1 00:00:00,090 --> 00:00:02,490 The following content is provided under a Creative 2 00:00:02,490 --> 00:00:04,059 Commons license. 3 00:00:04,059 --> 00:00:06,330 Your support will help MIT OpenCourseWare 4 00:00:06,330 --> 00:00:10,720 continue to offer high quality educational resources for free. 5 00:00:10,720 --> 00:00:13,350 To make a donation or view additional materials 6 00:00:13,350 --> 00:00:17,280 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,280 --> 00:00:18,480 at ocw.mit.edu. 8 00:00:30,732 --> 00:00:31,565 ROBERT TOWNSEND: OK. 9 00:00:34,480 --> 00:00:38,800 Today we're going to continue the topic of Consumption 10 00:00:38,800 --> 00:00:39,850 Smoothing. 11 00:00:39,850 --> 00:00:43,900 This sort of sequence began with the optimal allocation 12 00:00:43,900 --> 00:00:48,070 of risk bearing and what you would see in the data. 13 00:00:48,070 --> 00:00:53,440 We saw the benchmark was doing well in many but not all cases. 14 00:00:53,440 --> 00:00:58,780 And there were some examples where coefficients on income 15 00:00:58,780 --> 00:01:03,550 were higher and for certain occupations 16 00:01:03,550 --> 00:01:05,725 and certain types of income. 17 00:01:09,760 --> 00:01:13,710 Then we took that same benchmark still clinging to it 18 00:01:13,710 --> 00:01:17,273 and looked at a whole different kind of data, production data. 19 00:01:17,273 --> 00:01:18,690 And we're going to come back to it 20 00:01:18,690 --> 00:01:22,290 next time when we talk about labor supply. 21 00:01:22,290 --> 00:01:25,080 But while we're on the subject of consumption and consumption 22 00:01:25,080 --> 00:01:28,110 smoothing, I thought it would be good to go 23 00:01:28,110 --> 00:01:30,030 through some alternative models that 24 00:01:30,030 --> 00:01:34,680 are widely used and different data sets 25 00:01:34,680 --> 00:01:41,910 and give you a sense of what people do in the literature. 26 00:01:41,910 --> 00:01:47,400 So a lot of this has to do with the permanent income model. 27 00:01:47,400 --> 00:01:51,580 It's just kind of the basic sort of thing 28 00:01:51,580 --> 00:01:55,210 that people rely on and fall back on constantly 29 00:01:55,210 --> 00:01:58,655 or say consumption smoothing over the life cycle. 30 00:02:02,410 --> 00:02:03,880 These markets are not complete. 31 00:02:03,880 --> 00:02:08,680 They shut down a lot of the risk contingencies allowing 32 00:02:08,680 --> 00:02:15,610 households to trade only in risk free bonds or maybe have some 33 00:02:15,610 --> 00:02:19,240 other savings account which cannot go below zero or limited 34 00:02:19,240 --> 00:02:21,970 credit. 35 00:02:21,970 --> 00:02:23,740 The papers were going to cover, first one, 36 00:02:23,740 --> 00:02:27,550 there's one by Kaplan and Violante, 37 00:02:27,550 --> 00:02:30,250 which is going to look at the degree of consumption 38 00:02:30,250 --> 00:02:34,780 through smoothing from this SIM, which is Standard Incomplete 39 00:02:34,780 --> 00:02:35,730 Market model. 40 00:02:35,730 --> 00:02:37,150 They're also going to simulate it. 41 00:02:37,150 --> 00:02:43,000 So that's using it two purposes there. 42 00:02:43,000 --> 00:02:46,990 And we're going to look at smoothing 43 00:02:46,990 --> 00:02:49,990 through the lens of that model and in the data 44 00:02:49,990 --> 00:02:52,980 against permanent shocks and transitory shocks. 45 00:02:52,980 --> 00:02:57,610 This is a language we have not been using so far. 46 00:02:57,610 --> 00:03:04,650 But it is standard language in this other literature, 47 00:03:04,650 --> 00:03:08,250 and look at how smoothing varies against these various shocks 48 00:03:08,250 --> 00:03:11,400 [? varies ?] over the life cycle. 49 00:03:11,400 --> 00:03:13,740 The Violante paper and others draw 50 00:03:13,740 --> 00:03:16,470 on this [? Blundell, ?] Pistaferri, 51 00:03:16,470 --> 00:03:20,340 and Preston method, which is looking 52 00:03:20,340 --> 00:03:23,835 at consumption and income data. 53 00:03:27,450 --> 00:03:31,080 And in fact, there is not typically a very long time 54 00:03:31,080 --> 00:03:33,930 series in the US to use. 55 00:03:33,930 --> 00:03:37,770 The best is a PSID , which used to only have food. 56 00:03:37,770 --> 00:03:40,950 So part of this paper is about how to splice together 57 00:03:40,950 --> 00:03:46,170 two different databases to create a longer panel 58 00:03:46,170 --> 00:03:48,270 and measure the degree of smoothing in the data. 59 00:03:49,335 --> 00:03:52,500 Then we'll move to Deaton and Paxson, which 60 00:03:52,500 --> 00:03:56,340 is the same overall topic but actually 61 00:03:56,340 --> 00:03:57,780 quite interesting because they're 62 00:03:57,780 --> 00:04:03,450 going to be looking more at the variance of consumption 63 00:04:03,450 --> 00:04:08,740 in cross sections, which is an implication of the models. 64 00:04:08,740 --> 00:04:10,410 But you don't need these panel. 65 00:04:10,410 --> 00:04:14,100 You just need a bunch of cross sections for various years. 66 00:04:14,100 --> 00:04:16,510 So effectively, if it's representative, 67 00:04:16,510 --> 00:04:18,110 you can track people by age. 68 00:04:20,680 --> 00:04:24,090 And again, they do that through a permanent income 69 00:04:24,090 --> 00:04:27,600 model, a buffer stock model, a model with borrowing 70 00:04:27,600 --> 00:04:32,070 constraints, as well as in the background, the full insurance 71 00:04:32,070 --> 00:04:36,870 model, and relate it to things in the data. 72 00:04:36,870 --> 00:04:41,160 Then there's this Campbell and Deaton paper, which 73 00:04:41,160 --> 00:04:44,330 is about excess smoothness. 74 00:04:44,330 --> 00:04:49,580 And I kind of smile every time I see this title because 75 00:04:49,580 --> 00:04:54,290 from the standpoint of the permanent income model, 76 00:04:54,290 --> 00:04:57,305 you should respond to shocks to permanent income. 77 00:05:01,300 --> 00:05:03,800 And they see in the data that consumption 78 00:05:03,800 --> 00:05:06,190 is smoother than that. 79 00:05:06,190 --> 00:05:09,550 So they call it excess smoothness. 80 00:05:09,550 --> 00:05:11,800 My smiles come from the fact that they 81 00:05:11,800 --> 00:05:15,850 haven't considered the full risk-sharing benchmark, which 82 00:05:15,850 --> 00:05:19,190 may not fit perfectly well either 83 00:05:19,190 --> 00:05:21,910 but may be part of the explanation in the background. 84 00:05:24,820 --> 00:05:28,430 And then finally, we have this Krueger and Perri 85 00:05:28,430 --> 00:05:33,990 paper, which looks at the US and Italian data. 86 00:05:33,990 --> 00:05:36,720 And I hope we get time to say a few words about this today 87 00:05:36,720 --> 00:05:39,660 because 88 00:05:39,660 --> 00:05:41,635 AUDIENCE: I'm doing it in the recitation. 89 00:05:41,635 --> 00:05:43,760 ROBERT TOWNSEND: You're doing it in the recitation? 90 00:05:43,760 --> 00:05:44,260 OK. 91 00:05:50,900 --> 00:05:54,430 Yeah, I originally had this as part of the primary lecture, 92 00:05:54,430 --> 00:05:56,320 and then we thought there wasn't enough time 93 00:05:56,320 --> 00:05:58,970 in class, which may yet turn out to be true. 94 00:05:58,970 --> 00:06:02,500 And then I looked at it again, and I really like it. 95 00:06:02,500 --> 00:06:05,295 So I'm glad one way or the other, you're going to see it. 96 00:06:05,295 --> 00:06:07,170 AUDIENCE: [INAUDIBLE] I'll do something else. 97 00:06:07,170 --> 00:06:09,820 ROBERT TOWNSEND: That's fine. 98 00:06:09,820 --> 00:06:11,716 Maybe we'll get a lot of questions. 99 00:06:21,850 --> 00:06:23,200 So what's the problem? 100 00:06:23,200 --> 00:06:26,950 In the US as I was saying, we need longitudinal data 101 00:06:26,950 --> 00:06:28,900 on consumption and income. 102 00:06:28,900 --> 00:06:34,660 And on consumption, we need a comprehensive measure. 103 00:06:34,660 --> 00:06:39,410 No one's been gathering these kinds of data. 104 00:06:39,410 --> 00:06:41,950 So how do people cope with it? 105 00:06:41,950 --> 00:06:44,725 They could use the PS and just look at food. 106 00:06:48,040 --> 00:06:51,070 Or they could look exclusively at the Consumer Expenditure 107 00:06:51,070 --> 00:06:55,090 Survey, which has a whole bunch of line items. 108 00:06:55,090 --> 00:06:58,647 But people are not in that sample for more than three 109 00:06:58,647 --> 00:06:59,355 or four quarters. 110 00:07:04,080 --> 00:07:09,960 Or you could sort of basically create these synthetic cohorts 111 00:07:09,960 --> 00:07:13,415 by sort of extrapolating and merging, 112 00:07:13,415 --> 00:07:15,915 which is increasingly a common way to deal with the problem. 113 00:07:23,930 --> 00:07:27,430 Another way to sort of think about this upfront 114 00:07:27,430 --> 00:07:33,250 is these models are making a distinction 115 00:07:33,250 --> 00:07:37,270 between permanent and transitory shocks, but we only see income. 116 00:07:37,270 --> 00:07:40,810 We don't see each of these different kinds of shocks 117 00:07:40,810 --> 00:07:42,590 individually. 118 00:07:42,590 --> 00:07:45,608 So what to do about that? 119 00:07:45,608 --> 00:07:47,650 You could ignore it and just look at the response 120 00:07:47,650 --> 00:07:49,540 to total income change, which is kind 121 00:07:49,540 --> 00:07:52,380 of what we've been doing, actually, in the development 122 00:07:52,380 --> 00:07:52,965 data sets. 123 00:07:55,790 --> 00:07:59,280 You could use proxies for permanent 124 00:07:59,280 --> 00:08:00,660 versus transitory shocks. 125 00:08:00,660 --> 00:08:02,970 For example, disability might rightly 126 00:08:02,970 --> 00:08:06,150 be thought of as a rather permanent shock. 127 00:08:06,150 --> 00:08:08,070 Short-term unemployment might be thought 128 00:08:08,070 --> 00:08:10,380 of as a transitory shock. 129 00:08:10,380 --> 00:08:16,230 So that's another way to try to deal with a problem. 130 00:08:16,230 --> 00:08:20,450 And then there's sort of a public finance tax literature. 131 00:08:20,450 --> 00:08:22,610 Different people assume different things 132 00:08:22,610 --> 00:08:24,170 about different kinds of taxes. 133 00:08:24,170 --> 00:08:26,150 Some tax is assumed to be permanent, 134 00:08:26,150 --> 00:08:28,850 others assumed to be transitory. 135 00:08:28,850 --> 00:08:31,550 And then you kind of see how households react to that. 136 00:08:40,850 --> 00:08:45,640 So the benchmark model people use for saying, 137 00:08:45,640 --> 00:08:49,570 quote, "How much insurance is there actually in the data?" 138 00:08:49,570 --> 00:08:54,820 Is this Blundell, Pistaferri, Preston paper, 139 00:08:54,820 --> 00:08:56,650 I doubt if we'll get to that today. 140 00:08:56,650 --> 00:08:59,080 It is in the appendix, so I have it 141 00:08:59,080 --> 00:09:02,980 in the slides, time permitting. 142 00:09:02,980 --> 00:09:07,450 But it's basically covariance decomposition of the income 143 00:09:07,450 --> 00:09:10,580 and consumption process. 144 00:09:10,580 --> 00:09:13,750 So that's the quote view of the data. 145 00:09:13,750 --> 00:09:16,300 Then for the models, you start with the standard incomplete 146 00:09:16,300 --> 00:09:20,710 markets model, assuming no access to contingent claims 147 00:09:20,710 --> 00:09:24,310 but allowing some kind of insurance 148 00:09:24,310 --> 00:09:26,600 through buying and selling bonds. 149 00:09:26,600 --> 00:09:31,300 Now let me pause for a second, just in case it's not clear. 150 00:09:31,300 --> 00:09:35,350 And this literature uses confusing language, actually. 151 00:09:35,350 --> 00:09:39,400 If you thought about a household in isolation or a business, 152 00:09:39,400 --> 00:09:41,720 they have ups and downs of income. 153 00:09:41,720 --> 00:09:45,850 And it's clear that by saving, you kind of smooth off 154 00:09:45,850 --> 00:09:49,210 the peaks so that higher income does not 155 00:09:49,210 --> 00:09:51,220 make its way into consumption. 156 00:09:51,220 --> 00:09:55,480 And likewise, in the valleys, when income is really low, 157 00:09:55,480 --> 00:09:58,180 you can carry forward that savings to that 158 00:09:58,180 --> 00:10:02,050 spot or borrow, which makes the valley less deep. 159 00:10:02,050 --> 00:10:04,940 So consumption is smooth to a large degree, 160 00:10:04,940 --> 00:10:10,360 but not completely against these fluctuations. 161 00:10:10,360 --> 00:10:11,890 What's the difference between that 162 00:10:11,890 --> 00:10:14,830 and the full risk-sharing model? 163 00:10:14,830 --> 00:10:17,590 The idea there is that you don't have-- not everyone's 164 00:10:17,590 --> 00:10:21,430 facing idiosyncratic and transitory shocks 165 00:10:21,430 --> 00:10:23,180 at the same time. 166 00:10:23,180 --> 00:10:26,560 So as in the Rocky Mountains diagram, 167 00:10:26,560 --> 00:10:29,560 peaks and valleys come at different stages. 168 00:10:29,560 --> 00:10:34,570 And even after you act as if a household would do everything 169 00:10:34,570 --> 00:10:37,750 that it could on its own, you're still 170 00:10:37,750 --> 00:10:40,550 left with this asynchronous timing. 171 00:10:40,550 --> 00:10:43,060 So what the risk-sharing model is basically doing 172 00:10:43,060 --> 00:10:47,260 is transferring consumption around in the cross-section 173 00:10:47,260 --> 00:10:50,388 to get even flatter consumption. 174 00:10:50,388 --> 00:10:52,180 And the only thing that would be left then, 175 00:10:52,180 --> 00:10:54,130 if you believe the full risk-sharing model, 176 00:10:54,130 --> 00:10:57,220 are those shocks that basically somehow get 177 00:10:57,220 --> 00:11:00,610 left in aggregate consumption after all that smoothing. 178 00:11:00,610 --> 00:11:02,630 The only part of the peaks and valleys 179 00:11:02,630 --> 00:11:06,070 that's common across all the households would be left. 180 00:11:06,070 --> 00:11:09,050 And everything else would be flattened out. 181 00:11:09,050 --> 00:11:12,880 So this literature, it's true that you 182 00:11:12,880 --> 00:11:15,070 can do an enormous amount of smoothing 183 00:11:15,070 --> 00:11:17,630 by borrowing and lending. 184 00:11:17,630 --> 00:11:19,600 But it is not true that you can do 185 00:11:19,600 --> 00:11:23,230 everything that would be possible with greater 186 00:11:23,230 --> 00:11:24,870 amounts of insurance. 187 00:11:24,870 --> 00:11:28,510 Anyway, so they start with the standard-- 188 00:11:28,510 --> 00:11:31,150 note the word standard-- it's standard 189 00:11:31,150 --> 00:11:35,140 for the certain branches of the macro literature, 190 00:11:35,140 --> 00:11:38,770 incomplete markets literature. 191 00:11:38,770 --> 00:11:41,140 You may or may not put on a lifecycle. 192 00:11:41,140 --> 00:11:44,800 To be realistic, you'd say, the household faith 193 00:11:44,800 --> 00:11:47,440 sees a stochastic probability of dying. 194 00:11:47,440 --> 00:11:53,687 And that makes them more and more vulnerable 195 00:11:53,687 --> 00:11:56,020 as they get older and older, in some sense, because they 196 00:11:56,020 --> 00:11:58,090 can't smooth that out. 197 00:11:58,090 --> 00:12:01,900 Or they have to front-load stuff into savings 198 00:12:01,900 --> 00:12:05,750 to be able to cope with fluctuations as they get older. 199 00:12:05,750 --> 00:12:08,815 So it does matter whether the horizon is infinite or finite. 200 00:12:12,102 --> 00:12:13,810 There are permanent and transitory shocks 201 00:12:13,810 --> 00:12:15,490 to earnings while they earn. 202 00:12:15,490 --> 00:12:19,470 But if it's the life cycle model as in the US, 203 00:12:19,470 --> 00:12:21,370 where there is literally retirement, 204 00:12:21,370 --> 00:12:23,830 then earnings go to zero. 205 00:12:23,830 --> 00:12:27,430 You may have some income stream from social security, 206 00:12:27,430 --> 00:12:31,120 and these guys will load that in. 207 00:12:31,120 --> 00:12:32,950 And you may have some assets you've 208 00:12:32,950 --> 00:12:38,530 put in a pension fund, which has kind of an insurance component 209 00:12:38,530 --> 00:12:42,010 to it, in the sense that you're getting an income 210 00:12:42,010 --> 00:12:48,250 stream from the pension but averaging over the mortality 211 00:12:48,250 --> 00:12:49,790 risk in the population. 212 00:12:49,790 --> 00:12:53,170 So there's a bit of insurance in the standard pension funds. 213 00:12:57,010 --> 00:13:00,510 Another version has borrowing limits. 214 00:13:00,510 --> 00:13:03,000 There's something called the natural borrowing 215 00:13:03,000 --> 00:13:04,500 limit or the zero. 216 00:13:04,500 --> 00:13:06,240 Zero is obvious. 217 00:13:06,240 --> 00:13:07,830 You can't borrow anything at all, 218 00:13:07,830 --> 00:13:10,290 or you'll put just a bound, can borrow 219 00:13:10,290 --> 00:13:13,650 10% of your assets or your income. 220 00:13:13,650 --> 00:13:17,490 The natural borrowing limit is something like this. 221 00:13:17,490 --> 00:13:19,200 You always have to repay your debt. 222 00:13:19,200 --> 00:13:20,910 So you can't borrow more than what 223 00:13:20,910 --> 00:13:24,180 you could repay in the worst possible income 224 00:13:24,180 --> 00:13:26,790 realization in the future. 225 00:13:26,790 --> 00:13:29,580 And then it matters a lot what you're assuming 226 00:13:29,580 --> 00:13:31,140 about the income process. 227 00:13:31,140 --> 00:13:34,320 If there's a small chance of a zero income, 228 00:13:34,320 --> 00:13:37,720 and your debt is due in that situation, 229 00:13:37,720 --> 00:13:39,820 then effectively you can't borrow at all. 230 00:13:39,820 --> 00:13:42,870 So it's a rather stringent criterion. 231 00:13:48,270 --> 00:13:49,770 And then they'll take-- 232 00:13:49,770 --> 00:13:54,500 you'll see Kaplan and Violante then take the model. 233 00:13:54,500 --> 00:13:59,130 And they simulate, hence the SIM, artificial data 234 00:13:59,130 --> 00:14:00,245 from the model itself. 235 00:14:04,330 --> 00:14:05,990 There's two reasons for doing that. 236 00:14:05,990 --> 00:14:11,050 First of all, this Blundell, Pistaferri, Preston paper 237 00:14:11,050 --> 00:14:12,700 is doing something with the data. 238 00:14:12,700 --> 00:14:15,670 It's not a direct look at the data. 239 00:14:15,670 --> 00:14:19,100 But the summary statistics come from this BPP algorithm. 240 00:14:19,100 --> 00:14:20,590 So they want us-- 241 00:14:20,590 --> 00:14:23,230 if you want a common ground, which is what's in the data 242 00:14:23,230 --> 00:14:27,010 through BPP, then let's look at the data generated by the model 243 00:14:27,010 --> 00:14:30,040 through BPP and compare apples to apples. 244 00:14:33,610 --> 00:14:38,380 On the other hand, when you have a model and you simulated it, 245 00:14:38,380 --> 00:14:39,640 that is the reality. 246 00:14:39,640 --> 00:14:43,540 You know exactly what the economy is like. 247 00:14:43,540 --> 00:14:46,270 So they also use this-- 248 00:14:46,270 --> 00:14:49,720 pick up distortions, where BPP is 249 00:14:49,720 --> 00:14:53,050 kind of giving you a summary statistic of the degree 250 00:14:53,050 --> 00:14:55,480 of insurance, which is not actually what's going 251 00:14:55,480 --> 00:14:57,460 on in the underlying model. 252 00:14:57,460 --> 00:15:00,640 So they use this to look at the biases 253 00:15:00,640 --> 00:15:03,030 or what can generate the bias. 254 00:15:03,030 --> 00:15:06,580 The intuition there is pretty straightforward. 255 00:15:06,580 --> 00:15:12,460 Zero borrowing or limits to borrowing are like a corner. 256 00:15:12,460 --> 00:15:14,830 And you're either constrained or you're not constrained, 257 00:15:14,830 --> 00:15:19,270 so that's a non-linearity, whereas BPP algorithm 258 00:15:19,270 --> 00:15:22,510 is basically linear. 259 00:15:22,510 --> 00:15:28,000 So the distortions get introduced by the more likely 260 00:15:28,000 --> 00:15:31,780 you are to be hitting corners, the higher the distortion is. 261 00:15:36,390 --> 00:15:41,630 So the standard incomplete market model 262 00:15:41,630 --> 00:15:43,490 generates an insurance coefficient 263 00:15:43,490 --> 00:15:50,590 for transitory shocks of 94% in the natural borrowing 264 00:15:50,590 --> 00:15:54,430 constraint economy, or 82% in the zero borrowing constraint 265 00:15:54,430 --> 00:15:56,200 economy. 266 00:15:56,200 --> 00:15:58,190 That's a coefficient for insurance, 267 00:15:58,190 --> 00:16:00,713 so that's a good thing. 268 00:16:00,713 --> 00:16:02,380 Be careful you don't get flipped around, 269 00:16:02,380 --> 00:16:06,340 because we've been looking at the degree to which consumption 270 00:16:06,340 --> 00:16:09,170 fluctuates with income, so you start to think high numbers 271 00:16:09,170 --> 00:16:09,670 are bad. 272 00:16:09,670 --> 00:16:12,510 But this is 1 minus that. 273 00:16:12,510 --> 00:16:15,610 So for them, high numbers means insurance, 274 00:16:15,610 --> 00:16:17,500 which means a good thing. 275 00:16:17,500 --> 00:16:20,590 Those are numbers, 94, 82, compared 276 00:16:20,590 --> 00:16:24,850 to the BPP run on the actual data, which is 95. 277 00:16:24,850 --> 00:16:28,580 So that's an excellent fit. 278 00:16:28,580 --> 00:16:30,880 But when they look at the insurance coefficient 279 00:16:30,880 --> 00:16:35,170 for permanent shocks, it's 22% or 7%, 280 00:16:35,170 --> 00:16:38,800 depending in the model what you assume about credit. 281 00:16:38,800 --> 00:16:42,790 But in the actual data, it's 36%. 282 00:16:42,790 --> 00:16:46,390 And here already you're seeing this recurrent theme 283 00:16:46,390 --> 00:16:49,000 that there's better smoothing against even 284 00:16:49,000 --> 00:16:55,150 the permanent shocks in the data than these models allow. 285 00:16:55,150 --> 00:16:58,840 And then if you looked at the life cycle 286 00:16:58,840 --> 00:17:01,450 through the lens of the model, you 287 00:17:01,450 --> 00:17:05,770 would see better insurance as people get older. 288 00:17:05,770 --> 00:17:08,290 But in the data, it's not there. 289 00:17:08,290 --> 00:17:10,450 There's no age profile in the data. 290 00:17:13,230 --> 00:17:15,099 So the model-- another way to say this, 291 00:17:15,099 --> 00:17:16,839 is generating too much consumption 292 00:17:16,839 --> 00:17:20,530 smoothing for the older workers, relative to the data, 293 00:17:20,530 --> 00:17:23,290 or too little smoothing for workers 294 00:17:23,290 --> 00:17:26,470 in the early stage of their lifecycle, 295 00:17:26,470 --> 00:17:28,600 relative to the data. 296 00:17:28,600 --> 00:17:31,720 If you're skeptical, you've got to be skeptical about BPP 297 00:17:31,720 --> 00:17:33,460 because it's supposed to be, quote, 298 00:17:33,460 --> 00:17:37,180 a "fact" that they're finding. 299 00:17:37,180 --> 00:17:41,380 We'll look at some of that data though through the lens 300 00:17:41,380 --> 00:17:43,060 of the cross-sectional distributions 301 00:17:43,060 --> 00:17:44,680 when we get to Deaton and Paxson. 302 00:17:44,680 --> 00:17:47,980 And then you'll kind of see something else. 303 00:17:47,980 --> 00:17:52,510 And I haven't thought about how to reconcile that yet. 304 00:17:52,510 --> 00:17:57,580 So what I said about the reliability, when they simulate 305 00:17:57,580 --> 00:17:59,680 and use the data from the model, it's 306 00:17:59,680 --> 00:18:03,850 fine for the transitory shocks, largely. 307 00:18:03,850 --> 00:18:06,430 But it tends to underestimate the true coefficient 308 00:18:06,430 --> 00:18:09,550 for the permanent shocks. 309 00:18:09,550 --> 00:18:12,490 That's actually making this situation worse 310 00:18:12,490 --> 00:18:14,980 because then the BPP measure, which 311 00:18:14,980 --> 00:18:16,930 shows good insurance for the permanent shocks, 312 00:18:16,930 --> 00:18:21,550 is a lower bound estimate of the actual insurance in the data, 313 00:18:21,550 --> 00:18:23,310 so there's an even greater divergence. 314 00:18:23,310 --> 00:18:23,837 Yes? 315 00:18:23,837 --> 00:18:25,670 AUDIENCE: Can I just make sure I understood? 316 00:18:25,670 --> 00:18:29,520 So in the data, we see changes in how 317 00:18:29,520 --> 00:18:31,275 I smoothed over the lifecycle. 318 00:18:31,275 --> 00:18:33,810 But in the model, we don't see any changes? 319 00:18:33,810 --> 00:18:35,280 Or have I got it wrong way around? 320 00:18:35,280 --> 00:18:37,530 ROBERT TOWNSEND: No, it's almost the other way around. 321 00:18:37,530 --> 00:18:38,420 AUDIENCE: Right. 322 00:18:38,420 --> 00:18:40,850 So the model we see it as [? profile, ?] but in real life 323 00:18:40,850 --> 00:18:41,450 we don't see-- 324 00:18:41,450 --> 00:18:43,543 ROBERT TOWNSEND: Yeah. 325 00:18:43,543 --> 00:18:45,960 AUDIENCE: So that seems kind of counterintuitive, I guess, 326 00:18:45,960 --> 00:18:46,640 to us. 327 00:18:46,640 --> 00:18:51,063 Wouldn't we expect-- maybe I'm thinking of a different method. 328 00:18:51,063 --> 00:18:52,980 ROBERT TOWNSEND: Yeah, the problem is taking-- 329 00:18:57,190 --> 00:19:00,810 the model is generating differences 330 00:19:00,810 --> 00:19:03,610 by age because of the life cycle. 331 00:19:03,610 --> 00:19:06,720 But the data does not show that. 332 00:19:06,720 --> 00:19:12,540 So that's why you get this sort of odd-looking statement 333 00:19:12,540 --> 00:19:15,600 that looks like it's more criticism of the model. 334 00:19:15,600 --> 00:19:18,710 But it's of the model relative to the flat data. 335 00:19:18,710 --> 00:19:21,030 AUDIENCE: Yeah, once we [INAUDIBLE].. 336 00:19:21,030 --> 00:19:22,680 ROBERT TOWNSEND: Someone once said, 337 00:19:22,680 --> 00:19:24,960 if the data don't fit the model, it 338 00:19:24,960 --> 00:19:26,550 must be something wrong with the data. 339 00:19:30,090 --> 00:19:32,190 So we're feeling at pressure here. 340 00:19:35,340 --> 00:19:36,090 I didn't say that. 341 00:19:42,730 --> 00:19:47,200 How can you get more smoothing to generate 342 00:19:47,200 --> 00:19:55,395 less sensitivity of consumption to these permanent shocks? 343 00:19:59,940 --> 00:20:03,310 Because again, there's-- it seemed to get turned around 344 00:20:03,310 --> 00:20:04,420 so easily. 345 00:20:04,420 --> 00:20:07,310 There's more smoothing in the data than in the models. 346 00:20:07,310 --> 00:20:10,480 So you want the model to allow more smoothing to catch up 347 00:20:10,480 --> 00:20:12,020 to the data. 348 00:20:12,020 --> 00:20:15,640 And one thing you could do is give households 349 00:20:15,640 --> 00:20:18,710 a little more information about the future. 350 00:20:18,710 --> 00:20:19,720 And then the idea-- 351 00:20:19,720 --> 00:20:20,830 it's a smoothing model. 352 00:20:20,830 --> 00:20:23,680 So if they know things are going to get better or worse, 353 00:20:23,680 --> 00:20:27,790 they can take actions now and adjust consumption. 354 00:20:27,790 --> 00:20:30,430 So the overall profile that would result 355 00:20:30,430 --> 00:20:34,630 would be smoother if they could anticipate future income, 356 00:20:34,630 --> 00:20:42,610 rather than having to react to sudden information. 357 00:20:42,610 --> 00:20:46,930 And a close cousin of that is to move away 358 00:20:46,930 --> 00:20:54,010 from some random walk, to put in some serially correlated income 359 00:20:54,010 --> 00:20:55,690 process. 360 00:20:55,690 --> 00:20:58,660 And that, actually, does a better job 361 00:20:58,660 --> 00:21:02,300 in getting the model to match the data. 362 00:21:07,180 --> 00:21:12,010 As I said, so far in this class, we haven't talked too, too much 363 00:21:12,010 --> 00:21:15,890 about these income processes. 364 00:21:15,890 --> 00:21:20,030 But it's really front and center here. 365 00:21:20,030 --> 00:21:23,760 What you assume about an income process, is it IID? 366 00:21:23,760 --> 00:21:26,780 Is it autoregressive, for that matter, 367 00:21:26,780 --> 00:21:27,980 with high frequency data? 368 00:21:27,980 --> 00:21:30,590 What about the seasonality and everything? 369 00:21:34,190 --> 00:21:37,920 That makes you aware of both the great strength 370 00:21:37,920 --> 00:21:40,770 and vulnerability of the risk-sharing model, which 371 00:21:40,770 --> 00:21:45,270 says it doesn't matter what time it is or what state it is. 372 00:21:45,270 --> 00:21:48,960 Just add up total consumption and smooth it out. 373 00:21:48,960 --> 00:21:53,040 There's a fixed static rule for allocating risk. 374 00:21:53,040 --> 00:21:56,550 There could be predictable periodic seasonal fluctuations 375 00:21:56,550 --> 00:21:58,530 or trends in income. 376 00:21:58,530 --> 00:22:00,780 It doesn't matter for the risk-sharing model. 377 00:22:00,780 --> 00:22:07,454 But here with incomplete models, it matters much more. 378 00:22:07,454 --> 00:22:09,835 AUDIENCE: You say that two is better than one. 379 00:22:09,835 --> 00:22:11,715 If it's AR, it's going to be better 380 00:22:11,715 --> 00:22:13,560 than predicting the future. 381 00:22:13,560 --> 00:22:19,012 But AR, to a degree, is also the ability to predict the future. 382 00:22:19,012 --> 00:22:20,720 ROBERT TOWNSEND: Yeah, it's very related. 383 00:22:20,720 --> 00:22:23,090 AUDIENCE: So there's something else from the AR 384 00:22:23,090 --> 00:22:24,585 that's making it better? 385 00:22:24,585 --> 00:22:26,460 ROBERT TOWNSEND: I guess there are other ways 386 00:22:26,460 --> 00:22:27,990 to predict the future. 387 00:22:27,990 --> 00:22:31,080 Even if the process itself is not autoregressive, 388 00:22:31,080 --> 00:22:33,850 you could get signals about what it's going to be in the future. 389 00:22:33,850 --> 00:22:35,800 AUDIENCE: That's not as good as-- 390 00:22:35,800 --> 00:22:37,800 ROBERT TOWNSEND: That's what the claim is, yeah. 391 00:22:37,800 --> 00:22:41,320 That's what they find. 392 00:22:41,320 --> 00:22:43,510 So here's the model, finally. 393 00:22:43,510 --> 00:22:45,560 There is no aggregate uncertainty. 394 00:22:48,900 --> 00:22:53,610 Agents work until retirement, but they don't die then. 395 00:22:53,610 --> 00:22:56,670 There's a probability [? z ?] of surviving. 396 00:22:59,340 --> 00:23:03,530 This is, I guess, retirement is a really bad thing 397 00:23:03,530 --> 00:23:07,000 because if you don't retire, you're 398 00:23:07,000 --> 00:23:10,000 going to live with probability 1. 399 00:23:10,000 --> 00:23:13,540 So anyway, this is a simplification. 400 00:23:16,120 --> 00:23:21,310 So they only start using these actuarial tables after age 401 00:23:21,310 --> 00:23:25,900 60 or 65, whatever they put in for retirement age. 402 00:23:25,900 --> 00:23:29,110 So it's maximizing discounted expected utility, 403 00:23:29,110 --> 00:23:31,970 common utility function. 404 00:23:31,970 --> 00:23:33,950 We've been doing a lot of that too. 405 00:23:33,950 --> 00:23:37,940 Beta is the standard discount rate. [? Z ?] is this-- 406 00:23:37,940 --> 00:23:41,270 you only get the utility if you're alive, basically. 407 00:23:41,270 --> 00:23:44,330 So that's a standard adjustment to the discount rate. 408 00:23:44,330 --> 00:23:49,860 The income process is a bit complicated. 409 00:23:49,860 --> 00:23:55,560 First of all, there is a possible nonstochastic trend, 410 00:23:55,560 --> 00:23:59,240 sort of the deterministic part, which could move income 411 00:23:59,240 --> 00:24:04,170 along with T. And then you have income, quote, "standard." 412 00:24:04,170 --> 00:24:05,690 Here's the decomposition. 413 00:24:05,690 --> 00:24:09,800 Income is equal to z, which is this permanent thing, 414 00:24:09,800 --> 00:24:13,470 in this case, entirely a random walk, and epsilon, 415 00:24:13,470 --> 00:24:18,170 which is the IID transitory shock. 416 00:24:18,170 --> 00:24:21,410 So these papers use different notation. 417 00:24:21,410 --> 00:24:25,530 And this paper, z, is permanent, and epsilon is transitory. 418 00:24:25,530 --> 00:24:27,110 And eta is another shock. 419 00:24:27,110 --> 00:24:29,930 And that's the shock to permanent income, basically. 420 00:24:33,780 --> 00:24:38,320 So in expectation, you expect your income to be what it was. 421 00:24:38,320 --> 00:24:40,240 You expect the permanent part of your income 422 00:24:40,240 --> 00:24:42,790 to be exactly what it was last period. 423 00:24:42,790 --> 00:24:48,600 But this thing will move that around. 424 00:24:48,600 --> 00:24:50,820 And then these have variances-- 425 00:24:50,820 --> 00:24:54,140 sigma eta, sigma epsilon. 426 00:24:54,140 --> 00:24:59,670 The budget constraint, again, is like this bond, which you may 427 00:24:59,670 --> 00:25:02,190 or may not be able to short. 428 00:25:02,190 --> 00:25:07,730 So you've got your assets from last period. 429 00:25:07,730 --> 00:25:11,240 That's earning interest, plus your income. 430 00:25:11,240 --> 00:25:14,510 So this is like your disposable income, 431 00:25:14,510 --> 00:25:18,100 which you can spend on consumption and assets, 432 00:25:18,100 --> 00:25:20,290 going forward. 433 00:25:20,290 --> 00:25:21,280 Watch the subscript. 434 00:25:21,280 --> 00:25:22,330 It'll drive you crazy. 435 00:25:22,330 --> 00:25:24,220 It does me. 436 00:25:24,220 --> 00:25:28,360 This is dated t plus 1. 437 00:25:28,360 --> 00:25:31,210 But it's decided on a t, and consumption is also 438 00:25:31,210 --> 00:25:32,770 decided on a t. 439 00:25:32,770 --> 00:25:34,270 So in some of these formulas, you're 440 00:25:34,270 --> 00:25:37,330 going to see a mysterious interest rate adjustment. 441 00:25:37,330 --> 00:25:43,630 And it has to do with this sort of convention of the timing. 442 00:25:43,630 --> 00:25:46,840 This looks the same, except as I said, 443 00:25:46,840 --> 00:25:50,120 it's like a pension fund in your assets. 444 00:25:50,120 --> 00:25:52,495 So effectively, this gets adjusted. 445 00:25:55,060 --> 00:25:59,590 It's not like everyone has their own individual retirement 446 00:25:59,590 --> 00:26:02,410 account, which you draw down. 447 00:26:02,410 --> 00:26:04,600 There's a pool of money there. 448 00:26:04,600 --> 00:26:08,330 Some people continue to live, and some don't. 449 00:26:08,330 --> 00:26:12,280 And so those-- in other words, if you're, quote, "lucky," 450 00:26:12,280 --> 00:26:14,080 and you keep living, you could actually 451 00:26:14,080 --> 00:26:18,730 draw more from the fund than what you put in there. 452 00:26:18,730 --> 00:26:21,895 And this is a very convenient way to kind of adjust. 453 00:26:26,280 --> 00:26:30,510 Oh, and if you're retired you get your social security 454 00:26:30,510 --> 00:26:32,940 benefits. 455 00:26:32,940 --> 00:26:35,400 They're going to put some numbers in here 456 00:26:35,400 --> 00:26:39,480 from the life cycle literature and other sources, 457 00:26:39,480 --> 00:26:42,480 using various US data sets. 458 00:26:42,480 --> 00:26:45,490 And I'm not going to dwell on the numbers. 459 00:26:45,490 --> 00:26:51,050 But this is a classic picture of the life cycle. 460 00:26:51,050 --> 00:26:56,940 So here are the earnings going up. 461 00:26:56,940 --> 00:27:02,370 You guys are down here somewhere, on average. 462 00:27:02,370 --> 00:27:06,780 You can expect to do better eventually. 463 00:27:06,780 --> 00:27:10,800 And then you get to be 60, and it doesn't go to zero. 464 00:27:10,800 --> 00:27:14,490 That's if you were a US citizen, that's where you start drawing. 465 00:27:14,490 --> 00:27:17,070 Actually, you could just be an immigrant. 466 00:27:17,070 --> 00:27:22,080 You start drawing social security benefits. 467 00:27:22,080 --> 00:27:29,310 With this profile, you try to keep consumption steady. 468 00:27:29,310 --> 00:27:30,690 It's not completely flat. 469 00:27:30,690 --> 00:27:32,760 It just looks flat relative to everything else 470 00:27:32,760 --> 00:27:33,570 on this diagram. 471 00:27:33,570 --> 00:27:36,810 It's actually increasing somewhat. 472 00:27:36,810 --> 00:27:41,082 But the goal of the life cycle smoothing 473 00:27:41,082 --> 00:27:44,340 is to try to have more or less steady consumption. 474 00:27:47,940 --> 00:27:51,270 Again, this is-- there are two lines here. 475 00:27:51,270 --> 00:27:53,995 There's a natural borrowing constraint and zero borrowing 476 00:27:53,995 --> 00:27:54,495 constraint. 477 00:27:54,495 --> 00:27:57,270 It doesn't make too much different for consumption. 478 00:28:01,510 --> 00:28:04,080 I guess here the zero borrowing constraint 479 00:28:04,080 --> 00:28:05,790 looks more constraining. 480 00:28:05,790 --> 00:28:09,510 So when you're young, expecting on average higher 481 00:28:09,510 --> 00:28:13,110 future income, you might want to borrow against that 482 00:28:13,110 --> 00:28:15,240 and repay the debt later. 483 00:28:15,240 --> 00:28:17,760 But you hit one or the other of these constraints, 484 00:28:17,760 --> 00:28:19,710 so you can't do that too much. 485 00:28:19,710 --> 00:28:28,030 Of course, the gorilla in the room is this wealth profile. 486 00:28:28,030 --> 00:28:31,320 And that's where all the action is, basically. 487 00:28:31,320 --> 00:28:35,910 In fact, you're basically over the life cycle, 488 00:28:35,910 --> 00:28:40,608 accumulating and then deaccumulating wealth. 489 00:28:40,608 --> 00:28:43,085 That's what's keeping consumption steady. 490 00:28:43,085 --> 00:28:45,660 And remember, when income goes to virtually zero, 491 00:28:45,660 --> 00:28:47,190 apart from social security, you've 492 00:28:47,190 --> 00:28:49,020 got to live off the interest in your-- 493 00:28:51,990 --> 00:28:56,700 you have social security, plus the adjusted actuarial interest 494 00:28:56,700 --> 00:28:57,840 off the pension fund. 495 00:28:57,840 --> 00:29:01,500 And that's typically a lot smaller flow 496 00:29:01,500 --> 00:29:04,230 than was your previous income. 497 00:29:04,230 --> 00:29:07,650 So you need a ton of assets to be 498 00:29:07,650 --> 00:29:10,770 able to survive into old age. 499 00:29:10,770 --> 00:29:13,785 This is drawn out, looks like to 90 something, 95. 500 00:29:23,390 --> 00:29:24,770 That could have been shown first, 501 00:29:24,770 --> 00:29:28,250 but that's kind of a summary of the life cycle model 502 00:29:28,250 --> 00:29:31,940 and what Kaplan and Violante are doing, 503 00:29:31,940 --> 00:29:38,450 and they're generating these smoothing statistics from date 504 00:29:38,450 --> 00:29:40,010 by date with shocks. 505 00:29:40,010 --> 00:29:43,730 But this is the overall pattern you would see. 506 00:29:43,730 --> 00:29:48,560 Let's go to Deaton and Paxson for a very different look at it 507 00:29:48,560 --> 00:29:53,580 through the lens of these cross sections. 508 00:29:53,580 --> 00:29:56,450 The starting point, again, is that with a permanent income 509 00:29:56,450 --> 00:29:59,480 hypothesis, consumption of each person 510 00:29:59,480 --> 00:30:04,820 should basically follow a random walk. 511 00:30:04,820 --> 00:30:09,650 Again, the idea is you should basically 512 00:30:09,650 --> 00:30:12,035 be eating at the level of your permanent income. 513 00:30:14,690 --> 00:30:16,880 And when you're permanent income is shock, 514 00:30:16,880 --> 00:30:18,290 then your consumption is shock. 515 00:30:25,090 --> 00:30:27,100 But the implication that consumption 516 00:30:27,100 --> 00:30:31,510 follows a random walk means, basically, you'll 517 00:30:31,510 --> 00:30:34,150 see the equations for it. 518 00:30:34,150 --> 00:30:37,330 Date by date by date, you get hit 519 00:30:37,330 --> 00:30:41,110 with positive or negative shocks and their IID. 520 00:30:41,110 --> 00:30:44,230 So basically, some people have their ups 521 00:30:44,230 --> 00:30:46,510 and other people have their downs. 522 00:30:46,510 --> 00:30:49,290 So you start getting this fanning out. 523 00:30:49,290 --> 00:30:51,880 And then you go-- then you take the cohort that is still all 524 00:30:51,880 --> 00:30:52,690 alike. 525 00:30:52,690 --> 00:30:54,220 Go one more period. 526 00:30:54,220 --> 00:30:55,510 They have ups and downs. 527 00:30:55,510 --> 00:30:57,580 Those guys fan out a bit. 528 00:30:57,580 --> 00:31:00,520 So the cross-sectional distribution 529 00:31:00,520 --> 00:31:02,350 just keeps getting fatter and fatter 530 00:31:02,350 --> 00:31:04,300 with bigger and bigger tails. 531 00:31:06,820 --> 00:31:10,660 So all of the slides, basically, are 532 00:31:10,660 --> 00:31:15,190 going to be about this increasing consumption 533 00:31:15,190 --> 00:31:17,065 inequality in the cross-section. 534 00:31:17,065 --> 00:31:20,560 They measure it by the standard deviation 535 00:31:20,560 --> 00:31:24,610 of the log of consumption, age group by age group. 536 00:31:28,690 --> 00:31:34,750 But again, if you thought about full risk-sharing, 537 00:31:34,750 --> 00:31:37,650 you get this dramatic contrast. 538 00:31:37,650 --> 00:31:41,340 At least for the cases where people have uniform risk 539 00:31:41,340 --> 00:31:45,030 aversion and so on, then we know that what pins down 540 00:31:45,030 --> 00:31:47,880 the level of your consumption, on average, is 541 00:31:47,880 --> 00:31:49,710 going to be your Pareto weight. 542 00:31:49,710 --> 00:31:53,310 And you kind of have those fixed at t equals 0. 543 00:31:53,310 --> 00:31:55,800 That's going to fix the intercepts. 544 00:31:55,800 --> 00:31:59,220 And your consumption might fluctuate with aggregate shocks 545 00:31:59,220 --> 00:32:01,680 around that, but it's not going to move 546 00:32:01,680 --> 00:32:04,060 with age or anything else. 547 00:32:04,060 --> 00:32:06,030 So basically, the cross-sectional dispersion 548 00:32:06,030 --> 00:32:10,930 of consumption does not increase in the full risk-sharing model. 549 00:32:10,930 --> 00:32:15,270 But you will see that in the data, depending on the country, 550 00:32:15,270 --> 00:32:15,980 it does happen. 551 00:32:23,220 --> 00:32:27,930 You have to be a little mindful of going back and forth 552 00:32:27,930 --> 00:32:33,090 between this cross-sectional age-dependent inequality, 553 00:32:33,090 --> 00:32:38,470 and inequality for the economy as a whole, 554 00:32:38,470 --> 00:32:40,810 because demographics can shift. 555 00:32:40,810 --> 00:32:44,650 Even if you give me someone's age, 556 00:32:44,650 --> 00:32:47,560 and I'll tell you sort of what the cross-sectional dispersion 557 00:32:47,560 --> 00:32:51,015 is in the population, when you have demographics going on, 558 00:32:51,015 --> 00:32:52,390 you may have an increasing number 559 00:32:52,390 --> 00:32:57,380 of young people or old people, depending on the economy. 560 00:32:57,380 --> 00:33:01,690 So you're basically taking an age-weighted average 561 00:33:01,690 --> 00:33:05,560 as the demographics shift, and that will shift inequality. 562 00:33:05,560 --> 00:33:07,000 So an issue in this literature is 563 00:33:07,000 --> 00:33:08,950 how much of aggregate inequality can 564 00:33:08,950 --> 00:33:13,780 be explained by these kinds of life cycle smoothing 565 00:33:13,780 --> 00:33:18,820 considerations, and how much by baby booms 566 00:33:18,820 --> 00:33:21,700 versus fertility drops and all of that. 567 00:33:27,570 --> 00:33:33,250 So this is kind of nice because they have the US, Britain, 568 00:33:33,250 --> 00:33:37,360 and cross sections, which are three countries that 569 00:33:37,360 --> 00:33:43,180 have a quite ample amount of cross-sectional consumption, 570 00:33:43,180 --> 00:33:46,840 for that matter, also, income data. 571 00:33:46,840 --> 00:33:50,980 They're going to use 47 annual surveys spread out 572 00:33:50,980 --> 00:33:54,350 over the three countries and look 573 00:33:54,350 --> 00:33:59,450 at the implications of these models for the kind 574 00:33:59,450 --> 00:34:02,000 of cross-sectional inequality and see 575 00:34:02,000 --> 00:34:04,580 what it takes to explain it. 576 00:34:04,580 --> 00:34:06,875 So how does this work exactly? 577 00:34:10,300 --> 00:34:13,210 So we want to follow cohorts over time. 578 00:34:13,210 --> 00:34:17,230 We cannot follow an individual person over time, 579 00:34:17,230 --> 00:34:20,230 because it's not panel data. 580 00:34:20,230 --> 00:34:24,920 But you make the assumption that, for example, 581 00:34:24,920 --> 00:34:33,179 if you see a bunch of 31-year-olds in 1976 in Taiwan, 582 00:34:33,179 --> 00:34:35,310 you're getting a good summary statistic 583 00:34:35,310 --> 00:34:36,840 of the cross-sectional dispersion 584 00:34:36,840 --> 00:34:39,150 of their consumption in 1976. 585 00:34:39,150 --> 00:34:43,230 And then you go to 1977, and they are now 32. 586 00:34:43,230 --> 00:34:45,060 Actually, "they" isn't quite correct, 587 00:34:45,060 --> 00:34:47,370 because it's a different set of people. 588 00:34:47,370 --> 00:34:50,850 But again, you hope you have enough of them 589 00:34:50,850 --> 00:34:55,170 and that the basic assumptions are correct, 590 00:34:55,170 --> 00:34:59,230 that you can take these kinds of statistics 591 00:34:59,230 --> 00:35:02,230 as representative of what you would have seen 592 00:35:02,230 --> 00:35:04,180 if you could have been able to continue 593 00:35:04,180 --> 00:35:05,950 to track the same people. 594 00:35:08,860 --> 00:35:12,672 Some people actually think this is better than panel data, 595 00:35:12,672 --> 00:35:14,380 in the sense that you don't have to worry 596 00:35:14,380 --> 00:35:16,600 about people dropping out, and the data 597 00:35:16,600 --> 00:35:18,280 becomes unrepresentative. 598 00:35:18,280 --> 00:35:21,897 And there is some truth to that. 599 00:35:21,897 --> 00:35:23,980 There are issues about whether the data are coming 600 00:35:23,980 --> 00:35:26,700 from households or individuals. 601 00:35:26,700 --> 00:35:29,590 You have to make some adjustments 602 00:35:29,590 --> 00:35:32,700 for household composition. 603 00:35:32,700 --> 00:35:35,220 And the surveys being used here are the Personal Income 604 00:35:35,220 --> 00:35:38,610 Distribution Survey in Taiwan, the Consumer Expenditure Survey 605 00:35:38,610 --> 00:35:42,000 in the US-- that's the same one we've referred to before-- 606 00:35:42,000 --> 00:35:46,080 and this Family Expenditure Survey in Great Britain. 607 00:35:46,080 --> 00:35:51,960 So it takes a bit of staring to get used to this. 608 00:35:51,960 --> 00:36:01,500 So we start out with people who are age 15 in 1976. 609 00:36:01,500 --> 00:36:06,510 And they kind of start here in calendar time, 1982 610 00:36:06,510 --> 00:36:08,520 or something like that. 611 00:36:08,520 --> 00:36:12,600 Again, we don't track the same people. 612 00:36:12,600 --> 00:36:15,450 But we can look what happens. 613 00:36:15,450 --> 00:36:18,210 This paper is not the most recent thing in the world. 614 00:36:18,210 --> 00:36:19,560 It's just a really nice one. 615 00:36:19,560 --> 00:36:23,620 So they basically stopped using data after 1990. 616 00:36:23,620 --> 00:36:28,680 So we go back to the 1976 survey, 617 00:36:28,680 --> 00:36:32,490 all the way up to the 1990 survey, with repeated cross 618 00:36:32,490 --> 00:36:34,980 sections and looking what happens to inequality 619 00:36:34,980 --> 00:36:39,700 in this cohort, as they age. 620 00:36:39,700 --> 00:36:41,325 These guys were 15. 621 00:36:41,325 --> 00:36:44,470 These guys were 20 in 1976. 622 00:36:44,470 --> 00:36:47,460 So they start older, and they're going to end a bit older. 623 00:36:47,460 --> 00:36:56,800 And then you keep going here to the aged 55 people in 1976 624 00:36:56,800 --> 00:36:59,110 and so on. 625 00:36:59,110 --> 00:37:01,270 These are pretty flat, then these profiles 626 00:37:01,270 --> 00:37:02,840 start to pick up. 627 00:37:02,840 --> 00:37:06,880 You kind of in your mind sort of can imagine. 628 00:37:06,880 --> 00:37:08,890 And I'll show you what happens when 629 00:37:08,890 --> 00:37:10,840 we splice all this together. 630 00:37:15,680 --> 00:37:18,140 AUDIENCE: It seems like a lot of the action 631 00:37:18,140 --> 00:37:20,320 is brought about by the-- 632 00:37:20,320 --> 00:37:23,930 towards those middle-aged cohorts. 633 00:37:23,930 --> 00:37:30,530 Those who start middle-aged did in '76, like, from 40 to 55. 634 00:37:30,530 --> 00:37:31,780 ROBERT TOWNSEND: Let me just-- 635 00:37:31,780 --> 00:37:34,250 AUDIENCE: The rest is kind of flat. 636 00:37:34,250 --> 00:37:37,370 ROBERT TOWNSEND: Let me just jump because I-- 637 00:37:37,370 --> 00:37:38,660 those are the three countries. 638 00:37:38,660 --> 00:37:40,280 Here's what's going to-- 639 00:37:40,280 --> 00:37:43,130 when you use all the surveys over all the years 640 00:37:43,130 --> 00:37:45,650 and just focus on the age-- 641 00:37:45,650 --> 00:37:47,690 yeah, so you see this. 642 00:37:47,690 --> 00:37:48,530 You're right. 643 00:37:48,530 --> 00:37:51,200 You see this is pretty flat, and then it 644 00:37:51,200 --> 00:37:57,233 picks up around age whatever, 45 or 50 or something. 645 00:38:01,020 --> 00:38:04,142 And these are the results from the other countries. 646 00:38:04,142 --> 00:38:06,890 AUDIENCE: So is there any explanation 647 00:38:06,890 --> 00:38:08,175 for why that's the case? 648 00:38:08,175 --> 00:38:10,947 ROBERT TOWNSEND: Yeah, we're going to get into that. 649 00:38:10,947 --> 00:38:12,030 You'll be sorry you asked. 650 00:38:15,236 --> 00:38:16,565 AUDIENCE: And only in Taiwan. 651 00:38:16,565 --> 00:38:17,440 ROBERT TOWNSEND: Huh? 652 00:38:17,440 --> 00:38:18,648 AUDIENCE: And only in Taiwan. 653 00:38:18,648 --> 00:38:20,040 The others seem to be-- 654 00:38:20,040 --> 00:38:23,730 ROBERT TOWNSEND: OK, so this is kind of flat, 655 00:38:23,730 --> 00:38:27,150 and then it kind of comes up, and then it flattens out again. 656 00:38:27,150 --> 00:38:33,210 So Taiwan is flattening out, although, unfortunately, 657 00:38:33,210 --> 00:38:35,790 the cohorts are getting thin the older they are. 658 00:38:35,790 --> 00:38:38,280 So you get some sort of shaky data 659 00:38:38,280 --> 00:38:40,950 because you can't average quite so well. 660 00:38:40,950 --> 00:38:42,840 This one flattens out. 661 00:38:42,840 --> 00:38:45,720 Great Britain kind of flattens out. 662 00:38:45,720 --> 00:38:47,580 The US, I don't know, wasn't very 663 00:38:47,580 --> 00:38:50,010 steeply climbing to begin with. 664 00:38:50,010 --> 00:38:52,200 It's not so obvious. 665 00:38:52,200 --> 00:38:55,530 This kind of looks concave. 666 00:38:55,530 --> 00:38:59,310 This looks concave but almost linear. 667 00:38:59,310 --> 00:39:03,150 This actually has almost an inflection point 668 00:39:03,150 --> 00:39:05,680 and then comes in. 669 00:39:05,680 --> 00:39:09,990 So the question is concave, convex, et cetera, 670 00:39:09,990 --> 00:39:13,870 and that's where we'll do a little modeling. 671 00:39:17,540 --> 00:39:21,980 By the way, you saw a little bit about demographics 672 00:39:21,980 --> 00:39:23,000 when we did China. 673 00:39:23,000 --> 00:39:25,710 One of those explanations of the savings rates, 674 00:39:25,710 --> 00:39:28,620 et cetera, wasn't so much about state-owned enterprise 675 00:39:28,620 --> 00:39:34,580 as it was the different demographics, and young savers 676 00:39:34,580 --> 00:39:40,880 in China, and sort of debt-loaded or less 677 00:39:40,880 --> 00:39:43,353 saving-inclined households in the US, and so different 678 00:39:43,353 --> 00:39:43,895 demographics. 679 00:39:43,895 --> 00:39:49,490 Just to remind you, it's not the first time 680 00:39:49,490 --> 00:39:51,510 that we've thought about demographics. 681 00:39:51,510 --> 00:39:55,380 So it's possible to put that-- 682 00:39:55,380 --> 00:39:58,700 there's trivial demographics in some of the macro models, 683 00:39:58,700 --> 00:40:01,490 in the sense that they start with a lifecycle model 684 00:40:01,490 --> 00:40:05,120 or two-period overlapping generations model. 685 00:40:05,120 --> 00:40:09,680 But we haven't actually focused on much 686 00:40:09,680 --> 00:40:12,545 of this in the sort of micro part of the class. 687 00:40:16,280 --> 00:40:18,800 So this is what I said in words. 688 00:40:18,800 --> 00:40:20,990 They claim Britain is slightly convex. 689 00:40:20,990 --> 00:40:22,340 I didn't see that just now. 690 00:40:29,930 --> 00:40:33,380 And again, don't misread those things 691 00:40:33,380 --> 00:40:36,530 to be measures of the total increases 692 00:40:36,530 --> 00:40:38,450 or decreases in inequality, because 693 00:40:38,450 --> 00:40:43,340 the demographic structure is moving around by age 694 00:40:43,340 --> 00:40:46,340 over those 20 or so years. 695 00:40:50,270 --> 00:40:51,530 Let's start with the basics. 696 00:40:51,530 --> 00:40:58,330 Here is basically Hall's permanent income implication 697 00:40:58,330 --> 00:41:00,070 for consumption. 698 00:41:00,070 --> 00:41:04,990 Consumption should essentially be a random walk. 699 00:41:04,990 --> 00:41:06,640 And it's only moving around because 700 00:41:06,640 --> 00:41:11,830 of the innovations or the shock to permanent income. 701 00:41:11,830 --> 00:41:15,700 I think that was [? JPE, ?] 1970. 702 00:41:15,700 --> 00:41:19,330 The dates here, I think it was in the [? JPE. ?] 703 00:41:19,330 --> 00:41:20,320 There are assumptions. 704 00:41:20,320 --> 00:41:23,170 This isn't always true. 705 00:41:23,170 --> 00:41:29,110 He assumed quadratic utility, additive preferences, 706 00:41:29,110 --> 00:41:35,640 discount rates equal to interest rates, and, I think, 707 00:41:35,640 --> 00:41:38,100 another life cycle. 708 00:41:38,100 --> 00:41:39,900 This is supposed to be an innovation, 709 00:41:39,900 --> 00:41:47,610 so for every person at least, there's 710 00:41:47,610 --> 00:41:50,760 no covariance between lagged consumption 711 00:41:50,760 --> 00:41:52,470 and this innovation, because it wasn't 712 00:41:52,470 --> 00:41:54,460 supposed to be predictable. 713 00:41:54,460 --> 00:41:57,750 That's the same conversation, just how much, if anything, 714 00:41:57,750 --> 00:41:59,360 you see about the future. 715 00:41:59,360 --> 00:42:02,250 Here, zero is seen. 716 00:42:02,250 --> 00:42:05,130 So I described this in words. 717 00:42:05,130 --> 00:42:10,830 But basically, if it were stable like this on average, 718 00:42:10,830 --> 00:42:15,670 then consumption dispersion shouldn't be changing. 719 00:42:15,670 --> 00:42:18,670 But you're just layering on repeatedly, 720 00:42:18,670 --> 00:42:21,100 shock after shock after shock. 721 00:42:21,100 --> 00:42:24,800 So with that zero covariance assumption, 722 00:42:24,800 --> 00:42:28,270 the variances are increasing by the variance of that [? u ?] 723 00:42:28,270 --> 00:42:29,200 t shock. 724 00:42:39,700 --> 00:42:44,980 And basically, if you started plotting these distributions, 725 00:42:44,980 --> 00:42:47,230 the one at t is going to have fatter tails 726 00:42:47,230 --> 00:42:49,660 than the one at t minus 1. 727 00:42:49,660 --> 00:42:53,950 So t minus 1, [? quotient, ?] first order stochastically 728 00:42:53,950 --> 00:42:54,730 dominates. 729 00:43:00,680 --> 00:43:03,000 You have to be a little bit careful throughout all 730 00:43:03,000 --> 00:43:04,920 of this stuff. 731 00:43:04,920 --> 00:43:06,750 You think about things in the point 732 00:43:06,750 --> 00:43:09,780 of view of a person tracking a person over time. 733 00:43:09,780 --> 00:43:12,540 But that statement about c t and [? u t ?] 734 00:43:12,540 --> 00:43:17,310 is actually a statement about the cross section, as well as 735 00:43:17,310 --> 00:43:19,240 the intertemporal dimension. 736 00:43:29,460 --> 00:43:32,340 This model typically didn't have taste shifters 737 00:43:32,340 --> 00:43:35,310 or heterogeneous preferences. 738 00:43:35,310 --> 00:43:37,440 You can put those things in. 739 00:43:37,440 --> 00:43:41,630 Depending on how you put them in, it does make a difference. 740 00:43:41,630 --> 00:43:45,010 Arguably, if we hadn't done the demographics right, 741 00:43:45,010 --> 00:43:46,590 but they claim-- 742 00:43:46,590 --> 00:43:50,060 Deaton and Paxson claim for Taiwan, 743 00:43:50,060 --> 00:43:54,530 then you kind of need preference shocks to help 744 00:43:54,530 --> 00:43:56,090 with the observed dispersion. 745 00:44:02,190 --> 00:44:05,125 Here is the basic sort of budget equation again. 746 00:44:14,770 --> 00:44:16,460 And I'm afraid each one of these papers 747 00:44:16,460 --> 00:44:19,080 kind of has a different convention about the timing. 748 00:44:19,080 --> 00:44:23,610 So it's really kind of hard to keep tracking and track it. 749 00:44:23,610 --> 00:44:31,170 But basically, you have sources and uses of money. 750 00:44:31,170 --> 00:44:34,640 The sources are previous assets plus interest. 751 00:44:34,640 --> 00:44:37,560 The uses are-- source also is income, 752 00:44:37,560 --> 00:44:38,890 and the use is consumption. 753 00:44:38,890 --> 00:44:42,800 And then what you don't spend accumulates on 754 00:44:42,800 --> 00:44:45,000 to the next period. 755 00:44:45,000 --> 00:44:52,880 If you do do the life cycle with a terminal date, for sure, 756 00:44:52,880 --> 00:44:58,900 say, age 99 or whatever you want, 757 00:44:58,900 --> 00:45:03,190 then you can actually get a formula closed form 758 00:45:03,190 --> 00:45:07,400 for consumption, under these other maintained assumptions. 759 00:45:07,400 --> 00:45:12,760 And basically, it's kind of saying, 760 00:45:12,760 --> 00:45:15,790 consumption ought to equal something about the return 761 00:45:15,790 --> 00:45:19,060 stream through the interest rate on assets, 762 00:45:19,060 --> 00:45:23,230 and something about the forward-looking part, which is 763 00:45:23,230 --> 00:45:25,900 expected future income shocks. 764 00:45:25,900 --> 00:45:33,640 So this kind of helps you see how future things are already-- 765 00:45:33,640 --> 00:45:35,140 if this is going to be very high, 766 00:45:35,140 --> 00:45:38,800 for example, then this is already going up. 767 00:45:38,800 --> 00:45:40,900 So it's kind of smooth against-- 768 00:45:40,900 --> 00:45:43,750 or low, vise versa. 769 00:45:43,750 --> 00:45:46,510 It's tricky with a finite horizon and a cap t 770 00:45:46,510 --> 00:45:51,520 because there is a coefficient premultiplying this, 771 00:45:51,520 --> 00:45:53,410 but it's for that reason, basically. 772 00:45:53,410 --> 00:45:59,320 Obviously, the closer you are to the end to cap t, 773 00:45:59,320 --> 00:46:01,090 the less smoothing you can accomplish. 774 00:46:01,090 --> 00:46:04,480 And that's inherited into this formula. 775 00:46:06,990 --> 00:46:07,490 Yep? 776 00:46:07,490 --> 00:46:10,175 AUDIENCE: The shocks here are IID all the time? 777 00:46:10,175 --> 00:46:11,050 ROBERT TOWNSEND: Yes. 778 00:46:14,090 --> 00:46:19,455 Well, the shock to permanent income is IID. 779 00:46:22,460 --> 00:46:25,240 But permanent income is an autoregressive process. 780 00:46:34,560 --> 00:46:37,695 The standard incomplete markets model had an infinite horizon. 781 00:46:37,695 --> 00:46:39,900 And it had a discount rate equal to 1, 782 00:46:39,900 --> 00:46:46,025 or basically beta times 1 plus r equals 1. 783 00:46:46,025 --> 00:46:48,390 In the finite horizon case, beta, 784 00:46:48,390 --> 00:46:51,540 that thing premultiplying consumption, 785 00:46:51,540 --> 00:46:56,160 turns out if you stare at it, is concave. 786 00:46:56,160 --> 00:47:00,610 We're already beginning to anticipate these formulas 787 00:47:00,610 --> 00:47:02,940 and decreasing in t. 788 00:47:02,940 --> 00:47:05,310 And if you go back to those two equations, 789 00:47:05,310 --> 00:47:08,050 you'll get kind of a simplified version, 790 00:47:08,050 --> 00:47:11,190 that beta t times the change in consumption 791 00:47:11,190 --> 00:47:17,730 is equal to this, quote, "consumption innovation." 792 00:47:17,730 --> 00:47:20,410 And here's a formula for the consumption innovation, 793 00:47:20,410 --> 00:47:27,620 which is, again, the difference in expectation. 794 00:47:27,620 --> 00:47:31,650 So you're forecasting the future all the time. 795 00:47:31,650 --> 00:47:34,480 But you're also getting these shocks. 796 00:47:34,480 --> 00:47:42,170 So as of t and t minus 1, you were forecasting y t 797 00:47:42,170 --> 00:47:43,400 at t plus k. 798 00:47:43,400 --> 00:47:48,710 Sorry, y of t plus k, not either to either, to t or t minus 1. 799 00:47:48,710 --> 00:47:50,360 It could be 10 years out. 800 00:47:50,360 --> 00:47:54,080 And you're constantly adjusting your expectations, 801 00:47:54,080 --> 00:47:55,940 based on the current information you 802 00:47:55,940 --> 00:47:57,500 have from the income process. 803 00:47:57,500 --> 00:47:59,900 And you're summing up over all those future income 804 00:47:59,900 --> 00:48:06,380 shocks and discounting backwards to get 805 00:48:06,380 --> 00:48:08,600 these, quote, "innovations." 806 00:48:11,390 --> 00:48:16,700 So then imagine starting this out at some date t 807 00:48:16,700 --> 00:48:22,340 equals 0, and then t equals 1, and t equals 2, and so on. 808 00:48:22,340 --> 00:48:24,650 And you could just write out, literally, 809 00:48:24,650 --> 00:48:26,300 consumption in each one of those dates. 810 00:48:29,310 --> 00:48:32,930 And of course, when you go from one date to another, 811 00:48:32,930 --> 00:48:34,730 you get hit with this shock. 812 00:48:34,730 --> 00:48:37,430 And you're premultiplying by the beta, 813 00:48:37,430 --> 00:48:42,140 so you end up with this, an explicit formula 814 00:48:42,140 --> 00:48:46,220 for consumption equal to its initial given level. 815 00:48:46,220 --> 00:48:49,160 Plus, the beta moves on the right-hand side, 816 00:48:49,160 --> 00:48:51,410 this sort of beta discounted. 817 00:48:51,410 --> 00:48:54,260 But it's not beta in the preference function. 818 00:48:54,260 --> 00:48:58,040 This is that beta thing that had to do with little t, 819 00:48:58,040 --> 00:49:00,350 big T, and all of that, that took 820 00:49:00,350 --> 00:49:03,010 care of the lifecycle considerations. 821 00:49:06,140 --> 00:49:09,910 So finally, we see again the familiar theme 822 00:49:09,910 --> 00:49:14,170 that the variance at t is related 823 00:49:14,170 --> 00:49:17,170 to the initial cross-sectional variance at zero, 824 00:49:17,170 --> 00:49:21,250 plus the sum of variance terms. 825 00:49:24,490 --> 00:49:28,000 So the issue-- so roughly speaking, 826 00:49:28,000 --> 00:49:32,470 it looks like, yeah, it ought to increase-- unless you retire 827 00:49:32,470 --> 00:49:34,680 and you have no more things then forecast, 828 00:49:34,680 --> 00:49:37,120 then this piece goes away. 829 00:49:37,120 --> 00:49:41,910 But before that happens, you're looking at future 830 00:49:41,910 --> 00:49:44,920 and making expectations of future income. 831 00:49:44,920 --> 00:49:48,120 So you just keep adding on. 832 00:49:48,120 --> 00:49:51,000 So that's why inequality is increasing in the data, 833 00:49:51,000 --> 00:49:53,010 through the lens of these models. 834 00:49:53,010 --> 00:50:00,030 And then the issue is, is it linear or concave or convex? 835 00:50:00,030 --> 00:50:01,980 That has to do with this beta and also 836 00:50:01,980 --> 00:50:08,690 has to do with what we can infer about sigma, 837 00:50:08,690 --> 00:50:10,550 about the consumption innovations. 838 00:50:19,070 --> 00:50:24,100 So in response to your question, if we 839 00:50:24,100 --> 00:50:27,130 assume this innovation is entirely 840 00:50:27,130 --> 00:50:32,050 white noise, normalized by the interest rate, 841 00:50:32,050 --> 00:50:35,560 then sigma square eta at t is a constant 842 00:50:35,560 --> 00:50:37,000 that doesn't depend on t. 843 00:50:37,000 --> 00:50:41,470 And this is the resulting expression 844 00:50:41,470 --> 00:50:43,700 with the sigma square eta pulled out front. 845 00:50:43,700 --> 00:50:49,030 And then the convexity is entirely 846 00:50:49,030 --> 00:50:52,720 due to this beta thing, which if you 847 00:50:52,720 --> 00:50:57,130 start taking some derivatives and so on, it's a bit messy. 848 00:50:57,130 --> 00:51:01,930 You can convince yourself that that thing is convex. 849 00:51:01,930 --> 00:51:04,710 Here's an orthogonal example. 850 00:51:04,710 --> 00:51:06,460 I guess, [? Jan, ?] I jumped the gun a bit 851 00:51:06,460 --> 00:51:08,800 because this actually allows something a bit 852 00:51:08,800 --> 00:51:13,180 different, which is this autoregressive thing. 853 00:51:13,180 --> 00:51:15,430 This is IID, and then this is autoregressive, 854 00:51:15,430 --> 00:51:20,260 so this income process is persistent. 855 00:51:27,470 --> 00:51:31,760 It's a bit odd because this was the innovation that had 856 00:51:31,760 --> 00:51:38,210 to do with the innovation to-- 857 00:51:38,210 --> 00:51:40,970 the right-hand side had to do with all those expectation 858 00:51:40,970 --> 00:51:41,640 differences. 859 00:51:41,640 --> 00:51:44,640 So it's like, let's just assume it looks something like this. 860 00:51:44,640 --> 00:51:48,020 This is more explicit about the income process. 861 00:51:48,020 --> 00:51:50,750 And you can derive the formula for the change 862 00:51:50,750 --> 00:51:55,210 in consumption, where this beta r thing is now this mess. 863 00:51:57,920 --> 00:52:05,330 And it turns out, this will be concave 864 00:52:05,330 --> 00:52:08,320 if you can sign this expression. 865 00:52:08,320 --> 00:52:11,480 And it may also be decreasing in age 866 00:52:11,480 --> 00:52:16,580 if this is true, and so actually, except for some days 867 00:52:16,580 --> 00:52:17,780 of theta, both things-- 868 00:52:23,380 --> 00:52:26,050 So two of those three countries, the profile 869 00:52:26,050 --> 00:52:28,450 was, say, not concave. 870 00:52:28,450 --> 00:52:31,750 It could have been linear, which is a weak case of concavity, 871 00:52:31,750 --> 00:52:33,580 or even convex. 872 00:52:33,580 --> 00:52:37,240 And so basically, then you could rule this out 873 00:52:37,240 --> 00:52:38,770 because these are-- 874 00:52:38,770 --> 00:52:41,110 this kind of persistence would give you concavity. 875 00:52:41,110 --> 00:52:42,160 But you don't see that. 876 00:52:46,990 --> 00:52:49,870 But then we have the sort of paradox 877 00:52:49,870 --> 00:52:55,910 that something like these white noise processes 878 00:52:55,910 --> 00:52:57,680 must be closer to the truth if we're 879 00:52:57,680 --> 00:52:59,660 going to get convex profiles. 880 00:52:59,660 --> 00:53:05,090 But that's an assumption about the income process. 881 00:53:05,090 --> 00:53:09,720 And in particular, one way to get it 882 00:53:09,720 --> 00:53:14,650 is to say that there's a large stationary component to income. 883 00:53:14,650 --> 00:53:20,620 So you're not getting those innovations in your forecasts. 884 00:53:20,620 --> 00:53:24,460 And we don't see that in the data. 885 00:53:24,460 --> 00:53:27,200 Income profiles are not stationary. 886 00:53:27,200 --> 00:53:31,050 There's heavy lifecycle components. 887 00:53:38,700 --> 00:53:42,190 So nothing's perfect, I guess. 888 00:53:42,190 --> 00:53:45,100 Every model is a benchmark. 889 00:53:45,100 --> 00:53:46,810 Almost every model is going to deliver 890 00:53:46,810 --> 00:53:48,430 something that might fit well. 891 00:53:48,430 --> 00:53:52,450 Otherwise, we're probably not reading it in a journal. 892 00:53:52,450 --> 00:53:56,260 Or it may actually also generate things 893 00:53:56,260 --> 00:53:58,080 that are not consistent with the data, 894 00:53:58,080 --> 00:54:01,300 and if you're a good scholar, you're reporting that too. 895 00:54:05,790 --> 00:54:10,020 What about the permanent income and the dispersion 896 00:54:10,020 --> 00:54:10,965 of income by age? 897 00:54:16,740 --> 00:54:20,090 So again, disposable income takes 898 00:54:20,090 --> 00:54:28,300 on this form, which is sort of asset return 899 00:54:28,300 --> 00:54:30,520 stream, plus income. 900 00:54:30,520 --> 00:54:32,920 And then you use it for consumption and savings, 901 00:54:32,920 --> 00:54:36,430 adjusting for where you are in the life cycle. 902 00:54:36,430 --> 00:54:37,990 Or you could take the difference. 903 00:54:37,990 --> 00:54:40,420 Savings is the difference between income 904 00:54:40,420 --> 00:54:44,140 and this beta-adjusted consumption. 905 00:54:44,140 --> 00:54:48,710 And some of these models you can get a closed form 906 00:54:48,710 --> 00:54:53,210 expression for savings, namely the so-called Campbell's "rainy 907 00:54:53,210 --> 00:54:59,960 day," which is really kind of cool, which is you 908 00:54:59,960 --> 00:55:05,450 save enough at t to be able to cover the discounted 909 00:55:05,450 --> 00:55:10,700 shortfalls in sort of these earnings innovations. 910 00:55:14,140 --> 00:55:16,900 So you want to smooth those out. 911 00:55:16,900 --> 00:55:20,310 And you save just enough to do that in expectation. 912 00:55:24,110 --> 00:55:30,010 Anyway, so we're rewriting disposable income 913 00:55:30,010 --> 00:55:31,750 equal to the savings component. 914 00:55:31,750 --> 00:55:37,410 We already had that, less the savings-- 915 00:55:37,410 --> 00:55:39,120 plus the savings component. 916 00:55:39,120 --> 00:55:42,450 Sorry, I get confused because savings was negative. 917 00:55:42,450 --> 00:55:46,200 It used to be here, and now it's out here. 918 00:55:46,200 --> 00:55:49,170 Savings is not negative, but these innovations 919 00:55:49,170 --> 00:55:53,340 are negative because you save to cover shortfalls. 920 00:55:53,340 --> 00:55:55,170 And then you get implications here 921 00:55:55,170 --> 00:56:00,528 for if one thing is a random walk, 922 00:56:00,528 --> 00:56:02,070 and the other thing is a random walk, 923 00:56:02,070 --> 00:56:04,070 then the sum of two things that are random walks 924 00:56:04,070 --> 00:56:05,430 is also a random walk. 925 00:56:10,910 --> 00:56:16,410 So basically, savings ought to be stationary in that sense. 926 00:56:16,410 --> 00:56:18,500 And it ought to be dispersing at the rate 927 00:56:18,500 --> 00:56:21,720 that consumption is dispersing. 928 00:56:21,720 --> 00:56:23,900 And they don't see that in the data either. 929 00:56:27,760 --> 00:56:33,030 And in particular, earnings is dispersing, 930 00:56:33,030 --> 00:56:37,680 which is a point that was made on the other slide as well. 931 00:56:42,810 --> 00:56:45,890 And then finally, I guess this is 932 00:56:45,890 --> 00:56:49,550 like the fourth version of something that starts 933 00:56:49,550 --> 00:56:51,110 to look like the same thing. 934 00:56:54,320 --> 00:56:57,470 Most of those analytic expressions 935 00:56:57,470 --> 00:56:59,720 were assuming something like quadratic utility. 936 00:56:59,720 --> 00:57:03,560 That's how you managed to get this really tight reduced form 937 00:57:03,560 --> 00:57:05,480 analytic expression. 938 00:57:05,480 --> 00:57:07,910 If you don't do that, if you have constant relative risk 939 00:57:07,910 --> 00:57:12,500 aversion, for example, or a more general utility function, 940 00:57:12,500 --> 00:57:15,580 than the Euler equation basically 941 00:57:15,580 --> 00:57:23,150 is going to equate the marginal utility today to something 942 00:57:23,150 --> 00:57:24,710 like marginal utility tomorrow. 943 00:57:32,546 --> 00:57:36,030 We might say, well, where's the expectation operator? 944 00:57:36,030 --> 00:57:39,190 Instead, the shock is put over here on the right-hand side. 945 00:57:39,190 --> 00:57:42,300 So this is like an Euler equation. 946 00:57:42,300 --> 00:57:45,670 If this were 0, and the interest rate 947 00:57:45,670 --> 00:57:49,610 was equal to this delta discount rate, 948 00:57:49,610 --> 00:57:53,290 then basically the marginal utility of consumption, 949 00:57:53,290 --> 00:58:00,240 if we could deduce it, would be not going anywhere. 950 00:58:00,240 --> 00:58:04,450 It would be the same over time. 951 00:58:04,450 --> 00:58:09,490 But again, with r equal to delta, 952 00:58:09,490 --> 00:58:12,220 we kick on this extra orthogonal shock, 953 00:58:12,220 --> 00:58:15,820 which makes the marginal utility of consumption dispersing 954 00:58:15,820 --> 00:58:18,580 in the future, relative today. 955 00:58:18,580 --> 00:58:21,310 And you can even have r not equal 956 00:58:21,310 --> 00:58:25,720 to delta, as long as delta is greater than r. 957 00:58:25,720 --> 00:58:31,050 The same logic applies because you've kind of like 958 00:58:31,050 --> 00:58:35,390 amplified this thing, carrying it through to tomorrow, 959 00:58:35,390 --> 00:58:37,420 along with the u shock. 960 00:58:44,650 --> 00:58:47,430 So that's another way to get at the variance of consumption 961 00:58:47,430 --> 00:58:53,850 increasing, depending on what you assume about the utility 962 00:58:53,850 --> 00:58:55,080 function. 963 00:58:55,080 --> 00:59:03,110 Some functions, though, have a force that go the other way. 964 00:59:03,110 --> 00:59:06,650 In particular, if you're really, really into it, 965 00:59:06,650 --> 00:59:11,080 you get into third derivatives. 966 00:59:11,080 --> 00:59:15,100 But when you're really sort of cautious, 967 00:59:15,100 --> 00:59:21,200 that lambda is convex. 968 00:59:21,200 --> 00:59:25,610 So you're taking a second derivative of already 969 00:59:25,610 --> 00:59:26,650 the marginal utility. 970 00:59:26,650 --> 00:59:29,500 That's why I commented about third derivatives of utility 971 00:59:29,500 --> 00:59:30,970 functions. 972 00:59:30,970 --> 00:59:34,610 And that, if you start staring at this thing, 973 00:59:34,610 --> 00:59:40,580 can actually push you back against this dispersion 974 00:59:40,580 --> 00:59:41,854 of consumption. 975 00:59:58,160 --> 01:00:01,990 So I'm having a sense that this is going on and on. 976 01:00:01,990 --> 01:00:05,170 But the point is to take each of these different forces 977 01:00:05,170 --> 01:00:08,140 and then tell stories about what must be true in Taiwan, 978 01:00:08,140 --> 01:00:12,680 versus Britain, versus the US, to try 979 01:00:12,680 --> 01:00:18,970 to rationalize what we're seeing in the data, 980 01:00:18,970 --> 01:00:20,380 and similarly, here. 981 01:00:25,980 --> 01:00:29,220 So let's just say three words about excess smoothness. 982 01:00:33,270 --> 01:00:35,610 To repeat, the lifecycle model implies 983 01:00:35,610 --> 01:00:38,550 that shocks to permanent income should be fully incorporated 984 01:00:38,550 --> 01:00:44,150 into consumption, while innovations 985 01:00:44,150 --> 01:00:48,335 to the transitory part are not. 986 01:00:54,870 --> 01:00:57,240 Basically, all the income-- 987 01:00:57,240 --> 01:00:59,890 all the transitory income fluctuations 988 01:00:59,890 --> 01:01:03,837 should not be appearing in consumption, which actually 989 01:01:03,837 --> 01:01:05,670 is something we've talked about with regards 990 01:01:05,670 --> 01:01:07,590 to the full risk-sharing model, except there, 991 01:01:07,590 --> 01:01:10,080 we didn't make this distinction between 992 01:01:10,080 --> 01:01:11,960 transitory and permanent. 993 01:01:15,960 --> 01:01:18,750 But when they go and look at the data, 994 01:01:18,750 --> 01:01:21,280 they say, hey, consumption is too smooth. 995 01:01:21,280 --> 01:01:25,950 It doesn't react to innovations in the permanent component. 996 01:01:25,950 --> 01:01:29,505 And other people have found something similar. 997 01:01:32,450 --> 01:01:35,920 And we're inching forward to models 998 01:01:35,920 --> 01:01:38,120 where we're going to need to modify the models. 999 01:01:38,120 --> 01:01:40,120 We're going to have to introduce something else, 1000 01:01:40,120 --> 01:01:45,640 like private information, and more on that in a second. 1001 01:01:53,290 --> 01:01:54,290 Yup? 1002 01:01:54,290 --> 01:01:55,790 AUDIENCE: Why do all these assume 1003 01:01:55,790 --> 01:01:58,110 the market is incomplete? 1004 01:01:58,110 --> 01:02:01,590 So maybe just because the market is relatively complete, 1005 01:02:01,590 --> 01:02:04,698 so these [INAUDIBLE]? 1006 01:02:04,698 --> 01:02:06,490 ROBERT TOWNSEND: So that's my gut reaction. 1007 01:02:09,380 --> 01:02:15,580 Actually, so this Pavoni paper puts 1008 01:02:15,580 --> 01:02:22,280 in sort of some unobserved savings and other things. 1009 01:02:22,280 --> 01:02:24,880 And it actually comes close to the data. 1010 01:02:24,880 --> 01:02:28,930 So it isn't all the way toward full insurance, 1011 01:02:28,930 --> 01:02:33,670 but it is more full insurance than what these models imply. 1012 01:02:36,260 --> 01:02:38,440 So it's trying to reconcile the puzzle. 1013 01:02:42,350 --> 01:02:45,335 I'd like to think I'm quite agnostic. 1014 01:02:48,860 --> 01:02:52,310 In my rural [? Thai ?] data, certainly, 1015 01:02:52,310 --> 01:02:54,920 when you include other variables and not just consumption, 1016 01:02:54,920 --> 01:02:56,870 we see rejections of full risk-sharing. 1017 01:02:56,870 --> 01:02:59,000 I'm not determined to always find 1018 01:02:59,000 --> 01:03:01,160 full risk-sharing in the data. 1019 01:03:01,160 --> 01:03:05,580 But likewise, I would hope these guys aren't clinging 1020 01:03:05,580 --> 01:03:08,430 to the permanent income model as the only game in town, 1021 01:03:08,430 --> 01:03:11,700 because it's clearly also suffering 1022 01:03:11,700 --> 01:03:17,370 from its own sort of anomalies, relative to the data. 1023 01:03:19,927 --> 01:03:21,510 And there's no reason to think that it 1024 01:03:21,510 --> 01:03:28,095 has to be this same model for every village or every country, 1025 01:03:28,095 --> 01:03:29,790 and actually, Deaton and Paxson's 1026 01:03:29,790 --> 01:03:31,650 stuff, looking at the cross sections, kind 1027 01:03:31,650 --> 01:03:33,000 of saying that it's different. 1028 01:03:33,000 --> 01:03:34,833 It could be different in different countries 1029 01:03:34,833 --> 01:03:37,470 if you're going to try to reconcile the observed 1030 01:03:37,470 --> 01:03:38,473 movements. 1031 01:03:43,570 --> 01:03:46,180 But anyway, you guys need to know about this literature. 1032 01:03:49,390 --> 01:03:53,170 You need to have a view of the different consumption smoothing 1033 01:03:53,170 --> 01:03:54,370 literature. 1034 01:03:54,370 --> 01:04:00,750 I guess I should also say sort of, 1035 01:04:00,750 --> 01:04:06,270 it looks as though it's a macro-ish, US-ish literature. 1036 01:04:06,270 --> 01:04:09,960 But that's not true, certainly, for Paxson and Deaton, who 1037 01:04:09,960 --> 01:04:15,040 are avid development economists and looking at that data 1038 01:04:15,040 --> 01:04:16,330 from developing countries. 1039 01:04:16,330 --> 01:04:19,420 And likewise, the initial risk-sharing stuff, 1040 01:04:19,420 --> 01:04:21,370 that wasn't peculiar to development. 1041 01:04:21,370 --> 01:04:23,830 That was being tested by Cochrane and Mace 1042 01:04:23,830 --> 01:04:26,050 and so on in US data. 1043 01:04:26,050 --> 01:04:30,040 So there's really never been this idea 1044 01:04:30,040 --> 01:04:34,780 that somehow macro is in one room, using one subset of data, 1045 01:04:34,780 --> 01:04:38,650 and micro is another room, using another subset. 1046 01:04:38,650 --> 01:04:40,360 That would be rather silly. 1047 01:04:40,360 --> 01:04:44,760 So we really need to know how all these models work. 1048 01:04:54,300 --> 01:04:57,690 So this is, again, Campbell's saving for a rainy day. 1049 01:05:01,055 --> 01:05:02,930 It's repeated because it's a different paper. 1050 01:05:06,750 --> 01:05:07,950 They look at-- 1051 01:05:07,950 --> 01:05:14,330 Campbell and Deaton now are looking at US data 1052 01:05:14,330 --> 01:05:16,370 and saying the labor income is described 1053 01:05:16,370 --> 01:05:22,280 by this autoregressive process with a positive serial 1054 01:05:22,280 --> 01:05:23,120 correlation. 1055 01:05:26,890 --> 01:05:31,740 And what that means is innovations are, quote unquote, 1056 01:05:31,740 --> 01:05:34,680 "more than permanent," not just random walk-ish, 1057 01:05:34,680 --> 01:05:36,770 but basically-- 1058 01:05:36,770 --> 01:05:38,670 Now you get even into more trouble 1059 01:05:38,670 --> 01:05:41,880 because if consumption should reflect the innovations 1060 01:05:41,880 --> 01:05:44,370 to permanent income, and what you see in innovations 1061 01:05:44,370 --> 01:05:47,910 is more than permanent, that means consumption 1062 01:05:47,910 --> 01:05:51,090 should respond even more. 1063 01:05:51,090 --> 01:05:54,660 And it's not, in the data, responding that much. 1064 01:05:54,660 --> 01:05:58,080 It's much less variable. 1065 01:05:58,080 --> 01:06:00,090 So either they're getting this fact wrong. 1066 01:06:00,090 --> 01:06:07,440 Or, again, maybe the households have more information somehow. 1067 01:06:07,440 --> 01:06:12,690 Or they have stupid expectations or whatever. 1068 01:06:12,690 --> 01:06:16,470 These guys were not able to resolve the puzzle. 1069 01:06:16,470 --> 01:06:18,520 If you want to see the equations, there they are. 1070 01:06:18,520 --> 01:06:21,720 I'm not sure at this point that it adds all that much 1071 01:06:21,720 --> 01:06:23,442 more to the discussion. 1072 01:06:29,850 --> 01:06:33,380 And this is what I was saying about Attanasio and Pavoni. 1073 01:06:37,460 --> 01:06:42,642 So the plan is-- 1074 01:06:42,642 --> 01:06:44,100 there's a little more coming today. 1075 01:06:44,100 --> 01:06:45,870 Don't worry. 1076 01:06:45,870 --> 01:06:49,190 Or you might say, oh, darn. 1077 01:06:49,190 --> 01:06:51,630 But the plan in the ordering of the lectures 1078 01:06:51,630 --> 01:06:58,050 is to do labor and wage variation 1079 01:06:58,050 --> 01:07:03,090 and smoothing, adding labor supply to a consumption model, 1080 01:07:03,090 --> 01:07:07,230 and talk about elasticities and sensitivities. 1081 01:07:07,230 --> 01:07:10,110 That will be done with both the full risk-sharing model, 1082 01:07:10,110 --> 01:07:14,580 as well as a version of these incomplete market models. 1083 01:07:14,580 --> 01:07:18,450 So we'll see what survives, depending on what you assume 1084 01:07:18,450 --> 01:07:20,400 about the market structure. 1085 01:07:20,400 --> 01:07:25,200 And then we're going to go to have a whole lecture on models 1086 01:07:25,200 --> 01:07:29,910 that are much more explicit about moral hazard, unobserved 1087 01:07:29,910 --> 01:07:34,120 income, and so on. 1088 01:07:34,120 --> 01:07:38,760 And this Pavoni paper is one of them in that literature. 1089 01:07:38,760 --> 01:07:41,070 We're not going to cover it in class. 1090 01:07:48,670 --> 01:07:57,200 So actually, the front part of the lecture was about this BPP. 1091 01:07:57,200 --> 01:08:00,730 It's probably a bit mysterious what it was, 1092 01:08:00,730 --> 01:08:02,620 so we can review that for a second. 1093 01:08:05,730 --> 01:08:19,729 The idea is that you postulate that log of earnings 1094 01:08:19,729 --> 01:08:24,200 takes on this process where x is a vector of shocks, 1095 01:08:24,200 --> 01:08:30,609 a is some vector of coefficients, 1096 01:08:30,609 --> 01:08:38,420 the shocks are IID, the x's are, and they have variances. 1097 01:08:41,410 --> 01:08:46,130 This allows a whole bunch of stuff, not only just random 1098 01:08:46,130 --> 01:08:52,140 walks, but autoregressive integrated moving 1099 01:08:52,140 --> 01:08:56,340 average processes on income. 1100 01:08:56,340 --> 01:08:58,609 This is what you see. 1101 01:08:58,609 --> 01:09:00,899 And then this general formulation 1102 01:09:00,899 --> 01:09:06,779 allows a bunch of different specifications, which they're 1103 01:09:06,779 --> 01:09:08,010 going to try to estimate. 1104 01:09:15,519 --> 01:09:18,520 And somehow what they want to back out 1105 01:09:18,520 --> 01:09:21,609 is this insurance coefficient. 1106 01:09:21,609 --> 01:09:25,090 So here's, again, how it's easy to get turned around. 1107 01:09:25,090 --> 01:09:28,210 This is how a sort of, like, quote unquote, 1108 01:09:28,210 --> 01:09:31,479 a regression coefficient of how consumption 1109 01:09:31,479 --> 01:09:37,370 is moving with this particular shock, inferred somehow. 1110 01:09:37,370 --> 01:09:42,910 But 1 minus that is then the degree of insurance 1111 01:09:42,910 --> 01:09:46,630 because when consumption doesn't move with that shock, 1112 01:09:46,630 --> 01:09:47,819 this is zero. 1113 01:09:47,819 --> 01:09:51,670 And so insurance is like, perfect, measured at 1. 1114 01:09:58,460 --> 01:10:01,430 And you could put t's on these things 1115 01:10:01,430 --> 01:10:08,030 if you sort the data by age, which came up earlier. 1116 01:10:17,400 --> 01:10:24,630 So we don't really see all those permanent 1117 01:10:24,630 --> 01:10:26,385 versus transitory shocks. 1118 01:10:29,430 --> 01:10:31,635 You kind of have to infer them, somehow. 1119 01:10:35,820 --> 01:10:50,810 And this is a bit like using some assumed function 1120 01:10:50,810 --> 01:10:57,360 on the income process, and then filtering 1121 01:10:57,360 --> 01:11:02,328 the data through that function and looking at the covariance 1122 01:11:02,328 --> 01:11:03,120 with income change. 1123 01:11:06,370 --> 01:11:08,070 But they don't just do three alone, 1124 01:11:08,070 --> 01:11:15,590 because this would be a statement about income alone. 1125 01:11:15,590 --> 01:11:22,360 They jointly estimate this function, g, essentially, 1126 01:11:22,360 --> 01:11:23,830 jointly with consumption. 1127 01:11:48,890 --> 01:11:55,120 So for example, if you assume income 1128 01:11:55,120 --> 01:11:58,690 took on this classic form that we were actually 1129 01:11:58,690 --> 01:12:01,930 tracking through the lectures, then income 1130 01:12:01,930 --> 01:12:09,430 would be the sum of a random walk with its own innovation 1131 01:12:09,430 --> 01:12:12,400 and variance and epsilon, which would 1132 01:12:12,400 --> 01:12:18,780 be this IID transitory shock. 1133 01:12:18,780 --> 01:12:22,820 If you believe this to be the structure, and there are many, 1134 01:12:22,820 --> 01:12:27,520 many other candidates, then you take a first difference. 1135 01:12:27,520 --> 01:12:31,510 And by construction then, what would be left 1136 01:12:31,510 --> 01:12:38,420 would be this innovation in the permanent part and a time 1137 01:12:38,420 --> 01:12:41,360 difference in the transitory part, which 1138 01:12:41,360 --> 01:12:42,680 is still transitory. 1139 01:12:47,600 --> 01:12:49,990 So then the consumption model tells you about-- 1140 01:12:54,910 --> 01:13:03,420 puts restrictions on how the change in consumption 1141 01:13:03,420 --> 01:13:15,360 should be responding, basically taking advantage of the time 1142 01:13:15,360 --> 01:13:15,930 delays. 1143 01:13:15,930 --> 01:13:19,500 As you go back like, two, three periods, 1144 01:13:19,500 --> 01:13:22,020 there is nothing that happened that far back that's 1145 01:13:22,020 --> 01:13:24,550 influencing anything at all today. 1146 01:13:24,550 --> 01:13:29,640 So those past data kind of become predetermined variables, 1147 01:13:29,640 --> 01:13:31,390 almost as if they were instruments. 1148 01:13:31,390 --> 01:13:39,150 And so that kind of mysterious notation about g on y, this 1149 01:13:39,150 --> 01:13:42,960 is a version of it, postulating a model 1150 01:13:42,960 --> 01:13:47,400 and then going back far enough time, so you would see, 1151 01:13:47,400 --> 01:13:49,650 basically, zero covariance. 1152 01:14:00,220 --> 01:14:01,570 So here it is, actually. 1153 01:14:01,570 --> 01:14:08,110 This g is just basically the time difference 1154 01:14:08,110 --> 01:14:12,990 in income at t plus 1. 1155 01:14:15,880 --> 01:14:20,590 And given the other assumptions they make, 1156 01:14:20,590 --> 01:14:25,700 you back out some of the key things that you want. 1157 01:14:25,700 --> 01:14:27,950 For example, how on earth are we going 1158 01:14:27,950 --> 01:14:30,290 to know about the variance of the transitory shocks 1159 01:14:30,290 --> 01:14:34,340 if we never see transitory shocks? 1160 01:14:34,340 --> 01:14:38,930 Basically, that turns out to be the covariance of two things we 1161 01:14:38,930 --> 01:14:43,700 do see, the time difference of consumption at income at t 1162 01:14:43,700 --> 01:14:47,852 and the time difference of income at t plus 1. 1163 01:14:47,852 --> 01:14:49,310 Hopefully, you're seeing the spirit 1164 01:14:49,310 --> 01:14:54,442 of this, if not following every line of the algebra. 1165 01:14:54,442 --> 01:14:55,900 So that's where we get that object. 1166 01:14:59,250 --> 01:15:00,860 And how would you get the variance 1167 01:15:00,860 --> 01:15:03,410 of the permanent income part, the innovation 1168 01:15:03,410 --> 01:15:05,350 to permanent income? 1169 01:15:05,350 --> 01:15:09,210 Remember, that thing is persisting over time. 1170 01:15:09,210 --> 01:15:11,540 So it's a bit more complicated. 1171 01:15:14,110 --> 01:15:20,660 It turns out to be this daunting object, which 1172 01:15:20,660 --> 01:15:23,090 is to-- and everything here you see. 1173 01:15:23,090 --> 01:15:24,260 That's point number one. 1174 01:15:24,260 --> 01:15:26,540 It's the covariance of the time difference of income 1175 01:15:26,540 --> 01:15:33,530 at t, against the sum of the changes in income at t minus 1, 1176 01:15:33,530 --> 01:15:35,730 t and t plus 1. 1177 01:15:35,730 --> 01:15:41,600 So there, again, you see this sort of time structure at work. 1178 01:15:41,600 --> 01:15:45,640 The spirit of it is go back far enough in time 1179 01:15:45,640 --> 01:15:47,440 so everything is predetermined. 1180 01:15:51,580 --> 01:15:53,710 And this is the covariance of consumption 1181 01:15:53,710 --> 01:15:55,900 with that permanent shock. 1182 01:15:55,900 --> 01:15:58,290 So this is a key object. 1183 01:15:58,290 --> 01:16:01,210 Remember, that insurance formula is, how much is consumption 1184 01:16:01,210 --> 01:16:06,780 moving with the innovation to permanent income? 1185 01:16:06,780 --> 01:16:12,190 It all seems quite mysterious, but here is an explicit formula 1186 01:16:12,190 --> 01:16:13,440 for how they get it. 1187 01:16:16,170 --> 01:16:20,130 So clearly, it's a linear model, using 1188 01:16:20,130 --> 01:16:22,260 a lot of these variance covariance formulas, 1189 01:16:22,260 --> 01:16:25,682 given the assumed structure. 1190 01:16:25,682 --> 01:16:27,390 They don't have to-- their starting point 1191 01:16:27,390 --> 01:16:30,960 could have been something else. 1192 01:16:30,960 --> 01:16:33,150 As I said, you had these ARIMA processes, 1193 01:16:33,150 --> 01:16:35,070 but it is some structure. 1194 01:16:35,070 --> 01:16:39,660 When you specify the order of the moving average part 1195 01:16:39,660 --> 01:16:42,690 and the order of the autoregressive part, 1196 01:16:42,690 --> 01:16:44,280 you get restrictions on the data. 1197 01:16:47,730 --> 01:16:52,400 So hopefully that helps resolve some of the mysteries 1198 01:16:52,400 --> 01:16:57,750 about what this BPP algorithm and what they do to the data 1199 01:16:57,750 --> 01:17:01,320 to measure these insurance against idiosyncratic and 1200 01:17:01,320 --> 01:17:03,780 permanent shocks. 1201 01:17:03,780 --> 01:17:05,280 So I'm going to leave for [? Whit ?] 1202 01:17:05,280 --> 01:17:13,010 to do the version of smoothing, a bit in the Italian data. 1203 01:17:13,010 --> 01:17:16,410 But I will just say, by way of motivation, 1204 01:17:16,410 --> 01:17:19,490 it's again looking at various models, 1205 01:17:19,490 --> 01:17:21,860 although they're not exactly nested, 1206 01:17:21,860 --> 01:17:26,150 and looking at the responses of consumption 1207 01:17:26,150 --> 01:17:32,330 to innovations, but also of wealth to innovations. 1208 01:17:32,330 --> 01:17:37,220 So we saw in my data sort of how wealth in various lectures 1209 01:17:37,220 --> 01:17:39,260 is moving around in the cross section 1210 01:17:39,260 --> 01:17:41,990 and moving around over time. 1211 01:17:41,990 --> 01:17:44,180 We talked about responses to shocks 1212 01:17:44,180 --> 01:17:48,110 and whether they're using savings accounts and so on. 1213 01:17:48,110 --> 01:17:52,490 So these guys in their own way are doing something similar. 1214 01:17:52,490 --> 01:17:57,470 And the paper backs out the movements 1215 01:17:57,470 --> 01:17:59,930 in consumption and wealth that are predicted 1216 01:17:59,930 --> 01:18:01,670 from certain kinds of innovations, 1217 01:18:01,670 --> 01:18:05,450 but not just between this year and next year, but this year 1218 01:18:05,450 --> 01:18:09,210 and two years from now, all the way up to six years, 1219 01:18:09,210 --> 01:18:10,590 or even longer. 1220 01:18:10,590 --> 01:18:14,240 So you kind of get the sort of time profiles 1221 01:18:14,240 --> 01:18:16,090 of responsiveness. 1222 01:18:16,090 --> 01:18:20,030 And very much in the spirit of what we're talking about today, 1223 01:18:20,030 --> 01:18:23,382 yet again, a bit different, those response patterns 1224 01:18:23,382 --> 01:18:25,340 are very different, depending on whether you're 1225 01:18:25,340 --> 01:18:30,390 talking about the permanent income model or the life cycle 1226 01:18:30,390 --> 01:18:32,180 buffer stock type model. 1227 01:18:35,970 --> 01:18:38,030 That's all for today.