much as he values the dollars at w minus 10. 01:01:39.000 --> 01:01:41.670 What does that mean is that if you go from minus 10 01:01:41.670 --> 01:01:46.650 to a plus 11 essentially the marginal dollar that you get 01:01:46.650 --> 01:01:51.420 is worth 10 11th as much for every $21 01:01:51.420 --> 01:01:53.880 that he increases his Wilson. 01:01:58.210 --> 01:02:04.540 So I think, given some of the confused faces I see, 01:02:04.540 --> 01:02:06.940 we might do some of this in recitation. 01:02:06.940 --> 01:02:10.150 But this is essentially simple algebra and using 01:02:10.150 --> 01:02:13.730 the minimal assumptions that I made. 01:02:13.730 --> 01:02:15.190 Now, you can do the same thing as 01:02:15.190 --> 01:02:17.203 like if the person were $21 richer. 01:02:17.203 --> 01:02:19.120 So essentially, now, I'm doing the same thing, 01:02:19.120 --> 01:02:22.330 just adding $21 on each side. 01:02:22.330 --> 01:02:24.070 I'm doing the exact same thing. 01:02:24.070 --> 01:02:28.420 And I'm going to get essentially the exact same thing. 01:02:28.420 --> 01:02:32.890 It's essentially saying that he values each dollar that he gets 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 01:02:38.110 --> 01:02:40.928 as he values the dollars at w minus 10. 01:02:40.928 --> 01:02:43.220 So what I'm essentially doing is I'm iterating forward. 01:02:43.220 --> 01:02:45.940 So I know the utility function is concave by sort 01:02:45.940 --> 01:02:47.020 of your first choice. 01:02:47.020 --> 01:02:49.030 I know that essentially [INAUDIBLE] utility 01:02:49.030 --> 01:02:51.982 is declining going on one side. 01:02:51.982 --> 01:02:54.190 So now, essentially taking this forward-- essentially 01:02:54.190 --> 01:02:59.080 saying, well, for every $21, you value each dollar by 10/11 01:02:59.080 --> 01:02:59.860 as much. 01:02:59.860 --> 01:03:01.360 So now, I'm saying, well, if you had 01:03:01.360 --> 01:03:07.090 $21 plus $21 is $42 plus $29 is $63, 01:03:07.090 --> 01:03:09.620 your marginal utility must be really declining very, 01:03:09.620 --> 01:03:11.060 very rapidly. 01:03:11.060 --> 01:03:14.380 So once you have a lot more money, then essentially you 01:03:14.380 --> 01:03:17.500 just don't care at all about any marginal dollar that you get. 01:03:17.500 --> 01:03:21.640 So you can do this by if the person was $42 richer. 01:03:21.640 --> 01:03:24.470 Essentially, you'd care about each dollar 5/6 as much. 01:03:24.470 --> 01:03:27.830 If it's $420, you care about it 3/20 as much. 01:03:27.830 --> 01:03:30.580 And if you were $840 richer, you care about it 01:03:30.580 --> 01:03:32.480 only 2/100 as much. 01:03:32.480 --> 01:03:34.480 Essentially, that's to say-- and this is exactly 01:03:34.480 --> 01:03:36.188 as you were saying-- the marginal utility 01:03:36.188 --> 01:03:38.950 plummets for substantial changes in lifetime wealth. 01:03:38.950 --> 01:03:42.430 So you care less than 2% about an additional dollar 01:03:42.430 --> 01:03:48.250 when you are $900 richer than you are right now. 01:03:48.250 --> 01:03:51.730 That doesn't feel right, but essentially it's 01:03:51.730 --> 01:03:55.840 a simple implication of what was just assumed. 01:03:55.840 --> 01:03:56.890 There's no magic here. 01:03:56.890 --> 01:03:59.830 This is very simple algebra and using 01:03:59.830 --> 01:04:01.930 very simple minor assumptions. 01:04:01.930 --> 01:04:04.660 But essentially, it's saying, if this person rejects this gamble 01:04:04.660 --> 01:04:07.570 as we just had, it follows-- 01:04:07.570 --> 01:04:10.090 and there's sort of complicated proofs in the paper. 01:04:10.090 --> 01:04:11.800 But it follows that, essentially, 01:04:11.800 --> 01:04:17.080 the additional for, if you give the person $900 more, 01:04:17.080 --> 01:04:19.630 the person values each dollar only 2% 01:04:19.630 --> 01:04:24.370 as much as when the person is $900 richer. 01:04:24.370 --> 01:04:27.130 And so then you look at these consequences. 01:04:27.130 --> 01:04:29.140 And you can read this in the Rabin and Thaler 01:04:29.140 --> 01:04:32.560 paper or the original Rabin paper if you like. 01:04:32.560 --> 01:04:35.943 Essentially, you get these absurd conclusions. 01:04:35.943 --> 01:04:37.360 If you look at the left-hand side, 01:04:37.360 --> 01:04:40.150 these are sort of like if an expected utility maximizer 01:04:40.150 --> 01:04:42.010 always turns down certain bets. 01:04:42.010 --> 01:04:43.840 On the left-hand side, it follows 01:04:43.840 --> 01:04:47.770 that he also turns on the bets on the right-hand side. 01:04:47.770 --> 01:04:51.890 And we think, you know, for example, 01:04:51.890 --> 01:04:54.820 if I told you losing $10 or gaining 01:04:54.820 --> 01:04:57.280 $11, that seems like a reasonable thing 01:04:57.280 --> 01:04:58.330 to reject perhaps. 01:04:58.330 --> 01:05:00.520 That seems like a thing that one might do. 01:05:00.520 --> 01:05:03.500 At least, you guys were saying that you might do that. 01:05:03.500 --> 01:05:05.080 Well, if that's the case, then you 01:05:05.080 --> 01:05:11.620 should also accept or reject the gamble of losing $100 01:05:11.620 --> 01:05:14.080 and gaining infinite amount of dollars. 01:05:14.080 --> 01:05:17.170 And that seems obviously absurd. 01:05:17.170 --> 01:05:22.030 And so that can't be really true. 01:05:22.030 --> 01:05:25.300 Now, what's going on here essentially 01:05:25.300 --> 01:05:28.540 is to say is that the utility function, as it 01:05:28.540 --> 01:05:32.200 is an expected utility, has trouble reconciling 01:05:32.200 --> 01:05:35.650 people's small scale choices and large scale choices. 01:05:35.650 --> 01:05:37.690 And it's similar to what we talked about, 01:05:37.690 --> 01:05:39.370 like exponential discounting. 01:05:39.370 --> 01:05:41.410 We only have one parameter here, which 01:05:41.410 --> 01:05:44.350 is gamma for both gains and losses 01:05:44.350 --> 01:05:46.150 and for all sorts of scales. 01:05:46.150 --> 01:05:49.570 And that parameter is just not able to fit people's choices 01:05:49.570 --> 01:05:50.560 in sensible ways. 01:05:50.560 --> 01:05:52.810 It seems to be people have small scale risk 01:05:52.810 --> 01:05:54.410 aversion in some sense. 01:05:54.410 --> 01:05:58.540 And it seems to be people are not incredibly risk averse 01:05:58.540 --> 01:06:00.490 for large amounts of money. 01:06:00.490 --> 01:06:04.180 And so, now, the expected utility model cannot match both 01:06:04.180 --> 01:06:06.430 of those things. 01:06:06.430 --> 01:06:11.050 That's essentially what the Rabin paper does. 01:06:11.050 --> 01:06:16.270 We'll talk about this in some slower reform in recitation 01:06:16.270 --> 01:06:17.680 to sort of go over this. 01:06:17.680 --> 01:06:19.690 But in some sense, the important part here 01:06:19.690 --> 01:06:21.550 is to understand the intuition. 01:06:21.550 --> 01:06:24.310 And intuition, essentially, is that, if there's 01:06:24.310 --> 01:06:28.270 curvature over very small scales or over very small stakes, 01:06:28.270 --> 01:06:30.940 it must be there's lots of curvature going forward 01:06:30.940 --> 01:06:32.200 over large scales. 01:06:32.200 --> 01:06:34.130 And that's just not plausible. 01:06:34.130 --> 01:06:36.130 Because, essentially, then people would just not 01:06:36.130 --> 01:06:39.400 value really, really large amounts. 01:06:39.400 --> 01:06:44.380 And we know that people do value money at least to some extent. 01:06:44.380 --> 01:06:47.200 Any questions on this overall? 01:06:52.470 --> 01:06:53.752 Yeah. 01:06:53.752 --> 01:06:57.810 AUDIENCE: [INAUDIBLE] I guess [INAUDIBLE] [? mimicked ?] 01:06:57.810 --> 01:06:59.850 the [INAUDIBLE]. 01:06:59.850 --> 01:07:02.783 I guess, does the [INAUDIBLE] hyperbolic model essentially 01:07:02.783 --> 01:07:05.800 almost [? work ?] [? here ?] where [INAUDIBLE] 01:07:05.800 --> 01:07:11.420 to [INAUDIBLE] singular [INAUDIBLE] if someone tried 01:07:11.420 --> 01:07:15.210 to do the long-term, short-term thing, [INAUDIBLE].. 01:07:15.210 --> 01:07:16.560 FRANK SCHILBACH: Yeah. 01:07:16.560 --> 01:07:18.690 So what we're going to do is-- so notice 01:07:18.690 --> 01:07:20.970 that, here, he was not assuming anything 01:07:20.970 --> 01:07:22.380 about the utility function. 01:07:22.380 --> 01:07:25.860 The only thing he was assuming, or Rabin was assuming here, 01:07:25.860 --> 01:07:30.480 is that the person is expected utility maximizer 01:07:30.480 --> 01:07:33.240 and that the utility function is weakly, not even 01:07:33.240 --> 01:07:35.370 strictly, concave. 01:07:35.370 --> 01:07:38.820 Now, what that means is you can't sort of just 01:07:38.820 --> 01:07:41.130 change the functional form. 01:07:41.130 --> 01:07:45.280 This is a general proof for any utility function that you use. 01:07:45.280 --> 01:07:47.350 So what you have to do now is either sort of say, 01:07:47.350 --> 01:07:49.770 well, there's some other assumptions 01:07:49.770 --> 01:07:54.690 wrong about expected utility in terms of weighting 01:07:54.690 --> 01:07:59.760 the probabilities or stuff like that that essentially 01:07:59.760 --> 01:08:00.885 can explain the phenomenon. 01:08:00.885 --> 01:08:04.120 It could be something about [INAUDIBLE] aversion and so on. 01:08:04.120 --> 01:08:05.532 These seem kind of unlikely. 01:08:05.532 --> 01:08:06.990 The most likely thing-- and this is 01:08:06.990 --> 01:08:08.782 what I'm going to talk about next week-- is 01:08:08.782 --> 01:08:12.480 Kahneman-Tversky's sort of loss aversion framework where you 01:08:12.480 --> 01:08:16.649 say, if you put different weight on gains versus losses, 01:08:16.649 --> 01:08:19.229 then essentially you have two parameters. 01:08:19.229 --> 01:08:22.830 You have one parameter about your risk aversion over gains. 01:08:22.830 --> 01:08:26.430 And you have a parameter that's steers kind of how you feel 01:08:26.430 --> 01:08:28.529 about losses compared to gains. 01:08:28.529 --> 01:08:31.140 So once you do that, then you have another degree of freedom. 01:08:31.140 --> 01:08:34.950 And you can explain a lot of [? favors ?] potentially. 01:08:34.950 --> 01:08:37.152 But that's kind of the equivalent of that exactly. 01:08:37.152 --> 01:08:38.819 But the difference here is that it's not 01:08:38.819 --> 01:08:41.236 coming through the utility function, the reason 01:08:41.236 --> 01:08:43.319 being that the problem is actually not the utility 01:08:43.319 --> 01:08:43.819 function. 01:08:43.819 --> 01:08:46.830 Because as I said, there's actually no assumption here 01:08:46.830 --> 01:08:49.080 that can even be changed because it's 01:08:49.080 --> 01:08:51.510 very general for any function that you assume, 01:08:51.510 --> 01:08:54.680 be it any of the ones that I just showed you previously. 01:08:58.680 --> 01:08:59.180 OK. 01:09:03.870 --> 01:09:05.743 So then the last choice-- 01:09:05.743 --> 01:09:08.160 [INAUDIBLE] doing we'll get started on this and then going 01:09:08.160 --> 01:09:09.450 to finish next time-- 01:09:09.450 --> 01:09:11.100 is, as your classmate was saying, 01:09:11.100 --> 01:09:12.450 about insurance choices. 01:09:12.450 --> 01:09:14.050 So how do we do that? 01:09:14.050 --> 01:09:16.649 So this is a very nice paper by Justin Sydnor, 01:09:16.649 --> 01:09:19.920 who's using sort of real world insurance choices. 01:09:19.920 --> 01:09:23.288 And what's very nice about it is that you might not say, well, 01:09:23.288 --> 01:09:25.080 I might sort of say, well, college students 01:09:25.080 --> 01:09:27.990 and lab choices gives you funky answers. 01:09:27.990 --> 01:09:29.760 And you might not sort of believe 01:09:29.760 --> 01:09:32.529 that this is really predictive of anything in the real world. 01:09:32.529 --> 01:09:34.439 So we really want real world choices 01:09:34.439 --> 01:09:37.410 that people make in their lives. 01:09:37.410 --> 01:09:40.260 And sort of you might also worry about demand effects 01:09:40.260 --> 01:09:42.240 and about sort of people behaving a little bit 01:09:42.240 --> 01:09:43.630 funny in experiment. 01:09:43.630 --> 01:09:46.020 So let's find real world choices that people have made 01:09:46.020 --> 01:09:46.770 and try to see. 01:09:46.770 --> 01:09:49.569 Maybe we can estimate gamma using that. 01:09:49.569 --> 01:09:54.029 And so what Justin Sydnor has is data from a large home 01:09:54.029 --> 01:09:56.250 insurance provider. 01:09:56.250 --> 01:09:58.625 He has a bunch of standard policies. 01:09:58.625 --> 01:10:00.000 There's a random sample of those. 01:10:00.000 --> 01:10:03.150 So there are 50,000 standard policies. 01:10:03.150 --> 01:10:06.900 What he has, importantly, he has both the options 01:10:06.900 --> 01:10:09.390 that people had-- so what is your choice set? 01:10:09.390 --> 01:10:11.490 Here's four different choices for each person. 01:10:11.490 --> 01:10:14.790 And he has then the choices that people made. 01:10:14.790 --> 01:10:17.550 Plus, he has claims that people made after that. 01:10:17.550 --> 01:10:19.035 He has all the new customers, which 01:10:19.035 --> 01:10:20.660 matters a little bit because, you know, 01:10:20.660 --> 01:10:22.440 you might say new customers are confused. 01:10:22.440 --> 01:10:24.900 Maybe the old ones are the ones that are right. 01:10:24.900 --> 01:10:28.527 Now, the key part here is the deductible 01:10:28.527 --> 01:10:29.610 that people were choosing. 01:10:29.610 --> 01:10:31.030 What is a deductible? 01:10:37.400 --> 01:10:38.208 Yes. 01:10:38.208 --> 01:10:40.000 AUDIENCE: How much you'll pay out of pocket 01:10:40.000 --> 01:10:41.598 before the insurance kicks in? 01:10:41.598 --> 01:10:42.640 FRANK SCHILBACH: Exactly. 01:10:42.640 --> 01:10:45.620 So this is expenses paid out of pocket 01:10:45.620 --> 01:10:48.980 before the insurer starts paying any expenses. 01:10:48.980 --> 01:10:52.430 That would be like, if you had some damage to your house 01:10:52.430 --> 01:10:56.330 for some small amount, you would have to pay that for yourself. 01:10:56.330 --> 01:10:58.065 If you have some large amount of damage, 01:10:58.065 --> 01:10:59.690 you have to still pay the small amount. 01:10:59.690 --> 01:11:02.360 And then the insurer would pay the rest. 01:11:02.360 --> 01:11:05.458 And that's usually used to deter a large number of claims 01:11:05.458 --> 01:11:07.250 because you know the insurance company just 01:11:07.250 --> 01:11:09.860 doesn't want to pay for every $50 of damage 01:11:09.860 --> 01:11:10.930 that you might have. 01:11:10.930 --> 01:11:12.680 Because that's just really costly for them 01:11:12.680 --> 01:11:15.720 to do for administrative costs. 01:11:15.720 --> 01:11:20.370 Now, what Sydnor has is choices over menus of four deductibles. 01:11:20.370 --> 01:11:25.070 And again, as I said, he has both individual choice set 01:11:25.070 --> 01:11:26.967 and their preferred options. 01:11:26.967 --> 01:11:28.550 If you only had the preferred options, 01:11:28.550 --> 01:11:32.330 it would be very hard to figure out kind of what actually-- 01:11:32.330 --> 01:11:36.560 because you then can't really say what's the counterfactual. 01:11:36.560 --> 01:11:39.180 You don't essentially what else he could have chosen 01:11:39.180 --> 01:11:41.610 or he or she should have chosen. 01:11:41.610 --> 01:11:43.482 So you kind of want to different options 01:11:43.482 --> 01:11:44.690 and then sort of the outcome. 01:11:44.690 --> 01:11:47.090 And then say, OK, since you had these different options 01:11:47.090 --> 01:11:49.980 available, it must be that you preferred one or the other. 01:11:49.980 --> 01:11:53.370 It must be that you're risk averse or not. 01:11:53.370 --> 01:11:56.540 So here's kind of what these data look like. 01:11:56.540 --> 01:11:59.010 The sample data are deductibles. 01:11:59.010 --> 01:11:59.510 OK. 01:11:59.510 --> 01:12:01.220 This is, again, the amount that you 01:12:01.220 --> 01:12:04.310 have to pay out of pocket until the insurer sort of kicks 01:12:04.310 --> 01:12:05.720 in and pays for you. 01:12:05.720 --> 01:12:08.060 There is the premium, which is how much you 01:12:08.060 --> 01:12:09.920 have to pay every year anyway regardless 01:12:09.920 --> 01:12:12.910 of what anything would happen. 01:12:12.910 --> 01:12:17.150 There's sort of, relative to the $1,000 policy, kind of what's 01:12:17.150 --> 01:12:17.990 the premium. 01:12:17.990 --> 01:12:20.420 That's to say how much more money you have 01:12:20.420 --> 01:12:22.340 to pay for a certain premium. 01:12:22.340 --> 01:12:26.900 So for example, choice one has a premium of $504. 01:12:26.900 --> 01:12:31.400 Choice two has a premium of $588. 01:12:31.400 --> 01:12:34.490 So that's $84 higher. 01:12:34.490 --> 01:12:38.570 You pay essentially $84 in premium every year 01:12:38.570 --> 01:12:43.080 to reduce your deductible from $1,000 to $500. 01:12:43.080 --> 01:12:43.580 OK. 01:12:43.580 --> 01:12:45.080 So what you can do, essentially, you 01:12:45.080 --> 01:12:47.900 can reduce your deductible at a price. 01:12:47.900 --> 01:12:51.350 The price relative to the $1,000 policy is in the third column. 01:12:51.350 --> 01:12:53.970 And you see the deductible on the left-hand side. 01:12:53.970 --> 01:12:56.120 So this person is like policyholder-- 01:12:56.120 --> 01:12:57.130 yeah. 01:12:57.130 --> 01:12:59.030 AUDIENCE: If you're comparing their choices, 01:12:59.030 --> 01:13:02.060 couldn't it be that they're just a more risky person and not 01:13:02.060 --> 01:13:04.658 necessarily risk averse? 01:13:04.658 --> 01:13:05.700 FRANK SCHILBACH: Correct. 01:13:05.700 --> 01:13:07.130 So that's exactly right. 01:13:07.130 --> 01:13:10.273 So there's sort of unobservable risk that people might have. 01:13:10.273 --> 01:13:11.190 I'll get back to that. 01:13:11.190 --> 01:13:15.410 But essentially, what you see is that a lot of people 01:13:15.410 --> 01:13:16.940 make very similar choices. 01:13:16.940 --> 01:13:19.910 Then on average, people's risk is relatively low. 01:13:19.910 --> 01:13:21.410 So what you're saying-- essentially, 01:13:21.410 --> 01:13:22.730 I need to know your claim rate. 01:13:22.730 --> 01:13:25.147 I need to know kind of what's your probability of actually 01:13:25.147 --> 01:13:26.510 having any damages. 01:13:26.510 --> 01:13:28.520 And it turns out claim rates are extremely 01:13:28.520 --> 01:13:31.070 low in the sample, the order of magnitude something 01:13:31.070 --> 01:13:32.330 like below 5%. 01:13:32.330 --> 01:13:34.320 Or I think it's even lower. 01:13:34.320 --> 01:13:37.460 So it cannot be that everybody is a high risk person. 01:13:37.460 --> 01:13:39.830 It can be potentially that everybody thinks 01:13:39.830 --> 01:13:41.270 they're a high risk person. 01:13:41.270 --> 01:13:45.990 But, you know, then there's a different mistake going on. 01:13:45.990 --> 01:13:47.600 So what he's assuming, essentially, 01:13:47.600 --> 01:13:51.800 is, on average, it must be that there's some high risk people 01:13:51.800 --> 01:13:53.070 and some low risk people. 01:13:53.070 --> 01:13:55.403 But essentially, he's sort of kind of assuming this away 01:13:55.403 --> 01:13:57.560 and sort of saying, look, on average claim rates 01:13:57.560 --> 01:13:58.590 are really low. 01:13:58.590 --> 01:14:03.890 It could be that there is some fraction of really high risk 01:14:03.890 --> 01:14:04.610 people. 01:14:04.610 --> 01:14:07.340 But by definition, since they're only 01:14:07.340 --> 01:14:09.830 something like 5% of claim rates, 01:14:09.830 --> 01:14:11.420 it can't be that there's everybody 01:14:11.420 --> 01:14:14.330 is a high risk person. 01:14:14.330 --> 01:14:18.230 So it must be that there's some people who behave as if they're 01:14:18.230 --> 01:14:21.050 either really risk averse or as if they think they're really 01:14:21.050 --> 01:14:22.040 high risk people. 01:14:22.040 --> 01:14:24.680 And this is kind of where the old and new customers are 01:14:24.680 --> 01:14:25.250 helpful for. 01:14:25.250 --> 01:14:28.220 Because there are some customers who have been at this company 01:14:28.220 --> 01:14:29.962 for, like, 10, 15 years. 01:14:29.962 --> 01:14:31.670 And sort of, there, you know, you kind of 01:14:31.670 --> 01:14:35.660 should know what kind of risk person you are perhaps. 01:14:35.660 --> 01:14:37.410 But that's a great question. 01:14:37.410 --> 01:14:39.590 I'll actually get back to that. 01:14:39.590 --> 01:14:43.610 OK, so policy holder one, their home was built in 1966. 01:14:43.610 --> 01:14:45.850 He had an insured value of 180,000. 01:14:45.850 --> 01:14:48.380 The menu available for this policy in the same year 01:14:48.380 --> 01:14:50.138 was the following. 01:14:50.138 --> 01:14:52.430 And then he has also the choice on the right-hand side. 01:14:52.430 --> 01:14:54.740 You see the policies that are chosen. 01:14:54.740 --> 01:15:00.160 So that person chose, for example, a deductible of $200 01:15:00.160 --> 01:15:05.120 and for a price of $157 relative to paying 01:15:05.120 --> 01:15:07.790 the $1,000 deductible. 01:15:07.790 --> 01:15:14.390 Policyholder two, similarly, sort of chose the first option. 01:15:14.390 --> 01:15:16.640 Notice that the price has changed a little bit in part 01:15:16.640 --> 01:15:18.230 because the company has sort of taken 01:15:18.230 --> 01:15:21.680 into account some covariates and some risk in some ways already. 01:15:21.680 --> 01:15:23.960 So the company is kind of pricing specifically 01:15:23.960 --> 01:15:26.390 depending on what your home value is and maybe the area 01:15:26.390 --> 01:15:27.660 and so on and so forth. 01:15:27.660 --> 01:15:29.510 But since Sydnor has all that information, 01:15:29.510 --> 01:15:32.370 he can sort of just take that into account. 01:15:32.370 --> 01:15:35.970 Now, what can we now say about risk aversion? 01:15:35.970 --> 01:15:38.460 How can we now sort of estimate risk 01:15:38.460 --> 01:15:40.830 aversion using these choices? 01:15:51.150 --> 01:15:51.650 Yes. 01:15:51.650 --> 01:15:53.108 AUDIENCE: If you know your house is 01:15:53.108 --> 01:15:58.152 [INAUDIBLE] and your [INAUDIBLE] problems [INAUDIBLE] 01:15:58.152 --> 01:16:01.140 so then you don't have to pay [INAUDIBLE].. 01:16:03.595 --> 01:16:04.470 FRANK SCHILBACH: Yes. 01:16:04.470 --> 01:16:05.910 So what you need to know is essentially 01:16:05.910 --> 01:16:06.840 a number of different things. 01:16:06.840 --> 01:16:08.757 You need to know the deductibles, the premiums 01:16:08.757 --> 01:16:11.090 for each option, the claim probabilities, and the wealth 01:16:11.090 --> 01:16:11.850 levels. 01:16:11.850 --> 01:16:13.540 I'll talk about this in more detail. 01:16:13.540 --> 01:16:17.220 But essentially, what you can do is, for each of these options, 01:16:17.220 --> 01:16:21.030 you can write down an indirect utility of wealth function. 01:16:21.030 --> 01:16:23.160 You essentially can write down what's the expected 01:16:23.160 --> 01:16:25.660 utility of that option. 01:16:25.660 --> 01:16:30.760 And then you can essentially just put bounds essentially 01:16:30.760 --> 01:16:34.000 on if you preferred option one or option two. 01:16:34.000 --> 01:16:36.910 That tells me something about your gamma. 01:16:36.910 --> 01:16:39.850 And so what Sydnor then does is essentially estimate gamma 01:16:39.850 --> 01:16:41.980 using those different choices. 01:16:41.980 --> 01:16:43.810 I'm going to go over that in a lot more 01:16:43.810 --> 01:16:48.090 detail and slower next time.