WEBVTT 00:00:00.000 --> 00:00:05.412 [SQUEAKING] [RUSTLING] [CLICKING] 00:00:10.340 --> 00:00:13.590 FRANK SCHILBACH: OK, so what happened last time? 00:00:13.590 --> 00:00:15.650 So we talked about the workhorse model 00:00:15.650 --> 00:00:20.060 of classical or classical economics, 00:00:20.060 --> 00:00:23.960 in terms of discounting-- the exponential discounted utility 00:00:23.960 --> 00:00:25.080 model. 00:00:25.080 --> 00:00:28.160 This is a very useful model for many settings. 00:00:28.160 --> 00:00:30.320 It's been very useful for explain and understand 00:00:30.320 --> 00:00:32.220 a bunch of behaviors. 00:00:32.220 --> 00:00:34.760 However, this model has a few assumptions 00:00:34.760 --> 00:00:37.370 that create some predictions that are not necessarily 00:00:37.370 --> 00:00:38.810 borne out in the data. 00:00:38.810 --> 00:00:41.810 And we're trying to improve on those assumptions 00:00:41.810 --> 00:00:44.972 and make the model more realistic. 00:00:44.972 --> 00:00:47.180 What are these assumptions and what kinds of examples 00:00:47.180 --> 00:00:48.860 did I show you that perhaps were not 00:00:48.860 --> 00:00:51.590 consistent with the exponential discounting model? 00:00:53.928 --> 00:00:55.220 I'll actually show them to you. 00:00:55.220 --> 00:00:57.570 But can somebody explain to you what they are 00:00:57.570 --> 00:01:00.110 and why those are not consistent with the exponential 00:01:00.110 --> 00:01:00.860 discounting model? 00:01:04.060 --> 00:01:05.209 Yes. 00:01:05.209 --> 00:01:06.790 AUDIENCE: You shouldn't determine-- 00:01:06.790 --> 00:01:12.010 you shouldn't care about whether it's a [INAUDIBLE].. 00:01:12.010 --> 00:01:12.970 FRANK SCHILBACH: Right. 00:01:12.970 --> 00:01:15.850 So one key assumption in the exponential discounting model 00:01:15.850 --> 00:01:17.680 is that there's one parameter, delta, 00:01:17.680 --> 00:01:22.210 that essentially steers how much you care about 00:01:22.210 --> 00:01:25.120 different periods of time, the present and the future, 00:01:25.120 --> 00:01:27.160 or two future periods. 00:01:27.160 --> 00:01:29.840 The key assumption here is that how much weight 00:01:29.840 --> 00:01:31.720 do you put on different time periods, 00:01:31.720 --> 00:01:35.090 on early and a later date, is constant across time. 00:01:35.090 --> 00:01:37.360 So from today versus tomorrow, there's 00:01:37.360 --> 00:01:40.210 the same difference compared to, like, when you look at a year 00:01:40.210 --> 00:01:42.220 from now and a year and a day from now, 00:01:42.220 --> 00:01:44.410 or 20 days and 21 days. 00:01:44.410 --> 00:01:46.930 The difference, if you care more about the present, 00:01:46.930 --> 00:01:50.620 that's constant across time from today's perspective, 00:01:50.620 --> 00:01:52.163 also from future perspective. 00:01:52.163 --> 00:01:53.080 That's one assumption. 00:01:53.080 --> 00:01:55.030 And what evidence did we see or show 00:01:55.030 --> 00:01:58.888 that that's not consistent with? 00:01:58.888 --> 00:02:00.055 AUDIENCE: Choosing a reward. 00:02:00.055 --> 00:02:02.380 Do you want the money now or is this today or in 00:02:02.380 --> 00:02:05.772 a year or [INAUDIBLE]? 00:02:05.772 --> 00:02:06.730 FRANK SCHILBACH: Right. 00:02:06.730 --> 00:02:08.320 So we saw some evidence that people 00:02:08.320 --> 00:02:10.729 are impatient in the short run. 00:02:10.729 --> 00:02:12.950 So when it comes to today versus tomorrow or today 00:02:12.950 --> 00:02:14.325 versus in a week from now, people 00:02:14.325 --> 00:02:15.770 tend to be fairly impatient. 00:02:15.770 --> 00:02:18.450 They tend to discount the future a lot. 00:02:18.450 --> 00:02:20.200 Now, there's sort of two issues with that. 00:02:20.200 --> 00:02:22.600 One is, if you do the same thing about asking people 00:02:22.600 --> 00:02:25.420 about future rewards, people tend to be more patient. 00:02:25.420 --> 00:02:27.860 So the discount factors that you elicit, 00:02:27.860 --> 00:02:30.910 we'll talk a little bit about that in a recitation, as well. 00:02:30.910 --> 00:02:32.560 The discount factors are just different 00:02:32.560 --> 00:02:35.890 for the same intervals of time. 00:02:35.890 --> 00:02:39.078 Second, if you take the short run and patience seriously-- 00:02:39.078 --> 00:02:40.870 if you sort of say, OK, I take your choices 00:02:40.870 --> 00:02:43.780 from today versus tomorrow or from today versus next week 00:02:43.780 --> 00:02:45.800 and [INAUDIBLE] run that forward, you 00:02:45.800 --> 00:02:47.740 got sort of absurd implications as in, like, 00:02:47.740 --> 00:02:51.580 if you really seriously discount a week from now by a lot, 00:02:51.580 --> 00:02:53.510 then you shouldn't care about a year from now, 00:02:53.510 --> 00:02:54.400 five years from now. 00:02:54.400 --> 00:02:56.073 You shouldn't care about that at all. 00:02:56.073 --> 00:02:57.490 However, we see in the real world, 00:02:57.490 --> 00:03:00.100 people have lots of-- people care about the future a lot. 00:03:00.100 --> 00:03:00.970 People save money. 00:03:00.970 --> 00:03:04.220 People get education and so on and so forth. 00:03:04.220 --> 00:03:06.370 So it can't be in some ways that they're 00:03:06.370 --> 00:03:09.500 really impatient in the long run, as well. 00:03:09.500 --> 00:03:11.680 So that's, like, number one. 00:03:11.680 --> 00:03:15.650 What about point number two? 00:03:15.650 --> 00:03:17.140 Yes. 00:03:17.140 --> 00:03:20.010 AUDIENCE: Your decision now for the future 00:03:20.010 --> 00:03:22.190 should be the same as [INAUDIBLE].. 00:03:25.218 --> 00:03:26.260 FRANK SCHILBACH: Exactly. 00:03:26.260 --> 00:03:28.930 That's called dynamic or time consistency. 00:03:28.930 --> 00:03:31.990 That's an assumption or implication of the exponential 00:03:31.990 --> 00:03:33.520 discounting model. 00:03:33.520 --> 00:03:35.410 That is to say, if I make some choices 00:03:35.410 --> 00:03:39.610 for the future, for future periods, about how I-- 00:03:39.610 --> 00:03:42.370 what I'm going to study next week or in a year from now, 00:03:42.370 --> 00:03:45.070 or whether I'm going to exercise and so on, for choices 00:03:45.070 --> 00:03:49.240 that involve time in the future, once that time comes, 00:03:49.240 --> 00:03:52.580 absent new information or absent circumstances change, 00:03:52.580 --> 00:03:56.290 I should follow through with my plans. 00:03:56.290 --> 00:03:58.900 And so if that's not the case, then what we say 00:03:58.900 --> 00:04:01.990 is that preferences are dynamically inconsistent. 00:04:01.990 --> 00:04:05.710 That is to say, I have all sorts of plans of exercising 00:04:05.710 --> 00:04:06.847 next week and so on. 00:04:06.847 --> 00:04:07.680 The next week comes. 00:04:07.680 --> 00:04:09.340 Surprise, I'm not following through. 00:04:09.340 --> 00:04:12.010 That essentially means my preferences are inconsistent. 00:04:12.010 --> 00:04:14.230 And that's sort of evidence against the exponential 00:04:14.230 --> 00:04:16.250 discounting model. 00:04:16.250 --> 00:04:17.200 OK. 00:04:17.200 --> 00:04:18.910 Number three, demand for commitment. 00:04:18.910 --> 00:04:20.169 Yes? 00:04:20.169 --> 00:04:23.770 AUDIENCE: [INAUDIBLE]. 00:04:23.770 --> 00:04:28.192 There are [INAUDIBLE] people will often do that [INAUDIBLE] 00:04:28.192 --> 00:04:31.780 and that shows that people [INAUDIBLE].. 00:04:31.780 --> 00:04:32.820 FRANK SCHILBACH: Right. 00:04:32.820 --> 00:04:35.560 So one sort of key assumption or one sort 00:04:35.560 --> 00:04:38.545 of key insight from sort of economics in general, 00:04:38.545 --> 00:04:41.440 or classical economics, and it's like, more choices are good. 00:04:41.440 --> 00:04:43.180 Like, if you have more options available, 00:04:43.180 --> 00:04:45.760 that's great for you, because you can take advantage of them. 00:04:45.760 --> 00:04:47.260 You never know whether there's going 00:04:47.260 --> 00:04:49.392 to be uncertainty or certain circumstances change. 00:04:49.392 --> 00:04:51.100 So you should never restrict your choices 00:04:51.100 --> 00:04:52.058 because you never know. 00:04:52.058 --> 00:04:54.790 Maybe in the future, maybe circumstances change. 00:04:54.790 --> 00:04:56.650 Maybe I got really busy, or whatever. 00:04:56.650 --> 00:04:57.620 Things happen. 00:04:57.620 --> 00:04:59.350 So more choice tends to be good. 00:04:59.350 --> 00:05:01.810 So in the neoclassical or classical economics model, 00:05:01.810 --> 00:05:04.360 there's no scope for or no reason 00:05:04.360 --> 00:05:08.900 to restrict your choices because more choices in the future 00:05:08.900 --> 00:05:10.190 are always good. 00:05:10.190 --> 00:05:12.813 However, if you're worried about your future self misbehaving 00:05:12.813 --> 00:05:14.230 in certain ways, if you're worried 00:05:14.230 --> 00:05:17.200 about your future self not exercising, 00:05:17.200 --> 00:05:19.660 eating too many potato chips, and so on and so forth, 00:05:19.660 --> 00:05:21.910 you might want to engage in commitment devices, 00:05:21.910 --> 00:05:23.950 either by taking away certain options, 00:05:23.950 --> 00:05:27.220 like restricting your choice set to a smaller choice set, 00:05:27.220 --> 00:05:31.155 or, less drastically, making future choices more expensive. 00:05:31.155 --> 00:05:32.530 That is to say, for example, if I 00:05:32.530 --> 00:05:34.480 say I'm going to submit or write a paper 00:05:34.480 --> 00:05:36.820 by the end of this week, if I'm going to tell you 00:05:36.820 --> 00:05:39.370 if I don't do that I'm going to give you $100, 00:05:39.370 --> 00:05:41.530 well, what I'm going to do essentially 00:05:41.530 --> 00:05:45.610 is I'm making not writing the paper more expensive. 00:05:45.610 --> 00:05:47.402 And the neoclassical or the classical model 00:05:47.402 --> 00:05:48.943 had the exponential discounting model 00:05:48.943 --> 00:05:50.570 has essentially no scope for that. 00:05:50.570 --> 00:05:52.030 Why would I ever do that? 00:05:52.030 --> 00:05:52.780 Because who knows. 00:05:52.780 --> 00:05:55.137 Maybe I'll get sick or stuff happens. 00:05:55.137 --> 00:05:56.470 So there's no reason to do that. 00:05:56.470 --> 00:05:57.845 There's no benefit of doing that. 00:05:57.845 --> 00:05:59.750 And it's a potential cost. 00:05:59.750 --> 00:06:03.800 So if I see myself or somebody else restricting their choices, 00:06:03.800 --> 00:06:07.640 that's a violation of the exponential discounting model. 00:06:07.640 --> 00:06:10.360 And the reason, of course, for that is number two. 00:06:10.360 --> 00:06:11.920 We know there's preference for it. 00:06:11.920 --> 00:06:14.437 If you think there are future preference reversals, 00:06:14.437 --> 00:06:16.270 if I think that in the future I might change 00:06:16.270 --> 00:06:18.550 my preferences in a way that I don't like, 00:06:18.550 --> 00:06:21.190 if I want my future self to behave in certain ways 00:06:21.190 --> 00:06:24.460 that I prefer right now, I might want to restrict my choice set. 00:06:24.460 --> 00:06:27.040 I might certain unpreferrable-- like, less preferable 00:06:27.040 --> 00:06:30.242 options more costly. 00:06:30.242 --> 00:06:31.970 OK. 00:06:31.970 --> 00:06:32.470 Good. 00:06:32.470 --> 00:06:36.730 So then what we did next is to say, OK, now-- 00:06:36.730 --> 00:06:38.960 so I showed you a bunch of evidence of that. 00:06:38.960 --> 00:06:42.250 And then what we did is then we sort of presented 00:06:42.250 --> 00:06:44.620 a slight deviation from the exponential discounting 00:06:44.620 --> 00:06:46.840 model, which is the quasi-hyperbolic discounting 00:06:46.840 --> 00:06:47.740 model. 00:06:47.740 --> 00:06:49.210 That model is, in some sense, very 00:06:49.210 --> 00:06:51.790 similar to the exponential discounting model 00:06:51.790 --> 00:06:54.280 that I showed you, except for some small difference. 00:06:54.280 --> 00:06:57.070 There's an additional parameter that's called beta. 00:06:57.070 --> 00:06:58.120 What does this beta do? 00:06:58.120 --> 00:07:02.440 It's like a short term discount factor that essentially guides 00:07:02.440 --> 00:07:05.230 all discounting or determines all discounting 00:07:05.230 --> 00:07:07.780 between the present period, right now, 00:07:07.780 --> 00:07:10.180 versus anything that's in the future. 00:07:10.180 --> 00:07:13.000 One broad question is like, what are the time periods? 00:07:13.000 --> 00:07:13.810 Is it daily? 00:07:13.810 --> 00:07:14.410 Is it yearly? 00:07:14.410 --> 00:07:15.950 Is it monthly or whatever? 00:07:15.950 --> 00:07:17.950 There's actually quite a bit of research on this 00:07:17.950 --> 00:07:19.660 that people try to figure this out. 00:07:19.660 --> 00:07:22.270 Usually we think the beta or the time horizon of the beta 00:07:22.270 --> 00:07:25.200 is actually just a few days, even just a few hours. 00:07:25.200 --> 00:07:28.728 So for our purposes, we can say it's daily or today. 00:07:28.728 --> 00:07:30.520 And anything that you'll see in the problem 00:07:30.520 --> 00:07:32.530 sets and so on, it needs to be always defined. 00:07:32.530 --> 00:07:34.660 But think of beta essentially anything 00:07:34.660 --> 00:07:37.390 that's like today or in the next couple of days. 00:07:37.390 --> 00:07:40.900 Anything outside of that scope is essentially outside 00:07:40.900 --> 00:07:44.450 of the scope of beta and sort of in the future. 00:07:44.450 --> 00:07:45.890 Now, what does this beta do? 00:07:45.890 --> 00:07:48.640 Well, it helps us to separate discounting 00:07:48.640 --> 00:07:51.160 for short horizons and long horizons, 00:07:51.160 --> 00:07:54.310 because if you think about discounting between the present 00:07:54.310 --> 00:07:58.570 and anything in the future, the data can steer that, right? 00:07:58.570 --> 00:08:02.260 If beta is 0.7, 0.6, or 0.8 or whatever, 00:08:02.260 --> 00:08:04.060 I can now be impatient for the present. 00:08:04.060 --> 00:08:07.960 I can now prefer, say, $10 today versus $12 in the future. 00:08:07.960 --> 00:08:10.430 The beta will make sure that that happens. 00:08:10.430 --> 00:08:12.160 But when you look at all future periods, 00:08:12.160 --> 00:08:13.960 the beta is in all future periods. 00:08:13.960 --> 00:08:16.090 It appears everywhere in the utility function 00:08:16.090 --> 00:08:17.570 in all future periods. 00:08:17.570 --> 00:08:22.990 So the beta does not affect how am I discounting 00:08:22.990 --> 00:08:24.800 any future time periods. 00:08:24.800 --> 00:08:27.970 So then the delta is steering that. 00:08:27.970 --> 00:08:30.390 We usually think that delta is close to 1. 00:08:30.390 --> 00:08:34.590 It's something like yearly 0.95 or 0.99 or the like. 00:08:34.590 --> 00:08:38.860 So delta is essentially reasonably close to 1, 00:08:38.860 --> 00:08:40.900 such that I can be fairly patient 00:08:40.900 --> 00:08:44.110 between 10 years from now and 11 years from now and 15 years 00:08:44.110 --> 00:08:45.140 from now. 00:08:45.140 --> 00:08:46.490 It doesn't matter much to me. 00:08:46.490 --> 00:08:48.580 There's only going to be some slight discounting. 00:08:48.580 --> 00:08:50.860 I prefer probably things that are happening five years 00:08:50.860 --> 00:08:53.260 from now from things that are happening 00:08:53.260 --> 00:08:57.580 30 years from now for the same sort of stuff happening. 00:08:57.580 --> 00:09:00.718 But people tend to be fairly patient. 00:09:00.718 --> 00:09:02.260 Do you have any questions about that? 00:09:12.860 --> 00:09:13.480 OK. 00:09:13.480 --> 00:09:17.760 So let me now sort of spend, in fact, the rest of the lecture 00:09:17.760 --> 00:09:20.040 just talking about details of this model, 00:09:20.040 --> 00:09:21.540 in part sort of building intuition, 00:09:21.540 --> 00:09:23.730 sort of showing you the mechanics of how that works 00:09:23.730 --> 00:09:27.630 and how, essentially, having an additional discount 00:09:27.630 --> 00:09:29.940 parameter of the data affects people's choices. 00:09:29.940 --> 00:09:32.190 And second, we're going to talk about something that's 00:09:32.190 --> 00:09:34.523 quite important, which is the question of sophistication 00:09:34.523 --> 00:09:35.850 versus naivete. 00:09:35.850 --> 00:09:36.880 What do I mean by that? 00:09:36.880 --> 00:09:40.320 Well, in the exponential discounting model, 00:09:40.320 --> 00:09:43.530 by assumption, the preferences are time consistent. 00:09:43.530 --> 00:09:44.370 What does that mean? 00:09:44.370 --> 00:09:46.470 If I make plans for the future, I 00:09:46.470 --> 00:09:48.792 will follow through with those plans. 00:09:48.792 --> 00:09:50.250 So in some sense, it doesn't really 00:09:50.250 --> 00:09:52.020 matter what I think I'm going to do in the future, 00:09:52.020 --> 00:09:53.370 because essentially, I'm going to do anyway 00:09:53.370 --> 00:09:54.840 what I'm going to plan anyway. 00:09:54.840 --> 00:09:56.460 So the only thing I need to know is 00:09:56.460 --> 00:09:58.420 right now what I'm going to do. 00:09:58.420 --> 00:10:01.200 And then if I make that plan, unless circumstances change, 00:10:01.200 --> 00:10:03.318 I'm going to just follow through. 00:10:03.318 --> 00:10:05.610 That's not true here anymore, as I'm going to show you. 00:10:05.610 --> 00:10:08.490 So now it's the case that if I make some plans right now, 00:10:08.490 --> 00:10:10.470 these plans might change in the future because 00:10:10.470 --> 00:10:12.090 of my preferences. 00:10:12.090 --> 00:10:13.830 Even in the absence of new information 00:10:13.830 --> 00:10:17.160 or new circumstances, once tomorrow comes or next week 00:10:17.160 --> 00:10:20.170 comes, I might sort of prefer different things. 00:10:20.170 --> 00:10:23.890 So now the preference are not dynamically consistent anymore. 00:10:23.890 --> 00:10:28.080 So what I prefer today might not be what I prefer next week. 00:10:28.080 --> 00:10:29.730 So that now leads to a complication. 00:10:29.730 --> 00:10:32.323 Now I need to understand, well, what 00:10:32.323 --> 00:10:34.740 are my beliefs about what I'm going to do in the future is 00:10:34.740 --> 00:10:35.340 quite important. 00:10:35.340 --> 00:10:36.270 Do I have correct beliefs? 00:10:36.270 --> 00:10:37.973 Do I understand that I'm present biased? 00:10:37.973 --> 00:10:39.390 Do I understand that in the future 00:10:39.390 --> 00:10:41.160 I might be impatient, as well? 00:10:41.160 --> 00:10:42.300 Or am I naive? 00:10:42.300 --> 00:10:44.940 Do I think right now I'm present biased, but tomorrow comes 00:10:44.940 --> 00:10:47.430 or next week I'm going to exercise, do the problem set 00:10:47.430 --> 00:10:49.240 early, and so on and so forth? 00:10:49.240 --> 00:10:52.650 And as we're going to see, that will lead to quite different-- 00:10:52.650 --> 00:10:56.820 starkly different conclusions or implications 00:10:56.820 --> 00:11:01.890 that are quite important for outcomes, welfare, and so on. 00:11:01.890 --> 00:11:02.670 OK. 00:11:02.670 --> 00:11:06.330 So let me give you some examples first. 00:11:06.330 --> 00:11:11.460 So first, if you have a discount function for beta 00:11:11.460 --> 00:11:13.895 equals 1/2 and delta close to 1-- 00:11:13.895 --> 00:11:15.270 for our purposes, often I'm going 00:11:15.270 --> 00:11:17.460 to set delta to 1, not because I necessarily 00:11:17.460 --> 00:11:19.410 think that delta is 1. 00:11:19.410 --> 00:11:22.530 Delta is probably 0.99, 0.95, or the like. 00:11:22.530 --> 00:11:24.960 I'm just setting it to 1 to make the algebra 00:11:24.960 --> 00:11:27.510 or sort of any problem set exercises 00:11:27.510 --> 00:11:30.870 and so on being less messy. 00:11:30.870 --> 00:11:32.620 Speaking of which, problem set exercises-- 00:11:32.620 --> 00:11:34.440 Pierre-Luc who sits in the very back and checks 00:11:34.440 --> 00:11:36.023 whether you are using your laptop only 00:11:36.023 --> 00:11:39.540 for classwork, Pierre-Luc sort of mostly in charge 00:11:39.540 --> 00:11:40.870 of doing the problem sets. 00:11:40.870 --> 00:11:42.505 So he also has office hours, to which 00:11:42.505 --> 00:11:44.880 you can come and ask specific questions about the problem 00:11:44.880 --> 00:11:45.150 sets. 00:11:45.150 --> 00:11:47.275 Of course, he's also very happy to answer questions 00:11:47.275 --> 00:11:51.150 about Piazza or in any other way. 00:11:51.150 --> 00:11:52.668 When are your office hours? 00:11:52.668 --> 00:11:54.437 AUDIENCE: [INAUDIBLE]. 00:11:54.437 --> 00:11:55.770 FRANK SCHILBACH: 1:30 on Friday. 00:11:55.770 --> 00:11:57.540 And where are they? 00:11:57.540 --> 00:11:59.828 AUDIENCE: [INAUDIBLE]. 00:11:59.828 --> 00:12:00.870 FRANK SCHILBACH: Perfect. 00:12:00.870 --> 00:12:02.585 So it's on the course website. 00:12:02.585 --> 00:12:03.960 So if you have specific questions 00:12:03.960 --> 00:12:07.530 about the problem set, again, in the recitation, 00:12:07.530 --> 00:12:09.960 we'll discuss quite a few issues related to that. 00:12:09.960 --> 00:12:12.335 But then if you have specific questions about the problem 00:12:12.335 --> 00:12:16.840 set, Pierre-Luc will be the best equipped to answer those. 00:12:16.840 --> 00:12:17.520 OK. 00:12:17.520 --> 00:12:22.440 So if you have quasi-hyperbolic discounting preferences, 00:12:22.440 --> 00:12:25.080 with beta equals 1/2 and delta equals 1, 00:12:25.080 --> 00:12:28.750 your discounting function looks, essentially, as follows. 00:12:28.750 --> 00:12:30.900 The first period is sort of normalized to 1. 00:12:30.900 --> 00:12:34.410 [INAUDIBLE] like one about the current period. 00:12:34.410 --> 00:12:37.530 In the future then it's, like, beta delta, beta delta square, 00:12:37.530 --> 00:12:39.790 beta delta to the power of 3, and so on. 00:12:39.790 --> 00:12:42.053 But if you sort of now use delta equals 1, 00:12:42.053 --> 00:12:44.220 you get, essentially-- you care about the present 1. 00:12:44.220 --> 00:12:47.570 And everything in the future is discounted by 1/2. 00:12:47.570 --> 00:12:50.160 OK, so relative to the present period, 00:12:50.160 --> 00:12:51.900 all future periods are worth less. 00:12:51.900 --> 00:12:53.340 So I care a lot about the present. 00:12:53.340 --> 00:12:55.980 That's why we call it sort of present bias or present focus. 00:12:55.980 --> 00:12:58.290 I care a lot more about the present than anything 00:12:58.290 --> 00:12:59.800 in the future. 00:12:59.800 --> 00:13:02.610 Now, second, all discounting in this specific example 00:13:02.610 --> 00:13:05.470 takes place between the present and the immediate future. 00:13:05.470 --> 00:13:06.870 So I only care about-- 00:13:06.870 --> 00:13:08.707 in terms of discounting-- all future periods 00:13:08.707 --> 00:13:09.540 are the same for me. 00:13:09.540 --> 00:13:10.915 I don't care about whether things 00:13:10.915 --> 00:13:13.170 are in five periods or six or seven periods from now. 00:13:13.170 --> 00:13:15.720 That's all the same for me, because delta, in this case, 00:13:15.720 --> 00:13:17.040 is 1. 00:13:17.040 --> 00:13:18.750 Instead, what I care about is that today 00:13:18.750 --> 00:13:22.500 versus tomorrow or today versus three days from now, and so on. 00:13:22.500 --> 00:13:24.680 Again, usually delta would not be one. 00:13:24.680 --> 00:13:27.330 So if you had a delta that's, like, 0.99 or the like, 00:13:27.330 --> 00:13:30.880 there would be some discounting in the future, as well. 00:13:30.880 --> 00:13:32.290 But not in this case. 00:13:32.290 --> 00:13:35.280 So that's sort of capturing the intuition that the long run-- 00:13:35.280 --> 00:13:37.500 in the long run, we are relatively patient. 00:13:37.500 --> 00:13:40.690 There is essentially no discounting happening anymore. 00:13:40.690 --> 00:13:43.110 And so the utils a year from now are just 00:13:43.110 --> 00:13:47.050 as valuable as utils in two years from now. 00:13:47.050 --> 00:13:50.312 So then that also means that the timing of decisions or-- 00:13:50.312 --> 00:13:52.020 the decisions are sensitive to the timing 00:13:52.020 --> 00:13:55.080 of costs and benefits, when exactly did they occur. 00:13:55.080 --> 00:13:56.910 It matters a lot whether stuff happens 00:13:56.910 --> 00:14:00.985 today versus tomorrow or today versus three days from now. 00:14:00.985 --> 00:14:03.360 It matters much less about whether stuff happens in three 00:14:03.360 --> 00:14:04.652 days versus four days from now. 00:14:04.652 --> 00:14:06.578 I'm going to show you some examples of that. 00:14:06.578 --> 00:14:08.370 But just to sort of give you some sense of, 00:14:08.370 --> 00:14:10.662 like, why is this called quasi-hyperbolic or hyperbolic 00:14:10.662 --> 00:14:12.760 discounting? 00:14:12.760 --> 00:14:14.005 So have your three functions. 00:14:14.005 --> 00:14:15.630 I'm not sure how well you can see this. 00:14:15.630 --> 00:14:17.460 But there's, like, a sort of pink line 00:14:17.460 --> 00:14:20.472 that's essentially like an exponential curve. 00:14:20.472 --> 00:14:22.680 That's essentially what exponential discounting looks 00:14:22.680 --> 00:14:23.240 like. 00:14:23.240 --> 00:14:25.740 Essentially what you see is sort of a constant, if you want, 00:14:25.740 --> 00:14:30.690 sort of decline of like the discount function. 00:14:30.690 --> 00:14:33.447 And then I've also plotted to you 00:14:33.447 --> 00:14:35.280 hyperbolic discounting, which is essentially 00:14:35.280 --> 00:14:36.810 like a true hyperbolic curve. 00:14:36.810 --> 00:14:38.352 That's essentially the thing that you 00:14:38.352 --> 00:14:43.640 see on the left, the one that's sort of like much 00:14:43.640 --> 00:14:45.190 steeper at the beginning. 00:14:45.190 --> 00:14:47.880 And then there is quasi-hyperbolic discounting 00:14:47.880 --> 00:14:49.830 that's essentially quite similar in shape, 00:14:49.830 --> 00:14:52.440 as you can see, to the hyperbolic discounting, 00:14:52.440 --> 00:14:54.750 except for the fact that it's not continuous. 00:14:54.750 --> 00:14:58.710 There's a jump from going one to beta at the very beginning. 00:14:58.710 --> 00:15:00.480 It's not a continuous function. 00:15:00.480 --> 00:15:01.980 Essentially, there's a discrete jump 00:15:01.980 --> 00:15:04.410 between today and the future. 00:15:04.410 --> 00:15:06.690 And then essentially it behaves very similarly 00:15:06.690 --> 00:15:08.842 to the exponential discounting curve. 00:15:08.842 --> 00:15:10.800 But that's just to tell you it doesn't really-- 00:15:10.800 --> 00:15:12.600 you don't have to worry about the hyperbolic discounting 00:15:12.600 --> 00:15:13.100 and so on. 00:15:13.100 --> 00:15:15.480 We're not going to discuss that very much. 00:15:15.480 --> 00:15:17.070 But that's just for you to understand 00:15:17.070 --> 00:15:18.690 why is that the name? 00:15:18.690 --> 00:15:21.150 Well, it's because essentially it's quasi-hyperbolic. 00:15:21.150 --> 00:15:22.942 It's not really hyperbolic because it's not 00:15:22.942 --> 00:15:24.840 really hyperbola. 00:15:24.840 --> 00:15:29.520 But in fact, it looks quite similar, effectively. 00:15:29.520 --> 00:15:37.295 So then when you think about goods that you might consume, 00:15:37.295 --> 00:15:38.670 there's different types of goods. 00:15:38.670 --> 00:15:40.890 There's leisure goods and there's investment goods. 00:15:40.890 --> 00:15:42.515 Let's sort of start with leisure goods. 00:15:42.515 --> 00:15:43.515 What's a leisure good? 00:15:43.515 --> 00:15:46.650 A leisure good is a good that has immediate rewards 00:15:46.650 --> 00:15:48.780 and delayed costs. 00:15:48.780 --> 00:15:50.760 One example would be eating candy. 00:15:50.760 --> 00:15:53.700 So eating candy, of course, you get immediate utility benefits. 00:15:53.700 --> 00:15:55.800 It's pleasurable to eat candy. 00:15:55.800 --> 00:15:57.030 So that's positive. 00:15:57.030 --> 00:16:01.680 In this case, suppose the benefits are the pleasure 00:16:01.680 --> 00:16:03.420 of eating candy right now. 00:16:03.420 --> 00:16:09.150 But often eating candy, it leads to delayed health costs 00:16:09.150 --> 00:16:12.120 or delayed costs at the dentist's office, 00:16:12.120 --> 00:16:17.280 which summarizes C health of 3 in the future. 00:16:17.280 --> 00:16:21.270 If you now say, well, if beta equals 1/2 00:16:21.270 --> 00:16:25.380 and a delta equals 1, well, you can sort think about, 00:16:25.380 --> 00:16:29.620 would you eat candy today or candy in the future? 00:16:29.620 --> 00:16:32.320 So first starting off with eating candy today-- 00:16:32.320 --> 00:16:35.040 well, if you sort of calculate the costs and benefits 00:16:35.040 --> 00:16:39.540 of eating candy, the pleasure that you get from candy is 2. 00:16:39.540 --> 00:16:42.690 If you discount the future by beta, 00:16:42.690 --> 00:16:45.240 essentially everything in the future is discounted by beta, 00:16:45.240 --> 00:16:47.310 it's like 1/2 times 3. 00:16:47.310 --> 00:16:49.140 So if you sort of do that calculation, 00:16:49.140 --> 00:16:50.330 you get something positive. 00:16:50.330 --> 00:16:52.320 So if you think about eating candy right now, 00:16:52.320 --> 00:16:56.250 the answer is yes, because 2 minus 1/2 times 3 is positive 00:16:56.250 --> 00:16:57.990 and you're going to do that. 00:16:57.990 --> 00:16:59.490 If instead you think about, should I 00:16:59.490 --> 00:17:01.050 eat candy in the future? 00:17:01.050 --> 00:17:02.820 Well, you get different implications. 00:17:02.820 --> 00:17:03.680 The answer is no. 00:17:03.680 --> 00:17:04.589 Why is the answer no? 00:17:04.589 --> 00:17:07.079 Because if you're in the future, everything 00:17:07.079 --> 00:17:09.510 is discounted that's happening in the future, both 00:17:09.510 --> 00:17:12.119 the pleasure that comes from eating candy next week, 00:17:12.119 --> 00:17:16.680 but also the delayed costs are essentially discounted by beta. 00:17:16.680 --> 00:17:18.690 So then you essentially just have, like, 1/2. 00:17:18.690 --> 00:17:21.540 This is the beta for everything in the future times two, 00:17:21.540 --> 00:17:23.950 which are the benefits, minus 3, which are the costs. 00:17:23.950 --> 00:17:26.730 And that's smaller than 0. 00:17:26.730 --> 00:17:28.740 So you're not going to do that. 00:17:28.740 --> 00:17:31.110 And that's sort of a general feature for leisure 00:17:31.110 --> 00:17:32.440 good, as we call them. 00:17:32.440 --> 00:17:36.455 These have immediate rewards and delayed benefits. 00:17:36.455 --> 00:17:37.830 And so what you tend to do is you 00:17:37.830 --> 00:17:42.300 tend to overconsume them in the present relative 00:17:42.300 --> 00:17:43.890 to long run plans. 00:17:43.890 --> 00:17:44.608 Yeah? 00:17:44.608 --> 00:17:47.473 AUDIENCE: Are you only considering [INAUDIBLE] 00:17:47.473 --> 00:17:48.390 FRANK SCHILBACH: Yeah. 00:17:48.390 --> 00:17:51.840 So yeah, you can think of this as, like, a shorthand 00:17:51.840 --> 00:17:56.340 form of saying, for example, suppose you eat a lot of candy 00:17:56.340 --> 00:17:58.597 or, like, on one day you eat candy and suppose 00:17:58.597 --> 00:18:00.180 you know-- these are repeated choices, 00:18:00.180 --> 00:18:02.730 but I'm sort of aggregating it into one. 00:18:02.730 --> 00:18:05.400 You'll have, essentially, health costs in the future. 00:18:05.400 --> 00:18:07.390 Suppose you get dental pain in the future. 00:18:07.390 --> 00:18:12.310 Each period you have dental pain starting at age 30 or 40 or 50. 00:18:12.310 --> 00:18:15.660 Now, you can sort of think of this as like each day 00:18:15.660 --> 00:18:17.368 you're going to have negative utility. 00:18:17.368 --> 00:18:19.410 What I'm doing now is I'm sort of collapsing that 00:18:19.410 --> 00:18:22.350 into one day in a sense of just making sure that-- to make 00:18:22.350 --> 00:18:23.520 it sort of tractable. 00:18:23.520 --> 00:18:25.140 So you can think of the delayed health 00:18:25.140 --> 00:18:28.200 costs as a summary of the health costs overall. 00:18:28.200 --> 00:18:32.680 Instead you could also write down 0.1 for your 40, 00:18:32.680 --> 00:18:35.830 0.1 for your 41, and so on and so forth, 00:18:35.830 --> 00:18:37.560 and sort of aggregating in that way. 00:18:37.560 --> 00:18:40.050 But that's just for simplicity here. 00:18:40.050 --> 00:18:43.320 Similarly, you could also say each day 00:18:43.320 --> 00:18:45.300 you'll have essentially a choice to eat candy. 00:18:45.300 --> 00:18:46.673 And these things sort of add up. 00:18:46.673 --> 00:18:48.840 And again, sort of simplifying in a sense of saying, 00:18:48.840 --> 00:18:51.300 like, should I eat candy overall, 00:18:51.300 --> 00:18:52.920 which is a number of different choices 00:18:52.920 --> 00:18:55.420 that each are between the present and the future. 00:18:55.420 --> 00:18:58.410 That's just like changing the units in some way overall. 00:18:58.410 --> 00:19:01.380 I think the structure of the problem is the same. 00:19:01.380 --> 00:19:02.694 Yeah? 00:19:02.694 --> 00:19:04.955 AUDIENCE: So obviously this is kind 00:19:04.955 --> 00:19:07.473 of comparing apples and oranges. 00:19:07.473 --> 00:19:15.490 But I the one kind of [INAUDIBLE] is your health is 00:19:15.490 --> 00:19:19.382 kind of the sum of a bunch of actions that you did over 00:19:19.382 --> 00:19:20.965 your lifetime that affect your health, 00:19:20.965 --> 00:19:25.590 versus candy is something that-- 00:19:25.590 --> 00:19:28.630 the pleasure that you get out of candy is exactly-- 00:19:28.630 --> 00:19:30.640 fully [INAUDIBLE]. 00:19:30.640 --> 00:19:33.280 So when people-- when you do this kind of [INAUDIBLE] 00:19:33.280 --> 00:19:36.670 discounting and you're trying to compare health in the future, 00:19:36.670 --> 00:19:41.580 like, pleasure now, the fact that the candy contributes such 00:19:41.580 --> 00:19:45.670 a small amount to your overall health, 00:19:45.670 --> 00:19:47.843 it seems kind of like an apples to oranges-- 00:19:47.843 --> 00:19:48.760 FRANK SCHILBACH: Yeah. 00:19:48.760 --> 00:19:49.820 To some degree, I think that's right. 00:19:49.820 --> 00:19:51.860 I think it's, in some sense, that's just an example. 00:19:51.860 --> 00:19:53.260 So I could show you many different things 00:19:53.260 --> 00:19:54.940 that are sort of similar in structure. 00:19:54.940 --> 00:19:57.520 I'm using candy just to make it concrete. 00:19:57.520 --> 00:20:00.580 You could do the same with problem sets and other pain, 00:20:00.580 --> 00:20:03.010 or exercising, and so on and so forth. 00:20:03.010 --> 00:20:05.950 I think at the end of the day, I think that's exactly right. 00:20:05.950 --> 00:20:07.910 For a lot of choices that people make-- 00:20:07.910 --> 00:20:11.845 be it brushing their teeth, be it exercising, 00:20:11.845 --> 00:20:13.600 be it eating healthily and so on, 00:20:13.600 --> 00:20:15.610 often the costs or the benefits are 00:20:15.610 --> 00:20:16.900 very salient in the present. 00:20:16.900 --> 00:20:19.007 They're very salient and concrete. 00:20:19.007 --> 00:20:20.840 Right now you have a cookie in front of you. 00:20:20.840 --> 00:20:21.465 You can eat it. 00:20:21.465 --> 00:20:23.620 You'll be happy, and that's for sure. 00:20:23.620 --> 00:20:25.540 Sometime in 20 years from now, you 00:20:25.540 --> 00:20:27.160 might be sort of like unhealthy. 00:20:27.160 --> 00:20:29.800 You might get dental problems and so on and so forth. 00:20:29.800 --> 00:20:31.970 Not only is it sort of very far away, 00:20:31.970 --> 00:20:33.640 but it's also very diffuse. 00:20:33.640 --> 00:20:35.322 It's also maybe unlikely. 00:20:35.322 --> 00:20:37.030 Like, there's a chance of getting a heart 00:20:37.030 --> 00:20:38.680 attack at age 70. 00:20:38.680 --> 00:20:39.610 Maybe, maybe not. 00:20:39.610 --> 00:20:41.220 Maybe you'll be just fine. 00:20:41.220 --> 00:20:43.760 So it's more complicated in a lot of health decisions. 00:20:43.760 --> 00:20:46.120 So there's other research saying, like, well, partially 00:20:46.120 --> 00:20:47.380 it's about uncertainty. 00:20:47.380 --> 00:20:49.930 Partially it's about the future being diffuse 00:20:49.930 --> 00:20:52.540 and very sort of unclear. 00:20:52.540 --> 00:20:55.150 One part of that people tend to think is time preferences. 00:20:55.150 --> 00:20:56.590 But I think what you're saying is the world is 00:20:56.590 --> 00:20:57.730 more complicated than that. 00:20:57.730 --> 00:20:59.710 And that's for sure true. 00:20:59.710 --> 00:21:02.260 What I'm sort of saying is, like, thinking about time 00:21:02.260 --> 00:21:04.690 preferences can help you understand some choices 00:21:04.690 --> 00:21:06.722 that people make over time. 00:21:06.722 --> 00:21:08.680 Having said that, there's lots of other aspects 00:21:08.680 --> 00:21:10.990 here, which we're sort of grossly simplifying. 00:21:10.990 --> 00:21:12.850 But I think the key part here-- 00:21:12.850 --> 00:21:15.310 I think what's really important for a lot of health choices 00:21:15.310 --> 00:21:17.320 tends to be that people-- 00:21:17.320 --> 00:21:19.690 that exactly as you say, there's a lot 00:21:19.690 --> 00:21:21.928 of-- like, thousands of really small choices 00:21:21.928 --> 00:21:24.220 that sort of add up to something like-- what we call it 00:21:24.220 --> 00:21:26.200 unhealthy behavior in some way. 00:21:26.200 --> 00:21:29.290 And each of them are concrete in some sense in terms 00:21:29.290 --> 00:21:30.490 of the costs and benefits. 00:21:30.490 --> 00:21:32.890 Like, brushing your teeth is like costly in some sense 00:21:32.890 --> 00:21:35.290 for five minutes or whatever. 00:21:35.290 --> 00:21:38.710 Eating candy is happy for a few minutes, 00:21:38.710 --> 00:21:40.480 as well, very concretely. 00:21:40.480 --> 00:21:42.710 And then the costs are often diffuse in the future 00:21:42.710 --> 00:21:43.210 and so on. 00:21:43.210 --> 00:21:44.470 That's really important. 00:21:44.470 --> 00:21:46.303 We're going to talk a little bit about this. 00:21:46.303 --> 00:21:47.740 But we sort of-- for now at least 00:21:47.740 --> 00:21:50.530 abstracting, essentially, that away. 00:21:50.530 --> 00:21:52.838 Yes? 00:21:52.838 --> 00:21:55.760 AUDIENCE: [INAUDIBLE]. 00:21:55.760 --> 00:21:59.841 Why is it better than the [INAUDIBLE].. 00:21:59.841 --> 00:22:03.997 Why is it [INAUDIBLE] and what actually [INAUDIBLE] 00:22:03.997 --> 00:22:06.622 better than the exponential model? 00:22:06.622 --> 00:22:08.330 FRANK SCHILBACH: So the exponential model 00:22:08.330 --> 00:22:12.110 would not predict you this type of behavior. 00:22:12.110 --> 00:22:15.320 So if you think about now we get to this-- like, 00:22:15.320 --> 00:22:17.960 if you sort of say you want to make choices for the future, 00:22:17.960 --> 00:22:20.120 the exponential discounter would give you 00:22:20.120 --> 00:22:23.330 the same choices for the future versus what 00:22:23.330 --> 00:22:25.040 actually-- when the future arrives. 00:22:25.040 --> 00:22:27.500 So I'm going to show you a sort of-- more in the context 00:22:27.500 --> 00:22:30.500 of problem set, I'm going to show you this behavior that 00:22:30.500 --> 00:22:32.330 the exponential model cannot-- 00:22:32.330 --> 00:22:34.380 just not explain. 00:22:34.380 --> 00:22:37.190 Like, the exponential discounter would say, either I like candy 00:22:37.190 --> 00:22:38.900 and I don't care about-- 00:22:38.900 --> 00:22:41.450 or I just don't worry that much about the health costs and I 00:22:41.450 --> 00:22:42.940 eat candy, or I don't. 00:22:42.940 --> 00:22:44.690 I'm really worried about the health costs, 00:22:44.690 --> 00:22:46.400 and therefore I don't eat candy. 00:22:46.400 --> 00:22:47.900 And that choice is the same today 00:22:47.900 --> 00:22:49.770 versus next week versus two weeks from now, 00:22:49.770 --> 00:22:50.850 and so on and so forth. 00:22:50.850 --> 00:22:53.240 So once I make a choice for eating candy-- 00:22:53.240 --> 00:22:56.120 so here notice that the person who will make the plans 00:22:56.120 --> 00:22:59.570 to not eat candy in the future, once the future arrives, 00:22:59.570 --> 00:23:02.427 that person will change their choice 00:23:02.427 --> 00:23:04.010 and then actually surprise themselves, 00:23:04.010 --> 00:23:05.989 potentially by eating candy. 00:23:05.989 --> 00:23:07.426 AUDIENCE: [INAUDIBLE]. 00:23:14.185 --> 00:23:16.560 FRANK SCHILBACH: There's just behaviors in the world that 00:23:16.560 --> 00:23:18.960 the exponential discounting model cannot explain. 00:23:18.960 --> 00:23:19.840 That is one of them. 00:23:19.840 --> 00:23:21.682 AUDIENCE: [INAUDIBLE]. 00:23:21.682 --> 00:23:22.890 FRANK SCHILBACH: So there's-- 00:23:22.890 --> 00:23:23.160 yeah. 00:23:23.160 --> 00:23:24.750 So I think there's a question on what 00:23:24.750 --> 00:23:26.347 other models can explain this. 00:23:26.347 --> 00:23:28.680 I think the hyperbolic model is, in fact, quite similar, 00:23:28.680 --> 00:23:30.750 as it sort of showed you in the curve here. 00:23:30.750 --> 00:23:34.440 You sort of see the discount functions are quite similar. 00:23:34.440 --> 00:23:38.430 There's research using the hyperbolic model. 00:23:38.430 --> 00:23:41.340 In economics in the last sort of-- in behavioral economics 00:23:41.340 --> 00:23:43.080 in the last something like 20 years, 00:23:43.080 --> 00:23:45.540 the quasi-hyperbolic model is the model 00:23:45.540 --> 00:23:48.810 that everybody uses, partially for tractability and simplicity 00:23:48.810 --> 00:23:53.190 for no other good reasons in many settings. 00:23:53.190 --> 00:23:55.440 But in some sense, what we care about-- in some sense, 00:23:55.440 --> 00:23:58.050 I don't care actually that much about which model among sort 00:23:58.050 --> 00:24:00.870 of a class of model that are quite similar can explain 00:24:00.870 --> 00:24:02.640 things sort of-- 00:24:02.640 --> 00:24:06.368 if two models explain the same thing in similar ways, 00:24:06.368 --> 00:24:08.160 I don't care about which one we should use. 00:24:08.160 --> 00:24:10.452 In a sense, the simpler model is sort of easier to use, 00:24:10.452 --> 00:24:12.322 and that's why we sort of do it. 00:24:12.322 --> 00:24:14.280 What I care about is there are some predictions 00:24:14.280 --> 00:24:17.310 from the exponential model that are sort of just not-- 00:24:17.310 --> 00:24:18.540 that are just false. 00:24:18.540 --> 00:24:20.400 And those we need to improve on. 00:24:20.400 --> 00:24:23.640 That could be either through a hyperbolic model 00:24:23.640 --> 00:24:25.170 or quasi-hyperbolic model. 00:24:25.170 --> 00:24:28.170 To keep things simple, I'm using the quasi-hyperbolic model, 00:24:28.170 --> 00:24:30.750 in part because it nests very simply 00:24:30.750 --> 00:24:32.350 in the exponential model. 00:24:32.350 --> 00:24:33.933 And the reason why a lot of economists 00:24:33.933 --> 00:24:36.267 have used it is to say, OK, here's an exponential model. 00:24:36.267 --> 00:24:37.590 We know how to use that model. 00:24:37.590 --> 00:24:39.450 Now we're going to add one parameter 00:24:39.450 --> 00:24:40.950 and things look very similar. 00:24:40.950 --> 00:24:43.800 And beta equals 1 essentially collapses that model back 00:24:43.800 --> 00:24:45.120 to the exponential model. 00:24:45.120 --> 00:24:47.460 And therefore, people have used it. 00:24:47.460 --> 00:24:49.740 And that's essentially what we do. 00:24:49.740 --> 00:24:50.430 OK. 00:24:50.430 --> 00:24:53.790 So now the flip side of those kinds of choices 00:24:53.790 --> 00:24:54.993 are investment goods. 00:24:54.993 --> 00:24:56.910 Investment goods are essentially very similar. 00:24:56.910 --> 00:24:58.618 These are goods that have immediate costs 00:24:58.618 --> 00:25:00.450 but delayed benefits. 00:25:00.450 --> 00:25:02.130 An example would be go to the gym. 00:25:02.130 --> 00:25:03.780 Like, you can go to the gym right now. 00:25:03.780 --> 00:25:06.840 Some people find that fun, but many people also 00:25:06.840 --> 00:25:07.950 find it costly. 00:25:07.950 --> 00:25:10.050 There's some effort cost of, say, in this case, 2. 00:25:10.050 --> 00:25:13.020 There's benefits, health benefits, of 3. 00:25:13.020 --> 00:25:15.210 Again, that's really sort of like a stark example. 00:25:15.210 --> 00:25:17.877 But I'm just trying to make sort of a point to make this simple. 00:25:17.877 --> 00:25:21.720 Now, again, if we have beta equals 1/2 and delta equals 1, 00:25:21.720 --> 00:25:23.970 if you think about should you go to the gym today, 00:25:23.970 --> 00:25:25.330 the answer is no. 00:25:25.330 --> 00:25:28.590 And the reason is that you put a lot of weight on the present. 00:25:28.590 --> 00:25:30.850 You put sort of weight of 1 on the present, 00:25:30.850 --> 00:25:33.150 the cost of minus 1-- 00:25:33.150 --> 00:25:33.780 sorry. 00:25:33.780 --> 00:25:36.370 You put a weight of 1 on the cost of minus 2. 00:25:36.370 --> 00:25:38.310 So you have minus 2 costs. 00:25:38.310 --> 00:25:39.700 The benefits are in the future. 00:25:39.700 --> 00:25:41.220 You discount them by beta. 00:25:41.220 --> 00:25:44.810 So you have 1/2 times 3, which is smaller than 0. 00:25:44.810 --> 00:25:46.860 Now, if you think about, then, are 00:25:46.860 --> 00:25:49.680 you planning to go to the gym next week, the answer is yes. 00:25:49.680 --> 00:25:50.345 Why is that? 00:25:50.345 --> 00:25:52.470 Well, now you're essentially discounting everything 00:25:52.470 --> 00:25:55.472 that's in the future, including the costs of going to the gym. 00:25:55.472 --> 00:25:57.930 So you can think about, should you go to the gym next week? 00:25:57.930 --> 00:26:00.120 The answer will be yes. 00:26:00.120 --> 00:26:04.200 The reason is because the health benefits overall 00:26:04.200 --> 00:26:06.870 are larger than the costs. 00:26:06.870 --> 00:26:09.120 Now, again, what we're going to see then 00:26:09.120 --> 00:26:12.840 is people deviate from their long-run plans. 00:26:12.840 --> 00:26:15.090 Now they under-consume investment goods 00:26:15.090 --> 00:26:17.100 relative to long run plans. 00:26:17.100 --> 00:26:19.710 So we saw previously that people over consume leisure goods. 00:26:19.710 --> 00:26:21.390 They do too much fun stuff that has 00:26:21.390 --> 00:26:23.220 bad consequences in the future. 00:26:23.220 --> 00:26:27.150 And people tend to do too little of tedious stuff 00:26:27.150 --> 00:26:31.650 that will yield benefits in the future relative 00:26:31.650 --> 00:26:33.810 to their long run plans. 00:26:33.810 --> 00:26:36.480 Again, you look at sort of timing consistency 00:26:36.480 --> 00:26:39.420 in a sense of, like, if I plan to go to the gym next week, 00:26:39.420 --> 00:26:40.680 I'm going to say yes. 00:26:40.680 --> 00:26:44.695 Now unless things change, once next week arrives, 00:26:44.695 --> 00:26:46.320 I'm going to be at the choice of, like, 00:26:46.320 --> 00:26:47.610 should I go to the gym today? 00:26:47.610 --> 00:26:48.540 I'm going to say no. 00:26:48.540 --> 00:26:51.630 I would like to not do that because now I'm 00:26:51.630 --> 00:26:56.700 essentially discounting the future but not the present. 00:26:56.700 --> 00:26:57.930 Any questions on that? 00:26:57.930 --> 00:26:58.820 Yes. 00:26:58.820 --> 00:27:03.030 AUDIENCE: [INAUDIBLE] one more time why you discount 00:27:03.030 --> 00:27:08.302 the efforts as in the future and not-- 00:27:08.302 --> 00:27:09.260 FRANK SCHILBACH: Right. 00:27:09.260 --> 00:27:12.490 So think of these as different periods-- so the effort-- 00:27:12.490 --> 00:27:16.070 so if you think about, should you go until the costs are 00:27:16.070 --> 00:27:17.713 today-- 00:27:17.713 --> 00:27:19.380 think about these are different periods. 00:27:19.380 --> 00:27:20.910 Period right now. 00:27:20.910 --> 00:27:23.210 Health benefits are, like, say, a week later. 00:27:23.210 --> 00:27:24.240 OK. 00:27:24.240 --> 00:27:25.710 In the choice about doing it today, 00:27:25.710 --> 00:27:28.060 the costs are right now-- that's the present period. 00:27:28.060 --> 00:27:30.780 So if you go back to the discount function, 00:27:30.780 --> 00:27:33.515 you put a weight of 1 on anything that's in the present. 00:27:33.515 --> 00:27:35.640 And anything that's in the future, a future period, 00:27:35.640 --> 00:27:37.448 you put in a weight of 1/2. 00:27:37.448 --> 00:27:39.906 AUDIENCE: OK, so we can see every [INAUDIBLE] in the future 00:27:39.906 --> 00:27:40.788 because [INAUDIBLE]. 00:27:40.788 --> 00:27:41.830 FRANK SCHILBACH: Exactly. 00:27:41.830 --> 00:27:44.140 So the effort right now is in the present. 00:27:44.140 --> 00:27:47.252 So for like-- so start with a choice of, like, today. 00:27:47.252 --> 00:27:48.460 The effort is in the present. 00:27:48.460 --> 00:27:50.252 That's why I'm not sort of discounting that 00:27:50.252 --> 00:27:51.930 in the first choice for today. 00:27:51.930 --> 00:27:53.740 But if I think about doing it next week, 00:27:53.740 --> 00:27:55.360 then next week is also in the future. 00:27:55.360 --> 00:27:57.360 I'm discounting everything that's in the future, 00:27:57.360 --> 00:27:59.290 whether it's a week away or two weeks ago. 00:27:59.290 --> 00:28:00.160 I don't care. 00:28:00.160 --> 00:28:04.070 And therefore, everything is discounted by 1/2. 00:28:04.070 --> 00:28:05.030 OK. 00:28:05.030 --> 00:28:11.150 So now one important distinction now is demand for commitment, 00:28:11.150 --> 00:28:13.520 or is there commitment available? 00:28:13.520 --> 00:28:15.260 So what we're going to do is think 00:28:15.260 --> 00:28:19.940 about like students who have to do problem sets with very 00:28:19.940 --> 00:28:22.340 simple beta delta preferences. 00:28:22.340 --> 00:28:25.580 So consider a student with beta equals 1/2, delta equals 1. 00:28:25.580 --> 00:28:26.503 There's three periods. 00:28:26.503 --> 00:28:27.920 And this is sort of getting pretty 00:28:27.920 --> 00:28:30.087 close to what you're going to do in the problem set, 00:28:30.087 --> 00:28:31.140 actually, yourself. 00:28:31.140 --> 00:28:32.480 There are three periods. 00:28:32.480 --> 00:28:34.770 You have to do the problem set in exactly one of three 00:28:34.770 --> 00:28:35.270 periods. 00:28:35.270 --> 00:28:37.395 That's, of course, contrived and a little stylized. 00:28:37.395 --> 00:28:40.340 But that's just an example for now. 00:28:40.340 --> 00:28:43.400 So there's periods T equals 0, T equals 1, T equals 2. 00:28:43.400 --> 00:28:46.460 The instantaneous utility is of minus 1, three halves, 00:28:46.460 --> 00:28:47.240 and five halves. 00:28:47.240 --> 00:28:49.800 So the problem set becomes more and more painful the later 00:28:49.800 --> 00:28:51.440 we actually do it. 00:28:51.440 --> 00:28:52.500 OK. 00:28:52.500 --> 00:28:56.190 And there's only one day in which you can actually do it. 00:28:56.190 --> 00:28:58.158 So now the first thing that I think about is 00:28:58.158 --> 00:28:59.700 suppose there's commitment available. 00:28:59.700 --> 00:29:00.220 What does that mean? 00:29:00.220 --> 00:29:01.803 Suppose a student can essentially just 00:29:01.803 --> 00:29:03.860 pick, when is she going to do the problem set, 00:29:03.860 --> 00:29:05.180 and actually stick to that. 00:29:05.180 --> 00:29:06.805 Suppose they could just sort of dictate 00:29:06.805 --> 00:29:09.600 what she's going to do in the future, what would she choose? 00:29:09.600 --> 00:29:13.577 Well-- and then she actually has to sort of stick with that. 00:29:13.577 --> 00:29:16.160 So now we can sort think about, from the perspective of period 00:29:16.160 --> 00:29:20.000 zero, remember the person is a hyperbolic discounter 00:29:20.000 --> 00:29:22.520 with beta equals 1/2. 00:29:22.520 --> 00:29:26.630 From the perspective of right now, I'm going to say, well, 00:29:26.630 --> 00:29:29.100 the discounted utility today is minus 1. 00:29:29.100 --> 00:29:32.030 There's no discounting happening for today if I do it today. 00:29:32.030 --> 00:29:34.730 For tomorrow, I'm going to discount the future by 1/2. 00:29:34.730 --> 00:29:36.770 So I'm going to get minus 3/4. 00:29:36.770 --> 00:29:39.140 And in the period 2 in 2 days from now, 00:29:39.140 --> 00:29:40.700 I'm going to do 1/2 minus-- 00:29:40.700 --> 00:29:44.030 times minus five halves, which is five quarters. 00:29:44.030 --> 00:29:46.940 So if I could sort of predict-- if I could sort of say what 00:29:46.940 --> 00:29:50.025 I would like to do, I would say, well, I'm 00:29:50.025 --> 00:29:51.650 going to do it in [INAUDIBLE] equals 1. 00:29:51.650 --> 00:29:57.700 I'm going to do it tomorrow if I could follow through with that. 00:29:57.700 --> 00:29:58.320 Is that clear? 00:30:03.690 --> 00:30:05.100 OK. 00:30:05.100 --> 00:30:06.810 So that's if commitment is available. 00:30:06.810 --> 00:30:08.700 That is if I could essentially just force 00:30:08.700 --> 00:30:10.890 myself to do stuff in the future and not 00:30:10.890 --> 00:30:12.990 deviate from that at all. 00:30:12.990 --> 00:30:15.420 Now if no commitment is available, 00:30:15.420 --> 00:30:17.430 how does that thinking change? 00:30:22.230 --> 00:30:23.240 Yes. 00:30:23.240 --> 00:30:24.730 AUDIENCE: T equals 1 [INAUDIBLE].. 00:30:24.730 --> 00:30:25.980 FRANK SCHILBACH: Yes, exactly. 00:30:25.980 --> 00:30:30.150 Once T equals 1 arrives, I might actually 00:30:30.150 --> 00:30:32.100 prefer not to do it in T equals 1 00:30:32.100 --> 00:30:36.137 but rather say I'd rather do it in T equals 2. 00:30:36.137 --> 00:30:38.220 And this is exactly what you're going to see here. 00:30:38.220 --> 00:30:41.018 This is the exact same problem that I showed you before. 00:30:41.018 --> 00:30:42.810 Now, suppose the student has no [INAUDIBLE] 00:30:42.810 --> 00:30:44.995 so the commitment technology is just to say, 00:30:44.995 --> 00:30:47.370 what if the student can just choose in every period, what 00:30:47.370 --> 00:30:50.220 is she going to do, would she actually do it in period one? 00:30:50.220 --> 00:30:53.670 Well, if period one arrives, if the problem set is not 00:30:53.670 --> 00:30:56.610 done, if she does it at period one, 00:30:56.610 --> 00:30:58.440 from the perspective of period one, 00:30:58.440 --> 00:31:01.240 the discounted costs are minus three halves. 00:31:01.240 --> 00:31:03.240 That's just because that's in the current period 00:31:03.240 --> 00:31:05.520 from the perspective of period one. 00:31:05.520 --> 00:31:08.100 If she instead sort of were to do it in period two, 00:31:08.100 --> 00:31:11.130 she now discounts, again, period two from the perspective 00:31:11.130 --> 00:31:12.630 of period one by 1/2. 00:31:12.630 --> 00:31:16.290 So 1/2 times minus 5/2 hops is 5/4. 00:31:16.290 --> 00:31:20.790 Well, 5/4 is less bad than 3/2. 00:31:20.790 --> 00:31:24.000 So she is going to say, I'm going to do it in period two. 00:31:24.000 --> 00:31:27.060 So that's to say that students' preferences are dynamically 00:31:27.060 --> 00:31:27.653 inconsistent. 00:31:27.653 --> 00:31:29.820 Again, that's sort of something that the exponential 00:31:29.820 --> 00:31:32.880 discounting model would not predict or cannot explain 00:31:32.880 --> 00:31:36.690 and the quasi-hyperbolic model is one way of simply creating 00:31:36.690 --> 00:31:37.920 such timing consistency. 00:31:37.920 --> 00:31:38.720 Yes. 00:31:38.720 --> 00:31:41.220 AUDIENCE: I was wondering how we should think about the fact 00:31:41.220 --> 00:31:42.845 that, for example, you know that you're 00:31:42.845 --> 00:31:46.890 going to experience [INAUDIBLE] on the second period. 00:31:46.890 --> 00:31:49.070 So should then your second period activity function 00:31:49.070 --> 00:31:50.070 be the one that matters? 00:31:50.070 --> 00:31:54.820 Shouldn't you, as a sophisticated [INAUDIBLE] 00:31:54.820 --> 00:31:59.010 minus 3/2 that it's worse from your perspective [INAUDIBLE].. 00:32:01.680 --> 00:32:05.490 That utility function should be the one that matters 00:32:05.490 --> 00:32:07.140 and is used [INAUDIBLE]. 00:32:07.140 --> 00:32:08.440 FRANK SCHILBACH: Right so you're sort of saying-- 00:32:08.440 --> 00:32:10.357 and sounds if I understood right-- is to say-- 00:32:10.357 --> 00:32:12.300 and let's see whether that's true. 00:32:12.300 --> 00:32:14.730 You're saying, well, if no commitment is available, 00:32:14.730 --> 00:32:17.070 I should never let it get to that point. 00:32:17.070 --> 00:32:18.900 If I'm in period zero, I should know 00:32:18.900 --> 00:32:21.000 I'm not going to do it actually in period one. 00:32:21.000 --> 00:32:23.190 Therefore, I'd rather do it right now 00:32:23.190 --> 00:32:26.220 to avoid that all sort of like procrastinated from period one 00:32:26.220 --> 00:32:27.282 to period two. 00:32:27.282 --> 00:32:28.740 And if I'm not in period 0, I might 00:32:28.740 --> 00:32:31.115 say I do it rather right now, because otherwise I'm going 00:32:31.115 --> 00:32:32.430 to just do it in period two. 00:32:32.430 --> 00:32:34.140 And from the perspective of period zero, 00:32:34.140 --> 00:32:36.570 I'd rather do it right now, compared to period two. 00:32:36.570 --> 00:32:38.280 I would prefer to do it in period one, 00:32:38.280 --> 00:32:41.820 but that's not feasible because my period one self will not 00:32:41.820 --> 00:32:43.920 behave in the absence of commitment. 00:32:43.920 --> 00:32:46.170 AUDIENCE: I was more thinking in a way that, why would 00:32:46.170 --> 00:32:49.230 you want to commit your previous one [INAUDIBLE] 00:32:49.230 --> 00:32:52.780 that your [INAUDIBLE]? 00:32:52.780 --> 00:32:54.280 Because you have a different utility 00:32:54.280 --> 00:32:55.690 function in that period. 00:32:55.690 --> 00:32:56.640 [INAUDIBLE] 00:33:00.910 --> 00:33:02.170 FRANK SCHILBACH: It's just a-- 00:33:02.170 --> 00:33:03.753 I mean, something that's an assumption 00:33:03.753 --> 00:33:06.850 in the sense of from the perspective of period zero, 00:33:06.850 --> 00:33:08.220 you make certain choices. 00:33:08.220 --> 00:33:10.270 You're going to say, I could do it right now. 00:33:10.270 --> 00:33:11.530 I could do it in period one. 00:33:11.530 --> 00:33:13.150 Or I could do it in period two. 00:33:13.150 --> 00:33:14.830 Now, you have certain preferences. 00:33:14.830 --> 00:33:16.150 And you're saying maybe your preferences 00:33:16.150 --> 00:33:16.983 should be different. 00:33:16.983 --> 00:33:18.280 And that's obviously fine. 00:33:18.280 --> 00:33:21.310 I sort of specified the preferences for the student. 00:33:21.310 --> 00:33:23.350 I said that beta is 1/2. 00:33:23.350 --> 00:33:25.493 So she cares about 1/2 about anything 00:33:25.493 --> 00:33:27.160 that happens in the future in period one 00:33:27.160 --> 00:33:28.930 and two compared to period zero. 00:33:28.930 --> 00:33:32.200 And then sort of just sort of like-- 00:33:32.200 --> 00:33:34.120 you just look at what the utilities are and it 00:33:34.120 --> 00:33:37.030 sort of turns out that from her perspective, from period zero, 00:33:37.030 --> 00:33:38.830 she prefers period one. 00:33:38.830 --> 00:33:40.960 Now, you could sort of specify the utility function 00:33:40.960 --> 00:33:42.647 differently. 00:33:42.647 --> 00:33:44.230 But for that specific example, I guess 00:33:44.230 --> 00:33:48.560 that's what sort of the algebra tells us. 00:33:48.560 --> 00:33:49.060 Yeah. 00:33:51.970 --> 00:33:55.060 So now the key question now is to say, OK, 00:33:55.060 --> 00:33:57.197 now the preferences are dynamically inconsistent. 00:33:57.197 --> 00:33:59.530 So now what I said-- well, what's really important now-- 00:33:59.530 --> 00:34:01.510 and in some sense, maybe you were asking about that, 00:34:01.510 --> 00:34:02.110 as well-- 00:34:02.110 --> 00:34:05.890 is, well, it's the question on, like, 00:34:05.890 --> 00:34:08.560 is the student aware of this time of consistency? 00:34:08.560 --> 00:34:12.347 So you could say, well, when deciding in period zero, 00:34:12.347 --> 00:34:14.889 you might sort of say, well, I'd like to do it in period one. 00:34:14.889 --> 00:34:17.920 If I believe that in period one, I'm time consistent, 00:34:17.920 --> 00:34:20.409 or if I believe that I'm an exponential discounter 00:34:20.409 --> 00:34:22.960 in the future, I will be very virtuous in the future, 00:34:22.960 --> 00:34:25.300 well then, I'm very happy to wait until period one. 00:34:25.300 --> 00:34:28.060 And then I'm going to follow through with my plans. 00:34:28.060 --> 00:34:30.130 If instead I know that in period one 00:34:30.130 --> 00:34:32.238 I'm going to be present bias, well then 00:34:32.238 --> 00:34:34.780 what's going to happen is then I can't trust myself in period 00:34:34.780 --> 00:34:35.650 one to actually do it. 00:34:35.650 --> 00:34:37.358 I know I'm going to procrastinate further 00:34:37.358 --> 00:34:38.199 until period two. 00:34:38.199 --> 00:34:40.120 So I'd rather do it at period zero 00:34:40.120 --> 00:34:44.139 to avoid sort of having to deal with it in period two. 00:34:44.139 --> 00:34:46.070 Let me sort of walk you through that. 00:34:46.070 --> 00:34:49.719 So I guess we need sort of additional parameters 00:34:49.719 --> 00:34:52.000 to start with which is called beta hat. 00:34:52.000 --> 00:34:54.520 Beta hat does essentially the sophistication or naivete 00:34:54.520 --> 00:34:55.570 parameter. 00:34:55.570 --> 00:34:57.760 Beta hat is your belief about what 00:34:57.760 --> 00:35:00.460 you think your beta will be in the future. 00:35:00.460 --> 00:35:03.220 So beta is like what the actual beta is. 00:35:03.220 --> 00:35:06.520 That's the true value of beta in the present and in the future. 00:35:06.520 --> 00:35:08.590 And beta hat is like what you think 00:35:08.590 --> 00:35:11.260 your beta is in the future, what you 00:35:11.260 --> 00:35:15.310 believe your true or your beta is going forward. 00:35:15.310 --> 00:35:17.560 It's not what you believe-- you know your beta today. 00:35:17.560 --> 00:35:20.140 You know that essentially your present bias today. 00:35:20.140 --> 00:35:21.670 Everybody understands that well. 00:35:21.670 --> 00:35:23.620 That's an assumption, as well. 00:35:23.620 --> 00:35:25.120 But people do not know or may not 00:35:25.120 --> 00:35:27.140 know what their beta is in the future. 00:35:27.140 --> 00:35:29.925 And that's what the parameter of beta hat measures. 00:35:29.925 --> 00:35:31.300 You're going to have three cases. 00:35:31.300 --> 00:35:33.790 I'm going to talk about two cases today. 00:35:33.790 --> 00:35:37.390 There's going to be a third case starting on Tuesday. 00:35:37.390 --> 00:35:40.390 And so the two cases that we are discussing is full naivete. 00:35:40.390 --> 00:35:42.940 That's to say my beta hat equals 1. 00:35:42.940 --> 00:35:44.470 That's to say I think-- essentially, 00:35:44.470 --> 00:35:45.803 I know I'm present biased today. 00:35:45.803 --> 00:35:49.900 But I think I'm an exponential discounter in the future. 00:35:49.900 --> 00:35:52.570 OK, so that's to say I know I have self 00:35:52.570 --> 00:35:54.010 control problems right now. 00:35:54.010 --> 00:35:56.200 But next week surely will be different. 00:35:56.200 --> 00:35:58.510 Like this is like in the beginning of the semester, 00:35:58.510 --> 00:36:00.850 you know you kind of like screwed up in the past. 00:36:00.850 --> 00:36:02.950 But this semester will be very different. 00:36:02.950 --> 00:36:04.390 You'll be virtuous and so on. 00:36:04.390 --> 00:36:07.750 That happens kind of every semester. 00:36:07.750 --> 00:36:09.790 So that's beta hat equals 1. 00:36:09.790 --> 00:36:12.370 So the person does not realize that she will change her mind. 00:36:12.370 --> 00:36:15.070 She thinks that she's going to follow through with her plan. 00:36:15.070 --> 00:36:17.320 Her plan is to do it in T equals 1. 00:36:17.320 --> 00:36:19.990 She thinks she's going to follow through. 00:36:19.990 --> 00:36:21.740 There will be surprises about present bias 00:36:21.740 --> 00:36:23.990 because you think you're going to do it in period one. 00:36:23.990 --> 00:36:26.350 Period one arrives, and surprise, she's present biased. 00:36:26.350 --> 00:36:28.150 She misestimated what she's going to do 00:36:28.150 --> 00:36:29.830 and then ends up sort of not doing it 00:36:29.830 --> 00:36:32.020 and has to do it then in period two. 00:36:32.020 --> 00:36:33.670 There's a sort of like false optimism, 00:36:33.670 --> 00:36:36.490 if you want, about future plans and sort of the attitude 00:36:36.490 --> 00:36:37.852 of this time is different. 00:36:37.852 --> 00:36:40.060 From tomorrow onwards, things will be very different. 00:36:40.060 --> 00:36:43.690 We'll be all virtuous in the future. 00:36:43.690 --> 00:36:45.580 And then the second part is sort of like-- 00:36:45.580 --> 00:36:47.170 call it like perfect sophistication. 00:36:47.170 --> 00:36:49.150 That's bets hat equals beta. 00:36:49.150 --> 00:36:50.848 That is essentially rational expectation 00:36:50.848 --> 00:36:53.140 in a sense-- this is a person who perfectly understands 00:36:53.140 --> 00:36:54.100 their preferences. 00:36:54.100 --> 00:36:56.150 I know I have seen this movie before. 00:36:56.150 --> 00:36:58.780 I know tomorrow I'm going to procrastinate, 00:36:58.780 --> 00:37:00.670 or I'm going to be present biased. 00:37:00.670 --> 00:37:02.590 I perfectly understand what I'm going to do. 00:37:02.590 --> 00:37:05.710 And therefore I take into account that when 00:37:05.710 --> 00:37:08.380 making choices right now. 00:37:08.380 --> 00:37:11.320 And so she understands perfectly that she will change her mind. 00:37:11.320 --> 00:37:14.360 So she understands that she has plans to do it in period one. 00:37:14.360 --> 00:37:15.985 But she understands that the period one 00:37:15.985 --> 00:37:17.560 self has different preferences. 00:37:17.560 --> 00:37:19.900 The period one self prefers to do it in period two 00:37:19.900 --> 00:37:21.700 rather than in period one. 00:37:21.700 --> 00:37:26.320 So she's kind of like, in some sense, sort of correctly 00:37:26.320 --> 00:37:28.210 pessimistic about her future self. 00:37:28.210 --> 00:37:31.030 And sort of then in the case of these kinds of investment 00:37:31.030 --> 00:37:33.030 goods, that's a good thing, because she doesn't 00:37:33.030 --> 00:37:34.030 sort of leave stuff out. 00:37:34.030 --> 00:37:36.400 She doesn't delay things a lot for the future. 00:37:36.400 --> 00:37:38.590 She doesn't let things get bad because she knows 00:37:38.590 --> 00:37:41.140 if she procrastinates further, she'd 00:37:41.140 --> 00:37:42.850 rather do it right now, anticipating 00:37:42.850 --> 00:37:45.430 that the future self will not follow through. 00:37:45.430 --> 00:37:48.350 And here in the perfect sophistication case, 00:37:48.350 --> 00:37:50.410 there will be no surprises. 00:37:50.410 --> 00:37:53.140 The person always follows through with their plans. 00:37:53.140 --> 00:37:55.330 The third case I'm going to talk about next week 00:37:55.330 --> 00:37:57.220 is when beta hat equals-- 00:37:57.220 --> 00:37:59.140 is between beta and one, which is we 00:37:59.140 --> 00:38:02.920 call a partial sophistication or partial naivety. 00:38:02.920 --> 00:38:05.140 So it's a little more complicated, but in fact, 00:38:05.140 --> 00:38:06.130 quite similar. 00:38:06.130 --> 00:38:07.338 I think there was a question. 00:38:07.338 --> 00:38:08.308 Yeah. 00:38:08.308 --> 00:38:11.284 AUDIENCE: [INAUDIBLE]. 00:38:11.284 --> 00:38:14.260 But the future self actually can [INAUDIBLE].. 00:38:16.795 --> 00:38:18.420 FRANK SCHILBACH: Sorry, say that again? 00:38:18.420 --> 00:38:21.000 AUDIENCE: So the person does not realize 00:38:21.000 --> 00:38:22.984 that she will change her mind over the course 00:38:22.984 --> 00:38:28.285 of the semester, but she [INAUDIBLE] her plans. 00:38:28.285 --> 00:38:29.660 FRANK SCHILBACH: So you would not 00:38:29.660 --> 00:38:32.097 sort of-- so you wouldn't really carry-- so if you change 00:38:32.097 --> 00:38:33.680 your mind in the future, you would not 00:38:33.680 --> 00:38:37.188 carry through with your plans. 00:38:37.188 --> 00:38:40.930 AUDIENCE: [INAUDIBLE]. 00:38:40.930 --> 00:38:43.750 FRANK SCHILBACH: So either she will change her mind 00:38:43.750 --> 00:38:45.420 in the future or not. 00:38:45.420 --> 00:38:47.420 So if she doesn't change her mind in the future, 00:38:47.420 --> 00:38:50.003 there's no problem, because then there is nothing to be aware. 00:38:50.003 --> 00:38:53.110 That's kind of like the case of the exponential discounter. 00:38:53.110 --> 00:38:56.240 So if beta hat-- sorry, if beta is actually one to start with, 00:38:56.240 --> 00:38:58.525 which is kind of like exponential discounting, 00:38:58.525 --> 00:39:00.400 then there's no problem because in the future 00:39:00.400 --> 00:39:02.680 she will just want the same as in the present. 00:39:02.680 --> 00:39:06.160 So then sort of by construction or by sort of assumption, 00:39:06.160 --> 00:39:09.550 then beta hat equals beta equals 1. 00:39:09.550 --> 00:39:12.190 And now if she changes her mind in the future 00:39:12.190 --> 00:39:14.140 about her preferences-- essentially 00:39:14.140 --> 00:39:18.220 if her beta is smaller than 1, then the question arises, 00:39:18.220 --> 00:39:19.090 what's the beta hat? 00:39:19.090 --> 00:39:20.080 Is it like one? 00:39:20.080 --> 00:39:22.540 That's the perfect sophistication case. 00:39:22.540 --> 00:39:25.600 Or is it beta, which is-- 00:39:25.600 --> 00:39:26.630 beta hat equals beta. 00:39:26.630 --> 00:39:28.540 That's the perfect sophistication case. 00:39:28.540 --> 00:39:32.580 Or if beta hat equals 1, that's the full naivete case. 00:39:32.580 --> 00:39:34.330 And then there's sort of cases in between, 00:39:34.330 --> 00:39:37.510 where she sort of-- she does understand that the beta is 00:39:37.510 --> 00:39:40.270 smaller than 1 in the future, but doesn't fully understand 00:39:40.270 --> 00:39:42.190 that and underestimates-- 00:39:42.190 --> 00:39:48.220 overestimates her beta, but at least only to some extent. 00:39:48.220 --> 00:39:49.701 Any other questions? 00:39:53.510 --> 00:39:54.010 OK. 00:39:54.010 --> 00:39:55.870 So now when we sort of look at now, 00:39:55.870 --> 00:39:58.640 what does a naive student actually do? 00:39:58.640 --> 00:40:02.080 So what does the naive student do at T equals zero? 00:40:02.080 --> 00:40:03.550 Well, from above, we sort of know 00:40:03.550 --> 00:40:07.720 that the self zero prefers to do the problem set at T equals 1. 00:40:07.720 --> 00:40:10.120 So since she's naive, she thinks she's 00:40:10.120 --> 00:40:11.950 going to follow through with those plans. 00:40:11.950 --> 00:40:15.460 So she believes that she will actually do it at T equals 1. 00:40:15.460 --> 00:40:17.717 So she doesn't do it at T equals 0. 00:40:17.717 --> 00:40:19.300 Now, of course, what does she actually 00:40:19.300 --> 00:40:21.430 do at period T equals 1? 00:40:21.430 --> 00:40:22.640 We already said that. 00:40:22.640 --> 00:40:24.640 She does actually not want to do the period in T 00:40:24.640 --> 00:40:28.330 equals 1, the p set at period T equals 1. 00:40:28.330 --> 00:40:31.360 So then hence the person sort of surprises herself and actually 00:40:31.360 --> 00:40:33.580 ends up doing it in period two. 00:40:33.580 --> 00:40:35.010 Right. 00:40:35.010 --> 00:40:36.760 And so what's sort of the summary of that? 00:40:36.760 --> 00:40:38.770 And this is a more general phenomenon. 00:40:38.770 --> 00:40:41.890 If you read the paper for class today, 00:40:41.890 --> 00:40:44.380 that's sort of much more general in that paper 00:40:44.380 --> 00:40:47.660 and you could do that in a much more complicated way. 00:40:47.660 --> 00:40:50.890 So essentially, there is the belief in period zero-- 00:40:50.890 --> 00:40:52.840 she thinks, well, I can not do it right now. 00:40:52.840 --> 00:40:53.830 I can delay it. 00:40:53.830 --> 00:40:55.930 The cost of delaying it will not be that large 00:40:55.930 --> 00:40:57.928 because I'm going to just do it in period one. 00:40:57.928 --> 00:40:59.470 But it turns out the cost of delaying 00:40:59.470 --> 00:41:01.330 is actually much larger, because in period one, 00:41:01.330 --> 00:41:02.140 she doesn't do it. 00:41:02.140 --> 00:41:03.497 She'll do it in period two. 00:41:03.497 --> 00:41:05.080 Now, if you had more and more periods, 00:41:05.080 --> 00:41:07.630 you could sort of have a whole cascade of doing it every day-- 00:41:07.630 --> 00:41:09.672 every day you say you're going to do it tomorrow, 00:41:09.672 --> 00:41:11.480 but you're never actually going to do it. 00:41:11.480 --> 00:41:13.930 And so that can lead to actually very large costs 00:41:13.930 --> 00:41:16.990 of procrastination, because you can essentially delay things 00:41:16.990 --> 00:41:19.000 infinitely by every time thinking 00:41:19.000 --> 00:41:20.870 you're going to do it in the future. 00:41:20.870 --> 00:41:24.738 And so that kind of behavior might persist for a long time. 00:41:24.738 --> 00:41:26.530 And it's sort of an example, as we call it, 00:41:26.530 --> 00:41:27.995 like naive procrastination. 00:41:27.995 --> 00:41:29.620 Every day you think-- or every week you 00:41:29.620 --> 00:41:31.810 think you're going to do it tomorrow or next week and so 00:41:31.810 --> 00:41:32.310 on. 00:41:32.310 --> 00:41:34.280 But you're never going to actually do it. 00:41:34.280 --> 00:41:37.873 And then that can lead to really large welfare costs, 00:41:37.873 --> 00:41:40.290 because there's stuff that's actually not that hard to do. 00:41:40.290 --> 00:41:41.410 But you just don't do it every day 00:41:41.410 --> 00:41:43.240 and it gets more and more costly over time. 00:41:43.240 --> 00:41:44.750 And you never end up doing it. 00:41:44.750 --> 00:41:47.770 And it's way worse to do it in 50 periods from now. 00:41:47.770 --> 00:41:49.270 You could have just done it early on 00:41:49.270 --> 00:41:52.240 if you had understood that you were not 00:41:52.240 --> 00:41:53.650 going to do it any time soon. 00:41:56.353 --> 00:41:57.270 Any questions on that? 00:41:57.270 --> 00:41:58.650 Yeah. 00:41:58.650 --> 00:42:01.770 AUDIENCE: [INAUDIBLE] what's the interplay between learning 00:42:01.770 --> 00:42:05.790 and sophistication [INAUDIBLE]? 00:42:05.790 --> 00:42:07.190 What type of people [INAUDIBLE]. 00:42:15.605 --> 00:42:16.480 FRANK SCHILBACH: Yes. 00:42:16.480 --> 00:42:18.970 So one big question is, how is this even possible 00:42:18.970 --> 00:42:19.720 that we have here? 00:42:19.720 --> 00:42:22.270 Here's a person who keeps surprising herself 00:42:22.270 --> 00:42:23.000 every period. 00:42:23.000 --> 00:42:24.640 I mean, like, OK, actually, I thought I was going to do it. 00:42:24.640 --> 00:42:26.557 But surprise, I'm actually not going to do it. 00:42:26.557 --> 00:42:29.002 But I'll tomorrow I'll do it. 00:42:29.002 --> 00:42:31.210 In a way, that's sort of surprising, in the sense of, 00:42:31.210 --> 00:42:33.380 like, there are these behaviors-- like, for example, 00:42:33.380 --> 00:42:35.047 when people think about-- when do people 00:42:35.047 --> 00:42:36.970 go to bed, for example? 00:42:36.970 --> 00:42:39.730 And people think people systematically 00:42:39.730 --> 00:42:41.770 under invest in sleep. 00:42:41.770 --> 00:42:43.570 And in some sense, it's an odd sort 00:42:43.570 --> 00:42:47.027 of behavior in the sense of, you go to bed every night. 00:42:47.027 --> 00:42:49.360 You kind of know that you're going to be tired tomorrow. 00:42:49.360 --> 00:42:51.340 Yet, every day you sort of have this belief 00:42:51.340 --> 00:42:53.545 that tomorrow you'll be just fine. 00:42:53.545 --> 00:42:56.030 And from tomorrow, things will not change. 00:42:56.030 --> 00:42:58.780 So there are some behaviors that people tend to not learn. 00:42:58.780 --> 00:43:01.510 And we don't quite understand why that is. 00:43:01.510 --> 00:43:04.720 In general, sort of like learning about beta hat 00:43:04.720 --> 00:43:05.590 is sort of-- 00:43:05.590 --> 00:43:08.200 kind of like at the frontier of research right now. 00:43:08.200 --> 00:43:10.090 People have started estimating beta hat. 00:43:10.090 --> 00:43:11.980 They have found people tend to be fairly 00:43:11.980 --> 00:43:14.227 naive in various situations. 00:43:14.227 --> 00:43:16.060 But then the question is, how is it possible 00:43:16.060 --> 00:43:18.340 that people are so naive in situations where, like-- 00:43:18.340 --> 00:43:19.660 we're going to the gym. 00:43:19.660 --> 00:43:22.390 Every week you're going to have the choice of going to the gym. 00:43:22.390 --> 00:43:24.430 You should have learned by now what 00:43:24.430 --> 00:43:26.573 your type is, in some sense, what your beta is. 00:43:26.573 --> 00:43:28.240 And you should have sort of then updated 00:43:28.240 --> 00:43:31.510 your beliefs accordingly and sort of changed your decisions. 00:43:31.510 --> 00:43:33.490 But somehow people have not done that. 00:43:33.490 --> 00:43:36.098 And people tend to be naive in situations 00:43:36.098 --> 00:43:38.140 where really they have lots of situations or lots 00:43:38.140 --> 00:43:39.510 of occasions to learn. 00:43:39.510 --> 00:43:41.260 Similarly, if you think about problem sets 00:43:41.260 --> 00:43:42.790 that you're doing, in some ways you 00:43:42.790 --> 00:43:46.180 know at the beginning of the semester kind of what's 00:43:46.180 --> 00:43:47.690 going to happen, in some ways. 00:43:47.690 --> 00:43:49.150 We should now. 00:43:49.150 --> 00:43:51.490 Yet, people tend to be overoptimistic 00:43:51.490 --> 00:43:52.510 in various cases. 00:43:52.510 --> 00:43:54.340 I was an undergrad advisor for a while. 00:43:54.340 --> 00:43:57.058 And I was sort of advising students on course choices. 00:43:57.058 --> 00:43:58.600 Every semester it was the same thing. 00:43:58.600 --> 00:44:01.570 I would say, like, four classes are grades, and so on. 00:44:01.570 --> 00:44:03.850 Students would take, like, six or seven. 00:44:03.850 --> 00:44:08.290 And then I would say, well, you know, that tends to not end up 00:44:08.290 --> 00:44:08.980 very well. 00:44:08.980 --> 00:44:10.230 Students are like, no, no, no. 00:44:10.230 --> 00:44:12.270 This semester is different. 00:44:12.270 --> 00:44:13.520 I'm going to work really hard. 00:44:13.520 --> 00:44:14.320 It's going to be all great. 00:44:14.320 --> 00:44:16.050 And then a month later, we would meet. 00:44:16.050 --> 00:44:17.800 And then we would go down to five classes. 00:44:17.800 --> 00:44:19.523 And I'd be like, well, maybe four classes are also fine. 00:44:19.523 --> 00:44:20.650 They're like, no, no, no, no. 00:44:20.650 --> 00:44:21.640 Five classes are great. 00:44:21.640 --> 00:44:24.100 And then at the end, we end up at four or three. 00:44:24.100 --> 00:44:27.340 So in a way, there are a bunch of behaviors 00:44:27.340 --> 00:44:28.390 that repeat over time. 00:44:28.390 --> 00:44:29.807 And in some sense, you would still 00:44:29.807 --> 00:44:31.630 think, why are people not learning? 00:44:31.630 --> 00:44:34.338 One explanation why people don't learn is in some sense, 00:44:34.338 --> 00:44:35.380 they don't want to learn. 00:44:35.380 --> 00:44:37.780 In the sense of like, I like to be a person. 00:44:37.780 --> 00:44:39.520 I like to think of myself as a person who 00:44:39.520 --> 00:44:42.940 is virtuous, who is hardworking, who is going to be really doing 00:44:42.940 --> 00:44:44.600 great at classes and so on. 00:44:44.600 --> 00:44:46.100 So I want to be that person. 00:44:46.100 --> 00:44:48.610 I feel better about myself by wanting that. 00:44:48.610 --> 00:44:51.280 And therefore, I might not learn as much as I could, 00:44:51.280 --> 00:44:52.905 even though that's costly for me to do. 00:44:52.905 --> 00:44:54.697 And we're going to talk a little about this 00:44:54.697 --> 00:44:57.340 in terms of overconfidence and so on, where essentially people 00:44:57.340 --> 00:44:58.750 have motivated beliefs and people 00:44:58.750 --> 00:45:01.900 want to be the person with beta equals 1. 00:45:01.900 --> 00:45:05.170 But in fact, they might not be. 00:45:05.170 --> 00:45:06.340 OK. 00:45:06.340 --> 00:45:08.680 So now what does the sophisticated student do? 00:45:08.680 --> 00:45:11.020 We already discussed that. 00:45:11.020 --> 00:45:12.868 Essentially, the person already knows. 00:45:12.868 --> 00:45:14.410 The person has rational expectations. 00:45:14.410 --> 00:45:17.020 So the person knows that if she doesn't do it in period zero, 00:45:17.020 --> 00:45:18.645 she's not going to do it in period one, 00:45:18.645 --> 00:45:21.160 because the period one self will change their minds 00:45:21.160 --> 00:45:22.870 and not follow through with her plans. 00:45:22.870 --> 00:45:24.730 So she's going to do it in period two. 00:45:24.730 --> 00:45:26.335 Now anticipating that for a choice 00:45:26.335 --> 00:45:28.210 is essentially, effectively, between doing it 00:45:28.210 --> 00:45:30.700 right now versus in period two. 00:45:30.700 --> 00:45:34.411 That's the effective choice that she has. 00:45:34.411 --> 00:45:36.220 And we can now just make the choice. 00:45:36.220 --> 00:45:38.980 Does she prefer doing it period zero versus period two? 00:45:38.980 --> 00:45:41.860 Well, she prefers doing it in period zero, 00:45:41.860 --> 00:45:43.930 because period two is too costly for her, 00:45:43.930 --> 00:45:45.880 even if that's in the future. 00:45:45.880 --> 00:45:48.400 And therefore, she does the problem set at period T 00:45:48.400 --> 00:45:50.570 equals zero. 00:45:50.570 --> 00:45:52.260 OK. 00:45:52.260 --> 00:45:53.537 Any questions? 00:45:57.140 --> 00:45:57.640 OK. 00:45:57.640 --> 00:45:59.530 So what's the summary of that? 00:45:59.530 --> 00:46:04.390 Well, the sophisticated student, for a case of investment goods, 00:46:04.390 --> 00:46:07.370 the person knows that if she delays, she'll delay even more. 00:46:07.370 --> 00:46:08.950 So once you start procrastinating, 00:46:08.950 --> 00:46:10.120 you know this is going to unravel. 00:46:10.120 --> 00:46:11.537 I'm never going to actually do it. 00:46:11.537 --> 00:46:13.460 And anticipating that, she's going to say, 00:46:13.460 --> 00:46:14.920 well, I'd rather do it right now, 00:46:14.920 --> 00:46:16.280 because I know this is going to unravel 00:46:16.280 --> 00:46:17.988 or this is going to derail in the future. 00:46:17.988 --> 00:46:20.512 I'd rather not have to do it very late, late at night, 00:46:20.512 --> 00:46:21.470 and so on and so forth. 00:46:21.470 --> 00:46:24.290 So let me do it right now. 00:46:24.290 --> 00:46:27.040 So that student in that specific case 00:46:27.040 --> 00:46:28.930 does better than the naive student. 00:46:28.930 --> 00:46:32.140 And for the case of investment goods, 00:46:32.140 --> 00:46:34.090 sophisticated procrastination does not 00:46:34.090 --> 00:46:35.410 cause large welfare costs. 00:46:35.410 --> 00:46:38.530 It's not possible for a perfectly sophisticated person 00:46:38.530 --> 00:46:42.430 to procrastinate things for a long time and sort of lead 00:46:42.430 --> 00:46:45.250 to a very inefficient or costly outcomes, the reason 00:46:45.250 --> 00:46:47.890 being if you know that's going to be costly in the future, 00:46:47.890 --> 00:46:51.490 if it's really that bad, you would rather do it right now. 00:46:51.490 --> 00:46:53.980 And so therefore, they cannot be-- 00:46:53.980 --> 00:46:55.608 there can be some costs of delaying. 00:46:55.608 --> 00:46:58.150 You might do it tomorrow-- you might do it a little bit later 00:46:58.150 --> 00:46:59.920 than optimally. 00:46:59.920 --> 00:47:02.800 But it cannot be that you procrastinated for a long time 00:47:02.800 --> 00:47:06.110 and never do it and therefore get like really large costs 00:47:06.110 --> 00:47:06.610 of that. 00:47:11.600 --> 00:47:12.290 OK. 00:47:12.290 --> 00:47:17.275 So one question that also came up in the online forum 00:47:17.275 --> 00:47:18.650 that you also saw in the readings 00:47:18.650 --> 00:47:20.670 that we're going to also talk a little bit about in the problem 00:47:20.670 --> 00:47:22.980 set is, well, is sophistication always good? 00:47:22.980 --> 00:47:26.170 And it's very intuitive to think that sophistication always 00:47:26.170 --> 00:47:26.670 helps. 00:47:26.670 --> 00:47:29.040 After all, knowing things better, 00:47:29.040 --> 00:47:31.242 having correct beliefs about yourself, 00:47:31.242 --> 00:47:32.700 that seems to be the correct thing. 00:47:32.700 --> 00:47:34.980 So intuitively, it feels like that should only help, 00:47:34.980 --> 00:47:36.070 should only make things better. 00:47:36.070 --> 00:47:37.470 If I understood my biases better, 00:47:37.470 --> 00:47:39.720 I should be doing better. 00:47:39.720 --> 00:47:42.563 Now, it turns out that's true for investment goods. 00:47:42.563 --> 00:47:43.980 So for investment goods, these are 00:47:43.980 --> 00:47:46.313 the goods where you have to do something in the present, 00:47:46.313 --> 00:47:48.660 but the costs-- sorry, the benefits are in the future. 00:47:48.660 --> 00:47:50.280 For that, sophistication is always 00:47:50.280 --> 00:47:52.320 better, or weakly better, the reason 00:47:52.320 --> 00:47:54.660 being that, again, you can sort of understand 00:47:54.660 --> 00:47:56.190 your future misbehavior. 00:47:56.190 --> 00:47:58.740 And by that understanding of future misbehavior, 00:47:58.740 --> 00:48:01.500 you can sort of avoid bad things happening in the future 00:48:01.500 --> 00:48:03.820 by doing it right now and earlier. 00:48:03.820 --> 00:48:06.960 So in that case, sophistication is always better. 00:48:06.960 --> 00:48:08.520 Now, it turns out for leisure goods, 00:48:08.520 --> 00:48:09.820 that's actually not the case. 00:48:09.820 --> 00:48:11.640 So leisure goods, again, are goods 00:48:11.640 --> 00:48:13.890 where you can enjoy something in the present 00:48:13.890 --> 00:48:17.590 and there may be some costs delayed in the future. 00:48:17.590 --> 00:48:22.740 And so let's look at-- and this is very close to now the paper 00:48:22.740 --> 00:48:24.390 that you read. 00:48:24.390 --> 00:48:25.770 Suppose there's a student who has 00:48:25.770 --> 00:48:28.920 beta equals 1/2 and delta equals 1, as before. 00:48:28.920 --> 00:48:32.730 Suppose the student can go to only one movie in exactly 00:48:32.730 --> 00:48:33.810 one of the four periods. 00:48:33.810 --> 00:48:35.643 There's only one movie ticket that she could 00:48:35.643 --> 00:48:37.313 use in period 0, 1, 2, and 3. 00:48:37.313 --> 00:48:39.480 By the way, Matthew Rabin is a huge Johnny Depp fan, 00:48:39.480 --> 00:48:42.000 in case you haven't noticed. 00:48:42.000 --> 00:48:44.520 So he uses Johnny Depp in various of his papers, 00:48:44.520 --> 00:48:46.520 and so on. 00:48:46.520 --> 00:48:50.100 He also had a huge Johnny Depp poster in his office. 00:48:50.100 --> 00:48:52.590 So the instantaneous utilities are 00:48:52.590 --> 00:48:57.880 such that they're 1, 3/4, 9/4, and 27/8, so they're 00:48:57.880 --> 00:48:59.850 sort of increasing over time. 00:48:59.850 --> 00:49:01.830 So if you-- so there's essentially 00:49:01.830 --> 00:49:04.287 one day where it's like the most fun to watch the movie, 00:49:04.287 --> 00:49:06.120 perhaps because you can go with your friends 00:49:06.120 --> 00:49:08.610 or whatever-- like, it's a better day to do it. 00:49:08.610 --> 00:49:11.160 Maybe you're a bit better rested or whatever it is. 00:49:11.160 --> 00:49:13.028 But sort of delaying would be good. 00:49:13.028 --> 00:49:15.570 Now, the problem, of course, is that the person is impatient. 00:49:15.570 --> 00:49:17.620 The person might not want to wait because the person is 00:49:17.620 --> 00:49:18.245 present biased. 00:49:18.245 --> 00:49:19.958 He might want to watch it earlier. 00:49:19.958 --> 00:49:21.750 The question now is, when does she actually 00:49:21.750 --> 00:49:23.880 go watch that movie? 00:49:23.880 --> 00:49:27.810 So now there's a way in which you can sort of write this down 00:49:27.810 --> 00:49:32.340 in a very simple form, which is a table of discounted 00:49:32.340 --> 00:49:32.850 utilities. 00:49:32.850 --> 00:49:35.857 That's a simple tool for solving these kinds of problems. 00:49:35.857 --> 00:49:37.440 This is supposed to come sequentially, 00:49:37.440 --> 00:49:39.435 but it isn't today, it's on something that's 00:49:39.435 --> 00:49:40.560 already filled out for you. 00:49:40.560 --> 00:49:42.040 So that's easier for you. 00:49:42.040 --> 00:49:44.550 So what I have filled out for you here 00:49:44.550 --> 00:49:46.860 is the instantaneous utility. 00:49:46.860 --> 00:49:49.050 So the first row here is essentially 00:49:49.050 --> 00:49:51.450 to say, these are sort of the assumptions that we have. 00:49:51.450 --> 00:49:53.033 You have the instantaneous utilities-- 00:49:53.033 --> 00:49:56.022 U0, U1, UT, U3, and so on. 00:49:56.022 --> 00:49:57.480 So this is essentially what you see 00:49:57.480 --> 00:49:59.910 on the first row of this table. 00:49:59.910 --> 00:50:02.700 Second then I filled out for you sort of the utilities 00:50:02.700 --> 00:50:05.880 from the perspective of period zero, period one, and period 00:50:05.880 --> 00:50:07.230 two. 00:50:07.230 --> 00:50:08.880 So from the perspective of T equals 00:50:08.880 --> 00:50:12.070 0, the first period T equals 0 equals just the same. 00:50:12.070 --> 00:50:14.585 That's just 1, because she puts weight one on that. 00:50:14.585 --> 00:50:15.960 But then everything in the future 00:50:15.960 --> 00:50:20.460 is discounted by 1/2, because the beta is 1/2. 00:50:20.460 --> 00:50:23.120 Yes? 00:50:23.120 --> 00:50:25.040 And then from the perspective of T 00:50:25.040 --> 00:50:27.652 equals 1, of course T equals 0 is sort of irrelevant 00:50:27.652 --> 00:50:28.860 because that was in the past. 00:50:28.860 --> 00:50:30.440 By definition, we only care about stuff 00:50:30.440 --> 00:50:32.023 that happens in the future, because we 00:50:32.023 --> 00:50:32.965 can't change the past. 00:50:32.965 --> 00:50:34.340 Notice that's also an assumption, 00:50:34.340 --> 00:50:36.590 but it's a common assumption made in economics. 00:50:36.590 --> 00:50:39.860 So there 3/2 now is in the present. 00:50:39.860 --> 00:50:41.180 So that gets weight 1. 00:50:41.180 --> 00:50:43.560 And everything that's in the future gets weight 1/2. 00:50:43.560 --> 00:50:47.180 So you have 9/8 and 27/16. 00:50:47.180 --> 00:50:49.670 And now for period 2 again-- 00:50:49.670 --> 00:50:52.310 period now 0 and 1 are in the past. 00:50:52.310 --> 00:50:54.260 Now she cares about the present [INAUDIBLE] 00:50:54.260 --> 00:50:56.480 T equals 2 with the weight of 1. 00:50:56.480 --> 00:50:57.470 That's 9/4. 00:50:57.470 --> 00:51:00.110 And now T equals 3 is in the future. 00:51:00.110 --> 00:51:02.200 That's discounted by 1/2. 00:51:02.200 --> 00:51:02.960 OK. 00:51:02.960 --> 00:51:04.520 And now what I also have done, I've 00:51:04.520 --> 00:51:07.610 written down the ranking of these different periods 00:51:07.610 --> 00:51:09.050 from the perspective of-- 00:51:09.050 --> 00:51:11.965 from the sort of just looking at the instantaneous utilities, 00:51:11.965 --> 00:51:13.340 three's better than two is better 00:51:13.340 --> 00:51:15.290 than one is better than zero. 00:51:15.290 --> 00:51:18.770 From the perspective of T equals 0, you prefer three over two 00:51:18.770 --> 00:51:20.180 over zero over one. 00:51:20.180 --> 00:51:22.700 From T equals 1, you prefer three over one over two. 00:51:22.700 --> 00:51:24.590 And from the perspective of T equals 2, 00:51:24.590 --> 00:51:27.080 you prefer two over three. 00:51:27.080 --> 00:51:29.696 Does this all make sense what I've written down here? 00:51:29.696 --> 00:51:31.330 I'll let you look at this for a second. 00:51:36.910 --> 00:51:37.410 OK. 00:51:37.410 --> 00:51:40.320 So what does the naive person do with beta hat equals 1? 00:51:48.640 --> 00:51:49.140 Yes. 00:51:52.600 --> 00:51:53.950 AUDIENCE: Oh, wait, hold on. 00:51:53.950 --> 00:51:57.108 FRANK SCHILBACH: We can do this step by step. 00:51:57.108 --> 00:51:58.960 AUDIENCE: OK, so [INAUDIBLE] zero. 00:51:58.960 --> 00:52:00.900 And then from the perspective of T equals 0, 00:52:00.900 --> 00:52:04.980 you would most prefer to do something at time three. 00:52:04.980 --> 00:52:06.480 FRANK SCHILBACH: Yes. 00:52:06.480 --> 00:52:08.280 AUDIENCE: So I guess that means that you 00:52:08.280 --> 00:52:11.164 don't do it in period one and then move on to T equals 1. 00:52:11.164 --> 00:52:13.164 And then again you want to do it in period three 00:52:13.164 --> 00:52:15.840 so you don't do it in period one here. 00:52:15.840 --> 00:52:18.400 And then you end up at T equals 2. 00:52:18.400 --> 00:52:21.205 And then you'd rather do it in period two than period three, 00:52:21.205 --> 00:52:22.330 so you do it in period two. 00:52:22.330 --> 00:52:22.650 FRANK SCHILBACH: Yes. 00:52:22.650 --> 00:52:23.190 Correct. 00:52:23.190 --> 00:52:25.770 So let me do that in slow motion. 00:52:25.770 --> 00:52:29.600 So in period T, she makes some plans. 00:52:29.600 --> 00:52:32.640 You wrote down what is her preferred plan in period 00:52:32.640 --> 00:52:33.810 T equals zero. 00:52:33.810 --> 00:52:35.730 We have our ranking at the very right 00:52:35.730 --> 00:52:37.980 in the right-- in the last column on the right. 00:52:37.980 --> 00:52:39.720 She prefers to do it in period three. 00:52:39.720 --> 00:52:42.670 She thinks that she's going to follow through with her plans. 00:52:42.670 --> 00:52:44.580 So she's not going to do it in period 0 00:52:44.580 --> 00:52:46.590 because she thinks she prefers period three. 00:52:46.590 --> 00:52:48.390 So let's just wait. 00:52:48.390 --> 00:52:55.800 So she doesn't go in in periods T equals 0. 00:52:55.800 --> 00:52:58.120 And period T equals 1 is the same thing. 00:52:58.120 --> 00:53:00.180 And now she essentially says, well, she 00:53:00.180 --> 00:53:01.980 prefers three over one over two. 00:53:01.980 --> 00:53:03.490 It's better to do it in period three 00:53:03.490 --> 00:53:05.970 so let's just wait until period three. 00:53:05.970 --> 00:53:07.710 Now, of course, period two comes. 00:53:07.710 --> 00:53:10.680 Once period two comes, it turns out 00:53:10.680 --> 00:53:14.160 we cooked up the number such as like prefers a period 00:53:14.160 --> 00:53:15.450 two over period three. 00:53:15.450 --> 00:53:18.300 So she surprises herself by actually watching the movie 00:53:18.300 --> 00:53:20.440 in period two. 00:53:20.440 --> 00:53:22.950 OK. 00:53:22.950 --> 00:53:24.242 Any questions? 00:53:27.140 --> 00:53:27.640 OK. 00:53:27.640 --> 00:53:30.160 So now instead, what does a sophisticated student do? 00:53:32.770 --> 00:53:36.220 So this was the perfectly naive student doing it and watching 00:53:36.220 --> 00:53:37.540 the movie in period two. 00:53:37.540 --> 00:53:39.740 No, if you're sophisticated, what do you do? 00:53:39.740 --> 00:53:40.928 Yes. 00:53:40.928 --> 00:53:43.060 AUDIENCE: She starts thinking that if she waits, 00:53:43.060 --> 00:53:47.235 [INAUDIBLE] equals 2, she's going to at two-- 00:53:47.235 --> 00:53:48.714 wait. 00:53:48.714 --> 00:53:50.193 FRANK SCHILBACH: Correct. 00:53:50.193 --> 00:53:52.668 AUDIENCE: So then she knows that at T equals 1, 00:53:52.668 --> 00:53:53.960 she's not going wait until two. 00:53:53.960 --> 00:53:54.640 She's going to-- 00:54:03.647 --> 00:54:04.730 FRANK SCHILBACH: Any help? 00:54:04.730 --> 00:54:05.230 Yes, OK. 00:54:11.340 --> 00:54:16.970 AUDIENCE: So first student, at T equals 2, she would go. 00:54:16.970 --> 00:54:24.190 So if she were at T equals 1, she knows that if she waits, 00:54:24.190 --> 00:54:30.160 then she would go at two instead of three. 00:54:30.160 --> 00:54:33.190 But she likes one. 00:54:33.190 --> 00:54:35.860 So her choice is not between one and three, 00:54:35.860 --> 00:54:37.930 but between one and two. 00:54:37.930 --> 00:54:42.250 So if she were at time period one, then she would go-- 00:54:42.250 --> 00:54:43.720 choose to go at one. 00:54:43.720 --> 00:54:48.250 And then if she's at time T equals 0, 00:54:48.250 --> 00:54:53.810 her choice is going to be between zero and one, not zero 00:54:53.810 --> 00:54:54.310 and three. 00:54:54.310 --> 00:54:58.840 So that if she were at time period zero, 00:54:58.840 --> 00:55:01.248 she would just end up going at time period zero. 00:55:01.248 --> 00:55:02.290 FRANK SCHILBACH: Correct. 00:55:02.290 --> 00:55:05.930 So let me also say that a little slower again. 00:55:05.930 --> 00:55:09.130 So if we look at perfectly naive people, 00:55:09.130 --> 00:55:12.520 they're going to start from the beginning and go forwards. 00:55:12.520 --> 00:55:15.400 We have a naive person who has plans going forward. 00:55:15.400 --> 00:55:17.620 And then we just look at how does this plan evolve? 00:55:17.620 --> 00:55:20.920 So you start at how does this person person 00:55:20.920 --> 00:55:22.910 decide at period T equals zero, thinking 00:55:22.910 --> 00:55:24.160 she's going to follow through? 00:55:24.160 --> 00:55:25.750 Then we go to period one thinking 00:55:25.750 --> 00:55:26.740 she's going to follow through. 00:55:26.740 --> 00:55:28.060 Then we go to period two thinking 00:55:28.060 --> 00:55:29.310 she's going to follow through. 00:55:29.310 --> 00:55:31.150 And that's how we sort of solve the problem. 00:55:31.150 --> 00:55:34.057 Now, for the sophisticated person, 00:55:34.057 --> 00:55:35.390 you would do things differently. 00:55:35.390 --> 00:55:37.682 We essentially do this backwards deduction, essentially 00:55:37.682 --> 00:55:39.610 to say let's start at the very end. 00:55:39.610 --> 00:55:41.980 The reason that we can use backwards induction 00:55:41.980 --> 00:55:44.260 is because people have rational expectations. 00:55:44.260 --> 00:55:46.410 The person knows exactly what she's going to do, 00:55:46.410 --> 00:55:47.680 which is she's going to start from the end 00:55:47.680 --> 00:55:49.472 and say, OK, how is this going to play out? 00:55:49.472 --> 00:55:51.100 What am I going to do in the end? 00:55:51.100 --> 00:55:54.080 And sort of anticipating that perfectly, we're 00:55:54.080 --> 00:55:56.510 going to then solve backwards. 00:55:56.510 --> 00:56:00.503 OK, so as you just said, in period two, 00:56:00.503 --> 00:56:02.920 we know that she's going to go, if she hasn't, because she 00:56:02.920 --> 00:56:04.125 prefers two over three. 00:56:04.125 --> 00:56:05.500 That's the last row that we have. 00:56:05.500 --> 00:56:09.970 She likes two better than three once she comes to period two. 00:56:09.970 --> 00:56:12.350 Now, in period T equals 1, she knows 00:56:12.350 --> 00:56:14.350 that she's not going to wait until period three. 00:56:14.350 --> 00:56:16.270 So period three is actually not an option for her. 00:56:16.270 --> 00:56:17.500 She knows that's not credible. 00:56:17.500 --> 00:56:18.920 She's not going to follow through. 00:56:18.920 --> 00:56:21.370 So then it's just a choice between one and two. 00:56:21.370 --> 00:56:22.780 She prefers one over two. 00:56:22.780 --> 00:56:25.660 So she's going to-- 00:56:25.660 --> 00:56:27.220 going in period one. 00:56:27.220 --> 00:56:29.470 Now then, in period one two equals 0, 00:56:29.470 --> 00:56:31.090 now we know-- she realized that she 00:56:31.090 --> 00:56:32.945 won't wait until two or three. 00:56:32.945 --> 00:56:34.570 Two or three are not an option for her. 00:56:34.570 --> 00:56:37.510 She would actually prefer both two and three. 00:56:37.510 --> 00:56:39.910 But that's not possible because her future self will not 00:56:39.910 --> 00:56:41.440 stick to her choice. 00:56:41.440 --> 00:56:45.610 So then the choice really just becomes between zero and one, 00:56:45.610 --> 00:56:48.312 and she prefers zero over one. 00:56:48.312 --> 00:56:50.020 Now, essentially, she goes to that movie, 00:56:50.020 --> 00:56:51.940 and gets a trilogy of one. 00:56:51.940 --> 00:56:54.568 But actually, she would prefer any of these other outcomes-- 00:56:54.568 --> 00:56:56.110 actually, any of her other self would 00:56:56.110 --> 00:56:57.550 prefer her to not do that. 00:56:57.550 --> 00:57:00.580 But she actually picks period one. 00:57:00.580 --> 00:57:02.290 So that's an example. 00:57:02.290 --> 00:57:03.820 And there's several examples of that 00:57:03.820 --> 00:57:05.910 where sophistication can hurt. 00:57:05.910 --> 00:57:08.800 Now, why is sophistication hurting here? 00:57:08.800 --> 00:57:11.470 What's the key part, and why is it 00:57:11.470 --> 00:57:15.250 worse for the student to be sophisticated? 00:57:15.250 --> 00:57:16.750 In some sense, if you think about it 00:57:16.750 --> 00:57:20.560 from the perspective of T equals 0, 00:57:20.560 --> 00:57:23.830 she would prefer a three over two over zero over one. 00:57:23.830 --> 00:57:27.700 Or overall, if you look at the instantaneous utilities, 00:57:27.700 --> 00:57:29.450 period two is better. 00:57:29.450 --> 00:57:31.220 So from the perspective of T equals 0, 00:57:31.220 --> 00:57:33.400 period two is better than period zero. 00:57:33.400 --> 00:57:35.630 Yet, he ends up going in period zero. 00:57:35.630 --> 00:57:37.480 So a sophisticated person actually 00:57:37.480 --> 00:57:39.340 would be better off if she were naive. 00:57:39.340 --> 00:57:41.470 If she could sort of commit to something and say, 00:57:41.470 --> 00:57:45.250 I would prefer to go in period two, if she could say-- 00:57:45.250 --> 00:57:47.200 if I only could be naive, that would sort of 00:57:47.200 --> 00:57:49.060 help her to actually do it in period two. 00:57:49.060 --> 00:57:52.330 Of course, you can't sort of choose that. 00:57:52.330 --> 00:57:55.930 But here she's worse off from being sophisticated. 00:57:55.930 --> 00:57:57.040 But what's going on here? 00:57:57.040 --> 00:57:58.532 Like, why is that happening? 00:58:04.810 --> 00:58:05.620 Yes. 00:58:05.620 --> 00:58:08.650 AUDIENCE: So she almost mistrusts her future self 00:58:08.650 --> 00:58:11.980 and so preempts that by taking the previous decision. 00:58:11.980 --> 00:58:13.600 But then also preempting that, she 00:58:13.600 --> 00:58:15.400 would preempt her future self. 00:58:15.400 --> 00:58:18.250 She would take the previous decision again. 00:58:18.250 --> 00:58:21.475 And so that makes it so that she does the action 00:58:21.475 --> 00:58:24.130 at the very start instead. 00:58:24.130 --> 00:58:27.010 For us, the naive person always blunders through 00:58:27.010 --> 00:58:29.530 and manages to take the more-- 00:58:29.530 --> 00:58:31.982 the action with the higher utility. 00:58:31.982 --> 00:58:32.940 FRANK SCHILBACH: Right. 00:58:32.940 --> 00:58:38.800 So in some ways, the problem is set up in a way that, in a way, 00:58:38.800 --> 00:58:41.380 realistic pessimism-- the sophisticated person 00:58:41.380 --> 00:58:43.300 is, like, realistic in their pessimism. 00:58:43.300 --> 00:58:46.570 She knows, essentially, that in the future 00:58:46.570 --> 00:58:48.290 she's not going to behave. 00:58:48.290 --> 00:58:50.180 So she would love to wait. 00:58:50.180 --> 00:58:51.770 But what she needs to do to wait, 00:58:51.770 --> 00:58:54.550 she needs to have a sufficiently high benefit of waiting. 00:58:54.550 --> 00:58:56.440 Now, how high is the benefit of waiting? 00:58:56.440 --> 00:58:58.900 It depends on what your future self is going to do. 00:58:58.900 --> 00:59:01.840 If you only wait a little bit, the person will say, 00:59:01.840 --> 00:59:03.970 if I go-- if the choice is between zero and one, 00:59:03.970 --> 00:59:04.928 it's not worth waiting. 00:59:04.928 --> 00:59:06.620 I might as well go right now. 00:59:06.620 --> 00:59:09.550 So if I can wrongly sort of have the illusion to myself 00:59:09.550 --> 00:59:12.340 that I say, well, I'm going to not 00:59:12.340 --> 00:59:16.750 go in one, or in two, for that matter, then in some sense 00:59:16.750 --> 00:59:19.600 the benefits of waiting-- the perceived benefits of waiting 00:59:19.600 --> 00:59:21.470 are higher than they actually are. 00:59:21.470 --> 00:59:24.820 And in this case, it mitigates the self-control problem 00:59:24.820 --> 00:59:26.630 or the present bias. 00:59:26.630 --> 00:59:28.630 The present bias person wants to do it right now 00:59:28.630 --> 00:59:32.140 and needs a sufficiently high reward for waiting. 00:59:32.140 --> 00:59:34.270 So if you can sort of perceive-- 00:59:34.270 --> 00:59:36.100 if you can sort of deceive yourself 00:59:36.100 --> 00:59:38.450 into thinking that the rewards of waiting are high, 00:59:38.450 --> 00:59:39.700 you're going to actually wait. 00:59:39.700 --> 00:59:42.760 And that's good for you in this case. 00:59:42.760 --> 00:59:45.023 If, instead, you're realistic about your future self, 00:59:45.023 --> 00:59:47.440 you know that waiting is not really helping you very much. 00:59:47.440 --> 00:59:50.050 You know that essentially, if you wait for one period, 00:59:50.050 --> 00:59:52.300 you're going to go and go in the next period, anyway. 00:59:52.300 --> 00:59:53.300 So then the reward-- 00:59:53.300 --> 00:59:55.800 and that's in part because the numbers are set up that way-- 00:59:55.800 --> 00:59:58.807 but that's now essentially sort of telling you, 00:59:58.807 --> 01:00:00.640 well, waiting is not really doing very much, 01:00:00.640 --> 01:00:03.100 because your future self is also misbehaving. 01:00:03.100 --> 01:00:06.190 It sort of makes it impossible to actually wait 01:00:06.190 --> 01:00:08.525 all the way until the very end. 01:00:08.525 --> 01:00:10.900 And therefore, it sort of makes the self-control problem, 01:00:10.900 --> 01:00:12.850 the present bias, worse, because now it's 01:00:12.850 --> 01:00:16.270 like it's not worth-- why even bother to wait a little bit, 01:00:16.270 --> 01:00:18.280 because that's literally not worth doing? 01:00:18.280 --> 01:00:21.150 Really what you would need is wait all the way through. 01:00:21.150 --> 01:00:22.153 Yeah. 01:00:22.153 --> 01:00:23.986 AUDIENCE: So I think this is related to what 01:00:23.986 --> 01:00:25.470 I was trying to ask before. 01:00:25.470 --> 01:00:28.676 If you're sophisticated, you know you have [INAUDIBLE].. 01:00:28.676 --> 01:00:30.100 If you are in period zero, you'll 01:00:30.100 --> 01:00:33.550 know that on the next period, you're [INAUDIBLE].. 01:00:40.070 --> 01:00:43.090 So why would you prefer to experience [INAUDIBLE] one now 01:00:43.090 --> 01:00:44.920 [INAUDIBLE] experience [INAUDIBLE].. 01:00:48.892 --> 01:00:51.820 FRANK SCHILBACH: No, but I think it's-- 01:00:51.820 --> 01:00:54.902 in a way, there is a preference over-- 01:00:54.902 --> 01:00:56.860 and something like that's, again, an assumption 01:00:56.860 --> 01:00:58.060 how people behave. 01:00:58.060 --> 01:00:59.930 People care a lot about the present. 01:00:59.930 --> 01:01:01.160 And that's sort of like, in some sense, 01:01:01.160 --> 01:01:03.243 in a bunch of experiments and so on, people really 01:01:03.243 --> 01:01:05.560 want stuff right now, even if they 01:01:05.560 --> 01:01:08.790 know that they will prefer stuff in two days from now 01:01:08.790 --> 01:01:10.300 or three days from now and so on. 01:01:10.300 --> 01:01:14.050 You just-- you are impatient right now. 01:01:14.050 --> 01:01:16.780 And that's what the utility function is like. 01:01:16.780 --> 01:01:19.610 And so you put less weight on stuff that's in the future. 01:01:19.610 --> 01:01:22.858 Now, if you sort think about your future preferences, 01:01:22.858 --> 01:01:25.150 there's a question on-- that's a philosophical question 01:01:25.150 --> 01:01:27.067 in some ways-- how do you think about the fact 01:01:27.067 --> 01:01:29.260 that your future self wants something different? 01:01:29.260 --> 01:01:32.860 That is to say, for example, if I want to exercise a lot 01:01:32.860 --> 01:01:36.640 and I also like to sit on the couch and watch TV a lot, 01:01:36.640 --> 01:01:40.270 now my current self wants to exercise a lot in the future. 01:01:40.270 --> 01:01:42.700 My future self wants to-- and I know that-- 01:01:42.700 --> 01:01:44.290 wants to sit on the couch. 01:01:44.290 --> 01:01:46.443 Now the question is which-- and when 01:01:46.443 --> 01:01:47.860 you think about welfare and so on, 01:01:47.860 --> 01:01:49.573 which self should we respect? 01:01:49.573 --> 01:01:51.490 And one assumption-- and this is an assumption 01:01:51.490 --> 01:01:55.270 that's built in here-- is to say my current self has 01:01:55.270 --> 01:01:56.652 certain plans for the future. 01:01:56.652 --> 01:01:58.360 And those preferences are the preferences 01:01:58.360 --> 01:02:00.250 that I'm using to maximize. 01:02:00.250 --> 01:02:02.650 I know that my future self wants other things. 01:02:02.650 --> 01:02:05.650 But in some sense, I'm assuming I know that I know better. 01:02:05.650 --> 01:02:08.590 This is the utility function that counts is the current one, 01:02:08.590 --> 01:02:10.030 not the future one. 01:02:10.030 --> 01:02:12.070 And so then I respect that one and I'm 01:02:12.070 --> 01:02:15.040 trying to maximize that sort of subject 01:02:15.040 --> 01:02:18.520 to my future preferences being different. 01:02:18.520 --> 01:02:20.187 But in some sense, you're exactly right. 01:02:20.187 --> 01:02:21.645 If you think about, like, should we 01:02:21.645 --> 01:02:23.230 tax potato chips, for example-- 01:02:23.230 --> 01:02:24.880 talk about welfare and so on-- 01:02:24.880 --> 01:02:26.330 should we tax potato chips? 01:02:26.330 --> 01:02:28.040 You could say, well, on the one hand, 01:02:28.040 --> 01:02:30.077 I might say I would like to tax potato chips, 01:02:30.077 --> 01:02:31.660 because I know in the future I'm going 01:02:31.660 --> 01:02:33.100 to eat too many potato chips. 01:02:33.100 --> 01:02:34.630 That's good for me. 01:02:34.630 --> 01:02:36.100 But there's a future self-- 01:02:36.100 --> 01:02:38.590 actually, myself-- who would love to eat potato chips. 01:02:38.590 --> 01:02:40.900 That self would be really unhappy. 01:02:40.900 --> 01:02:43.420 Now you get very tricky questions of welfare 01:02:43.420 --> 01:02:45.130 and a sense of saying, like, well, 01:02:45.130 --> 01:02:46.870 who are we to say that the current self 01:02:46.870 --> 01:02:49.420 is different or should get priority over the future self? 01:02:49.420 --> 01:02:51.820 The future self will really be unhappy. 01:02:51.820 --> 01:02:54.250 So there are different views on this. 01:02:54.250 --> 01:02:56.950 Some people, including Matthew Rabin including David Laibson 01:02:56.950 --> 01:02:58.367 and so on, would sort of say, what 01:02:58.367 --> 01:03:00.670 counts is the current self, or a self 01:03:00.670 --> 01:03:02.077 that chooses for the future. 01:03:02.077 --> 01:03:03.910 That's sort of the virtue of self and so on. 01:03:03.910 --> 01:03:06.340 We should use that for welfare evaluation. 01:03:06.340 --> 01:03:07.542 That's an assumption. 01:03:07.542 --> 01:03:10.000 There's other people who would argue that no, like, there's 01:03:10.000 --> 01:03:11.740 all sorts of self who want different things. 01:03:11.740 --> 01:03:13.615 So if you think about, is it good to increase 01:03:13.615 --> 01:03:15.400 taxes for potato chips? 01:03:15.400 --> 01:03:17.530 Maybe, because some selves are better off 01:03:17.530 --> 01:03:18.942 and some selves are worse off. 01:03:18.942 --> 01:03:21.400 And how do we ever aggregate across those different selves? 01:03:21.400 --> 01:03:23.210 So you get very tricky questions. 01:03:23.210 --> 01:03:25.210 But here for our purposes what we're going to do 01:03:25.210 --> 01:03:27.550 is we're going to say the current self is essentially 01:03:27.550 --> 01:03:30.820 disrespecting future utility functions 01:03:30.820 --> 01:03:33.580 and preferences in the own maximization 01:03:33.580 --> 01:03:34.960 and the maximization problem. 01:03:34.960 --> 01:03:37.450 That is to say, I have a utility function right now, 01:03:37.450 --> 01:03:40.270 and sort of discounting function that tells me 01:03:40.270 --> 01:03:44.260 how I want to aggregate my future utility over time. 01:03:44.260 --> 01:03:45.920 That is what I want. 01:03:45.920 --> 01:03:49.000 And then I have essentially like a-- sort of like constraints 01:03:49.000 --> 01:03:51.460 which are coming sort of in the-- when I think about sort 01:03:51.460 --> 01:03:54.088 of like when you write down a utility maximization problem, 01:03:54.088 --> 01:03:56.380 there's an objective function, which is my maximization 01:03:56.380 --> 01:03:56.880 problem. 01:03:56.880 --> 01:03:59.110 That's the utility function that I want right now. 01:03:59.110 --> 01:04:01.180 And then there's constraints in your maximization 01:04:01.180 --> 01:04:03.220 problem, which are in the future, 01:04:03.220 --> 01:04:04.760 my preferences will change. 01:04:04.760 --> 01:04:06.430 So some options might not be feasible 01:04:06.430 --> 01:04:09.122 because of these preference reversals, and so on. 01:04:09.122 --> 01:04:10.080 But that's not to say-- 01:04:10.080 --> 01:04:12.610 I'm respecting your future preferences to the extent 01:04:12.610 --> 01:04:15.070 that I need to have feasible plans. 01:04:15.070 --> 01:04:16.960 I'm not respecting them in the sense of, 01:04:16.960 --> 01:04:18.070 like, I know right now. 01:04:18.070 --> 01:04:20.691 I know better what's good for myself. 01:04:20.691 --> 01:04:22.060 Did that answer your question? 01:04:22.060 --> 01:04:23.840 OK. 01:04:23.840 --> 01:04:25.372 Any other-- yeah. 01:04:25.372 --> 01:04:26.830 AUDIENCE: [INAUDIBLE]. 01:04:35.480 --> 01:04:37.730 FRANK SCHILBACH: Sorry, what exactly is the question? 01:04:37.730 --> 01:04:42.720 AUDIENCE: So does that mean that if you go see the movie in T 01:04:42.720 --> 01:04:47.580 equals 2, do you evaluate that as-- sorry, [INAUDIBLE].. 01:04:47.580 --> 01:04:50.050 FRANK SCHILBACH: So from the perspective of period T equals 01:04:50.050 --> 01:04:52.870 2, you evaluate it with 9/4. 01:04:52.870 --> 01:04:54.970 From the perspective of period T equals 01:04:54.970 --> 01:04:57.560 1 or T equals 0, that is in the future. 01:04:57.560 --> 01:05:02.230 So you multiply the 9/4 times 1/2, 01:05:02.230 --> 01:05:04.167 which is the beta because it's in the future. 01:05:04.167 --> 01:05:06.125 AUDIENCE: So then when you say the student does 01:05:06.125 --> 01:05:07.320 better [INAUDIBLE]. 01:05:12.545 --> 01:05:14.920 FRANK SCHILBACH: I'm using sort of from that perspective. 01:05:14.920 --> 01:05:17.553 So in some sense, that's a bit of a question philosophically, 01:05:17.553 --> 01:05:20.220 what's better and worse, because you have different perspective. 01:05:20.220 --> 01:05:22.770 You can take from the perspective of T equals 0-- 01:05:22.770 --> 01:05:24.750 for example, a sophisticated person 01:05:24.750 --> 01:05:28.615 would much prefer period two over period zero, one 01:05:28.615 --> 01:05:30.210 over zero. 01:05:30.210 --> 01:05:33.120 So I just showed you that the sophisticated person 01:05:33.120 --> 01:05:35.340 goes in period zero. 01:05:35.340 --> 01:05:39.340 But in fact, the person would prefer a three and two. 01:05:39.340 --> 01:05:41.110 So the outcome of the naive person 01:05:41.110 --> 01:05:43.030 would be better for the sophisticated person 01:05:43.030 --> 01:05:44.830 from the perspective of T equals 0. 01:05:48.613 --> 01:05:50.280 And so then there's a bit of a question. 01:05:50.280 --> 01:05:52.200 From the perspective of t equals 2, 01:05:52.200 --> 01:05:54.333 if you had gone already in the previous period, 01:05:54.333 --> 01:05:56.250 probably prefer if you hadn't gone previously. 01:05:56.250 --> 01:05:58.740 But that's a bit silly, in some sense. 01:05:58.740 --> 01:06:01.230 But you can essentially-- you can write down for each self, 01:06:01.230 --> 01:06:02.880 what would each self prefer? 01:06:02.880 --> 01:06:05.760 And I think as it is in this example, it's essentially, 01:06:05.760 --> 01:06:08.400 the sophisticated essentially does worse for all selves 01:06:08.400 --> 01:06:10.980 compared to a-- weakly worse compared to the naive person. 01:06:14.640 --> 01:06:18.250 OK, but happy to talk after. 01:06:18.250 --> 01:06:19.830 OK, so I think we have all of that. 01:06:19.830 --> 01:06:22.540 Sophistication can make things worse. 01:06:22.540 --> 01:06:24.930 So now overall let me-- 01:06:24.930 --> 01:06:26.830 so more generally, the lessons are-- 01:06:26.830 --> 01:06:29.820 so the question is kind of like whether future misbehavior 01:06:29.820 --> 01:06:33.090 raises or lowers the cost of current misbehavior. 01:06:33.090 --> 01:06:35.890 So essentially, whether future and current misbehavior 01:06:35.890 --> 01:06:39.755 are compliments or substitutes-- so if future misbehavior raises 01:06:39.755 --> 01:06:41.130 the costs of current misbehavior, 01:06:41.130 --> 01:06:44.100 then sophistication helps in overcoming short run 01:06:44.100 --> 01:06:45.150 impatience. 01:06:45.150 --> 01:06:47.085 That tends to be true for investment goods. 01:06:47.085 --> 01:06:48.960 That was the example that I showed you first. 01:06:48.960 --> 01:06:50.700 If I know I'm going to misbehave in the future, 01:06:50.700 --> 01:06:51.420 I'm not going to like-- 01:06:51.420 --> 01:06:54.090 I'm going to procrastinate a lot if I don't do it right now. 01:06:54.090 --> 01:06:55.680 Then sophistication is good because I 01:06:55.680 --> 01:06:59.490 can sort of prevent that by just doing stuff right now. 01:06:59.490 --> 01:07:02.133 So those are the investment goods with immediate cost. 01:07:02.133 --> 01:07:03.550 There are some exceptions to that. 01:07:03.550 --> 01:07:05.550 But generally, that tends to be true. 01:07:05.550 --> 01:07:07.650 Now, if instead future misbehavior 01:07:07.650 --> 01:07:10.230 lowers the costs of current misbehavior, 01:07:10.230 --> 01:07:13.985 because essentially the benefits of waiting in this case 01:07:13.985 --> 01:07:16.110 that I showed you for the movie are just lower now, 01:07:16.110 --> 01:07:19.117 so the costs of misbehaving now have become lower, then I say, 01:07:19.117 --> 01:07:20.700 well, I might as well do it right now. 01:07:20.700 --> 01:07:22.500 I might as well eat the cake right now, or whatever. 01:07:22.500 --> 01:07:23.770 There's no point in waiting. 01:07:23.770 --> 01:07:26.380 So then sophistication hurts in overcoming short run 01:07:26.380 --> 01:07:27.300 impatience. 01:07:27.300 --> 01:07:31.590 And that tends to be the case for leisure goods. 01:07:31.590 --> 01:07:34.050 So avoid immediate rewards. 01:07:34.050 --> 01:07:36.054 Now-- yes? 01:07:36.054 --> 01:07:37.530 AUDIENCE: [INAUDIBLE]. 01:07:43.940 --> 01:07:45.835 FRANK SCHILBACH: It has to-- 01:07:45.835 --> 01:07:46.710 it's a little tricky. 01:07:46.710 --> 01:07:47.752 It's kind of complicated. 01:07:47.752 --> 01:07:50.150 In some sense, it has to do with specific cases. 01:07:50.150 --> 01:07:53.060 But the key question is essentially is like, 01:07:53.060 --> 01:07:57.740 in the future, does sophistication or misbehavior 01:07:57.740 --> 01:08:00.750 raise or lower the costs of future misbehavior? 01:08:00.750 --> 01:08:04.370 Does it raise or lower the costs of current misbehavior? 01:08:04.370 --> 01:08:07.580 And then depending on whether that's the case, sophistication 01:08:07.580 --> 01:08:10.700 or naivete go in different directions. 01:08:10.700 --> 01:08:13.140 So essentially there's a true answer to that. 01:08:13.140 --> 01:08:14.450 And then essentially if you're naive to this, 01:08:14.450 --> 01:08:17.330 it sort of flips the direction, depending on the numbers. 01:08:17.330 --> 01:08:19.365 But it's more complicated to that. 01:08:19.365 --> 01:08:21.740 It sort of-- these are sort of fairly general statements. 01:08:21.740 --> 01:08:23.090 So it's a little complicated. 01:08:23.090 --> 01:08:25.830 But you'll see some examples again in problem sets 01:08:25.830 --> 01:08:26.330 and so on. 01:08:26.330 --> 01:08:27.060 Yes. 01:08:27.060 --> 01:08:28.810 AUDIENCE: Does anybody model [INAUDIBLE]?? 01:08:32.762 --> 01:08:33.970 FRANK SCHILBACH: Not so much. 01:08:33.970 --> 01:08:36.979 So usually people tend to-- so that's an interesting question. 01:08:36.979 --> 01:08:39.920 So usually people think beta hat or any preference parameters 01:08:39.920 --> 01:08:43.899 are often independent of the costs and choices that you see. 01:08:43.899 --> 01:08:47.160 So the idea often is you are born 01:08:47.160 --> 01:08:49.200 with a beta and a beta hat and a delta 01:08:49.200 --> 01:08:51.630 and so on that fell somehow from the sky. 01:08:51.630 --> 01:08:54.342 There's some research on how environmental factors and so 01:08:54.342 --> 01:08:55.259 on affect preferences. 01:08:55.259 --> 01:08:57.660 For example, we'll show you some research 01:08:57.660 --> 01:09:00.223 on how contact with different types of people 01:09:00.223 --> 01:09:01.515 affect your social preferences. 01:09:01.515 --> 01:09:05.939 For example, if you are exposed to many poor people 01:09:05.939 --> 01:09:07.378 as a rich person in your life, you 01:09:07.378 --> 01:09:09.420 might become a nicer person and things like that. 01:09:09.420 --> 01:09:11.260 I'll show you some research about that. 01:09:11.260 --> 01:09:13.979 So there's some research on how exposure to environments 01:09:13.979 --> 01:09:15.960 affects people's preferences. 01:09:15.960 --> 01:09:18.120 In the case of time preferences, usually people 01:09:18.120 --> 01:09:20.220 just think by assumption, somehow you 01:09:20.220 --> 01:09:22.800 came with a certain discount factor, 01:09:22.800 --> 01:09:25.660 and that's how it is, or beta delta and so on. 01:09:25.660 --> 01:09:28.540 That applies to all sorts of settings. 01:09:28.540 --> 01:09:29.359 Yeah. 01:09:29.359 --> 01:09:30.450 AUDIENCE: [INAUDIBLE]. 01:09:37.050 --> 01:09:38.760 But if it's less costly, you should be 01:09:38.760 --> 01:09:41.270 able to be more sophisticated. 01:09:41.270 --> 01:09:42.932 So I mean-- 01:09:42.932 --> 01:09:43.890 FRANK SCHILBACH: Right. 01:09:43.890 --> 01:09:44.590 That's an interesting question. 01:09:44.590 --> 01:09:47.130 So that's not what people have done and thought about. 01:09:47.130 --> 01:09:48.870 In a way, there's a bit of a question 01:09:48.870 --> 01:09:50.910 whether your cost and benefit structure 01:09:50.910 --> 01:09:53.490 can explain your behavior for a given beta hat. 01:09:53.490 --> 01:09:56.710 But it might also be that for some case-- in some situations, 01:09:56.710 --> 01:09:58.025 you might say you want to be-- 01:09:58.025 --> 01:09:59.650 for example, what I was saying earlier, 01:09:59.650 --> 01:10:01.717 it's like, why are people not learning? 01:10:01.717 --> 01:10:03.300 For some behaviors, maybe you actually 01:10:03.300 --> 01:10:05.970 don't care if your beta is 0.7 or whatever. 01:10:05.970 --> 01:10:06.872 It's like, fine. 01:10:06.872 --> 01:10:09.330 But some people really care about being a good and virtuous 01:10:09.330 --> 01:10:09.830 person. 01:10:09.830 --> 01:10:12.152 And therefore these might be important choices in life 01:10:12.152 --> 01:10:13.860 that you would say, I'm a serious person. 01:10:13.860 --> 01:10:14.460 I do this well. 01:10:14.460 --> 01:10:15.835 My beta hat-- you'd like to think 01:10:15.835 --> 01:10:19.718 of yourself as your beta being high. 01:10:19.718 --> 01:10:21.510 That's not what people have done very much. 01:10:21.510 --> 01:10:23.490 So there's a little bit of research 01:10:23.490 --> 01:10:26.580 of good, specific discounting, like your discounting 01:10:26.580 --> 01:10:29.180 for certain goods might be different than for others, 01:10:29.180 --> 01:10:30.930 depending on what kinds of goods they are. 01:10:30.930 --> 01:10:33.360 So some goods are temptation goods and others are not. 01:10:33.360 --> 01:10:36.360 Even that is not really in the mainstream of economics 01:10:36.360 --> 01:10:40.470 very much, let alone sort of saying your beta hat varies 01:10:40.470 --> 01:10:41.280 by circumstance. 01:10:41.280 --> 01:10:42.613 I think that's a very nice idea. 01:10:42.613 --> 01:10:46.870 I don't know any research that has done that so far. 01:10:46.870 --> 01:10:48.000 OK. 01:10:48.000 --> 01:10:49.620 So now one question you might ask-- 01:10:49.620 --> 01:10:53.520 well, is it beneficial to be sophisticated? 01:10:53.520 --> 01:10:56.170 Couldn't we just all be naive and everybody's better off? 01:10:56.170 --> 01:10:57.780 So in theory-- at least in principle-- 01:10:57.780 --> 01:11:00.300 it's sort of unclear whether sophistication is good. 01:11:00.300 --> 01:11:01.070 As I told you-- 01:11:01.070 --> 01:11:02.320 I showed you just an example-- 01:11:02.320 --> 01:11:05.100 in some cases it's good and other cases it's bad. 01:11:05.100 --> 01:11:08.040 If you think overall many important decisions 01:11:08.040 --> 01:11:12.120 or choices in life tend to be decisions 01:11:12.120 --> 01:11:13.830 that involve one term-- 01:11:13.830 --> 01:11:15.900 one time efforts that yield future benefits, 01:11:15.900 --> 01:11:17.220 these are investment goods. 01:11:17.220 --> 01:11:20.130 So in many cases in life, you have sort of investment goods-- 01:11:20.130 --> 01:11:23.760 like finishing papers, presentations, reports, 01:11:23.760 --> 01:11:27.450 finding good investment options for retirement, 01:11:27.450 --> 01:11:30.510 quitting bad habits, quitting smoking, finding a job, 01:11:30.510 --> 01:11:31.810 and so on and so forth. 01:11:31.810 --> 01:11:33.540 So lots of choices are essentially 01:11:33.540 --> 01:11:36.480 immediate effort, or at one time or several times 01:11:36.480 --> 01:11:39.190 putting in effort right now where you get future benefits. 01:11:39.190 --> 01:11:40.690 So a lot of important things in life 01:11:40.690 --> 01:11:42.630 tend to be investment goods. 01:11:42.630 --> 01:11:45.870 And in that case, I guess sophistication 01:11:45.870 --> 01:11:46.620 tends to be good. 01:11:46.620 --> 01:11:49.020 So essentially it helps you. 01:11:49.020 --> 01:11:53.068 Now, in addition, sophisticates take advantage 01:11:53.068 --> 01:11:53.985 of commitment devices. 01:11:53.985 --> 01:11:55.680 So I offer you a commitment device 01:11:55.680 --> 01:11:57.540 that I was discussing earlier. 01:11:57.540 --> 01:12:00.100 The sophisticated person will say, great. 01:12:00.100 --> 01:12:01.600 The commitment device might help me. 01:12:01.600 --> 01:12:02.100 Great. 01:12:02.100 --> 01:12:05.070 I'm going to demand it and might be better off because of that. 01:12:05.070 --> 01:12:07.350 I'm going to show you next week commitment devices don't always 01:12:07.350 --> 01:12:07.850 work. 01:12:07.850 --> 01:12:10.240 Maybe sometimes they could actually make things worse. 01:12:10.240 --> 01:12:13.500 But in principle, at least, you think commitment devices could 01:12:13.500 --> 01:12:16.500 improve things, and sort of in that sense, being sophisticated 01:12:16.500 --> 01:12:17.400 is good. 01:12:17.400 --> 01:12:19.140 So I think overall, if I had to choose 01:12:19.140 --> 01:12:21.720 if I'm sophisticated or naive, I would probably 01:12:21.720 --> 01:12:24.600 choose to be sophisticated, at least in this case. 01:12:24.600 --> 01:12:28.920 Whether that's actually true, I'm not so sure. 01:12:28.920 --> 01:12:32.520 There's one somewhat more subtle thing here 01:12:32.520 --> 01:12:35.100 is to say, like, is it sort of-- is the issue here really 01:12:35.100 --> 01:12:39.030 impatience or time inconsistency-- in a sense of, 01:12:39.030 --> 01:12:41.460 is it just about people not caring sufficiently much 01:12:41.460 --> 01:12:42.360 for the future? 01:12:42.360 --> 01:12:46.050 Or is it about how important is time inconsistency? 01:12:46.050 --> 01:12:48.340 And as I said, some of the behavior that I'm going to 01:12:48.340 --> 01:12:48.840 show-- 01:12:48.840 --> 01:12:51.720 that I showed you is, impatience is not really 01:12:51.720 --> 01:12:52.950 the key issue here. 01:12:52.950 --> 01:12:55.350 It's not about people not necessarily caring 01:12:55.350 --> 01:12:58.620 about the future, but rather, people switching their choices 01:12:58.620 --> 01:13:00.780 and choosing dominated options in the sense 01:13:00.780 --> 01:13:02.580 of overall dominated. 01:13:02.580 --> 01:13:04.680 If you sort of commit, there are some options 01:13:04.680 --> 01:13:07.770 that you prefer that you end up not choosing because you 01:13:07.770 --> 01:13:09.300 change your choices over time. 01:13:09.300 --> 01:13:11.740 Impatience cannot create this type of behavior. 01:13:11.740 --> 01:13:14.290 What I showed you, where the sophisticated person says, 01:13:14.290 --> 01:13:16.560 I would like these options but I'm not choosing them 01:13:16.560 --> 01:13:19.260 because I know my future self will change their minds, 01:13:19.260 --> 01:13:20.440 that is not possible. 01:13:20.440 --> 01:13:22.860 You cannot generate this behavior coming from just 01:13:22.860 --> 01:13:23.970 impatience. 01:13:23.970 --> 01:13:26.310 A delta being 0.5 or whatever would not 01:13:26.310 --> 01:13:27.990 generate you this behavior. 01:13:27.990 --> 01:13:29.550 What you need is time inconsistency. 01:13:29.550 --> 01:13:33.900 You need, essentially, preference reversals over time. 01:13:33.900 --> 01:13:35.880 OK, so then in some ways I think-- 01:13:35.880 --> 01:13:39.810 perhaps more most practical for your purposes, in part, 01:13:39.810 --> 01:13:41.340 for the problem set-- 01:13:41.340 --> 01:13:43.080 how do we solve sort of problems with 01:13:43.080 --> 01:13:44.440 quasi-hyperbolic discounting? 01:13:44.440 --> 01:13:47.820 So as I told you before, for the naive person, 01:13:47.820 --> 01:13:49.350 we can start from the beginning. 01:13:49.350 --> 01:13:52.530 And why do we start from the beginning as a naive person? 01:13:52.530 --> 01:13:55.040 Why does this work? 01:13:55.040 --> 01:13:57.218 So I sort of showed you already how to solve it. 01:13:57.218 --> 01:13:59.260 Now I'm sort of generalizing that, in some sense. 01:13:59.260 --> 01:14:00.635 Why is that a useful thing to do? 01:14:00.635 --> 01:14:01.258 Yeah. 01:14:01.258 --> 01:14:02.993 AUDIENCE: [INAUDIBLE]. 01:14:02.993 --> 01:14:03.910 FRANK SCHILBACH: Yeah. 01:14:03.910 --> 01:14:06.360 So the naive person thinks, I'm going to make plans now 01:14:06.360 --> 01:14:07.570 for the future. 01:14:07.570 --> 01:14:10.410 And by assumption, the naive person 01:14:10.410 --> 01:14:12.750 thinks they're going to follow through on those plans. 01:14:12.750 --> 01:14:14.190 So what you can essentially do is 01:14:14.190 --> 01:14:17.400 you can start with some plans, see 01:14:17.400 --> 01:14:19.600 what the person is choosing thinking they're 01:14:19.600 --> 01:14:20.600 going to follow through. 01:14:20.600 --> 01:14:21.780 You don't have to worry about what's 01:14:21.780 --> 01:14:23.640 going to happen in the future, because you 01:14:23.640 --> 01:14:26.250 can explain perfectly what the person is doing in the present 01:14:26.250 --> 01:14:28.320 by making plans for-- 01:14:28.320 --> 01:14:31.087 sorry, by making your choice for the future periods. 01:14:31.087 --> 01:14:32.670 You don't have to actually worry about 01:14:32.670 --> 01:14:34.170 whether the person is going to follow through, 01:14:34.170 --> 01:14:36.290 because the person doesn't even think about that. 01:14:36.290 --> 01:14:38.020 So you say, I make a plan for the future, 01:14:38.020 --> 01:14:39.937 assuming I'm going to stick through with that, 01:14:39.937 --> 01:14:40.830 or stick to this. 01:14:40.830 --> 01:14:42.622 And then you can just sort of roll forwards 01:14:42.622 --> 01:14:44.460 and say, OK, I start with period T equals 0, 01:14:44.460 --> 01:14:46.450 make the plan for that, think I'm going to follow through. 01:14:46.450 --> 01:14:47.950 Surprise, maybe period one I'm going 01:14:47.950 --> 01:14:49.290 to do something different. 01:14:49.290 --> 01:14:51.707 But then I'm going to have the same assumption, and so on. 01:14:51.707 --> 01:14:53.850 I can just go from T equals 0 going forward 01:14:53.850 --> 01:14:58.350 under the assumption that I'm going to stick to those plans. 01:14:58.350 --> 01:14:59.790 For the sophisticated person, that 01:14:59.790 --> 01:15:02.790 doesn't work, because a sophisticated person knows 01:15:02.790 --> 01:15:04.690 that if I make some plans for the future, 01:15:04.690 --> 01:15:07.110 those might not be feasible because the future self will 01:15:07.110 --> 01:15:09.220 misbehave and change their plans. 01:15:09.220 --> 01:15:12.853 I know essentially that some plans are not feasible. 01:15:12.853 --> 01:15:14.520 So what I need to do is essentially just 01:15:14.520 --> 01:15:16.830 start from the end and see, OK, if certain options are 01:15:16.830 --> 01:15:18.780 available, what I'm going to do, and then 01:15:18.780 --> 01:15:20.590 walk backwards to solve it. 01:15:20.590 --> 01:15:22.800 And that's essentially rational expectations 01:15:22.800 --> 01:15:26.610 where essentially you perfectly understand your future behavior 01:15:26.610 --> 01:15:29.730 and sort of take into account your future choices. 01:15:29.730 --> 01:15:32.800 You're going to make them current choices at the end. 01:15:32.800 --> 01:15:34.500 What about the exponential person? 01:15:34.500 --> 01:15:37.280 How does that person solve the problem? 01:15:37.280 --> 01:15:38.020 AUDIENCE: I just had a question about what you just said. 01:15:38.020 --> 01:15:38.880 FRANK SCHILBACH: Go ahead. 01:15:38.880 --> 01:15:41.172 AUDIENCE: So to summarize a sophisticated person, where 01:15:41.172 --> 01:15:43.940 they're going from the end to the beginning, 01:15:43.940 --> 01:15:47.690 as they move backwards, are you just removing choices 01:15:47.690 --> 01:15:49.030 that you know you won't ever-- 01:15:49.030 --> 01:15:49.430 FRANK SCHILBACH: Correct. 01:15:49.430 --> 01:15:49.930 Exactly. 01:15:49.930 --> 01:15:51.830 So what we did in the movie choice, 01:15:51.830 --> 01:15:54.530 if you go through this example in more detail, 01:15:54.530 --> 01:15:57.168 you'll notice that essentially, if I know that, 01:15:57.168 --> 01:15:59.210 for example, suppose I want to go in period three 01:15:59.210 --> 01:16:00.877 but I know I'm going to go in period two 01:16:00.877 --> 01:16:02.450 if it comes down to that, then I'm 01:16:02.450 --> 01:16:06.830 going to remove period three for my choice set or for my options 01:16:06.830 --> 01:16:09.380 when optimizing in period one or period zero, 01:16:09.380 --> 01:16:14.150 anticipating what I'm going to do in the future. 01:16:14.150 --> 01:16:17.390 So what about the exponential discounter? 01:16:17.390 --> 01:16:19.752 Yes? 01:16:19.752 --> 01:16:21.231 AUDIENCE: [INAUDIBLE]. 01:16:26.215 --> 01:16:27.090 FRANK SCHILBACH: Yes. 01:16:27.090 --> 01:16:30.012 So there's two options, in fact, for the exponential discounter. 01:16:30.012 --> 01:16:32.220 It actually doesn't matter because you follow through 01:16:32.220 --> 01:16:33.198 with your plans anyway. 01:16:33.198 --> 01:16:34.740 So you could start from the beginning 01:16:34.740 --> 01:16:36.070 and just walk forward. 01:16:36.070 --> 01:16:38.740 In fact, what you can do is you can start in period zero 01:16:38.740 --> 01:16:40.902 make a plan for everything and just follow through. 01:16:40.902 --> 01:16:42.360 You don't even have to go to period 01:16:42.360 --> 01:16:43.740 1, 2, and 3 because you know you're 01:16:43.740 --> 01:16:44.980 going to stick to that plan. 01:16:44.980 --> 01:16:46.590 So you can essentially just do that. 01:16:46.590 --> 01:16:48.750 You could actually also do backward transactions. 01:16:48.750 --> 01:16:50.940 And I'm pretty sure you get the exact same answer. 01:16:50.940 --> 01:16:51.960 It doesn't matter. 01:16:51.960 --> 01:16:53.620 The much easier thing to do, of course, 01:16:53.620 --> 01:16:55.380 is to solve the problem in period 0 01:16:55.380 --> 01:16:58.570 and then just assuming you're going to follow through. 01:16:58.570 --> 01:17:01.530 So sorry, this should say readings for Tuesday. 01:17:01.530 --> 01:17:05.650 The class is on Tuesday, not on Monday. 01:17:05.650 --> 01:17:11.280 Please read the paper by Ariely and Wortenbroch. 01:17:11.280 --> 01:17:12.850 Read the entire article. 01:17:12.850 --> 01:17:15.240 We're going to discuss applications from smoking 01:17:15.240 --> 01:17:17.670 to drinking, setting deadlines, and so on, 01:17:17.670 --> 01:17:20.620 and apply these models in real-world settings. 01:17:20.620 --> 01:17:22.580 Thank you very much.