1 00:00:00,000 --> 00:00:05,412 [SQUEAKING] [RUSTLING] [CLICKING] 2 00:00:10,340 --> 00:00:13,590 FRANK SCHILBACH: OK, so what happened last time? 3 00:00:13,590 --> 00:00:15,650 So we talked about the workhorse model 4 00:00:15,650 --> 00:00:20,060 of classical or classical economics, 5 00:00:20,060 --> 00:00:23,960 in terms of discounting-- the exponential discounted utility 6 00:00:23,960 --> 00:00:25,080 model. 7 00:00:25,080 --> 00:00:28,160 This is a very useful model for many settings. 8 00:00:28,160 --> 00:00:30,320 It's been very useful for explain and understand 9 00:00:30,320 --> 00:00:32,220 a bunch of behaviors. 10 00:00:32,220 --> 00:00:34,760 However, this model has a few assumptions 11 00:00:34,760 --> 00:00:37,370 that create some predictions that are not necessarily 12 00:00:37,370 --> 00:00:38,810 borne out in the data. 13 00:00:38,810 --> 00:00:41,810 And we're trying to improve on those assumptions 14 00:00:41,810 --> 00:00:44,972 and make the model more realistic. 15 00:00:44,972 --> 00:00:47,180 What are these assumptions and what kinds of examples 16 00:00:47,180 --> 00:00:48,860 did I show you that perhaps were not 17 00:00:48,860 --> 00:00:51,590 consistent with the exponential discounting model? 18 00:00:53,928 --> 00:00:55,220 I'll actually show them to you. 19 00:00:55,220 --> 00:00:57,570 But can somebody explain to you what they are 20 00:00:57,570 --> 00:01:00,110 and why those are not consistent with the exponential 21 00:01:00,110 --> 00:01:00,860 discounting model? 22 00:01:04,060 --> 00:01:05,209 Yes. 23 00:01:05,209 --> 00:01:06,790 AUDIENCE: You shouldn't determine-- 24 00:01:06,790 --> 00:01:12,010 you shouldn't care about whether it's a [INAUDIBLE].. 25 00:01:12,010 --> 00:01:12,970 FRANK SCHILBACH: Right. 26 00:01:12,970 --> 00:01:15,850 So one key assumption in the exponential discounting model 27 00:01:15,850 --> 00:01:17,680 is that there's one parameter, delta, 28 00:01:17,680 --> 00:01:22,210 that essentially steers how much you care about 29 00:01:22,210 --> 00:01:25,120 different periods of time, the present and the future, 30 00:01:25,120 --> 00:01:27,160 or two future periods. 31 00:01:27,160 --> 00:01:29,840 The key assumption here is that how much weight 32 00:01:29,840 --> 00:01:31,720 do you put on different time periods, 33 00:01:31,720 --> 00:01:35,090 on early and a later date, is constant across time. 34 00:01:35,090 --> 00:01:37,360 So from today versus tomorrow, there's 35 00:01:37,360 --> 00:01:40,210 the same difference compared to, like, when you look at a year 36 00:01:40,210 --> 00:01:42,220 from now and a year and a day from now, 37 00:01:42,220 --> 00:01:44,410 or 20 days and 21 days. 38 00:01:44,410 --> 00:01:46,930 The difference, if you care more about the present, 39 00:01:46,930 --> 00:01:50,620 that's constant across time from today's perspective, 40 00:01:50,620 --> 00:01:52,163 also from future perspective. 41 00:01:52,163 --> 00:01:53,080 That's one assumption. 42 00:01:53,080 --> 00:01:55,030 And what evidence did we see or show 43 00:01:55,030 --> 00:01:58,888 that that's not consistent with? 44 00:01:58,888 --> 00:02:00,055 AUDIENCE: Choosing a reward. 45 00:02:00,055 --> 00:02:02,380 Do you want the money now or is this today or in 46 00:02:02,380 --> 00:02:05,772 a year or [INAUDIBLE]? 47 00:02:05,772 --> 00:02:06,730 FRANK SCHILBACH: Right. 48 00:02:06,730 --> 00:02:08,320 So we saw some evidence that people 49 00:02:08,320 --> 00:02:10,729 are impatient in the short run. 50 00:02:10,729 --> 00:02:12,950 So when it comes to today versus tomorrow or today 51 00:02:12,950 --> 00:02:14,325 versus in a week from now, people 52 00:02:14,325 --> 00:02:15,770 tend to be fairly impatient. 53 00:02:15,770 --> 00:02:18,450 They tend to discount the future a lot. 54 00:02:18,450 --> 00:02:20,200 Now, there's sort of two issues with that. 55 00:02:20,200 --> 00:02:22,600 One is, if you do the same thing about asking people 56 00:02:22,600 --> 00:02:25,420 about future rewards, people tend to be more patient. 57 00:02:25,420 --> 00:02:27,860 So the discount factors that you elicit, 58 00:02:27,860 --> 00:02:30,910 we'll talk a little bit about that in a recitation, as well. 59 00:02:30,910 --> 00:02:32,560 The discount factors are just different 60 00:02:32,560 --> 00:02:35,890 for the same intervals of time. 61 00:02:35,890 --> 00:02:39,078 Second, if you take the short run and patience seriously-- 62 00:02:39,078 --> 00:02:40,870 if you sort of say, OK, I take your choices 63 00:02:40,870 --> 00:02:43,780 from today versus tomorrow or from today versus next week 64 00:02:43,780 --> 00:02:45,800 and [INAUDIBLE] run that forward, you 65 00:02:45,800 --> 00:02:47,740 got sort of absurd implications as in, like, 66 00:02:47,740 --> 00:02:51,580 if you really seriously discount a week from now by a lot, 67 00:02:51,580 --> 00:02:53,510 then you shouldn't care about a year from now, 68 00:02:53,510 --> 00:02:54,400 five years from now. 69 00:02:54,400 --> 00:02:56,073 You shouldn't care about that at all. 70 00:02:56,073 --> 00:02:57,490 However, we see in the real world, 71 00:02:57,490 --> 00:03:00,100 people have lots of-- people care about the future a lot. 72 00:03:00,100 --> 00:03:00,970 People save money. 73 00:03:00,970 --> 00:03:04,220 People get education and so on and so forth. 74 00:03:04,220 --> 00:03:06,370 So it can't be in some ways that they're 75 00:03:06,370 --> 00:03:09,500 really impatient in the long run, as well. 76 00:03:09,500 --> 00:03:11,680 So that's, like, number one. 77 00:03:11,680 --> 00:03:15,650 What about point number two? 78 00:03:15,650 --> 00:03:17,140 Yes. 79 00:03:17,140 --> 00:03:20,010 AUDIENCE: Your decision now for the future 80 00:03:20,010 --> 00:03:22,190 should be the same as [INAUDIBLE].. 81 00:03:25,218 --> 00:03:26,260 FRANK SCHILBACH: Exactly. 82 00:03:26,260 --> 00:03:28,930 That's called dynamic or time consistency. 83 00:03:28,930 --> 00:03:31,990 That's an assumption or implication of the exponential 84 00:03:31,990 --> 00:03:33,520 discounting model. 85 00:03:33,520 --> 00:03:35,410 That is to say, if I make some choices 86 00:03:35,410 --> 00:03:39,610 for the future, for future periods, about how I-- 87 00:03:39,610 --> 00:03:42,370 what I'm going to study next week or in a year from now, 88 00:03:42,370 --> 00:03:45,070 or whether I'm going to exercise and so on, for choices 89 00:03:45,070 --> 00:03:49,240 that involve time in the future, once that time comes, 90 00:03:49,240 --> 00:03:52,580 absent new information or absent circumstances change, 91 00:03:52,580 --> 00:03:56,290 I should follow through with my plans. 92 00:03:56,290 --> 00:03:58,900 And so if that's not the case, then what we say 93 00:03:58,900 --> 00:04:01,990 is that preferences are dynamically inconsistent. 94 00:04:01,990 --> 00:04:05,710 That is to say, I have all sorts of plans of exercising 95 00:04:05,710 --> 00:04:06,847 next week and so on. 96 00:04:06,847 --> 00:04:07,680 The next week comes. 97 00:04:07,680 --> 00:04:09,340 Surprise, I'm not following through. 98 00:04:09,340 --> 00:04:12,010 That essentially means my preferences are inconsistent. 99 00:04:12,010 --> 00:04:14,230 And that's sort of evidence against the exponential 100 00:04:14,230 --> 00:04:16,250 discounting model. 101 00:04:16,250 --> 00:04:17,200 OK. 102 00:04:17,200 --> 00:04:18,910 Number three, demand for commitment. 103 00:04:18,910 --> 00:04:20,169 Yes? 104 00:04:20,169 --> 00:04:23,770 AUDIENCE: [INAUDIBLE]. 105 00:04:23,770 --> 00:04:28,192 There are [INAUDIBLE] people will often do that [INAUDIBLE] 106 00:04:28,192 --> 00:04:31,780 and that shows that people [INAUDIBLE].. 107 00:04:31,780 --> 00:04:32,820 FRANK SCHILBACH: Right. 108 00:04:32,820 --> 00:04:35,560 So one sort of key assumption or one sort 109 00:04:35,560 --> 00:04:38,545 of key insight from sort of economics in general, 110 00:04:38,545 --> 00:04:41,440 or classical economics, and it's like, more choices are good. 111 00:04:41,440 --> 00:04:43,180 Like, if you have more options available, 112 00:04:43,180 --> 00:04:45,760 that's great for you, because you can take advantage of them. 113 00:04:45,760 --> 00:04:47,260 You never know whether there's going 114 00:04:47,260 --> 00:04:49,392 to be uncertainty or certain circumstances change. 115 00:04:49,392 --> 00:04:51,100 So you should never restrict your choices 116 00:04:51,100 --> 00:04:52,058 because you never know. 117 00:04:52,058 --> 00:04:54,790 Maybe in the future, maybe circumstances change. 118 00:04:54,790 --> 00:04:56,650 Maybe I got really busy, or whatever. 119 00:04:56,650 --> 00:04:57,620 Things happen. 120 00:04:57,620 --> 00:04:59,350 So more choice tends to be good. 121 00:04:59,350 --> 00:05:01,810 So in the neoclassical or classical economics model, 122 00:05:01,810 --> 00:05:04,360 there's no scope for or no reason 123 00:05:04,360 --> 00:05:08,900 to restrict your choices because more choices in the future 124 00:05:08,900 --> 00:05:10,190 are always good. 125 00:05:10,190 --> 00:05:12,813 However, if you're worried about your future self misbehaving 126 00:05:12,813 --> 00:05:14,230 in certain ways, if you're worried 127 00:05:14,230 --> 00:05:17,200 about your future self not exercising, 128 00:05:17,200 --> 00:05:19,660 eating too many potato chips, and so on and so forth, 129 00:05:19,660 --> 00:05:21,910 you might want to engage in commitment devices, 130 00:05:21,910 --> 00:05:23,950 either by taking away certain options, 131 00:05:23,950 --> 00:05:27,220 like restricting your choice set to a smaller choice set, 132 00:05:27,220 --> 00:05:31,155 or, less drastically, making future choices more expensive. 133 00:05:31,155 --> 00:05:32,530 That is to say, for example, if I 134 00:05:32,530 --> 00:05:34,480 say I'm going to submit or write a paper 135 00:05:34,480 --> 00:05:36,820 by the end of this week, if I'm going to tell you 136 00:05:36,820 --> 00:05:39,370 if I don't do that I'm going to give you $100, 137 00:05:39,370 --> 00:05:41,530 well, what I'm going to do essentially 138 00:05:41,530 --> 00:05:45,610 is I'm making not writing the paper more expensive. 139 00:05:45,610 --> 00:05:47,402 And the neoclassical or the classical model 140 00:05:47,402 --> 00:05:48,943 had the exponential discounting model 141 00:05:48,943 --> 00:05:50,570 has essentially no scope for that. 142 00:05:50,570 --> 00:05:52,030 Why would I ever do that? 143 00:05:52,030 --> 00:05:52,780 Because who knows. 144 00:05:52,780 --> 00:05:55,137 Maybe I'll get sick or stuff happens. 145 00:05:55,137 --> 00:05:56,470 So there's no reason to do that. 146 00:05:56,470 --> 00:05:57,845 There's no benefit of doing that. 147 00:05:57,845 --> 00:05:59,750 And it's a potential cost. 148 00:05:59,750 --> 00:06:03,800 So if I see myself or somebody else restricting their choices, 149 00:06:03,800 --> 00:06:07,640 that's a violation of the exponential discounting model. 150 00:06:07,640 --> 00:06:10,360 And the reason, of course, for that is number two. 151 00:06:10,360 --> 00:06:11,920 We know there's preference for it. 152 00:06:11,920 --> 00:06:14,437 If you think there are future preference reversals, 153 00:06:14,437 --> 00:06:16,270 if I think that in the future I might change 154 00:06:16,270 --> 00:06:18,550 my preferences in a way that I don't like, 155 00:06:18,550 --> 00:06:21,190 if I want my future self to behave in certain ways 156 00:06:21,190 --> 00:06:24,460 that I prefer right now, I might want to restrict my choice set. 157 00:06:24,460 --> 00:06:27,040 I might certain unpreferrable-- like, less preferable 158 00:06:27,040 --> 00:06:30,242 options more costly. 159 00:06:30,242 --> 00:06:31,970 OK. 160 00:06:31,970 --> 00:06:32,470 Good. 161 00:06:32,470 --> 00:06:36,730 So then what we did next is to say, OK, now-- 162 00:06:36,730 --> 00:06:38,960 so I showed you a bunch of evidence of that. 163 00:06:38,960 --> 00:06:42,250 And then what we did is then we sort of presented 164 00:06:42,250 --> 00:06:44,620 a slight deviation from the exponential discounting 165 00:06:44,620 --> 00:06:46,840 model, which is the quasi-hyperbolic discounting 166 00:06:46,840 --> 00:06:47,740 model. 167 00:06:47,740 --> 00:06:49,210 That model is, in some sense, very 168 00:06:49,210 --> 00:06:51,790 similar to the exponential discounting model 169 00:06:51,790 --> 00:06:54,280 that I showed you, except for some small difference. 170 00:06:54,280 --> 00:06:57,070 There's an additional parameter that's called beta. 171 00:06:57,070 --> 00:06:58,120 What does this beta do? 172 00:06:58,120 --> 00:07:02,440 It's like a short term discount factor that essentially guides 173 00:07:02,440 --> 00:07:05,230 all discounting or determines all discounting 174 00:07:05,230 --> 00:07:07,780 between the present period, right now, 175 00:07:07,780 --> 00:07:10,180 versus anything that's in the future. 176 00:07:10,180 --> 00:07:13,000 One broad question is like, what are the time periods? 177 00:07:13,000 --> 00:07:13,810 Is it daily? 178 00:07:13,810 --> 00:07:14,410 Is it yearly? 179 00:07:14,410 --> 00:07:15,950 Is it monthly or whatever? 180 00:07:15,950 --> 00:07:17,950 There's actually quite a bit of research on this 181 00:07:17,950 --> 00:07:19,660 that people try to figure this out. 182 00:07:19,660 --> 00:07:22,270 Usually we think the beta or the time horizon of the beta 183 00:07:22,270 --> 00:07:25,200 is actually just a few days, even just a few hours. 184 00:07:25,200 --> 00:07:28,728 So for our purposes, we can say it's daily or today. 185 00:07:28,728 --> 00:07:30,520 And anything that you'll see in the problem 186 00:07:30,520 --> 00:07:32,530 sets and so on, it needs to be always defined. 187 00:07:32,530 --> 00:07:34,660 But think of beta essentially anything 188 00:07:34,660 --> 00:07:37,390 that's like today or in the next couple of days. 189 00:07:37,390 --> 00:07:40,900 Anything outside of that scope is essentially outside 190 00:07:40,900 --> 00:07:44,450 of the scope of beta and sort of in the future. 191 00:07:44,450 --> 00:07:45,890 Now, what does this beta do? 192 00:07:45,890 --> 00:07:48,640 Well, it helps us to separate discounting 193 00:07:48,640 --> 00:07:51,160 for short horizons and long horizons, 194 00:07:51,160 --> 00:07:54,310 because if you think about discounting between the present 195 00:07:54,310 --> 00:07:58,570 and anything in the future, the data can steer that, right? 196 00:07:58,570 --> 00:08:02,260 If beta is 0.7, 0.6, or 0.8 or whatever, 197 00:08:02,260 --> 00:08:04,060 I can now be impatient for the present. 198 00:08:04,060 --> 00:08:07,960 I can now prefer, say, $10 today versus $12 in the future. 199 00:08:07,960 --> 00:08:10,430 The beta will make sure that that happens. 200 00:08:10,430 --> 00:08:12,160 But when you look at all future periods, 201 00:08:12,160 --> 00:08:13,960 the beta is in all future periods. 202 00:08:13,960 --> 00:08:16,090 It appears everywhere in the utility function 203 00:08:16,090 --> 00:08:17,570 in all future periods. 204 00:08:17,570 --> 00:08:22,990 So the beta does not affect how am I discounting 205 00:08:22,990 --> 00:08:24,800 any future time periods. 206 00:08:24,800 --> 00:08:27,970 So then the delta is steering that. 207 00:08:27,970 --> 00:08:30,390 We usually think that delta is close to 1. 208 00:08:30,390 --> 00:08:34,590 It's something like yearly 0.95 or 0.99 or the like. 209 00:08:34,590 --> 00:08:38,860 So delta is essentially reasonably close to 1, 210 00:08:38,860 --> 00:08:40,900 such that I can be fairly patient 211 00:08:40,900 --> 00:08:44,110 between 10 years from now and 11 years from now and 15 years 212 00:08:44,110 --> 00:08:45,140 from now. 213 00:08:45,140 --> 00:08:46,490 It doesn't matter much to me. 214 00:08:46,490 --> 00:08:48,580 There's only going to be some slight discounting. 215 00:08:48,580 --> 00:08:50,860 I prefer probably things that are happening five years 216 00:08:50,860 --> 00:08:53,260 from now from things that are happening 217 00:08:53,260 --> 00:08:57,580 30 years from now for the same sort of stuff happening. 218 00:08:57,580 --> 00:09:00,718 But people tend to be fairly patient. 219 00:09:00,718 --> 00:09:02,260 Do you have any questions about that? 220 00:09:12,860 --> 00:09:13,480 OK. 221 00:09:13,480 --> 00:09:17,760 So let me now sort of spend, in fact, the rest of the lecture 222 00:09:17,760 --> 00:09:20,040 just talking about details of this model, 223 00:09:20,040 --> 00:09:21,540 in part sort of building intuition, 224 00:09:21,540 --> 00:09:23,730 sort of showing you the mechanics of how that works 225 00:09:23,730 --> 00:09:27,630 and how, essentially, having an additional discount 226 00:09:27,630 --> 00:09:29,940 parameter of the data affects people's choices. 227 00:09:29,940 --> 00:09:32,190 And second, we're going to talk about something that's 228 00:09:32,190 --> 00:09:34,523 quite important, which is the question of sophistication 229 00:09:34,523 --> 00:09:35,850 versus naivete. 230 00:09:35,850 --> 00:09:36,880 What do I mean by that? 231 00:09:36,880 --> 00:09:40,320 Well, in the exponential discounting model, 232 00:09:40,320 --> 00:09:43,530 by assumption, the preferences are time consistent. 233 00:09:43,530 --> 00:09:44,370 What does that mean? 234 00:09:44,370 --> 00:09:46,470 If I make plans for the future, I 235 00:09:46,470 --> 00:09:48,792 will follow through with those plans. 236 00:09:48,792 --> 00:09:50,250 So in some sense, it doesn't really 237 00:09:50,250 --> 00:09:52,020 matter what I think I'm going to do in the future, 238 00:09:52,020 --> 00:09:53,370 because essentially, I'm going to do anyway 239 00:09:53,370 --> 00:09:54,840 what I'm going to plan anyway. 240 00:09:54,840 --> 00:09:56,460 So the only thing I need to know is 241 00:09:56,460 --> 00:09:58,420 right now what I'm going to do. 242 00:09:58,420 --> 00:10:01,200 And then if I make that plan, unless circumstances change, 243 00:10:01,200 --> 00:10:03,318 I'm going to just follow through. 244 00:10:03,318 --> 00:10:05,610 That's not true here anymore, as I'm going to show you. 245 00:10:05,610 --> 00:10:08,490 So now it's the case that if I make some plans right now, 246 00:10:08,490 --> 00:10:10,470 these plans might change in the future because 247 00:10:10,470 --> 00:10:12,090 of my preferences. 248 00:10:12,090 --> 00:10:13,830 Even in the absence of new information 249 00:10:13,830 --> 00:10:17,160 or new circumstances, once tomorrow comes or next week 250 00:10:17,160 --> 00:10:20,170 comes, I might sort of prefer different things. 251 00:10:20,170 --> 00:10:23,890 So now the preference are not dynamically consistent anymore. 252 00:10:23,890 --> 00:10:28,080 So what I prefer today might not be what I prefer next week. 253 00:10:28,080 --> 00:10:29,730 So that now leads to a complication. 254 00:10:29,730 --> 00:10:32,323 Now I need to understand, well, what 255 00:10:32,323 --> 00:10:34,740 are my beliefs about what I'm going to do in the future is 256 00:10:34,740 --> 00:10:35,340 quite important. 257 00:10:35,340 --> 00:10:36,270 Do I have correct beliefs? 258 00:10:36,270 --> 00:10:37,973 Do I understand that I'm present biased? 259 00:10:37,973 --> 00:10:39,390 Do I understand that in the future 260 00:10:39,390 --> 00:10:41,160 I might be impatient, as well? 261 00:10:41,160 --> 00:10:42,300 Or am I naive? 262 00:10:42,300 --> 00:10:44,940 Do I think right now I'm present biased, but tomorrow comes 263 00:10:44,940 --> 00:10:47,430 or next week I'm going to exercise, do the problem set 264 00:10:47,430 --> 00:10:49,240 early, and so on and so forth? 265 00:10:49,240 --> 00:10:52,650 And as we're going to see, that will lead to quite different-- 266 00:10:52,650 --> 00:10:56,820 starkly different conclusions or implications 267 00:10:56,820 --> 00:11:01,890 that are quite important for outcomes, welfare, and so on. 268 00:11:01,890 --> 00:11:02,670 OK. 269 00:11:02,670 --> 00:11:06,330 So let me give you some examples first. 270 00:11:06,330 --> 00:11:11,460 So first, if you have a discount function for beta 271 00:11:11,460 --> 00:11:13,895 equals 1/2 and delta close to 1-- 272 00:11:13,895 --> 00:11:15,270 for our purposes, often I'm going 273 00:11:15,270 --> 00:11:17,460 to set delta to 1, not because I necessarily 274 00:11:17,460 --> 00:11:19,410 think that delta is 1. 275 00:11:19,410 --> 00:11:22,530 Delta is probably 0.99, 0.95, or the like. 276 00:11:22,530 --> 00:11:24,960 I'm just setting it to 1 to make the algebra 277 00:11:24,960 --> 00:11:27,510 or sort of any problem set exercises 278 00:11:27,510 --> 00:11:30,870 and so on being less messy. 279 00:11:30,870 --> 00:11:32,620 Speaking of which, problem set exercises-- 280 00:11:32,620 --> 00:11:34,440 Pierre-Luc who sits in the very back and checks 281 00:11:34,440 --> 00:11:36,023 whether you are using your laptop only 282 00:11:36,023 --> 00:11:39,540 for classwork, Pierre-Luc sort of mostly in charge 283 00:11:39,540 --> 00:11:40,870 of doing the problem sets. 284 00:11:40,870 --> 00:11:42,505 So he also has office hours, to which 285 00:11:42,505 --> 00:11:44,880 you can come and ask specific questions about the problem 286 00:11:44,880 --> 00:11:45,150 sets. 287 00:11:45,150 --> 00:11:47,275 Of course, he's also very happy to answer questions 288 00:11:47,275 --> 00:11:51,150 about Piazza or in any other way. 289 00:11:51,150 --> 00:11:52,668 When are your office hours? 290 00:11:52,668 --> 00:11:54,437 AUDIENCE: [INAUDIBLE]. 291 00:11:54,437 --> 00:11:55,770 FRANK SCHILBACH: 1:30 on Friday. 292 00:11:55,770 --> 00:11:57,540 And where are they? 293 00:11:57,540 --> 00:11:59,828 AUDIENCE: [INAUDIBLE]. 294 00:11:59,828 --> 00:12:00,870 FRANK SCHILBACH: Perfect. 295 00:12:00,870 --> 00:12:02,585 So it's on the course website. 296 00:12:02,585 --> 00:12:03,960 So if you have specific questions 297 00:12:03,960 --> 00:12:07,530 about the problem set, again, in the recitation, 298 00:12:07,530 --> 00:12:09,960 we'll discuss quite a few issues related to that. 299 00:12:09,960 --> 00:12:12,335 But then if you have specific questions about the problem 300 00:12:12,335 --> 00:12:16,840 set, Pierre-Luc will be the best equipped to answer those. 301 00:12:16,840 --> 00:12:17,520 OK. 302 00:12:17,520 --> 00:12:22,440 So if you have quasi-hyperbolic discounting preferences, 303 00:12:22,440 --> 00:12:25,080 with beta equals 1/2 and delta equals 1, 304 00:12:25,080 --> 00:12:28,750 your discounting function looks, essentially, as follows. 305 00:12:28,750 --> 00:12:30,900 The first period is sort of normalized to 1. 306 00:12:30,900 --> 00:12:34,410 [INAUDIBLE] like one about the current period. 307 00:12:34,410 --> 00:12:37,530 In the future then it's, like, beta delta, beta delta square, 308 00:12:37,530 --> 00:12:39,790 beta delta to the power of 3, and so on. 309 00:12:39,790 --> 00:12:42,053 But if you sort of now use delta equals 1, 310 00:12:42,053 --> 00:12:44,220 you get, essentially-- you care about the present 1. 311 00:12:44,220 --> 00:12:47,570 And everything in the future is discounted by 1/2. 312 00:12:47,570 --> 00:12:50,160 OK, so relative to the present period, 313 00:12:50,160 --> 00:12:51,900 all future periods are worth less. 314 00:12:51,900 --> 00:12:53,340 So I care a lot about the present. 315 00:12:53,340 --> 00:12:55,980 That's why we call it sort of present bias or present focus. 316 00:12:55,980 --> 00:12:58,290 I care a lot more about the present than anything 317 00:12:58,290 --> 00:12:59,800 in the future. 318 00:12:59,800 --> 00:13:02,610 Now, second, all discounting in this specific example 319 00:13:02,610 --> 00:13:05,470 takes place between the present and the immediate future. 320 00:13:05,470 --> 00:13:06,870 So I only care about-- 321 00:13:06,870 --> 00:13:08,707 in terms of discounting-- all future periods 322 00:13:08,707 --> 00:13:09,540 are the same for me. 323 00:13:09,540 --> 00:13:10,915 I don't care about whether things 324 00:13:10,915 --> 00:13:13,170 are in five periods or six or seven periods from now. 325 00:13:13,170 --> 00:13:15,720 That's all the same for me, because delta, in this case, 326 00:13:15,720 --> 00:13:17,040 is 1. 327 00:13:17,040 --> 00:13:18,750 Instead, what I care about is that today 328 00:13:18,750 --> 00:13:22,500 versus tomorrow or today versus three days from now, and so on. 329 00:13:22,500 --> 00:13:24,680 Again, usually delta would not be one. 330 00:13:24,680 --> 00:13:27,330 So if you had a delta that's, like, 0.99 or the like, 331 00:13:27,330 --> 00:13:30,880 there would be some discounting in the future, as well. 332 00:13:30,880 --> 00:13:32,290 But not in this case. 333 00:13:32,290 --> 00:13:35,280 So that's sort of capturing the intuition that the long run-- 334 00:13:35,280 --> 00:13:37,500 in the long run, we are relatively patient. 335 00:13:37,500 --> 00:13:40,690 There is essentially no discounting happening anymore. 336 00:13:40,690 --> 00:13:43,110 And so the utils a year from now are just 337 00:13:43,110 --> 00:13:47,050 as valuable as utils in two years from now. 338 00:13:47,050 --> 00:13:50,312 So then that also means that the timing of decisions or-- 339 00:13:50,312 --> 00:13:52,020 the decisions are sensitive to the timing 340 00:13:52,020 --> 00:13:55,080 of costs and benefits, when exactly did they occur. 341 00:13:55,080 --> 00:13:56,910 It matters a lot whether stuff happens 342 00:13:56,910 --> 00:14:00,985 today versus tomorrow or today versus three days from now. 343 00:14:00,985 --> 00:14:03,360 It matters much less about whether stuff happens in three 344 00:14:03,360 --> 00:14:04,652 days versus four days from now. 345 00:14:04,652 --> 00:14:06,578 I'm going to show you some examples of that. 346 00:14:06,578 --> 00:14:08,370 But just to sort of give you some sense of, 347 00:14:08,370 --> 00:14:10,662 like, why is this called quasi-hyperbolic or hyperbolic 348 00:14:10,662 --> 00:14:12,760 discounting? 349 00:14:12,760 --> 00:14:14,005 So have your three functions. 350 00:14:14,005 --> 00:14:15,630 I'm not sure how well you can see this. 351 00:14:15,630 --> 00:14:17,460 But there's, like, a sort of pink line 352 00:14:17,460 --> 00:14:20,472 that's essentially like an exponential curve. 353 00:14:20,472 --> 00:14:22,680 That's essentially what exponential discounting looks 354 00:14:22,680 --> 00:14:23,240 like. 355 00:14:23,240 --> 00:14:25,740 Essentially what you see is sort of a constant, if you want, 356 00:14:25,740 --> 00:14:30,690 sort of decline of like the discount function. 357 00:14:30,690 --> 00:14:33,447 And then I've also plotted to you 358 00:14:33,447 --> 00:14:35,280 hyperbolic discounting, which is essentially 359 00:14:35,280 --> 00:14:36,810 like a true hyperbolic curve. 360 00:14:36,810 --> 00:14:38,352 That's essentially the thing that you 361 00:14:38,352 --> 00:14:43,640 see on the left, the one that's sort of like much 362 00:14:43,640 --> 00:14:45,190 steeper at the beginning. 363 00:14:45,190 --> 00:14:47,880 And then there is quasi-hyperbolic discounting 364 00:14:47,880 --> 00:14:49,830 that's essentially quite similar in shape, 365 00:14:49,830 --> 00:14:52,440 as you can see, to the hyperbolic discounting, 366 00:14:52,440 --> 00:14:54,750 except for the fact that it's not continuous. 367 00:14:54,750 --> 00:14:58,710 There's a jump from going one to beta at the very beginning. 368 00:14:58,710 --> 00:15:00,480 It's not a continuous function. 369 00:15:00,480 --> 00:15:01,980 Essentially, there's a discrete jump 370 00:15:01,980 --> 00:15:04,410 between today and the future. 371 00:15:04,410 --> 00:15:06,690 And then essentially it behaves very similarly 372 00:15:06,690 --> 00:15:08,842 to the exponential discounting curve. 373 00:15:08,842 --> 00:15:10,800 But that's just to tell you it doesn't really-- 374 00:15:10,800 --> 00:15:12,600 you don't have to worry about the hyperbolic discounting 375 00:15:12,600 --> 00:15:13,100 and so on. 376 00:15:13,100 --> 00:15:15,480 We're not going to discuss that very much. 377 00:15:15,480 --> 00:15:17,070 But that's just for you to understand 378 00:15:17,070 --> 00:15:18,690 why is that the name? 379 00:15:18,690 --> 00:15:21,150 Well, it's because essentially it's quasi-hyperbolic. 380 00:15:21,150 --> 00:15:22,942 It's not really hyperbolic because it's not 381 00:15:22,942 --> 00:15:24,840 really hyperbola. 382 00:15:24,840 --> 00:15:29,520 But in fact, it looks quite similar, effectively. 383 00:15:29,520 --> 00:15:37,295 So then when you think about goods that you might consume, 384 00:15:37,295 --> 00:15:38,670 there's different types of goods. 385 00:15:38,670 --> 00:15:40,890 There's leisure goods and there's investment goods. 386 00:15:40,890 --> 00:15:42,515 Let's sort of start with leisure goods. 387 00:15:42,515 --> 00:15:43,515 What's a leisure good? 388 00:15:43,515 --> 00:15:46,650 A leisure good is a good that has immediate rewards 389 00:15:46,650 --> 00:15:48,780 and delayed costs. 390 00:15:48,780 --> 00:15:50,760 One example would be eating candy. 391 00:15:50,760 --> 00:15:53,700 So eating candy, of course, you get immediate utility benefits. 392 00:15:53,700 --> 00:15:55,800 It's pleasurable to eat candy. 393 00:15:55,800 --> 00:15:57,030 So that's positive. 394 00:15:57,030 --> 00:16:01,680 In this case, suppose the benefits are the pleasure 395 00:16:01,680 --> 00:16:03,420 of eating candy right now. 396 00:16:03,420 --> 00:16:09,150 But often eating candy, it leads to delayed health costs 397 00:16:09,150 --> 00:16:12,120 or delayed costs at the dentist's office, 398 00:16:12,120 --> 00:16:17,280 which summarizes C health of 3 in the future. 399 00:16:17,280 --> 00:16:21,270 If you now say, well, if beta equals 1/2 400 00:16:21,270 --> 00:16:25,380 and a delta equals 1, well, you can sort think about, 401 00:16:25,380 --> 00:16:29,620 would you eat candy today or candy in the future? 402 00:16:29,620 --> 00:16:32,320 So first starting off with eating candy today-- 403 00:16:32,320 --> 00:16:35,040 well, if you sort of calculate the costs and benefits 404 00:16:35,040 --> 00:16:39,540 of eating candy, the pleasure that you get from candy is 2. 405 00:16:39,540 --> 00:16:42,690 If you discount the future by beta, 406 00:16:42,690 --> 00:16:45,240 essentially everything in the future is discounted by beta, 407 00:16:45,240 --> 00:16:47,310 it's like 1/2 times 3. 408 00:16:47,310 --> 00:16:49,140 So if you sort of do that calculation, 409 00:16:49,140 --> 00:16:50,330 you get something positive. 410 00:16:50,330 --> 00:16:52,320 So if you think about eating candy right now, 411 00:16:52,320 --> 00:16:56,250 the answer is yes, because 2 minus 1/2 times 3 is positive 412 00:16:56,250 --> 00:16:57,990 and you're going to do that. 413 00:16:57,990 --> 00:16:59,490 If instead you think about, should I 414 00:16:59,490 --> 00:17:01,050 eat candy in the future? 415 00:17:01,050 --> 00:17:02,820 Well, you get different implications. 416 00:17:02,820 --> 00:17:03,680 The answer is no. 417 00:17:03,680 --> 00:17:04,589 Why is the answer no? 418 00:17:04,589 --> 00:17:07,079 Because if you're in the future, everything 419 00:17:07,079 --> 00:17:09,510 is discounted that's happening in the future, both 420 00:17:09,510 --> 00:17:12,119 the pleasure that comes from eating candy next week, 421 00:17:12,119 --> 00:17:16,680 but also the delayed costs are essentially discounted by beta. 422 00:17:16,680 --> 00:17:18,690 So then you essentially just have, like, 1/2. 423 00:17:18,690 --> 00:17:21,540 This is the beta for everything in the future times two, 424 00:17:21,540 --> 00:17:23,950 which are the benefits, minus 3, which are the costs. 425 00:17:23,950 --> 00:17:26,730 And that's smaller than 0. 426 00:17:26,730 --> 00:17:28,740 So you're not going to do that. 427 00:17:28,740 --> 00:17:31,110 And that's sort of a general feature for leisure 428 00:17:31,110 --> 00:17:32,440 good, as we call them. 429 00:17:32,440 --> 00:17:36,455 These have immediate rewards and delayed benefits. 430 00:17:36,455 --> 00:17:37,830 And so what you tend to do is you 431 00:17:37,830 --> 00:17:42,300 tend to overconsume them in the present relative 432 00:17:42,300 --> 00:17:43,890 to long run plans. 433 00:17:43,890 --> 00:17:44,608 Yeah? 434 00:17:44,608 --> 00:17:47,473 AUDIENCE: Are you only considering [INAUDIBLE] 435 00:17:47,473 --> 00:17:48,390 FRANK SCHILBACH: Yeah. 436 00:17:48,390 --> 00:17:51,840 So yeah, you can think of this as, like, a shorthand 437 00:17:51,840 --> 00:17:56,340 form of saying, for example, suppose you eat a lot of candy 438 00:17:56,340 --> 00:17:58,597 or, like, on one day you eat candy and suppose 439 00:17:58,597 --> 00:18:00,180 you know-- these are repeated choices, 440 00:18:00,180 --> 00:18:02,730 but I'm sort of aggregating it into one. 441 00:18:02,730 --> 00:18:05,400 You'll have, essentially, health costs in the future. 442 00:18:05,400 --> 00:18:07,390 Suppose you get dental pain in the future. 443 00:18:07,390 --> 00:18:12,310 Each period you have dental pain starting at age 30 or 40 or 50. 444 00:18:12,310 --> 00:18:15,660 Now, you can sort of think of this as like each day 445 00:18:15,660 --> 00:18:17,368 you're going to have negative utility. 446 00:18:17,368 --> 00:18:19,410 What I'm doing now is I'm sort of collapsing that 447 00:18:19,410 --> 00:18:22,350 into one day in a sense of just making sure that-- to make 448 00:18:22,350 --> 00:18:23,520 it sort of tractable. 449 00:18:23,520 --> 00:18:25,140 So you can think of the delayed health 450 00:18:25,140 --> 00:18:28,200 costs as a summary of the health costs overall. 451 00:18:28,200 --> 00:18:32,680 Instead you could also write down 0.1 for your 40, 452 00:18:32,680 --> 00:18:35,830 0.1 for your 41, and so on and so forth, 453 00:18:35,830 --> 00:18:37,560 and sort of aggregating in that way. 454 00:18:37,560 --> 00:18:40,050 But that's just for simplicity here. 455 00:18:40,050 --> 00:18:43,320 Similarly, you could also say each day 456 00:18:43,320 --> 00:18:45,300 you'll have essentially a choice to eat candy. 457 00:18:45,300 --> 00:18:46,673 And these things sort of add up. 458 00:18:46,673 --> 00:18:48,840 And again, sort of simplifying in a sense of saying, 459 00:18:48,840 --> 00:18:51,300 like, should I eat candy overall, 460 00:18:51,300 --> 00:18:52,920 which is a number of different choices 461 00:18:52,920 --> 00:18:55,420 that each are between the present and the future. 462 00:18:55,420 --> 00:18:58,410 That's just like changing the units in some way overall. 463 00:18:58,410 --> 00:19:01,380 I think the structure of the problem is the same. 464 00:19:01,380 --> 00:19:02,694 Yeah? 465 00:19:02,694 --> 00:19:04,955 AUDIENCE: So obviously this is kind 466 00:19:04,955 --> 00:19:07,473 of comparing apples and oranges. 467 00:19:07,473 --> 00:19:15,490 But I the one kind of [INAUDIBLE] is your health is 468 00:19:15,490 --> 00:19:19,382 kind of the sum of a bunch of actions that you did over 469 00:19:19,382 --> 00:19:20,965 your lifetime that affect your health, 470 00:19:20,965 --> 00:19:25,590 versus candy is something that-- 471 00:19:25,590 --> 00:19:28,630 the pleasure that you get out of candy is exactly-- 472 00:19:28,630 --> 00:19:30,640 fully [INAUDIBLE]. 473 00:19:30,640 --> 00:19:33,280 So when people-- when you do this kind of [INAUDIBLE] 474 00:19:33,280 --> 00:19:36,670 discounting and you're trying to compare health in the future, 475 00:19:36,670 --> 00:19:41,580 like, pleasure now, the fact that the candy contributes such 476 00:19:41,580 --> 00:19:45,670 a small amount to your overall health, 477 00:19:45,670 --> 00:19:47,843 it seems kind of like an apples to oranges-- 478 00:19:47,843 --> 00:19:48,760 FRANK SCHILBACH: Yeah. 479 00:19:48,760 --> 00:19:49,820 To some degree, I think that's right. 480 00:19:49,820 --> 00:19:51,860 I think it's, in some sense, that's just an example. 481 00:19:51,860 --> 00:19:53,260 So I could show you many different things 482 00:19:53,260 --> 00:19:54,940 that are sort of similar in structure. 483 00:19:54,940 --> 00:19:57,520 I'm using candy just to make it concrete. 484 00:19:57,520 --> 00:20:00,580 You could do the same with problem sets and other pain, 485 00:20:00,580 --> 00:20:03,010 or exercising, and so on and so forth. 486 00:20:03,010 --> 00:20:05,950 I think at the end of the day, I think that's exactly right. 487 00:20:05,950 --> 00:20:07,910 For a lot of choices that people make-- 488 00:20:07,910 --> 00:20:11,845 be it brushing their teeth, be it exercising, 489 00:20:11,845 --> 00:20:13,600 be it eating healthily and so on, 490 00:20:13,600 --> 00:20:15,610 often the costs or the benefits are 491 00:20:15,610 --> 00:20:16,900 very salient in the present. 492 00:20:16,900 --> 00:20:19,007 They're very salient and concrete. 493 00:20:19,007 --> 00:20:20,840 Right now you have a cookie in front of you. 494 00:20:20,840 --> 00:20:21,465 You can eat it. 495 00:20:21,465 --> 00:20:23,620 You'll be happy, and that's for sure. 496 00:20:23,620 --> 00:20:25,540 Sometime in 20 years from now, you 497 00:20:25,540 --> 00:20:27,160 might be sort of like unhealthy. 498 00:20:27,160 --> 00:20:29,800 You might get dental problems and so on and so forth. 499 00:20:29,800 --> 00:20:31,970 Not only is it sort of very far away, 500 00:20:31,970 --> 00:20:33,640 but it's also very diffuse. 501 00:20:33,640 --> 00:20:35,322 It's also maybe unlikely. 502 00:20:35,322 --> 00:20:37,030 Like, there's a chance of getting a heart 503 00:20:37,030 --> 00:20:38,680 attack at age 70. 504 00:20:38,680 --> 00:20:39,610 Maybe, maybe not. 505 00:20:39,610 --> 00:20:41,220 Maybe you'll be just fine. 506 00:20:41,220 --> 00:20:43,760 So it's more complicated in a lot of health decisions. 507 00:20:43,760 --> 00:20:46,120 So there's other research saying, like, well, partially 508 00:20:46,120 --> 00:20:47,380 it's about uncertainty. 509 00:20:47,380 --> 00:20:49,930 Partially it's about the future being diffuse 510 00:20:49,930 --> 00:20:52,540 and very sort of unclear. 511 00:20:52,540 --> 00:20:55,150 One part of that people tend to think is time preferences. 512 00:20:55,150 --> 00:20:56,590 But I think what you're saying is the world is 513 00:20:56,590 --> 00:20:57,730 more complicated than that. 514 00:20:57,730 --> 00:20:59,710 And that's for sure true. 515 00:20:59,710 --> 00:21:02,260 What I'm sort of saying is, like, thinking about time 516 00:21:02,260 --> 00:21:04,690 preferences can help you understand some choices 517 00:21:04,690 --> 00:21:06,722 that people make over time. 518 00:21:06,722 --> 00:21:08,680 Having said that, there's lots of other aspects 519 00:21:08,680 --> 00:21:10,990 here, which we're sort of grossly simplifying. 520 00:21:10,990 --> 00:21:12,850 But I think the key part here-- 521 00:21:12,850 --> 00:21:15,310 I think what's really important for a lot of health choices 522 00:21:15,310 --> 00:21:17,320 tends to be that people-- 523 00:21:17,320 --> 00:21:19,690 that exactly as you say, there's a lot 524 00:21:19,690 --> 00:21:21,928 of-- like, thousands of really small choices 525 00:21:21,928 --> 00:21:24,220 that sort of add up to something like-- what we call it 526 00:21:24,220 --> 00:21:26,200 unhealthy behavior in some way. 527 00:21:26,200 --> 00:21:29,290 And each of them are concrete in some sense in terms 528 00:21:29,290 --> 00:21:30,490 of the costs and benefits. 529 00:21:30,490 --> 00:21:32,890 Like, brushing your teeth is like costly in some sense 530 00:21:32,890 --> 00:21:35,290 for five minutes or whatever. 531 00:21:35,290 --> 00:21:38,710 Eating candy is happy for a few minutes, 532 00:21:38,710 --> 00:21:40,480 as well, very concretely. 533 00:21:40,480 --> 00:21:42,710 And then the costs are often diffuse in the future 534 00:21:42,710 --> 00:21:43,210 and so on. 535 00:21:43,210 --> 00:21:44,470 That's really important. 536 00:21:44,470 --> 00:21:46,303 We're going to talk a little bit about this. 537 00:21:46,303 --> 00:21:47,740 But we sort of-- for now at least 538 00:21:47,740 --> 00:21:50,530 abstracting, essentially, that away. 539 00:21:50,530 --> 00:21:52,838 Yes? 540 00:21:52,838 --> 00:21:55,760 AUDIENCE: [INAUDIBLE]. 541 00:21:55,760 --> 00:21:59,841 Why is it better than the [INAUDIBLE].. 542 00:21:59,841 --> 00:22:03,997 Why is it [INAUDIBLE] and what actually [INAUDIBLE] 543 00:22:03,997 --> 00:22:06,622 better than the exponential model? 544 00:22:06,622 --> 00:22:08,330 FRANK SCHILBACH: So the exponential model 545 00:22:08,330 --> 00:22:12,110 would not predict you this type of behavior. 546 00:22:12,110 --> 00:22:15,320 So if you think about now we get to this-- like, 547 00:22:15,320 --> 00:22:17,960 if you sort of say you want to make choices for the future, 548 00:22:17,960 --> 00:22:20,120 the exponential discounter would give you 549 00:22:20,120 --> 00:22:23,330 the same choices for the future versus what 550 00:22:23,330 --> 00:22:25,040 actually-- when the future arrives. 551 00:22:25,040 --> 00:22:27,500 So I'm going to show you a sort of-- more in the context 552 00:22:27,500 --> 00:22:30,500 of problem set, I'm going to show you this behavior that 553 00:22:30,500 --> 00:22:32,330 the exponential model cannot-- 554 00:22:32,330 --> 00:22:34,380 just not explain. 555 00:22:34,380 --> 00:22:37,190 Like, the exponential discounter would say, either I like candy 556 00:22:37,190 --> 00:22:38,900 and I don't care about-- 557 00:22:38,900 --> 00:22:41,450 or I just don't worry that much about the health costs and I 558 00:22:41,450 --> 00:22:42,940 eat candy, or I don't. 559 00:22:42,940 --> 00:22:44,690 I'm really worried about the health costs, 560 00:22:44,690 --> 00:22:46,400 and therefore I don't eat candy. 561 00:22:46,400 --> 00:22:47,900 And that choice is the same today 562 00:22:47,900 --> 00:22:49,770 versus next week versus two weeks from now, 563 00:22:49,770 --> 00:22:50,850 and so on and so forth. 564 00:22:50,850 --> 00:22:53,240 So once I make a choice for eating candy-- 565 00:22:53,240 --> 00:22:56,120 so here notice that the person who will make the plans 566 00:22:56,120 --> 00:22:59,570 to not eat candy in the future, once the future arrives, 567 00:22:59,570 --> 00:23:02,427 that person will change their choice 568 00:23:02,427 --> 00:23:04,010 and then actually surprise themselves, 569 00:23:04,010 --> 00:23:05,989 potentially by eating candy. 570 00:23:05,989 --> 00:23:07,426 AUDIENCE: [INAUDIBLE]. 571 00:23:14,185 --> 00:23:16,560 FRANK SCHILBACH: There's just behaviors in the world that 572 00:23:16,560 --> 00:23:18,960 the exponential discounting model cannot explain. 573 00:23:18,960 --> 00:23:19,840 That is one of them. 574 00:23:19,840 --> 00:23:21,682 AUDIENCE: [INAUDIBLE]. 575 00:23:21,682 --> 00:23:22,890 FRANK SCHILBACH: So there's-- 576 00:23:22,890 --> 00:23:23,160 yeah. 577 00:23:23,160 --> 00:23:24,750 So I think there's a question on what 578 00:23:24,750 --> 00:23:26,347 other models can explain this. 579 00:23:26,347 --> 00:23:28,680 I think the hyperbolic model is, in fact, quite similar, 580 00:23:28,680 --> 00:23:30,750 as it sort of showed you in the curve here. 581 00:23:30,750 --> 00:23:34,440 You sort of see the discount functions are quite similar. 582 00:23:34,440 --> 00:23:38,430 There's research using the hyperbolic model. 583 00:23:38,430 --> 00:23:41,340 In economics in the last sort of-- in behavioral economics 584 00:23:41,340 --> 00:23:43,080 in the last something like 20 years, 585 00:23:43,080 --> 00:23:45,540 the quasi-hyperbolic model is the model 586 00:23:45,540 --> 00:23:48,810 that everybody uses, partially for tractability and simplicity 587 00:23:48,810 --> 00:23:53,190 for no other good reasons in many settings. 588 00:23:53,190 --> 00:23:55,440 But in some sense, what we care about-- in some sense, 589 00:23:55,440 --> 00:23:58,050 I don't care actually that much about which model among sort 590 00:23:58,050 --> 00:24:00,870 of a class of model that are quite similar can explain 591 00:24:00,870 --> 00:24:02,640 things sort of-- 592 00:24:02,640 --> 00:24:06,368 if two models explain the same thing in similar ways, 593 00:24:06,368 --> 00:24:08,160 I don't care about which one we should use. 594 00:24:08,160 --> 00:24:10,452 In a sense, the simpler model is sort of easier to use, 595 00:24:10,452 --> 00:24:12,322 and that's why we sort of do it. 596 00:24:12,322 --> 00:24:14,280 What I care about is there are some predictions 597 00:24:14,280 --> 00:24:17,310 from the exponential model that are sort of just not-- 598 00:24:17,310 --> 00:24:18,540 that are just false. 599 00:24:18,540 --> 00:24:20,400 And those we need to improve on. 600 00:24:20,400 --> 00:24:23,640 That could be either through a hyperbolic model 601 00:24:23,640 --> 00:24:25,170 or quasi-hyperbolic model. 602 00:24:25,170 --> 00:24:28,170 To keep things simple, I'm using the quasi-hyperbolic model, 603 00:24:28,170 --> 00:24:30,750 in part because it nests very simply 604 00:24:30,750 --> 00:24:32,350 in the exponential model. 605 00:24:32,350 --> 00:24:33,933 And the reason why a lot of economists 606 00:24:33,933 --> 00:24:36,267 have used it is to say, OK, here's an exponential model. 607 00:24:36,267 --> 00:24:37,590 We know how to use that model. 608 00:24:37,590 --> 00:24:39,450 Now we're going to add one parameter 609 00:24:39,450 --> 00:24:40,950 and things look very similar. 610 00:24:40,950 --> 00:24:43,800 And beta equals 1 essentially collapses that model back 611 00:24:43,800 --> 00:24:45,120 to the exponential model. 612 00:24:45,120 --> 00:24:47,460 And therefore, people have used it. 613 00:24:47,460 --> 00:24:49,740 And that's essentially what we do. 614 00:24:49,740 --> 00:24:50,430 OK. 615 00:24:50,430 --> 00:24:53,790 So now the flip side of those kinds of choices 616 00:24:53,790 --> 00:24:54,993 are investment goods. 617 00:24:54,993 --> 00:24:56,910 Investment goods are essentially very similar. 618 00:24:56,910 --> 00:24:58,618 These are goods that have immediate costs 619 00:24:58,618 --> 00:25:00,450 but delayed benefits. 620 00:25:00,450 --> 00:25:02,130 An example would be go to the gym. 621 00:25:02,130 --> 00:25:03,780 Like, you can go to the gym right now. 622 00:25:03,780 --> 00:25:06,840 Some people find that fun, but many people also 623 00:25:06,840 --> 00:25:07,950 find it costly. 624 00:25:07,950 --> 00:25:10,050 There's some effort cost of, say, in this case, 2. 625 00:25:10,050 --> 00:25:13,020 There's benefits, health benefits, of 3. 626 00:25:13,020 --> 00:25:15,210 Again, that's really sort of like a stark example. 627 00:25:15,210 --> 00:25:17,877 But I'm just trying to make sort of a point to make this simple. 628 00:25:17,877 --> 00:25:21,720 Now, again, if we have beta equals 1/2 and delta equals 1, 629 00:25:21,720 --> 00:25:23,970 if you think about should you go to the gym today, 630 00:25:23,970 --> 00:25:25,330 the answer is no. 631 00:25:25,330 --> 00:25:28,590 And the reason is that you put a lot of weight on the present. 632 00:25:28,590 --> 00:25:30,850 You put sort of weight of 1 on the present, 633 00:25:30,850 --> 00:25:33,150 the cost of minus 1-- 634 00:25:33,150 --> 00:25:33,780 sorry. 635 00:25:33,780 --> 00:25:36,370 You put a weight of 1 on the cost of minus 2. 636 00:25:36,370 --> 00:25:38,310 So you have minus 2 costs. 637 00:25:38,310 --> 00:25:39,700 The benefits are in the future. 638 00:25:39,700 --> 00:25:41,220 You discount them by beta. 639 00:25:41,220 --> 00:25:44,810 So you have 1/2 times 3, which is smaller than 0. 640 00:25:44,810 --> 00:25:46,860 Now, if you think about, then, are 641 00:25:46,860 --> 00:25:49,680 you planning to go to the gym next week, the answer is yes. 642 00:25:49,680 --> 00:25:50,345 Why is that? 643 00:25:50,345 --> 00:25:52,470 Well, now you're essentially discounting everything 644 00:25:52,470 --> 00:25:55,472 that's in the future, including the costs of going to the gym. 645 00:25:55,472 --> 00:25:57,930 So you can think about, should you go to the gym next week? 646 00:25:57,930 --> 00:26:00,120 The answer will be yes. 647 00:26:00,120 --> 00:26:04,200 The reason is because the health benefits overall 648 00:26:04,200 --> 00:26:06,870 are larger than the costs. 649 00:26:06,870 --> 00:26:09,120 Now, again, what we're going to see then 650 00:26:09,120 --> 00:26:12,840 is people deviate from their long-run plans. 651 00:26:12,840 --> 00:26:15,090 Now they under-consume investment goods 652 00:26:15,090 --> 00:26:17,100 relative to long run plans. 653 00:26:17,100 --> 00:26:19,710 So we saw previously that people over consume leisure goods. 654 00:26:19,710 --> 00:26:21,390 They do too much fun stuff that has 655 00:26:21,390 --> 00:26:23,220 bad consequences in the future. 656 00:26:23,220 --> 00:26:27,150 And people tend to do too little of tedious stuff 657 00:26:27,150 --> 00:26:31,650 that will yield benefits in the future relative 658 00:26:31,650 --> 00:26:33,810 to their long run plans. 659 00:26:33,810 --> 00:26:36,480 Again, you look at sort of timing consistency 660 00:26:36,480 --> 00:26:39,420 in a sense of, like, if I plan to go to the gym next week, 661 00:26:39,420 --> 00:26:40,680 I'm going to say yes. 662 00:26:40,680 --> 00:26:44,695 Now unless things change, once next week arrives, 663 00:26:44,695 --> 00:26:46,320 I'm going to be at the choice of, like, 664 00:26:46,320 --> 00:26:47,610 should I go to the gym today? 665 00:26:47,610 --> 00:26:48,540 I'm going to say no. 666 00:26:48,540 --> 00:26:51,630 I would like to not do that because now I'm 667 00:26:51,630 --> 00:26:56,700 essentially discounting the future but not the present. 668 00:26:56,700 --> 00:26:57,930 Any questions on that? 669 00:26:57,930 --> 00:26:58,820 Yes. 670 00:26:58,820 --> 00:27:03,030 AUDIENCE: [INAUDIBLE] one more time why you discount 671 00:27:03,030 --> 00:27:08,302 the efforts as in the future and not-- 672 00:27:08,302 --> 00:27:09,260 FRANK SCHILBACH: Right. 673 00:27:09,260 --> 00:27:12,490 So think of these as different periods-- so the effort-- 674 00:27:12,490 --> 00:27:16,070 so if you think about, should you go until the costs are 675 00:27:16,070 --> 00:27:17,713 today-- 676 00:27:17,713 --> 00:27:19,380 think about these are different periods. 677 00:27:19,380 --> 00:27:20,910 Period right now. 678 00:27:20,910 --> 00:27:23,210 Health benefits are, like, say, a week later. 679 00:27:23,210 --> 00:27:24,240 OK. 680 00:27:24,240 --> 00:27:25,710 In the choice about doing it today, 681 00:27:25,710 --> 00:27:28,060 the costs are right now-- that's the present period. 682 00:27:28,060 --> 00:27:30,780 So if you go back to the discount function, 683 00:27:30,780 --> 00:27:33,515 you put a weight of 1 on anything that's in the present. 684 00:27:33,515 --> 00:27:35,640 And anything that's in the future, a future period, 685 00:27:35,640 --> 00:27:37,448 you put in a weight of 1/2. 686 00:27:37,448 --> 00:27:39,906 AUDIENCE: OK, so we can see every [INAUDIBLE] in the future 687 00:27:39,906 --> 00:27:40,788 because [INAUDIBLE]. 688 00:27:40,788 --> 00:27:41,830 FRANK SCHILBACH: Exactly. 689 00:27:41,830 --> 00:27:44,140 So the effort right now is in the present. 690 00:27:44,140 --> 00:27:47,252 So for like-- so start with a choice of, like, today. 691 00:27:47,252 --> 00:27:48,460 The effort is in the present. 692 00:27:48,460 --> 00:27:50,252 That's why I'm not sort of discounting that 693 00:27:50,252 --> 00:27:51,930 in the first choice for today. 694 00:27:51,930 --> 00:27:53,740 But if I think about doing it next week, 695 00:27:53,740 --> 00:27:55,360 then next week is also in the future. 696 00:27:55,360 --> 00:27:57,360 I'm discounting everything that's in the future, 697 00:27:57,360 --> 00:27:59,290 whether it's a week away or two weeks ago. 698 00:27:59,290 --> 00:28:00,160 I don't care. 699 00:28:00,160 --> 00:28:04,070 And therefore, everything is discounted by 1/2. 700 00:28:04,070 --> 00:28:05,030 OK. 701 00:28:05,030 --> 00:28:11,150 So now one important distinction now is demand for commitment, 702 00:28:11,150 --> 00:28:13,520 or is there commitment available? 703 00:28:13,520 --> 00:28:15,260 So what we're going to do is think 704 00:28:15,260 --> 00:28:19,940 about like students who have to do problem sets with very 705 00:28:19,940 --> 00:28:22,340 simple beta delta preferences. 706 00:28:22,340 --> 00:28:25,580 So consider a student with beta equals 1/2, delta equals 1. 707 00:28:25,580 --> 00:28:26,503 There's three periods. 708 00:28:26,503 --> 00:28:27,920 And this is sort of getting pretty 709 00:28:27,920 --> 00:28:30,087 close to what you're going to do in the problem set, 710 00:28:30,087 --> 00:28:31,140 actually, yourself. 711 00:28:31,140 --> 00:28:32,480 There are three periods. 712 00:28:32,480 --> 00:28:34,770 You have to do the problem set in exactly one of three 713 00:28:34,770 --> 00:28:35,270 periods. 714 00:28:35,270 --> 00:28:37,395 That's, of course, contrived and a little stylized. 715 00:28:37,395 --> 00:28:40,340 But that's just an example for now. 716 00:28:40,340 --> 00:28:43,400 So there's periods T equals 0, T equals 1, T equals 2. 717 00:28:43,400 --> 00:28:46,460 The instantaneous utility is of minus 1, three halves, 718 00:28:46,460 --> 00:28:47,240 and five halves. 719 00:28:47,240 --> 00:28:49,800 So the problem set becomes more and more painful the later 720 00:28:49,800 --> 00:28:51,440 we actually do it. 721 00:28:51,440 --> 00:28:52,500 OK. 722 00:28:52,500 --> 00:28:56,190 And there's only one day in which you can actually do it. 723 00:28:56,190 --> 00:28:58,158 So now the first thing that I think about is 724 00:28:58,158 --> 00:28:59,700 suppose there's commitment available. 725 00:28:59,700 --> 00:29:00,220 What does that mean? 726 00:29:00,220 --> 00:29:01,803 Suppose a student can essentially just 727 00:29:01,803 --> 00:29:03,860 pick, when is she going to do the problem set, 728 00:29:03,860 --> 00:29:05,180 and actually stick to that. 729 00:29:05,180 --> 00:29:06,805 Suppose they could just sort of dictate 730 00:29:06,805 --> 00:29:09,600 what she's going to do in the future, what would she choose? 731 00:29:09,600 --> 00:29:13,577 Well-- and then she actually has to sort of stick with that. 732 00:29:13,577 --> 00:29:16,160 So now we can sort think about, from the perspective of period 733 00:29:16,160 --> 00:29:20,000 zero, remember the person is a hyperbolic discounter 734 00:29:20,000 --> 00:29:22,520 with beta equals 1/2. 735 00:29:22,520 --> 00:29:26,630 From the perspective of right now, I'm going to say, well, 736 00:29:26,630 --> 00:29:29,100 the discounted utility today is minus 1. 737 00:29:29,100 --> 00:29:32,030 There's no discounting happening for today if I do it today. 738 00:29:32,030 --> 00:29:34,730 For tomorrow, I'm going to discount the future by 1/2. 739 00:29:34,730 --> 00:29:36,770 So I'm going to get minus 3/4. 740 00:29:36,770 --> 00:29:39,140 And in the period 2 in 2 days from now, 741 00:29:39,140 --> 00:29:40,700 I'm going to do 1/2 minus-- 742 00:29:40,700 --> 00:29:44,030 times minus five halves, which is five quarters. 743 00:29:44,030 --> 00:29:46,940 So if I could sort of predict-- if I could sort of say what 744 00:29:46,940 --> 00:29:50,025 I would like to do, I would say, well, I'm 745 00:29:50,025 --> 00:29:51,650 going to do it in [INAUDIBLE] equals 1. 746 00:29:51,650 --> 00:29:57,700 I'm going to do it tomorrow if I could follow through with that. 747 00:29:57,700 --> 00:29:58,320 Is that clear? 748 00:30:03,690 --> 00:30:05,100 OK. 749 00:30:05,100 --> 00:30:06,810 So that's if commitment is available. 750 00:30:06,810 --> 00:30:08,700 That is if I could essentially just force 751 00:30:08,700 --> 00:30:10,890 myself to do stuff in the future and not 752 00:30:10,890 --> 00:30:12,990 deviate from that at all. 753 00:30:12,990 --> 00:30:15,420 Now if no commitment is available, 754 00:30:15,420 --> 00:30:17,430 how does that thinking change? 755 00:30:22,230 --> 00:30:23,240 Yes. 756 00:30:23,240 --> 00:30:24,730 AUDIENCE: T equals 1 [INAUDIBLE].. 757 00:30:24,730 --> 00:30:25,980 FRANK SCHILBACH: Yes, exactly. 758 00:30:25,980 --> 00:30:30,150 Once T equals 1 arrives, I might actually 759 00:30:30,150 --> 00:30:32,100 prefer not to do it in T equals 1 760 00:30:32,100 --> 00:30:36,137 but rather say I'd rather do it in T equals 2. 761 00:30:36,137 --> 00:30:38,220 And this is exactly what you're going to see here. 762 00:30:38,220 --> 00:30:41,018 This is the exact same problem that I showed you before. 763 00:30:41,018 --> 00:30:42,810 Now, suppose the student has no [INAUDIBLE] 764 00:30:42,810 --> 00:30:44,995 so the commitment technology is just to say, 765 00:30:44,995 --> 00:30:47,370 what if the student can just choose in every period, what 766 00:30:47,370 --> 00:30:50,220 is she going to do, would she actually do it in period one? 767 00:30:50,220 --> 00:30:53,670 Well, if period one arrives, if the problem set is not 768 00:30:53,670 --> 00:30:56,610 done, if she does it at period one, 769 00:30:56,610 --> 00:30:58,440 from the perspective of period one, 770 00:30:58,440 --> 00:31:01,240 the discounted costs are minus three halves. 771 00:31:01,240 --> 00:31:03,240 That's just because that's in the current period 772 00:31:03,240 --> 00:31:05,520 from the perspective of period one. 773 00:31:05,520 --> 00:31:08,100 If she instead sort of were to do it in period two, 774 00:31:08,100 --> 00:31:11,130 she now discounts, again, period two from the perspective 775 00:31:11,130 --> 00:31:12,630 of period one by 1/2. 776 00:31:12,630 --> 00:31:16,290 So 1/2 times minus 5/2 hops is 5/4. 777 00:31:16,290 --> 00:31:20,790 Well, 5/4 is less bad than 3/2. 778 00:31:20,790 --> 00:31:24,000 So she is going to say, I'm going to do it in period two. 779 00:31:24,000 --> 00:31:27,060 So that's to say that students' preferences are dynamically 780 00:31:27,060 --> 00:31:27,653 inconsistent. 781 00:31:27,653 --> 00:31:29,820 Again, that's sort of something that the exponential 782 00:31:29,820 --> 00:31:32,880 discounting model would not predict or cannot explain 783 00:31:32,880 --> 00:31:36,690 and the quasi-hyperbolic model is one way of simply creating 784 00:31:36,690 --> 00:31:37,920 such timing consistency. 785 00:31:37,920 --> 00:31:38,720 Yes. 786 00:31:38,720 --> 00:31:41,220 AUDIENCE: I was wondering how we should think about the fact 787 00:31:41,220 --> 00:31:42,845 that, for example, you know that you're 788 00:31:42,845 --> 00:31:46,890 going to experience [INAUDIBLE] on the second period. 789 00:31:46,890 --> 00:31:49,070 So should then your second period activity function 790 00:31:49,070 --> 00:31:50,070 be the one that matters? 791 00:31:50,070 --> 00:31:54,820 Shouldn't you, as a sophisticated [INAUDIBLE] 792 00:31:54,820 --> 00:31:59,010 minus 3/2 that it's worse from your perspective [INAUDIBLE].. 793 00:32:01,680 --> 00:32:05,490 That utility function should be the one that matters 794 00:32:05,490 --> 00:32:07,140 and is used [INAUDIBLE]. 795 00:32:07,140 --> 00:32:08,440 FRANK SCHILBACH: Right so you're sort of saying-- 796 00:32:08,440 --> 00:32:10,357 and sounds if I understood right-- is to say-- 797 00:32:10,357 --> 00:32:12,300 and let's see whether that's true. 798 00:32:12,300 --> 00:32:14,730 You're saying, well, if no commitment is available, 799 00:32:14,730 --> 00:32:17,070 I should never let it get to that point. 800 00:32:17,070 --> 00:32:18,900 If I'm in period zero, I should know 801 00:32:18,900 --> 00:32:21,000 I'm not going to do it actually in period one. 802 00:32:21,000 --> 00:32:23,190 Therefore, I'd rather do it right now 803 00:32:23,190 --> 00:32:26,220 to avoid that all sort of like procrastinated from period one 804 00:32:26,220 --> 00:32:27,282 to period two. 805 00:32:27,282 --> 00:32:28,740 And if I'm not in period 0, I might 806 00:32:28,740 --> 00:32:31,115 say I do it rather right now, because otherwise I'm going 807 00:32:31,115 --> 00:32:32,430 to just do it in period two. 808 00:32:32,430 --> 00:32:34,140 And from the perspective of period zero, 809 00:32:34,140 --> 00:32:36,570 I'd rather do it right now, compared to period two. 810 00:32:36,570 --> 00:32:38,280 I would prefer to do it in period one, 811 00:32:38,280 --> 00:32:41,820 but that's not feasible because my period one self will not 812 00:32:41,820 --> 00:32:43,920 behave in the absence of commitment. 813 00:32:43,920 --> 00:32:46,170 AUDIENCE: I was more thinking in a way that, why would 814 00:32:46,170 --> 00:32:49,230 you want to commit your previous one [INAUDIBLE] 815 00:32:49,230 --> 00:32:52,780 that your [INAUDIBLE]? 816 00:32:52,780 --> 00:32:54,280 Because you have a different utility 817 00:32:54,280 --> 00:32:55,690 function in that period. 818 00:32:55,690 --> 00:32:56,640 [INAUDIBLE] 819 00:33:00,910 --> 00:33:02,170 FRANK SCHILBACH: It's just a-- 820 00:33:02,170 --> 00:33:03,753 I mean, something that's an assumption 821 00:33:03,753 --> 00:33:06,850 in the sense of from the perspective of period zero, 822 00:33:06,850 --> 00:33:08,220 you make certain choices. 823 00:33:08,220 --> 00:33:10,270 You're going to say, I could do it right now. 824 00:33:10,270 --> 00:33:11,530 I could do it in period one. 825 00:33:11,530 --> 00:33:13,150 Or I could do it in period two. 826 00:33:13,150 --> 00:33:14,830 Now, you have certain preferences. 827 00:33:14,830 --> 00:33:16,150 And you're saying maybe your preferences 828 00:33:16,150 --> 00:33:16,983 should be different. 829 00:33:16,983 --> 00:33:18,280 And that's obviously fine. 830 00:33:18,280 --> 00:33:21,310 I sort of specified the preferences for the student. 831 00:33:21,310 --> 00:33:23,350 I said that beta is 1/2. 832 00:33:23,350 --> 00:33:25,493 So she cares about 1/2 about anything 833 00:33:25,493 --> 00:33:27,160 that happens in the future in period one 834 00:33:27,160 --> 00:33:28,930 and two compared to period zero. 835 00:33:28,930 --> 00:33:32,200 And then sort of just sort of like-- 836 00:33:32,200 --> 00:33:34,120 you just look at what the utilities are and it 837 00:33:34,120 --> 00:33:37,030 sort of turns out that from her perspective, from period zero, 838 00:33:37,030 --> 00:33:38,830 she prefers period one. 839 00:33:38,830 --> 00:33:40,960 Now, you could sort of specify the utility function 840 00:33:40,960 --> 00:33:42,647 differently. 841 00:33:42,647 --> 00:33:44,230 But for that specific example, I guess 842 00:33:44,230 --> 00:33:48,560 that's what sort of the algebra tells us. 843 00:33:48,560 --> 00:33:49,060 Yeah. 844 00:33:51,970 --> 00:33:55,060 So now the key question now is to say, OK, 845 00:33:55,060 --> 00:33:57,197 now the preferences are dynamically inconsistent. 846 00:33:57,197 --> 00:33:59,530 So now what I said-- well, what's really important now-- 847 00:33:59,530 --> 00:34:01,510 and in some sense, maybe you were asking about that, 848 00:34:01,510 --> 00:34:02,110 as well-- 849 00:34:02,110 --> 00:34:05,890 is, well, it's the question on, like, 850 00:34:05,890 --> 00:34:08,560 is the student aware of this time of consistency? 851 00:34:08,560 --> 00:34:12,347 So you could say, well, when deciding in period zero, 852 00:34:12,347 --> 00:34:14,889 you might sort of say, well, I'd like to do it in period one. 853 00:34:14,889 --> 00:34:17,920 If I believe that in period one, I'm time consistent, 854 00:34:17,920 --> 00:34:20,409 or if I believe that I'm an exponential discounter 855 00:34:20,409 --> 00:34:22,960 in the future, I will be very virtuous in the future, 856 00:34:22,960 --> 00:34:25,300 well then, I'm very happy to wait until period one. 857 00:34:25,300 --> 00:34:28,060 And then I'm going to follow through with my plans. 858 00:34:28,060 --> 00:34:30,130 If instead I know that in period one 859 00:34:30,130 --> 00:34:32,238 I'm going to be present bias, well then 860 00:34:32,238 --> 00:34:34,780 what's going to happen is then I can't trust myself in period 861 00:34:34,780 --> 00:34:35,650 one to actually do it. 862 00:34:35,650 --> 00:34:37,358 I know I'm going to procrastinate further 863 00:34:37,358 --> 00:34:38,199 until period two. 864 00:34:38,199 --> 00:34:40,120 So I'd rather do it at period zero 865 00:34:40,120 --> 00:34:44,139 to avoid sort of having to deal with it in period two. 866 00:34:44,139 --> 00:34:46,070 Let me sort of walk you through that. 867 00:34:46,070 --> 00:34:49,719 So I guess we need sort of additional parameters 868 00:34:49,719 --> 00:34:52,000 to start with which is called beta hat. 869 00:34:52,000 --> 00:34:54,520 Beta hat does essentially the sophistication or naivete 870 00:34:54,520 --> 00:34:55,570 parameter. 871 00:34:55,570 --> 00:34:57,760 Beta hat is your belief about what 872 00:34:57,760 --> 00:35:00,460 you think your beta will be in the future. 873 00:35:00,460 --> 00:35:03,220 So beta is like what the actual beta is. 874 00:35:03,220 --> 00:35:06,520 That's the true value of beta in the present and in the future. 875 00:35:06,520 --> 00:35:08,590 And beta hat is like what you think 876 00:35:08,590 --> 00:35:11,260 your beta is in the future, what you 877 00:35:11,260 --> 00:35:15,310 believe your true or your beta is going forward. 878 00:35:15,310 --> 00:35:17,560 It's not what you believe-- you know your beta today. 879 00:35:17,560 --> 00:35:20,140 You know that essentially your present bias today. 880 00:35:20,140 --> 00:35:21,670 Everybody understands that well. 881 00:35:21,670 --> 00:35:23,620 That's an assumption, as well. 882 00:35:23,620 --> 00:35:25,120 But people do not know or may not 883 00:35:25,120 --> 00:35:27,140 know what their beta is in the future. 884 00:35:27,140 --> 00:35:29,925 And that's what the parameter of beta hat measures. 885 00:35:29,925 --> 00:35:31,300 You're going to have three cases. 886 00:35:31,300 --> 00:35:33,790 I'm going to talk about two cases today. 887 00:35:33,790 --> 00:35:37,390 There's going to be a third case starting on Tuesday. 888 00:35:37,390 --> 00:35:40,390 And so the two cases that we are discussing is full naivete. 889 00:35:40,390 --> 00:35:42,940 That's to say my beta hat equals 1. 890 00:35:42,940 --> 00:35:44,470 That's to say I think-- essentially, 891 00:35:44,470 --> 00:35:45,803 I know I'm present biased today. 892 00:35:45,803 --> 00:35:49,900 But I think I'm an exponential discounter in the future. 893 00:35:49,900 --> 00:35:52,570 OK, so that's to say I know I have self 894 00:35:52,570 --> 00:35:54,010 control problems right now. 895 00:35:54,010 --> 00:35:56,200 But next week surely will be different. 896 00:35:56,200 --> 00:35:58,510 Like this is like in the beginning of the semester, 897 00:35:58,510 --> 00:36:00,850 you know you kind of like screwed up in the past. 898 00:36:00,850 --> 00:36:02,950 But this semester will be very different. 899 00:36:02,950 --> 00:36:04,390 You'll be virtuous and so on. 900 00:36:04,390 --> 00:36:07,750 That happens kind of every semester. 901 00:36:07,750 --> 00:36:09,790 So that's beta hat equals 1. 902 00:36:09,790 --> 00:36:12,370 So the person does not realize that she will change her mind. 903 00:36:12,370 --> 00:36:15,070 She thinks that she's going to follow through with her plan. 904 00:36:15,070 --> 00:36:17,320 Her plan is to do it in T equals 1. 905 00:36:17,320 --> 00:36:19,990 She thinks she's going to follow through. 906 00:36:19,990 --> 00:36:21,740 There will be surprises about present bias 907 00:36:21,740 --> 00:36:23,990 because you think you're going to do it in period one. 908 00:36:23,990 --> 00:36:26,350 Period one arrives, and surprise, she's present biased. 909 00:36:26,350 --> 00:36:28,150 She misestimated what she's going to do 910 00:36:28,150 --> 00:36:29,830 and then ends up sort of not doing it 911 00:36:29,830 --> 00:36:32,020 and has to do it then in period two. 912 00:36:32,020 --> 00:36:33,670 There's a sort of like false optimism, 913 00:36:33,670 --> 00:36:36,490 if you want, about future plans and sort of the attitude 914 00:36:36,490 --> 00:36:37,852 of this time is different. 915 00:36:37,852 --> 00:36:40,060 From tomorrow onwards, things will be very different. 916 00:36:40,060 --> 00:36:43,690 We'll be all virtuous in the future. 917 00:36:43,690 --> 00:36:45,580 And then the second part is sort of like-- 918 00:36:45,580 --> 00:36:47,170 call it like perfect sophistication. 919 00:36:47,170 --> 00:36:49,150 That's bets hat equals beta. 920 00:36:49,150 --> 00:36:50,848 That is essentially rational expectation 921 00:36:50,848 --> 00:36:53,140 in a sense-- this is a person who perfectly understands 922 00:36:53,140 --> 00:36:54,100 their preferences. 923 00:36:54,100 --> 00:36:56,150 I know I have seen this movie before. 924 00:36:56,150 --> 00:36:58,780 I know tomorrow I'm going to procrastinate, 925 00:36:58,780 --> 00:37:00,670 or I'm going to be present biased. 926 00:37:00,670 --> 00:37:02,590 I perfectly understand what I'm going to do. 927 00:37:02,590 --> 00:37:05,710 And therefore I take into account that when 928 00:37:05,710 --> 00:37:08,380 making choices right now. 929 00:37:08,380 --> 00:37:11,320 And so she understands perfectly that she will change her mind. 930 00:37:11,320 --> 00:37:14,360 So she understands that she has plans to do it in period one. 931 00:37:14,360 --> 00:37:15,985 But she understands that the period one 932 00:37:15,985 --> 00:37:17,560 self has different preferences. 933 00:37:17,560 --> 00:37:19,900 The period one self prefers to do it in period two 934 00:37:19,900 --> 00:37:21,700 rather than in period one. 935 00:37:21,700 --> 00:37:26,320 So she's kind of like, in some sense, sort of correctly 936 00:37:26,320 --> 00:37:28,210 pessimistic about her future self. 937 00:37:28,210 --> 00:37:31,030 And sort of then in the case of these kinds of investment 938 00:37:31,030 --> 00:37:33,030 goods, that's a good thing, because she doesn't 939 00:37:33,030 --> 00:37:34,030 sort of leave stuff out. 940 00:37:34,030 --> 00:37:36,400 She doesn't delay things a lot for the future. 941 00:37:36,400 --> 00:37:38,590 She doesn't let things get bad because she knows 942 00:37:38,590 --> 00:37:41,140 if she procrastinates further, she'd 943 00:37:41,140 --> 00:37:42,850 rather do it right now, anticipating 944 00:37:42,850 --> 00:37:45,430 that the future self will not follow through. 945 00:37:45,430 --> 00:37:48,350 And here in the perfect sophistication case, 946 00:37:48,350 --> 00:37:50,410 there will be no surprises. 947 00:37:50,410 --> 00:37:53,140 The person always follows through with their plans. 948 00:37:53,140 --> 00:37:55,330 The third case I'm going to talk about next week 949 00:37:55,330 --> 00:37:57,220 is when beta hat equals-- 950 00:37:57,220 --> 00:37:59,140 is between beta and one, which is we 951 00:37:59,140 --> 00:38:02,920 call a partial sophistication or partial naivety. 952 00:38:02,920 --> 00:38:05,140 So it's a little more complicated, but in fact, 953 00:38:05,140 --> 00:38:06,130 quite similar. 954 00:38:06,130 --> 00:38:07,338 I think there was a question. 955 00:38:07,338 --> 00:38:08,308 Yeah. 956 00:38:08,308 --> 00:38:11,284 AUDIENCE: [INAUDIBLE]. 957 00:38:11,284 --> 00:38:14,260 But the future self actually can [INAUDIBLE].. 958 00:38:16,795 --> 00:38:18,420 FRANK SCHILBACH: Sorry, say that again? 959 00:38:18,420 --> 00:38:21,000 AUDIENCE: So the person does not realize 960 00:38:21,000 --> 00:38:22,984 that she will change her mind over the course 961 00:38:22,984 --> 00:38:28,285 of the semester, but she [INAUDIBLE] her plans. 962 00:38:28,285 --> 00:38:29,660 FRANK SCHILBACH: So you would not 963 00:38:29,660 --> 00:38:32,097 sort of-- so you wouldn't really carry-- so if you change 964 00:38:32,097 --> 00:38:33,680 your mind in the future, you would not 965 00:38:33,680 --> 00:38:37,188 carry through with your plans. 966 00:38:37,188 --> 00:38:40,930 AUDIENCE: [INAUDIBLE]. 967 00:38:40,930 --> 00:38:43,750 FRANK SCHILBACH: So either she will change her mind 968 00:38:43,750 --> 00:38:45,420 in the future or not. 969 00:38:45,420 --> 00:38:47,420 So if she doesn't change her mind in the future, 970 00:38:47,420 --> 00:38:50,003 there's no problem, because then there is nothing to be aware. 971 00:38:50,003 --> 00:38:53,110 That's kind of like the case of the exponential discounter. 972 00:38:53,110 --> 00:38:56,240 So if beta hat-- sorry, if beta is actually one to start with, 973 00:38:56,240 --> 00:38:58,525 which is kind of like exponential discounting, 974 00:38:58,525 --> 00:39:00,400 then there's no problem because in the future 975 00:39:00,400 --> 00:39:02,680 she will just want the same as in the present. 976 00:39:02,680 --> 00:39:06,160 So then sort of by construction or by sort of assumption, 977 00:39:06,160 --> 00:39:09,550 then beta hat equals beta equals 1. 978 00:39:09,550 --> 00:39:12,190 And now if she changes her mind in the future 979 00:39:12,190 --> 00:39:14,140 about her preferences-- essentially 980 00:39:14,140 --> 00:39:18,220 if her beta is smaller than 1, then the question arises, 981 00:39:18,220 --> 00:39:19,090 what's the beta hat? 982 00:39:19,090 --> 00:39:20,080 Is it like one? 983 00:39:20,080 --> 00:39:22,540 That's the perfect sophistication case. 984 00:39:22,540 --> 00:39:25,600 Or is it beta, which is-- 985 00:39:25,600 --> 00:39:26,630 beta hat equals beta. 986 00:39:26,630 --> 00:39:28,540 That's the perfect sophistication case. 987 00:39:28,540 --> 00:39:32,580 Or if beta hat equals 1, that's the full naivete case. 988 00:39:32,580 --> 00:39:34,330 And then there's sort of cases in between, 989 00:39:34,330 --> 00:39:37,510 where she sort of-- she does understand that the beta is 990 00:39:37,510 --> 00:39:40,270 smaller than 1 in the future, but doesn't fully understand 991 00:39:40,270 --> 00:39:42,190 that and underestimates-- 992 00:39:42,190 --> 00:39:48,220 overestimates her beta, but at least only to some extent. 993 00:39:48,220 --> 00:39:49,701 Any other questions? 994 00:39:53,510 --> 00:39:54,010 OK. 995 00:39:54,010 --> 00:39:55,870 So now when we sort of look at now, 996 00:39:55,870 --> 00:39:58,640 what does a naive student actually do? 997 00:39:58,640 --> 00:40:02,080 So what does the naive student do at T equals zero? 998 00:40:02,080 --> 00:40:03,550 Well, from above, we sort of know 999 00:40:03,550 --> 00:40:07,720 that the self zero prefers to do the problem set at T equals 1. 1000 00:40:07,720 --> 00:40:10,120 So since she's naive, she thinks she's 1001 00:40:10,120 --> 00:40:11,950 going to follow through with those plans. 1002 00:40:11,950 --> 00:40:15,460 So she believes that she will actually do it at T equals 1. 1003 00:40:15,460 --> 00:40:17,717 So she doesn't do it at T equals 0. 1004 00:40:17,717 --> 00:40:19,300 Now, of course, what does she actually 1005 00:40:19,300 --> 00:40:21,430 do at period T equals 1? 1006 00:40:21,430 --> 00:40:22,640 We already said that. 1007 00:40:22,640 --> 00:40:24,640 She does actually not want to do the period in T 1008 00:40:24,640 --> 00:40:28,330 equals 1, the p set at period T equals 1. 1009 00:40:28,330 --> 00:40:31,360 So then hence the person sort of surprises herself and actually 1010 00:40:31,360 --> 00:40:33,580 ends up doing it in period two. 1011 00:40:33,580 --> 00:40:35,010 Right. 1012 00:40:35,010 --> 00:40:36,760 And so what's sort of the summary of that? 1013 00:40:36,760 --> 00:40:38,770 And this is a more general phenomenon. 1014 00:40:38,770 --> 00:40:41,890 If you read the paper for class today, 1015 00:40:41,890 --> 00:40:44,380 that's sort of much more general in that paper 1016 00:40:44,380 --> 00:40:47,660 and you could do that in a much more complicated way. 1017 00:40:47,660 --> 00:40:50,890 So essentially, there is the belief in period zero-- 1018 00:40:50,890 --> 00:40:52,840 she thinks, well, I can not do it right now. 1019 00:40:52,840 --> 00:40:53,830 I can delay it. 1020 00:40:53,830 --> 00:40:55,930 The cost of delaying it will not be that large 1021 00:40:55,930 --> 00:40:57,928 because I'm going to just do it in period one. 1022 00:40:57,928 --> 00:40:59,470 But it turns out the cost of delaying 1023 00:40:59,470 --> 00:41:01,330 is actually much larger, because in period one, 1024 00:41:01,330 --> 00:41:02,140 she doesn't do it. 1025 00:41:02,140 --> 00:41:03,497 She'll do it in period two. 1026 00:41:03,497 --> 00:41:05,080 Now, if you had more and more periods, 1027 00:41:05,080 --> 00:41:07,630 you could sort of have a whole cascade of doing it every day-- 1028 00:41:07,630 --> 00:41:09,672 every day you say you're going to do it tomorrow, 1029 00:41:09,672 --> 00:41:11,480 but you're never actually going to do it. 1030 00:41:11,480 --> 00:41:13,930 And so that can lead to actually very large costs 1031 00:41:13,930 --> 00:41:16,990 of procrastination, because you can essentially delay things 1032 00:41:16,990 --> 00:41:19,000 infinitely by every time thinking 1033 00:41:19,000 --> 00:41:20,870 you're going to do it in the future. 1034 00:41:20,870 --> 00:41:24,738 And so that kind of behavior might persist for a long time. 1035 00:41:24,738 --> 00:41:26,530 And it's sort of an example, as we call it, 1036 00:41:26,530 --> 00:41:27,995 like naive procrastination. 1037 00:41:27,995 --> 00:41:29,620 Every day you think-- or every week you 1038 00:41:29,620 --> 00:41:31,810 think you're going to do it tomorrow or next week and so 1039 00:41:31,810 --> 00:41:32,310 on. 1040 00:41:32,310 --> 00:41:34,280 But you're never going to actually do it. 1041 00:41:34,280 --> 00:41:37,873 And then that can lead to really large welfare costs, 1042 00:41:37,873 --> 00:41:40,290 because there's stuff that's actually not that hard to do. 1043 00:41:40,290 --> 00:41:41,410 But you just don't do it every day 1044 00:41:41,410 --> 00:41:43,240 and it gets more and more costly over time. 1045 00:41:43,240 --> 00:41:44,750 And you never end up doing it. 1046 00:41:44,750 --> 00:41:47,770 And it's way worse to do it in 50 periods from now. 1047 00:41:47,770 --> 00:41:49,270 You could have just done it early on 1048 00:41:49,270 --> 00:41:52,240 if you had understood that you were not 1049 00:41:52,240 --> 00:41:53,650 going to do it any time soon. 1050 00:41:56,353 --> 00:41:57,270 Any questions on that? 1051 00:41:57,270 --> 00:41:58,650 Yeah. 1052 00:41:58,650 --> 00:42:01,770 AUDIENCE: [INAUDIBLE] what's the interplay between learning 1053 00:42:01,770 --> 00:42:05,790 and sophistication [INAUDIBLE]? 1054 00:42:05,790 --> 00:42:07,190 What type of people [INAUDIBLE]. 1055 00:42:15,605 --> 00:42:16,480 FRANK SCHILBACH: Yes. 1056 00:42:16,480 --> 00:42:18,970 So one big question is, how is this even possible 1057 00:42:18,970 --> 00:42:19,720 that we have here? 1058 00:42:19,720 --> 00:42:22,270 Here's a person who keeps surprising herself 1059 00:42:22,270 --> 00:42:23,000 every period. 1060 00:42:23,000 --> 00:42:24,640 I mean, like, OK, actually, I thought I was going to do it. 1061 00:42:24,640 --> 00:42:26,557 But surprise, I'm actually not going to do it. 1062 00:42:26,557 --> 00:42:29,002 But I'll tomorrow I'll do it. 1063 00:42:29,002 --> 00:42:31,210 In a way, that's sort of surprising, in the sense of, 1064 00:42:31,210 --> 00:42:33,380 like, there are these behaviors-- like, for example, 1065 00:42:33,380 --> 00:42:35,047 when people think about-- when do people 1066 00:42:35,047 --> 00:42:36,970 go to bed, for example? 1067 00:42:36,970 --> 00:42:39,730 And people think people systematically 1068 00:42:39,730 --> 00:42:41,770 under invest in sleep. 1069 00:42:41,770 --> 00:42:43,570 And in some sense, it's an odd sort 1070 00:42:43,570 --> 00:42:47,027 of behavior in the sense of, you go to bed every night. 1071 00:42:47,027 --> 00:42:49,360 You kind of know that you're going to be tired tomorrow. 1072 00:42:49,360 --> 00:42:51,340 Yet, every day you sort of have this belief 1073 00:42:51,340 --> 00:42:53,545 that tomorrow you'll be just fine. 1074 00:42:53,545 --> 00:42:56,030 And from tomorrow, things will not change. 1075 00:42:56,030 --> 00:42:58,780 So there are some behaviors that people tend to not learn. 1076 00:42:58,780 --> 00:43:01,510 And we don't quite understand why that is. 1077 00:43:01,510 --> 00:43:04,720 In general, sort of like learning about beta hat 1078 00:43:04,720 --> 00:43:05,590 is sort of-- 1079 00:43:05,590 --> 00:43:08,200 kind of like at the frontier of research right now. 1080 00:43:08,200 --> 00:43:10,090 People have started estimating beta hat. 1081 00:43:10,090 --> 00:43:11,980 They have found people tend to be fairly 1082 00:43:11,980 --> 00:43:14,227 naive in various situations. 1083 00:43:14,227 --> 00:43:16,060 But then the question is, how is it possible 1084 00:43:16,060 --> 00:43:18,340 that people are so naive in situations where, like-- 1085 00:43:18,340 --> 00:43:19,660 we're going to the gym. 1086 00:43:19,660 --> 00:43:22,390 Every week you're going to have the choice of going to the gym. 1087 00:43:22,390 --> 00:43:24,430 You should have learned by now what 1088 00:43:24,430 --> 00:43:26,573 your type is, in some sense, what your beta is. 1089 00:43:26,573 --> 00:43:28,240 And you should have sort of then updated 1090 00:43:28,240 --> 00:43:31,510 your beliefs accordingly and sort of changed your decisions. 1091 00:43:31,510 --> 00:43:33,490 But somehow people have not done that. 1092 00:43:33,490 --> 00:43:36,098 And people tend to be naive in situations 1093 00:43:36,098 --> 00:43:38,140 where really they have lots of situations or lots 1094 00:43:38,140 --> 00:43:39,510 of occasions to learn. 1095 00:43:39,510 --> 00:43:41,260 Similarly, if you think about problem sets 1096 00:43:41,260 --> 00:43:42,790 that you're doing, in some ways you 1097 00:43:42,790 --> 00:43:46,180 know at the beginning of the semester kind of what's 1098 00:43:46,180 --> 00:43:47,690 going to happen, in some ways. 1099 00:43:47,690 --> 00:43:49,150 We should now. 1100 00:43:49,150 --> 00:43:51,490 Yet, people tend to be overoptimistic 1101 00:43:51,490 --> 00:43:52,510 in various cases. 1102 00:43:52,510 --> 00:43:54,340 I was an undergrad advisor for a while. 1103 00:43:54,340 --> 00:43:57,058 And I was sort of advising students on course choices. 1104 00:43:57,058 --> 00:43:58,600 Every semester it was the same thing. 1105 00:43:58,600 --> 00:44:01,570 I would say, like, four classes are grades, and so on. 1106 00:44:01,570 --> 00:44:03,850 Students would take, like, six or seven. 1107 00:44:03,850 --> 00:44:08,290 And then I would say, well, you know, that tends to not end up 1108 00:44:08,290 --> 00:44:08,980 very well. 1109 00:44:08,980 --> 00:44:10,230 Students are like, no, no, no. 1110 00:44:10,230 --> 00:44:12,270 This semester is different. 1111 00:44:12,270 --> 00:44:13,520 I'm going to work really hard. 1112 00:44:13,520 --> 00:44:14,320 It's going to be all great. 1113 00:44:14,320 --> 00:44:16,050 And then a month later, we would meet. 1114 00:44:16,050 --> 00:44:17,800 And then we would go down to five classes. 1115 00:44:17,800 --> 00:44:19,523 And I'd be like, well, maybe four classes are also fine. 1116 00:44:19,523 --> 00:44:20,650 They're like, no, no, no, no. 1117 00:44:20,650 --> 00:44:21,640 Five classes are great. 1118 00:44:21,640 --> 00:44:24,100 And then at the end, we end up at four or three. 1119 00:44:24,100 --> 00:44:27,340 So in a way, there are a bunch of behaviors 1120 00:44:27,340 --> 00:44:28,390 that repeat over time. 1121 00:44:28,390 --> 00:44:29,807 And in some sense, you would still 1122 00:44:29,807 --> 00:44:31,630 think, why are people not learning? 1123 00:44:31,630 --> 00:44:34,338 One explanation why people don't learn is in some sense, 1124 00:44:34,338 --> 00:44:35,380 they don't want to learn. 1125 00:44:35,380 --> 00:44:37,780 In the sense of like, I like to be a person. 1126 00:44:37,780 --> 00:44:39,520 I like to think of myself as a person who 1127 00:44:39,520 --> 00:44:42,940 is virtuous, who is hardworking, who is going to be really doing 1128 00:44:42,940 --> 00:44:44,600 great at classes and so on. 1129 00:44:44,600 --> 00:44:46,100 So I want to be that person. 1130 00:44:46,100 --> 00:44:48,610 I feel better about myself by wanting that. 1131 00:44:48,610 --> 00:44:51,280 And therefore, I might not learn as much as I could, 1132 00:44:51,280 --> 00:44:52,905 even though that's costly for me to do. 1133 00:44:52,905 --> 00:44:54,697 And we're going to talk a little about this 1134 00:44:54,697 --> 00:44:57,340 in terms of overconfidence and so on, where essentially people 1135 00:44:57,340 --> 00:44:58,750 have motivated beliefs and people 1136 00:44:58,750 --> 00:45:01,900 want to be the person with beta equals 1. 1137 00:45:01,900 --> 00:45:05,170 But in fact, they might not be. 1138 00:45:05,170 --> 00:45:06,340 OK. 1139 00:45:06,340 --> 00:45:08,680 So now what does the sophisticated student do? 1140 00:45:08,680 --> 00:45:11,020 We already discussed that. 1141 00:45:11,020 --> 00:45:12,868 Essentially, the person already knows. 1142 00:45:12,868 --> 00:45:14,410 The person has rational expectations. 1143 00:45:14,410 --> 00:45:17,020 So the person knows that if she doesn't do it in period zero, 1144 00:45:17,020 --> 00:45:18,645 she's not going to do it in period one, 1145 00:45:18,645 --> 00:45:21,160 because the period one self will change their minds 1146 00:45:21,160 --> 00:45:22,870 and not follow through with her plans. 1147 00:45:22,870 --> 00:45:24,730 So she's going to do it in period two. 1148 00:45:24,730 --> 00:45:26,335 Now anticipating that for a choice 1149 00:45:26,335 --> 00:45:28,210 is essentially, effectively, between doing it 1150 00:45:28,210 --> 00:45:30,700 right now versus in period two. 1151 00:45:30,700 --> 00:45:34,411 That's the effective choice that she has. 1152 00:45:34,411 --> 00:45:36,220 And we can now just make the choice. 1153 00:45:36,220 --> 00:45:38,980 Does she prefer doing it period zero versus period two? 1154 00:45:38,980 --> 00:45:41,860 Well, she prefers doing it in period zero, 1155 00:45:41,860 --> 00:45:43,930 because period two is too costly for her, 1156 00:45:43,930 --> 00:45:45,880 even if that's in the future. 1157 00:45:45,880 --> 00:45:48,400 And therefore, she does the problem set at period T 1158 00:45:48,400 --> 00:45:50,570 equals zero. 1159 00:45:50,570 --> 00:45:52,260 OK. 1160 00:45:52,260 --> 00:45:53,537 Any questions? 1161 00:45:57,140 --> 00:45:57,640 OK. 1162 00:45:57,640 --> 00:45:59,530 So what's the summary of that? 1163 00:45:59,530 --> 00:46:04,390 Well, the sophisticated student, for a case of investment goods, 1164 00:46:04,390 --> 00:46:07,370 the person knows that if she delays, she'll delay even more. 1165 00:46:07,370 --> 00:46:08,950 So once you start procrastinating, 1166 00:46:08,950 --> 00:46:10,120 you know this is going to unravel. 1167 00:46:10,120 --> 00:46:11,537 I'm never going to actually do it. 1168 00:46:11,537 --> 00:46:13,460 And anticipating that, she's going to say, 1169 00:46:13,460 --> 00:46:14,920 well, I'd rather do it right now, 1170 00:46:14,920 --> 00:46:16,280 because I know this is going to unravel 1171 00:46:16,280 --> 00:46:17,988 or this is going to derail in the future. 1172 00:46:17,988 --> 00:46:20,512 I'd rather not have to do it very late, late at night, 1173 00:46:20,512 --> 00:46:21,470 and so on and so forth. 1174 00:46:21,470 --> 00:46:24,290 So let me do it right now. 1175 00:46:24,290 --> 00:46:27,040 So that student in that specific case 1176 00:46:27,040 --> 00:46:28,930 does better than the naive student. 1177 00:46:28,930 --> 00:46:32,140 And for the case of investment goods, 1178 00:46:32,140 --> 00:46:34,090 sophisticated procrastination does not 1179 00:46:34,090 --> 00:46:35,410 cause large welfare costs. 1180 00:46:35,410 --> 00:46:38,530 It's not possible for a perfectly sophisticated person 1181 00:46:38,530 --> 00:46:42,430 to procrastinate things for a long time and sort of lead 1182 00:46:42,430 --> 00:46:45,250 to a very inefficient or costly outcomes, the reason 1183 00:46:45,250 --> 00:46:47,890 being if you know that's going to be costly in the future, 1184 00:46:47,890 --> 00:46:51,490 if it's really that bad, you would rather do it right now. 1185 00:46:51,490 --> 00:46:53,980 And so therefore, they cannot be-- 1186 00:46:53,980 --> 00:46:55,608 there can be some costs of delaying. 1187 00:46:55,608 --> 00:46:58,150 You might do it tomorrow-- you might do it a little bit later 1188 00:46:58,150 --> 00:46:59,920 than optimally. 1189 00:46:59,920 --> 00:47:02,800 But it cannot be that you procrastinated for a long time 1190 00:47:02,800 --> 00:47:06,110 and never do it and therefore get like really large costs 1191 00:47:06,110 --> 00:47:06,610 of that. 1192 00:47:11,600 --> 00:47:12,290 OK. 1193 00:47:12,290 --> 00:47:17,275 So one question that also came up in the online forum 1194 00:47:17,275 --> 00:47:18,650 that you also saw in the readings 1195 00:47:18,650 --> 00:47:20,670 that we're going to also talk a little bit about in the problem 1196 00:47:20,670 --> 00:47:22,980 set is, well, is sophistication always good? 1197 00:47:22,980 --> 00:47:26,170 And it's very intuitive to think that sophistication always 1198 00:47:26,170 --> 00:47:26,670 helps. 1199 00:47:26,670 --> 00:47:29,040 After all, knowing things better, 1200 00:47:29,040 --> 00:47:31,242 having correct beliefs about yourself, 1201 00:47:31,242 --> 00:47:32,700 that seems to be the correct thing. 1202 00:47:32,700 --> 00:47:34,980 So intuitively, it feels like that should only help, 1203 00:47:34,980 --> 00:47:36,070 should only make things better. 1204 00:47:36,070 --> 00:47:37,470 If I understood my biases better, 1205 00:47:37,470 --> 00:47:39,720 I should be doing better. 1206 00:47:39,720 --> 00:47:42,563 Now, it turns out that's true for investment goods. 1207 00:47:42,563 --> 00:47:43,980 So for investment goods, these are 1208 00:47:43,980 --> 00:47:46,313 the goods where you have to do something in the present, 1209 00:47:46,313 --> 00:47:48,660 but the costs-- sorry, the benefits are in the future. 1210 00:47:48,660 --> 00:47:50,280 For that, sophistication is always 1211 00:47:50,280 --> 00:47:52,320 better, or weakly better, the reason 1212 00:47:52,320 --> 00:47:54,660 being that, again, you can sort of understand 1213 00:47:54,660 --> 00:47:56,190 your future misbehavior. 1214 00:47:56,190 --> 00:47:58,740 And by that understanding of future misbehavior, 1215 00:47:58,740 --> 00:48:01,500 you can sort of avoid bad things happening in the future 1216 00:48:01,500 --> 00:48:03,820 by doing it right now and earlier. 1217 00:48:03,820 --> 00:48:06,960 So in that case, sophistication is always better. 1218 00:48:06,960 --> 00:48:08,520 Now, it turns out for leisure goods, 1219 00:48:08,520 --> 00:48:09,820 that's actually not the case. 1220 00:48:09,820 --> 00:48:11,640 So leisure goods, again, are goods 1221 00:48:11,640 --> 00:48:13,890 where you can enjoy something in the present 1222 00:48:13,890 --> 00:48:17,590 and there may be some costs delayed in the future. 1223 00:48:17,590 --> 00:48:22,740 And so let's look at-- and this is very close to now the paper 1224 00:48:22,740 --> 00:48:24,390 that you read. 1225 00:48:24,390 --> 00:48:25,770 Suppose there's a student who has 1226 00:48:25,770 --> 00:48:28,920 beta equals 1/2 and delta equals 1, as before. 1227 00:48:28,920 --> 00:48:32,730 Suppose the student can go to only one movie in exactly 1228 00:48:32,730 --> 00:48:33,810 one of the four periods. 1229 00:48:33,810 --> 00:48:35,643 There's only one movie ticket that she could 1230 00:48:35,643 --> 00:48:37,313 use in period 0, 1, 2, and 3. 1231 00:48:37,313 --> 00:48:39,480 By the way, Matthew Rabin is a huge Johnny Depp fan, 1232 00:48:39,480 --> 00:48:42,000 in case you haven't noticed. 1233 00:48:42,000 --> 00:48:44,520 So he uses Johnny Depp in various of his papers, 1234 00:48:44,520 --> 00:48:46,520 and so on. 1235 00:48:46,520 --> 00:48:50,100 He also had a huge Johnny Depp poster in his office. 1236 00:48:50,100 --> 00:48:52,590 So the instantaneous utilities are 1237 00:48:52,590 --> 00:48:57,880 such that they're 1, 3/4, 9/4, and 27/8, so they're 1238 00:48:57,880 --> 00:48:59,850 sort of increasing over time. 1239 00:48:59,850 --> 00:49:01,830 So if you-- so there's essentially 1240 00:49:01,830 --> 00:49:04,287 one day where it's like the most fun to watch the movie, 1241 00:49:04,287 --> 00:49:06,120 perhaps because you can go with your friends 1242 00:49:06,120 --> 00:49:08,610 or whatever-- like, it's a better day to do it. 1243 00:49:08,610 --> 00:49:11,160 Maybe you're a bit better rested or whatever it is. 1244 00:49:11,160 --> 00:49:13,028 But sort of delaying would be good. 1245 00:49:13,028 --> 00:49:15,570 Now, the problem, of course, is that the person is impatient. 1246 00:49:15,570 --> 00:49:17,620 The person might not want to wait because the person is 1247 00:49:17,620 --> 00:49:18,245 present biased. 1248 00:49:18,245 --> 00:49:19,958 He might want to watch it earlier. 1249 00:49:19,958 --> 00:49:21,750 The question now is, when does she actually 1250 00:49:21,750 --> 00:49:23,880 go watch that movie? 1251 00:49:23,880 --> 00:49:27,810 So now there's a way in which you can sort of write this down 1252 00:49:27,810 --> 00:49:32,340 in a very simple form, which is a table of discounted 1253 00:49:32,340 --> 00:49:32,850 utilities. 1254 00:49:32,850 --> 00:49:35,857 That's a simple tool for solving these kinds of problems. 1255 00:49:35,857 --> 00:49:37,440 This is supposed to come sequentially, 1256 00:49:37,440 --> 00:49:39,435 but it isn't today, it's on something that's 1257 00:49:39,435 --> 00:49:40,560 already filled out for you. 1258 00:49:40,560 --> 00:49:42,040 So that's easier for you. 1259 00:49:42,040 --> 00:49:44,550 So what I have filled out for you here 1260 00:49:44,550 --> 00:49:46,860 is the instantaneous utility. 1261 00:49:46,860 --> 00:49:49,050 So the first row here is essentially 1262 00:49:49,050 --> 00:49:51,450 to say, these are sort of the assumptions that we have. 1263 00:49:51,450 --> 00:49:53,033 You have the instantaneous utilities-- 1264 00:49:53,033 --> 00:49:56,022 U0, U1, UT, U3, and so on. 1265 00:49:56,022 --> 00:49:57,480 So this is essentially what you see 1266 00:49:57,480 --> 00:49:59,910 on the first row of this table. 1267 00:49:59,910 --> 00:50:02,700 Second then I filled out for you sort of the utilities 1268 00:50:02,700 --> 00:50:05,880 from the perspective of period zero, period one, and period 1269 00:50:05,880 --> 00:50:07,230 two. 1270 00:50:07,230 --> 00:50:08,880 So from the perspective of T equals 1271 00:50:08,880 --> 00:50:12,070 0, the first period T equals 0 equals just the same. 1272 00:50:12,070 --> 00:50:14,585 That's just 1, because she puts weight one on that. 1273 00:50:14,585 --> 00:50:15,960 But then everything in the future 1274 00:50:15,960 --> 00:50:20,460 is discounted by 1/2, because the beta is 1/2. 1275 00:50:20,460 --> 00:50:23,120 Yes? 1276 00:50:23,120 --> 00:50:25,040 And then from the perspective of T 1277 00:50:25,040 --> 00:50:27,652 equals 1, of course T equals 0 is sort of irrelevant 1278 00:50:27,652 --> 00:50:28,860 because that was in the past. 1279 00:50:28,860 --> 00:50:30,440 By definition, we only care about stuff 1280 00:50:30,440 --> 00:50:32,023 that happens in the future, because we 1281 00:50:32,023 --> 00:50:32,965 can't change the past. 1282 00:50:32,965 --> 00:50:34,340 Notice that's also an assumption, 1283 00:50:34,340 --> 00:50:36,590 but it's a common assumption made in economics. 1284 00:50:36,590 --> 00:50:39,860 So there 3/2 now is in the present. 1285 00:50:39,860 --> 00:50:41,180 So that gets weight 1. 1286 00:50:41,180 --> 00:50:43,560 And everything that's in the future gets weight 1/2. 1287 00:50:43,560 --> 00:50:47,180 So you have 9/8 and 27/16. 1288 00:50:47,180 --> 00:50:49,670 And now for period 2 again-- 1289 00:50:49,670 --> 00:50:52,310 period now 0 and 1 are in the past. 1290 00:50:52,310 --> 00:50:54,260 Now she cares about the present [INAUDIBLE] 1291 00:50:54,260 --> 00:50:56,480 T equals 2 with the weight of 1. 1292 00:50:56,480 --> 00:50:57,470 That's 9/4. 1293 00:50:57,470 --> 00:51:00,110 And now T equals 3 is in the future. 1294 00:51:00,110 --> 00:51:02,200 That's discounted by 1/2. 1295 00:51:02,200 --> 00:51:02,960 OK. 1296 00:51:02,960 --> 00:51:04,520 And now what I also have done, I've 1297 00:51:04,520 --> 00:51:07,610 written down the ranking of these different periods 1298 00:51:07,610 --> 00:51:09,050 from the perspective of-- 1299 00:51:09,050 --> 00:51:11,965 from the sort of just looking at the instantaneous utilities, 1300 00:51:11,965 --> 00:51:13,340 three's better than two is better 1301 00:51:13,340 --> 00:51:15,290 than one is better than zero. 1302 00:51:15,290 --> 00:51:18,770 From the perspective of T equals 0, you prefer three over two 1303 00:51:18,770 --> 00:51:20,180 over zero over one. 1304 00:51:20,180 --> 00:51:22,700 From T equals 1, you prefer three over one over two. 1305 00:51:22,700 --> 00:51:24,590 And from the perspective of T equals 2, 1306 00:51:24,590 --> 00:51:27,080 you prefer two over three. 1307 00:51:27,080 --> 00:51:29,696 Does this all make sense what I've written down here? 1308 00:51:29,696 --> 00:51:31,330 I'll let you look at this for a second. 1309 00:51:36,910 --> 00:51:37,410 OK. 1310 00:51:37,410 --> 00:51:40,320 So what does the naive person do with beta hat equals 1? 1311 00:51:48,640 --> 00:51:49,140 Yes. 1312 00:51:52,600 --> 00:51:53,950 AUDIENCE: Oh, wait, hold on. 1313 00:51:53,950 --> 00:51:57,108 FRANK SCHILBACH: We can do this step by step. 1314 00:51:57,108 --> 00:51:58,960 AUDIENCE: OK, so [INAUDIBLE] zero. 1315 00:51:58,960 --> 00:52:00,900 And then from the perspective of T equals 0, 1316 00:52:00,900 --> 00:52:04,980 you would most prefer to do something at time three. 1317 00:52:04,980 --> 00:52:06,480 FRANK SCHILBACH: Yes. 1318 00:52:06,480 --> 00:52:08,280 AUDIENCE: So I guess that means that you 1319 00:52:08,280 --> 00:52:11,164 don't do it in period one and then move on to T equals 1. 1320 00:52:11,164 --> 00:52:13,164 And then again you want to do it in period three 1321 00:52:13,164 --> 00:52:15,840 so you don't do it in period one here. 1322 00:52:15,840 --> 00:52:18,400 And then you end up at T equals 2. 1323 00:52:18,400 --> 00:52:21,205 And then you'd rather do it in period two than period three, 1324 00:52:21,205 --> 00:52:22,330 so you do it in period two. 1325 00:52:22,330 --> 00:52:22,650 FRANK SCHILBACH: Yes. 1326 00:52:22,650 --> 00:52:23,190 Correct. 1327 00:52:23,190 --> 00:52:25,770 So let me do that in slow motion. 1328 00:52:25,770 --> 00:52:29,600 So in period T, she makes some plans. 1329 00:52:29,600 --> 00:52:32,640 You wrote down what is her preferred plan in period 1330 00:52:32,640 --> 00:52:33,810 T equals zero. 1331 00:52:33,810 --> 00:52:35,730 We have our ranking at the very right 1332 00:52:35,730 --> 00:52:37,980 in the right-- in the last column on the right. 1333 00:52:37,980 --> 00:52:39,720 She prefers to do it in period three. 1334 00:52:39,720 --> 00:52:42,670 She thinks that she's going to follow through with her plans. 1335 00:52:42,670 --> 00:52:44,580 So she's not going to do it in period 0 1336 00:52:44,580 --> 00:52:46,590 because she thinks she prefers period three. 1337 00:52:46,590 --> 00:52:48,390 So let's just wait. 1338 00:52:48,390 --> 00:52:55,800 So she doesn't go in in periods T equals 0. 1339 00:52:55,800 --> 00:52:58,120 And period T equals 1 is the same thing. 1340 00:52:58,120 --> 00:53:00,180 And now she essentially says, well, she 1341 00:53:00,180 --> 00:53:01,980 prefers three over one over two. 1342 00:53:01,980 --> 00:53:03,490 It's better to do it in period three 1343 00:53:03,490 --> 00:53:05,970 so let's just wait until period three. 1344 00:53:05,970 --> 00:53:07,710 Now, of course, period two comes. 1345 00:53:07,710 --> 00:53:10,680 Once period two comes, it turns out 1346 00:53:10,680 --> 00:53:14,160 we cooked up the number such as like prefers a period 1347 00:53:14,160 --> 00:53:15,450 two over period three. 1348 00:53:15,450 --> 00:53:18,300 So she surprises herself by actually watching the movie 1349 00:53:18,300 --> 00:53:20,440 in period two. 1350 00:53:20,440 --> 00:53:22,950 OK. 1351 00:53:22,950 --> 00:53:24,242 Any questions? 1352 00:53:27,140 --> 00:53:27,640 OK. 1353 00:53:27,640 --> 00:53:30,160 So now instead, what does a sophisticated student do? 1354 00:53:32,770 --> 00:53:36,220 So this was the perfectly naive student doing it and watching 1355 00:53:36,220 --> 00:53:37,540 the movie in period two. 1356 00:53:37,540 --> 00:53:39,740 No, if you're sophisticated, what do you do? 1357 00:53:39,740 --> 00:53:40,928 Yes. 1358 00:53:40,928 --> 00:53:43,060 AUDIENCE: She starts thinking that if she waits, 1359 00:53:43,060 --> 00:53:47,235 [INAUDIBLE] equals 2, she's going to at two-- 1360 00:53:47,235 --> 00:53:48,714 wait. 1361 00:53:48,714 --> 00:53:50,193 FRANK SCHILBACH: Correct. 1362 00:53:50,193 --> 00:53:52,668 AUDIENCE: So then she knows that at T equals 1, 1363 00:53:52,668 --> 00:53:53,960 she's not going wait until two. 1364 00:53:53,960 --> 00:53:54,640 She's going to-- 1365 00:54:03,647 --> 00:54:04,730 FRANK SCHILBACH: Any help? 1366 00:54:04,730 --> 00:54:05,230 Yes, OK. 1367 00:54:11,340 --> 00:54:16,970 AUDIENCE: So first student, at T equals 2, she would go. 1368 00:54:16,970 --> 00:54:24,190 So if she were at T equals 1, she knows that if she waits, 1369 00:54:24,190 --> 00:54:30,160 then she would go at two instead of three. 1370 00:54:30,160 --> 00:54:33,190 But she likes one. 1371 00:54:33,190 --> 00:54:35,860 So her choice is not between one and three, 1372 00:54:35,860 --> 00:54:37,930 but between one and two. 1373 00:54:37,930 --> 00:54:42,250 So if she were at time period one, then she would go-- 1374 00:54:42,250 --> 00:54:43,720 choose to go at one. 1375 00:54:43,720 --> 00:54:48,250 And then if she's at time T equals 0, 1376 00:54:48,250 --> 00:54:53,810 her choice is going to be between zero and one, not zero 1377 00:54:53,810 --> 00:54:54,310 and three. 1378 00:54:54,310 --> 00:54:58,840 So that if she were at time period zero, 1379 00:54:58,840 --> 00:55:01,248 she would just end up going at time period zero. 1380 00:55:01,248 --> 00:55:02,290 FRANK SCHILBACH: Correct. 1381 00:55:02,290 --> 00:55:05,930 So let me also say that a little slower again. 1382 00:55:05,930 --> 00:55:09,130 So if we look at perfectly naive people, 1383 00:55:09,130 --> 00:55:12,520 they're going to start from the beginning and go forwards. 1384 00:55:12,520 --> 00:55:15,400 We have a naive person who has plans going forward. 1385 00:55:15,400 --> 00:55:17,620 And then we just look at how does this plan evolve? 1386 00:55:17,620 --> 00:55:20,920 So you start at how does this person person 1387 00:55:20,920 --> 00:55:22,910 decide at period T equals zero, thinking 1388 00:55:22,910 --> 00:55:24,160 she's going to follow through? 1389 00:55:24,160 --> 00:55:25,750 Then we go to period one thinking 1390 00:55:25,750 --> 00:55:26,740 she's going to follow through. 1391 00:55:26,740 --> 00:55:28,060 Then we go to period two thinking 1392 00:55:28,060 --> 00:55:29,310 she's going to follow through. 1393 00:55:29,310 --> 00:55:31,150 And that's how we sort of solve the problem. 1394 00:55:31,150 --> 00:55:34,057 Now, for the sophisticated person, 1395 00:55:34,057 --> 00:55:35,390 you would do things differently. 1396 00:55:35,390 --> 00:55:37,682 We essentially do this backwards deduction, essentially 1397 00:55:37,682 --> 00:55:39,610 to say let's start at the very end. 1398 00:55:39,610 --> 00:55:41,980 The reason that we can use backwards induction 1399 00:55:41,980 --> 00:55:44,260 is because people have rational expectations. 1400 00:55:44,260 --> 00:55:46,410 The person knows exactly what she's going to do, 1401 00:55:46,410 --> 00:55:47,680 which is she's going to start from the end 1402 00:55:47,680 --> 00:55:49,472 and say, OK, how is this going to play out? 1403 00:55:49,472 --> 00:55:51,100 What am I going to do in the end? 1404 00:55:51,100 --> 00:55:54,080 And sort of anticipating that perfectly, we're 1405 00:55:54,080 --> 00:55:56,510 going to then solve backwards. 1406 00:55:56,510 --> 00:56:00,503 OK, so as you just said, in period two, 1407 00:56:00,503 --> 00:56:02,920 we know that she's going to go, if she hasn't, because she 1408 00:56:02,920 --> 00:56:04,125 prefers two over three. 1409 00:56:04,125 --> 00:56:05,500 That's the last row that we have. 1410 00:56:05,500 --> 00:56:09,970 She likes two better than three once she comes to period two. 1411 00:56:09,970 --> 00:56:12,350 Now, in period T equals 1, she knows 1412 00:56:12,350 --> 00:56:14,350 that she's not going to wait until period three. 1413 00:56:14,350 --> 00:56:16,270 So period three is actually not an option for her. 1414 00:56:16,270 --> 00:56:17,500 She knows that's not credible. 1415 00:56:17,500 --> 00:56:18,920 She's not going to follow through. 1416 00:56:18,920 --> 00:56:21,370 So then it's just a choice between one and two. 1417 00:56:21,370 --> 00:56:22,780 She prefers one over two. 1418 00:56:22,780 --> 00:56:25,660 So she's going to-- 1419 00:56:25,660 --> 00:56:27,220 going in period one. 1420 00:56:27,220 --> 00:56:29,470 Now then, in period one two equals 0, 1421 00:56:29,470 --> 00:56:31,090 now we know-- she realized that she 1422 00:56:31,090 --> 00:56:32,945 won't wait until two or three. 1423 00:56:32,945 --> 00:56:34,570 Two or three are not an option for her. 1424 00:56:34,570 --> 00:56:37,510 She would actually prefer both two and three. 1425 00:56:37,510 --> 00:56:39,910 But that's not possible because her future self will not 1426 00:56:39,910 --> 00:56:41,440 stick to her choice. 1427 00:56:41,440 --> 00:56:45,610 So then the choice really just becomes between zero and one, 1428 00:56:45,610 --> 00:56:48,312 and she prefers zero over one. 1429 00:56:48,312 --> 00:56:50,020 Now, essentially, she goes to that movie, 1430 00:56:50,020 --> 00:56:51,940 and gets a trilogy of one. 1431 00:56:51,940 --> 00:56:54,568 But actually, she would prefer any of these other outcomes-- 1432 00:56:54,568 --> 00:56:56,110 actually, any of her other self would 1433 00:56:56,110 --> 00:56:57,550 prefer her to not do that. 1434 00:56:57,550 --> 00:57:00,580 But she actually picks period one. 1435 00:57:00,580 --> 00:57:02,290 So that's an example. 1436 00:57:02,290 --> 00:57:03,820 And there's several examples of that 1437 00:57:03,820 --> 00:57:05,910 where sophistication can hurt. 1438 00:57:05,910 --> 00:57:08,800 Now, why is sophistication hurting here? 1439 00:57:08,800 --> 00:57:11,470 What's the key part, and why is it 1440 00:57:11,470 --> 00:57:15,250 worse for the student to be sophisticated? 1441 00:57:15,250 --> 00:57:16,750 In some sense, if you think about it 1442 00:57:16,750 --> 00:57:20,560 from the perspective of T equals 0, 1443 00:57:20,560 --> 00:57:23,830 she would prefer a three over two over zero over one. 1444 00:57:23,830 --> 00:57:27,700 Or overall, if you look at the instantaneous utilities, 1445 00:57:27,700 --> 00:57:29,450 period two is better. 1446 00:57:29,450 --> 00:57:31,220 So from the perspective of T equals 0, 1447 00:57:31,220 --> 00:57:33,400 period two is better than period zero. 1448 00:57:33,400 --> 00:57:35,630 Yet, he ends up going in period zero. 1449 00:57:35,630 --> 00:57:37,480 So a sophisticated person actually 1450 00:57:37,480 --> 00:57:39,340 would be better off if she were naive. 1451 00:57:39,340 --> 00:57:41,470 If she could sort of commit to something and say, 1452 00:57:41,470 --> 00:57:45,250 I would prefer to go in period two, if she could say-- 1453 00:57:45,250 --> 00:57:47,200 if I only could be naive, that would sort of 1454 00:57:47,200 --> 00:57:49,060 help her to actually do it in period two. 1455 00:57:49,060 --> 00:57:52,330 Of course, you can't sort of choose that. 1456 00:57:52,330 --> 00:57:55,930 But here she's worse off from being sophisticated. 1457 00:57:55,930 --> 00:57:57,040 But what's going on here? 1458 00:57:57,040 --> 00:57:58,532 Like, why is that happening? 1459 00:58:04,810 --> 00:58:05,620 Yes. 1460 00:58:05,620 --> 00:58:08,650 AUDIENCE: So she almost mistrusts her future self 1461 00:58:08,650 --> 00:58:11,980 and so preempts that by taking the previous decision. 1462 00:58:11,980 --> 00:58:13,600 But then also preempting that, she 1463 00:58:13,600 --> 00:58:15,400 would preempt her future self. 1464 00:58:15,400 --> 00:58:18,250 She would take the previous decision again. 1465 00:58:18,250 --> 00:58:21,475 And so that makes it so that she does the action 1466 00:58:21,475 --> 00:58:24,130 at the very start instead. 1467 00:58:24,130 --> 00:58:27,010 For us, the naive person always blunders through 1468 00:58:27,010 --> 00:58:29,530 and manages to take the more-- 1469 00:58:29,530 --> 00:58:31,982 the action with the higher utility. 1470 00:58:31,982 --> 00:58:32,940 FRANK SCHILBACH: Right. 1471 00:58:32,940 --> 00:58:38,800 So in some ways, the problem is set up in a way that, in a way, 1472 00:58:38,800 --> 00:58:41,380 realistic pessimism-- the sophisticated person 1473 00:58:41,380 --> 00:58:43,300 is, like, realistic in their pessimism. 1474 00:58:43,300 --> 00:58:46,570 She knows, essentially, that in the future 1475 00:58:46,570 --> 00:58:48,290 she's not going to behave. 1476 00:58:48,290 --> 00:58:50,180 So she would love to wait. 1477 00:58:50,180 --> 00:58:51,770 But what she needs to do to wait, 1478 00:58:51,770 --> 00:58:54,550 she needs to have a sufficiently high benefit of waiting. 1479 00:58:54,550 --> 00:58:56,440 Now, how high is the benefit of waiting? 1480 00:58:56,440 --> 00:58:58,900 It depends on what your future self is going to do. 1481 00:58:58,900 --> 00:59:01,840 If you only wait a little bit, the person will say, 1482 00:59:01,840 --> 00:59:03,970 if I go-- if the choice is between zero and one, 1483 00:59:03,970 --> 00:59:04,928 it's not worth waiting. 1484 00:59:04,928 --> 00:59:06,620 I might as well go right now. 1485 00:59:06,620 --> 00:59:09,550 So if I can wrongly sort of have the illusion to myself 1486 00:59:09,550 --> 00:59:12,340 that I say, well, I'm going to not 1487 00:59:12,340 --> 00:59:16,750 go in one, or in two, for that matter, then in some sense 1488 00:59:16,750 --> 00:59:19,600 the benefits of waiting-- the perceived benefits of waiting 1489 00:59:19,600 --> 00:59:21,470 are higher than they actually are. 1490 00:59:21,470 --> 00:59:24,820 And in this case, it mitigates the self-control problem 1491 00:59:24,820 --> 00:59:26,630 or the present bias. 1492 00:59:26,630 --> 00:59:28,630 The present bias person wants to do it right now 1493 00:59:28,630 --> 00:59:32,140 and needs a sufficiently high reward for waiting. 1494 00:59:32,140 --> 00:59:34,270 So if you can sort of perceive-- 1495 00:59:34,270 --> 00:59:36,100 if you can sort of deceive yourself 1496 00:59:36,100 --> 00:59:38,450 into thinking that the rewards of waiting are high, 1497 00:59:38,450 --> 00:59:39,700 you're going to actually wait. 1498 00:59:39,700 --> 00:59:42,760 And that's good for you in this case. 1499 00:59:42,760 --> 00:59:45,023 If, instead, you're realistic about your future self, 1500 00:59:45,023 --> 00:59:47,440 you know that waiting is not really helping you very much. 1501 00:59:47,440 --> 00:59:50,050 You know that essentially, if you wait for one period, 1502 00:59:50,050 --> 00:59:52,300 you're going to go and go in the next period, anyway. 1503 00:59:52,300 --> 00:59:53,300 So then the reward-- 1504 00:59:53,300 --> 00:59:55,800 and that's in part because the numbers are set up that way-- 1505 00:59:55,800 --> 00:59:58,807 but that's now essentially sort of telling you, 1506 00:59:58,807 --> 01:00:00,640 well, waiting is not really doing very much, 1507 01:00:00,640 --> 01:00:03,100 because your future self is also misbehaving. 1508 01:00:03,100 --> 01:00:06,190 It sort of makes it impossible to actually wait 1509 01:00:06,190 --> 01:00:08,525 all the way until the very end. 1510 01:00:08,525 --> 01:00:10,900 And therefore, it sort of makes the self-control problem, 1511 01:00:10,900 --> 01:00:12,850 the present bias, worse, because now it's 1512 01:00:12,850 --> 01:00:16,270 like it's not worth-- why even bother to wait a little bit, 1513 01:00:16,270 --> 01:00:18,280 because that's literally not worth doing? 1514 01:00:18,280 --> 01:00:21,150 Really what you would need is wait all the way through. 1515 01:00:21,150 --> 01:00:22,153 Yeah. 1516 01:00:22,153 --> 01:00:23,986 AUDIENCE: So I think this is related to what 1517 01:00:23,986 --> 01:00:25,470 I was trying to ask before. 1518 01:00:25,470 --> 01:00:28,676 If you're sophisticated, you know you have [INAUDIBLE].. 1519 01:00:28,676 --> 01:00:30,100 If you are in period zero, you'll 1520 01:00:30,100 --> 01:00:33,550 know that on the next period, you're [INAUDIBLE].. 1521 01:00:40,070 --> 01:00:43,090 So why would you prefer to experience [INAUDIBLE] one now 1522 01:00:43,090 --> 01:00:44,920 [INAUDIBLE] experience [INAUDIBLE].. 1523 01:00:48,892 --> 01:00:51,820 FRANK SCHILBACH: No, but I think it's-- 1524 01:00:51,820 --> 01:00:54,902 in a way, there is a preference over-- 1525 01:00:54,902 --> 01:00:56,860 and something like that's, again, an assumption 1526 01:00:56,860 --> 01:00:58,060 how people behave. 1527 01:00:58,060 --> 01:00:59,930 People care a lot about the present. 1528 01:00:59,930 --> 01:01:01,160 And that's sort of like, in some sense, 1529 01:01:01,160 --> 01:01:03,243 in a bunch of experiments and so on, people really 1530 01:01:03,243 --> 01:01:05,560 want stuff right now, even if they 1531 01:01:05,560 --> 01:01:08,790 know that they will prefer stuff in two days from now 1532 01:01:08,790 --> 01:01:10,300 or three days from now and so on. 1533 01:01:10,300 --> 01:01:14,050 You just-- you are impatient right now. 1534 01:01:14,050 --> 01:01:16,780 And that's what the utility function is like. 1535 01:01:16,780 --> 01:01:19,610 And so you put less weight on stuff that's in the future. 1536 01:01:19,610 --> 01:01:22,858 Now, if you sort think about your future preferences, 1537 01:01:22,858 --> 01:01:25,150 there's a question on-- that's a philosophical question 1538 01:01:25,150 --> 01:01:27,067 in some ways-- how do you think about the fact 1539 01:01:27,067 --> 01:01:29,260 that your future self wants something different? 1540 01:01:29,260 --> 01:01:32,860 That is to say, for example, if I want to exercise a lot 1541 01:01:32,860 --> 01:01:36,640 and I also like to sit on the couch and watch TV a lot, 1542 01:01:36,640 --> 01:01:40,270 now my current self wants to exercise a lot in the future. 1543 01:01:40,270 --> 01:01:42,700 My future self wants to-- and I know that-- 1544 01:01:42,700 --> 01:01:44,290 wants to sit on the couch. 1545 01:01:44,290 --> 01:01:46,443 Now the question is which-- and when 1546 01:01:46,443 --> 01:01:47,860 you think about welfare and so on, 1547 01:01:47,860 --> 01:01:49,573 which self should we respect? 1548 01:01:49,573 --> 01:01:51,490 And one assumption-- and this is an assumption 1549 01:01:51,490 --> 01:01:55,270 that's built in here-- is to say my current self has 1550 01:01:55,270 --> 01:01:56,652 certain plans for the future. 1551 01:01:56,652 --> 01:01:58,360 And those preferences are the preferences 1552 01:01:58,360 --> 01:02:00,250 that I'm using to maximize. 1553 01:02:00,250 --> 01:02:02,650 I know that my future self wants other things. 1554 01:02:02,650 --> 01:02:05,650 But in some sense, I'm assuming I know that I know better. 1555 01:02:05,650 --> 01:02:08,590 This is the utility function that counts is the current one, 1556 01:02:08,590 --> 01:02:10,030 not the future one. 1557 01:02:10,030 --> 01:02:12,070 And so then I respect that one and I'm 1558 01:02:12,070 --> 01:02:15,040 trying to maximize that sort of subject 1559 01:02:15,040 --> 01:02:18,520 to my future preferences being different. 1560 01:02:18,520 --> 01:02:20,187 But in some sense, you're exactly right. 1561 01:02:20,187 --> 01:02:21,645 If you think about, like, should we 1562 01:02:21,645 --> 01:02:23,230 tax potato chips, for example-- 1563 01:02:23,230 --> 01:02:24,880 talk about welfare and so on-- 1564 01:02:24,880 --> 01:02:26,330 should we tax potato chips? 1565 01:02:26,330 --> 01:02:28,040 You could say, well, on the one hand, 1566 01:02:28,040 --> 01:02:30,077 I might say I would like to tax potato chips, 1567 01:02:30,077 --> 01:02:31,660 because I know in the future I'm going 1568 01:02:31,660 --> 01:02:33,100 to eat too many potato chips. 1569 01:02:33,100 --> 01:02:34,630 That's good for me. 1570 01:02:34,630 --> 01:02:36,100 But there's a future self-- 1571 01:02:36,100 --> 01:02:38,590 actually, myself-- who would love to eat potato chips. 1572 01:02:38,590 --> 01:02:40,900 That self would be really unhappy. 1573 01:02:40,900 --> 01:02:43,420 Now you get very tricky questions of welfare 1574 01:02:43,420 --> 01:02:45,130 and a sense of saying, like, well, 1575 01:02:45,130 --> 01:02:46,870 who are we to say that the current self 1576 01:02:46,870 --> 01:02:49,420 is different or should get priority over the future self? 1577 01:02:49,420 --> 01:02:51,820 The future self will really be unhappy. 1578 01:02:51,820 --> 01:02:54,250 So there are different views on this. 1579 01:02:54,250 --> 01:02:56,950 Some people, including Matthew Rabin including David Laibson 1580 01:02:56,950 --> 01:02:58,367 and so on, would sort of say, what 1581 01:02:58,367 --> 01:03:00,670 counts is the current self, or a self 1582 01:03:00,670 --> 01:03:02,077 that chooses for the future. 1583 01:03:02,077 --> 01:03:03,910 That's sort of the virtue of self and so on. 1584 01:03:03,910 --> 01:03:06,340 We should use that for welfare evaluation. 1585 01:03:06,340 --> 01:03:07,542 That's an assumption. 1586 01:03:07,542 --> 01:03:10,000 There's other people who would argue that no, like, there's 1587 01:03:10,000 --> 01:03:11,740 all sorts of self who want different things. 1588 01:03:11,740 --> 01:03:13,615 So if you think about, is it good to increase 1589 01:03:13,615 --> 01:03:15,400 taxes for potato chips? 1590 01:03:15,400 --> 01:03:17,530 Maybe, because some selves are better off 1591 01:03:17,530 --> 01:03:18,942 and some selves are worse off. 1592 01:03:18,942 --> 01:03:21,400 And how do we ever aggregate across those different selves? 1593 01:03:21,400 --> 01:03:23,210 So you get very tricky questions. 1594 01:03:23,210 --> 01:03:25,210 But here for our purposes what we're going to do 1595 01:03:25,210 --> 01:03:27,550 is we're going to say the current self is essentially 1596 01:03:27,550 --> 01:03:30,820 disrespecting future utility functions 1597 01:03:30,820 --> 01:03:33,580 and preferences in the own maximization 1598 01:03:33,580 --> 01:03:34,960 and the maximization problem. 1599 01:03:34,960 --> 01:03:37,450 That is to say, I have a utility function right now, 1600 01:03:37,450 --> 01:03:40,270 and sort of discounting function that tells me 1601 01:03:40,270 --> 01:03:44,260 how I want to aggregate my future utility over time. 1602 01:03:44,260 --> 01:03:45,920 That is what I want. 1603 01:03:45,920 --> 01:03:49,000 And then I have essentially like a-- sort of like constraints 1604 01:03:49,000 --> 01:03:51,460 which are coming sort of in the-- when I think about sort 1605 01:03:51,460 --> 01:03:54,088 of like when you write down a utility maximization problem, 1606 01:03:54,088 --> 01:03:56,380 there's an objective function, which is my maximization 1607 01:03:56,380 --> 01:03:56,880 problem. 1608 01:03:56,880 --> 01:03:59,110 That's the utility function that I want right now. 1609 01:03:59,110 --> 01:04:01,180 And then there's constraints in your maximization 1610 01:04:01,180 --> 01:04:03,220 problem, which are in the future, 1611 01:04:03,220 --> 01:04:04,760 my preferences will change. 1612 01:04:04,760 --> 01:04:06,430 So some options might not be feasible 1613 01:04:06,430 --> 01:04:09,122 because of these preference reversals, and so on. 1614 01:04:09,122 --> 01:04:10,080 But that's not to say-- 1615 01:04:10,080 --> 01:04:12,610 I'm respecting your future preferences to the extent 1616 01:04:12,610 --> 01:04:15,070 that I need to have feasible plans. 1617 01:04:15,070 --> 01:04:16,960 I'm not respecting them in the sense of, 1618 01:04:16,960 --> 01:04:18,070 like, I know right now. 1619 01:04:18,070 --> 01:04:20,691 I know better what's good for myself. 1620 01:04:20,691 --> 01:04:22,060 Did that answer your question? 1621 01:04:22,060 --> 01:04:23,840 OK. 1622 01:04:23,840 --> 01:04:25,372 Any other-- yeah. 1623 01:04:25,372 --> 01:04:26,830 AUDIENCE: [INAUDIBLE]. 1624 01:04:35,480 --> 01:04:37,730 FRANK SCHILBACH: Sorry, what exactly is the question? 1625 01:04:37,730 --> 01:04:42,720 AUDIENCE: So does that mean that if you go see the movie in T 1626 01:04:42,720 --> 01:04:47,580 equals 2, do you evaluate that as-- sorry, [INAUDIBLE].. 1627 01:04:47,580 --> 01:04:50,050 FRANK SCHILBACH: So from the perspective of period T equals 1628 01:04:50,050 --> 01:04:52,870 2, you evaluate it with 9/4. 1629 01:04:52,870 --> 01:04:54,970 From the perspective of period T equals 1630 01:04:54,970 --> 01:04:57,560 1 or T equals 0, that is in the future. 1631 01:04:57,560 --> 01:05:02,230 So you multiply the 9/4 times 1/2, 1632 01:05:02,230 --> 01:05:04,167 which is the beta because it's in the future. 1633 01:05:04,167 --> 01:05:06,125 AUDIENCE: So then when you say the student does 1634 01:05:06,125 --> 01:05:07,320 better [INAUDIBLE]. 1635 01:05:12,545 --> 01:05:14,920 FRANK SCHILBACH: I'm using sort of from that perspective. 1636 01:05:14,920 --> 01:05:17,553 So in some sense, that's a bit of a question philosophically, 1637 01:05:17,553 --> 01:05:20,220 what's better and worse, because you have different perspective. 1638 01:05:20,220 --> 01:05:22,770 You can take from the perspective of T equals 0-- 1639 01:05:22,770 --> 01:05:24,750 for example, a sophisticated person 1640 01:05:24,750 --> 01:05:28,615 would much prefer period two over period zero, one 1641 01:05:28,615 --> 01:05:30,210 over zero. 1642 01:05:30,210 --> 01:05:33,120 So I just showed you that the sophisticated person 1643 01:05:33,120 --> 01:05:35,340 goes in period zero. 1644 01:05:35,340 --> 01:05:39,340 But in fact, the person would prefer a three and two. 1645 01:05:39,340 --> 01:05:41,110 So the outcome of the naive person 1646 01:05:41,110 --> 01:05:43,030 would be better for the sophisticated person 1647 01:05:43,030 --> 01:05:44,830 from the perspective of T equals 0. 1648 01:05:48,613 --> 01:05:50,280 And so then there's a bit of a question. 1649 01:05:50,280 --> 01:05:52,200 From the perspective of t equals 2, 1650 01:05:52,200 --> 01:05:54,333 if you had gone already in the previous period, 1651 01:05:54,333 --> 01:05:56,250 probably prefer if you hadn't gone previously. 1652 01:05:56,250 --> 01:05:58,740 But that's a bit silly, in some sense. 1653 01:05:58,740 --> 01:06:01,230 But you can essentially-- you can write down for each self, 1654 01:06:01,230 --> 01:06:02,880 what would each self prefer? 1655 01:06:02,880 --> 01:06:05,760 And I think as it is in this example, it's essentially, 1656 01:06:05,760 --> 01:06:08,400 the sophisticated essentially does worse for all selves 1657 01:06:08,400 --> 01:06:10,980 compared to a-- weakly worse compared to the naive person. 1658 01:06:14,640 --> 01:06:18,250 OK, but happy to talk after. 1659 01:06:18,250 --> 01:06:19,830 OK, so I think we have all of that. 1660 01:06:19,830 --> 01:06:22,540 Sophistication can make things worse. 1661 01:06:22,540 --> 01:06:24,930 So now overall let me-- 1662 01:06:24,930 --> 01:06:26,830 so more generally, the lessons are-- 1663 01:06:26,830 --> 01:06:29,820 so the question is kind of like whether future misbehavior 1664 01:06:29,820 --> 01:06:33,090 raises or lowers the cost of current misbehavior. 1665 01:06:33,090 --> 01:06:35,890 So essentially, whether future and current misbehavior 1666 01:06:35,890 --> 01:06:39,755 are compliments or substitutes-- so if future misbehavior raises 1667 01:06:39,755 --> 01:06:41,130 the costs of current misbehavior, 1668 01:06:41,130 --> 01:06:44,100 then sophistication helps in overcoming short run 1669 01:06:44,100 --> 01:06:45,150 impatience. 1670 01:06:45,150 --> 01:06:47,085 That tends to be true for investment goods. 1671 01:06:47,085 --> 01:06:48,960 That was the example that I showed you first. 1672 01:06:48,960 --> 01:06:50,700 If I know I'm going to misbehave in the future, 1673 01:06:50,700 --> 01:06:51,420 I'm not going to like-- 1674 01:06:51,420 --> 01:06:54,090 I'm going to procrastinate a lot if I don't do it right now. 1675 01:06:54,090 --> 01:06:55,680 Then sophistication is good because I 1676 01:06:55,680 --> 01:06:59,490 can sort of prevent that by just doing stuff right now. 1677 01:06:59,490 --> 01:07:02,133 So those are the investment goods with immediate cost. 1678 01:07:02,133 --> 01:07:03,550 There are some exceptions to that. 1679 01:07:03,550 --> 01:07:05,550 But generally, that tends to be true. 1680 01:07:05,550 --> 01:07:07,650 Now, if instead future misbehavior 1681 01:07:07,650 --> 01:07:10,230 lowers the costs of current misbehavior, 1682 01:07:10,230 --> 01:07:13,985 because essentially the benefits of waiting in this case 1683 01:07:13,985 --> 01:07:16,110 that I showed you for the movie are just lower now, 1684 01:07:16,110 --> 01:07:19,117 so the costs of misbehaving now have become lower, then I say, 1685 01:07:19,117 --> 01:07:20,700 well, I might as well do it right now. 1686 01:07:20,700 --> 01:07:22,500 I might as well eat the cake right now, or whatever. 1687 01:07:22,500 --> 01:07:23,770 There's no point in waiting. 1688 01:07:23,770 --> 01:07:26,380 So then sophistication hurts in overcoming short run 1689 01:07:26,380 --> 01:07:27,300 impatience. 1690 01:07:27,300 --> 01:07:31,590 And that tends to be the case for leisure goods. 1691 01:07:31,590 --> 01:07:34,050 So avoid immediate rewards. 1692 01:07:34,050 --> 01:07:36,054 Now-- yes? 1693 01:07:36,054 --> 01:07:37,530 AUDIENCE: [INAUDIBLE]. 1694 01:07:43,940 --> 01:07:45,835 FRANK SCHILBACH: It has to-- 1695 01:07:45,835 --> 01:07:46,710 it's a little tricky. 1696 01:07:46,710 --> 01:07:47,752 It's kind of complicated. 1697 01:07:47,752 --> 01:07:50,150 In some sense, it has to do with specific cases. 1698 01:07:50,150 --> 01:07:53,060 But the key question is essentially is like, 1699 01:07:53,060 --> 01:07:57,740 in the future, does sophistication or misbehavior 1700 01:07:57,740 --> 01:08:00,750 raise or lower the costs of future misbehavior? 1701 01:08:00,750 --> 01:08:04,370 Does it raise or lower the costs of current misbehavior? 1702 01:08:04,370 --> 01:08:07,580 And then depending on whether that's the case, sophistication 1703 01:08:07,580 --> 01:08:10,700 or naivete go in different directions. 1704 01:08:10,700 --> 01:08:13,140 So essentially there's a true answer to that. 1705 01:08:13,140 --> 01:08:14,450 And then essentially if you're naive to this, 1706 01:08:14,450 --> 01:08:17,330 it sort of flips the direction, depending on the numbers. 1707 01:08:17,330 --> 01:08:19,365 But it's more complicated to that. 1708 01:08:19,365 --> 01:08:21,740 It sort of-- these are sort of fairly general statements. 1709 01:08:21,740 --> 01:08:23,090 So it's a little complicated. 1710 01:08:23,090 --> 01:08:25,830 But you'll see some examples again in problem sets 1711 01:08:25,830 --> 01:08:26,330 and so on. 1712 01:08:26,330 --> 01:08:27,060 Yes. 1713 01:08:27,060 --> 01:08:28,810 AUDIENCE: Does anybody model [INAUDIBLE]?? 1714 01:08:32,762 --> 01:08:33,970 FRANK SCHILBACH: Not so much. 1715 01:08:33,970 --> 01:08:36,979 So usually people tend to-- so that's an interesting question. 1716 01:08:36,979 --> 01:08:39,920 So usually people think beta hat or any preference parameters 1717 01:08:39,920 --> 01:08:43,899 are often independent of the costs and choices that you see. 1718 01:08:43,899 --> 01:08:47,160 So the idea often is you are born 1719 01:08:47,160 --> 01:08:49,200 with a beta and a beta hat and a delta 1720 01:08:49,200 --> 01:08:51,630 and so on that fell somehow from the sky. 1721 01:08:51,630 --> 01:08:54,342 There's some research on how environmental factors and so 1722 01:08:54,342 --> 01:08:55,259 on affect preferences. 1723 01:08:55,259 --> 01:08:57,660 For example, we'll show you some research 1724 01:08:57,660 --> 01:09:00,223 on how contact with different types of people 1725 01:09:00,223 --> 01:09:01,515 affect your social preferences. 1726 01:09:01,515 --> 01:09:05,939 For example, if you are exposed to many poor people 1727 01:09:05,939 --> 01:09:07,378 as a rich person in your life, you 1728 01:09:07,378 --> 01:09:09,420 might become a nicer person and things like that. 1729 01:09:09,420 --> 01:09:11,260 I'll show you some research about that. 1730 01:09:11,260 --> 01:09:13,979 So there's some research on how exposure to environments 1731 01:09:13,979 --> 01:09:15,960 affects people's preferences. 1732 01:09:15,960 --> 01:09:18,120 In the case of time preferences, usually people 1733 01:09:18,120 --> 01:09:20,220 just think by assumption, somehow you 1734 01:09:20,220 --> 01:09:22,800 came with a certain discount factor, 1735 01:09:22,800 --> 01:09:25,660 and that's how it is, or beta delta and so on. 1736 01:09:25,660 --> 01:09:28,540 That applies to all sorts of settings. 1737 01:09:28,540 --> 01:09:29,359 Yeah. 1738 01:09:29,359 --> 01:09:30,450 AUDIENCE: [INAUDIBLE]. 1739 01:09:37,050 --> 01:09:38,760 But if it's less costly, you should be 1740 01:09:38,760 --> 01:09:41,270 able to be more sophisticated. 1741 01:09:41,270 --> 01:09:42,932 So I mean-- 1742 01:09:42,932 --> 01:09:43,890 FRANK SCHILBACH: Right. 1743 01:09:43,890 --> 01:09:44,590 That's an interesting question. 1744 01:09:44,590 --> 01:09:47,130 So that's not what people have done and thought about. 1745 01:09:47,130 --> 01:09:48,870 In a way, there's a bit of a question 1746 01:09:48,870 --> 01:09:50,910 whether your cost and benefit structure 1747 01:09:50,910 --> 01:09:53,490 can explain your behavior for a given beta hat. 1748 01:09:53,490 --> 01:09:56,710 But it might also be that for some case-- in some situations, 1749 01:09:56,710 --> 01:09:58,025 you might say you want to be-- 1750 01:09:58,025 --> 01:09:59,650 for example, what I was saying earlier, 1751 01:09:59,650 --> 01:10:01,717 it's like, why are people not learning? 1752 01:10:01,717 --> 01:10:03,300 For some behaviors, maybe you actually 1753 01:10:03,300 --> 01:10:05,970 don't care if your beta is 0.7 or whatever. 1754 01:10:05,970 --> 01:10:06,872 It's like, fine. 1755 01:10:06,872 --> 01:10:09,330 But some people really care about being a good and virtuous 1756 01:10:09,330 --> 01:10:09,830 person. 1757 01:10:09,830 --> 01:10:12,152 And therefore these might be important choices in life 1758 01:10:12,152 --> 01:10:13,860 that you would say, I'm a serious person. 1759 01:10:13,860 --> 01:10:14,460 I do this well. 1760 01:10:14,460 --> 01:10:15,835 My beta hat-- you'd like to think 1761 01:10:15,835 --> 01:10:19,718 of yourself as your beta being high. 1762 01:10:19,718 --> 01:10:21,510 That's not what people have done very much. 1763 01:10:21,510 --> 01:10:23,490 So there's a little bit of research 1764 01:10:23,490 --> 01:10:26,580 of good, specific discounting, like your discounting 1765 01:10:26,580 --> 01:10:29,180 for certain goods might be different than for others, 1766 01:10:29,180 --> 01:10:30,930 depending on what kinds of goods they are. 1767 01:10:30,930 --> 01:10:33,360 So some goods are temptation goods and others are not. 1768 01:10:33,360 --> 01:10:36,360 Even that is not really in the mainstream of economics 1769 01:10:36,360 --> 01:10:40,470 very much, let alone sort of saying your beta hat varies 1770 01:10:40,470 --> 01:10:41,280 by circumstance. 1771 01:10:41,280 --> 01:10:42,613 I think that's a very nice idea. 1772 01:10:42,613 --> 01:10:46,870 I don't know any research that has done that so far. 1773 01:10:46,870 --> 01:10:48,000 OK. 1774 01:10:48,000 --> 01:10:49,620 So now one question you might ask-- 1775 01:10:49,620 --> 01:10:53,520 well, is it beneficial to be sophisticated? 1776 01:10:53,520 --> 01:10:56,170 Couldn't we just all be naive and everybody's better off? 1777 01:10:56,170 --> 01:10:57,780 So in theory-- at least in principle-- 1778 01:10:57,780 --> 01:11:00,300 it's sort of unclear whether sophistication is good. 1779 01:11:00,300 --> 01:11:01,070 As I told you-- 1780 01:11:01,070 --> 01:11:02,320 I showed you just an example-- 1781 01:11:02,320 --> 01:11:05,100 in some cases it's good and other cases it's bad. 1782 01:11:05,100 --> 01:11:08,040 If you think overall many important decisions 1783 01:11:08,040 --> 01:11:12,120 or choices in life tend to be decisions 1784 01:11:12,120 --> 01:11:13,830 that involve one term-- 1785 01:11:13,830 --> 01:11:15,900 one time efforts that yield future benefits, 1786 01:11:15,900 --> 01:11:17,220 these are investment goods. 1787 01:11:17,220 --> 01:11:20,130 So in many cases in life, you have sort of investment goods-- 1788 01:11:20,130 --> 01:11:23,760 like finishing papers, presentations, reports, 1789 01:11:23,760 --> 01:11:27,450 finding good investment options for retirement, 1790 01:11:27,450 --> 01:11:30,510 quitting bad habits, quitting smoking, finding a job, 1791 01:11:30,510 --> 01:11:31,810 and so on and so forth. 1792 01:11:31,810 --> 01:11:33,540 So lots of choices are essentially 1793 01:11:33,540 --> 01:11:36,480 immediate effort, or at one time or several times 1794 01:11:36,480 --> 01:11:39,190 putting in effort right now where you get future benefits. 1795 01:11:39,190 --> 01:11:40,690 So a lot of important things in life 1796 01:11:40,690 --> 01:11:42,630 tend to be investment goods. 1797 01:11:42,630 --> 01:11:45,870 And in that case, I guess sophistication 1798 01:11:45,870 --> 01:11:46,620 tends to be good. 1799 01:11:46,620 --> 01:11:49,020 So essentially it helps you. 1800 01:11:49,020 --> 01:11:53,068 Now, in addition, sophisticates take advantage 1801 01:11:53,068 --> 01:11:53,985 of commitment devices. 1802 01:11:53,985 --> 01:11:55,680 So I offer you a commitment device 1803 01:11:55,680 --> 01:11:57,540 that I was discussing earlier. 1804 01:11:57,540 --> 01:12:00,100 The sophisticated person will say, great. 1805 01:12:00,100 --> 01:12:01,600 The commitment device might help me. 1806 01:12:01,600 --> 01:12:02,100 Great. 1807 01:12:02,100 --> 01:12:05,070 I'm going to demand it and might be better off because of that. 1808 01:12:05,070 --> 01:12:07,350 I'm going to show you next week commitment devices don't always 1809 01:12:07,350 --> 01:12:07,850 work. 1810 01:12:07,850 --> 01:12:10,240 Maybe sometimes they could actually make things worse. 1811 01:12:10,240 --> 01:12:13,500 But in principle, at least, you think commitment devices could 1812 01:12:13,500 --> 01:12:16,500 improve things, and sort of in that sense, being sophisticated 1813 01:12:16,500 --> 01:12:17,400 is good. 1814 01:12:17,400 --> 01:12:19,140 So I think overall, if I had to choose 1815 01:12:19,140 --> 01:12:21,720 if I'm sophisticated or naive, I would probably 1816 01:12:21,720 --> 01:12:24,600 choose to be sophisticated, at least in this case. 1817 01:12:24,600 --> 01:12:28,920 Whether that's actually true, I'm not so sure. 1818 01:12:28,920 --> 01:12:32,520 There's one somewhat more subtle thing here 1819 01:12:32,520 --> 01:12:35,100 is to say, like, is it sort of-- is the issue here really 1820 01:12:35,100 --> 01:12:39,030 impatience or time inconsistency-- in a sense of, 1821 01:12:39,030 --> 01:12:41,460 is it just about people not caring sufficiently much 1822 01:12:41,460 --> 01:12:42,360 for the future? 1823 01:12:42,360 --> 01:12:46,050 Or is it about how important is time inconsistency? 1824 01:12:46,050 --> 01:12:48,340 And as I said, some of the behavior that I'm going to 1825 01:12:48,340 --> 01:12:48,840 show-- 1826 01:12:48,840 --> 01:12:51,720 that I showed you is, impatience is not really 1827 01:12:51,720 --> 01:12:52,950 the key issue here. 1828 01:12:52,950 --> 01:12:55,350 It's not about people not necessarily caring 1829 01:12:55,350 --> 01:12:58,620 about the future, but rather, people switching their choices 1830 01:12:58,620 --> 01:13:00,780 and choosing dominated options in the sense 1831 01:13:00,780 --> 01:13:02,580 of overall dominated. 1832 01:13:02,580 --> 01:13:04,680 If you sort of commit, there are some options 1833 01:13:04,680 --> 01:13:07,770 that you prefer that you end up not choosing because you 1834 01:13:07,770 --> 01:13:09,300 change your choices over time. 1835 01:13:09,300 --> 01:13:11,740 Impatience cannot create this type of behavior. 1836 01:13:11,740 --> 01:13:14,290 What I showed you, where the sophisticated person says, 1837 01:13:14,290 --> 01:13:16,560 I would like these options but I'm not choosing them 1838 01:13:16,560 --> 01:13:19,260 because I know my future self will change their minds, 1839 01:13:19,260 --> 01:13:20,440 that is not possible. 1840 01:13:20,440 --> 01:13:22,860 You cannot generate this behavior coming from just 1841 01:13:22,860 --> 01:13:23,970 impatience. 1842 01:13:23,970 --> 01:13:26,310 A delta being 0.5 or whatever would not 1843 01:13:26,310 --> 01:13:27,990 generate you this behavior. 1844 01:13:27,990 --> 01:13:29,550 What you need is time inconsistency. 1845 01:13:29,550 --> 01:13:33,900 You need, essentially, preference reversals over time. 1846 01:13:33,900 --> 01:13:35,880 OK, so then in some ways I think-- 1847 01:13:35,880 --> 01:13:39,810 perhaps more most practical for your purposes, in part, 1848 01:13:39,810 --> 01:13:41,340 for the problem set-- 1849 01:13:41,340 --> 01:13:43,080 how do we solve sort of problems with 1850 01:13:43,080 --> 01:13:44,440 quasi-hyperbolic discounting? 1851 01:13:44,440 --> 01:13:47,820 So as I told you before, for the naive person, 1852 01:13:47,820 --> 01:13:49,350 we can start from the beginning. 1853 01:13:49,350 --> 01:13:52,530 And why do we start from the beginning as a naive person? 1854 01:13:52,530 --> 01:13:55,040 Why does this work? 1855 01:13:55,040 --> 01:13:57,218 So I sort of showed you already how to solve it. 1856 01:13:57,218 --> 01:13:59,260 Now I'm sort of generalizing that, in some sense. 1857 01:13:59,260 --> 01:14:00,635 Why is that a useful thing to do? 1858 01:14:00,635 --> 01:14:01,258 Yeah. 1859 01:14:01,258 --> 01:14:02,993 AUDIENCE: [INAUDIBLE]. 1860 01:14:02,993 --> 01:14:03,910 FRANK SCHILBACH: Yeah. 1861 01:14:03,910 --> 01:14:06,360 So the naive person thinks, I'm going to make plans now 1862 01:14:06,360 --> 01:14:07,570 for the future. 1863 01:14:07,570 --> 01:14:10,410 And by assumption, the naive person 1864 01:14:10,410 --> 01:14:12,750 thinks they're going to follow through on those plans. 1865 01:14:12,750 --> 01:14:14,190 So what you can essentially do is 1866 01:14:14,190 --> 01:14:17,400 you can start with some plans, see 1867 01:14:17,400 --> 01:14:19,600 what the person is choosing thinking they're 1868 01:14:19,600 --> 01:14:20,600 going to follow through. 1869 01:14:20,600 --> 01:14:21,780 You don't have to worry about what's 1870 01:14:21,780 --> 01:14:23,640 going to happen in the future, because you 1871 01:14:23,640 --> 01:14:26,250 can explain perfectly what the person is doing in the present 1872 01:14:26,250 --> 01:14:28,320 by making plans for-- 1873 01:14:28,320 --> 01:14:31,087 sorry, by making your choice for the future periods. 1874 01:14:31,087 --> 01:14:32,670 You don't have to actually worry about 1875 01:14:32,670 --> 01:14:34,170 whether the person is going to follow through, 1876 01:14:34,170 --> 01:14:36,290 because the person doesn't even think about that. 1877 01:14:36,290 --> 01:14:38,020 So you say, I make a plan for the future, 1878 01:14:38,020 --> 01:14:39,937 assuming I'm going to stick through with that, 1879 01:14:39,937 --> 01:14:40,830 or stick to this. 1880 01:14:40,830 --> 01:14:42,622 And then you can just sort of roll forwards 1881 01:14:42,622 --> 01:14:44,460 and say, OK, I start with period T equals 0, 1882 01:14:44,460 --> 01:14:46,450 make the plan for that, think I'm going to follow through. 1883 01:14:46,450 --> 01:14:47,950 Surprise, maybe period one I'm going 1884 01:14:47,950 --> 01:14:49,290 to do something different. 1885 01:14:49,290 --> 01:14:51,707 But then I'm going to have the same assumption, and so on. 1886 01:14:51,707 --> 01:14:53,850 I can just go from T equals 0 going forward 1887 01:14:53,850 --> 01:14:58,350 under the assumption that I'm going to stick to those plans. 1888 01:14:58,350 --> 01:14:59,790 For the sophisticated person, that 1889 01:14:59,790 --> 01:15:02,790 doesn't work, because a sophisticated person knows 1890 01:15:02,790 --> 01:15:04,690 that if I make some plans for the future, 1891 01:15:04,690 --> 01:15:07,110 those might not be feasible because the future self will 1892 01:15:07,110 --> 01:15:09,220 misbehave and change their plans. 1893 01:15:09,220 --> 01:15:12,853 I know essentially that some plans are not feasible. 1894 01:15:12,853 --> 01:15:14,520 So what I need to do is essentially just 1895 01:15:14,520 --> 01:15:16,830 start from the end and see, OK, if certain options are 1896 01:15:16,830 --> 01:15:18,780 available, what I'm going to do, and then 1897 01:15:18,780 --> 01:15:20,590 walk backwards to solve it. 1898 01:15:20,590 --> 01:15:22,800 And that's essentially rational expectations 1899 01:15:22,800 --> 01:15:26,610 where essentially you perfectly understand your future behavior 1900 01:15:26,610 --> 01:15:29,730 and sort of take into account your future choices. 1901 01:15:29,730 --> 01:15:32,800 You're going to make them current choices at the end. 1902 01:15:32,800 --> 01:15:34,500 What about the exponential person? 1903 01:15:34,500 --> 01:15:37,280 How does that person solve the problem? 1904 01:15:37,280 --> 01:15:38,020 AUDIENCE: I just had a question about what you just said. 1905 01:15:38,020 --> 01:15:38,880 FRANK SCHILBACH: Go ahead. 1906 01:15:38,880 --> 01:15:41,172 AUDIENCE: So to summarize a sophisticated person, where 1907 01:15:41,172 --> 01:15:43,940 they're going from the end to the beginning, 1908 01:15:43,940 --> 01:15:47,690 as they move backwards, are you just removing choices 1909 01:15:47,690 --> 01:15:49,030 that you know you won't ever-- 1910 01:15:49,030 --> 01:15:49,430 FRANK SCHILBACH: Correct. 1911 01:15:49,430 --> 01:15:49,930 Exactly. 1912 01:15:49,930 --> 01:15:51,830 So what we did in the movie choice, 1913 01:15:51,830 --> 01:15:54,530 if you go through this example in more detail, 1914 01:15:54,530 --> 01:15:57,168 you'll notice that essentially, if I know that, 1915 01:15:57,168 --> 01:15:59,210 for example, suppose I want to go in period three 1916 01:15:59,210 --> 01:16:00,877 but I know I'm going to go in period two 1917 01:16:00,877 --> 01:16:02,450 if it comes down to that, then I'm 1918 01:16:02,450 --> 01:16:06,830 going to remove period three for my choice set or for my options 1919 01:16:06,830 --> 01:16:09,380 when optimizing in period one or period zero, 1920 01:16:09,380 --> 01:16:14,150 anticipating what I'm going to do in the future. 1921 01:16:14,150 --> 01:16:17,390 So what about the exponential discounter? 1922 01:16:17,390 --> 01:16:19,752 Yes? 1923 01:16:19,752 --> 01:16:21,231 AUDIENCE: [INAUDIBLE]. 1924 01:16:26,215 --> 01:16:27,090 FRANK SCHILBACH: Yes. 1925 01:16:27,090 --> 01:16:30,012 So there's two options, in fact, for the exponential discounter. 1926 01:16:30,012 --> 01:16:32,220 It actually doesn't matter because you follow through 1927 01:16:32,220 --> 01:16:33,198 with your plans anyway. 1928 01:16:33,198 --> 01:16:34,740 So you could start from the beginning 1929 01:16:34,740 --> 01:16:36,070 and just walk forward. 1930 01:16:36,070 --> 01:16:38,740 In fact, what you can do is you can start in period zero 1931 01:16:38,740 --> 01:16:40,902 make a plan for everything and just follow through. 1932 01:16:40,902 --> 01:16:42,360 You don't even have to go to period 1933 01:16:42,360 --> 01:16:43,740 1, 2, and 3 because you know you're 1934 01:16:43,740 --> 01:16:44,980 going to stick to that plan. 1935 01:16:44,980 --> 01:16:46,590 So you can essentially just do that. 1936 01:16:46,590 --> 01:16:48,750 You could actually also do backward transactions. 1937 01:16:48,750 --> 01:16:50,940 And I'm pretty sure you get the exact same answer. 1938 01:16:50,940 --> 01:16:51,960 It doesn't matter. 1939 01:16:51,960 --> 01:16:53,620 The much easier thing to do, of course, 1940 01:16:53,620 --> 01:16:55,380 is to solve the problem in period 0 1941 01:16:55,380 --> 01:16:58,570 and then just assuming you're going to follow through. 1942 01:16:58,570 --> 01:17:01,530 So sorry, this should say readings for Tuesday. 1943 01:17:01,530 --> 01:17:05,650 The class is on Tuesday, not on Monday. 1944 01:17:05,650 --> 01:17:11,280 Please read the paper by Ariely and Wortenbroch. 1945 01:17:11,280 --> 01:17:12,850 Read the entire article. 1946 01:17:12,850 --> 01:17:15,240 We're going to discuss applications from smoking 1947 01:17:15,240 --> 01:17:17,670 to drinking, setting deadlines, and so on, 1948 01:17:17,670 --> 01:17:20,620 and apply these models in real-world settings. 1949 01:17:20,620 --> 01:17:22,580 Thank you very much.