WEBVTT 00:00:00.000 --> 00:00:01.948 align:middle line:90% [SQUEAKING] 00:00:01.948 --> 00:00:03.896 align:middle line:90% [RUSTLING] 00:00:03.896 --> 00:00:06.331 align:middle line:90% [CLICKING] 00:00:06.331 --> 00:00:11.690 align:middle line:90% 00:00:11.690 --> 00:00:14.990 align:middle line:84% ROBERT TOWNSEND: Thanks, everyone, for coming today. 00:00:14.990 --> 00:00:18.680 align:middle line:84% So first thing I wanted to do is just 00:00:18.680 --> 00:00:24.440 align:middle line:84% review where we are, as usual, in terms of the calendar. 00:00:24.440 --> 00:00:29.180 align:middle line:84% So we did the first part of contracts and mechanism design 00:00:29.180 --> 00:00:31.730 align:middle line:84% as kind of an introduction last time. 00:00:31.730 --> 00:00:33.590 align:middle line:84% And now we're going to do the second, which 00:00:33.590 --> 00:00:36.590 align:middle line:84% is very explicit about another application 00:00:36.590 --> 00:00:38.870 align:middle line:90% beyond medieval villages. 00:00:38.870 --> 00:00:42.990 align:middle line:84% And we'll definitely have real, live data and so on. 00:00:42.990 --> 00:00:48.410 align:middle line:84% And then by Thursday, we will get into general Equilibrium, 00:00:48.410 --> 00:00:51.800 align:middle line:84% again, Walraisian worlds, and begin 00:00:51.800 --> 00:00:55.880 align:middle line:84% to look at trade applications both in emerging markets 00:00:55.880 --> 00:00:58.640 align:middle line:90% and then later in the US. 00:00:58.640 --> 00:01:00.860 align:middle line:84% I'll say a little bit about the reading list, 00:01:00.860 --> 00:01:03.170 align:middle line:84% especially since you might miss this. 00:01:03.170 --> 00:01:05.840 align:middle line:84% The paper application that we're going to feature today 00:01:05.840 --> 00:01:12.320 align:middle line:84% is this paper with my coauthors on five villages. 00:01:12.320 --> 00:01:16.280 align:middle line:84% And we're going to both stress the application using 00:01:16.280 --> 00:01:20.090 align:middle line:84% the tools you've already learned in a different context 00:01:20.090 --> 00:01:22.100 align:middle line:90% but also some of the techniques. 00:01:22.100 --> 00:01:24.350 align:middle line:84% Remember, the class is trying to balance 00:01:24.350 --> 00:01:27.500 align:middle line:84% both learning tools and how to use them as well 00:01:27.500 --> 00:01:32.990 align:middle line:84% as the economics so please don't miss this Karaivanov starred 00:01:32.990 --> 00:01:37.580 align:middle line:84% article, including moral hazard programs with lotteries 00:01:37.580 --> 00:01:41.000 align:middle line:84% because I will say a lot about those techniques today 00:01:41.000 --> 00:01:42.260 align:middle line:90% but not enough. 00:01:42.260 --> 00:01:45.560 align:middle line:90% So there's two starred articles. 00:01:45.560 --> 00:01:48.470 align:middle line:84% Again, I have earmarked a few of these 00:01:48.470 --> 00:01:50.540 align:middle line:90% from what we did last time. 00:01:50.540 --> 00:01:54.410 align:middle line:84% For mechanism design, we did a single period. 00:01:54.410 --> 00:01:57.840 align:middle line:84% We worked through the so-called revelation principle. 00:01:57.840 --> 00:02:00.980 align:middle line:84% And finally, we got to a two-period problem. 00:02:00.980 --> 00:02:03.770 align:middle line:84% And the review question is written here 00:02:03.770 --> 00:02:06.080 align:middle line:84% is, now maintaining the lotteries, 00:02:06.080 --> 00:02:08.270 align:middle line:84% write down the programming problem for the two 00:02:08.270 --> 00:02:10.130 align:middle line:90% periods, dates one and two. 00:02:10.130 --> 00:02:12.590 align:middle line:84% I'm not asking you to literally write it down. 00:02:12.590 --> 00:02:14.990 align:middle line:84% But could someone volunteer to tell me 00:02:14.990 --> 00:02:17.090 align:middle line:84% about the truth-telling constraints 00:02:17.090 --> 00:02:21.780 align:middle line:84% at the final date two, in words, what they look like? 00:02:21.780 --> 00:02:25.520 align:middle line:84% And then also in words, what the true telling constraint of date 00:02:25.520 --> 00:02:28.370 align:middle line:90% one looks like. 00:02:28.370 --> 00:02:31.910 align:middle line:84% AUDIENCE: I remember the truth-telling constraint 00:02:31.910 --> 00:02:36.680 align:middle line:84% at the final entry is that no matter what you already 00:02:36.680 --> 00:02:44.060 align:middle line:84% announce at the date 1, based on the [INAUDIBLE] how would you 00:02:44.060 --> 00:02:49.820 align:middle line:84% announce at the date 1, you want to choose-- 00:02:49.820 --> 00:02:57.276 align:middle line:84% The truth-telling bring you the maximized utility. 00:02:57.276 --> 00:03:03.280 align:middle line:84% [INAUDIBLE] function is like the utility at the date two 00:03:03.280 --> 00:03:14.110 align:middle line:84% is the [INAUDIBLE] and which modify the probability 00:03:14.110 --> 00:03:14.980 align:middle line:90% function. 00:03:14.980 --> 00:03:16.960 align:middle line:84% The probability function was depending 00:03:16.960 --> 00:03:20.500 align:middle line:84% on what you announce in the [INAUDIBLE] one. 00:03:20.500 --> 00:03:25.150 align:middle line:84% And then the whole function would be bigger 00:03:25.150 --> 00:03:29.410 align:middle line:84% than any announcement at the [INAUDIBLE].. 00:03:29.410 --> 00:03:32.750 align:middle line:90% 00:03:32.750 --> 00:03:36.800 align:middle line:84% ROBERT TOWNSEND: OK, and what about at date one? 00:03:36.800 --> 00:03:40.910 align:middle line:84% AUDIENCE: The date one is that you do not only 00:03:40.910 --> 00:03:47.120 align:middle line:84% care about what you will get at this moment. 00:03:47.120 --> 00:03:50.030 align:middle line:84% But you also care about the future. 00:03:50.030 --> 00:03:56.780 align:middle line:84% I mean, that for date one, the maximize the utility. 00:03:56.780 --> 00:04:00.940 align:middle line:84% Not maximize, the you're telling the truth 00:04:00.940 --> 00:04:03.290 align:middle line:84% that bring you the utility, which 00:04:03.290 --> 00:04:10.240 align:middle line:90% is larger than any date 1. 00:04:10.240 --> 00:04:14.500 align:middle line:84% ROBERT TOWNSEND: Yeah, and what is it assuming about date two, 00:04:14.500 --> 00:04:19.269 align:middle line:84% even though it's a date one constraint? 00:04:19.269 --> 00:04:21.944 align:middle line:84% AUDIENCE: Assuming about the date two is that it-- 00:04:21.944 --> 00:04:25.660 align:middle line:90% 00:04:25.660 --> 00:04:27.990 align:middle line:84% The date two not care about what-- 00:04:27.990 --> 00:04:29.700 align:middle line:90% Yeah. 00:04:29.700 --> 00:04:31.982 align:middle line:90% They do not care. 00:04:31.982 --> 00:04:33.690 align:middle line:84% ROBERT TOWNSEND: Yeah, you're very close. 00:04:33.690 --> 00:04:37.020 align:middle line:84% So the point of working backwards, at date two, 00:04:37.020 --> 00:04:39.270 align:middle line:84% we get the truth-telling constraint. 00:04:39.270 --> 00:04:41.670 align:middle line:84% So the utility is greater for telling the truth 00:04:41.670 --> 00:04:44.490 align:middle line:84% and announcing something counterfactual. 00:04:44.490 --> 00:04:49.590 align:middle line:84% That's now imposed as part of the solution as a constraint. 00:04:49.590 --> 00:04:53.120 align:middle line:84% So working back to date one, it assumes 00:04:53.120 --> 00:04:55.850 align:middle line:90% truth telling at date two. 00:04:55.850 --> 00:05:00.020 align:middle line:84% So we only have to worry about whether to be truthful at date 00:05:00.020 --> 00:05:04.760 align:middle line:90% one or lie at date one. 00:05:04.760 --> 00:05:07.940 align:middle line:84% Because whatever they do, truth or lie at date one, 00:05:07.940 --> 00:05:11.450 align:middle line:84% they will tell the truth that date two. 00:05:11.450 --> 00:05:15.800 align:middle line:84% So related to all of this is the message, 00:05:15.800 --> 00:05:17.330 align:middle line:90% the announcement of date one. 00:05:17.330 --> 00:05:19.700 align:middle line:84% You said something not quite right. 00:05:19.700 --> 00:05:21.530 align:middle line:90% But I may have heard it wrong. 00:05:21.530 --> 00:05:24.740 align:middle line:84% There's a probability transition function 00:05:24.740 --> 00:05:27.410 align:middle line:84% that has to do with a probability of states 00:05:27.410 --> 00:05:30.470 align:middle line:84% at date two, conditioned on dates at state one. 00:05:30.470 --> 00:05:31.860 align:middle line:90% And that never changes. 00:05:31.860 --> 00:05:34.480 align:middle line:84% That's just part of the environment. 00:05:34.480 --> 00:05:38.640 align:middle line:84% What changes, until the one that you mentioned, 00:05:38.640 --> 00:05:42.480 align:middle line:84% is the message at date one, depending on whether or not the 00:05:42.480 --> 00:05:43.170 align:middle line:90% total the truth. 00:05:43.170 --> 00:05:46.310 align:middle line:90% 00:05:46.310 --> 00:05:51.470 align:middle line:84% So the very last part of this review question 00:05:51.470 --> 00:05:55.940 align:middle line:84% asks to describe the way in which 00:05:55.940 --> 00:06:01.410 align:middle line:84% past history matters or contemporary outcomes. 00:06:01.410 --> 00:06:05.060 align:middle line:84% AUDIENCE: So the key is that the history matters, 00:06:05.060 --> 00:06:07.670 align:middle line:90% the probability function, right? 00:06:07.670 --> 00:06:10.520 align:middle line:90% Because if you're telling the-- 00:06:10.520 --> 00:06:13.310 align:middle line:84% Whatever you tell at the date one, that 00:06:13.310 --> 00:06:19.100 align:middle line:84% will decide the probability because the probability was 00:06:19.100 --> 00:06:24.262 align:middle line:84% conditioning on what are you are telling, what do you announce. 00:06:24.262 --> 00:06:25.720 align:middle line:84% ROBERT TOWNSEND: So I don't think I 00:06:25.720 --> 00:06:27.220 align:middle line:90% have that lecture open anymore. 00:06:27.220 --> 00:06:30.070 align:middle line:84% We'd have to go back and look at it. 00:06:30.070 --> 00:06:33.480 align:middle line:90% 00:06:33.480 --> 00:06:36.090 align:middle line:84% No, it's buried back deeper in them. 00:06:36.090 --> 00:06:38.430 align:middle line:84% Go back and look at the Markov Process. 00:06:38.430 --> 00:06:42.720 align:middle line:84% The probability P of theta 2, condition on theta 1, 00:06:42.720 --> 00:06:44.010 align:middle line:90% there's never-- 00:06:44.010 --> 00:06:45.810 align:middle line:90% That part never changes. 00:06:45.810 --> 00:06:46.680 align:middle line:90% AUDIENCE: Oh, sorry. 00:06:46.680 --> 00:06:48.030 align:middle line:90% I'm mixing it. 00:06:48.030 --> 00:06:49.380 align:middle line:90% I should say the lottery. 00:06:49.380 --> 00:06:50.790 align:middle line:90% I always say the probability. 00:06:50.790 --> 00:06:51.630 align:middle line:90% Yeah. 00:06:51.630 --> 00:06:54.240 align:middle line:84% ROBERT TOWNSEND: OK, OK, yeah, lottery. 00:06:54.240 --> 00:06:55.740 align:middle line:84% Yeah, they're both probabilities. 00:06:55.740 --> 00:06:56.940 align:middle line:90% I understand. 00:06:56.940 --> 00:06:58.050 align:middle line:90% OK, good. 00:06:58.050 --> 00:06:58.830 align:middle line:90% Thank you. 00:06:58.830 --> 00:07:00.150 align:middle line:90% That's perfect. 00:07:00.150 --> 00:07:05.840 align:middle line:84% OK, and then relatedly, there's this question right afterwards, 00:07:05.840 --> 00:07:09.840 align:middle line:84% what does the solution to that two-period problem look like? 00:07:09.840 --> 00:07:11.810 align:middle line:90% Is it full insurance? 00:07:11.810 --> 00:07:14.830 align:middle line:90% Is it borrowing and lending? 00:07:14.830 --> 00:07:18.820 align:middle line:84% And if it's not either, one what is the logic of why 00:07:18.820 --> 00:07:23.310 align:middle line:90% we know it can't be either? 00:07:23.310 --> 00:07:25.970 align:middle line:90% So let me take-- 00:07:25.970 --> 00:07:29.180 align:middle line:84% AUDIENCE: Let me take a stab at this. 00:07:29.180 --> 00:07:31.280 align:middle line:84% But yeah, so I remember that we said 00:07:31.280 --> 00:07:34.070 align:middle line:84% that the full insurance wasn't optimal 00:07:34.070 --> 00:07:36.650 align:middle line:84% because if you had full insurance, then 00:07:36.650 --> 00:07:38.720 align:middle line:90% it wouldn't be truth-telling. 00:07:38.720 --> 00:07:40.790 align:middle line:84% And so you would never be able to reach 00:07:40.790 --> 00:07:43.960 align:middle line:90% that optimal equilibrium there. 00:07:43.960 --> 00:07:45.730 align:middle line:84% For the borrowing and lending, I remember 00:07:45.730 --> 00:07:47.770 align:middle line:84% we had some kind of argument where 00:07:47.770 --> 00:07:51.670 align:middle line:84% we said that the incentive constraints won't bind. 00:07:51.670 --> 00:07:54.610 align:middle line:84% And so because those didn't bind, 00:07:54.610 --> 00:07:57.068 align:middle line:84% it's equivalent to just not having the incentive 00:07:57.068 --> 00:07:57.860 align:middle line:90% constraints at all. 00:07:57.860 --> 00:08:00.460 align:middle line:84% Which means you might as well just do full risk sharing. 00:08:00.460 --> 00:08:03.160 align:middle line:84% But we already showed that we could do that. 00:08:03.160 --> 00:08:06.160 align:middle line:84% But I don't think I quite recall why the incentive constraints 00:08:06.160 --> 00:08:08.365 align:middle line:90% don't bind in the first place. 00:08:08.365 --> 00:08:10.240 align:middle line:84% ROBERT TOWNSEND: Well, it's a perfect answer. 00:08:10.240 --> 00:08:10.900 align:middle line:90% Thank you. 00:08:10.900 --> 00:08:15.820 align:middle line:84% And to answer your question, the presumption is somehow, 00:08:15.820 --> 00:08:18.130 align:middle line:84% if your income is low, you want to borrow. 00:08:18.130 --> 00:08:20.890 align:middle line:84% And you strictly prefer that to lending. 00:08:20.890 --> 00:08:25.120 align:middle line:84% So that strict preference is a strict inequality 00:08:25.120 --> 00:08:29.660 align:middle line:84% in the constraint and hence, not binding. 00:08:29.660 --> 00:08:32.480 align:middle line:84% And likewise, if your income is high, 00:08:32.480 --> 00:08:38.625 align:middle line:84% you strictly prefer to lend rather than borrow, OK? 00:08:38.625 --> 00:08:39.750 align:middle line:90% AUDIENCE: That makes sense. 00:08:39.750 --> 00:08:40.520 align:middle line:90% Thanks. 00:08:40.520 --> 00:08:41.570 align:middle line:90% ROBERT TOWNSEND: Yep. 00:08:41.570 --> 00:08:42.830 align:middle line:90% Your answer was really good. 00:08:42.830 --> 00:08:44.070 align:middle line:90% Thank you. 00:08:44.070 --> 00:08:49.730 align:middle line:84% OK, so let's go to maybe one more thing here. 00:08:49.730 --> 00:08:53.270 align:middle line:84% I did feel that I was rushing a bit 00:08:53.270 --> 00:08:55.470 align:middle line:90% toward the end of the lecture. 00:08:55.470 --> 00:08:58.100 align:middle line:84% So I'm happy to take questions rather 00:08:58.100 --> 00:09:00.770 align:middle line:90% than going through these. 00:09:00.770 --> 00:09:04.520 align:middle line:84% Let's try a couple of them to get the conversation going. 00:09:04.520 --> 00:09:08.150 align:middle line:84% I drew a distinction between encryption, hashing, 00:09:08.150 --> 00:09:10.970 align:middle line:90% and cryptographic puzzles. 00:09:10.970 --> 00:09:12.783 align:middle line:90% Does anyone remember? 00:09:12.783 --> 00:09:14.450 align:middle line:84% AUDIENCE: Yeah, I think I know this one. 00:09:14.450 --> 00:09:18.540 align:middle line:84% So encryption is where you have some specific key secret key 00:09:18.540 --> 00:09:19.700 align:middle line:90% shared between two parties. 00:09:19.700 --> 00:09:22.250 align:middle line:84% And then you can use that key to encrypt a message 00:09:22.250 --> 00:09:24.170 align:middle line:84% and then decrypt it at the other end. 00:09:24.170 --> 00:09:30.110 align:middle line:84% Hashing is some function that it changes pretty randomly, 00:09:30.110 --> 00:09:31.100 align:middle line:90% depending on the input. 00:09:31.100 --> 00:09:34.940 align:middle line:84% So it's distorts things that encapsulates the whole message. 00:09:34.940 --> 00:09:38.090 align:middle line:84% And if you change a message, it's 00:09:38.090 --> 00:09:40.658 align:middle line:84% very hard to change a message to keep the same hash. 00:09:40.658 --> 00:09:42.200 align:middle line:84% A cryptographic puzzle, I think, it's 00:09:42.200 --> 00:09:44.150 align:middle line:90% something that is hard to do. 00:09:44.150 --> 00:09:47.190 align:middle line:84% And it's known to be hard in some way. 00:09:47.190 --> 00:09:49.340 align:middle line:84% And I think homomorphic encryption, 00:09:49.340 --> 00:09:52.582 align:middle line:84% I think that's the one where you have basically what 00:09:52.582 --> 00:09:53.790 align:middle line:90% amounts to a linear function. 00:09:53.790 --> 00:09:57.050 align:middle line:90% So you just encrypt something. 00:09:57.050 --> 00:09:59.430 align:middle line:84% Add together all the encrypted things, 00:09:59.430 --> 00:10:01.280 align:middle line:84% and then you can decrypt the sum. 00:10:01.280 --> 00:10:06.050 align:middle line:84% And then you can get the correct decrypted sum 00:10:06.050 --> 00:10:08.420 align:middle line:84% without having to know any of the individual components, 00:10:08.420 --> 00:10:09.575 align:middle line:90% or something like that. 00:10:09.575 --> 00:10:10.700 align:middle line:90% ROBERT TOWNSEND: Very good. 00:10:10.700 --> 00:10:12.440 align:middle line:90% Excellent. 00:10:12.440 --> 00:10:16.160 align:middle line:90% Just a couple words of comment. 00:10:16.160 --> 00:10:20.420 align:middle line:84% The encryption part, it's private and public keys. 00:10:20.420 --> 00:10:22.340 align:middle line:84% And the private keys are never shared. 00:10:22.340 --> 00:10:25.263 align:middle line:84% It's the public key that's shared between the parties. 00:10:25.263 --> 00:10:28.610 align:middle line:90% 00:10:28.610 --> 00:10:31.260 align:middle line:84% AUDIENCE: I just described symmetric encryption. 00:10:31.260 --> 00:10:34.160 align:middle line:84% Yeah, it's also private, public keys. 00:10:34.160 --> 00:10:37.310 align:middle line:84% ROBERT TOWNSEND: OK, you have the background for this. 00:10:37.310 --> 00:10:40.250 align:middle line:90% OK, excellent. 00:10:40.250 --> 00:10:41.900 align:middle line:84% Yeah, and hashing is what you said. 00:10:41.900 --> 00:10:44.540 align:middle line:90% It's kind of a one-way function. 00:10:44.540 --> 00:10:45.500 align:middle line:90% You know what goes in. 00:10:45.500 --> 00:10:48.230 align:middle line:84% But you cannot interpret what goes out. 00:10:48.230 --> 00:10:50.750 align:middle line:90% And the puzzles are fine. 00:10:50.750 --> 00:10:53.000 align:middle line:84% And homomorphic encryption is fine. 00:10:53.000 --> 00:10:54.440 align:middle line:90% So thank you, that's great. 00:10:54.440 --> 00:10:57.630 align:middle line:90% 00:10:57.630 --> 00:11:00.200 align:middle line:84% Sounds like you might have known the answers to these things 00:11:00.200 --> 00:11:01.220 align:middle line:90% before the class. 00:11:01.220 --> 00:11:05.930 align:middle line:84% But I mean, from other work that you're doing. 00:11:05.930 --> 00:11:08.690 align:middle line:90% But that's fine. 00:11:08.690 --> 00:11:12.430 align:middle line:90% Let's see, one last thing. 00:11:12.430 --> 00:11:14.080 align:middle line:90% Consensus Protocol. 00:11:14.080 --> 00:11:16.390 align:middle line:84% Is a consensus protocol necessarily 00:11:16.390 --> 00:11:18.490 align:middle line:90% incentive compatible? 00:11:18.490 --> 00:11:21.100 align:middle line:84% So this is like begging for a discussion of how 00:11:21.100 --> 00:11:26.200 align:middle line:84% computer science use the word trust and economics use 00:11:26.200 --> 00:11:28.370 align:middle line:90% the word trust. 00:11:28.370 --> 00:11:32.490 align:middle line:84% And again, I'm just taking volunteers today. 00:11:32.490 --> 00:11:35.720 align:middle line:84% So again, lots of information on those 00:11:35.720 --> 00:11:38.090 align:middle line:84% slides just kind of appeared on one slide 00:11:38.090 --> 00:11:40.100 align:middle line:90% and I didn't belabor it. 00:11:40.100 --> 00:11:42.110 align:middle line:84% The basic idea in computer science 00:11:42.110 --> 00:11:45.230 align:middle line:84% is that most nodes are trustworthy. 00:11:45.230 --> 00:11:47.510 align:middle line:84% They're going to follow the protocol. 00:11:47.510 --> 00:11:53.180 align:middle line:84% But a handful of nodes or actors are either faulty, 00:11:53.180 --> 00:11:55.430 align:middle line:84% in the sense of the computer doesn't work well, 00:11:55.430 --> 00:11:58.520 align:middle line:84% or nefarious in the sense that they're determined 00:11:58.520 --> 00:12:00.450 align:middle line:90% to undercut the system. 00:12:00.450 --> 00:12:04.670 align:middle line:84% So the basic premise is, most nodes are honest in the sense 00:12:04.670 --> 00:12:08.690 align:middle line:84% that they're going to follow the algorithm. 00:12:08.690 --> 00:12:10.910 align:middle line:84% In economics, it's a dismal science. 00:12:10.910 --> 00:12:12.800 align:middle line:90% We don't trust anybody. 00:12:12.800 --> 00:12:18.050 align:middle line:84% So everyone, on the other hand, can be given incentives. 00:12:18.050 --> 00:12:23.780 align:middle line:84% So we assume maximizing utility or profit-maximizing behavior. 00:12:23.780 --> 00:12:25.670 align:middle line:84% And then we load things up in a way 00:12:25.670 --> 00:12:30.140 align:middle line:84% that even though there are secrets, like preference shocks 00:12:30.140 --> 00:12:33.530 align:middle line:84% or unobserved states and so on, the actors 00:12:33.530 --> 00:12:38.800 align:middle line:84% have an incentive to reveal what those states are. 00:12:38.800 --> 00:12:42.460 align:middle line:84% So the message is, as in mechanism design 00:12:42.460 --> 00:12:45.520 align:middle line:84% that we did earlier in the lecture, 00:12:45.520 --> 00:12:48.070 align:middle line:90% are part of the contract. 00:12:48.070 --> 00:12:51.370 align:middle line:84% And they're going to be sent honestly. 00:12:51.370 --> 00:12:54.790 align:middle line:84% But it's due to the incentive constraints. 00:12:54.790 --> 00:12:56.410 align:middle line:84% And without the incentive constraints, 00:12:56.410 --> 00:13:00.100 align:middle line:84% we kind of assume everyone's going to cheat. 00:13:00.100 --> 00:13:05.060 align:middle line:84% So it is kind of a philosophical difference. 00:13:05.060 --> 00:13:06.890 align:middle line:84% Anyway, that's why, in the lecture 00:13:06.890 --> 00:13:13.300 align:middle line:84% I put the discussion of bitcoin and other algorithms 00:13:13.300 --> 00:13:19.890 align:middle line:84% in the context of mechanism design to draw this contrast. 00:13:19.890 --> 00:13:23.390 align:middle line:90% OK, so that's the review sheet. 00:13:23.390 --> 00:13:29.090 align:middle line:84% And let's get to don't lecture here. 00:13:29.090 --> 00:13:31.600 align:middle line:90% 00:13:31.600 --> 00:13:37.940 align:middle line:84% OK, so today part two, more on contracts. 00:13:37.940 --> 00:13:42.010 align:middle line:84% So the application is going to be financial markets. 00:13:42.010 --> 00:13:45.820 align:middle line:84% And we're going to try to figure out what kind of contracts 00:13:45.820 --> 00:13:48.850 align:middle line:84% a small business would write with a lender. 00:13:48.850 --> 00:13:53.020 align:middle line:84% In particular, what the underlying obstacles to trade 00:13:53.020 --> 00:13:53.590 align:middle line:90% are. 00:13:53.590 --> 00:13:57.820 align:middle line:84% We're going to want to identify, from data using the theory, 00:13:57.820 --> 00:14:02.080 align:middle line:84% what those obstacles are that limit the ability to go 00:14:02.080 --> 00:14:03.910 align:middle line:84% into business or limit the ability 00:14:03.910 --> 00:14:08.350 align:middle line:84% to finance the business once you're already in business. 00:14:08.350 --> 00:14:10.870 align:middle line:84% So that's the economics part of it. 00:14:10.870 --> 00:14:13.360 align:middle line:84% The technique part of it is, we're 00:14:13.360 --> 00:14:17.200 align:middle line:84% going to do a structural estimation of the model. 00:14:17.200 --> 00:14:22.210 align:middle line:84% But we will also look at some reduced form techniques that 00:14:22.210 --> 00:14:24.130 align:middle line:84% are data summaries that are consistent 00:14:24.130 --> 00:14:25.900 align:middle line:90% with the structural model. 00:14:25.900 --> 00:14:28.090 align:middle line:84% Essentially, we use reduced-form techniques 00:14:28.090 --> 00:14:30.700 align:middle line:84% to identify stylized facts different 00:14:30.700 --> 00:14:31.970 align:middle line:90% across different regions. 00:14:31.970 --> 00:14:34.180 align:middle line:84% And then we use the theory to try 00:14:34.180 --> 00:14:36.070 align:middle line:84% to make sense of what we're seeing. 00:14:36.070 --> 00:14:38.440 align:middle line:84% It's kind of an experimental laboratory. 00:14:38.440 --> 00:14:41.240 align:middle line:84% And there are going to be two sources of constraints. 00:14:41.240 --> 00:14:45.580 align:middle line:84% So one is for short, a collateral constraint. 00:14:45.580 --> 00:14:49.330 align:middle line:84% Agents can borrow, but potentially not much. 00:14:49.330 --> 00:14:52.630 align:middle line:84% In order to borrow, they have to post collateral 00:14:52.630 --> 00:14:54.640 align:middle line:84% so that the amount they can borrow 00:14:54.640 --> 00:14:58.120 align:middle line:90% is limited by their wealth. 00:14:58.120 --> 00:15:02.800 align:middle line:84% That means low-wealth households may not borrow very much. 00:15:02.800 --> 00:15:06.790 align:middle line:84% And it may not make sense to go into a business at all 00:15:06.790 --> 00:15:10.180 align:middle line:84% because they can only operate at a very small scale. 00:15:10.180 --> 00:15:13.060 align:middle line:84% Or if they do go into business, because it's the best 00:15:13.060 --> 00:15:15.610 align:middle line:84% alternative notwithstanding, they 00:15:15.610 --> 00:15:18.820 align:middle line:84% are not investing very much because of that collateral 00:15:18.820 --> 00:15:19.930 align:middle line:90% constraint. 00:15:19.930 --> 00:15:23.260 align:middle line:84% Now when there's a collateral constraint that's binding, 00:15:23.260 --> 00:15:27.320 align:middle line:84% the borrowing is a proportion of wealth. 00:15:27.320 --> 00:15:30.380 align:middle line:84% So if you're thinking about going across different firms 00:15:30.380 --> 00:15:35.120 align:middle line:84% in the cross section, as net worth increases, 00:15:35.120 --> 00:15:41.260 align:middle line:84% borrowing would increase, again, for constrained entrepreneurs. 00:15:41.260 --> 00:15:43.030 align:middle line:84% On the other hand, it doesn't necessarily 00:15:43.030 --> 00:15:45.550 align:middle line:84% mean that with this collateral constraint everyone's 00:15:45.550 --> 00:15:46.930 align:middle line:90% going to be borrowing. 00:15:46.930 --> 00:15:51.370 align:middle line:84% They may have enough wealth to entirely self-finance. 00:15:51.370 --> 00:15:56.800 align:middle line:84% Or the borrowing constraint isn't binding in the sense 00:15:56.800 --> 00:15:58.690 align:middle line:84% that they don't go up to the limit. 00:15:58.690 --> 00:15:59.650 align:middle line:90% They have some wealth. 00:15:59.650 --> 00:16:01.720 align:middle line:84% They borrow additional resources. 00:16:01.720 --> 00:16:05.000 align:middle line:84% But they could have borrowed more and they don't do it. 00:16:05.000 --> 00:16:09.320 align:middle line:84% On the other hand, a different constraint is a moral hazard. 00:16:09.320 --> 00:16:12.970 align:middle line:84% Now moral hazard means that, it's a funny terminology. 00:16:12.970 --> 00:16:16.870 align:middle line:84% It's like you buy an insurance policy that's 00:16:16.870 --> 00:16:20.410 align:middle line:84% supposed to pay off if your house burns down. 00:16:20.410 --> 00:16:22.750 align:middle line:84% But because you're insured, then you 00:16:22.750 --> 00:16:27.190 align:middle line:84% don't pay attention and take the appropriate precautionary 00:16:27.190 --> 00:16:28.300 align:middle line:90% measures. 00:16:28.300 --> 00:16:31.510 align:middle line:84% So the house is likely to burn down. 00:16:31.510 --> 00:16:33.440 align:middle line:84% For some reason, in the insurance industry, 00:16:33.440 --> 00:16:36.160 align:middle line:84% this is referred to as moral hazard 00:16:36.160 --> 00:16:38.230 align:middle line:90% as if it were, quote, "immoral." 00:16:38.230 --> 00:16:41.300 align:middle line:84% But again, from our dismal science, 00:16:41.300 --> 00:16:42.670 align:middle line:90% economics point of view. 00:16:42.670 --> 00:16:45.385 align:middle line:90% It's not immoral, per se. 00:16:45.385 --> 00:16:48.550 align:middle line:84% It's just that it didn't have the right incentives. 00:16:48.550 --> 00:16:53.740 align:middle line:84% And in this moral hazard world, effort, diligence, taking care 00:16:53.740 --> 00:16:55.130 align:middle line:90% is not observed. 00:16:55.130 --> 00:16:58.360 align:middle line:84% So the only way the insurance company or the lender 00:16:58.360 --> 00:17:03.100 align:middle line:84% can get the money back is when there's not an adverse event 00:17:03.100 --> 00:17:06.250 align:middle line:84% or the firm is successful in making profit. 00:17:06.250 --> 00:17:08.680 align:middle line:84% Now that means that poor borrowers who 00:17:08.680 --> 00:17:11.800 align:middle line:84% owe a lot of money don't have an incentive 00:17:11.800 --> 00:17:14.500 align:middle line:84% to work very hard at being diligent because they're going 00:17:14.500 --> 00:17:16.359 align:middle line:84% to pay the bulk of their returns back 00:17:16.359 --> 00:17:18.670 align:middle line:84% if they're successful to the bank 00:17:18.670 --> 00:17:21.140 align:middle line:90% or to the insurance company. 00:17:21.140 --> 00:17:22.930 align:middle line:90% So they don't take care. 00:17:22.930 --> 00:17:25.660 align:middle line:84% And the probability of failure is high. 00:17:25.660 --> 00:17:27.160 align:middle line:90% It's a constraint. 00:17:27.160 --> 00:17:28.960 align:middle line:84% Because the probability of failure 00:17:28.960 --> 00:17:33.290 align:middle line:84% could be high, especially for low-wealth agents, 00:17:33.290 --> 00:17:35.780 align:middle line:84% the banks, in order to break even on those loans, 00:17:35.780 --> 00:17:37.970 align:middle line:84% have to charge high interest rates. 00:17:37.970 --> 00:17:40.415 align:middle line:84% And in fact, the rate could be so high, 00:17:40.415 --> 00:17:42.170 align:middle line:84% it would be high enough for the lender 00:17:42.170 --> 00:17:43.700 align:middle line:84% to break even but the borrower is 00:17:43.700 --> 00:17:49.730 align:middle line:84% no longer interested because it's just too high of a rate. 00:17:49.730 --> 00:17:52.700 align:middle line:84% And likewise, high rates, they may not 00:17:52.700 --> 00:17:56.280 align:middle line:84% want to borrow very much, even if they do go into business. 00:17:56.280 --> 00:17:58.820 align:middle line:84% Another difference with the collateral constraint 00:17:58.820 --> 00:18:02.840 align:middle line:84% is in the moral hazard world, the incentive constraint 00:18:02.840 --> 00:18:05.090 align:middle line:90% is always binding. 00:18:05.090 --> 00:18:07.700 align:middle line:84% That's a version of what we were just discussing, 00:18:07.700 --> 00:18:11.270 align:middle line:84% full insurance is never optimal because under full insurance, 00:18:11.270 --> 00:18:13.740 align:middle line:90% you exert minimal effort. 00:18:13.740 --> 00:18:16.130 align:middle line:84% So you don't offer full insurance. 00:18:16.130 --> 00:18:18.890 align:middle line:84% But likewise, then effort it is lower 00:18:18.890 --> 00:18:21.300 align:middle line:84% than it would have been in a full information world. 00:18:21.300 --> 00:18:25.970 align:middle line:84% So the incentive constraint, to be diligent, is always binding. 00:18:25.970 --> 00:18:30.230 align:middle line:84% And the way out of that problem, if in a cross section, 00:18:30.230 --> 00:18:33.110 align:middle line:84% entrepreneurs have more and more wealth comparing one 00:18:33.110 --> 00:18:36.080 align:middle line:84% to the other, then they can self-finance more. 00:18:36.080 --> 00:18:41.060 align:middle line:84% And the more you self-finance, the less you have to pay back. 00:18:41.060 --> 00:18:44.920 align:middle line:84% So in this case, as wealth goes up, borrowing goes down. 00:18:44.920 --> 00:18:46.930 align:middle line:84% That's exactly the opposite from what 00:18:46.930 --> 00:18:49.000 align:middle line:84% we got in the limited liability case 00:18:49.000 --> 00:18:50.770 align:middle line:90% for constrained entrepreneurs. 00:18:50.770 --> 00:18:52.790 align:middle line:84% When wealth went up, borrowing went up. 00:18:52.790 --> 00:18:56.260 align:middle line:84% So I alluded to these reduced-form statistics. 00:18:56.260 --> 00:19:00.040 align:middle line:84% We will see again at some point a summary of the data 00:19:00.040 --> 00:19:03.730 align:middle line:84% that, depending on the region that they're in, 00:19:03.730 --> 00:19:07.390 align:middle line:84% we will see either this one result in the cross section 00:19:07.390 --> 00:19:09.230 align:middle line:90% or the other one. 00:19:09.230 --> 00:19:14.080 align:middle line:84% And the goal then is to take the full-blown model 00:19:14.080 --> 00:19:16.270 align:middle line:84% and do structural estimates to determine 00:19:16.270 --> 00:19:17.920 align:middle line:90% which constrain is binding. 00:19:17.920 --> 00:19:18.850 align:middle line:90% It could be one. 00:19:18.850 --> 00:19:19.780 align:middle line:90% It could be the other. 00:19:19.780 --> 00:19:22.390 align:middle line:84% Actually, technically, it could be both. 00:19:22.390 --> 00:19:26.500 align:middle line:84% And I'm going to show you that once we review the tools we 00:19:26.500 --> 00:19:29.740 align:middle line:84% already have, pending on the appropriate constraints, 00:19:29.740 --> 00:19:33.460 align:middle line:84% it's actually easy to test one versus the other versus 00:19:33.460 --> 00:19:34.600 align:middle line:90% multiple. 00:19:34.600 --> 00:19:37.120 align:middle line:90% It's relatively easy to do. 00:19:37.120 --> 00:19:40.390 align:middle line:84% But we are learning some of those new tools today. 00:19:40.390 --> 00:19:43.340 align:middle line:84% That's half of the point of the lecture. 00:19:43.340 --> 00:19:48.100 align:middle line:84% So I've made reference twice to differences across regions. 00:19:48.100 --> 00:19:51.040 align:middle line:84% I think I may have shown you this picture before. 00:19:51.040 --> 00:19:52.240 align:middle line:90% But I'm not sure. 00:19:52.240 --> 00:19:54.910 align:middle line:84% We certainly looked at the Thai data. 00:19:54.910 --> 00:19:59.050 align:middle line:84% We looked at the monthly data when we did risk and return 00:19:59.050 --> 00:20:02.140 align:middle line:84% in village Thailand, which was the second application 00:20:02.140 --> 00:20:04.480 align:middle line:90% of the risk-sharing sections. 00:20:04.480 --> 00:20:07.240 align:middle line:90% So anyway, Bangkok's over here. 00:20:07.240 --> 00:20:09.430 align:middle line:90% This is central region. 00:20:09.430 --> 00:20:13.390 align:middle line:84% These yellow provinces were ones that I had surveyed 00:20:13.390 --> 00:20:16.870 align:middle line:90% in annual data since 1997. 00:20:16.870 --> 00:20:20.980 align:middle line:84% And over here in the East, but they call it the Northeast, 00:20:20.980 --> 00:20:23.260 align:middle line:90% we have two other provinces. 00:20:23.260 --> 00:20:26.410 align:middle line:84% These are predominantly rural, agricultural. 00:20:26.410 --> 00:20:30.520 align:middle line:84% The ones near Bangkok are much more industrialized. 00:20:30.520 --> 00:20:34.330 align:middle line:84% And here's a map of Sisaket, just to show you 00:20:34.330 --> 00:20:36.490 align:middle line:90% where the data are coming from. 00:20:36.490 --> 00:20:38.620 align:middle line:84% We've got a lot of little villages 00:20:38.620 --> 00:20:43.180 align:middle line:84% here, these little dots, as well as parts of the road network. 00:20:43.180 --> 00:20:46.540 align:middle line:84% And then the colored circles correspond to, 00:20:46.540 --> 00:20:49.570 align:middle line:84% if they're purple, these clusters 00:20:49.570 --> 00:20:52.240 align:middle line:84% are where we gather the annual data that we're 00:20:52.240 --> 00:20:54.160 align:middle line:90% going to be using today. 00:20:54.160 --> 00:20:57.880 align:middle line:84% In the previous lectures, Risk and Return in Village Thailand, 00:20:57.880 --> 00:21:00.670 align:middle line:90% we were using the monthly data. 00:21:00.670 --> 00:21:02.110 align:middle line:90% And those are stars. 00:21:02.110 --> 00:21:05.230 align:middle line:84% And if you look really closely, you'll 00:21:05.230 --> 00:21:08.590 align:middle line:84% eventually find a cluster with the stars that 00:21:08.590 --> 00:21:10.420 align:middle line:90% correspond to the monthly data. 00:21:10.420 --> 00:21:14.420 align:middle line:84% The annual data are spread out much more. 00:21:14.420 --> 00:21:15.580 align:middle line:90% Those stars are up here. 00:21:15.580 --> 00:21:17.560 align:middle line:90% They're just not visible. 00:21:17.560 --> 00:21:20.170 align:middle line:84% I know these provinces like the back of my hand 00:21:20.170 --> 00:21:22.090 align:middle line:84% because I've been there so often. 00:21:22.090 --> 00:21:27.850 align:middle line:84% OK, so again, Thai data, 1997 onwards, 00:21:27.850 --> 00:21:30.190 align:middle line:90% almost 3,000 households. 00:21:30.190 --> 00:21:32.260 align:middle line:84% They're running their businesses. 00:21:32.260 --> 00:21:35.800 align:middle line:84% As you know, livestock, fish, shrimp, farm, 00:21:35.800 --> 00:21:38.470 align:middle line:90% and small business like vendors. 00:21:38.470 --> 00:21:40.870 align:middle line:84% And we have those two regions of the country. 00:21:40.870 --> 00:21:43.900 align:middle line:84% The cool thing is that in 1997, we 00:21:43.900 --> 00:21:46.240 align:middle line:84% had the foresight to ask about some 00:21:46.240 --> 00:21:49.790 align:middle line:84% of the things that had happened in the last five years. 00:21:49.790 --> 00:21:53.200 align:middle line:84% So we have their wealth retrospectively, 00:21:53.200 --> 00:21:56.260 align:middle line:84% what it was five years ago before 1997, 00:21:56.260 --> 00:22:00.970 align:middle line:84% and also what kind of occupation they were engaged in five years 00:22:00.970 --> 00:22:02.440 align:middle line:90% before 1997. 00:22:02.440 --> 00:22:06.580 align:middle line:84% So that those are two of the key variables, namely, 00:22:06.580 --> 00:22:09.640 align:middle line:84% how much wealth did you have in 1992? 00:22:09.640 --> 00:22:13.330 align:middle line:84% And what business were you in 1992? 00:22:13.330 --> 00:22:16.330 align:middle line:84% And then, did you change your occupation, say, 00:22:16.330 --> 00:22:19.960 align:middle line:84% going from being a wage earner to going into business 00:22:19.960 --> 00:22:22.090 align:middle line:90% over those five year periods? 00:22:22.090 --> 00:22:24.940 align:middle line:84% And again, we're going to find the bottom line is 00:22:24.940 --> 00:22:28.990 align:middle line:84% the data on wealth and occupation transitions 00:22:28.990 --> 00:22:31.510 align:middle line:84% as well as the cross-sectional data is going 00:22:31.510 --> 00:22:35.590 align:middle line:84% to favor moral hazard as being the constraint in the wealthier 00:22:35.590 --> 00:22:36.760 align:middle line:90% central region. 00:22:36.760 --> 00:22:40.600 align:middle line:84% And in the Northeast, it's going to be that limited liability, 00:22:40.600 --> 00:22:43.420 align:middle line:84% although frequently, both limited liability 00:22:43.420 --> 00:22:46.270 align:middle line:90% and moral hazard in combination. 00:22:46.270 --> 00:22:48.340 align:middle line:84% So hopefully, you're wondering how on Earth we 00:22:48.340 --> 00:22:50.740 align:middle line:90% could ever figure this all out. 00:22:50.740 --> 00:22:54.670 align:middle line:84% Here, by the way, is the picture of increasing wealth 00:22:54.670 --> 00:22:58.060 align:middle line:84% and increasing probability of making 00:22:58.060 --> 00:22:59.590 align:middle line:90% a transition into business. 00:22:59.590 --> 00:23:04.270 align:middle line:84% So this line here is upward sloping, the higher the wealth, 00:23:04.270 --> 00:23:06.260 align:middle line:90% the higher the transition. 00:23:06.260 --> 00:23:10.180 align:middle line:84% But this could, in theory, be a very steep profile 00:23:10.180 --> 00:23:12.040 align:middle line:90% or a very flat one. 00:23:12.040 --> 00:23:16.360 align:middle line:84% So part of it is estimating the profile suggested by the theory 00:23:16.360 --> 00:23:19.120 align:middle line:84% and then comparing it to the actual data. 00:23:19.120 --> 00:23:20.320 align:middle line:90% Here's the model. 00:23:20.320 --> 00:23:24.850 align:middle line:84% So agents, all these ingredients should be very familiar by now. 00:23:24.850 --> 00:23:28.180 align:middle line:84% You've seen them at least twice and maybe more. 00:23:28.180 --> 00:23:32.650 align:middle line:84% Households that could run a firm or could just be a wage earner 00:23:32.650 --> 00:23:35.840 align:middle line:84% cares about the utility of consumption and effort. 00:23:35.840 --> 00:23:39.310 align:middle line:84% So the consumption part is constant relative risk 00:23:39.310 --> 00:23:40.580 align:middle line:90% aversion. 00:23:40.580 --> 00:23:44.750 align:middle line:84% And the degree of risk aversion is gamma when gamma is zero. 00:23:44.750 --> 00:23:45.860 align:middle line:90% This thing is linear. 00:23:45.860 --> 00:23:48.710 align:middle line:84% That's risk neutral so not risk averse at all. 00:23:48.710 --> 00:23:50.960 align:middle line:84% As gamma gets higher and higher, you 00:23:50.960 --> 00:23:53.250 align:middle line:90% have more and more curvature. 00:23:53.250 --> 00:23:56.990 align:middle line:84% And then entering inseparably, linearly 00:23:56.990 --> 00:24:01.670 align:middle line:84% is this utility of effort, Z being effort, taking care, 00:24:01.670 --> 00:24:04.370 align:middle line:84% due diligence, how hard you're working, 00:24:04.370 --> 00:24:08.420 align:middle line:84% again, raised to a power like constant relative risk aversion 00:24:08.420 --> 00:24:10.070 align:middle line:90% to a different degree. 00:24:10.070 --> 00:24:13.250 align:middle line:84% Gamma 2, rather than gamma 1 and kappa, 00:24:13.250 --> 00:24:17.870 align:middle line:84% reflects the utility trade-off between consumption and effort. 00:24:17.870 --> 00:24:20.580 align:middle line:84% So not to say you need to memorize this. 00:24:20.580 --> 00:24:22.940 align:middle line:84% But we can pay attention to the parameters. 00:24:22.940 --> 00:24:27.020 align:middle line:84% We got three of them here, gamma 1, gamma 2, and kappa. 00:24:27.020 --> 00:24:29.360 align:middle line:84% So we would like to estimate those. 00:24:29.360 --> 00:24:32.660 align:middle line:84% And we will start looking at the model 00:24:32.660 --> 00:24:35.750 align:middle line:84% when gamma 1 is zero, hence, risk neutral, 00:24:35.750 --> 00:24:38.810 align:middle line:84% and then let them be risk averse and estimate 00:24:38.810 --> 00:24:40.280 align:middle line:90% the model generally. 00:24:40.280 --> 00:24:44.000 align:middle line:84% The estimation will use linear programming. 00:24:44.000 --> 00:24:46.790 align:middle line:84% You've seen this trade-off between consumption and effort. 00:24:46.790 --> 00:24:50.690 align:middle line:84% When we did the lecture on utility and preferences, 00:24:50.690 --> 00:24:52.730 align:middle line:84% there was a slide at the very end 00:24:52.730 --> 00:24:56.270 align:middle line:84% that had the agent choosing between work and wheat 00:24:56.270 --> 00:24:57.530 align:middle line:90% as an output. 00:24:57.530 --> 00:25:00.770 align:middle line:84% And we actually did that in the right-hand side 00:25:00.770 --> 00:25:02.900 align:middle line:84% with respect to consumption and leisure 00:25:02.900 --> 00:25:04.520 align:middle line:84% or the left-hand side with respect 00:25:04.520 --> 00:25:06.050 align:middle line:90% to consumption and effort. 00:25:06.050 --> 00:25:11.240 align:middle line:84% So this is a parametric version of those same preferences. 00:25:11.240 --> 00:25:15.080 align:middle line:84% More on the model, households differ with respect 00:25:15.080 --> 00:25:16.550 align:middle line:90% to initial wealth. 00:25:16.550 --> 00:25:19.430 align:middle line:84% As I said, call that A for assets. 00:25:19.430 --> 00:25:22.220 align:middle line:84% They differ with respect to talent, theta. 00:25:22.220 --> 00:25:24.950 align:middle line:84% Some people are better things than other people 00:25:24.950 --> 00:25:26.780 align:middle line:90% like running a business. 00:25:26.780 --> 00:25:31.010 align:middle line:84% And S as is the level of schooling, formal education. 00:25:31.010 --> 00:25:36.410 align:middle line:84% All are observed by the agents and even by the banks. 00:25:36.410 --> 00:25:38.360 align:middle line:90% That's a bit of a stretch. 00:25:38.360 --> 00:25:41.060 align:middle line:84% But we are imagining the bank can see wealth 00:25:41.060 --> 00:25:43.670 align:middle line:90% and talent and education. 00:25:43.670 --> 00:25:47.660 align:middle line:84% We however, only see what we have in the data, which 00:25:47.660 --> 00:25:49.640 align:middle line:90% is wealth and schooling. 00:25:49.640 --> 00:25:53.060 align:middle line:84% We do not see talent as modelers. 00:25:53.060 --> 00:25:56.690 align:middle line:84% But we can make some assumption about it, namely, 00:25:56.690 --> 00:25:57.980 align:middle line:90% it's log linear. 00:25:57.980 --> 00:26:03.360 align:middle line:84% Talent log theta is log linear in assets and schooling. 00:26:03.360 --> 00:26:06.530 align:middle line:84% And we assume that error term is normally 00:26:06.530 --> 00:26:10.520 align:middle line:84% distributed with a mean 0 and variance of 1. 00:26:10.520 --> 00:26:12.210 align:middle line:90% Why are we doing this? 00:26:12.210 --> 00:26:14.180 align:middle line:84% Well, we want to distinguish the constraint. 00:26:14.180 --> 00:26:17.570 align:middle line:84% But the worry is that talented people in the past 00:26:17.570 --> 00:26:19.910 align:middle line:84% have been more successful and hence, already 00:26:19.910 --> 00:26:21.470 align:middle line:90% have higher assets. 00:26:21.470 --> 00:26:25.160 align:middle line:84% We want to be able to distinguish the set part, which 00:26:25.160 --> 00:26:29.480 align:middle line:84% is wealth, which plays a role in the financing constraints, 00:26:29.480 --> 00:26:32.750 align:middle line:84% versus talent, which is productivity, which is entry 00:26:32.750 --> 00:26:34.640 align:middle line:90% in the production function. 00:26:34.640 --> 00:26:37.790 align:middle line:84% If we didn't allow talent to depend on wealth, 00:26:37.790 --> 00:26:42.080 align:middle line:84% then we could incorrectly infer that financing constraints are 00:26:42.080 --> 00:26:44.750 align:middle line:84% playing a role because higher wealth allows 00:26:44.750 --> 00:26:45.890 align:middle line:90% people to do better. 00:26:45.890 --> 00:26:47.870 align:middle line:84% But actually, it could be playing a role 00:26:47.870 --> 00:26:49.670 align:middle line:84% through this third variable, namely 00:26:49.670 --> 00:26:52.190 align:middle line:84% talent, that higher wealth means higher talent, 00:26:52.190 --> 00:26:53.540 align:middle line:90% reflects higher talent. 00:26:53.540 --> 00:26:55.550 align:middle line:84% And it's actually higher talent that 00:26:55.550 --> 00:26:58.610 align:middle line:84% is the reason some people are in business and operating 00:26:58.610 --> 00:26:59.930 align:middle line:90% at a higher scale. 00:26:59.930 --> 00:27:02.630 align:middle line:84% So this is kind of a shorthand way 00:27:02.630 --> 00:27:08.390 align:middle line:84% to allow things to be correlated and not incorrectly infer 00:27:08.390 --> 00:27:10.520 align:middle line:90% something about causality. 00:27:10.520 --> 00:27:15.700 align:middle line:84% Other parts of the model, q is output, profits. 00:27:15.700 --> 00:27:19.690 align:middle line:84% It's a function of effort and capital if you're a firm. 00:27:19.690 --> 00:27:23.500 align:middle line:84% Or wage-earners, if you're not a firm, 00:27:23.500 --> 00:27:28.030 align:middle line:84% this output can take on two values for simplicity, 00:27:28.030 --> 00:27:30.710 align:middle line:90% namely success and failure. 00:27:30.710 --> 00:27:34.525 align:middle line:84% So when they're successful in the project, the value of q 00:27:34.525 --> 00:27:35.300 align:middle line:90% is theta. 00:27:35.300 --> 00:27:40.030 align:middle line:84% So more talented entrepreneurs have higher output conditioned 00:27:40.030 --> 00:27:41.770 align:middle line:90% on being successful. 00:27:41.770 --> 00:27:44.860 align:middle line:84% And the other simplification is the failure, which 00:27:44.860 --> 00:27:46.790 align:middle line:90% means they have zero output. 00:27:46.790 --> 00:27:50.290 align:middle line:84% And if you have zero output, then you're 00:27:50.290 --> 00:27:51.550 align:middle line:90% not going to repay a loan. 00:27:51.550 --> 00:27:54.800 align:middle line:84% And there's no output with which to repay the loan. 00:27:54.800 --> 00:27:59.410 align:middle line:84% So this whole branch of q equals 0 becomes simplistic. 00:27:59.410 --> 00:28:03.490 align:middle line:84% Anyway, yeah, two extremes here, three really. 00:28:03.490 --> 00:28:06.190 align:middle line:84% Talent only enters through success. 00:28:06.190 --> 00:28:09.340 align:middle line:84% There's only two values of profitability, success 00:28:09.340 --> 00:28:10.660 align:middle line:90% or failure. 00:28:10.660 --> 00:28:14.120 align:middle line:84% And failure corresponds with zero output. 00:28:14.120 --> 00:28:17.740 align:middle line:84% So let's look then at the probability of success. 00:28:17.740 --> 00:28:21.370 align:middle line:84% The probability of q is equal to theta, the high one, 00:28:21.370 --> 00:28:24.490 align:middle line:84% conditioned on effort and the level of capitalization 00:28:24.490 --> 00:28:25.520 align:middle line:90% of the firm. 00:28:25.520 --> 00:28:29.680 align:middle line:84% And that's essentially in the numerator like a Cobb-Douglass 00:28:29.680 --> 00:28:31.150 align:middle line:90% function. 00:28:31.150 --> 00:28:32.230 align:middle line:90% K is capital. 00:28:32.230 --> 00:28:36.040 align:middle line:84% z is effort to the power is alpha and 1 minus alpha, 00:28:36.040 --> 00:28:37.940 align:middle line:90% a function you've seen before. 00:28:37.940 --> 00:28:40.240 align:middle line:84% Now why is it being divided by something? 00:28:40.240 --> 00:28:44.830 align:middle line:84% Well, this whole thing is supposed to be a probability. 00:28:44.830 --> 00:28:50.050 align:middle line:84% Probability of success is a number between 0 and 1. 00:28:50.050 --> 00:28:55.180 align:middle line:84% So if k and z were 0, the numerator is 0. 00:28:55.180 --> 00:28:58.150 align:middle line:90% 0 divided by 1 is 0. 00:28:58.150 --> 00:29:00.700 align:middle line:90% So that's the left endpoint. 00:29:00.700 --> 00:29:05.410 align:middle line:84% And likewise, if k and z are getting really, really big 00:29:05.410 --> 00:29:08.060 align:middle line:84% and there's no natural bound here yet, 00:29:08.060 --> 00:29:10.750 align:middle line:84% then this numerator is getting really big. 00:29:10.750 --> 00:29:14.120 align:middle line:84% But so is the same term in the denominator. 00:29:14.120 --> 00:29:17.470 align:middle line:84% So this whole term is going to 1 because the numerator 00:29:17.470 --> 00:29:20.420 align:middle line:84% and denominator are getting very, very similar. 00:29:20.420 --> 00:29:25.510 align:middle line:84% So this P function is a probability between 0 and 1, 00:29:25.510 --> 00:29:30.490 align:middle line:84% no matter what k and z are put into the firm. 00:29:30.490 --> 00:29:32.830 align:middle line:84% Output is always going to be observed 00:29:32.830 --> 00:29:35.050 align:middle line:90% in the models that follow. 00:29:35.050 --> 00:29:39.130 align:middle line:84% The issue is going to be whether this effort z is observed 00:29:39.130 --> 00:29:43.660 align:middle line:84% or not and whether k is restricted by the collateral 00:29:43.660 --> 00:29:44.300 align:middle line:90% constraint. 00:29:44.300 --> 00:29:46.250 align:middle line:84% And I will show you that in a minute. 00:29:46.250 --> 00:29:48.730 align:middle line:84% And finally, the other branch, not to lose sight of it, 00:29:48.730 --> 00:29:50.680 align:middle line:84% they could choose not to be a firm, 00:29:50.680 --> 00:29:52.900 align:middle line:90% in which case k is equal to 0. 00:29:52.900 --> 00:29:57.460 align:middle line:84% And when k is equal to 0, the firm is not capitalized. 00:29:57.460 --> 00:30:00.520 align:middle line:84% And effectively, the household is a wage earner. 00:30:00.520 --> 00:30:04.120 align:middle line:84% So earnings in the wage sector are also 00:30:04.120 --> 00:30:06.730 align:middle line:90% stochastic and probabilistic. 00:30:06.730 --> 00:30:10.150 align:middle line:90% You can work hard to find a job. 00:30:10.150 --> 00:30:12.760 align:middle line:84% That doesn't mean you will find one. 00:30:12.760 --> 00:30:16.700 align:middle line:84% The higher effort you devote toward finding a job, 00:30:16.700 --> 00:30:19.210 align:middle line:84% the higher would be the probability 00:30:19.210 --> 00:30:21.850 align:middle line:90% of getting the wage. 00:30:21.850 --> 00:30:25.300 align:middle line:84% And again, this is bounded between 0 and 1. 00:30:25.300 --> 00:30:28.270 align:middle line:84% Now if you are a firm, you may or may not borrow. 00:30:28.270 --> 00:30:30.850 align:middle line:84% But if you borrow, there's going to be an interest rate 00:30:30.850 --> 00:30:33.700 align:middle line:84% schedule that determines how much you pay back. 00:30:33.700 --> 00:30:36.520 align:middle line:84% And that interest rate schedule is a function of two 00:30:36.520 --> 00:30:39.250 align:middle line:84% of the things the lending firm observes, 00:30:39.250 --> 00:30:42.640 align:middle line:84% the wealth of the household and the household's talent. 00:30:42.640 --> 00:30:44.920 align:middle line:84% And this schedule is going to be such 00:30:44.920 --> 00:30:47.890 align:middle line:84% that the banks, although maximizing profits, 00:30:47.890 --> 00:30:49.990 align:middle line:90% can at best break even. 00:30:49.990 --> 00:30:52.220 align:middle line:84% And I'll show you that constraint in a minute. 00:30:52.220 --> 00:30:55.660 align:middle line:84% But I already alluded to it in the sense of moral hazard being 00:30:55.660 --> 00:30:57.820 align:middle line:84% a problem because repayment going down 00:30:57.820 --> 00:31:00.790 align:middle line:84% and banks having to raise interest rates to cover 00:31:00.790 --> 00:31:02.830 align:middle line:90% what otherwise would be losses. 00:31:02.830 --> 00:31:06.130 align:middle line:84% They have to get enough from the successful firms 00:31:06.130 --> 00:31:09.010 align:middle line:84% to cover the fact that the unsuccessful ones are not 00:31:09.010 --> 00:31:10.600 align:middle line:90% paying off the loans. 00:31:10.600 --> 00:31:15.130 align:middle line:84% When you're a worker or a firm that is not 00:31:15.130 --> 00:31:16.990 align:middle line:84% using all their resources to borrow, 00:31:16.990 --> 00:31:19.510 align:middle line:84% you have some residual assets left. 00:31:19.510 --> 00:31:20.720 align:middle line:90% They put it in the bank. 00:31:20.720 --> 00:31:23.140 align:middle line:84% And they earn the riskless rate of return. 00:31:23.140 --> 00:31:26.350 align:middle line:84% So in some respects, there's both borrowing and saving 00:31:26.350 --> 00:31:30.280 align:middle line:84% going on here, depending on what occupation you choose 00:31:30.280 --> 00:31:32.780 align:middle line:84% and your underlying characteristics. 00:31:32.780 --> 00:31:35.660 align:middle line:84% So how are we going to solve this problem? 00:31:35.660 --> 00:31:39.130 align:middle line:84% We're going to solve for a constrained optimum. 00:31:39.130 --> 00:31:41.530 align:middle line:84% We are going to write down a quote, unquote 00:31:41.530 --> 00:31:45.220 align:middle line:84% "planner's problem," which I sometimes refer to the math 00:31:45.220 --> 00:31:49.930 align:middle line:84% problem, which is maximizing lambda weighted sums 00:31:49.930 --> 00:31:54.370 align:middle line:84% of utilities subject to resource, truth-telling, 00:31:54.370 --> 00:31:56.620 align:middle line:90% and liability constraints. 00:31:56.620 --> 00:32:01.240 align:middle line:84% Now to restate that, we're going to maximize 00:32:01.240 --> 00:32:05.320 align:middle line:84% the utility, a weighted sum of the utility of borrowers 00:32:05.320 --> 00:32:08.060 align:middle line:90% and the utility of the banks. 00:32:08.060 --> 00:32:10.790 align:middle line:84% The banks, however, could make profits. 00:32:10.790 --> 00:32:13.230 align:middle line:84% So we're just distinguishing, in their case, 00:32:13.230 --> 00:32:16.530 align:middle line:90% profits as a version of utility. 00:32:16.530 --> 00:32:19.800 align:middle line:84% The second thing is, and I didn't reload this picture, 00:32:19.800 --> 00:32:21.300 align:middle line:84% if you go back to the lecture where 00:32:21.300 --> 00:32:24.660 align:middle line:84% we introduced the notion of Pareto optimality. 00:32:24.660 --> 00:32:27.480 align:middle line:84% We had the so-called Pareto frontier. 00:32:27.480 --> 00:32:29.910 align:middle line:84% And we decided the points on the frontier 00:32:29.910 --> 00:32:31.930 align:middle line:90% would be Pareto optimal. 00:32:31.930 --> 00:32:33.540 align:middle line:84% And you could achieve those points 00:32:33.540 --> 00:32:36.690 align:middle line:84% by maximizing a particular lambda-weighted sum 00:32:36.690 --> 00:32:40.380 align:middle line:84% of utilities, or in this case, a particular lambda-weighted sum 00:32:40.380 --> 00:32:42.870 align:middle line:84% of profits and utility of the borrower. 00:32:42.870 --> 00:32:44.770 align:middle line:84% But there is another way to do it, 00:32:44.770 --> 00:32:47.580 align:middle line:84% which is to maximize the utility of the borrower, 00:32:47.580 --> 00:32:51.750 align:middle line:84% subject to a fixed profit level of the bank. 00:32:51.750 --> 00:32:56.760 align:middle line:84% Its equivalent, normally, with these concave frontiers. 00:32:56.760 --> 00:32:59.520 align:middle line:84% Then the next step is, OK, there are many, many banks. 00:32:59.520 --> 00:33:01.020 align:middle line:90% And they're competing. 00:33:01.020 --> 00:33:04.890 align:middle line:84% If one representative bank were to make a profit with respect 00:33:04.890 --> 00:33:07.620 align:middle line:84% to the borrowing customers, another bank 00:33:07.620 --> 00:33:10.260 align:middle line:84% could step in and undercut the first one 00:33:10.260 --> 00:33:12.250 align:middle line:90% and do slightly better. 00:33:12.250 --> 00:33:14.640 align:middle line:84% So this competitive process is going 00:33:14.640 --> 00:33:18.720 align:middle line:84% to drive the profits of the bank down to 0. 00:33:18.720 --> 00:33:22.020 align:middle line:84% So we're going to be looking at particular Pareto optimum 00:33:22.020 --> 00:33:24.030 align:middle line:84% where the utilities of the borrowers 00:33:24.030 --> 00:33:27.420 align:middle line:84% are maximized, subject to a zero profit constraint 00:33:27.420 --> 00:33:28.860 align:middle line:90% on the part of the lenders. 00:33:28.860 --> 00:33:32.460 align:middle line:84% There are other optima we're not going to look at today. 00:33:32.460 --> 00:33:35.250 align:middle line:84% Although, it's going to be clear from the equations how we 00:33:35.250 --> 00:33:38.490 align:middle line:84% could have done it more generally. 00:33:38.490 --> 00:33:41.970 align:middle line:84% So this is the utility of the borrower. 00:33:41.970 --> 00:33:45.820 align:middle line:84% There are three possible branches. 00:33:45.820 --> 00:33:47.970 align:middle line:84% This is, again, the risk-neutral borrower. 00:33:47.970 --> 00:33:53.350 align:middle line:84% To get warmed up, if k is 0, which is a choice. 00:33:53.350 --> 00:33:56.340 align:middle line:84% But if the solution is k equal to 0, 00:33:56.340 --> 00:33:59.850 align:middle line:84% then, in fact, the household is a wage-earner, not 00:33:59.850 --> 00:34:02.850 align:middle line:84% a firm, deciding on effort, which 00:34:02.850 --> 00:34:05.670 align:middle line:84% determines the probability of getting the wage, 00:34:05.670 --> 00:34:08.760 align:middle line:84% although it comes at a disutility cost of working. 00:34:08.760 --> 00:34:10.770 align:middle line:84% And they put all their wealth in the bank. 00:34:10.770 --> 00:34:14.040 align:middle line:84% So that risk free rate of interest times assets 00:34:14.040 --> 00:34:16.620 align:middle line:84% is something they get at the end of the period, 00:34:16.620 --> 00:34:18.270 align:middle line:90% the savings account. 00:34:18.270 --> 00:34:21.719 align:middle line:84% The second branch is they do go into business 00:34:21.719 --> 00:34:24.210 align:middle line:84% and there's capitalization is positive, 00:34:24.210 --> 00:34:29.880 align:middle line:84% but it's less than their assets, so they can basically 00:34:29.880 --> 00:34:34.139 align:middle line:84% take what's left, assets minus capitalization, 00:34:34.139 --> 00:34:35.400 align:middle line:90% and put it in the bank. 00:34:35.400 --> 00:34:38.489 align:middle line:84% So these guys also get a return on savings. 00:34:38.489 --> 00:34:41.580 align:middle line:84% But part of their wealth, the k part, 00:34:41.580 --> 00:34:43.989 align:middle line:84% is stuck into the production function. 00:34:43.989 --> 00:34:48.389 align:middle line:84% So the return on that comes from the possibility of profits. 00:34:48.389 --> 00:34:49.889 align:middle line:84% And you still have this trade-off 00:34:49.889 --> 00:34:53.980 align:middle line:84% of probability of success versus the disutility of effort. 00:34:53.980 --> 00:34:55.949 align:middle line:84% And then the final branch here is, 00:34:55.949 --> 00:34:59.850 align:middle line:84% these guys have a k, which is relatively large relative 00:34:59.850 --> 00:35:00.820 align:middle line:90% to their assets. 00:35:00.820 --> 00:35:02.460 align:middle line:90% So they got to borrow. 00:35:02.460 --> 00:35:05.820 align:middle line:84% And this sign here is a bit confusing. 00:35:05.820 --> 00:35:10.110 align:middle line:84% But if k is greater than a then a is less than k. 00:35:10.110 --> 00:35:11.670 align:middle line:90% So this term is negative. 00:35:11.670 --> 00:35:15.090 align:middle line:84% So naturally, they're quote, "negative" 00:35:15.090 --> 00:35:18.180 align:middle line:84% paying off the principal and the interest on the loan. 00:35:18.180 --> 00:35:21.100 align:middle line:84% And they only pay it off if they're successful. 00:35:21.100 --> 00:35:24.180 align:middle line:84% So again, this modified Cobb-Douglas probability 00:35:24.180 --> 00:35:27.240 align:middle line:84% expression is entering in there as it does 00:35:27.240 --> 00:35:30.070 align:middle line:90% for the probability of success. 00:35:30.070 --> 00:35:32.590 align:middle line:90% So those are the three branches. 00:35:32.590 --> 00:35:34.590 align:middle line:84% This is the break-even constraint 00:35:34.590 --> 00:35:37.830 align:middle line:84% of the bank, which as I've said in words a couple of times 00:35:37.830 --> 00:35:40.270 align:middle line:84% already, this is the risk-free rate. 00:35:40.270 --> 00:35:43.500 align:middle line:84% So a bank has basically got to get funds from somewhere, 00:35:43.500 --> 00:35:45.760 align:middle line:90% from depositors, actually. 00:35:45.760 --> 00:35:48.030 align:middle line:84% And they've got to break even because 00:35:48.030 --> 00:35:49.410 align:middle line:90% of all that competition. 00:35:49.410 --> 00:35:53.400 align:middle line:84% So they may get a higher return, depending on the borrower's 00:35:53.400 --> 00:35:54.960 align:middle line:90% wealth and talent. 00:35:54.960 --> 00:35:58.480 align:middle line:84% But they only get that back when that borrower is successful. 00:35:58.480 --> 00:36:01.470 align:middle line:84% So this is the expected return given the interest rate 00:36:01.470 --> 00:36:02.190 align:middle line:90% schedule. 00:36:02.190 --> 00:36:06.100 align:middle line:84% And that is driven down to the risk-free rate. 00:36:06.100 --> 00:36:09.060 align:middle line:84% So we have this 0 profit constraint 00:36:09.060 --> 00:36:12.070 align:middle line:84% to impose as part of the solution. 00:36:12.070 --> 00:36:14.340 align:middle line:84% So again, to repeat myself, instead 00:36:14.340 --> 00:36:17.100 align:middle line:84% of maximizing a lambda-weighted sum of utilities, 00:36:17.100 --> 00:36:19.620 align:middle line:84% we're going to maximize the utility of the borrower 00:36:19.620 --> 00:36:23.730 align:middle line:84% subject to a particular lambda for the bank, 00:36:23.730 --> 00:36:27.060 align:middle line:84% a lambda, which is associated with making zero profits. 00:36:27.060 --> 00:36:29.610 align:middle line:84% And we just impose the zero-profit constraint 00:36:29.610 --> 00:36:30.810 align:middle line:90% from the get go. 00:36:30.810 --> 00:36:33.300 align:middle line:84% It's also kind of interesting in terms 00:36:33.300 --> 00:36:36.000 align:middle line:84% of where we are in the class because when we first 00:36:36.000 --> 00:36:38.760 align:middle line:84% introduced utility maximization, we 00:36:38.760 --> 00:36:42.750 align:middle line:84% had these partial equilibrium exercises in which prices 00:36:42.750 --> 00:36:46.110 align:middle line:84% and so on were taken as given, although we varied them to see 00:36:46.110 --> 00:36:47.670 align:middle line:90% what the household will do. 00:36:47.670 --> 00:36:52.140 align:middle line:84% Likewise, when we did the firm, we had input prices as 00:36:52.140 --> 00:36:53.200 align:middle line:90% taken as given. 00:36:53.200 --> 00:36:55.090 align:middle line:90% And we did some experiments. 00:36:55.090 --> 00:36:58.020 align:middle line:84% And here, likewise, we're in quote, unquote 00:36:58.020 --> 00:37:00.060 align:middle line:84% "partial equilibrium" in the sense 00:37:00.060 --> 00:37:04.865 align:middle line:84% that wage and the interest rate are given to us. 00:37:04.865 --> 00:37:06.240 align:middle line:84% We're not trying to explain them. 00:37:06.240 --> 00:37:07.870 align:middle line:84% They're going to be part of the data. 00:37:07.870 --> 00:37:11.110 align:middle line:84% On the other hand, we're definitely doing a contracting 00:37:11.110 --> 00:37:12.640 align:middle line:90% a problem here. 00:37:12.640 --> 00:37:16.090 align:middle line:84% And to do it, we have to draw on those tools about Pareto 00:37:16.090 --> 00:37:19.180 align:middle line:84% optimality and so on and how to determine 00:37:19.180 --> 00:37:22.400 align:middle line:84% Pareto optimal outcomes via programming problems. 00:37:22.400 --> 00:37:26.860 align:middle line:84% So we kind of are drawing on to different segments of the class 00:37:26.860 --> 00:37:29.870 align:middle line:84% that we've covered already in this application. 00:37:29.870 --> 00:37:32.390 align:middle line:84% So let's talk about limited liability. 00:37:32.390 --> 00:37:35.890 align:middle line:84% So limited liability, let's just jump down here. 00:37:35.890 --> 00:37:37.060 align:middle line:90% It's easier here. 00:37:37.060 --> 00:37:40.870 align:middle line:84% k, that they can use the capitalization of the firm, 00:37:40.870 --> 00:37:44.740 align:middle line:84% is bounded above by their assets. 00:37:44.740 --> 00:37:48.760 align:middle line:84% Actually, it's lambda, some proportionality times assets. 00:37:48.760 --> 00:37:51.490 align:middle line:84% So this is referred to as a borrowing constraint. 00:37:51.490 --> 00:37:54.010 align:middle line:84% Now lambda could be greater than 1. 00:37:54.010 --> 00:37:56.900 align:middle line:84% They may be able to borrow more than their wealth. 00:37:56.900 --> 00:37:58.380 align:middle line:90% But it is limited. 00:37:58.380 --> 00:38:00.130 align:middle line:84% There's a little bit of a derivation here. 00:38:00.130 --> 00:38:01.672 align:middle line:84% I was thinking about it this morning. 00:38:01.672 --> 00:38:04.330 align:middle line:84% It's not really all that compelling. 00:38:04.330 --> 00:38:06.670 align:middle line:84% You can derive this constraint by saying 00:38:06.670 --> 00:38:09.940 align:middle line:84% there's a maximum amount they can invest in the firm. 00:38:09.940 --> 00:38:12.800 align:middle line:84% Then you write down the equation for borrowing, 00:38:12.800 --> 00:38:15.790 align:middle line:84% which is the difference between capital and assets. 00:38:15.790 --> 00:38:19.240 align:middle line:84% And then substitute in that maximum amount for capital 00:38:19.240 --> 00:38:21.130 align:middle line:90% and derive this equation. 00:38:21.130 --> 00:38:23.890 align:middle line:84% This now has a on both sides of the equation, which 00:38:23.890 --> 00:38:24.550 align:middle line:90% you could drop. 00:38:24.550 --> 00:38:27.200 align:middle line:84% And you get the equation 6 as a result. 00:38:27.200 --> 00:38:30.100 align:middle line:84% But I'm perfectly happy if you wanted to start with 6. 00:38:30.100 --> 00:38:34.540 align:middle line:84% The capital is bounded from above due to a collateral 00:38:34.540 --> 00:38:36.820 align:middle line:90% constraint related to wealth. 00:38:36.820 --> 00:38:39.430 align:middle line:84% That's the limited liability version. 00:38:39.430 --> 00:38:41.410 align:middle line:90% Here's the moral hazard version. 00:38:41.410 --> 00:38:46.060 align:middle line:84% In this case, the bank does not see the borrower's effort. 00:38:46.060 --> 00:38:49.540 align:middle line:84% So whatever the contract is in terms of that repayment 00:38:49.540 --> 00:38:53.530 align:middle line:84% schedule, and whatever the level of capitalization that 00:38:53.530 --> 00:38:58.150 align:middle line:84% the borrower can manage, the choice of how much to work is 00:38:58.150 --> 00:39:02.080 align:middle line:84% done by the borrower alone and cannot be dictated. 00:39:02.080 --> 00:39:06.380 align:middle line:84% And it's going to be summarized by a first-order condition, 00:39:06.380 --> 00:39:09.250 align:middle line:84% which is like a solution to the subproblem. 00:39:09.250 --> 00:39:11.020 align:middle line:90% Which subproblem? 00:39:11.020 --> 00:39:13.670 align:middle line:90% This subproblem here. 00:39:13.670 --> 00:39:17.710 align:middle line:84% So this is the branch where the household as firm is borrowing. 00:39:17.710 --> 00:39:22.930 align:middle line:84% And its payoff in curly brackets is, in part, a function of z. 00:39:22.930 --> 00:39:25.360 align:middle line:84% So if you differentiate this function 00:39:25.360 --> 00:39:27.400 align:middle line:84% with respect to effort, you're going 00:39:27.400 --> 00:39:30.070 align:middle line:84% to get the way that the probability of success 00:39:30.070 --> 00:39:31.720 align:middle line:90% is increasing with effort. 00:39:31.720 --> 00:39:34.450 align:middle line:84% You're going to get a part with a negative sign reflecting 00:39:34.450 --> 00:39:35.980 align:middle line:90% the utility of effort. 00:39:35.980 --> 00:39:41.110 align:middle line:84% And this probability of success is also entering into this-- 00:39:41.110 --> 00:39:42.760 align:middle line:90% It's like the winner's curse. 00:39:42.760 --> 00:39:43.630 align:middle line:90% You win. 00:39:43.630 --> 00:39:45.460 align:middle line:90% Your profits are successful. 00:39:45.460 --> 00:39:46.960 align:middle line:84% But you've got to pay off the bank. 00:39:46.960 --> 00:39:49.960 align:middle line:84% So the harder you work, the more you repay. 00:39:49.960 --> 00:39:52.240 align:middle line:90% So take the derivative of this. 00:39:52.240 --> 00:39:54.190 align:middle line:84% And you get this first-order condition 00:39:54.190 --> 00:39:58.830 align:middle line:90% over here, equation seven. 00:39:58.830 --> 00:40:03.220 align:middle line:84% So that's the formality of it that it captures the notion, 00:40:03.220 --> 00:40:06.600 align:middle line:84% as I've said, that no matter what contract the firm is 00:40:06.600 --> 00:40:10.620 align:middle line:84% entering into, the bank cannot see the borrower's effort 00:40:10.620 --> 00:40:13.950 align:middle line:84% but knows how the borrower is determining it. 00:40:13.950 --> 00:40:17.000 align:middle line:84% So we get this equation 7 as another constraint 00:40:17.000 --> 00:40:20.790 align:middle line:84% on the program, if we believe moral hazard is strained. 00:40:20.790 --> 00:40:23.730 align:middle line:90% So we did limited liability. 00:40:23.730 --> 00:40:25.620 align:middle line:90% We did moral hazard. 00:40:25.620 --> 00:40:27.210 align:middle line:90% We could have both. 00:40:27.210 --> 00:40:31.560 align:middle line:84% And now I'll show you a very cool picture. 00:40:31.560 --> 00:40:36.600 align:middle line:84% So this is utility of a household as a firm. 00:40:36.600 --> 00:40:41.010 align:middle line:84% But on the x and y-axis are the inputs, the capital level 00:40:41.010 --> 00:40:42.930 align:middle line:90% and the effort level. 00:40:42.930 --> 00:40:45.420 align:middle line:84% If we did what we would call first best, 00:40:45.420 --> 00:40:48.810 align:middle line:84% meaning that we ignore all the limited liability 00:40:48.810 --> 00:40:50.880 align:middle line:84% and moral hazard constraints, then 00:40:50.880 --> 00:40:55.110 align:middle line:84% the borrower would maximize these choices of capital 00:40:55.110 --> 00:40:58.950 align:middle line:84% in effort, choose then to have maximal utility. 00:40:58.950 --> 00:41:01.620 align:middle line:84% And where is the utility maximal utility? 00:41:01.620 --> 00:41:03.790 align:middle line:84% It's in this bull's eye over here. 00:41:03.790 --> 00:41:05.790 align:middle line:84% So in other lectures, we've talked 00:41:05.790 --> 00:41:10.410 align:middle line:84% about bliss points, meaning, if you're below bliss, 00:41:10.410 --> 00:41:13.080 align:middle line:90% utility is increasing. 00:41:13.080 --> 00:41:15.870 align:middle line:84% Or you could go above bliss, which 00:41:15.870 --> 00:41:18.900 align:middle line:84% is kind of weird, in which case you want to dump stuff. 00:41:18.900 --> 00:41:21.420 align:middle line:84% This is an endogenous bliss point. 00:41:21.420 --> 00:41:24.700 align:middle line:84% This came from solving an underlying problem. 00:41:24.700 --> 00:41:27.900 align:middle line:84% But we can, nevertheless, plot the solution this way. 00:41:27.900 --> 00:41:29.910 align:middle line:90% And where do they want to be? 00:41:29.910 --> 00:41:33.990 align:middle line:84% As close to the bull's eye as possible but not northeast 00:41:33.990 --> 00:41:35.330 align:middle line:90% of it. 00:41:35.330 --> 00:41:38.960 align:middle line:84% OK, so now what are the constraints on the problem? 00:41:38.960 --> 00:41:41.640 align:middle line:84% There's this liability constraint, 00:41:41.640 --> 00:41:43.610 align:middle line:90% which is capital times lambda. 00:41:43.610 --> 00:41:47.180 align:middle line:84% And if that's the constraint in the world and hence, 00:41:47.180 --> 00:41:49.700 align:middle line:84% in the program, it just simply says, 00:41:49.700 --> 00:41:51.710 align:middle line:84% capital cannot be to the right of it. 00:41:51.710 --> 00:41:53.570 align:middle line:84% It can be to the left of it or on it. 00:41:53.570 --> 00:41:56.720 align:middle line:84% So all these solutions on the vertical line and left 00:41:56.720 --> 00:42:00.350 align:middle line:84% of the vertical line correspond to satisfying this 00:42:00.350 --> 00:42:03.840 align:middle line:84% capitalisation constraint for a given value of lambda, 00:42:03.840 --> 00:42:06.110 align:middle line:84% which is listed down here at the bottom of the slide. 00:42:06.110 --> 00:42:08.300 align:middle line:84% And where is the maximal solution? 00:42:08.300 --> 00:42:11.120 align:middle line:90% At the tangency right here. 00:42:11.120 --> 00:42:16.070 align:middle line:84% That's where the slope of these concentric rings goes vertical. 00:42:16.070 --> 00:42:18.240 align:middle line:90% OK, let's do the moral hazard. 00:42:18.240 --> 00:42:21.450 align:middle line:84% So ignore limited liability constraint 00:42:21.450 --> 00:42:24.320 align:middle line:90% and trace out this guy. 00:42:24.320 --> 00:42:26.690 align:middle line:84% I did not a priori what this constraint 00:42:26.690 --> 00:42:29.080 align:middle line:90% was going to look like. 00:42:29.080 --> 00:42:35.680 align:middle line:84% But if you plot it in the space of k and z, it looks like this. 00:42:35.680 --> 00:42:37.530 align:middle line:90% It's like this parabola. 00:42:37.530 --> 00:42:41.220 align:middle line:84% Alex was my student and RA for this project. 00:42:41.220 --> 00:42:44.220 align:middle line:84% And Anna and I, former student, were writing this paper. 00:42:44.220 --> 00:42:46.320 align:middle line:90% We shared the problem with Alex. 00:42:46.320 --> 00:42:48.030 align:middle line:84% And Alex came up with this graph. 00:42:48.030 --> 00:42:51.540 align:middle line:84% And Alex became a coauthor of the paper and subsequence 00:42:51.540 --> 00:42:53.340 align:middle line:90% collaborator in many things. 00:42:53.340 --> 00:42:55.000 align:middle line:90% Anyway, I love this graph. 00:42:55.000 --> 00:42:58.380 align:middle line:84% So if you want to satisfy the moral hazard constraint, 00:42:58.380 --> 00:43:00.630 align:middle line:84% you're going to be on the parabola. 00:43:00.630 --> 00:43:02.400 align:middle line:90% And where is the maximal point? 00:43:02.400 --> 00:43:05.610 align:middle line:84% It's again, a tangency with a concentric circle. 00:43:05.610 --> 00:43:07.330 align:middle line:90% And it's right here. 00:43:07.330 --> 00:43:10.770 align:middle line:84% So interestingly, if you compare these two points, 00:43:10.770 --> 00:43:12.990 align:middle line:84% the limited-liability constrained solution 00:43:12.990 --> 00:43:14.880 align:middle line:84% and the moral hazard constrained solution, 00:43:14.880 --> 00:43:18.210 align:middle line:84% limited liability involves less capital and more effort 00:43:18.210 --> 00:43:21.120 align:middle line:84% relative to the moral hazard solution which kind of makes 00:43:21.120 --> 00:43:25.110 align:middle line:84% sense because with moral hazard, the problem is inducing effort, 00:43:25.110 --> 00:43:26.220 align:middle line:90% not capital. 00:43:26.220 --> 00:43:28.350 align:middle line:84% With limited liability, the problem 00:43:28.350 --> 00:43:30.450 align:middle line:84% is financing that level of capital. 00:43:30.450 --> 00:43:32.310 align:middle line:90% and effort's fully observed. 00:43:32.310 --> 00:43:35.220 align:middle line:84% Now it turns out, if you have both constraints, 00:43:35.220 --> 00:43:37.390 align:middle line:84% in this world with risk neutrality, 00:43:37.390 --> 00:43:38.730 align:middle line:90% there's nothing to optimize. 00:43:38.730 --> 00:43:41.310 align:middle line:90% It's like two lines cross. 00:43:41.310 --> 00:43:43.440 align:middle line:84% Actually, technically, it's a vertical line 00:43:43.440 --> 00:43:44.970 align:middle line:90% crossing with a parabola. 00:43:44.970 --> 00:43:47.410 align:middle line:84% But it completely nails down the solution. 00:43:47.410 --> 00:43:51.190 align:middle line:84% So k and z are at the crossing over here. 00:43:51.190 --> 00:43:53.940 align:middle line:84% So what we're doing conceptually then 00:43:53.940 --> 00:43:56.520 align:middle line:84% is loading in these parameter values 00:43:56.520 --> 00:44:00.420 align:middle line:84% for, in this case, a particular talent level, particular asset 00:44:00.420 --> 00:44:03.180 align:middle line:84% level, alpha in the production function, 00:44:03.180 --> 00:44:05.670 align:middle line:84% kappa, which is the disutility of effort. 00:44:05.670 --> 00:44:08.160 align:middle line:84% And the power is lambda lambda, 1 is 0, 00:44:08.160 --> 00:44:12.450 align:middle line:84% et cetera, solving the model and delineating 00:44:12.450 --> 00:44:15.570 align:middle line:84% what happens with these various constraints, one, 00:44:15.570 --> 00:44:17.390 align:middle line:90% the other, or both. 00:44:17.390 --> 00:44:21.120 align:middle line:84% OK, so now we're going to generalize this. 00:44:21.120 --> 00:44:25.620 align:middle line:84% And in particular, we're going to let there be some risk. 00:44:25.620 --> 00:44:27.180 align:middle line:90% There is already risk. 00:44:27.180 --> 00:44:30.480 align:middle line:84% But we're going to let the household be risk-averse. 00:44:30.480 --> 00:44:35.730 align:middle line:84% So their payoff can depend on q, which they now care about. 00:44:35.730 --> 00:44:38.130 align:middle line:84% The dispersion, because they're risk-averse, 00:44:38.130 --> 00:44:42.510 align:middle line:84% so there's a consumption, this profit-sharing schedule. 00:44:42.510 --> 00:44:46.320 align:middle line:84% And we're going to want to solve for these probabilities. 00:44:46.320 --> 00:44:48.690 align:middle line:84% This kind of came up in the beginning of class, 00:44:48.690 --> 00:44:52.920 align:middle line:84% this pi is a probability number, an endogenous number 00:44:52.920 --> 00:44:55.930 align:middle line:84% that reflects the solution to a programming problem. 00:44:55.930 --> 00:44:57.750 align:middle line:84% So we're going to want to determine 00:44:57.750 --> 00:45:02.460 align:middle line:84% the probability of seeing this quadruple, a particular value 00:45:02.460 --> 00:45:07.800 align:middle line:84% c, particular value of q, a particular value of effort z, 00:45:07.800 --> 00:45:10.620 align:middle line:84% and a particular capitalization level, as 00:45:10.620 --> 00:45:13.860 align:middle line:84% a function of observed and unobserved characteristics 00:45:13.860 --> 00:45:17.940 align:middle line:84% of the borrower, namely, theta a and s, talent, assets, 00:45:17.940 --> 00:45:19.290 align:middle line:90% and schooling. 00:45:19.290 --> 00:45:24.100 align:middle line:84% So again, I don't remember what slide it's on. 00:45:24.100 --> 00:45:26.100 align:middle line:84% But we will determine the solution 00:45:26.100 --> 00:45:28.800 align:middle line:90% by these probabilities. 00:45:28.800 --> 00:45:30.660 align:middle line:90% There are lotteries. 00:45:30.660 --> 00:45:35.290 align:middle line:84% They will make our program and turn it into a linear program. 00:45:35.290 --> 00:45:37.290 align:middle line:84% And again, this is a bit of a review, 00:45:37.290 --> 00:45:39.990 align:middle line:84% but now in an interesting applied context. 00:45:39.990 --> 00:45:43.140 align:middle line:84% Remember, we had discrete values for consumption 00:45:43.140 --> 00:45:45.480 align:middle line:84% when we introduced the notion of risk. 00:45:45.480 --> 00:45:47.880 align:middle line:84% And we talked about the probability pi, 00:45:47.880 --> 00:45:52.200 align:middle line:84% of choosing a certain bundle, discrete bundle, c, cs, 00:45:52.200 --> 00:45:56.610 align:middle line:84% where s delineated all the possible discrete values of c. 00:45:56.610 --> 00:45:58.710 align:middle line:84% So that was one place that we did it. 00:45:58.710 --> 00:45:59.940 align:middle line:90% And there's been others. 00:45:59.940 --> 00:46:03.360 align:middle line:84% But I don't have it right off the top of my head. 00:46:03.360 --> 00:46:07.620 align:middle line:84% Oh sorry, in the mechanism design literature 00:46:07.620 --> 00:46:09.930 align:middle line:84% in the previous lecture we did it. 00:46:09.930 --> 00:46:12.780 align:middle line:84% We had deterministic programs and programs 00:46:12.780 --> 00:46:13.830 align:middle line:90% with the lotteries. 00:46:13.830 --> 00:46:17.790 align:middle line:84% So that's the second reason to have the lotteries. 00:46:17.790 --> 00:46:21.040 align:middle line:84% And I made the point there that they were linear programs. 00:46:21.040 --> 00:46:24.330 align:middle line:84% So despite putting in truth-telling constraints, 00:46:24.330 --> 00:46:26.430 align:middle line:84% when we have the lotteries, the constraints 00:46:26.430 --> 00:46:30.340 align:middle line:84% are linear in the pi and so it was the objective function. 00:46:30.340 --> 00:46:33.360 align:middle line:84% So here, we're going to have these moral-hazard constraints, 00:46:33.360 --> 00:46:37.560 align:middle line:84% et cetera, which could turn this into a very nonlinear problem 00:46:37.560 --> 00:46:40.800 align:middle line:84% because we have the original maximum, 00:46:40.800 --> 00:46:43.515 align:middle line:84% the objective function subject to a derivative 00:46:43.515 --> 00:46:47.170 align:middle line:84% of part of the maximized function as a constraint. 00:46:47.170 --> 00:46:49.680 align:middle line:84% And Lord knows what that looks like. 00:46:49.680 --> 00:46:51.840 align:middle line:84% But we turn it all into a linear programming 00:46:51.840 --> 00:46:53.520 align:middle line:90% problem with these lotteries. 00:46:53.520 --> 00:46:57.340 align:middle line:84% Not only that, we're going to imagine discrete values. 00:46:57.340 --> 00:46:59.370 align:middle line:84% So it's not a semi-infinite program. 00:46:59.370 --> 00:47:02.310 align:middle line:84% It's a finite, discrete linear program. 00:47:02.310 --> 00:47:05.310 align:middle line:84% And that allows capitalization to be chunky. 00:47:05.310 --> 00:47:09.360 align:middle line:84% Maybe you get a machine or you don't, for example, literally, 00:47:09.360 --> 00:47:10.890 align:middle line:90% a discrete value. 00:47:10.890 --> 00:47:15.000 align:middle line:84% That also causes a problem, just the way chunky consumption 00:47:15.000 --> 00:47:16.300 align:middle line:90% causes a problem. 00:47:16.300 --> 00:47:17.400 align:middle line:90% But never mind. 00:47:17.400 --> 00:47:19.390 align:middle line:90% Lotteries are the cure-all. 00:47:19.390 --> 00:47:24.040 align:middle line:84% It just always works to turn it into this. 00:47:24.040 --> 00:47:26.190 align:middle line:90% So don't pass out. 00:47:26.190 --> 00:47:29.830 align:middle line:84% Each of these lines will make sense to you. 00:47:29.830 --> 00:47:31.440 align:middle line:90% This is the objective function. 00:47:31.440 --> 00:47:34.320 align:middle line:84% It's the utility of the household as a function 00:47:34.320 --> 00:47:36.420 align:middle line:90% of consumption and effort. 00:47:36.420 --> 00:47:40.740 align:middle line:84% This is expected utility because part of the probability 00:47:40.740 --> 00:47:44.820 align:middle line:84% involves consumption and effort, which may potentially be chosen 00:47:44.820 --> 00:47:46.890 align:middle line:90% at random, according to pi. 00:47:46.890 --> 00:47:50.460 align:middle line:84% And then we sum up over all these discrete values of c, q, 00:47:50.460 --> 00:47:52.980 align:middle line:84% z, k, summing them up, weighting them by pi. 00:47:52.980 --> 00:47:55.500 align:middle line:84% So this whole thing is just expected utility. 00:47:55.500 --> 00:47:57.600 align:middle line:84% In this case, the borrower's risk-averse. 00:47:57.600 --> 00:47:59.430 align:middle line:90% So we're allowing for that. 00:47:59.430 --> 00:48:01.950 align:middle line:84% Now this constraint is what I call 00:48:01.950 --> 00:48:03.630 align:middle line:90% a Mother-Nature constraint. 00:48:03.630 --> 00:48:07.890 align:middle line:84% What Mother Nature is giving us is the technology that maps 00:48:07.890 --> 00:48:12.720 align:middle line:84% z and k along with theta into the probability of success, q. 00:48:12.720 --> 00:48:15.810 align:middle line:84% So this p tilde function is given. 00:48:15.810 --> 00:48:17.790 align:middle line:84% It's part of the underlying environment. 00:48:17.790 --> 00:48:19.980 align:middle line:84% But you might think that, in part, we're 00:48:19.980 --> 00:48:23.490 align:middle line:84% solving for the relationship, the probabilistic relationship 00:48:23.490 --> 00:48:26.970 align:middle line:84% between q, z, and k because everything looks endogenous up 00:48:26.970 --> 00:48:27.820 align:middle line:90% here. 00:48:27.820 --> 00:48:29.820 align:middle line:84% So we need to impose another constraint 00:48:29.820 --> 00:48:32.760 align:middle line:84% to make sure we respect the Mother Nature. 00:48:32.760 --> 00:48:34.920 align:middle line:84% And if little statistics, this is 00:48:34.920 --> 00:48:37.770 align:middle line:84% like the probability of a conditioned on event 00:48:37.770 --> 00:48:40.470 align:middle line:84% b times the probability of event b 00:48:40.470 --> 00:48:43.830 align:middle line:84% is therefore the probability of the joint event a and b. 00:48:43.830 --> 00:48:45.600 align:middle line:84% And on the left-hand side, it's already 00:48:45.600 --> 00:48:47.610 align:middle line:90% the joint event, a and b. 00:48:47.610 --> 00:48:51.840 align:middle line:84% So this is the probability of q, conditioned on z and k. 00:48:51.840 --> 00:48:54.030 align:middle line:84% This is the probability of z and k 00:48:54.030 --> 00:48:57.390 align:middle line:84% because we've integrated out the other objects, z and q. 00:48:57.390 --> 00:49:00.990 align:middle line:84% So this is the probability of q, z, k. 00:49:00.990 --> 00:49:04.860 align:middle line:84% And likewise, the left-hand side is the probability of q, z, k, 00:49:04.860 --> 00:49:08.400 align:middle line:84% where we somehow integrate out the only other object, the c. 00:49:08.400 --> 00:49:10.920 align:middle line:84% So this is a Mother-Nature constraint. 00:49:10.920 --> 00:49:13.560 align:middle line:84% Again, it's all linear in the pis. 00:49:13.560 --> 00:49:16.440 align:middle line:90% So we just code it in to Matlab. 00:49:16.440 --> 00:49:18.840 align:middle line:84% This thing down here is the break-even constrain 00:49:18.840 --> 00:49:19.740 align:middle line:90% for the bank. 00:49:19.740 --> 00:49:22.230 align:middle line:84% And you can think of it as maybe the bank 00:49:22.230 --> 00:49:25.890 align:middle line:84% has to pay out more in consumption than output. 00:49:25.890 --> 00:49:28.890 align:middle line:84% In this case, by the way, when the firm is not successful, 00:49:28.890 --> 00:49:30.210 align:middle line:90% the output is 0. 00:49:30.210 --> 00:49:32.400 align:middle line:84% But the borrower is risk-averse and it's 00:49:32.400 --> 00:49:36.270 align:middle line:84% going to view it as a disaster to get 0 consumption, maybe 00:49:36.270 --> 00:49:38.820 align:middle line:90% even minus infinity utility. 00:49:38.820 --> 00:49:40.740 align:middle line:84% So typically, in the failure branch, 00:49:40.740 --> 00:49:42.270 align:middle line:90% consumption is greater than q. 00:49:42.270 --> 00:49:45.240 align:middle line:84% That means the bank, which is like taking all of the q 00:49:45.240 --> 00:49:46.860 align:middle line:84% and giving some of it back in terms 00:49:46.860 --> 00:49:50.340 align:middle line:84% of c is suffering a loss on the consumption part. 00:49:50.340 --> 00:49:52.800 align:middle line:84% On the other hand, on the right-hand side, 00:49:52.800 --> 00:49:54.660 align:middle line:84% it's like the firm, the household 00:49:54.660 --> 00:49:58.620 align:middle line:84% as a firm is surrendering all of its assets a to the bank 00:49:58.620 --> 00:49:59.550 align:middle line:90% to manage. 00:49:59.550 --> 00:50:03.180 align:middle line:84% And only some of it gets used to finance. 00:50:03.180 --> 00:50:06.090 align:middle line:84% So the firms make a profit on the right-hand side, 00:50:06.090 --> 00:50:08.550 align:middle line:84% times the difference the bank got 00:50:08.550 --> 00:50:11.760 align:middle line:84% that it didn't give back, times the external outside interest 00:50:11.760 --> 00:50:12.400 align:middle line:90% rate. 00:50:12.400 --> 00:50:16.230 align:middle line:84% So this is a zero break-even constraint with the lotteries. 00:50:16.230 --> 00:50:18.220 align:middle line:90% This is moral hazard. 00:50:18.220 --> 00:50:20.370 align:middle line:90% It's akin to truth-telling. 00:50:20.370 --> 00:50:23.760 align:middle line:84% So what this says is, the truth is 00:50:23.760 --> 00:50:28.440 align:middle line:84% that not only does the borrower characterize by theta a and s. 00:50:28.440 --> 00:50:32.670 align:middle line:84% The borrower contemplates doing the recommended action z. 00:50:32.670 --> 00:50:35.460 align:middle line:84% How much effort is supposed to be applied under the contract? 00:50:35.460 --> 00:50:38.070 align:middle line:84% But you can't make the borrower do it. 00:50:38.070 --> 00:50:41.370 align:middle line:84% The borrower has to be given incentive to work, especially 00:50:41.370 --> 00:50:43.650 align:middle line:90% if this is a high level of z. 00:50:43.650 --> 00:50:46.660 align:middle line:84% But the borrower says, nah, I might not do it. 00:50:46.660 --> 00:50:49.980 align:middle line:84% So even though z was recommended by the bank, 00:50:49.980 --> 00:50:51.750 align:middle line:84% the borrower does something else. 00:50:51.750 --> 00:50:53.910 align:middle line:90% The borrower does z prime. 00:50:53.910 --> 00:50:57.460 align:middle line:84% Note that z prime is entering into the utility function here. 00:50:57.460 --> 00:51:01.630 align:middle line:84% So he really is going to do that or is thinking about doing it. 00:51:01.630 --> 00:51:03.630 align:middle line:84% And this would be the utility consequence. 00:51:03.630 --> 00:51:07.470 align:middle line:84% This stupid thing here, we have to readjust the probabilities 00:51:07.470 --> 00:51:10.620 align:middle line:84% because when we impose that Mother-Nature constraint, 00:51:10.620 --> 00:51:12.930 align:middle line:84% we embedded the probability of success 00:51:12.930 --> 00:51:15.090 align:middle line:90% into the endogenous object. 00:51:15.090 --> 00:51:18.600 align:middle line:84% We would now be making an error if we did not 00:51:18.600 --> 00:51:20.790 align:middle line:84% adjust for the fact that the effort being taken 00:51:20.790 --> 00:51:23.670 align:middle line:90% is z prime rather than z. 00:51:23.670 --> 00:51:26.190 align:middle line:84% And this is derived in one of my papers. 00:51:26.190 --> 00:51:28.380 align:middle line:84% Hopefully, it's somewhat intuitive that at least one 00:51:28.380 --> 00:51:30.540 align:middle line:90% needs to do an adjustment. 00:51:30.540 --> 00:51:34.200 align:middle line:84% And finally, this just says the probabilities all add up to 1. 00:51:34.200 --> 00:51:37.950 align:middle line:84% So the programming problem is to maximize 00:51:37.950 --> 00:51:39.960 align:middle line:84% the expected utility of the borrower, 00:51:39.960 --> 00:51:42.720 align:middle line:84% subject to all these constraints, 00:51:42.720 --> 00:51:44.100 align:middle line:90% Mother-Nature constraints. 00:51:44.100 --> 00:51:45.330 align:middle line:90% There's a lot of them. 00:51:45.330 --> 00:51:49.140 align:middle line:84% For every q, z, and k, this is the break-even constraint. 00:51:49.140 --> 00:51:50.590 align:middle line:90% There's only one of them. 00:51:50.590 --> 00:51:53.190 align:middle line:84% This is the moral-hazard constraint 00:51:53.190 --> 00:51:55.710 align:middle line:84% to be obedient rather than shirk. 00:51:55.710 --> 00:51:57.990 align:middle line:84% And there's one of these for every k. 00:51:57.990 --> 00:51:59.850 align:middle line:84% That could be assigned and then for every z, 00:51:59.850 --> 00:52:01.650 align:middle line:90% an alternative value z prime. 00:52:01.650 --> 00:52:03.870 align:middle line:84% And there's only one of these constraints 11. 00:52:03.870 --> 00:52:07.080 align:middle line:84% So I'm actually enumerating the set of all constraints. 00:52:07.080 --> 00:52:10.860 align:middle line:84% You can solve these things for a large number of control 00:52:10.860 --> 00:52:13.140 align:middle line:90% variables pi, like thousands. 00:52:13.140 --> 00:52:15.990 align:middle line:84% And you can have hundreds of constraints. 00:52:15.990 --> 00:52:20.010 align:middle line:84% And it's still solvable in things like CPLEX, 00:52:20.010 --> 00:52:22.620 align:middle line:84% which is a version of which Gorubi 00:52:22.620 --> 00:52:25.330 align:middle line:90% is publicly available software. 00:52:25.330 --> 00:52:28.210 align:middle line:84% So we did this before Gorubi was on the market. 00:52:28.210 --> 00:52:31.420 align:middle line:84% So we paid $2,000 to get a hold of CPLEX. 00:52:31.420 --> 00:52:33.990 align:middle line:84% And we solved the linear programming problem. 00:52:33.990 --> 00:52:36.100 align:middle line:84% I'm going to call the solution the probability 00:52:36.100 --> 00:52:37.630 align:middle line:90% of being an entrepreneur. 00:52:37.630 --> 00:52:39.850 align:middle line:84% It's a pretty brute force, namely, 00:52:39.850 --> 00:52:42.250 align:middle line:84% what is the probability the capital level is positive? 00:52:42.250 --> 00:52:44.680 align:middle line:84% If it's positive, they must be a firm, the way 00:52:44.680 --> 00:52:46.210 align:middle line:90% we composed the problem. 00:52:46.210 --> 00:52:48.250 align:middle line:84% If capital were 0, they're a wage earner. 00:52:48.250 --> 00:52:50.980 align:middle line:84% So ignoring everything else by summing up 00:52:50.980 --> 00:52:53.740 align:middle line:84% over everything else, we only care about capital 00:52:53.740 --> 00:52:54.550 align:middle line:90% being positive. 00:52:54.550 --> 00:52:56.800 align:middle line:84% And we call that the probability of being a firm. 00:52:56.800 --> 00:53:00.070 align:middle line:84% It's still conditioned on talent, assets, and schooling. 00:53:00.070 --> 00:53:03.400 align:middle line:84% So we have to solve this problem for all those stratifications 00:53:03.400 --> 00:53:05.030 align:middle line:90% in the data. 00:53:05.030 --> 00:53:06.760 align:middle line:90% So let me go back again. 00:53:06.760 --> 00:53:08.440 align:middle line:90% Is it a moral-hazard problem? 00:53:08.440 --> 00:53:10.720 align:middle line:84% Is it a limited-liability problem? 00:53:10.720 --> 00:53:11.530 align:middle line:90% Is it both? 00:53:11.530 --> 00:53:12.730 align:middle line:90% Is it neither? 00:53:12.730 --> 00:53:17.150 align:middle line:84% So we have the master program here that allows everything. 00:53:17.150 --> 00:53:21.280 align:middle line:84% All we have to do is comment out the relevant constraint. 00:53:21.280 --> 00:53:25.710 align:middle line:90% If we want to look at the-- 00:53:25.710 --> 00:53:27.810 align:middle line:84% It should have been written here. 00:53:27.810 --> 00:53:30.270 align:middle line:84% If we want to delete the moral-hazard constraint, 00:53:30.270 --> 00:53:33.330 align:middle line:84% we comment out this thing, equation 10. 00:53:33.330 --> 00:53:36.540 align:middle line:84% And there's a limited-liability constraint, which somehow I'm 00:53:36.540 --> 00:53:38.530 align:middle line:90% not seeing in the notation. 00:53:38.530 --> 00:53:39.900 align:middle line:90% But it should have been there. 00:53:39.900 --> 00:53:41.880 align:middle line:90% And we can comment it out. 00:53:41.880 --> 00:53:44.760 align:middle line:84% We can allow both moral hazard and limited liability. 00:53:44.760 --> 00:53:46.362 align:middle line:90% Or we could have neither. 00:53:46.362 --> 00:53:48.570 align:middle line:84% Once you go to all the trouble to code this thing up, 00:53:48.570 --> 00:53:51.480 align:middle line:84% it's not hard to do all these different combinations 00:53:51.480 --> 00:53:53.050 align:middle line:90% and take it to the data. 00:53:53.050 --> 00:53:56.210 align:middle line:90% So how do we go to the data? 00:53:56.210 --> 00:53:59.860 align:middle line:90% We compute. 00:53:59.860 --> 00:54:03.280 align:middle line:84% So again, I'm not being shy about this because we advertise 00:54:03.280 --> 00:54:06.220 align:middle line:84% that numerical methods are important at the beginning 00:54:06.220 --> 00:54:06.950 align:middle line:90% of the class. 00:54:06.950 --> 00:54:09.250 align:middle line:84% So I do want occasionally to show you how 00:54:09.250 --> 00:54:11.780 align:middle line:90% numerical methods can get used. 00:54:11.780 --> 00:54:14.530 align:middle line:84% And also, I know you guys are a great class. 00:54:14.530 --> 00:54:17.620 align:middle line:84% So I'm not worried that this is necessarily too hard. 00:54:17.620 --> 00:54:20.290 align:middle line:84% But it may be the first time that you've seen it, 00:54:20.290 --> 00:54:21.790 align:middle line:84% which is kind of cool because you'll 00:54:21.790 --> 00:54:24.350 align:middle line:90% learn about maximum likelihood. 00:54:24.350 --> 00:54:25.840 align:middle line:90% So what do we do? 00:54:25.840 --> 00:54:29.950 align:middle line:84% Let's fix all the parameters, alpha, kappa, all of them, 00:54:29.950 --> 00:54:31.090 align:middle line:90% a whole array of them-- 00:54:31.090 --> 00:54:32.830 align:middle line:84% I have that on the slide coming-- 00:54:32.830 --> 00:54:35.200 align:middle line:84% and solve that programming problem 00:54:35.200 --> 00:54:39.790 align:middle line:84% for the stratification of ability, education, and wealth. 00:54:39.790 --> 00:54:42.760 align:middle line:84% And say, do that for the moral-hazard regime. 00:54:42.760 --> 00:54:44.770 align:middle line:84% Let's keep moral hazard in mind now. 00:54:44.770 --> 00:54:46.490 align:middle line:90% Drop limited liability. 00:54:46.490 --> 00:54:49.720 align:middle line:84% Now we want to construct the likelihood function, which 00:54:49.720 --> 00:54:52.900 align:middle line:84% is for given parameter values, the model 00:54:52.900 --> 00:54:57.850 align:middle line:84% predicts the probability of being a firm for households 00:54:57.850 --> 00:54:59.790 align:middle line:90% of this type. 00:54:59.790 --> 00:55:01.790 align:middle line:90% The model tells us that. 00:55:01.790 --> 00:55:05.890 align:middle line:84% And in the data, we see the number, 00:55:05.890 --> 00:55:11.860 align:middle line:84% the fraction of the sample that are firms in that wealth, 00:55:11.860 --> 00:55:14.080 align:middle line:90% talent, schooling, category. 00:55:14.080 --> 00:55:18.220 align:middle line:84% So there may be a bit of a mismatch in the sense 00:55:18.220 --> 00:55:21.340 align:middle line:84% that for given parameter values, the probability 00:55:21.340 --> 00:55:25.040 align:middle line:84% is low in the model and very high on the data or vice versa. 00:55:25.040 --> 00:55:27.370 align:middle line:84% So then logically, oh well, we can play around 00:55:27.370 --> 00:55:28.520 align:middle line:90% with the parameter values. 00:55:28.520 --> 00:55:30.880 align:middle line:84% We don't know what they are either. 00:55:30.880 --> 00:55:35.680 align:middle line:84% So we vary, kappa and alpha and all of those things, 00:55:35.680 --> 00:55:41.290 align:middle line:84% to make the likelihood to maximize the probability 00:55:41.290 --> 00:55:45.790 align:middle line:84% that we would see in the data what is predicted by the model. 00:55:45.790 --> 00:55:48.250 align:middle line:84% Maximize the probability, we would see 00:55:48.250 --> 00:55:50.590 align:middle line:90% in the data, which is a given. 00:55:50.590 --> 00:55:52.620 align:middle line:90% But it's predicted by the model. 00:55:52.620 --> 00:55:55.930 align:middle line:84% And again, the choice is varying over all possible parameter 00:55:55.930 --> 00:55:56.820 align:middle line:90% values. 00:55:56.820 --> 00:56:00.130 align:middle line:84% Now that doesn't mean the likelihood will match exactly. 00:56:00.130 --> 00:56:02.380 align:middle line:84% It just means the likelihood is as high 00:56:02.380 --> 00:56:05.860 align:middle line:84% as it can possibly be after searching over all parameter 00:56:05.860 --> 00:56:06.620 align:middle line:90% values. 00:56:06.620 --> 00:56:09.100 align:middle line:84% Here's a bit more of the math of it. 00:56:09.100 --> 00:56:11.830 align:middle line:84% The string of parameter values would 00:56:11.830 --> 00:56:17.380 align:middle line:84% be risk aversion, work aversion, the weight on disutility 00:56:17.380 --> 00:56:21.130 align:middle line:84% in the work part, alpha in the production function, 00:56:21.130 --> 00:56:25.720 align:middle line:84% delta 0, 1, 2, which are the weights on theta A, theta 00:56:25.720 --> 00:56:28.210 align:middle line:84% and S, I think, or the other way around, lambda 00:56:28.210 --> 00:56:30.170 align:middle line:84% being the limited-liability constraint. 00:56:30.170 --> 00:56:33.370 align:middle line:84% So we're going to maximize over all these parameters 00:56:33.370 --> 00:56:38.350 align:middle line:84% and get something like H of A to be the probability of being 00:56:38.350 --> 00:56:41.830 align:middle line:84% a firm, conditioned on wealth A. And it 00:56:41.830 --> 00:56:44.380 align:middle line:84% should have had schooling in here but not talent. 00:56:44.380 --> 00:56:46.280 align:middle line:84% We had to integrate out over talent. 00:56:46.280 --> 00:56:50.440 align:middle line:84% So this object comes from the model conditioning 00:56:50.440 --> 00:56:52.720 align:middle line:84% on the stratification in the data 00:56:52.720 --> 00:56:54.680 align:middle line:84% and a string of parameter values. 00:56:54.680 --> 00:56:58.480 align:middle line:84% So when we say maximize the likelihood, L, likelihood, 00:56:58.480 --> 00:57:00.910 align:middle line:84% is a function of the parameter values, which 00:57:00.910 --> 00:57:04.110 align:middle line:90% we will vary, to maximize what? 00:57:04.110 --> 00:57:07.040 align:middle line:84% Ei is a statement about the data. 00:57:07.040 --> 00:57:08.800 align:middle line:90% It's 0 or 1. 00:57:08.800 --> 00:57:11.870 align:middle line:84% Household i is either a firm or it isn't in the data. 00:57:11.870 --> 00:57:13.150 align:middle line:90% So we count up the number. 00:57:13.150 --> 00:57:17.080 align:middle line:84% Every time a household is in the data as a firm, 00:57:17.080 --> 00:57:19.900 align:middle line:84% we look at the associated probability of predicting that 00:57:19.900 --> 00:57:21.380 align:middle line:90% from the model. 00:57:21.380 --> 00:57:26.930 align:middle line:84% This is a probability, likewise, logs make it the same function. 00:57:26.930 --> 00:57:29.170 align:middle line:84% It's just a monotone function of the probability. 00:57:29.170 --> 00:57:31.000 align:middle line:84% And logs are cool because they allow 00:57:31.000 --> 00:57:33.100 align:middle line:84% you to write everything is separable instead 00:57:33.100 --> 00:57:34.360 align:middle line:90% of multiplicative. 00:57:34.360 --> 00:57:38.050 align:middle line:84% Here's the other event, a given household in the data 00:57:38.050 --> 00:57:39.010 align:middle line:90% is not a firm. 00:57:39.010 --> 00:57:39.910 align:middle line:90% It's a wage earner. 00:57:39.910 --> 00:57:42.550 align:middle line:90% So one minus 0 is 1. 00:57:42.550 --> 00:57:44.320 align:middle line:90% So this branch is wage earner. 00:57:44.320 --> 00:57:46.930 align:middle line:84% And what's the probability of being a wage earner? 00:57:46.930 --> 00:57:49.450 align:middle line:84% It's 1 minus the probability of being a firm. 00:57:49.450 --> 00:57:53.410 align:middle line:84% So this is the likelihood function, the log likelihood 00:57:53.410 --> 00:57:56.120 align:middle line:84% function, a function of the parameters. 00:57:56.120 --> 00:57:58.540 align:middle line:84% And this is where the code is maximized. 00:57:58.540 --> 00:58:00.220 align:middle line:90% This is not linear code. 00:58:00.220 --> 00:58:03.130 align:middle line:84% This is nonlinear optimization code. 00:58:03.130 --> 00:58:06.430 align:middle line:84% But there are many routines out there to do this. 00:58:06.430 --> 00:58:09.250 align:middle line:84% And if you don't want to think about maximizing its nonlinear 00:58:09.250 --> 00:58:11.470 align:middle line:84% function, you can just evaluate it 00:58:11.470 --> 00:58:14.530 align:middle line:84% at thousands of these parameter configurations 00:58:14.530 --> 00:58:19.240 align:middle line:84% and pick the max, which actually gets close to the maximum. 00:58:19.240 --> 00:58:22.210 align:middle line:84% So too tiny to read, but conceptually, 00:58:22.210 --> 00:58:25.780 align:middle line:84% we have a moral hazard column, a limited liability column, 00:58:25.780 --> 00:58:27.610 align:middle line:90% and both constraints column. 00:58:27.610 --> 00:58:31.220 align:middle line:84% And what we're doing with various specifications, 00:58:31.220 --> 00:58:33.850 align:middle line:84% including this one, estimating talent, 00:58:33.850 --> 00:58:37.370 align:middle line:84% is reporting the maximized parameter values. 00:58:37.370 --> 00:58:41.040 align:middle line:84% So again, that vector string was gamma 1, gamma 2, kappa, and so 00:58:41.040 --> 00:58:41.540 align:middle line:90% on. 00:58:41.540 --> 00:58:43.300 align:middle line:84% And you can see the point estimates. 00:58:43.300 --> 00:58:46.000 align:middle line:84% For risk aversion, which was gamma 1, 00:58:46.000 --> 00:58:51.040 align:middle line:84% we're getting the point estimates here of 0.06 or 0.02. 00:58:51.040 --> 00:58:53.050 align:middle line:84% So almost risk neutral, actually. 00:58:53.050 --> 00:58:56.330 align:middle line:84% But in parentheses is a standard error, 00:58:56.330 --> 00:58:58.720 align:middle line:84% which is expressed a degree of confidence 00:58:58.720 --> 00:59:00.340 align:middle line:90% about the point estimates. 00:59:00.340 --> 00:59:02.080 align:middle line:84% So those are the parameter estimates. 00:59:02.080 --> 00:59:03.710 align:middle line:90% So what do we find? 00:59:03.710 --> 00:59:07.720 align:middle line:84% We find at the end of the day, a couple of years of research, 00:59:07.720 --> 00:59:11.080 align:middle line:84% that the central region favors moral hazard. 00:59:11.080 --> 00:59:13.690 align:middle line:84% And likewise, in the cross section, 00:59:13.690 --> 00:59:19.030 align:middle line:84% as we increased the wealth going from one household to the next, 00:59:19.030 --> 00:59:21.250 align:middle line:84% an increase in wealth is associated 00:59:21.250 --> 00:59:24.680 align:middle line:84% with an increase in net saving, which we also measured. 00:59:24.680 --> 00:59:27.670 align:middle line:84% So this is consistent with moral hazard in the slide 00:59:27.670 --> 00:59:29.140 align:middle line:90% I showed you at the beginning. 00:59:29.140 --> 00:59:31.690 align:middle line:84% That if it's moral hazard and you have higher wealth, 00:59:31.690 --> 00:59:34.870 align:middle line:84% you avoid the damage caused by the moral hazard constraint 00:59:34.870 --> 00:59:36.520 align:middle line:90% by self-financing. 00:59:36.520 --> 00:59:39.220 align:middle line:84% So you should be saving more as wealth goes up. 00:59:39.220 --> 00:59:41.740 align:middle line:84% In the Northeast, the story is different. 00:59:41.740 --> 00:59:44.410 align:middle line:84% Being constrained, like below the constraint 00:59:44.410 --> 00:59:46.930 align:middle line:84% or at the constraint, is not related 00:59:46.930 --> 00:59:48.940 align:middle line:90% to borrowing particularly. 00:59:48.940 --> 00:59:52.060 align:middle line:84% Now it is true that if you were at a constraint, the liability 00:59:52.060 --> 00:59:54.850 align:middle line:84% constraint, and wealth went up, then 00:59:54.850 --> 00:59:57.170 align:middle line:84% they'd all be constrained by definition. 00:59:57.170 --> 00:59:58.990 align:middle line:84% But there's a branch of entrepreneurs, 00:59:58.990 --> 01:00:01.540 align:middle line:84% depending on talent, like if talent is low, 01:00:01.540 --> 01:00:03.370 align:middle line:84% their wealth is more than adequate. 01:00:03.370 --> 01:00:05.500 align:middle line:84% So they may not be borrowing at all. 01:00:05.500 --> 01:00:07.660 align:middle line:84% And likewise here, we get the opposite 01:00:07.660 --> 01:00:10.690 align:middle line:84% that when wealth goes up for constrained entrepreneurs, 01:00:10.690 --> 01:00:11.890 align:middle line:90% borrowing goes up. 01:00:11.890 --> 01:00:14.380 align:middle line:84% But again, there's this branch of entrepreneurs that 01:00:14.380 --> 01:00:16.540 align:middle line:90% are not necessarily borrowing. 01:00:16.540 --> 01:00:18.970 align:middle line:84% So that wording on that bottom bullet point 01:00:18.970 --> 01:00:20.570 align:middle line:90% is a bit difficult. 01:00:20.570 --> 01:00:23.860 align:middle line:84% So we have succeeded to solve the problem. 01:00:23.860 --> 01:00:28.480 align:middle line:84% We've identified the constraints that limit small businesses. 01:00:28.480 --> 01:00:30.250 align:middle line:84% Interestingly, the constraints are 01:00:30.250 --> 01:00:33.370 align:middle line:84% different in the different regions, in the industrialized 01:00:33.370 --> 01:00:36.460 align:middle line:84% area near Bangkok, which are very urban-- 01:00:36.460 --> 01:00:39.250 align:middle line:84% one of these villages is across the road from a Ford Motor 01:00:39.250 --> 01:00:41.240 align:middle line:90% Company plant, for example-- 01:00:41.240 --> 01:00:43.570 align:middle line:84% it looks like moral hazard's the problem. 01:00:43.570 --> 01:00:46.220 align:middle line:84% Out in the Northeast, the problem, 01:00:46.220 --> 01:00:49.120 align:middle line:84% which is agrarian, mostly rural, the problem 01:00:49.120 --> 01:00:53.830 align:middle line:84% seems to be there's a very limited financing constraint, 01:00:53.830 --> 01:00:54.790 align:middle line:90% limited liability. 01:00:54.790 --> 01:00:57.310 align:middle line:84% And a lot of the households don't have a lot of wealth 01:00:57.310 --> 01:01:01.090 align:middle line:84% so they're either constrained or don't go into business at all. 01:01:01.090 --> 01:01:03.280 align:middle line:84% Now we're not doing a policy thing here. 01:01:03.280 --> 01:01:05.980 align:middle line:84% But it would be good for policymakers to know this 01:01:05.980 --> 01:01:08.380 align:middle line:84% because if they want to alleviate the constraints 01:01:08.380 --> 01:01:11.440 align:middle line:84% on small businesses, they should direct their policy 01:01:11.440 --> 01:01:15.010 align:middle line:84% toward maybe in the Northeast, allowing more assets 01:01:15.010 --> 01:01:17.950 align:middle line:84% to qualify as collateral, not just land 01:01:17.950 --> 01:01:21.010 align:middle line:84% but their motorcycles, which they finally did, 01:01:21.010 --> 01:01:24.940 align:middle line:84% and other things, putting it in escrow to allow or to have 01:01:24.940 --> 01:01:26.650 align:middle line:84% the bank to have a claim on it and allow 01:01:26.650 --> 01:01:28.180 align:middle line:90% to increase borrowing. 01:01:28.180 --> 01:01:30.500 align:middle line:84% In the central, area it's an information problem. 01:01:30.500 --> 01:01:32.950 align:middle line:84% So there, if you're determined to try to solve it, 01:01:32.950 --> 01:01:34.820 align:middle line:90% it must be better monitoring. 01:01:34.820 --> 01:01:37.690 align:middle line:84% You need better signals of the underlying effort 01:01:37.690 --> 01:01:41.320 align:middle line:84% by, well, let's try costly state verification, 01:01:41.320 --> 01:01:44.020 align:middle line:84% for example, which is something I talked about last time. 01:01:44.020 --> 01:01:46.120 align:middle line:84% Not with respect to verifying output. 01:01:46.120 --> 01:01:48.970 align:middle line:84% But with respect to getting reliable signals 01:01:48.970 --> 01:01:51.550 align:middle line:84% of the underlying effort of the borrower. 01:01:51.550 --> 01:01:54.790 align:middle line:84% OK so this is the economic science part of it. 01:01:54.790 --> 01:01:55.660 align:middle line:90% We have models. 01:01:55.660 --> 01:01:56.320 align:middle line:90% We have data. 01:01:56.320 --> 01:01:58.790 align:middle line:84% We're trying to get as close to the data as possible. 01:01:58.790 --> 01:02:02.170 align:middle line:84% We're also solving an interesting financing, 01:02:02.170 --> 01:02:04.520 align:middle line:84% getting understanding of the financing constraint. 01:02:04.520 --> 01:02:06.730 align:middle line:84% And thinking about how policy would change, 01:02:06.730 --> 01:02:10.040 align:middle line:84% depending on what we find out rather than one size fits all. 01:02:10.040 --> 01:02:12.550 align:middle line:90% So that's all I have for today. 01:02:12.550 --> 01:02:15.360 align:middle line:90% OK, thank you very much. 01:02:15.360 --> 01:02:22.384 align:middle line:90%