WEBVTT 00:00:00.000 --> 00:00:02.440 align:middle line:90% [SQUEAKING] 00:00:02.440 --> 00:00:04.392 align:middle line:90% [RUSTLING] 00:00:04.392 --> 00:00:07.320 align:middle line:90% [CLICKING] 00:00:07.320 --> 00:00:16.410 align:middle line:90% 00:00:16.410 --> 00:00:18.420 align:middle line:84% TOBIAS SALZ: So let's get started. 00:00:18.420 --> 00:00:19.960 align:middle line:90% So welcome, everyone. 00:00:19.960 --> 00:00:23.970 align:middle line:84% I'm very excited to be here for a few lectures this semester. 00:00:23.970 --> 00:00:28.170 align:middle line:84% I thought I start by introducing myself. 00:00:28.170 --> 00:00:29.920 align:middle line:84% I haven't met many of you, in fact. 00:00:29.920 --> 00:00:32.125 align:middle line:84% So I was on sabbatical last year. 00:00:32.125 --> 00:00:33.250 align:middle line:90% Many of you are first year. 00:00:33.250 --> 00:00:36.240 align:middle line:90% So glad to meet all of you. 00:00:36.240 --> 00:00:38.160 align:middle line:90% So my name is Tobias Salz. 00:00:38.160 --> 00:00:41.225 align:middle line:84% I sit in E-52 on the fourth floor. 00:00:41.225 --> 00:00:42.600 align:middle line:84% As you have seen on the syllabus, 00:00:42.600 --> 00:00:46.140 align:middle line:84% my office hours are on Thursdays from 1:00 to 2:00 if you have 00:00:46.140 --> 00:00:49.050 align:middle line:84% any questions about the material. 00:00:49.050 --> 00:00:55.680 align:middle line:84% I received my PhD from NYU, stayed a bit longer in New York 00:00:55.680 --> 00:00:57.330 align:middle line:84% City, got my first job at Columbia 00:00:57.330 --> 00:01:00.360 align:middle line:90% before coming here to MIT. 00:01:00.360 --> 00:01:03.750 align:middle line:84% I'm interested in a variety of topics 00:01:03.750 --> 00:01:08.040 align:middle line:84% and different kinds of markets, so predominantly 00:01:08.040 --> 00:01:10.420 align:middle line:84% in what I call decentralized markets. 00:01:10.420 --> 00:01:13.320 align:middle line:84% So these are markets where participants 00:01:13.320 --> 00:01:14.590 align:middle line:90% face some sort of friction. 00:01:14.590 --> 00:01:16.450 align:middle line:84% So, for instance, consumers may not 00:01:16.450 --> 00:01:18.280 align:middle line:84% know what prices in the market are, 00:01:18.280 --> 00:01:21.280 align:middle line:84% or consumers and producers have to find each other in order 00:01:21.280 --> 00:01:21.940 align:middle line:90% to trade. 00:01:21.940 --> 00:01:23.440 align:middle line:84% This has, for instance, applications 00:01:23.440 --> 00:01:24.910 align:middle line:84% in transportation markets, on which 00:01:24.910 --> 00:01:26.470 align:middle line:90% I have done quite some work. 00:01:26.470 --> 00:01:29.980 align:middle line:84% Also very interested in digital markets where, 00:01:29.980 --> 00:01:32.200 align:middle line:84% as I'm sure if you have read the news, 00:01:32.200 --> 00:01:34.960 align:middle line:84% you've seen that there are a lot of interesting regulatory 00:01:34.960 --> 00:01:38.200 align:middle line:84% topics, topics concerning antitrust but also 00:01:38.200 --> 00:01:40.960 align:middle line:84% thinking about today's lecture, a lot of challenges, 00:01:40.960 --> 00:01:45.830 align:middle line:84% how we actually empirically address these kinds of markets. 00:01:45.830 --> 00:01:50.710 align:middle line:84% So I think there's a lot of interesting work 00:01:50.710 --> 00:01:52.000 align:middle line:90% to be done there. 00:01:52.000 --> 00:01:55.970 align:middle line:84% And then I'm interested also in consumer financial markets. 00:01:55.970 --> 00:01:59.990 align:middle line:90% So that's it about me, OK? 00:01:59.990 --> 00:02:04.270 align:middle line:84% So the goal of this and the next lecture 00:02:04.270 --> 00:02:08.470 align:middle line:84% is to teach you the essentials of static demand models. 00:02:08.470 --> 00:02:12.550 align:middle line:84% Hopefully, you get some appetite for this. 00:02:12.550 --> 00:02:14.380 align:middle line:84% And then you come back to [14.]273, 00:02:14.380 --> 00:02:17.410 align:middle line:84% and you learn a lot more about this. 00:02:17.410 --> 00:02:21.700 align:middle line:84% And I will really focus on the kinds of models 00:02:21.700 --> 00:02:23.920 align:middle line:84% that people use instead of giving you 00:02:23.920 --> 00:02:26.170 align:middle line:84% a long history of what people have tried beforehand 00:02:26.170 --> 00:02:27.370 align:middle line:90% that didn't quite work out. 00:02:27.370 --> 00:02:30.910 align:middle line:84% I'll just contrast on a few slides 00:02:30.910 --> 00:02:32.840 align:middle line:90% how the thinking has evolved. 00:02:32.840 --> 00:02:36.290 align:middle line:90% But I'll be very brief on this. 00:02:36.290 --> 00:02:37.790 align:middle line:90% OK, so why model demand? 00:02:37.790 --> 00:02:39.850 align:middle line:84% I've already mentioned we might, for instance, 00:02:39.850 --> 00:02:41.750 align:middle line:84% be interested in consumer welfare analysis. 00:02:41.750 --> 00:02:46.400 align:middle line:84% So any normative question or many normative questions 00:02:46.400 --> 00:02:48.260 align:middle line:84% need some notion of demand if we want 00:02:48.260 --> 00:02:49.710 align:middle line:84% to know what happens to consumers. 00:02:49.710 --> 00:02:52.850 align:middle line:90% 00:02:52.850 --> 00:02:56.330 align:middle line:84% Another reason is that we may want to back out the supply 00:02:56.330 --> 00:02:59.390 align:middle line:84% parameters, such as marginal cost or with more complicated 00:02:59.390 --> 00:03:04.620 align:middle line:84% models that we're going to learn about in [14.]273, fixed costs, 00:03:04.620 --> 00:03:05.300 align:middle line:90% OK? 00:03:05.300 --> 00:03:08.150 align:middle line:84% The problem is that this kind of cost data, 00:03:08.150 --> 00:03:12.710 align:middle line:84% even if you were looking at publicly-traded firms, 00:03:12.710 --> 00:03:14.990 align:middle line:90% is oftentimes not available. 00:03:14.990 --> 00:03:19.100 align:middle line:84% If we think about a firm, let's say, introducing a new product, 00:03:19.100 --> 00:03:23.210 align:middle line:84% they're not just taking into account the material costs 00:03:23.210 --> 00:03:25.440 align:middle line:84% and the production costs of that product. 00:03:25.440 --> 00:03:27.890 align:middle line:84% They're also going to take into account the opportunity 00:03:27.890 --> 00:03:29.750 align:middle line:84% cost of, let's say, cannibalization 00:03:29.750 --> 00:03:32.390 align:middle line:84% of other products that they are competing with. 00:03:32.390 --> 00:03:37.530 align:middle line:84% And this would not be captured in accounting data. 00:03:37.530 --> 00:03:41.790 align:middle line:84% You may have heard about a recent literature that has 00:03:41.790 --> 00:03:44.970 align:middle line:90% claimed that the US economy-- 00:03:44.970 --> 00:03:48.060 align:middle line:84% that markups are rising, which could 00:03:48.060 --> 00:03:52.350 align:middle line:84% be indicative of increasing market power in the economy. 00:03:52.350 --> 00:03:57.180 align:middle line:84% And so there's a paper that has made a big splash by Jan De 00:03:57.180 --> 00:04:01.442 align:middle line:84% Loecker and Jan Eeckhout, which basically shows these rising 00:04:01.442 --> 00:04:03.400 align:middle line:84% markups, and they take the production approach. 00:04:03.400 --> 00:04:05.340 align:middle line:84% That means that they're basically starting 00:04:05.340 --> 00:04:06.550 align:middle line:90% with a production function. 00:04:06.550 --> 00:04:10.410 align:middle line:84% And now there's some more recent work that actually goes market 00:04:10.410 --> 00:04:14.850 align:middle line:84% by market and studies, let's say, cars about 30, 40 years 00:04:14.850 --> 00:04:20.490 align:middle line:84% and asks, how do consumers fare over several years in the US car 00:04:20.490 --> 00:04:21.010 align:middle line:90% market? 00:04:21.010 --> 00:04:27.310 align:middle line:84% Is the US car market becoming less competitive? 00:04:27.310 --> 00:04:30.520 align:middle line:84% Counterfactual analysis, I've already talked about this. 00:04:30.520 --> 00:04:34.090 align:middle line:84% And sometimes you also want to predict demand for new goods 00:04:34.090 --> 00:04:37.790 align:middle line:84% with the kinds of models that we're going to study, 00:04:37.790 --> 00:04:38.920 align:middle line:90% you can actually do. 00:04:38.920 --> 00:04:44.050 align:middle line:84% So before I jump in, what I would like to do, 00:04:44.050 --> 00:04:48.130 align:middle line:84% and I think this is helpful, make you understand what 00:04:48.130 --> 00:04:49.610 align:middle line:90% is the goal of these models? 00:04:49.610 --> 00:04:52.190 align:middle line:84% So what are these models aiming for? 00:04:52.190 --> 00:04:56.280 align:middle line:84% And there's a big set of objectives here, 00:04:56.280 --> 00:04:58.950 align:middle line:84% and these objectives are oftentimes actually 00:04:58.950 --> 00:05:03.690 align:middle line:84% somewhat in conflict with each other, OK? 00:05:03.690 --> 00:05:09.010 align:middle line:84% So first, the models are to handle a lot of products. 00:05:09.010 --> 00:05:12.120 align:middle line:84% We don't want to be restricted in the number of products 00:05:12.120 --> 00:05:15.600 align:middle line:90% that we can actually handle, OK? 00:05:15.600 --> 00:05:20.820 align:middle line:84% Also, we want to estimate them with aggregate data. 00:05:20.820 --> 00:05:26.730 align:middle line:84% So what this means is we cannot see a specific consumer making 00:05:26.730 --> 00:05:30.990 align:middle line:84% a purchase decision, and we cannot link specific consumer 00:05:30.990 --> 00:05:33.270 align:middle line:84% demographics or other situational factors 00:05:33.270 --> 00:05:34.800 align:middle line:90% to a consumer. 00:05:34.800 --> 00:05:38.670 align:middle line:84% So instead, we have data of the sorts of what cars did people 00:05:38.670 --> 00:05:46.230 align:middle line:84% purchase in Massachusetts in 2021 over the course of a year, 00:05:46.230 --> 00:05:48.980 align:middle line:90% let's say. 00:05:48.980 --> 00:05:52.840 align:middle line:84% So the fact that we only have aggregate data 00:05:52.840 --> 00:05:56.230 align:middle line:84% is actually in conflict with another goal, 00:05:56.230 --> 00:05:58.930 align:middle line:84% which is that we want to generate realistic substitution 00:05:58.930 --> 00:06:01.430 align:middle line:90% patterns. 00:06:01.430 --> 00:06:06.260 align:middle line:84% So if I observe specific things about consumers, 00:06:06.260 --> 00:06:12.040 align:middle line:84% for instance, what their income is or where they live, 00:06:12.040 --> 00:06:14.315 align:middle line:84% then I have a much better idea of how 00:06:14.315 --> 00:06:15.440 align:middle line:90% they would be substituting. 00:06:15.440 --> 00:06:21.160 align:middle line:84% For instance, let's say, I think about stores around Kendall, 00:06:21.160 --> 00:06:22.340 align:middle line:90% Aceituna, let's say. 00:06:22.340 --> 00:06:24.050 align:middle line:84% And I know that you live around Kendall. 00:06:24.050 --> 00:06:25.540 align:middle line:84% I would know that you're probably 00:06:25.540 --> 00:06:30.130 align:middle line:84% more likely going to respond to a change in price of a store 00:06:30.130 --> 00:06:31.600 align:middle line:84% here than somebody else who lives, 00:06:31.600 --> 00:06:35.290 align:middle line:84% let's say, at Central or Harvard Square. 00:06:35.290 --> 00:06:37.933 align:middle line:84% But with aggregate data, we don't have that information. 00:06:37.933 --> 00:06:39.350 align:middle line:84% We don't know what your income is. 00:06:39.350 --> 00:06:40.790 align:middle line:90% We don't know where you live. 00:06:40.790 --> 00:06:44.770 align:middle line:84% And so it's harder to really pin down 00:06:44.770 --> 00:06:46.280 align:middle line:84% how people are going to substitute. 00:06:46.280 --> 00:06:50.830 align:middle line:84% And as we will see, this will lead to, 00:06:50.830 --> 00:06:53.620 align:middle line:84% for the models that people have been estimating, before moving 00:06:53.620 --> 00:06:55.800 align:middle line:84% to these modern models to unrealistic substitution 00:06:55.800 --> 00:06:58.300 align:middle line:84% patterns because we don't have all the detailed information. 00:06:58.300 --> 00:07:01.045 align:middle line:84% And we're not using it in ways to generate those substitution 00:07:01.045 --> 00:07:01.545 align:middle line:90% patterns. 00:07:01.545 --> 00:07:04.220 align:middle line:90% 00:07:04.220 --> 00:07:07.730 align:middle line:84% We also want to allow for unobserved product 00:07:07.730 --> 00:07:09.650 align:middle line:84% characteristics or sometimes referred 00:07:09.650 --> 00:07:12.750 align:middle line:84% to somewhat confusingly as demand shocks. 00:07:12.750 --> 00:07:17.010 align:middle line:84% So these are basically things that the consumers observe, 00:07:17.010 --> 00:07:20.640 align:middle line:84% that the firms observe, that we do not observe as the analysts 00:07:20.640 --> 00:07:22.860 align:middle line:90% or econometricians, OK? 00:07:22.860 --> 00:07:26.160 align:middle line:84% So, for instance, if you think about the market 00:07:26.160 --> 00:07:29.580 align:middle line:84% for smartphones, Apple will take into account 00:07:29.580 --> 00:07:32.400 align:middle line:84% that people like the Apple ecosystem, 00:07:32.400 --> 00:07:35.260 align:middle line:84% and therefore is able to raise prices. 00:07:35.260 --> 00:07:40.000 align:middle line:84% And so these are the kinds of things that are 00:07:40.000 --> 00:07:42.460 align:middle line:90% important to have in the model. 00:07:42.460 --> 00:07:45.460 align:middle line:84% But this causes an endogeneity problem 00:07:45.460 --> 00:07:47.720 align:middle line:90% that I will talk about next. 00:07:47.720 --> 00:07:50.440 align:middle line:84% We also want to maintain computational tractability, 00:07:50.440 --> 00:07:54.640 align:middle line:84% which is, again, somewhat in conflict with the demand 00:07:54.640 --> 00:07:58.960 align:middle line:84% to have many products and also with these realistic 00:07:58.960 --> 00:08:01.000 align:middle line:84% substitution patterns because, as it turns out, 00:08:01.000 --> 00:08:03.460 align:middle line:84% that makes the models very nonlinear and harder 00:08:03.460 --> 00:08:04.950 align:middle line:90% to deal with. 00:08:04.950 --> 00:08:07.560 align:middle line:84% So just to give you an idea, what 00:08:07.560 --> 00:08:09.910 align:middle line:84% was the goal when people constructed these models? 00:08:09.910 --> 00:08:15.130 align:middle line:84% These are basically what people try to accomplish. 00:08:15.130 --> 00:08:18.400 align:middle line:84% This has been tremendously successful. 00:08:18.400 --> 00:08:21.310 align:middle line:84% You can go through the literature, 00:08:21.310 --> 00:08:25.480 align:middle line:84% and it's not just narrowly in IO. 00:08:25.480 --> 00:08:28.427 align:middle line:84% You can go through pretty much any field and any kind 00:08:28.427 --> 00:08:30.010 align:middle line:84% of question that you're interested in, 00:08:30.010 --> 00:08:32.710 align:middle line:84% and you'll find people estimating these models 00:08:32.710 --> 00:08:36.570 align:middle line:84% to answer questions of all kinds. 00:08:36.570 --> 00:08:41.710 align:middle line:84% So from transportation to more IO topics, market power mergers, 00:08:41.710 --> 00:08:44.760 align:middle line:84% network effects, to things like residential sorting, 00:08:44.760 --> 00:08:46.860 align:middle line:90% and even voting, OK? 00:08:46.860 --> 00:08:48.990 align:middle line:84% So now I see more and more people 00:08:48.990 --> 00:08:52.020 align:middle line:84% are using exactly the kinds of models 00:08:52.020 --> 00:08:55.890 align:middle line:84% that we use in IO to study questions in labor 00:08:55.890 --> 00:08:57.005 align:middle line:90% about monopsony power. 00:08:57.005 --> 00:09:02.270 align:middle line:90% 00:09:02.270 --> 00:09:06.590 align:middle line:84% So very briefly, front and center-- 00:09:06.590 --> 00:09:10.670 align:middle line:84% and I'm sure you have encountered this somewhere-- 00:09:10.670 --> 00:09:13.610 align:middle line:84% when we estimate demand, we have to deal with the endogeneity 00:09:13.610 --> 00:09:16.140 align:middle line:90% or simultaneity problem. 00:09:16.140 --> 00:09:17.940 align:middle line:90% So what does this mean? 00:09:17.940 --> 00:09:22.140 align:middle line:84% So there's an interesting article 00:09:22.140 --> 00:09:25.950 align:middle line:84% that is actually fun to read because it really shows you 00:09:25.950 --> 00:09:27.960 align:middle line:84% how much our thinking has evolved 00:09:27.960 --> 00:09:31.080 align:middle line:84% and how much better understanding of even the most 00:09:31.080 --> 00:09:32.850 align:middle line:84% simple model that we can come up with, 00:09:32.850 --> 00:09:36.840 align:middle line:84% which is this linear supply and demand curves, 00:09:36.840 --> 00:09:40.230 align:middle line:84% how we can think about the kinds of empirical challenges 00:09:40.230 --> 00:09:41.910 align:middle line:90% that come up here. 00:09:41.910 --> 00:09:45.420 align:middle line:90% So start with a bunch of points. 00:09:45.420 --> 00:09:47.045 align:middle line:84% You want to estimate the demand curve. 00:09:47.045 --> 00:09:51.050 align:middle line:90% 00:09:51.050 --> 00:09:56.720 align:middle line:84% So let's say we have a simple linear demand and supply curve. 00:09:56.720 --> 00:09:59.600 align:middle line:90% 00:09:59.600 --> 00:10:03.560 align:middle line:90% We have some fixed intercept. 00:10:03.560 --> 00:10:07.580 align:middle line:84% We have some coefficients, some slope coefficients. 00:10:07.580 --> 00:10:11.930 align:middle line:84% And we have an unobservable part of the intercept, OK? 00:10:11.930 --> 00:10:16.220 align:middle line:84% So let's say I'm running this regression. 00:10:16.220 --> 00:10:18.775 align:middle line:90% What problem am I running into? 00:10:18.775 --> 00:10:23.960 align:middle line:90% 00:10:23.960 --> 00:10:27.000 align:middle line:90% Just estimate this via OLS. 00:10:27.000 --> 00:10:29.180 align:middle line:84% Conceptually, what is the problem? 00:10:29.180 --> 00:10:36.010 align:middle line:90% 00:10:36.010 --> 00:10:38.470 align:middle line:84% STUDENT: They're jointly determined in equilibrium. 00:10:38.470 --> 00:10:41.110 align:middle line:84% TOBIAS SALZ: They're jointly determined in equilibrium. 00:10:41.110 --> 00:10:43.160 align:middle line:90% That's right. 00:10:43.160 --> 00:10:45.520 align:middle line:84% So this is basically the economic reason 00:10:45.520 --> 00:10:46.760 align:middle line:90% why there is a problem. 00:10:46.760 --> 00:10:51.890 align:middle line:84% And what this means econometrically, 00:10:51.890 --> 00:10:53.530 align:middle line:84% so because they are jointly determined, 00:10:53.530 --> 00:10:57.730 align:middle line:84% the price is going to reflect information that's 00:10:57.730 --> 00:11:02.380 align:middle line:84% unobserved to the researcher, unobserved information that's 00:11:02.380 --> 00:11:05.110 align:middle line:90% in this random intercept. 00:11:05.110 --> 00:11:08.950 align:middle line:84% So if I write down the equilibrium price, 00:11:08.950 --> 00:11:10.630 align:middle line:84% I get an expression that contains 00:11:10.630 --> 00:11:14.510 align:middle line:84% both the random part of the demand and the supply intercept. 00:11:14.510 --> 00:11:17.220 align:middle line:90% 00:11:17.220 --> 00:11:22.140 align:middle line:84% And so what this means is that the price is not 00:11:22.140 --> 00:11:24.760 align:middle line:84% uncorrelated to the error term of this regression. 00:11:24.760 --> 00:11:30.390 align:middle line:90% 00:11:30.390 --> 00:11:33.200 align:middle line:90% How do I fix it? 00:11:33.200 --> 00:11:34.410 align:middle line:90% STUDENT: Instruments. 00:11:34.410 --> 00:11:36.660 align:middle line:84% TOBIAS SALZ: And what would be a good instrument here? 00:11:36.660 --> 00:11:38.160 align:middle line:84% STUDENT: Supply and demand shifters. 00:11:38.160 --> 00:11:42.290 align:middle line:84% TOBIAS SALZ: Right, so we want to find a shifter 00:11:42.290 --> 00:11:46.520 align:middle line:84% on the other market side that we believe 00:11:46.520 --> 00:11:52.760 align:middle line:84% is orthogonal to the error term, the supply shifter that is 00:11:52.760 --> 00:11:54.500 align:middle line:90% orthogonal to the error term. 00:11:54.500 --> 00:11:58.010 align:middle line:84% So you may be wondering why am I bringing this up here? 00:11:58.010 --> 00:12:00.590 align:middle line:84% You have probably encountered this beforehand, probably 00:12:00.590 --> 00:12:05.220 align:middle line:84% even during your bachelor in undergraduate. 00:12:05.220 --> 00:12:08.300 align:middle line:84% So the reason I'm bringing it up is 00:12:08.300 --> 00:12:10.100 align:middle line:84% that you'll be fixing this problem 00:12:10.100 --> 00:12:12.050 align:middle line:90% over and over and over again. 00:12:12.050 --> 00:12:16.190 align:middle line:84% So we will go to much more complicated models than this one 00:12:16.190 --> 00:12:18.160 align:middle line:90% here. 00:12:18.160 --> 00:12:23.480 align:middle line:84% And it turns out that you can't really escape it. 00:12:23.480 --> 00:12:25.240 align:middle line:84% I sometimes hear in talks people say, 00:12:25.240 --> 00:12:29.500 align:middle line:84% oh, OK, so now, I've sort of exhausted my exogenous variation 00:12:29.500 --> 00:12:30.440 align:middle line:90% in the data. 00:12:30.440 --> 00:12:32.170 align:middle line:84% Let me now put a model on top of this 00:12:32.170 --> 00:12:34.720 align:middle line:90% and fix the problem this way. 00:12:34.720 --> 00:12:36.410 align:middle line:84% It's almost the opposite of what's true. 00:12:36.410 --> 00:12:38.830 align:middle line:84% You actually oftentimes need more rather than less 00:12:38.830 --> 00:12:41.630 align:middle line:84% instruments for the kinds of models that we estimate. 00:12:41.630 --> 00:12:45.970 align:middle line:84% So we will think very carefully about what instruments you need, 00:12:45.970 --> 00:12:49.060 align:middle line:84% how many instruments you need, what are good instruments, 00:12:49.060 --> 00:12:50.980 align:middle line:90% and things like that. 00:12:50.980 --> 00:12:55.690 align:middle line:84% So just to prepare you for-- you will not 00:12:55.690 --> 00:12:58.025 align:middle line:84% be able to somehow get around this problem 00:12:58.025 --> 00:13:00.525 align:middle line:84% with the kinds of models that I'm going to talk about today. 00:13:00.525 --> 00:13:04.900 align:middle line:90% 00:13:04.900 --> 00:13:10.960 align:middle line:84% So we're going to estimate demand systems. 00:13:10.960 --> 00:13:14.620 align:middle line:84% And the initial approach here was 00:13:14.620 --> 00:13:17.440 align:middle line:84% what is called the product space approach. 00:13:17.440 --> 00:13:19.340 align:middle line:84% What is the product space approach? 00:13:19.340 --> 00:13:21.310 align:middle line:90% The product space approach-- 00:13:21.310 --> 00:13:23.210 align:middle line:84% and I'll just have one slide on this. 00:13:23.210 --> 00:13:25.660 align:middle line:84% I'm probably not doing this literature justice, 00:13:25.660 --> 00:13:26.590 align:middle line:90% I should say. 00:13:26.590 --> 00:13:29.140 align:middle line:84% Just very quickly want to give you 00:13:29.140 --> 00:13:31.840 align:middle line:84% the gist of what people have been doing here, OK? 00:13:31.840 --> 00:13:33.430 align:middle line:84% The product space approach basically 00:13:33.430 --> 00:13:39.380 align:middle line:84% means that I treat every product as its own unique thing. 00:13:39.380 --> 00:13:45.140 align:middle line:84% And I'm trying to model a demand system where 00:13:45.140 --> 00:13:48.890 align:middle line:84% I write the quantities demanded in terms 00:13:48.890 --> 00:13:52.610 align:middle line:84% of all the prices in the market, in terms of all the demand 00:13:52.610 --> 00:13:57.370 align:middle line:84% shocks in the market and all the unobserved shocks in the market. 00:13:57.370 --> 00:14:01.954 align:middle line:90% 00:14:01.954 --> 00:14:06.530 align:middle line:84% So let's think about already a much more restricted version 00:14:06.530 --> 00:14:08.760 align:middle line:84% than this very general formulation here, 00:14:08.760 --> 00:14:12.350 align:middle line:84% one where, let's say, the vector of quantities 00:14:12.350 --> 00:14:15.830 align:middle line:84% for different products in this demand system 00:14:15.830 --> 00:14:21.290 align:middle line:84% is a function of some matrix that premultiplies 00:14:21.290 --> 00:14:23.360 align:middle line:90% a vector of prices. 00:14:23.360 --> 00:14:27.620 align:middle line:84% So we have a market with many different products, 00:14:27.620 --> 00:14:29.120 align:middle line:84% let's say the car market since this 00:14:29.120 --> 00:14:30.990 align:middle line:90% is going to be our theme today. 00:14:30.990 --> 00:14:36.430 align:middle line:84% And so we basically, to understand the demand 00:14:36.430 --> 00:14:38.980 align:middle line:84% for each separate product in this market, 00:14:38.980 --> 00:14:41.710 align:middle line:84% I need to know the coefficients and all the prices 00:14:41.710 --> 00:14:44.990 align:middle line:90% for all the products. 00:14:44.990 --> 00:14:48.790 align:middle line:84% And so then there's going to be a scalar unobservable also. 00:14:48.790 --> 00:14:52.200 align:middle line:84% So this is already, again, a restriction because we could-- 00:14:52.200 --> 00:14:55.530 align:middle line:84% in principle, it may be true that the demand for each product 00:14:55.530 --> 00:14:59.880 align:middle line:84% depends on the whole vector of unobservables. 00:14:59.880 --> 00:15:03.810 align:middle line:84% So what is the issue, even in this very restricted version 00:15:03.810 --> 00:15:07.050 align:middle line:84% here, is I have a lot of parameters 00:15:07.050 --> 00:15:09.040 align:middle line:90% that are, again, unique. 00:15:09.040 --> 00:15:11.500 align:middle line:84% It's a unique set of parameters for each product. 00:15:11.500 --> 00:15:15.090 align:middle line:90% I need to estimate all of those. 00:15:15.090 --> 00:15:24.350 align:middle line:84% And so if I increase the number of products, 00:15:24.350 --> 00:15:27.270 align:middle line:84% I very quickly run into a curse of dimensionality 00:15:27.270 --> 00:15:34.520 align:middle line:84% because the number of parameters grows at a squared rate. 00:15:34.520 --> 00:15:37.370 align:middle line:84% So each new product that I'm adding to the market, 00:15:37.370 --> 00:15:41.780 align:middle line:84% I need to add in a row and a column to this matrix. 00:15:41.780 --> 00:15:44.810 align:middle line:84% So people have tried to reduce this problem, for instance, 00:15:44.810 --> 00:15:50.180 align:middle line:84% by restricting the matrix such that the substitution patterns 00:15:50.180 --> 00:15:53.360 align:middle line:84% are consistent with Slutsky's symmetry, 00:15:53.360 --> 00:15:56.880 align:middle line:84% or they introduced ideas like budgeting. 00:15:56.880 --> 00:15:59.840 align:middle line:84% So where people, let's say, have some budget for food 00:15:59.840 --> 00:16:03.710 align:middle line:84% and some budget for leisure and some budget for something else. 00:16:03.710 --> 00:16:06.650 align:middle line:84% And then the demand in each of those categories, 00:16:06.650 --> 00:16:10.140 align:middle line:84% you only need to know what's the budget for this category. 00:16:10.140 --> 00:16:12.300 align:middle line:84% And that restricts substitution patterns. 00:16:12.300 --> 00:16:14.562 align:middle line:84% But by and large, you don't get around 00:16:14.562 --> 00:16:15.770 align:middle line:90% this curse of dimensionality. 00:16:15.770 --> 00:16:17.270 align:middle line:84% And it has therefore turned out not 00:16:17.270 --> 00:16:19.850 align:middle line:90% to be a very practical approach. 00:16:19.850 --> 00:16:23.450 align:middle line:84% It's also very demanding in terms of instruments, 00:16:23.450 --> 00:16:27.840 align:middle line:84% if you think about it because all the prices here 00:16:27.840 --> 00:16:29.970 align:middle line:90% are potentially endogenous. 00:16:29.970 --> 00:16:33.990 align:middle line:84% And so for each product, I need the number of instruments 00:16:33.990 --> 00:16:39.760 align:middle line:90% equal the number of prices, OK? 00:16:39.760 --> 00:16:42.080 align:middle line:84% Another reason why people don't like these models-- 00:16:42.080 --> 00:16:44.590 align:middle line:84% I find this as somewhat less good justification 00:16:44.590 --> 00:16:47.290 align:middle line:84% because it's not that we do it all that much, that we can't 00:16:47.290 --> 00:16:51.790 align:middle line:84% predict demand for new goods because, again, I don't learn 00:16:51.790 --> 00:16:56.665 align:middle line:84% anything about other products by learning demand for the products 00:16:56.665 --> 00:16:58.540 align:middle line:84% that I'm currently estimating because there's 00:16:58.540 --> 00:17:00.080 align:middle line:90% nothing that translates. 00:17:00.080 --> 00:17:04.050 align:middle line:90% 00:17:04.050 --> 00:17:06.990 align:middle line:84% OK, so people have moved away from this-- although, 00:17:06.990 --> 00:17:10.290 align:middle line:84% there are nice applications of these kinds of models-- 00:17:10.290 --> 00:17:13.079 align:middle line:84% and instead move to something that is called 00:17:13.079 --> 00:17:16.020 align:middle line:84% the characteristic space approach, 00:17:16.020 --> 00:17:19.534 align:middle line:84% which typically comes together with discrete choice models. 00:17:19.534 --> 00:17:23.369 align:middle line:90% 00:17:23.369 --> 00:17:27.300 align:middle line:84% OK, so in this approach, products 00:17:27.300 --> 00:17:30.470 align:middle line:84% are described by their characteristics. 00:17:30.470 --> 00:17:33.300 align:middle line:84% So take the market for cars, let's say. 00:17:33.300 --> 00:17:39.830 align:middle line:84% So the car can be described by horsepower, top speed, trunk 00:17:39.830 --> 00:17:42.750 align:middle line:84% space, driving assistance features, and things like that, 00:17:42.750 --> 00:17:43.280 align:middle line:90% OK? 00:17:43.280 --> 00:17:45.560 align:middle line:84% The iPhone is a combination of, let's 00:17:45.560 --> 00:17:48.560 align:middle line:84% say, the megapixels of your camera, 00:17:48.560 --> 00:17:52.880 align:middle line:84% the resolution of your screen, your storage, and other kinds 00:17:52.880 --> 00:17:55.070 align:middle line:90% of gadgets that are built in. 00:17:55.070 --> 00:18:00.000 align:middle line:84% So we enumerate different product dimensions. 00:18:00.000 --> 00:18:04.520 align:middle line:84% Now, you will notice that if we add products to the market 00:18:04.520 --> 00:18:06.950 align:middle line:84% and we observe what are the product characteristics, 00:18:06.950 --> 00:18:09.450 align:middle line:84% we in principle are not adding any new parameters. 00:18:09.450 --> 00:18:14.930 align:middle line:90% 00:18:14.930 --> 00:18:19.070 align:middle line:84% So this idea of having products basically 00:18:19.070 --> 00:18:22.100 align:middle line:84% be collection of characteristics, as I said, 00:18:22.100 --> 00:18:24.740 align:middle line:84% comes together with what is called the discrete choice 00:18:24.740 --> 00:18:28.170 align:middle line:90% approach, which is that people-- 00:18:28.170 --> 00:18:30.020 align:middle line:90% there are a bunch of consumers. 00:18:30.020 --> 00:18:32.930 align:middle line:84% Each of them buys either one of the available products or none 00:18:32.930 --> 00:18:33.430 align:middle line:90% at all. 00:18:33.430 --> 00:18:37.070 align:middle line:90% 00:18:37.070 --> 00:18:42.650 align:middle line:84% So to summarize then, we can write-- 00:18:42.650 --> 00:18:48.290 align:middle line:84% sorry, I should have mentioned, a third foundational principle 00:18:48.290 --> 00:18:50.360 align:middle line:84% is that we want to build up these demand 00:18:50.360 --> 00:18:53.520 align:middle line:84% models from utilities, from indirect utilities. 00:18:53.520 --> 00:18:57.380 align:middle line:84% So we're describing people's utilities 00:18:57.380 --> 00:19:00.530 align:middle line:84% in terms of prices, how much they 00:19:00.530 --> 00:19:02.180 align:middle line:84% value each of these different product 00:19:02.180 --> 00:19:05.000 align:middle line:84% attributes-- so these are observed product attributes-- 00:19:05.000 --> 00:19:07.340 align:middle line:84% the unobserved product attributes. 00:19:07.340 --> 00:19:10.850 align:middle line:84% These are in IO religiously referred to as xj, OK? 00:19:10.850 --> 00:19:12.600 align:middle line:90% So everybody knows what xj is. 00:19:12.600 --> 00:19:15.350 align:middle line:84% And soon you'll also know that whenever you seek xj, 00:19:15.350 --> 00:19:17.400 align:middle line:84% these are unobserved product attributes, 00:19:17.400 --> 00:19:22.130 align:middle line:84% and demographic variables as well as unobserved random 00:19:22.130 --> 00:19:23.950 align:middle line:90% shifters at the consumer level. 00:19:23.950 --> 00:19:28.810 align:middle line:90% 00:19:28.810 --> 00:19:32.245 align:middle line:84% And then we make the assumption that consumers-- 00:19:32.245 --> 00:19:33.870 align:middle line:84% in most models, you make the assumption 00:19:33.870 --> 00:19:36.745 align:middle line:84% that consumers do the best they can and pick the product 00:19:36.745 --> 00:19:37.745 align:middle line:90% that they like the most. 00:19:37.745 --> 00:19:41.690 align:middle line:90% 00:19:41.690 --> 00:19:46.510 align:middle line:90% OK, so I was-- 00:19:46.510 --> 00:19:49.040 align:middle line:84% let me just go back once more here. 00:19:49.040 --> 00:19:51.610 align:middle line:84% So there's this sort of random part, 00:19:51.610 --> 00:19:54.400 align:middle line:84% the consumer-specific random part, 00:19:54.400 --> 00:19:57.533 align:middle line:84% that helps us explain why consumers may choose 00:19:57.533 --> 00:19:58.700 align:middle line:90% different kinds of products. 00:19:58.700 --> 00:20:01.120 align:middle line:84% It basically allows us to rationalize different patterns 00:20:01.120 --> 00:20:02.240 align:middle line:90% in the data. 00:20:02.240 --> 00:20:06.940 align:middle line:84% But it's random from the perspective of the researcher. 00:20:06.940 --> 00:20:11.770 align:middle line:84% The consumers, they know what their idiosyncratic valuations 00:20:11.770 --> 00:20:13.970 align:middle line:90% are for each product. 00:20:13.970 --> 00:20:16.990 align:middle line:84% So I'm going to just switch notation here just 00:20:16.990 --> 00:20:20.740 align:middle line:84% for this one slide, because I couldn't find an image like this 00:20:20.740 --> 00:20:22.930 align:middle line:90% with epsilons. 00:20:22.930 --> 00:20:26.770 align:middle line:84% So suppose that consumer utility can 00:20:26.770 --> 00:20:30.190 align:middle line:84% be written as the random part, which is mu ij. 00:20:30.190 --> 00:20:32.530 align:middle line:84% So each consumer goes to the market, 00:20:32.530 --> 00:20:37.650 align:middle line:84% takes a random draw for different kinds of products. 00:20:37.650 --> 00:20:41.710 align:middle line:84% And they all face the same price. 00:20:41.710 --> 00:20:46.540 align:middle line:84% So what you then can do is you can describe the consumer's 00:20:46.540 --> 00:20:53.112 align:middle line:84% choices in terms of these regions, which then give-- 00:20:53.112 --> 00:20:55.570 align:middle line:84% these are essentially measures that give rise to the market 00:20:55.570 --> 00:20:57.310 align:middle line:90% shares that we observe. 00:20:57.310 --> 00:20:59.950 align:middle line:84% So, for instance, there are some consumers 00:20:59.950 --> 00:21:06.440 align:middle line:84% who drew both a low mu i1 and a low mu i2, 00:21:06.440 --> 00:21:10.310 align:middle line:84% and they don't purchase anything because in both cases 00:21:10.310 --> 00:21:13.180 align:middle line:90% it's below the respective price. 00:21:13.180 --> 00:21:16.540 align:middle line:84% There are some other consumers who drew a very high mu 00:21:16.540 --> 00:21:19.550 align:middle line:90% i1 and a smaller mu i2. 00:21:19.550 --> 00:21:23.180 align:middle line:84% And they're in this ai1 region here. 00:21:23.180 --> 00:21:26.720 align:middle line:90% So we basically get these-- 00:21:26.720 --> 00:21:30.980 align:middle line:84% in terms of this distribution of the random part of utility, 00:21:30.980 --> 00:21:34.910 align:middle line:84% we get these choice regions that tell us what market shares are. 00:21:34.910 --> 00:21:37.730 align:middle line:84% So one reason I'm showing you this here 00:21:37.730 --> 00:21:42.740 align:middle line:84% is that if you want to compute market shares or choice 00:21:42.740 --> 00:21:48.990 align:middle line:84% probabilities, you have to come up 00:21:48.990 --> 00:21:52.750 align:middle line:84% with a way of finding these regions, in principle. 00:21:52.750 --> 00:21:57.400 align:middle line:84% You would have to figure out, in this region of integration 00:21:57.400 --> 00:22:00.740 align:middle line:84% of these different epsilon draws this is what consumers choose. 00:22:00.740 --> 00:22:03.005 align:middle line:90% And this other region is-- 00:22:03.005 --> 00:22:04.130 align:middle line:90% they choose something else. 00:22:04.130 --> 00:22:08.050 align:middle line:84% And you, in principle, unrestricted 00:22:08.050 --> 00:22:10.000 align:middle line:84% functions for these epsilon, that's 00:22:10.000 --> 00:22:12.693 align:middle line:84% a very cumbersome exercise and, in fact, 00:22:12.693 --> 00:22:14.235 align:middle line:84% computationally very difficult to do. 00:22:14.235 --> 00:22:17.140 align:middle line:90% 00:22:17.140 --> 00:22:23.760 align:middle line:84% OK, people have solved this the following way. 00:22:23.760 --> 00:22:26.670 align:middle line:84% So coming back to our utility function, 00:22:26.670 --> 00:22:28.890 align:middle line:84% I'm now just isolating the random term. 00:22:28.890 --> 00:22:33.150 align:middle line:84% What was beforehand called mu ij is now called epsilon ij. 00:22:33.150 --> 00:22:38.390 align:middle line:84% And it's typically assumed that this error 00:22:38.390 --> 00:22:42.240 align:middle line:90% is type I extreme value. 00:22:42.240 --> 00:22:46.980 align:middle line:84% So you may now be wondering what product-- 00:22:46.980 --> 00:22:49.320 align:middle line:84% what problem in life could possibly 00:22:49.320 --> 00:22:52.780 align:middle line:84% be solved by a double exponential functional form? 00:22:52.780 --> 00:22:59.030 align:middle line:84% As it turns out, this has a really nice property, 00:22:59.030 --> 00:23:02.360 align:middle line:84% which is that if we assume that consumers 00:23:02.360 --> 00:23:05.010 align:middle line:84% do the best for themselves, they observe everything, 00:23:05.010 --> 00:23:09.570 align:middle line:84% they choose the product that they like the most, 00:23:09.570 --> 00:23:13.830 align:middle line:84% then the choice probabilities or the market shares 00:23:13.830 --> 00:23:17.720 align:middle line:84% can be expressed in this logit form, OK? 00:23:17.720 --> 00:23:21.980 align:middle line:84% So we get a closed-form solution for those probabilities. 00:23:21.980 --> 00:23:24.850 align:middle line:84% Now, we can make some normalizations here. 00:23:24.850 --> 00:23:26.480 align:middle line:84% If you stare at this, you'll notice 00:23:26.480 --> 00:23:31.610 align:middle line:84% that we could add a constant to each of the uij's, and 00:23:31.610 --> 00:23:35.030 align:middle line:84% this constant would cancel out here, 00:23:35.030 --> 00:23:37.440 align:middle line:84% which means that we have a normalization to make. 00:23:37.440 --> 00:23:41.850 align:middle line:84% And typically, we normalize what is called the outside good to 0. 00:23:41.850 --> 00:23:44.610 align:middle line:84% So the outside good is basically everything else 00:23:44.610 --> 00:23:46.170 align:middle line:84% that consumers could be doing instead 00:23:46.170 --> 00:23:49.080 align:middle line:90% of buying some of the products. 00:23:49.080 --> 00:23:50.380 align:middle line:90% And so that's important. 00:23:50.380 --> 00:23:58.588 align:middle line:84% It's not just a mathematical decision to normalize this to 0. 00:23:58.588 --> 00:24:00.880 align:middle line:84% You have to always think about that consumer welfare is 00:24:00.880 --> 00:24:02.297 align:middle line:84% measured relative to this product. 00:24:02.297 --> 00:24:05.880 align:middle line:90% 00:24:05.880 --> 00:24:09.540 align:middle line:84% And it's therefore worthwhile to, in the interpretation 00:24:09.540 --> 00:24:13.380 align:middle line:84% of a consumer welfare calculation, keep that in mind. 00:24:13.380 --> 00:24:15.060 align:middle line:84% And that could sometimes be a problem 00:24:15.060 --> 00:24:16.743 align:middle line:84% if you compare markets from year to year 00:24:16.743 --> 00:24:18.785 align:middle line:84% because the outside option could actually change. 00:24:18.785 --> 00:24:22.680 align:middle line:90% 00:24:22.680 --> 00:24:25.680 align:middle line:84% So maybe as a question to you, let's think 00:24:25.680 --> 00:24:27.660 align:middle line:90% about the market for cars. 00:24:27.660 --> 00:24:32.058 align:middle line:84% So what could be problematic about this? 00:24:32.058 --> 00:24:33.850 align:middle line:84% So what is the outside option when we think 00:24:33.850 --> 00:24:36.090 align:middle line:90% about people purchasing cars? 00:24:36.090 --> 00:24:40.750 align:middle line:90% 00:24:40.750 --> 00:24:45.040 align:middle line:84% What is part of the outside option? 00:24:45.040 --> 00:24:45.540 align:middle line:90% Yeah? 00:24:45.540 --> 00:24:46.832 align:middle line:90% STUDENT: Public transportation? 00:24:46.832 --> 00:24:48.380 align:middle line:84% TOBIAS SALZ: Public transportation. 00:24:48.380 --> 00:24:50.720 align:middle line:90% STUDENT: Cycling. 00:24:50.720 --> 00:24:51.650 align:middle line:90% Cycling. 00:24:51.650 --> 00:24:53.990 align:middle line:90% TOBIAS SALZ: Cycling. 00:24:53.990 --> 00:24:56.155 align:middle line:84% I'm looking for something more long run. 00:24:56.155 --> 00:24:58.700 align:middle line:90% 00:24:58.700 --> 00:25:01.050 align:middle line:84% But all these are good responses. 00:25:01.050 --> 00:25:05.090 align:middle line:90% 00:25:05.090 --> 00:25:08.100 align:middle line:84% So most people own a car already. 00:25:08.100 --> 00:25:10.550 align:middle line:90% And the car is a durable good. 00:25:10.550 --> 00:25:13.610 align:middle line:84% And the decision whether or not to buy a car 00:25:13.610 --> 00:25:14.990 align:middle line:84% is in part a decision of how much 00:25:14.990 --> 00:25:17.480 align:middle line:90% I let my old car depreciate. 00:25:17.480 --> 00:25:19.670 align:middle line:84% And to what extent people are willing to do 00:25:19.670 --> 00:25:24.230 align:middle line:84% that might vary with, let's say, macroeconomic conditions, 00:25:24.230 --> 00:25:27.440 align:middle line:84% how easy it is to get credit, things like that. 00:25:27.440 --> 00:25:31.070 align:middle line:84% So if I now estimate over several-- 00:25:31.070 --> 00:25:34.130 align:middle line:84% if I estimate a demand model that spans several years, 00:25:34.130 --> 00:25:38.700 align:middle line:84% where this decision of consumers may change from year to year, 00:25:38.700 --> 00:25:41.690 align:middle line:90% I have to keep this in mind. 00:25:41.690 --> 00:25:45.500 align:middle line:84% I may have to do some adjustments for a substitution 00:25:45.500 --> 00:25:48.710 align:middle line:84% to the outside option from year to year. 00:25:48.710 --> 00:25:55.610 align:middle line:84% So that's something that's important to keep in mind. 00:25:55.610 --> 00:25:57.380 align:middle line:84% So what is the typical data scenario 00:25:57.380 --> 00:26:00.260 align:middle line:90% for these kinds of models? 00:26:00.260 --> 00:26:05.120 align:middle line:84% As I said, researchers observed aggregate market shares, prices 00:26:05.120 --> 00:26:07.580 align:middle line:90% and product attributes. 00:26:07.580 --> 00:26:10.610 align:middle line:84% For each market, they also observe 00:26:10.610 --> 00:26:14.450 align:middle line:84% or tend to use the distributions of certain consumer 00:26:14.450 --> 00:26:15.770 align:middle line:90% characteristics. 00:26:15.770 --> 00:26:18.590 align:middle line:84% These characteristics are not linked to a specific purchase 00:26:18.590 --> 00:26:19.230 align:middle line:90% decision. 00:26:19.230 --> 00:26:26.960 align:middle line:84% So I may know that the income distribution in Cambridge 00:26:26.960 --> 00:26:31.130 align:middle line:84% looks like this and that the family size distribution 00:26:31.130 --> 00:26:33.450 align:middle line:90% in Cambridge has this form. 00:26:33.450 --> 00:26:35.480 align:middle line:84% So these are things that you typically 00:26:35.480 --> 00:26:40.280 align:middle line:84% can get from census data or somewhere else. 00:26:40.280 --> 00:26:42.150 align:middle line:84% I'll talk more about instruments later. 00:26:42.150 --> 00:26:43.970 align:middle line:90% You need instruments. 00:26:43.970 --> 00:26:47.060 align:middle line:84% Importantly, because we're working with aggregate market 00:26:47.060 --> 00:26:49.220 align:middle line:84% shares, the typical assumption, although there 00:26:49.220 --> 00:26:51.140 align:middle line:84% is some recent work that tries to relax this, 00:26:51.140 --> 00:26:56.970 align:middle line:84% is that we can ignore sampling uncertainty in market shares. 00:26:56.970 --> 00:27:01.740 align:middle line:84% So we're saying we observe enough people buying 00:27:01.740 --> 00:27:04.290 align:middle line:84% each product that I can just take this share as given and do 00:27:04.290 --> 00:27:07.710 align:middle line:84% not have to econometrically deal with the fact there's 00:27:07.710 --> 00:27:09.490 align:middle line:84% some sort of sampling uncertainty. 00:27:09.490 --> 00:27:12.969 align:middle line:84% We just take these as numbers as given, OK? 00:27:12.969 --> 00:27:17.660 align:middle line:90% 00:27:17.660 --> 00:27:20.220 align:middle line:84% Typically, this requires some judgment. 00:27:20.220 --> 00:27:23.810 align:middle line:84% You have to make a decision on what is the size of the market. 00:27:23.810 --> 00:27:28.670 align:middle line:84% So, coming back to my example, in the market for cars, 00:27:28.670 --> 00:27:31.940 align:middle line:84% it's not immediately clear from year to year who's 00:27:31.940 --> 00:27:34.820 align:middle line:84% in the market to buy a car because it may depend on how 00:27:34.820 --> 00:27:37.970 align:middle line:84% much longer do people want to keep their old car 00:27:37.970 --> 00:27:40.290 align:middle line:84% and a variety of factors like that. 00:27:40.290 --> 00:27:43.670 align:middle line:84% So this oftentimes requires careful judgment 00:27:43.670 --> 00:27:46.550 align:middle line:84% of what is the size of the market. 00:27:46.550 --> 00:27:48.480 align:middle line:84% In some cases, it's a bit easier. 00:27:48.480 --> 00:27:51.390 align:middle line:84% For instance, let's say you have access to scanner data. 00:27:51.390 --> 00:27:54.230 align:middle line:84% You see how many people go to the supermarket. 00:27:54.230 --> 00:28:01.010 align:middle line:84% And you would be interested in, let's say, the market for milk. 00:28:01.010 --> 00:28:03.407 align:middle line:84% Then you know how many people have been in the store, 00:28:03.407 --> 00:28:05.990 align:middle line:84% and it gives you a pretty good idea how many people could have 00:28:05.990 --> 00:28:08.040 align:middle line:90% bought at this point in time. 00:28:08.040 --> 00:28:11.000 align:middle line:84% But you have to make assumptions on that because counterfactually 00:28:11.000 --> 00:28:12.750 align:middle line:84% you may be interested in something 00:28:12.750 --> 00:28:14.850 align:middle line:84% that either lowers or raises prices. 00:28:14.850 --> 00:28:17.070 align:middle line:84% And then how many people substitute 00:28:17.070 --> 00:28:20.310 align:middle line:84% from the outside option into the market and purchase a product 00:28:20.310 --> 00:28:25.800 align:middle line:84% depends on the size of the outside market. 00:28:25.800 --> 00:28:28.440 align:middle line:84% So what I'm going to do now is I'm 00:28:28.440 --> 00:28:31.540 align:middle line:84% going to show you the model that people estimate these days, 00:28:31.540 --> 00:28:33.820 align:middle line:90% OK, the canonical model. 00:28:33.820 --> 00:28:36.360 align:middle line:84% And then I'm of trying to go through the different pieces 00:28:36.360 --> 00:28:39.960 align:middle line:84% and tell you why do we need those different pieces? 00:28:39.960 --> 00:28:43.690 align:middle line:84% So this is the random coefficient demand model. 00:28:43.690 --> 00:28:45.690 align:middle line:90% It goes back to-- 00:28:45.690 --> 00:28:48.360 align:middle line:84% or it has been popularized by a paper 00:28:48.360 --> 00:28:50.130 align:middle line:84% by Berry, Levinsohn, and Pakes, much 00:28:50.130 --> 00:28:53.940 align:middle line:84% of the intellectual contribution of how to estimate these models 00:28:53.940 --> 00:28:56.880 align:middle line:84% and deal with some of the econometric challenges 00:28:56.880 --> 00:29:00.280 align:middle line:84% has have been sort of laid in this paper. 00:29:00.280 --> 00:29:04.310 align:middle line:84% So, as before, we have an indirect utility function, 00:29:04.310 --> 00:29:07.090 align:middle line:90% which is assumed to be linear. 00:29:07.090 --> 00:29:12.700 align:middle line:84% We have consumers i in market t purchasing products j. 00:29:12.700 --> 00:29:16.330 align:middle line:84% There again are product attributes, prices. 00:29:16.330 --> 00:29:19.930 align:middle line:84% And notice that these are now premultiplied by a coefficient 00:29:19.930 --> 00:29:22.130 align:middle line:90% that has an i subscript. 00:29:22.130 --> 00:29:27.230 align:middle line:84% So what this means is that this is a model that allows consumers 00:29:27.230 --> 00:29:31.370 align:middle line:84% to experience different utility from different product 00:29:31.370 --> 00:29:33.340 align:middle line:90% attributes, OK? 00:29:33.340 --> 00:29:35.350 align:middle line:90% There's some people who-- 00:29:35.350 --> 00:29:37.150 align:middle line:84% supposedly, those with families, they're 00:29:37.150 --> 00:29:39.280 align:middle line:84% more interested in having a lot of trunk space 00:29:39.280 --> 00:29:41.940 align:middle line:90% than some other people, OK? 00:29:41.940 --> 00:29:44.760 align:middle line:84% There are some people, supposedly, 00:29:44.760 --> 00:29:50.760 align:middle line:84% those with lower income, that are more price sensitive. 00:29:50.760 --> 00:29:53.910 align:middle line:84% So this is one of the key innovations 00:29:53.910 --> 00:29:57.900 align:middle line:84% of this model is that it allows different people to assign 00:29:57.900 --> 00:30:03.150 align:middle line:84% different value to both product attributes and prices. 00:30:03.150 --> 00:30:05.470 align:middle line:84% And then this introduces a lot of challenges. 00:30:05.470 --> 00:30:09.450 align:middle line:84% And then how do we deal with those challenges? 00:30:09.450 --> 00:30:12.408 align:middle line:84% So we have, again, the outside options normalized to 0. 00:30:12.408 --> 00:30:13.950 align:middle line:84% So the utility for the outside option 00:30:13.950 --> 00:30:17.010 align:middle line:84% is just given by the random part, the idiosyncratic random 00:30:17.010 --> 00:30:18.510 align:middle line:90% part. 00:30:18.510 --> 00:30:21.360 align:middle line:84% The epsilons R seem to be type I extreme value. 00:30:21.360 --> 00:30:24.300 align:middle line:84% x is a row vector of observed product characteristics. 00:30:24.300 --> 00:30:31.475 align:middle line:84% And then xj, xj is a product market-specific demand shock. 00:30:31.475 --> 00:30:38.310 align:middle line:90% 00:30:38.310 --> 00:30:43.000 align:middle line:84% And so these coefficients, they are typically 00:30:43.000 --> 00:30:49.160 align:middle line:84% assumed to be a combination of an intercept, the average, 00:30:49.160 --> 00:30:52.520 align:middle line:84% let's say, the average price sensitivity plus some things 00:30:52.520 --> 00:30:55.230 align:middle line:84% that scale with the demographics. 00:30:55.230 --> 00:30:58.110 align:middle line:84% Again, I already told you we might observe the income 00:30:58.110 --> 00:30:59.910 align:middle line:90% distribution. 00:30:59.910 --> 00:31:02.310 align:middle line:84% And so the important thing, though, 00:31:02.310 --> 00:31:06.620 align:middle line:84% is that we do not observe income at the consumer level. 00:31:06.620 --> 00:31:10.940 align:middle line:84% We just have the distribution, and we integrate it out, OK? 00:31:10.940 --> 00:31:14.780 align:middle line:84% So this coefficient depends on demographic variables 00:31:14.780 --> 00:31:16.940 align:middle line:84% that we observe, again, at the market level 00:31:16.940 --> 00:31:20.200 align:middle line:84% and then, in some cases, also a random part. 00:31:20.200 --> 00:31:22.900 align:middle line:90% 00:31:22.900 --> 00:31:26.680 align:middle line:84% So typically, this is referred to as nu. 00:31:26.680 --> 00:31:28.650 align:middle line:84% And most of the times, this is assumed 00:31:28.650 --> 00:31:30.180 align:middle line:84% to be either normally distributed 00:31:30.180 --> 00:31:32.790 align:middle line:90% or log normally distributed. 00:31:32.790 --> 00:31:36.440 align:middle line:90% And then similarly for price. 00:31:36.440 --> 00:31:39.450 align:middle line:90% Any questions up to this point? 00:31:39.450 --> 00:31:41.390 align:middle line:84% STUDENT: So tastes and price sensitivity 00:31:41.390 --> 00:31:45.483 align:middle line:90% only vary across markets? 00:31:45.483 --> 00:31:46.650 align:middle line:90% TOBIAS SALZ: No, no, no, no. 00:31:46.650 --> 00:31:48.050 align:middle line:90% They're buried within markets. 00:31:48.050 --> 00:31:49.050 align:middle line:90% STUDENT: Within markets. 00:31:49.050 --> 00:31:50.840 align:middle line:84% TOBIAS SALZ: Yeah, because, again, we 00:31:50.840 --> 00:31:56.360 align:middle line:84% have different consumers in each market, indexed by i. 00:31:56.360 --> 00:32:00.565 align:middle line:84% Again, we don't know that this purchase 00:32:00.565 --> 00:32:02.440 align:middle line:84% was linked to this consumer with this income. 00:32:02.440 --> 00:32:04.980 align:middle line:84% But I do know that this is the income distribution 00:32:04.980 --> 00:32:07.240 align:middle line:90% around Kendall Square. 00:32:07.240 --> 00:32:11.080 align:middle line:84% And I therefore know that some people in this market 00:32:11.080 --> 00:32:12.940 align:middle line:90% have this much income and so on. 00:32:12.940 --> 00:32:14.295 align:middle line:90% And I'm just integrating it out. 00:32:14.295 --> 00:32:19.550 align:middle line:90% 00:32:19.550 --> 00:32:20.640 align:middle line:90% Other questions? 00:32:20.640 --> 00:32:23.830 align:middle line:90% 00:32:23.830 --> 00:32:26.118 align:middle line:84% STUDENT: So the superscript k is just-- 00:32:26.118 --> 00:32:27.160 align:middle line:90% TOBIAS SALZ: This keeps-- 00:32:27.160 --> 00:32:28.650 align:middle line:84% STUDENT: --indexing on product characteristics. 00:32:28.650 --> 00:32:28.960 align:middle line:90% TOBIAS SALZ: Yep. 00:32:28.960 --> 00:32:29.460 align:middle line:90% STUDENT: OK. 00:32:29.460 --> 00:32:33.490 align:middle line:90% 00:32:33.490 --> 00:32:35.350 align:middle line:90% TOBIAS SALZ: OK. 00:32:35.350 --> 00:32:38.780 align:middle line:90% OK, so this is the model. 00:32:38.780 --> 00:32:42.370 align:middle line:84% Now, let's drill down a bit and understand 00:32:42.370 --> 00:32:44.650 align:middle line:84% why do we need these different pieces? 00:32:44.650 --> 00:32:46.900 align:middle line:84% So first of all, it's going to be 00:32:46.900 --> 00:32:51.490 align:middle line:84% useful to keep track of the things that are i-specific 00:32:51.490 --> 00:32:55.888 align:middle line:84% and not i-specific, so things that vary at the consumer level 00:32:55.888 --> 00:32:57.930 align:middle line:84% and things that are sometimes referred to as just 00:32:57.930 --> 00:33:00.440 align:middle line:90% the average product quality. 00:33:00.440 --> 00:33:03.300 align:middle line:84% OK, the average product quality is often to refer-- 00:33:03.300 --> 00:33:05.180 align:middle line:84% pretty much always refer to as delta. 00:33:05.180 --> 00:33:09.180 align:middle line:84% So one of these things, as xj people, when you say delta, 00:33:09.180 --> 00:33:11.290 align:middle line:84% they know what you're referring to in the model. 00:33:11.290 --> 00:33:14.850 align:middle line:84% So this is the average product quality. 00:33:14.850 --> 00:33:18.360 align:middle line:84% It includes basically the intercept 00:33:18.360 --> 00:33:23.180 align:middle line:84% of the random coefficient and the unobserved product 00:33:23.180 --> 00:33:26.290 align:middle line:90% characteristics. 00:33:26.290 --> 00:33:29.950 align:middle line:84% And then, in this case, we keep track 00:33:29.950 --> 00:33:33.250 align:middle line:84% of the consumer-specific part as mu ijt. 00:33:33.250 --> 00:33:38.590 align:middle line:84% And it's, again, multiplying both attributes and prices 00:33:38.590 --> 00:33:43.710 align:middle line:84% by these consumer attributes that are 00:33:43.710 --> 00:33:47.780 align:middle line:90% either unobserved or observed. 00:33:47.780 --> 00:33:50.840 align:middle line:84% OK, so now we can take a specific consumer. 00:33:50.840 --> 00:33:54.770 align:middle line:84% And, as before, this consumers purchase propensity 00:33:54.770 --> 00:33:59.600 align:middle line:84% for product j is simply given by this logit formula. 00:33:59.600 --> 00:34:02.390 align:middle line:84% But they're, as I said, different consumers 00:34:02.390 --> 00:34:05.690 align:middle line:90% within a given market, t, right? 00:34:05.690 --> 00:34:09.850 align:middle line:84% And so the overall market shares have to integrate out 00:34:09.850 --> 00:34:11.360 align:middle line:90% of all the different consumers. 00:34:11.360 --> 00:34:13.960 align:middle line:90% 00:34:13.960 --> 00:34:17.110 align:middle line:84% So we therefore integrate out over the distribution 00:34:17.110 --> 00:34:19.659 align:middle line:84% of demographics as well as if we allow 00:34:19.659 --> 00:34:23.055 align:middle line:84% for unobserved distributions over those as well. 00:34:23.055 --> 00:34:28.449 align:middle line:90% 00:34:28.449 --> 00:34:32.050 align:middle line:84% OK, so this thing here is much more nasty than this thing, 00:34:32.050 --> 00:34:34.650 align:middle line:90% as it will turn out, OK? 00:34:34.650 --> 00:34:37.590 align:middle line:84% I'll show you in a second why that is the case. 00:34:37.590 --> 00:34:40.650 align:middle line:84% STUDENT: So we set the distribution for nu. 00:34:40.650 --> 00:34:43.590 align:middle line:84% TOBIAS SALZ: You make a functional form assumption, 00:34:43.590 --> 00:34:49.790 align:middle line:84% but you don't know what the variance of that term is, yeah. 00:34:49.790 --> 00:34:56.590 align:middle line:90% 00:34:56.590 --> 00:35:03.880 align:middle line:84% OK, so question, why do we need this error term xj? 00:35:03.880 --> 00:35:08.910 align:middle line:84% If you think about it, we know what these-- 00:35:08.910 --> 00:35:13.780 align:middle line:84% we know how we compute probabilities. 00:35:13.780 --> 00:35:20.050 align:middle line:84% And if we only had observed product attributes and prices, 00:35:20.050 --> 00:35:23.050 align:middle line:84% what would happen is that our model is very quickly rejected 00:35:23.050 --> 00:35:26.920 align:middle line:84% by the data because what it would imply, because again, 00:35:26.920 --> 00:35:29.330 align:middle line:84% we assume we have many consumers in the market. 00:35:29.330 --> 00:35:32.050 align:middle line:84% We can therefore just write choice probabilities 00:35:32.050 --> 00:35:33.400 align:middle line:90% in this logit form. 00:35:33.400 --> 00:35:36.010 align:middle line:90% 00:35:36.010 --> 00:35:41.770 align:middle line:84% And that means that I only need to know x, beta, alpha, and p 00:35:41.770 --> 00:35:45.830 align:middle line:84% to know what the market share of a product is going to be. 00:35:45.830 --> 00:35:48.530 align:middle line:84% But what this implies is that any 00:35:48.530 --> 00:35:52.010 align:middle line:84% market where two products have the same attributes and prices, 00:35:52.010 --> 00:35:55.310 align:middle line:84% they would need to have exactly the same market share. 00:35:55.310 --> 00:35:59.060 align:middle line:84% Or, to pick a different example, if I look at a market 00:35:59.060 --> 00:36:04.270 align:middle line:84% where all the product attributes of one product are worse 00:36:04.270 --> 00:36:06.010 align:middle line:84% and that product has a higher price, 00:36:06.010 --> 00:36:08.380 align:middle line:84% that would not be allowed to happen in a model 00:36:08.380 --> 00:36:09.910 align:middle line:90% without such an error term. 00:36:09.910 --> 00:36:13.120 align:middle line:84% So think again back to the iPhone. 00:36:13.120 --> 00:36:17.590 align:middle line:84% So Apple, in the past at least, tended 00:36:17.590 --> 00:36:20.840 align:middle line:84% to not introduce new features as quickly as some other producers. 00:36:20.840 --> 00:36:24.790 align:middle line:84% So the camera didn't have the highest megapixels. 00:36:24.790 --> 00:36:27.520 align:middle line:84% And it didn't use the biggest storage space, 00:36:27.520 --> 00:36:30.450 align:middle line:84% and it wasn't the largest phone, and things like that. 00:36:30.450 --> 00:36:33.392 align:middle line:90% 00:36:33.392 --> 00:36:38.790 align:middle line:84% And yet, Apple had higher prices and larger market shares, 00:36:38.790 --> 00:36:43.830 align:middle line:84% at least in the US, than, let's say, cheaper Android phones. 00:36:43.830 --> 00:36:49.910 align:middle line:84% So without such an error, which is a purely vertical attribute 00:36:49.910 --> 00:36:53.830 align:middle line:84% of a product, that all consumers value the same, 00:36:53.830 --> 00:36:55.570 align:middle line:84% something like this couldn't happen. 00:36:55.570 --> 00:36:59.080 align:middle line:84% So we need xj in order to explain 00:36:59.080 --> 00:37:02.158 align:middle line:84% that there are some products that somehow are popular, 00:37:02.158 --> 00:37:04.450 align:middle line:84% even though they don't quite look very popular in terms 00:37:04.450 --> 00:37:05.690 align:middle line:90% of product attributes. 00:37:05.690 --> 00:37:10.290 align:middle line:90% 00:37:10.290 --> 00:37:13.218 align:middle line:84% This, of course, causes this problem 00:37:13.218 --> 00:37:14.760 align:middle line:84% that I've been talking about earlier. 00:37:14.760 --> 00:37:17.950 align:middle line:84% Firms-- Apple also knows it has this ecosystem. 00:37:17.950 --> 00:37:19.770 align:middle line:84% It has a good product and is therefore 00:37:19.770 --> 00:37:22.340 align:middle line:90% able to raise its price. 00:37:22.340 --> 00:37:25.060 align:middle line:84% And so this creates the endogeneity problem. 00:37:25.060 --> 00:37:28.940 align:middle line:90% 00:37:28.940 --> 00:37:30.145 align:middle line:90% Any questions about this. 00:37:30.145 --> 00:37:35.040 align:middle line:90% 00:37:35.040 --> 00:37:39.070 align:middle line:84% So why do we need the random coefficient? 00:37:39.070 --> 00:37:45.130 align:middle line:84% Again, this is one of the big, intellectual pushes 00:37:45.130 --> 00:37:48.970 align:middle line:84% in this paper is to introduce the fact 00:37:48.970 --> 00:37:51.250 align:middle line:84% that different consumers are allowed 00:37:51.250 --> 00:37:55.240 align:middle line:84% to value different products as well as prices differently. 00:37:55.240 --> 00:38:00.100 align:middle line:84% So think for a second about a model in which the coefficients 00:38:00.100 --> 00:38:05.300 align:middle line:90% do not have an i subscript, OK? 00:38:05.300 --> 00:38:07.910 align:middle line:84% Now we are allowed to write the market shares, not just 00:38:07.910 --> 00:38:10.280 align:middle line:84% the individual consumer probability of purchasing 00:38:10.280 --> 00:38:10.790 align:middle line:90% a product. 00:38:10.790 --> 00:38:14.510 align:middle line:84% We can write total market shares with our logit formula, 00:38:14.510 --> 00:38:17.210 align:middle line:84% and it's simply given by these delta 00:38:17.210 --> 00:38:19.570 align:middle line:84% terms, which is the average product quality, remember. 00:38:19.570 --> 00:38:24.380 align:middle line:90% 00:38:24.380 --> 00:38:28.550 align:middle line:84% It turns out, if we have aggregate market shares 00:38:28.550 --> 00:38:33.100 align:middle line:84% and is logit assumption, we get something really nice 00:38:33.100 --> 00:38:37.270 align:middle line:84% because we can just take the log of each of the market shares 00:38:37.270 --> 00:38:42.690 align:middle line:84% and subtract from that the log of the outside market share. 00:38:42.690 --> 00:38:47.520 align:middle line:84% Remember, we normalized the utility of the outside market 00:38:47.520 --> 00:38:51.190 align:middle line:90% share to 0, OK? 00:38:51.190 --> 00:38:53.980 align:middle line:90% So log of exponential of 0 is 0. 00:38:53.980 --> 00:38:56.650 align:middle line:84% This term here cancels out because it's 00:38:56.650 --> 00:39:00.760 align:middle line:84% in both the market share for the inside goods 00:39:00.760 --> 00:39:04.370 align:middle line:90% and the outside good, OK? 00:39:04.370 --> 00:39:06.860 align:middle line:84% So the denominator here cancels out. 00:39:06.860 --> 00:39:11.340 align:middle line:84% And what we get is on the left-hand side, 00:39:11.340 --> 00:39:13.140 align:middle line:84% log market share for each product 00:39:13.140 --> 00:39:19.360 align:middle line:84% minus the outside log of the outside good 00:39:19.360 --> 00:39:21.560 align:middle line:90% has this linear form here. 00:39:21.560 --> 00:39:22.850 align:middle line:90% So why is this so nice? 00:39:22.850 --> 00:39:24.710 align:middle line:84% Well, this is something we observe. 00:39:24.710 --> 00:39:26.780 align:middle line:84% We observe the aggregate market shares. 00:39:26.780 --> 00:39:28.940 align:middle line:90% I can just call this y, right? 00:39:28.940 --> 00:39:32.140 align:middle line:90% 00:39:32.140 --> 00:39:36.510 align:middle line:84% This is just a linear regression. 00:39:36.510 --> 00:39:39.330 align:middle line:84% So in a simple logit model, again, 00:39:39.330 --> 00:39:41.970 align:middle line:84% with aggregate market shares, we can just 00:39:41.970 --> 00:39:45.870 align:middle line:84% transform this whole thing into a linear equation. 00:39:45.870 --> 00:39:47.370 align:middle line:84% And we can actually, if we believe 00:39:47.370 --> 00:39:50.850 align:middle line:84% that prices are exogenous, which typically they're not, 00:39:50.850 --> 00:39:53.160 align:middle line:84% you can estimate this with OLS or otherwise 00:39:53.160 --> 00:39:54.540 align:middle line:90% with two-stage least squares. 00:39:54.540 --> 00:39:59.635 align:middle line:90% And we would be done, OK? 00:39:59.635 --> 00:40:03.070 align:middle line:84% So the simple logit model without the random coefficient 00:40:03.070 --> 00:40:07.670 align:middle line:84% has this great feature, that it would make things very simple, 00:40:07.670 --> 00:40:11.990 align:middle line:84% very transparent, much less room for coding errors, OK? 00:40:11.990 --> 00:40:16.450 align:middle line:84% So why do we go through all the lengths of avoiding this model? 00:40:16.450 --> 00:40:21.570 align:middle line:90% 00:40:21.570 --> 00:40:24.840 align:middle line:84% So I'll try to explain this first just 00:40:24.840 --> 00:40:27.990 align:middle line:84% in terms of some of the proper mathematical properties 00:40:27.990 --> 00:40:28.630 align:middle line:90% of this model. 00:40:28.630 --> 00:40:31.790 align:middle line:84% And then I'll also give you the intuition. 00:40:31.790 --> 00:40:35.120 align:middle line:84% So the problem is that the simple logit 00:40:35.120 --> 00:40:40.460 align:middle line:84% model generates unrealistic substitution patterns. 00:40:40.460 --> 00:40:44.930 align:middle line:84% So, for instance, if we're interested in price 00:40:44.930 --> 00:40:49.600 align:middle line:84% sensitivities, so how much does product j respond to change 00:40:49.600 --> 00:40:52.160 align:middle line:90% in the price of product k? 00:40:52.160 --> 00:40:54.140 align:middle line:84% Then, with a simple logit formula, 00:40:54.140 --> 00:40:58.880 align:middle line:84% this is simply given by alpha naught, the intercept 00:40:58.880 --> 00:41:02.120 align:middle line:84% of the price coefficient, right, or, in this case, the price 00:41:02.120 --> 00:41:11.020 align:middle line:84% coefficient and the product of the market shares of the two 00:41:11.020 --> 00:41:14.840 align:middle line:90% products, k and j. 00:41:14.840 --> 00:41:16.680 align:middle line:90% So why is this problematic? 00:41:16.680 --> 00:41:18.860 align:middle line:84% Actually, you get something similar 00:41:18.860 --> 00:41:20.160 align:middle line:90% for the diversion ratios. 00:41:20.160 --> 00:41:22.670 align:middle line:84% That is, how many people substitute from j to k if I 00:41:22.670 --> 00:41:24.353 align:middle line:90% change the price of product k? 00:41:24.353 --> 00:41:27.020 align:middle line:84% This is, again, only a function of the market share of product j 00:41:27.020 --> 00:41:29.240 align:middle line:84% and the market share of product k. 00:41:29.240 --> 00:41:32.170 align:middle line:90% Why do we not like this? 00:41:32.170 --> 00:41:35.260 align:middle line:84% So think, for instance, about a market where 00:41:35.260 --> 00:41:38.770 align:middle line:90% you have a spectrum of cars. 00:41:38.770 --> 00:41:43.460 align:middle line:84% And you order them from low quality to high quality. 00:41:43.460 --> 00:41:46.540 align:middle line:84% It may just turn out that the market 00:41:46.540 --> 00:41:50.530 align:middle line:84% share of the crappiest car is 10% 00:41:50.530 --> 00:41:54.580 align:middle line:84% and the market share of the best car in the market is also 10%. 00:41:54.580 --> 00:41:57.160 align:middle line:84% And now we're asking, how do people substitute 00:41:57.160 --> 00:41:58.490 align:middle line:90% from these two different cars? 00:41:58.490 --> 00:42:04.690 align:middle line:84% The Yugo-- this is a famously crappy car described in BLP. 00:42:04.690 --> 00:42:06.700 align:middle line:84% And let's say at the top end you have something 00:42:06.700 --> 00:42:08.990 align:middle line:90% like a Lexus or a BMW. 00:42:08.990 --> 00:42:11.740 align:middle line:84% Both of them have 10% market share. 00:42:11.740 --> 00:42:14.920 align:middle line:84% And you're asking, how do people respond 00:42:14.920 --> 00:42:19.550 align:middle line:84% to a change in prices of some third product, some third car, 00:42:19.550 --> 00:42:20.050 align:middle line:90% OK? 00:42:20.050 --> 00:42:22.900 align:middle line:84% Let's say you take the Lexus and the Yugo, 00:42:22.900 --> 00:42:25.160 align:middle line:84% and you change the price of a BMW. 00:42:25.160 --> 00:42:30.670 align:middle line:84% We would think that people who would purchase the Lexus 00:42:30.670 --> 00:42:32.770 align:middle line:84% and the people who purchased the Yugo would 00:42:32.770 --> 00:42:35.445 align:middle line:84% respond very differently to a change in the price of a BMW. 00:42:35.445 --> 00:42:38.260 align:middle line:90% 00:42:38.260 --> 00:42:40.840 align:middle line:84% This model does not allow for that. 00:42:40.840 --> 00:42:43.505 align:middle line:84% So it's not just about all we want the-- 00:42:43.505 --> 00:42:45.380 align:middle line:84% we want the model that's a bit more flexible. 00:42:45.380 --> 00:42:50.053 align:middle line:84% This is a really substantive restriction, 00:42:50.053 --> 00:42:52.470 align:middle line:84% that, for the kinds of questions that we're interested in, 00:42:52.470 --> 00:42:57.300 align:middle line:84% which is what happens if Lexus and Audi or Lexus and BMW merge, 00:42:57.300 --> 00:42:58.890 align:middle line:90% is crucial. 00:42:58.890 --> 00:43:05.130 align:middle line:84% So the reason we pick this functional form is really just 00:43:05.130 --> 00:43:08.010 align:middle line:90% for analytic tractability. 00:43:08.010 --> 00:43:12.810 align:middle line:84% There was no economic reason to choose the logit error terms. 00:43:12.810 --> 00:43:17.340 align:middle line:84% This was to avoid having to keep track of all these complicated 00:43:17.340 --> 00:43:19.570 align:middle line:90% regions of integration. 00:43:19.570 --> 00:43:21.760 align:middle line:84% We have to get a nice analytic formula 00:43:21.760 --> 00:43:24.160 align:middle line:90% for the choice probabilities. 00:43:24.160 --> 00:43:28.030 align:middle line:84% That was the rationale for picking this functional form. 00:43:28.030 --> 00:43:30.705 align:middle line:84% So basically, we want to fix this. 00:43:30.705 --> 00:43:33.960 align:middle line:90% 00:43:33.960 --> 00:43:37.680 align:middle line:84% So let me give you one more intuition 00:43:37.680 --> 00:43:41.490 align:middle line:84% for why this happens in the logit model, so 00:43:41.490 --> 00:43:42.650 align:middle line:90% going back here once more. 00:43:42.650 --> 00:43:45.160 align:middle line:90% 00:43:45.160 --> 00:43:52.400 align:middle line:84% So what leads consumers to make different choices in this model? 00:43:52.400 --> 00:43:54.140 align:middle line:84% Why do different consumers in this model 00:43:54.140 --> 00:43:56.970 align:middle line:90% make different choices? 00:43:56.970 --> 00:43:57.900 align:middle line:90% STUDENT: The epsilon. 00:43:57.900 --> 00:44:00.120 align:middle line:84% TOBIAS SALZ: Only the epsilon term, right? 00:44:00.120 --> 00:44:02.940 align:middle line:84% That's the only reason why somebody may pick 00:44:02.940 --> 00:44:06.040 align:middle line:90% a Lexus over a over a Yugo. 00:44:06.040 --> 00:44:10.840 align:middle line:84% But the epsilon terms are assumed to be i.i.d., OK? 00:44:10.840 --> 00:44:13.920 align:middle line:84% So the fact that you purchase a Lexus, 00:44:13.920 --> 00:44:17.120 align:middle line:84% it doesn't reveal anything about you 00:44:17.120 --> 00:44:19.700 align:middle line:84% because next time you go to the market you take a new epsilon 00:44:19.700 --> 00:44:22.170 align:middle line:90% draw. 00:44:22.170 --> 00:44:25.110 align:middle line:84% But what we want is, of course, we believe that somebody who 00:44:25.110 --> 00:44:29.140 align:middle line:84% buys a Lexus, there's something about that person 00:44:29.140 --> 00:44:32.200 align:middle line:84% that is different from a person that buys a Yugo. 00:44:32.200 --> 00:44:34.690 align:middle line:84% And the model does not allow for that. 00:44:34.690 --> 00:44:43.470 align:middle line:84% So that's why we need these random coefficients 00:44:43.470 --> 00:44:46.590 align:middle line:84% because now we do allow for the possibility 00:44:46.590 --> 00:44:50.580 align:middle line:84% that somebody with higher income is less price sensitive. 00:44:50.580 --> 00:44:52.440 align:middle line:84% And since they have a lot of income, 00:44:52.440 --> 00:44:56.010 align:middle line:84% they might as well get a car with more fancy features, better 00:44:56.010 --> 00:45:00.120 align:middle line:84% safety, and things like that, OK? 00:45:00.120 --> 00:45:03.130 align:middle line:84% Now, as it turns out, things get a lot more complicated. 00:45:03.130 --> 00:45:06.330 align:middle line:90% 00:45:06.330 --> 00:45:09.150 align:middle line:84% The formula for elasticities, which was just 00:45:09.150 --> 00:45:12.120 align:middle line:84% to show you this again, previously, again, 00:45:12.120 --> 00:45:14.790 align:middle line:84% just a function of prices, market shares, and the price 00:45:14.790 --> 00:45:16.350 align:middle line:90% coefficient. 00:45:16.350 --> 00:45:21.730 align:middle line:84% We now have to integrate out over all the different consumers 00:45:21.730 --> 00:45:26.680 align:middle line:84% and have to keep track of their purchase probabilities 00:45:26.680 --> 00:45:29.530 align:middle line:84% for our product j and k if we're interested in cross price 00:45:29.530 --> 00:45:32.320 align:middle line:84% elasticities or product j if we're interested in on price 00:45:32.320 --> 00:45:33.640 align:middle line:90% elasticities. 00:45:33.640 --> 00:45:36.430 align:middle line:84% So different consumers make different choices. 00:45:36.430 --> 00:45:40.420 align:middle line:84% And for a given guess of parameters, 00:45:40.420 --> 00:45:46.960 align:middle line:84% we get a distribution of nonlinear of these nus. 00:45:46.960 --> 00:45:50.697 align:middle line:84% And then, this leads to a weighted version 00:45:50.697 --> 00:45:52.780 align:middle line:84% of these elasticities, where different people have 00:45:52.780 --> 00:45:54.880 align:middle line:90% different substitution patterns. 00:45:54.880 --> 00:46:00.190 align:middle line:84% So let me talk about consumer welfare. 00:46:00.190 --> 00:46:02.360 align:middle line:84% Similarly, as the choice probabilities, 00:46:02.360 --> 00:46:05.290 align:middle line:84% if we took a random distribution, 00:46:05.290 --> 00:46:08.620 align:middle line:84% this would be a very complicated object 00:46:08.620 --> 00:46:13.180 align:middle line:84% because we have to keep track of-- 00:46:13.180 --> 00:46:14.740 align:middle line:90% consumers go to the market. 00:46:14.740 --> 00:46:17.210 align:middle line:84% They draw some of these epsilon terms. 00:46:17.210 --> 00:46:19.040 align:middle line:90% They then make optimal choices. 00:46:19.040 --> 00:46:21.950 align:middle line:84% And they have to form the expectation of that. 00:46:21.950 --> 00:46:24.010 align:middle line:84% Again, I have these regions of integration 00:46:24.010 --> 00:46:28.420 align:middle line:84% that I would have to keep track of and what consumers choose. 00:46:28.420 --> 00:46:30.190 align:middle line:84% Again, the logit model drastically 00:46:30.190 --> 00:46:32.680 align:middle line:84% simplifies this for us because we 00:46:32.680 --> 00:46:36.130 align:middle line:84% get something that's called the inclusive value formula, which 00:46:36.130 --> 00:46:40.210 align:middle line:84% tells us what the expected welfare is before consumers 00:46:40.210 --> 00:46:41.950 align:middle line:90% take these epsilon draws. 00:46:41.950 --> 00:46:46.260 align:middle line:84% So in expectation, get some draws, make optimal choices. 00:46:46.260 --> 00:46:52.610 align:middle line:84% This is the formula that you get for welfare, OK? 00:46:52.610 --> 00:46:54.540 align:middle line:90% Now, this is measured in utils. 00:46:54.540 --> 00:46:56.330 align:middle line:84% You can convert this into dollars 00:46:56.330 --> 00:46:59.380 align:middle line:84% by dividing through by the price coefficient. 00:46:59.380 --> 00:47:03.850 align:middle line:84% There's something that's-- this introduces some practical 00:47:03.850 --> 00:47:06.320 align:middle line:90% problem. 00:47:06.320 --> 00:47:10.700 align:middle line:84% Because of the-- and sorry, one thing I forgot to mention, 00:47:10.700 --> 00:47:12.752 align:middle line:84% this is just for one consumer i, OK? 00:47:12.752 --> 00:47:14.210 align:middle line:84% So in the random coefficient model, 00:47:14.210 --> 00:47:16.127 align:middle line:84% we would then have to integrate this again out 00:47:16.127 --> 00:47:20.010 align:middle line:90% over the distribution-- 00:47:20.010 --> 00:47:22.460 align:middle line:84% of those distributions of nus and ds. 00:47:22.460 --> 00:47:26.440 align:middle line:90% 00:47:26.440 --> 00:47:29.140 align:middle line:84% So there's something that people have 00:47:29.140 --> 00:47:32.920 align:middle line:84% found to be problematic in the literature, which 00:47:32.920 --> 00:47:35.350 align:middle line:84% is that if you have counterfactuals that drastically 00:47:35.350 --> 00:47:38.380 align:middle line:84% change the number of products, then 00:47:38.380 --> 00:47:42.070 align:middle line:84% you get, oftentimes, strong welfare implications from just 00:47:42.070 --> 00:47:44.740 align:middle line:84% adding and subtracting products because people harvest 00:47:44.740 --> 00:47:46.870 align:middle line:90% these epsilon draws, right? 00:47:46.870 --> 00:47:48.760 align:middle line:84% And the problem is that these epsilon draws 00:47:48.760 --> 00:47:52.750 align:middle line:84% are both an econometric error term that helps us rationalize 00:47:52.750 --> 00:47:56.400 align:middle line:84% choices; but also, we give them an economic interpretation. 00:47:56.400 --> 00:47:59.940 align:middle line:84% This actually, again, something that you have to, in your work, 00:47:59.940 --> 00:48:02.220 align:middle line:90% really-- 00:48:02.220 --> 00:48:05.100 align:middle line:84% it takes some getting used to to think that-- 00:48:05.100 --> 00:48:09.510 align:middle line:84% to understand that we actually give an interpretation 00:48:09.510 --> 00:48:11.040 align:middle line:90% to the error term. 00:48:11.040 --> 00:48:13.510 align:middle line:90% And it's part of the model. 00:48:13.510 --> 00:48:15.940 align:middle line:90% It's not just tacked on. 00:48:15.940 --> 00:48:18.790 align:middle line:84% And in this case, we typically assume 00:48:18.790 --> 00:48:20.500 align:middle line:84% that consumers know these epsilons, 00:48:20.500 --> 00:48:22.960 align:middle line:90% and they're not just errors. 00:48:22.960 --> 00:48:25.485 align:middle line:84% They actually take this into account when they make choices. 00:48:25.485 --> 00:48:28.030 align:middle line:90% 00:48:28.030 --> 00:48:32.560 align:middle line:84% And so this means that adding more products, right, that can 00:48:32.560 --> 00:48:35.625 align:middle line:84% harvest more of these epsilons, and it increases welfare. 00:48:35.625 --> 00:48:39.310 align:middle line:90% 00:48:39.310 --> 00:48:41.570 align:middle line:84% I don't want to make too big of a deal of this, 00:48:41.570 --> 00:48:44.335 align:middle line:84% but it's just good to be aware of this problem. 00:48:44.335 --> 00:48:46.210 align:middle line:84% Some people argue that the random coefficient 00:48:46.210 --> 00:48:50.950 align:middle line:84% model actually ameliorates this problem because, again, people, 00:48:50.950 --> 00:48:55.120 align:middle line:84% they're somewhere in a specific part of the product space 00:48:55.120 --> 00:48:59.410 align:middle line:84% by virtue of having a specific coefficient determined 00:48:59.410 --> 00:49:00.950 align:middle line:90% by income and other things. 00:49:00.950 --> 00:49:03.940 align:middle line:84% And they're not going to just substitute globally. 00:49:03.940 --> 00:49:05.990 align:middle line:84% But they may be substituting more locally. 00:49:05.990 --> 00:49:07.870 align:middle line:84% And therefore, the epsilon harvesting 00:49:07.870 --> 00:49:09.890 align:middle line:90% is not as big of a deal. 00:49:09.890 --> 00:49:15.160 align:middle line:90% 00:49:15.160 --> 00:49:24.260 align:middle line:84% So earlier I said that we want to think carefully 00:49:24.260 --> 00:49:26.126 align:middle line:90% about instruments. 00:49:26.126 --> 00:49:29.040 align:middle line:90% 00:49:29.040 --> 00:49:31.450 align:middle line:90% And again, what's the reason? 00:49:31.450 --> 00:49:33.160 align:middle line:90% I gave you this Apple example. 00:49:33.160 --> 00:49:37.085 align:middle line:84% Apple knows there's some secret sauce that 00:49:37.085 --> 00:49:39.210 align:middle line:84% makes its products better than some other products, 00:49:39.210 --> 00:49:41.420 align:middle line:90% and it might price this. 00:49:41.420 --> 00:49:44.900 align:middle line:84% So both the researchers-- sorry, the consumers and the firms 00:49:44.900 --> 00:49:47.660 align:middle line:84% observe this xj, the researchers do not. 00:49:47.660 --> 00:49:49.940 align:middle line:84% So this then raises the question, 00:49:49.940 --> 00:49:55.340 align:middle line:84% what makes good instruments for these kinds of models? 00:49:55.340 --> 00:49:58.090 align:middle line:84% And how many do we actually need? 00:49:58.090 --> 00:50:00.290 align:middle line:84% And you may be surprised by the second question 00:50:00.290 --> 00:50:05.010 align:middle line:84% because sometimes one is not enough. 00:50:05.010 --> 00:50:08.760 align:middle line:84% So if we just take our simple logit model, 00:50:08.760 --> 00:50:10.770 align:middle line:84% where we do not have random coefficients, 00:50:10.770 --> 00:50:13.560 align:middle line:84% we can do this inversion that I talked about. 00:50:13.560 --> 00:50:17.180 align:middle line:90% It gives us this linear form. 00:50:17.180 --> 00:50:19.610 align:middle line:84% And you stare at this, you say, well, this 00:50:19.610 --> 00:50:21.900 align:middle line:84% is just a linear equation, a regression equation. 00:50:21.900 --> 00:50:22.910 align:middle line:90% And you're right. 00:50:22.910 --> 00:50:26.600 align:middle line:84% We can estimate this if only prices are endogenous with one 00:50:26.600 --> 00:50:28.400 align:middle line:90% excluded instrument. 00:50:28.400 --> 00:50:31.730 align:middle line:84% So in this model, if you have a supply shifter 00:50:31.730 --> 00:50:35.830 align:middle line:84% that you think is uncorrelated to xj, 00:50:35.830 --> 00:50:40.820 align:middle line:84% you can just estimate this model, OK? 00:50:40.820 --> 00:50:44.740 align:middle line:84% The same is, unfortunately, not true for BLP, in general. 00:50:44.740 --> 00:50:47.860 align:middle line:90% 00:50:47.860 --> 00:50:51.880 align:middle line:84% We will go in [14.]273 and dive deeper in the identification 00:50:51.880 --> 00:50:52.950 align:middle line:90% of these models. 00:50:52.950 --> 00:50:56.770 align:middle line:84% So today I'm just giving you the intuition. 00:50:56.770 --> 00:50:59.270 align:middle line:84% So there's two ways to provide this intuition. 00:50:59.270 --> 00:51:01.030 align:middle line:84% One is, well, with nonlinear parameters, 00:51:01.030 --> 00:51:02.860 align:middle line:84% I can't quite separate things like this. 00:51:02.860 --> 00:51:05.290 align:middle line:84% And the demand for each product depends 00:51:05.290 --> 00:51:09.580 align:middle line:84% on the whole vector of unobserved product attributes. 00:51:09.580 --> 00:51:12.970 align:middle line:84% But perhaps a bit more intuitively, 00:51:12.970 --> 00:51:16.540 align:middle line:84% if I just have a supply shifter and change price, 00:51:16.540 --> 00:51:18.310 align:middle line:84% that does not necessarily tell me 00:51:18.310 --> 00:51:23.020 align:middle line:84% about whether somebody who purchases a Lexus substitutes 00:51:23.020 --> 00:51:25.240 align:middle line:90% to a Mercedes instead. 00:51:25.240 --> 00:51:28.510 align:middle line:84% And so for the nonlinear parameters, 00:51:28.510 --> 00:51:31.200 align:middle line:84% we want to identify the variants and the interaction terms 00:51:31.200 --> 00:51:31.700 align:middle line:90% with income. 00:51:31.700 --> 00:51:34.840 align:middle line:84% We want to know in which part of the product space 00:51:34.840 --> 00:51:37.000 align:middle line:90% do people substitute? 00:51:37.000 --> 00:51:39.580 align:middle line:84% And a simple supply shifter that's 00:51:39.580 --> 00:51:41.420 align:middle line:84% the same for all firms wouldn't do that, 00:51:41.420 --> 00:51:43.890 align:middle line:90% wouldn't tell us about that. 00:51:43.890 --> 00:51:46.350 align:middle line:84% So we need something that tells us 00:51:46.350 --> 00:51:50.040 align:middle line:84% something about where are these consumers that purchased 00:51:50.040 --> 00:51:55.890 align:middle line:84% this product would be going to alternatively, to understand-- 00:51:55.890 --> 00:51:58.180 align:middle line:84% to identify the nonlinear parameters. 00:51:58.180 --> 00:52:01.080 align:middle line:90% 00:52:01.080 --> 00:52:02.660 align:middle line:90% Any questions so far? 00:52:02.660 --> 00:52:11.170 align:middle line:90% 00:52:11.170 --> 00:52:11.670 align:middle line:90% OK. 00:52:11.670 --> 00:52:14.260 align:middle line:90% 00:52:14.260 --> 00:52:19.970 align:middle line:84% OK, so let's talk about some different instruments. 00:52:19.970 --> 00:52:23.720 align:middle line:84% So typically you get very good variation 00:52:23.720 --> 00:52:30.860 align:middle line:84% from looking at different markets, where in some markets, 00:52:30.860 --> 00:52:33.350 align:middle line:84% let's say there is a Lexus dealership 00:52:33.350 --> 00:52:37.230 align:middle line:84% and in some other markets there is not because then I 00:52:37.230 --> 00:52:42.030 align:middle line:84% can see in the markets where there's no Lexus dealership 00:52:42.030 --> 00:52:46.620 align:middle line:84% the market shares of which other products is changing the most. 00:52:46.620 --> 00:52:50.453 align:middle line:84% So that's usually very good variation. 00:52:50.453 --> 00:52:52.370 align:middle line:84% Can you think of a concern with this argument? 00:52:52.370 --> 00:52:56.060 align:middle line:90% 00:52:56.060 --> 00:52:56.630 align:middle line:90% Yeah. 00:52:56.630 --> 00:52:58.640 align:middle line:84% STUDENT: Could you expect the presence or not 00:52:58.640 --> 00:53:01.440 align:middle line:84% of the Lexus dealership to be correlated to [INAUDIBLE]? 00:53:01.440 --> 00:53:02.820 align:middle line:90% TOBIAS SALZ: Exactly, right? 00:53:02.820 --> 00:53:06.930 align:middle line:84% So we think that, at least in the long run, 00:53:06.930 --> 00:53:09.030 align:middle line:84% the Lexus dealerships open where people 00:53:09.030 --> 00:53:11.520 align:middle line:84% have high demand for those types of cars. 00:53:11.520 --> 00:53:15.030 align:middle line:84% And actually, people have estimated models 00:53:15.030 --> 00:53:19.230 align:middle line:84% where they look at combined, the antiproblem and the demand 00:53:19.230 --> 00:53:23.940 align:middle line:84% problem combined to make use of exactly that idea. 00:53:23.940 --> 00:53:25.720 align:middle line:90% That's precisely the problem. 00:53:25.720 --> 00:53:30.333 align:middle line:84% We think that firms know which markets are good ones to enter. 00:53:30.333 --> 00:53:32.000 align:middle line:84% And so this is something that's probably 00:53:32.000 --> 00:53:33.542 align:middle line:84% more likely to hold in the short run. 00:53:33.542 --> 00:53:36.050 align:middle line:90% 00:53:36.050 --> 00:53:39.590 align:middle line:84% Another set of instruments are cost shifters, so 00:53:39.590 --> 00:53:42.530 align:middle line:84% material costs, distribution costs, tariffs, taxes, 00:53:42.530 --> 00:53:43.760 align:middle line:90% things like that. 00:53:43.760 --> 00:53:46.440 align:middle line:84% These are oftentimes very good instruments. 00:53:46.440 --> 00:53:50.060 align:middle line:84% They have a clear story for relevance and the exclusion 00:53:50.060 --> 00:53:52.060 align:middle line:90% restriction. 00:53:52.060 --> 00:53:57.370 align:middle line:84% So the problem is that they're oftentimes not available. 00:53:57.370 --> 00:54:01.890 align:middle line:84% It's hard to learn about cost, as I actually argued earlier. 00:54:01.890 --> 00:54:06.680 align:middle line:90% 00:54:06.680 --> 00:54:09.350 align:middle line:84% So what sometimes people do is they argue 00:54:09.350 --> 00:54:12.260 align:middle line:84% for the following approach here, which is, OK, we 00:54:12.260 --> 00:54:17.920 align:middle line:84% may not observe cost, but maybe observe a proxy for cost, OK? 00:54:17.920 --> 00:54:20.020 align:middle line:84% These are called the Hausman instruments. 00:54:20.020 --> 00:54:22.660 align:middle line:84% So the idea here of these instruments 00:54:22.660 --> 00:54:28.930 align:middle line:84% is that if I have a cross-section of markets, 00:54:28.930 --> 00:54:31.300 align:middle line:84% I can look at a specific firm and can 00:54:31.300 --> 00:54:34.030 align:middle line:84% look at the prices of that firm in other markets, 00:54:34.030 --> 00:54:36.410 align:middle line:90% not the market of interest. 00:54:36.410 --> 00:54:39.590 align:middle line:84% So I take the average of prices in other markets, 00:54:39.590 --> 00:54:45.500 align:middle line:84% and I can take this as a proxy for cost shocks for this firm. 00:54:45.500 --> 00:54:49.430 align:middle line:84% So maybe in this specific year, the supplier 00:54:49.430 --> 00:54:54.020 align:middle line:84% of this manufacturer, I don't know, went bankrupt, 00:54:54.020 --> 00:54:57.000 align:middle line:84% and that caused some trouble and therefore have higher costs. 00:54:57.000 --> 00:54:59.690 align:middle line:84% And so that's reflected in all the prices of this firm 00:54:59.690 --> 00:55:02.830 align:middle line:90% across different markets. 00:55:02.830 --> 00:55:08.270 align:middle line:84% I do not observe this directly, but the average prices 00:55:08.270 --> 00:55:15.350 align:middle line:84% in other markets, in some sense, part of my data. 00:55:15.350 --> 00:55:17.880 align:middle line:84% Can you think of concerns with this reasoning? 00:55:17.880 --> 00:55:21.900 align:middle line:90% 00:55:21.900 --> 00:55:22.560 align:middle line:90% Yes. 00:55:22.560 --> 00:55:25.950 align:middle line:84% STUDENT: Prices are also based on demand for each of them? 00:55:25.950 --> 00:55:28.260 align:middle line:84% TOBIAS SALZ: Exactly, we're back to this problem 00:55:28.260 --> 00:55:30.570 align:middle line:90% that we had initially, right? 00:55:30.570 --> 00:55:33.430 align:middle line:84% Prices reflect both demand and supply factors. 00:55:33.430 --> 00:55:36.720 align:middle line:84% And this line of argument only works 00:55:36.720 --> 00:55:39.840 align:middle line:84% if the costs are very correlated across markets 00:55:39.840 --> 00:55:42.750 align:middle line:90% and the demand shocks are not. 00:55:42.750 --> 00:55:46.240 align:middle line:84% But then these Hausman instruments are convincing. 00:55:46.240 --> 00:55:48.810 align:middle line:84% Otherwise, you have to think hard about 00:55:48.810 --> 00:55:51.080 align:middle line:84% whether in your setting this is a good idea. 00:55:51.080 --> 00:55:54.770 align:middle line:90% 00:55:54.770 --> 00:55:57.170 align:middle line:84% Then there are what I call the BLP instruments. 00:55:57.170 --> 00:56:02.540 align:middle line:84% Those are the instruments that are actually used in BLP. 00:56:02.540 --> 00:56:10.850 align:middle line:84% So these are the attributes of other products in the market 00:56:10.850 --> 00:56:12.680 align:middle line:84% or some function of those attributes, so 00:56:12.680 --> 00:56:14.702 align:middle line:84% either the sum or the average or-- there 00:56:14.702 --> 00:56:16.660 align:middle line:84% are various ways of constructing them, in fact. 00:56:16.660 --> 00:56:19.400 align:middle line:90% 00:56:19.400 --> 00:56:22.190 align:middle line:84% So the idea here is all along we have 00:56:22.190 --> 00:56:26.480 align:middle line:84% been assuming that only prices are endogenous 00:56:26.480 --> 00:56:30.160 align:middle line:84% and product attributes are fixed. 00:56:30.160 --> 00:56:34.120 align:middle line:84% So now, if that's true, again-- you 00:56:34.120 --> 00:56:36.370 align:middle line:84% have to think about whether that's a good assumption-- 00:56:36.370 --> 00:56:43.480 align:middle line:84% then I can use the fact that I'm competing in a market 00:56:43.480 --> 00:56:47.770 align:middle line:84% where I'm trying to sell a very fast car to consumers. 00:56:47.770 --> 00:56:49.660 align:middle line:84% But there are also a lot of other producers 00:56:49.660 --> 00:56:54.880 align:middle line:84% that also offer fast cars, that the product attributes 00:56:54.880 --> 00:56:57.640 align:middle line:84% for other cars are excluded from the utility 00:56:57.640 --> 00:57:01.490 align:middle line:84% function of consumers that want to purchase my product. 00:57:01.490 --> 00:57:06.070 align:middle line:84% But they force me to respond to the fact 00:57:06.070 --> 00:57:09.920 align:middle line:84% that there are a lot of other fast cars in the market. 00:57:09.920 --> 00:57:16.730 align:middle line:84% So that's the idea, that it tells me how, 00:57:16.730 --> 00:57:18.920 align:middle line:84% in terms of the things that consumer value, 00:57:18.920 --> 00:57:21.840 align:middle line:90% how much competition I'm facing. 00:57:21.840 --> 00:57:24.990 align:middle line:84% And so I've sort of already alluded to this. 00:57:24.990 --> 00:57:30.870 align:middle line:84% The concern is, of course, that the product attributes are not 00:57:30.870 --> 00:57:33.950 align:middle line:90% in fact exogenous. 00:57:33.950 --> 00:57:37.460 align:middle line:84% So coming once more back to my favorite example of Apple, 00:57:37.460 --> 00:57:40.190 align:middle line:84% Apple has, again, as I said earlier, typically delayed 00:57:40.190 --> 00:57:41.670 align:middle line:84% the introduction of new features. 00:57:41.670 --> 00:57:43.910 align:middle line:84% And it knew it can do that because they're 00:57:43.910 --> 00:57:45.770 align:middle line:84% other things, unobserved things that people 00:57:45.770 --> 00:57:47.720 align:middle line:90% like about Apple, right? 00:57:47.720 --> 00:57:50.360 align:middle line:84% And so, again, you have to ask yourself, 00:57:50.360 --> 00:57:55.100 align:middle line:84% is it actually a good idea that product attributes 00:57:55.100 --> 00:57:58.623 align:middle line:90% are exogenous? 00:57:58.623 --> 00:58:00.040 align:middle line:84% There is a whole literature on how 00:58:00.040 --> 00:58:01.900 align:middle line:90% to construct these instruments. 00:58:01.900 --> 00:58:07.190 align:middle line:84% Again, this is the economic idea in a nutshell. 00:58:07.190 --> 00:58:09.985 align:middle line:84% There are ways-- some people have argued just 00:58:09.985 --> 00:58:11.860 align:middle line:84% taking the average or to leave one out is not 00:58:11.860 --> 00:58:14.830 align:middle line:84% a good idea because if you look at large markets, 00:58:14.830 --> 00:58:17.410 align:middle line:84% to leave one out is actually the same for all firms 00:58:17.410 --> 00:58:19.310 align:middle line:90% or close to the same. 00:58:19.310 --> 00:58:23.080 align:middle line:84% And then you want to basically take differences instead. 00:58:23.080 --> 00:58:26.200 align:middle line:84% There are also questions about how do you-- 00:58:26.200 --> 00:58:28.570 align:middle line:84% if we are in a many weak instrument situation, 00:58:28.570 --> 00:58:32.740 align:middle line:84% how do you construct the most powerful instruments? 00:58:32.740 --> 00:58:34.070 align:middle line:90% Or how do we approximate them? 00:58:34.070 --> 00:58:39.850 align:middle line:84% There's a paper by Gandhi and Houde on doing that. 00:58:39.850 --> 00:58:43.230 align:middle line:84% Again, in [14.]273, we'll talk a bit more about this. 00:58:43.230 --> 00:58:46.110 align:middle line:84% The last instrument that people sometimes use 00:58:46.110 --> 00:58:49.440 align:middle line:84% are what I call the Waldfogel or Waldfogel- Fan instruments. 00:58:49.440 --> 00:58:55.290 align:middle line:84% This is the idea that firms don't set prices just 00:58:55.290 --> 00:58:58.800 align:middle line:84% for one market, but they have larger zones 00:58:58.800 --> 00:59:00.280 align:middle line:90% for which they set prices. 00:59:00.280 --> 00:59:04.230 align:middle line:84% So for instance, a dealership network 00:59:04.230 --> 00:59:08.640 align:middle line:84% that spans both Massachusetts and New Hampshire 00:59:08.640 --> 00:59:11.560 align:middle line:84% may set prices for its cars both for Massachusetts and New 00:59:11.560 --> 00:59:12.060 align:middle line:90% Hampshire. 00:59:12.060 --> 00:59:14.700 align:middle line:84% Although, these are somewhat separate markets. 00:59:14.700 --> 00:59:18.090 align:middle line:84% You can argue with that as well, of course. 00:59:18.090 --> 00:59:20.047 align:middle line:84% And then the idea is that there are 00:59:20.047 --> 00:59:22.380 align:middle line:84% a lot of people in New Hampshire who like pickup trucks, 00:59:22.380 --> 00:59:24.172 align:middle line:84% and there are fewer people in Massachusetts 00:59:24.172 --> 00:59:25.150 align:middle line:90% who like pickup trucks. 00:59:25.150 --> 00:59:26.858 align:middle line:84% But the fact that there's a lot of demand 00:59:26.858 --> 00:59:30.210 align:middle line:84% in New Hampshire, combined with the idea of zone pricing, 00:59:30.210 --> 00:59:32.940 align:middle line:84% leads to higher prices for people in Massachusetts 00:59:32.940 --> 00:59:33.810 align:middle line:90% for pickup trucks. 00:59:33.810 --> 00:59:36.270 align:middle line:84% Although, that doesn't necessarily mean that 00:59:36.270 --> 00:59:38.420 align:middle line:90% they like pickup trucks. 00:59:38.420 --> 00:59:42.400 align:middle line:90% So that's kind of the idea. 00:59:42.400 --> 00:59:44.840 align:middle line:84% Again, there's a nice paper that actually documents 00:59:44.840 --> 00:59:48.650 align:middle line:84% that firms do price very coarsely across markets, do not 00:59:48.650 --> 00:59:51.770 align:middle line:84% take into account local demand variation 00:59:51.770 --> 00:59:56.130 align:middle line:84% as much as they should in a profit-maximizing way. 00:59:56.130 --> 00:59:59.237 align:middle line:90% 00:59:59.237 --> 01:00:00.820 align:middle line:84% There's an obvious concern, of course, 01:00:00.820 --> 01:00:06.910 align:middle line:84% with this instrument, that those demographic factors and what 01:00:06.910 --> 01:00:10.570 align:middle line:84% drives demand across markets is also correlated, that it's not 01:00:10.570 --> 01:00:15.700 align:middle line:90% as separable as we think. 01:00:15.700 --> 01:00:21.173 align:middle line:84% So I'll use the last 10 minutes for today to talk a little bit, 01:00:21.173 --> 01:00:22.340 align:middle line:90% how do you actually do this? 01:00:22.340 --> 01:00:24.070 align:middle line:84% I told you everything about instruments, 01:00:24.070 --> 01:00:28.330 align:middle line:84% but I actually haven't told you how you use them in this model. 01:00:28.330 --> 01:00:32.860 align:middle line:84% You know how you use them in two-stage least squares. 01:00:32.860 --> 01:00:36.550 align:middle line:84% But how do we use them in this complicated model? 01:00:36.550 --> 01:00:40.620 align:middle line:90% So remember, if we can-- 01:00:40.620 --> 01:00:42.870 align:middle line:84% in a simple logit model, we can do 01:00:42.870 --> 01:00:46.920 align:middle line:84% this inversion and express everything in a linear equation. 01:00:46.920 --> 01:00:52.830 align:middle line:84% So here, the problem is more complicated. 01:00:52.830 --> 01:00:57.300 align:middle line:84% So BLP is typically estimated via GMM. 01:00:57.300 --> 01:01:02.510 align:middle line:84% Although, there are other ways to estimate it that I'll, again, 01:01:02.510 --> 01:01:04.850 align:middle line:90% talk about in [14.]273. 01:01:04.850 --> 01:01:11.060 align:middle line:84% So this is a GMM problem, where I minimize some vector 01:01:11.060 --> 01:01:17.330 align:middle line:84% product of moments that may be weighted by some matrix omega. 01:01:17.330 --> 01:01:22.150 align:middle line:90% And those moments are simply-- 01:01:22.150 --> 01:01:24.670 align:middle line:84% these are the empirical counterparts to the moments. 01:01:24.670 --> 01:01:28.545 align:middle line:84% I'm interacting my instruments with the error term. 01:01:28.545 --> 01:01:31.560 align:middle line:90% 01:01:31.560 --> 01:01:33.270 align:middle line:90% Now, what is the error term? 01:01:33.270 --> 01:01:35.580 align:middle line:84% I can use-- remember, the definition of delta 01:01:35.580 --> 01:01:37.800 align:middle line:90% was it's all the non-i stuff. 01:01:37.800 --> 01:01:42.360 align:middle line:84% It's the average valuation of consumers for a product j. 01:01:42.360 --> 01:01:48.750 align:middle line:84% So I can subtract from that the product 01:01:48.750 --> 01:01:51.240 align:middle line:84% of attributes and coefficients that are non-i-specific. 01:01:51.240 --> 01:01:53.250 align:middle line:90% And I get back my error term. 01:01:53.250 --> 01:01:55.180 align:middle line:84% Remember the definition from earlier. 01:01:55.180 --> 01:01:58.930 align:middle line:90% So that's my error term. 01:01:58.930 --> 01:02:03.220 align:middle line:84% OK, but that's not super helpful because delta is stuck in here. 01:02:03.220 --> 01:02:06.010 align:middle line:84% So if I want to interact my arrow with the instruments, 01:02:06.010 --> 01:02:08.855 align:middle line:84% I need to know what delta is in order to know what delta is. 01:02:08.855 --> 01:02:15.810 align:middle line:84% And it's kind of stuck in this integral. 01:02:15.810 --> 01:02:17.790 align:middle line:84% Or the empirical counterpart to this 01:02:17.790 --> 01:02:23.345 align:middle line:84% would have a sum that approximates this integral. 01:02:23.345 --> 01:02:26.080 align:middle line:90% 01:02:26.080 --> 01:02:28.320 align:middle line:90% OK, so what do we do? 01:02:28.320 --> 01:02:29.950 align:middle line:84% I'm moving this to the side here. 01:02:29.950 --> 01:02:35.100 align:middle line:84% It's the same stuff but a bit more compactly written, OK? 01:02:35.100 --> 01:02:39.390 align:middle line:90% So here's how you estimate BLP. 01:02:39.390 --> 01:02:42.180 align:middle line:84% Again, there are many details that are left out here 01:02:42.180 --> 01:02:48.060 align:middle line:84% that, if you want to actually do this, you need to learn about. 01:02:48.060 --> 01:02:52.850 align:middle line:84% So the outer loop is just minimizing this thing here. 01:02:52.850 --> 01:02:58.040 align:middle line:84% And so, for reasons that I'll come back to in a second, 01:02:58.040 --> 01:03:00.990 align:middle line:84% in the outer loop, you only guess what I call the nonlinear 01:03:00.990 --> 01:03:01.820 align:middle line:90% parameters. 01:03:01.820 --> 01:03:07.950 align:middle line:84% These are the parameters not counting beta naught and alpha 01:03:07.950 --> 01:03:08.640 align:middle line:90% naught. 01:03:08.640 --> 01:03:11.370 align:middle line:84% These are the parameters that tell 01:03:11.370 --> 01:03:14.763 align:middle line:84% us something about how much consumers substitute 01:03:14.763 --> 01:03:16.680 align:middle line:84% across different products, different consumers 01:03:16.680 --> 01:03:19.170 align:middle line:84% differently across different products. 01:03:19.170 --> 01:03:21.930 align:middle line:84% So I'm guessing some nonlinear parameters. 01:03:21.930 --> 01:03:23.850 align:middle line:90% I fix a guess. 01:03:23.850 --> 01:03:27.750 align:middle line:84% And then, in the inner loop, I'm solving the following problem. 01:03:27.750 --> 01:03:29.940 align:middle line:84% For every market t, I want to know 01:03:29.940 --> 01:03:32.280 align:middle line:84% what my deltas are because if I know what my deltas are, 01:03:32.280 --> 01:03:33.280 align:middle line:90% I can build my size. 01:03:33.280 --> 01:03:37.680 align:middle line:84% If I know the size, I can build my moment conditions, OK? 01:03:37.680 --> 01:03:39.440 align:middle line:90% So what are the deltas? 01:03:39.440 --> 01:03:41.790 align:middle line:84% So this is where this paper, among many other things, 01:03:41.790 --> 01:03:44.940 align:middle line:90% does something really clever. 01:03:44.940 --> 01:03:48.630 align:middle line:84% They show that it can start with any initial guess 01:03:48.630 --> 01:03:52.420 align:middle line:90% of those deltas, OK? 01:03:52.420 --> 01:03:54.190 align:middle line:90% Start with any guess. 01:03:54.190 --> 01:03:56.750 align:middle line:84% And then I can iterate on the following thing. 01:03:56.750 --> 01:03:58.040 align:middle line:90% Start with this guess. 01:03:58.040 --> 01:04:02.100 align:middle line:84% Compute the market shares, the predicted market shares 01:04:02.100 --> 01:04:03.450 align:middle line:90% from the model. 01:04:03.450 --> 01:04:05.730 align:middle line:84% And then add to my initial guess of delta 01:04:05.730 --> 01:04:07.410 align:middle line:84% the difference between the actual market 01:04:07.410 --> 01:04:09.827 align:middle line:84% shares that I observe in the data and the predicted market 01:04:09.827 --> 01:04:11.040 align:middle line:90% shares. 01:04:11.040 --> 01:04:14.160 align:middle line:90% This gives me a new delta. 01:04:14.160 --> 01:04:16.080 align:middle line:84% And then I do this again and again 01:04:16.080 --> 01:04:19.710 align:middle line:90% and again, and it converges. 01:04:19.710 --> 01:04:21.490 align:middle line:84% In fact, this is a contraction mapping. 01:04:21.490 --> 01:04:24.600 align:middle line:84% So for any set of nonlinear parameters, 01:04:24.600 --> 01:04:30.300 align:middle line:84% it converges to a unique thing, that rationalizes the observed 01:04:30.300 --> 01:04:34.440 align:middle line:84% market shares exactly under this guess of parameters. 01:04:34.440 --> 01:04:36.720 align:middle line:84% This does not tell me that this guess of parameters 01:04:36.720 --> 01:04:38.137 align:middle line:84% is actually the one that minimizes 01:04:38.137 --> 01:04:39.350 align:middle line:90% the objective function. 01:04:39.350 --> 01:04:41.520 align:middle line:84% So in the outer loop, I still have 01:04:41.520 --> 01:04:44.520 align:middle line:84% to guess new parameters until the objective function is 01:04:44.520 --> 01:04:47.320 align:middle line:90% minimized. 01:04:47.320 --> 01:04:50.350 align:middle line:90% So you keep on doing that. 01:04:50.350 --> 01:04:51.850 align:middle line:84% The one thing I said, well, you only 01:04:51.850 --> 01:04:54.470 align:middle line:84% have to guess the nonlinear parameters. 01:04:54.470 --> 01:04:57.400 align:middle line:84% So one trick that people use is that if you know the nonlinear 01:04:57.400 --> 01:05:01.000 align:middle line:84% parameters and you do the contraction mapping, 01:05:01.000 --> 01:05:03.820 align:middle line:84% then it's as if I know delta, at least 01:05:03.820 --> 01:05:06.040 align:middle line:90% for this set of parameters. 01:05:06.040 --> 01:05:08.170 align:middle line:84% And then I can just run a regression 01:05:08.170 --> 01:05:14.180 align:middle line:84% here because for any given theta 2, delta is a known object. 01:05:14.180 --> 01:05:15.340 align:middle line:90% I can regress it on this. 01:05:15.340 --> 01:05:18.400 align:middle line:84% I don't have to search over those linear parameters here. 01:05:18.400 --> 01:05:21.130 align:middle line:84% This oftentimes leads-- you can speed up 01:05:21.130 --> 01:05:24.770 align:middle line:90% this problem quite a bit, OK? 01:05:24.770 --> 01:05:27.178 align:middle line:84% So you iterate on the outer loop. 01:05:27.178 --> 01:05:28.220 align:middle line:90% You guess new parameters. 01:05:28.220 --> 01:05:29.470 align:middle line:90% You iterate on the inner loop. 01:05:29.470 --> 01:05:30.740 align:middle line:90% You find your deltas. 01:05:30.740 --> 01:05:33.940 align:middle line:90% You run the regression. 01:05:33.940 --> 01:05:36.180 align:middle line:90% You built the moments. 01:05:36.180 --> 01:05:37.685 align:middle line:90% And you keep doing this. 01:05:37.685 --> 01:05:42.420 align:middle line:90% 01:05:42.420 --> 01:05:44.370 align:middle line:90% Any questions on this? 01:05:44.370 --> 01:05:47.500 align:middle line:90% This was fast. 01:05:47.500 --> 01:05:50.200 align:middle line:84% You may understand it at a high level. 01:05:50.200 --> 01:05:53.540 align:middle line:84% I encourage you highly to actually do it. 01:05:53.540 --> 01:05:58.540 align:middle line:84% Come to [14.]273, and you'll learn how to do it. 01:05:58.540 --> 01:06:02.383 align:middle line:84% STUDENT: I guess I'm curious when this would fail. 01:06:02.383 --> 01:06:04.550 align:middle line:84% TOBIAS SALZ: There are many ways that it could fail. 01:06:04.550 --> 01:06:07.010 align:middle line:90% [LAUGHTER] 01:06:07.010 --> 01:06:09.850 align:middle line:84% One of the most memorable things in grad school 01:06:09.850 --> 01:06:15.460 align:middle line:84% is when we all coded up BLP together, so the first time. 01:06:15.460 --> 01:06:17.850 align:middle line:90% Many things that can go wrong. 01:06:17.850 --> 01:06:36.000 align:middle line:90%