WEBVTT 00:00:00.000 --> 00:00:02.440 align:middle line:90% [SQUEAKING] 00:00:02.440 --> 00:00:04.880 align:middle line:90% [RUSTLING] 00:00:04.880 --> 00:00:07.808 align:middle line:90% [CLICKING] 00:00:07.808 --> 00:00:17.080 align:middle line:90% 00:00:17.080 --> 00:00:19.880 align:middle line:84% TOBIAS SALZ: OK, let me start here. 00:00:19.880 --> 00:00:23.920 align:middle line:84% So thanks for allowing me to be back one more time. 00:00:23.920 --> 00:00:27.970 align:middle line:84% Today I'm going to talk about empirical models of auctions 00:00:27.970 --> 00:00:33.250 align:middle line:84% and hopefully fill in a little bit what you have already 00:00:33.250 --> 00:00:34.900 align:middle line:90% learned from Glenn. 00:00:34.900 --> 00:00:39.190 align:middle line:90% So this is the roadmap. 00:00:39.190 --> 00:00:44.410 align:middle line:84% The goal is to introduce you a little bit to how 00:00:44.410 --> 00:00:48.640 align:middle line:84% the thinking has evolved on the empirics of auctions 00:00:48.640 --> 00:00:53.620 align:middle line:84% and then bring you to what is the state of the art still, 00:00:53.620 --> 00:00:55.420 align:middle line:84% which is Guerre, Perrigne, and Vuong, 00:00:55.420 --> 00:00:58.330 align:middle line:84% that has really had a huge influence in the way 00:00:58.330 --> 00:01:03.160 align:middle line:84% that people analyze auctions empirically. 00:01:03.160 --> 00:01:07.630 align:middle line:84% The gist of all of this is that sometimes it's 00:01:07.630 --> 00:01:09.790 align:middle line:84% hard to compute equilibrium for auctions, 00:01:09.790 --> 00:01:12.220 align:middle line:84% but it turns out that under the right conditions, 00:01:12.220 --> 00:01:17.130 align:middle line:84% it's actually really easy to estimate models for auctions. 00:01:17.130 --> 00:01:19.310 align:middle line:84% And I'll show you how to do that. 00:01:19.310 --> 00:01:24.110 align:middle line:84% And then we're going to talk about two different applications 00:01:24.110 --> 00:01:25.500 align:middle line:90% that are quite interesting. 00:01:25.500 --> 00:01:28.370 align:middle line:90% 00:01:28.370 --> 00:01:30.060 align:middle line:90% So what is the relevance? 00:01:30.060 --> 00:01:32.580 align:middle line:84% Why do we want to look at auctions? 00:01:32.580 --> 00:01:37.310 align:middle line:84% So for one, we are looking at, as IO commonly says, 00:01:37.310 --> 00:01:41.570 align:middle line:84% markets where firms or players have market power. 00:01:41.570 --> 00:01:46.100 align:middle line:84% And a seller, let's say, in an auction setting has, of course, 00:01:46.100 --> 00:01:47.087 align:middle line:90% market power. 00:01:47.087 --> 00:01:49.670 align:middle line:84% When you think about the problem of setting the reserve price, 00:01:49.670 --> 00:01:52.220 align:middle line:84% it looks almost like a monopoly pricing problem. 00:01:52.220 --> 00:01:54.860 align:middle line:84% So it's kind of squarely within the topics 00:01:54.860 --> 00:01:56.420 align:middle line:90% that we're interested in. 00:01:56.420 --> 00:01:59.360 align:middle line:84% There are estimates that about 10% of GDP 00:01:59.360 --> 00:02:02.460 align:middle line:84% is contracted through auctions and many different designs. 00:02:02.460 --> 00:02:05.880 align:middle line:84% So it's important to understand how this is being done. 00:02:05.880 --> 00:02:08.690 align:middle line:84% Very often, the government is involved 00:02:08.690 --> 00:02:10.470 align:middle line:90% as either a buyer or a seller. 00:02:10.470 --> 00:02:13.760 align:middle line:84% If you think, for instance, about spectrum auctions, 00:02:13.760 --> 00:02:19.400 align:middle line:84% if you think about highway procurement projects, 00:02:19.400 --> 00:02:24.290 align:middle line:84% the government gives projects to construction firms. 00:02:24.290 --> 00:02:27.020 align:middle line:84% Other settings, electricity auctions, treasury auctions, 00:02:27.020 --> 00:02:29.600 align:middle line:84% and so on, all of these have, of course, 00:02:29.600 --> 00:02:31.610 align:middle line:84% direct policy implications because let's say 00:02:31.610 --> 00:02:36.170 align:middle line:84% you want to procure a construction, road 00:02:36.170 --> 00:02:38.760 align:middle line:84% construction at the minimal cost to taxpayers, 00:02:38.760 --> 00:02:42.360 align:middle line:84% you want to figure out what is the right mechanism to use. 00:02:42.360 --> 00:02:46.880 align:middle line:84% So there is this tight link between the way 00:02:46.880 --> 00:02:48.890 align:middle line:84% we analyze these kinds of settings 00:02:48.890 --> 00:02:51.650 align:middle line:84% and what we can actually do as policy makers, such as setting 00:02:51.650 --> 00:02:58.528 align:middle line:84% the reserve price, thinking about which mechanism to use. 00:02:58.528 --> 00:03:00.590 align:middle line:84% More from a research point of view, 00:03:00.590 --> 00:03:04.350 align:middle line:84% auctions have been quite fruitful in analyzing collusion. 00:03:04.350 --> 00:03:10.402 align:middle line:84% So oftentimes, it's a bit easier to get traction on collusion 00:03:10.402 --> 00:03:11.860 align:middle line:84% than, let's say, in repeated games. 00:03:11.860 --> 00:03:16.530 align:middle line:84% And there are many nice studies, some of which we will discuss 00:03:16.530 --> 00:03:20.830 align:middle line:90% in [14.]273. 00:03:20.830 --> 00:03:23.530 align:middle line:84% What is also really nice about auctions 00:03:23.530 --> 00:03:29.980 align:middle line:84% is that the rules of the game are very defined. 00:03:29.980 --> 00:03:31.900 align:middle line:90% We know what the strategies are. 00:03:31.900 --> 00:03:34.390 align:middle line:90% We know who the players are. 00:03:34.390 --> 00:03:37.130 align:middle line:84% And we actually see a lot of things. 00:03:37.130 --> 00:03:40.210 align:middle line:84% So if you think, for instance, about something 00:03:40.210 --> 00:03:45.190 align:middle line:84% like multi-unit auctions, like let's say in electricity, 00:03:45.190 --> 00:03:48.880 align:middle line:84% we actually see the whole supply schedule that a firm bids. 00:03:48.880 --> 00:03:52.180 align:middle line:84% That's something that we spend a lot of time-- 00:03:52.180 --> 00:03:55.340 align:middle line:84% supply and demand curves usually spend a lot of time backing out, 00:03:55.340 --> 00:03:57.090 align:middle line:84% but in some settings, we actually directly 00:03:57.090 --> 00:04:00.430 align:middle line:84% observe at what prices a firm wants to supply. 00:04:00.430 --> 00:04:04.670 align:middle line:84% And so that gives us a lot of empirical traction. 00:04:04.670 --> 00:04:08.560 align:middle line:84% It also means that whatever model we write down 00:04:08.560 --> 00:04:12.730 align:middle line:84% is oftentimes very close to the model 00:04:12.730 --> 00:04:15.310 align:middle line:90% that firms are actually playing. 00:04:15.310 --> 00:04:17.897 align:middle line:90% So the link here is very tight. 00:04:17.897 --> 00:04:20.480 align:middle line:84% If you think, let's say, about entry games or other settings-- 00:04:20.480 --> 00:04:22.490 align:middle line:84% if you think about what Amazon can do, 00:04:22.490 --> 00:04:24.420 align:middle line:84% Amazon can do a million different things. 00:04:24.420 --> 00:04:27.680 align:middle line:84% But once we narrow it down to a specific auction setting, 00:04:27.680 --> 00:04:29.690 align:middle line:84% we kind of know what the rules of this auction 00:04:29.690 --> 00:04:33.740 align:middle line:90% are, how people are bidding. 00:04:33.740 --> 00:04:37.380 align:middle line:84% And then the participants are oftentimes quite sophisticated. 00:04:37.380 --> 00:04:43.620 align:middle line:84% So take, for instance, the example of spectrum auctions. 00:04:43.620 --> 00:04:51.390 align:middle line:84% So I mean, these are very, very expensive bits that, let's say, 00:04:51.390 --> 00:04:53.770 align:middle line:84% firms like AT&T or T-Mobile put in. 00:04:53.770 --> 00:04:56.400 align:middle line:84% And what they're typically doing is they hire a firm, 00:04:56.400 --> 00:04:57.700 align:middle line:90% like Paul Milgrom's firm. 00:04:57.700 --> 00:05:00.610 align:middle line:84% And then Paul Milgrom devises their bidding strategy. 00:05:00.610 --> 00:05:05.040 align:middle line:84% And so suffice it to say that they're probably bidding pretty 00:05:05.040 --> 00:05:06.960 align:middle line:90% sophisticated in that case. 00:05:06.960 --> 00:05:09.870 align:middle line:84% So that means that when we write down a model 00:05:09.870 --> 00:05:11.700 align:middle line:84% where firms are optimizing, maybe 00:05:11.700 --> 00:05:17.760 align:middle line:84% actually getting kind of close to what's actually happening. 00:05:17.760 --> 00:05:21.060 align:middle line:84% Always the goal is to recover a distribution 00:05:21.060 --> 00:05:23.010 align:middle line:90% of bidder valuations. 00:05:23.010 --> 00:05:26.850 align:middle line:84% So really, to the extent that we think of valuations, 00:05:26.850 --> 00:05:28.890 align:middle line:84% unobserved valuations or unobserved, let's say, 00:05:28.890 --> 00:05:31.687 align:middle line:84% costs in the procurement setting as the structural error term, 00:05:31.687 --> 00:05:33.270 align:middle line:84% we're really interested in backing out 00:05:33.270 --> 00:05:35.325 align:middle line:84% this one distribution, the structural error term. 00:05:35.325 --> 00:05:39.580 align:middle line:90% 00:05:39.580 --> 00:05:43.970 align:middle line:84% So let me just very briefly recap single-unit auctions. 00:05:43.970 --> 00:05:45.730 align:middle line:84% I know you have seen this probably 00:05:45.730 --> 00:05:49.210 align:middle line:84% multiple times at this stage, but I will refer back to it 00:05:49.210 --> 00:05:49.970 align:middle line:90% a few times. 00:05:49.970 --> 00:05:55.430 align:middle line:84% So we have n bidders, indexed by i. 00:05:55.430 --> 00:05:58.500 align:middle line:84% The evaluations are denoted by Vi. 00:05:58.500 --> 00:06:03.720 align:middle line:84% They privately observe a signal that summarizes the information 00:06:03.720 --> 00:06:05.160 align:middle line:90% that they hold. 00:06:05.160 --> 00:06:07.390 align:middle line:90% And they're bidding a bid Bi. 00:06:07.390 --> 00:06:09.960 align:middle line:84% And typically the convention is that we 00:06:09.960 --> 00:06:13.350 align:middle line:84% refer to random variables as upper case letters 00:06:13.350 --> 00:06:15.770 align:middle line:84% and realizations as lower case letters. 00:06:15.770 --> 00:06:18.390 align:middle line:90% 00:06:18.390 --> 00:06:22.420 align:middle line:84% We are staying today in the IPV paradigm. 00:06:22.420 --> 00:06:27.670 align:middle line:84% That means that signals are distributed i.i.d. 00:06:27.670 --> 00:06:31.220 align:middle line:84% And we also stick to the private value paradigm. 00:06:31.220 --> 00:06:34.690 align:middle line:84% That means that I can learn from my signal 00:06:34.690 --> 00:06:38.890 align:middle line:84% about what signals other players have drawn. 00:06:38.890 --> 00:06:42.825 align:middle line:84% So this is a specific case where I only 00:06:42.825 --> 00:06:45.200 align:middle line:84% need to look at my signal, and that's all I need to know. 00:06:45.200 --> 00:06:50.730 align:middle line:90% 00:06:50.730 --> 00:06:53.020 align:middle line:84% OK, again, this is recap, I notice. 00:06:53.020 --> 00:06:55.170 align:middle line:84% But because I come back to this, I 00:06:55.170 --> 00:06:57.000 align:middle line:84% want to walk you through this once more. 00:06:57.000 --> 00:07:00.750 align:middle line:84% So we can solve in the first price auction 00:07:00.750 --> 00:07:07.170 align:middle line:84% case for the unique symmetric Bayesian Nash equilibrium. 00:07:07.170 --> 00:07:11.220 align:middle line:84% Bidders are maximizing their valuation 00:07:11.220 --> 00:07:15.180 align:middle line:84% minus their bid times the probability of winning. 00:07:15.180 --> 00:07:17.920 align:middle line:84% And this is the distribution of valuation. 00:07:17.920 --> 00:07:19.870 align:middle line:90% So we want to map back to this. 00:07:19.870 --> 00:07:24.300 align:middle line:84% And so we take the inverse of the symmetric bidding function, 00:07:24.300 --> 00:07:27.990 align:middle line:84% mapping back from the bit to the valuation. 00:07:27.990 --> 00:07:31.990 align:middle line:84% You can take the first order condition. 00:07:31.990 --> 00:07:38.280 align:middle line:84% We get a differential equation that you have seen before. 00:07:38.280 --> 00:07:41.580 align:middle line:84% Later on, when I discuss GPV, I will come back to this. 00:07:41.580 --> 00:07:47.370 align:middle line:84% And here, you get with a boundary condition 00:07:47.370 --> 00:07:49.640 align:middle line:84% the closed-form solution for the bidding function. 00:07:49.640 --> 00:07:52.370 align:middle line:90% 00:07:52.370 --> 00:07:56.730 align:middle line:84% So let me just comment, first of all, 00:07:56.730 --> 00:07:59.400 align:middle line:84% that this doesn't have a great economic interpretation, 00:07:59.400 --> 00:08:05.010 align:middle line:84% but it's equal to the expected value of the valuation 00:08:05.010 --> 00:08:08.520 align:middle line:84% of the other remaining bidders, given that my valuation 00:08:08.520 --> 00:08:10.500 align:middle line:90% is higher than theirs. 00:08:10.500 --> 00:08:13.150 align:middle line:90% So that's what this is equal to. 00:08:13.150 --> 00:08:15.840 align:middle line:84% So that's a bit more interpretable. 00:08:15.840 --> 00:08:18.510 align:middle line:84% The other thing from an empirical point of view, 00:08:18.510 --> 00:08:21.330 align:middle line:84% if you stare at this expression here, 00:08:21.330 --> 00:08:25.260 align:middle line:90% this is an integral over a CDF. 00:08:25.260 --> 00:08:30.173 align:middle line:84% And for most common distribution functions, 00:08:30.173 --> 00:08:31.590 align:middle line:84% and especially if we do not impose 00:08:31.590 --> 00:08:35.070 align:middle line:84% any parametric restrictions, that does not 00:08:35.070 --> 00:08:36.250 align:middle line:90% have a closed form solution. 00:08:36.250 --> 00:08:37.770 align:middle line:84% That means that from an empirical point of view, 00:08:37.770 --> 00:08:39.570 align:middle line:84% this is kind of a messy thing here 00:08:39.570 --> 00:08:42.940 align:middle line:84% because we have to numerically integrate this. 00:08:42.940 --> 00:08:47.430 align:middle line:84% And so I come back why that's not a great thing 00:08:47.430 --> 00:08:49.805 align:middle line:84% and how to possibly sidestep this. 00:08:49.805 --> 00:08:55.490 align:middle line:90% 00:08:55.490 --> 00:09:01.970 align:middle line:84% So here is the solution with a reserve price. 00:09:01.970 --> 00:09:05.090 align:middle line:84% OK, so let me come to the first paper 00:09:05.090 --> 00:09:09.710 align:middle line:84% that I wanted to discuss today, Laffont, Ossard, and Vuong. 00:09:09.710 --> 00:09:14.070 align:middle line:84% This is one of the very early empirical auction papers. 00:09:14.070 --> 00:09:16.230 align:middle line:90% It has some really nice ideas. 00:09:16.230 --> 00:09:21.830 align:middle line:84% It's not really the way the literature has gone, 00:09:21.830 --> 00:09:25.310 align:middle line:84% but I think it helps the way to understand 00:09:25.310 --> 00:09:27.710 align:middle line:90% how the thinking has evolved. 00:09:27.710 --> 00:09:34.250 align:middle line:84% So again, we're in the symmetric IPV setting. 00:09:34.250 --> 00:09:39.207 align:middle line:84% These are descending auctions with a reserve price. 00:09:39.207 --> 00:09:40.790 align:middle line:84% These kinds of auctions are oftentimes 00:09:40.790 --> 00:09:44.090 align:middle line:84% used for perishables, things that have to be sold quickly. 00:09:44.090 --> 00:09:46.940 align:middle line:84% Because as soon as somebody stops-- 00:09:46.940 --> 00:09:49.250 align:middle line:84% you only need one bit to stop the auction. 00:09:49.250 --> 00:09:53.480 align:middle line:84% The setting here is a little town in the south of France 00:09:53.480 --> 00:09:56.900 align:middle line:84% where they're selling baskets of eggplants in a wholesale market. 00:09:56.900 --> 00:09:58.790 align:middle line:84% So there are sellers that buy these baskets 00:09:58.790 --> 00:10:03.420 align:middle line:84% and then go to a retail market and sell those. 00:10:03.420 --> 00:10:08.940 align:middle line:84% The imposing log normal distribution on the valuations. 00:10:08.940 --> 00:10:12.990 align:middle line:84% And the goal is to estimate the parameters of this log 00:10:12.990 --> 00:10:15.570 align:middle line:90% normal distribution. 00:10:15.570 --> 00:10:18.270 align:middle line:84% And they have data from 81 auctions 00:10:18.270 --> 00:10:21.935 align:middle line:84% with the same set of bidders in each of the auctions. 00:10:21.935 --> 00:10:25.300 align:middle line:90% 00:10:25.300 --> 00:10:32.080 align:middle line:84% OK, so how can we make progress on estimating this distribution 00:10:32.080 --> 00:10:33.926 align:middle line:90% of valuations? 00:10:33.926 --> 00:10:37.190 align:middle line:90% 00:10:37.190 --> 00:10:39.950 align:middle line:90% So one idea is to use the-- 00:10:39.950 --> 00:10:43.040 align:middle line:84% we have just seen a solution for first-price, sealed bid auction. 00:10:43.040 --> 00:10:47.180 align:middle line:84% One idea is to use the strategic equivalence between sealed bid, 00:10:47.180 --> 00:10:48.920 align:middle line:90% first-price auctions-- 00:10:48.920 --> 00:10:51.950 align:middle line:84% with first-price, sealed bid auction and use 00:10:51.950 --> 00:10:53.220 align:middle line:90% maximum likelihood. 00:10:53.220 --> 00:10:55.830 align:middle line:90% 00:10:55.830 --> 00:10:59.300 align:middle line:84% So let's see how far this gets us. 00:10:59.300 --> 00:11:03.860 align:middle line:84% So I want to maximize some likelihood function, where 00:11:03.860 --> 00:11:06.380 align:middle line:84% f is given by this log normal as the density of the log 00:11:06.380 --> 00:11:08.540 align:middle line:84% normal distribution and the vector of bids 00:11:08.540 --> 00:11:10.640 align:middle line:90% that are observed. 00:11:10.640 --> 00:11:16.160 align:middle line:84% And I know here, with a reserve price built in, 00:11:16.160 --> 00:11:19.130 align:middle line:84% I know that this is my closed-form solution 00:11:19.130 --> 00:11:20.850 align:middle line:90% to the bidding function. 00:11:20.850 --> 00:11:23.730 align:middle line:84% So now, if you think about how to actually do this, 00:11:23.730 --> 00:11:25.140 align:middle line:90% how would you do this? 00:11:25.140 --> 00:11:32.250 align:middle line:84% For a given parameter guess, I know what these objects are. 00:11:32.250 --> 00:11:33.635 align:middle line:90% What I observe are the bids. 00:11:33.635 --> 00:11:37.270 align:middle line:90% 00:11:37.270 --> 00:11:40.660 align:middle line:84% But I want to evaluate the likelihood, of course, 00:11:40.660 --> 00:11:44.710 align:middle line:84% at the valuations, which I do not observe. 00:11:44.710 --> 00:11:49.390 align:middle line:84% So what I need to do is for a given guess of parameters, 00:11:49.390 --> 00:11:53.080 align:middle line:90% I need to compute this thing. 00:11:53.080 --> 00:11:58.390 align:middle line:84% And I need to find the v under this expression that 00:11:58.390 --> 00:12:02.520 align:middle line:84% makes this equal to the bid that I observe. 00:12:02.520 --> 00:12:07.890 align:middle line:84% So I basically need to conduct a line search, where I repeatedly 00:12:07.890 --> 00:12:14.340 align:middle line:84% guess v's until this expression is equal to my b. 00:12:14.340 --> 00:12:18.510 align:middle line:84% And while I'm doing this, I need to repeatedly evaluate 00:12:18.510 --> 00:12:20.498 align:middle line:84% this thing that I told you is not 00:12:20.498 --> 00:12:22.290 align:middle line:84% super straightforward to compute because it 00:12:22.290 --> 00:12:25.530 align:middle line:90% has this integral over a CDF. 00:12:25.530 --> 00:12:27.030 align:middle line:84% So you need to numerically integrate 00:12:27.030 --> 00:12:31.150 align:middle line:84% this to support that integration limits are changing. 00:12:31.150 --> 00:12:33.005 align:middle line:84% That makes all of this not so easy. 00:12:33.005 --> 00:12:36.670 align:middle line:90% 00:12:36.670 --> 00:12:43.020 align:middle line:84% So you probably get the sense that this doesn't work great. 00:12:43.020 --> 00:12:46.680 align:middle line:84% In the early literature by papers by Harry Parr and others, 00:12:46.680 --> 00:12:48.450 align:middle line:90% they have done this. 00:12:48.450 --> 00:12:54.210 align:middle line:84% But this is no longer really the way people estimate auctions 00:12:54.210 --> 00:12:54.970 align:middle line:90% these days. 00:12:54.970 --> 00:12:58.980 align:middle line:84% It's computationally costly, as I hope I made clear here. 00:12:58.980 --> 00:13:01.140 align:middle line:84% Another issue is that we actually only 00:13:01.140 --> 00:13:02.880 align:middle line:90% observed the winning bid here. 00:13:02.880 --> 00:13:04.560 align:middle line:84% So what we would actually have to do 00:13:04.560 --> 00:13:08.040 align:middle line:84% is we have to first get the expression for the likelihood 00:13:08.040 --> 00:13:11.370 align:middle line:84% of the winning bid, which is something we can, of course, do. 00:13:11.370 --> 00:13:16.080 align:middle line:84% But there's an extra, more fundamental problem 00:13:16.080 --> 00:13:24.510 align:middle line:84% that the support of the distribution of the winning bid 00:13:24.510 --> 00:13:28.960 align:middle line:84% depends on the parameters, and in particular 00:13:28.960 --> 00:13:35.350 align:middle line:84% on the max of the largest out of N minus 1 00:13:35.350 --> 00:13:38.800 align:middle line:84% draws on the distribution of valuations and the reserve 00:13:38.800 --> 00:13:39.940 align:middle line:90% price. 00:13:39.940 --> 00:13:42.910 align:middle line:84% And that violates the regularity conditions 00:13:42.910 --> 00:13:44.030 align:middle line:90% of maximum likelihood. 00:13:44.030 --> 00:13:45.447 align:middle line:84% So maximum likelihood in this case 00:13:45.447 --> 00:13:48.100 align:middle line:90% is not a consistent estimator. 00:13:48.100 --> 00:13:50.830 align:middle line:84% So there again, there's early work 00:13:50.830 --> 00:13:54.680 align:middle line:84% by Harry Paarsch that tries to find ways around this. 00:13:54.680 --> 00:13:58.660 align:middle line:84% But as you will see, there are much 00:13:58.660 --> 00:14:00.360 align:middle line:90% better ways to go about this. 00:14:00.360 --> 00:14:04.030 align:middle line:90% 00:14:04.030 --> 00:14:07.030 align:middle line:90% OK, so here's another idea. 00:14:07.030 --> 00:14:14.080 align:middle line:84% So instead of having to map back from the expression for my bid 00:14:14.080 --> 00:14:17.290 align:middle line:84% to my valuation and then evaluate the likelihood, what 00:14:17.290 --> 00:14:20.710 align:middle line:84% I could instead do is I could simulate the object 00:14:20.710 --> 00:14:22.180 align:middle line:90% that I observe. 00:14:22.180 --> 00:14:28.390 align:middle line:84% So I see a bid, and with the closed form expression 00:14:28.390 --> 00:14:33.080 align:middle line:84% for my bidding function, I can simulate the integral 00:14:33.080 --> 00:14:35.530 align:middle line:84% and match this integral, the expected winning bid, 00:14:35.530 --> 00:14:38.130 align:middle line:90% to the observed winning bid. 00:14:38.130 --> 00:14:42.490 align:middle line:84% OK, so here is the expression for the expected winning 00:14:42.490 --> 00:14:49.590 align:middle line:84% bid, which integrates out over this bidding function 00:14:49.590 --> 00:14:55.200 align:middle line:84% and here uses the expression for the density of the highest 00:14:55.200 --> 00:14:56.900 align:middle line:90% valuation. 00:14:56.900 --> 00:14:59.700 align:middle line:84% And so when you plug this in, you 00:14:59.700 --> 00:15:04.980 align:middle line:84% can simplify this a little bit, and you get an expression 00:15:04.980 --> 00:15:07.500 align:middle line:90% that looks like this here. 00:15:07.500 --> 00:15:10.330 align:middle line:84% And typically, complicated integrals, 00:15:10.330 --> 00:15:13.020 align:middle line:84% one question you should always ask yourself is, instead 00:15:13.020 --> 00:15:16.030 align:middle line:84% of computing this integral exactly, 00:15:16.030 --> 00:15:17.590 align:middle line:84% do I somehow want to simulate this? 00:15:17.590 --> 00:15:19.890 align:middle line:84% Because simulation is often oftentimes easier. 00:15:19.890 --> 00:15:22.620 align:middle line:84% In BLP, that's something that we typically 00:15:22.620 --> 00:15:24.630 align:middle line:90% do for the random coefficient. 00:15:24.630 --> 00:15:28.560 align:middle line:84% We take a bunch of random draws and then integrate out. 00:15:28.560 --> 00:15:31.200 align:middle line:84% So that's something one could do. 00:15:31.200 --> 00:15:34.720 align:middle line:90% It's still somewhat cumbersome. 00:15:34.720 --> 00:15:37.240 align:middle line:84% I mean, you have to take random draws from the log normal. 00:15:37.240 --> 00:15:39.030 align:middle line:90% That's not easy with-- 00:15:39.030 --> 00:15:43.870 align:middle line:84% that's actually very easy with modern programming languages. 00:15:43.870 --> 00:15:47.400 align:middle line:84% But then you still have to-- for every draw of the evaluations, 00:15:47.400 --> 00:15:51.540 align:middle line:84% I have to compute this expression here 00:15:51.540 --> 00:15:53.530 align:middle line:90% over which I take an average. 00:15:53.530 --> 00:15:57.090 align:middle line:84% And here still I have to compute this integral over a CDF. 00:15:57.090 --> 00:16:00.750 align:middle line:84% So it's already much better than what we had before, 00:16:00.750 --> 00:16:02.890 align:middle line:84% but it's still somewhat cumbersome. 00:16:02.890 --> 00:16:06.930 align:middle line:90% 00:16:06.930 --> 00:16:08.075 align:middle line:90% Any questions so far? 00:16:08.075 --> 00:16:14.620 align:middle line:90% 00:16:14.620 --> 00:16:23.140 align:middle line:84% So here's a clever insight that Laffont, Ossard, and Vuong had. 00:16:23.140 --> 00:16:26.530 align:middle line:84% We stick with simulation, but we can use the revenue 00:16:26.530 --> 00:16:28.680 align:middle line:90% equivalence theorem. 00:16:28.680 --> 00:16:32.290 align:middle line:84% So I've seen that Glenn has talked about this. 00:16:32.290 --> 00:16:34.470 align:middle line:90% So I'm just repeating this here. 00:16:34.470 --> 00:16:39.540 align:middle line:84% So we're assuming a risk-neutral IPV setting 00:16:39.540 --> 00:16:42.600 align:middle line:90% with atomless signal support. 00:16:42.600 --> 00:16:45.690 align:middle line:84% We know that in this case, any mechanism which 00:16:45.690 --> 00:16:48.900 align:middle line:84% is efficient in that it awards the object to the bidder 00:16:48.900 --> 00:16:51.360 align:middle line:84% with the highest signal or with the lowest cost 00:16:51.360 --> 00:16:56.940 align:middle line:84% and leaves the weakest bidder with zero surplus, 00:16:56.940 --> 00:17:00.510 align:middle line:90% it's the same expected revenue. 00:17:00.510 --> 00:17:02.535 align:middle line:90% And so how can we use this? 00:17:02.535 --> 00:17:06.130 align:middle line:90% 00:17:06.130 --> 00:17:15.010 align:middle line:84% We know that using this result, for this specific sets 00:17:15.010 --> 00:17:20.319 align:middle line:84% of assumptions, the expected bid that we 00:17:20.319 --> 00:17:21.819 align:middle line:84% get from this closed-form solution 00:17:21.819 --> 00:17:26.109 align:middle line:84% for the first-price sealed bid auction, 00:17:26.109 --> 00:17:31.510 align:middle line:84% here using again the expectation over the valuations 00:17:31.510 --> 00:17:37.120 align:middle line:84% of the strongest bidder, so the highest order statistic 00:17:37.120 --> 00:17:39.370 align:middle line:84% and taking into account the reserve price, 00:17:39.370 --> 00:17:42.980 align:middle line:84% that the expected revenue from those bids 00:17:42.980 --> 00:17:46.580 align:middle line:84% has to be equal to the expected revenue 00:17:46.580 --> 00:17:50.900 align:middle line:84% from a second-price auction within the same setting. 00:17:50.900 --> 00:17:54.980 align:middle line:84% And remember, in a second-price auction, 00:17:54.980 --> 00:17:56.810 align:middle line:84% bidders' weakly dominant strategy 00:17:56.810 --> 00:17:59.560 align:middle line:90% is to bid their valuations. 00:17:59.560 --> 00:18:02.740 align:middle line:84% And so here we can basically make use of the fact 00:18:02.740 --> 00:18:07.030 align:middle line:84% that I no longer have to compute any complicated bidding 00:18:07.030 --> 00:18:07.850 align:middle line:90% function. 00:18:07.850 --> 00:18:11.516 align:middle line:84% I can directly take an expectation over valuations. 00:18:11.516 --> 00:18:19.410 align:middle line:90% 00:18:19.410 --> 00:18:23.570 align:middle line:90% So how would one then do this? 00:18:23.570 --> 00:18:26.450 align:middle line:90% This is actually really simple. 00:18:26.450 --> 00:18:28.460 align:middle line:84% So you generate-- you have your log normal. 00:18:28.460 --> 00:18:32.510 align:middle line:84% You generate some-- for a given simulation draw, 00:18:32.510 --> 00:18:35.420 align:middle line:84% you generate a vector of evaluations. 00:18:35.420 --> 00:18:39.980 align:middle line:84% You take the second highest one and set the winning bid 00:18:39.980 --> 00:18:43.820 align:middle line:84% as the maximum of that realization and the reserve 00:18:43.820 --> 00:18:45.210 align:middle line:90% price. 00:18:45.210 --> 00:18:48.870 align:middle line:84% You do this a bunch of times, and you get an expectation 00:18:48.870 --> 00:18:50.670 align:middle line:90% for the winning bid. 00:18:50.670 --> 00:18:53.010 align:middle line:84% You do this for every parameter guess 00:18:53.010 --> 00:18:55.660 align:middle line:84% and you minimize the squared deviation. 00:18:55.660 --> 00:18:57.510 align:middle line:84% So this is nonlinear least squares 00:18:57.510 --> 00:19:02.320 align:middle line:90% from the observed winning bids. 00:19:02.320 --> 00:19:08.380 align:middle line:84% So this is to show that sometimes you can use the theory 00:19:08.380 --> 00:19:10.100 align:middle line:90% to make your life really easy. 00:19:10.100 --> 00:19:11.920 align:middle line:84% In this case, this clever insight 00:19:11.920 --> 00:19:15.940 align:middle line:84% that instead of estimating this with a first-price auction, 00:19:15.940 --> 00:19:18.940 align:middle line:84% we just use a second-price auction instead. 00:19:18.940 --> 00:19:20.730 align:middle line:84% And this makes our life much, much easier. 00:19:20.730 --> 00:19:27.180 align:middle line:90% 00:19:27.180 --> 00:19:31.150 align:middle line:84% So let me comment on this a little bit. 00:19:31.150 --> 00:19:34.620 align:middle line:84% So this is, as neat as this, actually not an approach 00:19:34.620 --> 00:19:39.690 align:middle line:84% that's widely used anymore in empirical work. 00:19:39.690 --> 00:19:42.330 align:middle line:84% So one reason is certainly that there 00:19:42.330 --> 00:19:48.090 align:middle line:84% are many different ways that revenue equivalence breaks-- 00:19:48.090 --> 00:19:53.240 align:middle line:84% asymmetric bidders, risk aversion, endogenous-- 00:19:53.240 --> 00:19:59.040 align:middle line:84% I mean, cost of entering an auction, you know, collusion-- 00:19:59.040 --> 00:20:05.030 align:middle line:84% So many things that we believe are important in the real world 00:20:05.030 --> 00:20:07.040 align:middle line:90% lead this result to break. 00:20:07.040 --> 00:20:11.480 align:middle line:84% And so it might be maybe assuming 00:20:11.480 --> 00:20:16.610 align:middle line:84% a little too much to rely on this result. 00:20:16.610 --> 00:20:21.680 align:middle line:84% The other reason is that people, at least in this literature, 00:20:21.680 --> 00:20:26.180 align:middle line:84% in the auction literature, have moved away from strong reliance 00:20:26.180 --> 00:20:27.270 align:middle line:90% on functional forms. 00:20:27.270 --> 00:20:30.920 align:middle line:84% So in this paper, we just assumed 00:20:30.920 --> 00:20:34.850 align:middle line:84% a log normal distribution, and people are typically not 00:20:34.850 --> 00:20:36.980 align:middle line:84% comfortable to say from the get go, 00:20:36.980 --> 00:20:40.940 align:middle line:84% oh, this is what the distribution of valuations 00:20:40.940 --> 00:20:44.450 align:middle line:84% looks like, or this is the parametric family 00:20:44.450 --> 00:20:47.900 align:middle line:90% which in I believe it lies. 00:20:47.900 --> 00:20:51.800 align:middle line:84% And so instead, what people are doing is 00:20:51.800 --> 00:20:55.370 align:middle line:84% they typically try to identify models, 00:20:55.370 --> 00:20:57.350 align:middle line:84% what is called nonparametrically, 00:20:57.350 --> 00:21:02.060 align:middle line:84% and place strong emphasis on formal identification results. 00:21:02.060 --> 00:21:06.020 align:middle line:84% So I want to now just have a digression of one slide 00:21:06.020 --> 00:21:10.640 align:middle line:84% to talk you through a little bit what that actually means. 00:21:10.640 --> 00:21:11.420 align:middle line:90% Yes. 00:21:11.420 --> 00:21:16.640 align:middle line:84% AUDIENCE: Yeah, so was it the case that for each option, 00:21:16.640 --> 00:21:20.190 align:middle line:84% we're assuming that the bidders have a new valuation drawn? 00:21:20.190 --> 00:21:22.128 align:middle line:84% TOBIAS SALZ: Yes, in this setting. 00:21:22.128 --> 00:21:22.670 align:middle line:90% AUDIENCE: OK. 00:21:22.670 --> 00:21:24.440 align:middle line:84% And so I think at the very beginning, 00:21:24.440 --> 00:21:27.630 align:middle line:84% you said that there's the same 11 bidders throughout. 00:21:27.630 --> 00:21:30.203 align:middle line:84% And so for a given bidder, the valuation 00:21:30.203 --> 00:21:31.370 align:middle line:90% draws are correlated at all? 00:21:31.370 --> 00:21:33.335 align:middle line:84% Or are we also assuming that those are independent? 00:21:33.335 --> 00:21:35.270 align:middle line:84% TOBIAS SALZ: In this particular application, 00:21:35.270 --> 00:21:37.103 align:middle line:84% they're assuming that those are independent. 00:21:37.103 --> 00:21:38.930 align:middle line:84% But that's a good question, that you 00:21:38.930 --> 00:21:40.790 align:middle line:84% may think that some bidders maybe 00:21:40.790 --> 00:21:43.680 align:middle line:84% have better resale opportunities, 00:21:43.680 --> 00:21:44.930 align:middle line:90% have a better retail location. 00:21:44.930 --> 00:21:51.080 align:middle line:84% And for them, their valuations are kind of systematically 00:21:51.080 --> 00:21:53.240 align:middle line:84% different over a longer time horizon. 00:21:53.240 --> 00:21:56.390 align:middle line:84% And these kinds of asymmetries are oftentimes, 00:21:56.390 --> 00:21:59.900 align:middle line:84% in many modern applications of auction models, 00:21:59.900 --> 00:22:03.380 align:middle line:84% people try to take them into account. 00:22:03.380 --> 00:22:10.590 align:middle line:84% They make life very complicated because for asymmetric auctions, 00:22:10.590 --> 00:22:13.740 align:middle line:84% there's typically no closed-form solution for the bidding 00:22:13.740 --> 00:22:16.500 align:middle line:84% function in the first-price auction case. 00:22:16.500 --> 00:22:24.430 align:middle line:84% So it's estimation, as I will show you in two slides, is easy. 00:22:24.430 --> 00:22:28.180 align:middle line:84% But equilibrium computation is hard with asymmetries. 00:22:28.180 --> 00:22:32.060 align:middle line:90% 00:22:32.060 --> 00:22:34.280 align:middle line:84% So just very briefly, what does it 00:22:34.280 --> 00:22:37.730 align:middle line:84% mean for a model to be identified? 00:22:37.730 --> 00:22:39.770 align:middle line:84% People use the term identification 00:22:39.770 --> 00:22:40.830 align:middle line:90% in many different ways. 00:22:40.830 --> 00:22:46.510 align:middle line:84% I'm telling you how this term is used in the auction literature. 00:22:46.510 --> 00:22:50.870 align:middle line:84% So what people have in mind here is that-- 00:22:50.870 --> 00:22:53.810 align:middle line:84% so first, we are settling on the game, 00:22:53.810 --> 00:22:56.030 align:middle line:84% and we're settling typically on a solution 00:22:56.030 --> 00:22:59.270 align:middle line:84% concept for this game, let's say, a Bayesian Nash 00:22:59.270 --> 00:23:00.380 align:middle line:90% equilibrium. 00:23:00.380 --> 00:23:06.080 align:middle line:84% And given that, a model is identified 00:23:06.080 --> 00:23:09.860 align:middle line:84% if the joint distribution of bidder utilities and signals 00:23:09.860 --> 00:23:13.370 align:middle line:84% is uniquely determined by the joint distribution of things 00:23:13.370 --> 00:23:15.002 align:middle line:90% that I observe. 00:23:15.002 --> 00:23:16.460 align:middle line:84% Things that I observe are typically 00:23:16.460 --> 00:23:22.530 align:middle line:84% bids or bids and entry behavior, or in some settings, bids 00:23:22.530 --> 00:23:26.840 align:middle line:84% and, let's say, whether I'm drilling this oil field 00:23:26.840 --> 00:23:30.740 align:middle line:84% after the auction or not, so things that are 00:23:30.740 --> 00:23:32.440 align:middle line:90% observable to the researcher. 00:23:32.440 --> 00:23:36.120 align:middle line:90% 00:23:36.120 --> 00:23:39.480 align:middle line:84% OK, so here's a slightly more formal way of saying this. 00:23:39.480 --> 00:23:43.410 align:middle line:84% Let m star be the true vector of functions and distributions, 00:23:43.410 --> 00:23:47.100 align:middle line:84% and let P of m denote the joint distribution 00:23:47.100 --> 00:23:49.050 align:middle line:84% of observable variables under the assumption 00:23:49.050 --> 00:23:51.340 align:middle line:84% that the data is generated under m. 00:23:51.340 --> 00:23:54.715 align:middle line:84% So think of P as basically a mapping from my model. 00:23:54.715 --> 00:23:56.340 align:middle line:84% And just to make things simple for now, 00:23:56.340 --> 00:24:01.920 align:middle line:84% think about your model is the distribution that you 00:24:01.920 --> 00:24:04.930 align:middle line:90% assume for bid as valuations. 00:24:04.930 --> 00:24:09.780 align:middle line:84% And P basically maps that with some assumption on which game 00:24:09.780 --> 00:24:15.820 align:middle line:84% is being played and what equilibrium to the data. 00:24:15.820 --> 00:24:20.900 align:middle line:84% And we say that m star is identified in a class of models 00:24:20.900 --> 00:24:29.920 align:middle line:84% if and only if for all models in this set, whenever my model is 00:24:29.920 --> 00:24:31.390 align:middle line:84% different from m star, I would also 00:24:31.390 --> 00:24:32.690 align:middle line:90% observe something different. 00:24:32.690 --> 00:24:35.550 align:middle line:90% 00:24:35.550 --> 00:24:38.850 align:middle line:84% And so what is important here is that this-- 00:24:38.850 --> 00:24:42.460 align:middle line:90% we typically do this-- 00:24:42.460 --> 00:24:44.370 align:middle line:84% I mean, we do this under the assumption 00:24:44.370 --> 00:24:47.790 align:middle line:84% that we have infinite amount of data. 00:24:47.790 --> 00:24:51.840 align:middle line:84% So this is not something where we're worried about small sample 00:24:51.840 --> 00:24:52.510 align:middle line:90% properties. 00:24:52.510 --> 00:24:55.320 align:middle line:84% This is really in the ideal case. 00:24:55.320 --> 00:24:56.910 align:middle line:84% Sometimes it might be rare events 00:24:56.910 --> 00:24:58.860 align:middle line:90% that tell two models apart. 00:24:58.860 --> 00:25:01.710 align:middle line:84% Here we're assuming we have these rare events that allow us 00:25:01.710 --> 00:25:05.270 align:middle line:90% to tell the two models apart. 00:25:05.270 --> 00:25:08.450 align:middle line:84% So now with this, I can tell you what it means for something 00:25:08.450 --> 00:25:10.160 align:middle line:90% to be nonparametric. 00:25:10.160 --> 00:25:15.800 align:middle line:84% So first, a parametric model is if I restrict m 00:25:15.800 --> 00:25:18.360 align:middle line:84% to be a subset of a finite dimensional space. 00:25:18.360 --> 00:25:23.960 align:middle line:84% Let's say I'm searching over the set of normal distributions 00:25:23.960 --> 00:25:27.140 align:middle line:90% or exponential distributions. 00:25:27.140 --> 00:25:30.080 align:middle line:84% Sometimes one parameter may be enough. 00:25:30.080 --> 00:25:32.900 align:middle line:84% Or I could even allow for, let's say, 00:25:32.900 --> 00:25:35.750 align:middle line:84% a search over different kinds of parametric distributions 00:25:35.750 --> 00:25:42.530 align:middle line:84% that would still be parametric or semiparametric. 00:25:42.530 --> 00:25:48.050 align:middle line:84% If m, however, is not a subset of a finite dimensional space, 00:25:48.050 --> 00:25:52.100 align:middle line:84% we say that it's semiparametric if a subset of functions 00:25:52.100 --> 00:25:54.650 align:middle line:84% lies in the finite dimensional space and nonparametric 00:25:54.650 --> 00:25:57.300 align:middle line:84% if none of them lies in a finite dimensional space. 00:25:57.300 --> 00:26:00.110 align:middle line:84% So thing about nonparametric basically 00:26:00.110 --> 00:26:05.020 align:middle line:84% means that you can have any sort of weird density of valuations. 00:26:05.020 --> 00:26:07.800 align:middle line:90% It could have different modes. 00:26:07.800 --> 00:26:09.695 align:middle line:84% You're not placing any restrictions on it. 00:26:09.695 --> 00:26:16.020 align:middle line:90% 00:26:16.020 --> 00:26:17.560 align:middle line:90% So one more word on this. 00:26:17.560 --> 00:26:23.570 align:middle line:84% So how do we actually go about thinking about identification? 00:26:23.570 --> 00:26:25.800 align:middle line:84% So the typical approach is what is 00:26:25.800 --> 00:26:28.950 align:middle line:84% called the constructive approach, is to try and express 00:26:28.950 --> 00:26:32.780 align:middle line:84% the things that I do not know in terms of things that I observe. 00:26:32.780 --> 00:26:35.530 align:middle line:90% 00:26:35.530 --> 00:26:41.890 align:middle line:84% Because then it's crystal clear that what 00:26:41.890 --> 00:26:46.660 align:middle line:84% I'm looking for-- the primitive that I'm looking for 00:26:46.660 --> 00:26:50.710 align:middle line:84% can be expressed in terms of data directly. 00:26:50.710 --> 00:26:53.592 align:middle line:84% So just very, very simple example for this. 00:26:53.592 --> 00:26:55.050 align:middle line:84% Think about a second-price auction. 00:26:55.050 --> 00:27:01.500 align:middle line:90% 00:27:01.500 --> 00:27:04.830 align:middle line:84% So again, for us, we're typically 00:27:04.830 --> 00:27:09.770 align:middle line:84% interested in learning the distribution of valuations. 00:27:09.770 --> 00:27:13.085 align:middle line:84% And let's say we assume that the bidders here 00:27:13.085 --> 00:27:15.490 align:middle line:84% are playing the weakly dominant strategy of bidding 00:27:15.490 --> 00:27:17.036 align:middle line:90% their own valuation. 00:27:17.036 --> 00:27:19.870 align:middle line:90% 00:27:19.870 --> 00:27:22.220 align:middle line:84% I hope that-- you see this, right? 00:27:22.220 --> 00:27:24.670 align:middle line:84% This is basically almost immediate. 00:27:24.670 --> 00:27:28.120 align:middle line:84% I know that, in this case, my bids 00:27:28.120 --> 00:27:31.180 align:middle line:90% are equal to the valuations. 00:27:31.180 --> 00:27:33.680 align:middle line:84% This means I directly observe the valuations. 00:27:33.680 --> 00:27:37.870 align:middle line:84% So it's trivially identified because I can express-- 00:27:37.870 --> 00:27:40.840 align:middle line:84% every bid as valuation, I have a direct correspondence 00:27:40.840 --> 00:27:42.255 align:middle line:90% to that bidder's bid. 00:27:42.255 --> 00:27:45.520 align:middle line:90% 00:27:45.520 --> 00:27:49.020 align:middle line:84% So what, however, if only transaction prices are observed? 00:27:49.020 --> 00:27:51.430 align:middle line:90% OK, so now I can do this. 00:27:51.430 --> 00:27:54.970 align:middle line:84% I can't directly express the unknown thing, my v 00:27:54.970 --> 00:27:56.310 align:middle line:90% in terms of the known thing b. 00:27:56.310 --> 00:27:59.990 align:middle line:90% 00:27:59.990 --> 00:28:02.910 align:middle line:84% So here the following result comes in handy. 00:28:02.910 --> 00:28:07.510 align:middle line:84% So first, as you know, the winning bid-- 00:28:07.510 --> 00:28:13.080 align:middle line:84% sorry, the transaction price is given by the second highest 00:28:13.080 --> 00:28:13.786 align:middle line:90% valuation. 00:28:13.786 --> 00:28:16.930 align:middle line:90% 00:28:16.930 --> 00:28:22.610 align:middle line:84% So what I do observe is the second highest order statistic. 00:28:22.610 --> 00:28:24.570 align:middle line:90% And what we typically-- 00:28:24.570 --> 00:28:27.080 align:middle line:84% not always, but what we typically assume in auctions 00:28:27.080 --> 00:28:30.200 align:middle line:84% is that what we also know is the number of bidders. 00:28:30.200 --> 00:28:33.410 align:middle line:84% This is empirically not always crystal clear 00:28:33.410 --> 00:28:35.060 align:middle line:84% that that's really something that's 00:28:35.060 --> 00:28:38.760 align:middle line:84% observed without measurement error or precisely observed. 00:28:38.760 --> 00:28:42.010 align:middle line:84% But that's typically an assumption. 00:28:42.010 --> 00:28:44.450 align:middle line:90% So I know the number of bidders. 00:28:44.450 --> 00:28:48.890 align:middle line:84% I also know the second highest order statistic. 00:28:48.890 --> 00:28:51.320 align:middle line:90% I do not know f of v directly. 00:28:51.320 --> 00:28:53.840 align:middle line:84% I only know the second highest order statistic. 00:28:53.840 --> 00:28:58.730 align:middle line:90% So can I make progress here? 00:28:58.730 --> 00:29:01.070 align:middle line:84% The answer is yes because of this result. 00:29:01.070 --> 00:29:03.650 align:middle line:84% I think Glenn in his lecture had also 00:29:03.650 --> 00:29:05.130 align:middle line:84% an expression for order statistics. 00:29:05.130 --> 00:29:09.290 align:middle line:84% This is yet a different expression for order statistics. 00:29:09.290 --> 00:29:13.760 align:middle line:84% It makes it pretty clear why, from any order statistic, 00:29:13.760 --> 00:29:17.750 align:middle line:84% we can identify the underlying distribution. 00:29:17.750 --> 00:29:23.120 align:middle line:84% And that's because if you stare at this expression here, 00:29:23.120 --> 00:29:24.890 align:middle line:84% everything on the right-hand side 00:29:24.890 --> 00:29:30.350 align:middle line:84% here is known except for f of v. I know N. I know which order 00:29:30.350 --> 00:29:32.270 align:middle line:90% statistic I observe. 00:29:32.270 --> 00:29:36.410 align:middle line:84% And this is an integral that's strictly increasing in f of v. 00:29:36.410 --> 00:29:41.090 align:middle line:84% So that means I can pointwise invert this thing. 00:29:41.090 --> 00:29:45.080 align:middle line:90% I know this here pointwise. 00:29:45.080 --> 00:29:50.240 align:middle line:84% And so for every point in the support, 00:29:50.240 --> 00:30:00.320 align:middle line:84% I can basically map this to an f of an underlying f of v. 00:30:00.320 --> 00:30:04.250 align:middle line:84% So again, what this shows is that even though we do not 00:30:04.250 --> 00:30:11.155 align:middle line:84% observe all the bids, we can still make progress. 00:30:11.155 --> 00:30:12.780 align:middle line:84% And so what this, of course, also means 00:30:12.780 --> 00:30:16.560 align:middle line:84% is that any order statistic identifies any other order 00:30:16.560 --> 00:30:17.470 align:middle line:90% statistic. 00:30:17.470 --> 00:30:23.640 align:middle line:90% 00:30:23.640 --> 00:30:26.700 align:middle line:84% So I hope this gives you some sense of how people normally 00:30:26.700 --> 00:30:27.740 align:middle line:90% approach this. 00:30:27.740 --> 00:30:30.840 align:middle line:90% So again, here the idea was to-- 00:30:30.840 --> 00:30:35.483 align:middle line:84% just coming back to this once more-- this is theta, 00:30:35.483 --> 00:30:36.900 align:middle line:84% this is the thing that I'm looking 00:30:36.900 --> 00:30:39.540 align:middle line:84% for, this is a known function that I can invert. 00:30:39.540 --> 00:30:44.710 align:middle line:84% So I can express f of v in terms of theta 00:30:44.710 --> 00:30:46.080 align:middle line:90% or known functions of theta. 00:30:46.080 --> 00:30:52.530 align:middle line:90% 00:30:52.530 --> 00:30:56.730 align:middle line:84% OK, so this is really the landmark paper 00:30:56.730 --> 00:30:59.985 align:middle line:84% in this literature, Guerre, Perrigne, and Vuong. 00:30:59.985 --> 00:31:02.490 align:middle line:90% 00:31:02.490 --> 00:31:08.310 align:middle line:84% Think of this as a paper for auctions as BLP is for demand. 00:31:08.310 --> 00:31:13.110 align:middle line:84% This has really created a big literature. 00:31:13.110 --> 00:31:17.333 align:middle line:84% The idea of the paper is, again, similar to these easy steps 00:31:17.333 --> 00:31:18.750 align:middle line:84% that I've just walked you through, 00:31:18.750 --> 00:31:21.780 align:middle line:84% is that we can directly express the unobserved 00:31:21.780 --> 00:31:26.910 align:middle line:84% valuations in terms of things that we observe. 00:31:26.910 --> 00:31:30.210 align:middle line:84% And so I'm not going through all the details here, 00:31:30.210 --> 00:31:33.750 align:middle line:84% but this also works if we do only observe 00:31:33.750 --> 00:31:35.940 align:middle line:90% the winning bid in most cases. 00:31:35.940 --> 00:31:40.080 align:middle line:84% So I promised you I'd come back once more to this first order 00:31:40.080 --> 00:31:45.820 align:middle line:84% condition here from our first-price auction 00:31:45.820 --> 00:31:46.445 align:middle line:90% sealed bidding. 00:31:46.445 --> 00:31:50.160 align:middle line:90% 00:31:50.160 --> 00:31:54.510 align:middle line:84% So if you think about this, it looks pretty daunting, 00:31:54.510 --> 00:31:56.150 align:middle line:90% What we observe are the bids. 00:31:56.150 --> 00:31:59.230 align:middle line:90% 00:31:59.230 --> 00:32:04.900 align:middle line:84% And we know the number of bidders, but we do not know v, 00:32:04.900 --> 00:32:08.140 align:middle line:84% we do not know the distribution of valuations, 00:32:08.140 --> 00:32:11.650 align:middle line:84% and we do not know the derivative of the bidding 00:32:11.650 --> 00:32:13.810 align:middle line:90% function. 00:32:13.810 --> 00:32:19.630 align:middle line:84% You still have the insight that GPV had, 00:32:19.630 --> 00:32:22.090 align:middle line:84% which is that because of the monotonicity of the bidding 00:32:22.090 --> 00:32:27.910 align:middle line:84% function, a percentile of the bid distribution 00:32:27.910 --> 00:32:30.850 align:middle line:84% has to correspond to a percentile of the distribution 00:32:30.850 --> 00:32:32.710 align:middle line:90% of valuations. 00:32:32.710 --> 00:32:35.320 align:middle line:84% OK, so the 20th percentile of bids that are observed 00:32:35.320 --> 00:32:37.300 align:middle line:90% in my data must-- 00:32:37.300 --> 00:32:40.090 align:middle line:84% that percentile must have been submitted by somebody who is 00:32:40.090 --> 00:32:43.726 align:middle line:84% in the 20th percentile of the distribution of valuations. 00:32:43.726 --> 00:32:46.750 align:middle line:90% 00:32:46.750 --> 00:32:51.670 align:middle line:84% So that means that we know that G of b is equal to f of v. 00:32:51.670 --> 00:32:54.790 align:middle line:84% And we also know that G of b is actually given by this object 00:32:54.790 --> 00:33:01.460 align:middle line:84% here, G of the symmetric bidding function of v. 00:33:01.460 --> 00:33:04.010 align:middle line:84% And then you can take the derivative on both sides, 00:33:04.010 --> 00:33:09.710 align:middle line:84% and you get that G of b is equal to f of v times 00:33:09.710 --> 00:33:12.055 align:middle line:84% 1 over the derivative of the bidding function. 00:33:12.055 --> 00:33:15.010 align:middle line:90% 00:33:15.010 --> 00:33:20.650 align:middle line:84% So now you probably see that we can make some progress here. 00:33:20.650 --> 00:33:28.930 align:middle line:84% I can basically replace f of v here by G of b times beta prime. 00:33:28.930 --> 00:33:34.490 align:middle line:84% Beta prime cancels out, and I can replace f of v by G of b. 00:33:34.490 --> 00:33:38.040 align:middle line:90% 00:33:38.040 --> 00:33:43.710 align:middle line:84% And that means that I can-- again, as I said, 00:33:43.710 --> 00:33:46.040 align:middle line:84% this is what is called a constructive approach. 00:33:46.040 --> 00:33:48.660 align:middle line:84% We can express valuations in terms 00:33:48.660 --> 00:33:54.960 align:middle line:84% of bids and distributions, CDFs and PDFs of bids 00:33:54.960 --> 00:33:55.890 align:middle line:90% that we observe. 00:33:55.890 --> 00:33:59.460 align:middle line:84% So all of this here on the right-hand side is theta. 00:33:59.460 --> 00:34:01.360 align:middle line:84% This is the thing that we do not know. 00:34:01.360 --> 00:34:04.290 align:middle line:84% So for each bidder separately, we 00:34:04.290 --> 00:34:07.200 align:middle line:84% can figure out what is that bidder's valuation. 00:34:07.200 --> 00:34:10.781 align:middle line:84% And so this should also make it clear why this is-- 00:34:10.781 --> 00:34:12.989 align:middle line:84% automatically, it implies that it's nonparametrically 00:34:12.989 --> 00:34:18.880 align:middle line:84% identified because we don't place any restrictions. 00:34:18.880 --> 00:34:22.989 align:middle line:84% For every separate bidder, the bid 00:34:22.989 --> 00:34:27.310 align:middle line:84% is exactly rationalized by a specific valuation 00:34:27.310 --> 00:34:29.054 align:middle line:84% that I can back out point by point. 00:34:29.054 --> 00:34:35.449 align:middle line:90% 00:34:35.449 --> 00:34:39.300 align:middle line:84% So this is how this is derived in the paper. 00:34:39.300 --> 00:34:40.500 align:middle line:90% There's an even easier way. 00:34:40.500 --> 00:34:41.833 align:middle line:90% I want to show you this as well. 00:34:41.833 --> 00:34:46.610 align:middle line:84% And once you think about it this way, it's sort of ex-post 00:34:46.610 --> 00:34:49.020 align:middle line:90% obvious that you can do this. 00:34:49.020 --> 00:34:51.800 align:middle line:84% But oftentimes with good papers, they're 00:34:51.800 --> 00:34:54.290 align:middle line:90% ex-post obvious at least. 00:34:54.290 --> 00:34:57.139 align:middle line:84% So there's another way of deriving this. 00:34:57.139 --> 00:35:00.890 align:middle line:84% This, by the way, a trick that's used a lot in IO. 00:35:00.890 --> 00:35:05.820 align:middle line:84% So that's something that generally you should remember. 00:35:05.820 --> 00:35:09.800 align:middle line:84% So we observed the bids in the data, right? 00:35:09.800 --> 00:35:13.040 align:middle line:84% And we are already committed to our assumption 00:35:13.040 --> 00:35:15.890 align:middle line:84% that this is coming from some equilibrium, 00:35:15.890 --> 00:35:18.410 align:middle line:84% So that means that we observed the equilibrium distribution 00:35:18.410 --> 00:35:19.420 align:middle line:90% of bids in the data. 00:35:19.420 --> 00:35:23.640 align:middle line:90% 00:35:23.640 --> 00:35:29.950 align:middle line:84% And at the point where we're willing to stick 00:35:29.950 --> 00:35:35.020 align:middle line:84% to this assumption, we can write down a bid as a problem 00:35:35.020 --> 00:35:37.030 align:middle line:84% instead as what essentially looks 00:35:37.030 --> 00:35:41.230 align:middle line:84% like a single-agent problem, somebody 00:35:41.230 --> 00:35:44.680 align:middle line:84% who's maximizing against this distribution of bids 00:35:44.680 --> 00:35:46.125 align:middle line:90% that's just given by data. 00:35:46.125 --> 00:35:49.840 align:middle line:90% 00:35:49.840 --> 00:35:52.360 align:middle line:84% Because, I mean, that is the assumption that we're making-- 00:35:52.360 --> 00:35:56.930 align:middle line:84% the best responding to some equilibrium distribution 00:35:56.930 --> 00:35:59.240 align:middle line:84% of bids, and we observe what that distribution 00:35:59.240 --> 00:36:02.370 align:middle line:90% is in the data. 00:36:02.370 --> 00:36:09.080 align:middle line:84% And so this allows us to write this down in this way. 00:36:09.080 --> 00:36:12.260 align:middle line:84% And we get-- this is now really simple because we just take 00:36:12.260 --> 00:36:14.960 align:middle line:84% first order conditions and we directly arrive at this 00:36:14.960 --> 00:36:19.830 align:middle line:84% expression here after cancelling out and rearranging. 00:36:19.830 --> 00:36:23.310 align:middle line:84% So this is an idea that's also used 00:36:23.310 --> 00:36:26.340 align:middle line:84% in repeated games and other settings where typically 00:36:26.340 --> 00:36:28.620 align:middle line:90% equilibrium computation is hard. 00:36:28.620 --> 00:36:32.310 align:middle line:84% You say, let's not even try to first build things up 00:36:32.310 --> 00:36:34.590 align:middle line:84% from primitives and then compute from primitives what 00:36:34.590 --> 00:36:36.070 align:middle line:90% the equilibrium looks like. 00:36:36.070 --> 00:36:39.210 align:middle line:84% No, we observe the equilibrium in the data, 00:36:39.210 --> 00:36:41.170 align:middle line:84% so we don't actually need to compute it, 00:36:41.170 --> 00:36:42.380 align:middle line:90% because we already have it. 00:36:42.380 --> 00:36:52.230 align:middle line:90% 00:36:52.230 --> 00:37:00.540 align:middle line:84% So just a brief comment on how you actually do this. 00:37:00.540 --> 00:37:03.250 align:middle line:84% So people don't always follow these steps. 00:37:03.250 --> 00:37:07.650 align:middle line:84% But as you will see later on, in terms of-- 00:37:07.650 --> 00:37:13.620 align:middle line:84% just to remind you what we need to do to compute these v's, bid 00:37:13.620 --> 00:37:15.900 align:middle line:84% by bid-- we have the bids, but we still 00:37:15.900 --> 00:37:19.350 align:middle line:84% need to compute the CDF and the PDF. 00:37:19.350 --> 00:37:21.160 align:middle line:90% What people typically do is-- 00:37:21.160 --> 00:37:22.960 align:middle line:84% of course, the CDF is really easy. 00:37:22.960 --> 00:37:26.580 align:middle line:84% They use kernels for the densities. 00:37:26.580 --> 00:37:29.490 align:middle line:84% Then there are some practical questions 00:37:29.490 --> 00:37:31.980 align:middle line:84% like how to choose a bandwidth, and sometimes you 00:37:31.980 --> 00:37:35.760 align:middle line:84% want to trim in the tails because observations, 00:37:35.760 --> 00:37:36.400 align:middle line:90% they are noisy. 00:37:36.400 --> 00:37:38.610 align:middle line:84% And this term, as you see, because we're 00:37:38.610 --> 00:37:42.360 align:middle line:84% dividing by the densities, can easily 00:37:42.360 --> 00:37:46.170 align:middle line:84% explode if the density becomes very, very small. 00:37:46.170 --> 00:37:48.210 align:middle line:84% And so people sometimes throw away 00:37:48.210 --> 00:37:51.600 align:middle line:90% some observations in the tail. 00:37:51.600 --> 00:37:56.460 align:middle line:84% Standard errors are typically in practice computed via bootstrap 00:37:56.460 --> 00:38:02.980 align:middle line:84% or functions of interest such as the reserve price 00:38:02.980 --> 00:38:10.550 align:middle line:84% counterfactual objects that you get out of these estimates. 00:38:10.550 --> 00:38:14.080 align:middle line:90% Any questions? 00:38:14.080 --> 00:38:14.740 align:middle line:90% Yes. 00:38:14.740 --> 00:38:17.590 align:middle line:84% AUDIENCE: Yeah, so for this one, this specific example, 00:38:17.590 --> 00:38:22.670 align:middle line:84% we still have to go back from observing the highest 00:38:22.670 --> 00:38:27.635 align:middle line:84% bid to the density of the whole bid distribution, right? 00:38:27.635 --> 00:38:28.980 align:middle line:90% TOBIAS SALZ: You may have to. 00:38:28.980 --> 00:38:30.965 align:middle line:84% I mean, it depends on your setting. 00:38:30.965 --> 00:38:33.257 align:middle line:84% AUDIENCE: We're observing only the winning bids, right? 00:38:33.257 --> 00:38:34.048 align:middle line:90% TOBIAS SALZ: Right. 00:38:34.048 --> 00:38:36.420 align:middle line:84% And then you can, of course, map from the winning bid 00:38:36.420 --> 00:38:38.720 align:middle line:84% distribution to the bid distribution. 00:38:38.720 --> 00:38:43.220 align:middle line:84% And you can simulate from that bid distribution. 00:38:43.220 --> 00:38:46.370 align:middle line:90% And with that, you can then-- 00:38:46.370 --> 00:38:46.870 align:middle line:90% yeah. 00:38:46.870 --> 00:38:49.620 align:middle line:90% 00:38:49.620 --> 00:38:53.730 align:middle line:84% OK, so let me comment on this a little bit. 00:38:53.730 --> 00:38:56.280 align:middle line:90% This is really, really simple. 00:38:56.280 --> 00:38:59.550 align:middle line:84% One of my advisor, John Asker, he once 00:38:59.550 --> 00:39:02.585 align:middle line:84% joked that his most famous paper is probably 00:39:02.585 --> 00:39:04.210 align:middle line:84% the one on bidding rings that uses GPV. 00:39:04.210 --> 00:39:06.640 align:middle line:84% And he said he could have done that paper in Excel. 00:39:06.640 --> 00:39:08.820 align:middle line:84% And I think it's a bit of an exaggeration, 00:39:08.820 --> 00:39:12.570 align:middle line:84% but this is something that is so easy. 00:39:12.570 --> 00:39:14.020 align:middle line:90% I think Excel has kernels. 00:39:14.020 --> 00:39:18.240 align:middle line:84% You can probably compute valuations in Excel 00:39:18.240 --> 00:39:21.300 align:middle line:90% if you wanted to. 00:39:21.300 --> 00:39:23.933 align:middle line:84% And if you compare this to this process 00:39:23.933 --> 00:39:25.350 align:middle line:84% that I walked you through earlier, 00:39:25.350 --> 00:39:27.850 align:middle line:84% that's, of course, a great improvement. 00:39:27.850 --> 00:39:30.658 align:middle line:90% 00:39:30.658 --> 00:39:34.190 align:middle line:84% It has this advantage that it does not rely on functional form 00:39:34.190 --> 00:39:36.970 align:middle line:90% restrictions. 00:39:36.970 --> 00:39:40.990 align:middle line:84% And as I said, this has been a very influential paper, many, 00:39:40.990 --> 00:39:45.670 align:middle line:84% many different extensions to multi-unit auctions-- 00:39:45.670 --> 00:39:47.920 align:middle line:90% very similar ideas apply. 00:39:47.920 --> 00:39:51.700 align:middle line:84% If you have dynamics, you can still typically make 00:39:51.700 --> 00:39:52.930 align:middle line:90% a lot of progress. 00:39:52.930 --> 00:39:57.040 align:middle line:84% I'm going to talk about Athey, Levin, and Seira 00:39:57.040 --> 00:39:59.110 align:middle line:84% and some really interesting applications 00:39:59.110 --> 00:40:04.810 align:middle line:84% of using it to quantify the damages of bidding rings. 00:40:04.810 --> 00:40:10.300 align:middle line:84% The maybe criticism not of this paper but of the literature 00:40:10.300 --> 00:40:14.320 align:middle line:84% is that, well, the IPV assumptions 00:40:14.320 --> 00:40:16.780 align:middle line:90% are really, really convenient. 00:40:16.780 --> 00:40:20.770 align:middle line:84% And that leads people oftentimes to use the IPV assumption 00:40:20.770 --> 00:40:22.690 align:middle line:84% because they know how to make progress. 00:40:22.690 --> 00:40:27.910 align:middle line:84% And in many settings, we believe that maybe there 00:40:27.910 --> 00:40:31.160 align:middle line:90% is a common value component. 00:40:31.160 --> 00:40:34.330 align:middle line:84% Bidders do not know what they're really bidding for. 00:40:34.330 --> 00:40:36.250 align:middle line:84% And oftentimes, there are resale markets 00:40:36.250 --> 00:40:40.570 align:middle line:84% or other reasons why we believe that a common value 00:40:40.570 --> 00:40:42.810 align:middle line:90% problem may arise. 00:40:42.810 --> 00:40:46.800 align:middle line:90% 00:40:46.800 --> 00:40:49.440 align:middle line:84% So that's just something to keep in mind. 00:40:49.440 --> 00:40:52.260 align:middle line:84% Maybe one more comment on this, actually. 00:40:52.260 --> 00:40:55.560 align:middle line:84% So you may now wonder, well, if we 00:40:55.560 --> 00:41:00.480 align:middle line:84% believe that common values are an element of common values 00:41:00.480 --> 00:41:05.050 align:middle line:84% in many settings, why hasn't the literature done more 00:41:05.050 --> 00:41:05.800 align:middle line:90% in this direction? 00:41:05.800 --> 00:41:10.230 align:middle line:84% So it turns out that if you follow the same steps that I 00:41:10.230 --> 00:41:12.570 align:middle line:84% just walked you through, we basically 00:41:12.570 --> 00:41:15.090 align:middle line:90% have mapped one distribution-- 00:41:15.090 --> 00:41:17.460 align:middle line:84% we have identified one distribution of valuations 00:41:17.460 --> 00:41:20.500 align:middle line:84% from one observed distribution of bids. 00:41:20.500 --> 00:41:22.020 align:middle line:84% That means, loosely speaking, we're 00:41:22.020 --> 00:41:28.040 align:middle line:84% just identified in terms of backing out this unobserved 00:41:28.040 --> 00:41:29.660 align:middle line:90% distribution of valuations. 00:41:29.660 --> 00:41:31.370 align:middle line:84% In a common value setting, there are 00:41:31.370 --> 00:41:33.428 align:middle line:90% two things that you don't know. 00:41:33.428 --> 00:41:35.720 align:middle line:84% There is the distribution of underlying true valuations 00:41:35.720 --> 00:41:36.840 align:middle line:90% for the object. 00:41:36.840 --> 00:41:38.870 align:middle line:84% And then there's the distribution 00:41:38.870 --> 00:41:43.460 align:middle line:84% of signals that captures the uncertainty that-- 00:41:43.460 --> 00:41:47.750 align:middle line:84% with which bidders are forecasting what 00:41:47.750 --> 00:41:49.290 align:middle line:90% the valuation is going to be. 00:41:49.290 --> 00:41:51.320 align:middle line:84% And these are two unobserved objects, 00:41:51.320 --> 00:41:54.020 align:middle line:84% but you still only observe one distribution of bids. 00:41:54.020 --> 00:41:56.150 align:middle line:84% So you're fundamentally underidentified 00:41:56.150 --> 00:41:58.070 align:middle line:90% in these settings. 00:41:58.070 --> 00:42:01.520 align:middle line:84% And so that's why you see many often-- 00:42:01.520 --> 00:42:04.590 align:middle line:90% even when it's kind of a-- 00:42:04.590 --> 00:42:10.930 align:middle line:84% the people sticking to the IPV assumption. 00:42:10.930 --> 00:42:19.450 align:middle line:84% So let me now talk about a really interesting application 00:42:19.450 --> 00:42:22.815 align:middle line:90% by Athey, Levin, and Seira. 00:42:22.815 --> 00:42:26.600 align:middle line:90% 00:42:26.600 --> 00:42:33.290 align:middle line:84% The question that the paper asks is, should we use sealed bid 00:42:33.290 --> 00:42:35.665 align:middle line:90% or open auction format? 00:42:35.665 --> 00:42:38.240 align:middle line:90% 00:42:38.240 --> 00:42:44.000 align:middle line:84% So just to remind you, in some instances, 00:42:44.000 --> 00:42:46.040 align:middle line:84% the theory tells us it shouldn't matter. 00:42:46.040 --> 00:42:48.830 align:middle line:84% Because of revenue equivalence, the seller 00:42:48.830 --> 00:42:52.860 align:middle line:90% should be equally well off. 00:42:52.860 --> 00:42:56.550 align:middle line:84% But, again, there are many things 00:42:56.550 --> 00:42:58.710 align:middle line:84% that we believe are very plausible to occur 00:42:58.710 --> 00:43:02.550 align:middle line:84% in the real world, such as bidder asymmetries, collusion, 00:43:02.550 --> 00:43:08.740 align:middle line:84% risk aversion, and so on, that may break this result. 00:43:08.740 --> 00:43:11.630 align:middle line:84% So this is what they're basically asking. 00:43:11.630 --> 00:43:15.790 align:middle line:84% Well, if we actually test this in the real world, what do 00:43:15.790 --> 00:43:16.690 align:middle line:90% we find? 00:43:16.690 --> 00:43:18.880 align:middle line:84% And they look at this in a setting 00:43:18.880 --> 00:43:23.740 align:middle line:84% that-- you see a lot of timber applications 00:43:23.740 --> 00:43:27.940 align:middle line:84% in the early auction literature that there were some great data 00:43:27.940 --> 00:43:30.140 align:middle line:90% available from the government. 00:43:30.140 --> 00:43:32.463 align:middle line:84% This turned out to be a fairly large industry. 00:43:32.463 --> 00:43:34.880 align:middle line:84% If you're accounting for both the logging and the milling, 00:43:34.880 --> 00:43:37.720 align:middle line:84% it's about $100 billion industry-- 00:43:37.720 --> 00:43:40.510 align:middle line:90% $100 billion a year industry. 00:43:40.510 --> 00:43:43.720 align:middle line:84% And again, there's this tight link between policy 00:43:43.720 --> 00:43:48.730 align:middle line:84% and the setting and the game that we 00:43:48.730 --> 00:43:52.960 align:middle line:84% are estimating because the government typically puts up 00:43:52.960 --> 00:43:57.700 align:middle line:90% tracts of land up for auction. 00:43:57.700 --> 00:44:01.570 align:middle line:84% And then loggers or mills are bidding on these tracts. 00:44:01.570 --> 00:44:05.260 align:middle line:84% So the way this works is that they inspect or cruise 00:44:05.260 --> 00:44:07.550 align:middle line:84% this tract and look at what is there. 00:44:07.550 --> 00:44:12.220 align:middle line:84% And then tracts of lands are auctioned off. 00:44:12.220 --> 00:44:15.460 align:middle line:84% And they have data from what they 00:44:15.460 --> 00:44:18.130 align:middle line:84% call the northern regions, the Idaho-Montana border 00:44:18.130 --> 00:44:19.930 align:middle line:90% and California. 00:44:19.930 --> 00:44:22.870 align:middle line:84% What is really, really nice about this setting 00:44:22.870 --> 00:44:26.110 align:middle line:84% is that the US Forest Service uses 00:44:26.110 --> 00:44:28.660 align:middle line:90% both open and sealed bidding. 00:44:28.660 --> 00:44:33.090 align:middle line:84% And in some instances, even randomly so, it appears. 00:44:33.090 --> 00:44:37.390 align:middle line:90% 00:44:37.390 --> 00:44:40.420 align:middle line:84% The other thing that makes this interesting 00:44:40.420 --> 00:44:42.370 align:middle line:84% but also complicates things is that there 00:44:42.370 --> 00:44:49.300 align:middle line:84% has been a widespread suspicion, believed by not just theorists 00:44:49.300 --> 00:44:52.210 align:middle line:84% but by practitioners in this industry, 00:44:52.210 --> 00:44:57.545 align:middle line:84% that open auctions foster collusion. 00:44:57.545 --> 00:44:59.170 align:middle line:84% Actually, Congress at some point passed 00:44:59.170 --> 00:45:02.890 align:middle line:84% a law that says that all these tracts should be 00:45:02.890 --> 00:45:05.150 align:middle line:84% should be auctioned off by sealed bidding. 00:45:05.150 --> 00:45:08.260 align:middle line:84% And then, later on, they started making exceptions. 00:45:08.260 --> 00:45:10.870 align:middle line:84% And it turns out that the large bidders in this industry 00:45:10.870 --> 00:45:13.430 align:middle line:84% really favored the open auction format. 00:45:13.430 --> 00:45:14.980 align:middle line:90% And you can guess why. 00:45:14.980 --> 00:45:17.960 align:middle line:84% Maybe it's a bit easier to monitor who is doing what. 00:45:17.960 --> 00:45:20.710 align:middle line:84% And that makes it easier for bidders to collude. 00:45:20.710 --> 00:45:25.450 align:middle line:84% So collusion is something that has to be kind of accounted 00:45:25.450 --> 00:45:25.965 align:middle line:90% for here. 00:45:25.965 --> 00:45:28.910 align:middle line:90% 00:45:28.910 --> 00:45:32.540 align:middle line:84% So what they do is they write down 00:45:32.540 --> 00:45:36.830 align:middle line:84% a model that captures some salient features 00:45:36.830 --> 00:45:38.570 align:middle line:90% of this industry. 00:45:38.570 --> 00:45:41.360 align:middle line:84% One salient feature that I told you about 00:45:41.360 --> 00:45:44.370 align:middle line:84% is that the government uses both auction formats. 00:45:44.370 --> 00:45:47.930 align:middle line:84% So they actually have to think about equilibrium behavior, 00:45:47.930 --> 00:45:51.440 align:middle line:84% both in open and sealed bid auctions. 00:45:51.440 --> 00:45:52.940 align:middle line:84% The other really salient features 00:45:52.940 --> 00:45:57.040 align:middle line:84% is that they're loggers and mills. 00:45:57.040 --> 00:46:00.650 align:middle line:84% Mills are basically bidders that have some production 00:46:00.650 --> 00:46:06.380 align:middle line:84% capacity of their own, so they can refine and work 00:46:06.380 --> 00:46:07.790 align:middle line:90% with the timber. 00:46:07.790 --> 00:46:10.100 align:middle line:84% Whereas loggers, they actually first have 00:46:10.100 --> 00:46:12.690 align:middle line:84% to find a buyer in the form of a mill. 00:46:12.690 --> 00:46:16.160 align:middle line:90% So they have to pay-- 00:46:16.160 --> 00:46:19.220 align:middle line:84% they have to take an extra cut because they 00:46:19.220 --> 00:46:21.450 align:middle line:90% have to sell it to mills first. 00:46:21.450 --> 00:46:24.770 align:middle line:84% And so what they're assuming is that loggers are 00:46:24.770 --> 00:46:27.300 align:middle line:90% weaker bidders in this setting. 00:46:27.300 --> 00:46:30.090 align:middle line:84% And precisely, they assume that the hazard rate 00:46:30.090 --> 00:46:32.880 align:middle line:84% of the value of a mill's valuations 00:46:32.880 --> 00:46:34.355 align:middle line:90% dominates the ones of loggers. 00:46:34.355 --> 00:46:39.005 align:middle line:90% 00:46:39.005 --> 00:46:41.383 align:middle line:84% This is a setting where there is variation 00:46:41.383 --> 00:46:42.550 align:middle line:90% how many people are bidding. 00:46:42.550 --> 00:46:46.950 align:middle line:84% So they're accounting for endogenous entry. 00:46:46.950 --> 00:46:51.390 align:middle line:84% And they're searching for an equilibrium in type symmetric 00:46:51.390 --> 00:46:52.810 align:middle line:90% entry and bidding strategies. 00:46:52.810 --> 00:46:57.000 align:middle line:90% So loggers and mills-- 00:46:57.000 --> 00:46:59.010 align:middle line:84% so conditioning on loggers, they all 00:46:59.010 --> 00:47:01.200 align:middle line:84% use the same entry probability and bid 00:47:01.200 --> 00:47:03.480 align:middle line:84% once they're entering according to the same bidding 00:47:03.480 --> 00:47:06.225 align:middle line:90% function, and same for Mills. 00:47:06.225 --> 00:47:08.920 align:middle line:90% 00:47:08.920 --> 00:47:12.340 align:middle line:84% Two more assumptions that they're making is, first of all, 00:47:12.340 --> 00:47:14.310 align:middle line:90% mills are not just stronger. 00:47:14.310 --> 00:47:16.150 align:middle line:84% They're basically sufficiently strong 00:47:16.150 --> 00:47:19.990 align:middle line:84% so that your mills are always entering first. 00:47:19.990 --> 00:47:24.160 align:middle line:84% So basically, the profits of mills 00:47:24.160 --> 00:47:28.540 align:middle line:84% with an extra mill entering are still larger 00:47:28.540 --> 00:47:30.760 align:middle line:84% than the profits of loggers if there 00:47:30.760 --> 00:47:32.950 align:middle line:90% is no such additional entrant. 00:47:32.950 --> 00:47:36.970 align:middle line:84% And they make this assumption to reduce 00:47:36.970 --> 00:47:38.440 align:middle line:90% the number of equilibrium. 00:47:38.440 --> 00:47:43.570 align:middle line:84% And the second assumption is that only mills are colluding. 00:47:43.570 --> 00:47:48.130 align:middle line:84% So to the extent that there may be collusive equilibria, 00:47:48.130 --> 00:47:50.970 align:middle line:84% they're only coming from mills colluding with each other, 00:47:50.970 --> 00:47:54.520 align:middle line:84% maybe because these are players that have been in the market 00:47:54.520 --> 00:47:55.030 align:middle line:90% for longer. 00:47:55.030 --> 00:47:58.840 align:middle line:84% And for them, it's easier to meet repeatedly and organize 00:47:58.840 --> 00:48:01.320 align:middle line:90% this collusion. 00:48:01.320 --> 00:48:09.360 align:middle line:84% So they get a number of predictions out of the model. 00:48:09.360 --> 00:48:11.460 align:middle line:84% So the first one is that they get 00:48:11.460 --> 00:48:15.210 align:middle line:84% a unique type symmetric entry equilibrium, where 00:48:15.210 --> 00:48:20.400 align:middle line:84% either no loggers enter or all mills enter. 00:48:20.400 --> 00:48:27.600 align:middle line:84% So in other words, what we cannot have is that we see 00:48:27.600 --> 00:48:30.898 align:middle line:84% a logger entering, but not all of the mills enter. 00:48:30.898 --> 00:48:32.440 align:middle line:84% And that's because of this assumption 00:48:32.440 --> 00:48:38.230 align:middle line:84% that profits are sufficiently higher 00:48:38.230 --> 00:48:41.550 align:middle line:84% to overcome an additional bidder in the auction. 00:48:41.550 --> 00:48:45.320 align:middle line:90% 00:48:45.320 --> 00:48:50.090 align:middle line:84% So then the key question of interest, to remind you, 00:48:50.090 --> 00:48:53.090 align:middle line:84% is, should the government be using opened or sealed 00:48:53.090 --> 00:48:56.430 align:middle line:90% bidding in these auctions? 00:48:56.430 --> 00:49:00.370 align:middle line:84% And here are some comparisons of these two auction formats. 00:49:00.370 --> 00:49:03.930 align:middle line:84% The model tells us that in open auctions 00:49:03.930 --> 00:49:05.550 align:middle line:84% relative to sealed auctions, loggers 00:49:05.550 --> 00:49:11.630 align:middle line:84% are less likely to enter, mills are more likely to enter, 00:49:11.630 --> 00:49:16.810 align:middle line:84% and it is less likely that a logger will win. 00:49:16.810 --> 00:49:21.530 align:middle line:90% 00:49:21.530 --> 00:49:24.590 align:middle line:84% So just to explain this a little bit, 00:49:24.590 --> 00:49:29.240 align:middle line:84% this goes back to result in the auction literature that's 00:49:29.240 --> 00:49:32.510 align:middle line:84% well known by Maskin and Riley, which 00:49:32.510 --> 00:49:36.410 align:middle line:84% is that if you have asymmetric bidders, 00:49:36.410 --> 00:49:40.040 align:middle line:84% the weaker bidders tend to bid more aggressively. 00:49:40.040 --> 00:49:42.140 align:middle line:84% So in this case, they would be bidding 00:49:42.140 --> 00:49:45.200 align:middle line:84% higher markups over their valuations 00:49:45.200 --> 00:49:48.730 align:middle line:90% than stronger bidders. 00:49:48.730 --> 00:49:51.638 align:middle line:84% And so this means that sometimes-- first of all, 00:49:51.638 --> 00:49:53.930 align:middle line:84% it means that sometimes the auction can be inefficient. 00:49:53.930 --> 00:49:56.153 align:middle line:84% It doesn't actually award the object 00:49:56.153 --> 00:49:57.820 align:middle line:84% to the bidder with the highest valuation 00:49:57.820 --> 00:50:00.945 align:middle line:84% because the weaker bidders are bidding a higher markup. 00:50:00.945 --> 00:50:04.290 align:middle line:90% 00:50:04.290 --> 00:50:07.920 align:middle line:84% And it also means that the sealed auction format 00:50:07.920 --> 00:50:11.610 align:middle line:84% is more attractive to weaker bidders 00:50:11.610 --> 00:50:13.350 align:middle line:84% because in the open auction format, 00:50:13.350 --> 00:50:16.290 align:middle line:84% everybody just sticks in up to their valuation. 00:50:16.290 --> 00:50:18.720 align:middle line:84% And it's going to be efficient, and, more likely than not, 00:50:18.720 --> 00:50:20.490 align:middle line:84% because of the assumption that mills are stronger, 00:50:20.490 --> 00:50:21.500 align:middle line:90% a mill is going to win. 00:50:21.500 --> 00:50:25.294 align:middle line:90% 00:50:25.294 --> 00:50:28.150 align:middle line:84% So that's basically-- the explanation 00:50:28.150 --> 00:50:30.580 align:middle line:84% for these comparative static results 00:50:30.580 --> 00:50:33.990 align:middle line:84% is this result by Maskin and Riley. 00:50:33.990 --> 00:50:39.010 align:middle line:90% 00:50:39.010 --> 00:50:43.690 align:middle line:84% Lastly, they get some other competitive static 00:50:43.690 --> 00:50:45.980 align:middle line:84% by comparing in the open auction format. 00:50:45.980 --> 00:50:48.760 align:middle line:84% So they only consider collusion in the open auction. 00:50:48.760 --> 00:50:54.160 align:middle line:84% In the open auction format, comparing it to-- 00:50:54.160 --> 00:50:58.290 align:middle line:84% comparing collusive and noncollusive equilibria, 00:50:58.290 --> 00:51:01.600 align:middle line:84% and so here it's not too surprising that if only mills 00:51:01.600 --> 00:51:05.320 align:middle line:84% are colluding-- and remember, they're all antisymmetric-- 00:51:05.320 --> 00:51:07.000 align:middle line:84% so with some probability, each mill 00:51:07.000 --> 00:51:11.890 align:middle line:84% is going to benefit from collusion and being designated-- 00:51:11.890 --> 00:51:14.200 align:middle line:84% Sorry, one thing I forgot to mention, I should say, 00:51:14.200 --> 00:51:16.250 align:middle line:84% is what they assume is perfect collusion. 00:51:16.250 --> 00:51:19.420 align:middle line:84% So the mill with the highest valuation 00:51:19.420 --> 00:51:23.200 align:middle line:84% is going to be designated the winner. 00:51:23.200 --> 00:51:25.570 align:middle line:84% And all the other mills are not bidding 00:51:25.570 --> 00:51:29.460 align:middle line:84% to keep the price for the winning mill low. 00:51:29.460 --> 00:51:33.190 align:middle line:90% 00:51:33.190 --> 00:51:36.210 align:middle line:84% So because mills are antisymmetric, 00:51:36.210 --> 00:51:38.800 align:middle line:84% there's always some chance benefit from collusion. 00:51:38.800 --> 00:51:42.130 align:middle line:84% That means that collusive equilibrium make this even more 00:51:42.130 --> 00:51:43.250 align:middle line:90% attractive for mills. 00:51:43.250 --> 00:51:45.000 align:middle line:84% So mills are going to be more likely enter 00:51:45.000 --> 00:51:48.750 align:middle line:90% and crowding out loggers. 00:51:48.750 --> 00:51:54.740 align:middle line:90% 00:51:54.740 --> 00:52:01.350 align:middle line:84% So now we have some predictions from the model. 00:52:01.350 --> 00:52:05.010 align:middle line:84% So again, to remind you what's really nice in this setting 00:52:05.010 --> 00:52:09.330 align:middle line:84% is that the government, sometimes seemingly random, 00:52:09.330 --> 00:52:14.040 align:middle line:84% designates tracts either for sealed or for open auction 00:52:14.040 --> 00:52:14.830 align:middle line:90% bidding. 00:52:14.830 --> 00:52:17.100 align:middle line:84% And they run this regression here 00:52:17.100 --> 00:52:20.280 align:middle line:84% where they're regressing outcomes of interest 00:52:20.280 --> 00:52:24.540 align:middle line:84% on a sealed indicator plus a bunch of controls, 00:52:24.540 --> 00:52:27.450 align:middle line:84% including in some regressions the number of bidders 00:52:27.450 --> 00:52:29.000 align:middle line:90% that are in the auction. 00:52:29.000 --> 00:52:31.810 align:middle line:90% 00:52:31.810 --> 00:52:35.050 align:middle line:84% And they do this separately by the northern regions 00:52:35.050 --> 00:52:38.890 align:middle line:90% and in California. 00:52:38.890 --> 00:52:42.250 align:middle line:84% The reason that this matters is that the northern regions are-- 00:52:42.250 --> 00:52:45.030 align:middle line:84% there's more suspicion that there's collusive behavior here. 00:52:45.030 --> 00:52:48.530 align:middle line:90% 00:52:48.530 --> 00:52:52.340 align:middle line:84% And the other reason is that those are actually-- they 00:52:52.340 --> 00:52:54.720 align:middle line:84% claim that those are more likely to be randomly assigned. 00:52:54.720 --> 00:52:57.140 align:middle line:90% But that's just an aside. 00:52:57.140 --> 00:53:02.720 align:middle line:84% So what they find is consistent with what the model predicts 00:53:02.720 --> 00:53:05.330 align:middle line:84% is that in the sealed bidding format, 00:53:05.330 --> 00:53:08.100 align:middle line:90% more loggers are entering. 00:53:08.100 --> 00:53:14.010 align:middle line:84% There is no significant effect on mill entry. 00:53:14.010 --> 00:53:19.050 align:middle line:84% And so the fraction of loggers in the auction 00:53:19.050 --> 00:53:22.930 align:middle line:84% goes up in the sealed bidding format. 00:53:22.930 --> 00:53:28.400 align:middle line:84% Loggers are more likely to win, but this is not-- 00:53:28.400 --> 00:53:31.920 align:middle line:84% these effects are not significant. 00:53:31.920 --> 00:53:36.180 align:middle line:84% And the prices in the northern regions 00:53:36.180 --> 00:53:40.290 align:middle line:84% are significantly higher, both when 00:53:40.290 --> 00:53:43.470 align:middle line:84% accounting for the number of bidders and even-- sorry, 00:53:43.470 --> 00:53:45.690 align:middle line:84% without accounting for the number of bidders, 00:53:45.690 --> 00:53:47.110 align:middle line:90% you get more entrants. 00:53:47.110 --> 00:53:51.090 align:middle line:84% We know that more entrants are good for sellers. 00:53:51.090 --> 00:53:53.400 align:middle line:84% But even conditioning on the number of bidders, 00:53:53.400 --> 00:53:55.320 align:middle line:84% they find that the sealed bidding 00:53:55.320 --> 00:53:56.570 align:middle line:90% format leads to higher prices. 00:53:56.570 --> 00:54:02.170 align:middle line:90% 00:54:02.170 --> 00:54:05.380 align:middle line:84% Largely similar predictions for California, 00:54:05.380 --> 00:54:09.160 align:middle line:84% with the exception that there is no effect on prices 00:54:09.160 --> 00:54:10.770 align:middle line:84% here from the sealed bidding format. 00:54:10.770 --> 00:54:15.280 align:middle line:90% 00:54:15.280 --> 00:54:19.150 align:middle line:84% OK, so in other words, they find support 00:54:19.150 --> 00:54:22.660 align:middle line:84% for the predictions of the model, 00:54:22.660 --> 00:54:26.410 align:middle line:84% that the sealed bidding favors weaker bidders, leads 00:54:26.410 --> 00:54:29.890 align:middle line:84% to more entry of those bidders, and at least, in some settings, 00:54:29.890 --> 00:54:35.400 align:middle line:84% the sealed bidding format seems to benefit the seller. 00:54:35.400 --> 00:54:39.210 align:middle line:84% The second takeaway is that maybe there's 00:54:39.210 --> 00:54:43.920 align:middle line:84% something strange going on in the northern sales 00:54:43.920 --> 00:54:48.360 align:middle line:84% because the sealed bidding format leads to higher prices, 00:54:48.360 --> 00:54:50.975 align:middle line:84% perhaps because it shuts down this collusion channel. 00:54:50.975 --> 00:54:55.876 align:middle line:90% 00:54:55.876 --> 00:54:59.350 align:middle line:84% So with this in mind, what they do is 00:54:59.350 --> 00:55:02.080 align:middle line:84% they now want to quantify the model. 00:55:02.080 --> 00:55:05.260 align:middle line:84% And they follow the steps of GPV. 00:55:05.260 --> 00:55:06.980 align:middle line:84% I'll not go through the details here. 00:55:06.980 --> 00:55:08.985 align:middle line:84% So they need to do this for asymmetric bidders. 00:55:08.985 --> 00:55:11.920 align:middle line:90% 00:55:11.920 --> 00:55:14.950 align:middle line:84% And they deviate slightly from what 00:55:14.950 --> 00:55:17.590 align:middle line:84% I told you people would normally recommend that you 00:55:17.590 --> 00:55:19.390 align:middle line:90% do to estimate a kernel. 00:55:19.390 --> 00:55:24.100 align:middle line:84% They actually estimate a parametric function for bids. 00:55:24.100 --> 00:55:26.320 align:middle line:90% But these are just details. 00:55:26.320 --> 00:55:30.370 align:middle line:84% One thing that they do that I do want to mention-- 00:55:30.370 --> 00:55:32.620 align:middle line:84% although I'm not talking about the details here; 00:55:32.620 --> 00:55:34.180 align:middle line:84% we're going to do this in [14.]273-- 00:55:34.180 --> 00:55:39.650 align:middle line:84% is you could be in many settings worried about common values. 00:55:39.650 --> 00:55:41.650 align:middle line:84% But yet another thing you could be worried about 00:55:41.650 --> 00:55:45.280 align:middle line:84% is that there's something that all the bidders are actually 00:55:45.280 --> 00:55:46.010 align:middle line:90% observing. 00:55:46.010 --> 00:55:48.380 align:middle line:84% So they do not have any uncertainty about this 00:55:48.380 --> 00:55:52.190 align:middle line:84% but the econometrician does not observe. 00:55:52.190 --> 00:55:56.630 align:middle line:84% So maybe there's some tracts here in the setting where, 00:55:56.630 --> 00:55:59.630 align:middle line:84% I don't know, there's a steep incline or something that 00:55:59.630 --> 00:56:06.890 align:middle line:84% makes it much more difficult to log the trees. 00:56:06.890 --> 00:56:09.500 align:middle line:84% The bidders all know this, but this might not necessarily 00:56:09.500 --> 00:56:12.730 align:middle line:90% be recorded in our data. 00:56:12.730 --> 00:56:15.730 align:middle line:84% So that means that you find that the bids from one auction 00:56:15.730 --> 00:56:19.370 align:middle line:90% to another are correlated. 00:56:19.370 --> 00:56:21.590 align:middle line:84% And if you do not account for the fact 00:56:21.590 --> 00:56:24.590 align:middle line:84% that the bidders all observed this and take this into account, 00:56:24.590 --> 00:56:28.550 align:middle line:84% you might be overstating the allocative efficiency 00:56:28.550 --> 00:56:30.980 align:middle line:84% of auctions because you load all this heterogeneity 00:56:30.980 --> 00:56:33.823 align:middle line:90% as cross-bidder heterogeneity. 00:56:33.823 --> 00:56:35.240 align:middle line:84% You're not accounting for the fact 00:56:35.240 --> 00:56:37.130 align:middle line:84% that some auctions look really good, 00:56:37.130 --> 00:56:39.800 align:middle line:84% some auctions are really bad, and the average prices 00:56:39.800 --> 00:56:42.890 align:middle line:84% in each auction are accounting for that. 00:56:42.890 --> 00:56:44.326 align:middle line:90% Yes. 00:56:44.326 --> 00:56:47.450 align:middle line:84% AUDIENCE: What are the timing of the auctions for the tracts? 00:56:47.450 --> 00:56:49.890 align:middle line:84% Are they occurring simultaneously? 00:56:49.890 --> 00:56:51.920 align:middle line:84% Is there kind of like a continuous time 00:56:51.920 --> 00:56:54.500 align:middle line:84% aspect that the tracts to open up in the auction? 00:56:54.500 --> 00:56:56.750 align:middle line:84% So I guess the question is, how much does it 00:56:56.750 --> 00:57:01.852 align:middle line:84% become a multi-unit auction versus not? 00:57:01.852 --> 00:57:04.798 align:middle line:84% TOBIAS SALZ: I mean, so I don't know exactly how 00:57:04.798 --> 00:57:06.090 align:middle line:90% the timing works, to be honest. 00:57:06.090 --> 00:57:09.380 align:middle line:90% But there are many auctions. 00:57:09.380 --> 00:57:14.780 align:middle line:84% And this goes-- there are potential dynamics that 00:57:14.780 --> 00:57:15.720 align:middle line:90% result from that. 00:57:15.720 --> 00:57:19.610 align:middle line:84% So I think Susan and others they have or maybe Pat Bajari, 00:57:19.610 --> 00:57:23.840 align:middle line:84% they have a paper on capacity constraints of bidders 00:57:23.840 --> 00:57:26.280 align:middle line:84% or other dynamic things that may matter. 00:57:26.280 --> 00:57:29.210 align:middle line:84% So they occur frequently enough that these kinds of things 00:57:29.210 --> 00:57:31.405 align:middle line:90% might potentially be relevant. 00:57:31.405 --> 00:57:31.905 align:middle line:90% Yeah. 00:57:31.905 --> 00:57:35.470 align:middle line:90% 00:57:35.470 --> 00:57:37.130 align:middle line:84% I hope that answers your question. 00:57:37.130 --> 00:57:41.170 align:middle line:90% 00:57:41.170 --> 00:57:42.170 align:middle line:90% Where was I? 00:57:42.170 --> 00:57:45.310 align:middle line:84% OK, I was talking about this unobserved auction-specific 00:57:45.310 --> 00:57:46.460 align:middle line:90% heterogeneity. 00:57:46.460 --> 00:57:51.190 align:middle line:84% Again, I might see that there's a tract with low-quality wood 00:57:51.190 --> 00:57:54.740 align:middle line:84% and every bidder appropriately prices this in. 00:57:54.740 --> 00:57:58.870 align:middle line:84% And so there's basically a way to account 00:57:58.870 --> 00:58:02.920 align:middle line:84% for this that comes out of the nonlinear measurement error 00:58:02.920 --> 00:58:03.860 align:middle line:90% literature. 00:58:03.860 --> 00:58:08.050 align:middle line:84% The key paper here is the one by Li and Vuong. 00:58:08.050 --> 00:58:11.770 align:middle line:84% And this has been extended to asymmetric auctions 00:58:11.770 --> 00:58:13.450 align:middle line:90% by Krasnokutskaya. 00:58:13.450 --> 00:58:16.240 align:middle line:84% So this basically allows to account for the fact 00:58:16.240 --> 00:58:18.730 align:middle line:84% that there are systematic differences across auctions 00:58:18.730 --> 00:58:21.830 align:middle line:90% that bidders do not account for. 00:58:21.830 --> 00:58:24.190 align:middle line:84% And that, again, matters because otherwise you 00:58:24.190 --> 00:58:27.440 align:middle line:84% would say that this heterogeneity is across bidders. 00:58:27.440 --> 00:58:32.800 align:middle line:84% And then that would give us oftentimes very, very wrong 00:58:32.800 --> 00:58:36.015 align:middle line:84% estimates for, let's say, the efficiency of an auction. 00:58:36.015 --> 00:58:40.180 align:middle line:90% 00:58:40.180 --> 00:58:42.820 align:middle line:90% They estimate optimal entry-- 00:58:42.820 --> 00:58:44.380 align:middle line:84% and something really neat that they 00:58:44.380 --> 00:58:46.780 align:middle line:84% do that I want to discuss a little bit 00:58:46.780 --> 00:58:54.520 align:middle line:84% is they estimate only based on sealed bidding using GPV to have 00:58:54.520 --> 00:58:55.580 align:middle line:90% the open-auction format. 00:58:55.580 --> 00:58:57.080 align:middle line:84% They have the sealed bidding format. 00:58:57.080 --> 00:58:59.350 align:middle line:84% They only estimate based on sealed bidding, 00:58:59.350 --> 00:59:04.650 align:middle line:84% but they generate predictions for both auction formats. 00:59:04.650 --> 00:59:06.810 align:middle line:84% So that is a really strong test if you 00:59:06.810 --> 00:59:08.077 align:middle line:90% think about it of the model. 00:59:08.077 --> 00:59:12.360 align:middle line:90% 00:59:12.360 --> 00:59:14.910 align:middle line:84% You're estimating the valuations based on sealed bidding, 00:59:14.910 --> 00:59:19.930 align:middle line:84% and you generate predictions for the open auction. 00:59:19.930 --> 00:59:25.100 align:middle line:84% So let's see kind of how well they're doing. 00:59:25.100 --> 00:59:32.570 align:middle line:84% So here is-- here's a table that compares separately 00:59:32.570 --> 00:59:34.940 align:middle line:84% for the northern sales in California, 00:59:34.940 --> 00:59:39.300 align:middle line:84% the out-of-sample performance of their models. 00:59:39.300 --> 00:59:43.300 align:middle line:84% So they have some holdout auctions. 00:59:43.300 --> 00:59:47.060 align:middle line:84% And they simulate outcomes for this holdout auction 00:59:47.060 --> 00:59:49.550 align:middle line:84% from their model and compare it to what actually 00:59:49.550 --> 00:59:50.970 align:middle line:90% happened in those auctions. 00:59:50.970 --> 00:59:53.870 align:middle line:84% And then they do this for a sealed bid. 00:59:53.870 --> 00:59:57.110 align:middle line:84% So holding the mechanism on which they estimate constant, 00:59:57.110 --> 00:59:59.450 align:middle line:84% and they also do this for the open auction 00:59:59.450 --> 01:00:03.240 align:middle line:84% format, which they actually never use for estimation. 01:00:03.240 --> 01:00:05.950 align:middle line:90% 01:00:05.950 --> 01:00:10.630 align:middle line:84% So what they find here is you can go through this-- 01:00:10.630 --> 01:00:12.770 align:middle line:84% so the big picture is for sealed bids, 01:00:12.770 --> 01:00:14.440 align:middle line:84% the model does really, really well, 01:00:14.440 --> 01:00:16.900 align:middle line:90% as we would typically expect. 01:00:16.900 --> 01:00:18.710 align:middle line:90% If you think about-- 01:00:18.710 --> 01:00:22.420 align:middle line:84% if you think back to what we did in GPV, 01:00:22.420 --> 01:00:27.170 align:middle line:84% we rationalized each bid exactly, 01:00:27.170 --> 01:00:29.450 align:middle line:84% by finding a valuation that matches each bid exactly. 01:00:29.450 --> 01:00:32.780 align:middle line:84% So you would actually think that if you follow exactly 01:00:32.780 --> 01:00:35.210 align:middle line:84% all the steps, then your model should predict 01:00:35.210 --> 01:00:37.910 align:middle line:90% exactly what is happening. 01:00:37.910 --> 01:00:41.340 align:middle line:84% Here, there's some things that deviate a little bit from this. 01:00:41.340 --> 01:00:44.180 align:middle line:84% They put a parametric distribution on the bid, 01:00:44.180 --> 01:00:46.070 align:middle line:90% so that might-- 01:00:46.070 --> 01:00:54.140 align:middle line:84% that could introduce some prediction error. 01:00:54.140 --> 01:01:00.410 align:middle line:84% But what they basically find is that the average bid is very 01:01:00.410 --> 01:01:04.110 align:middle line:90% close to what is predicted. 01:01:04.110 --> 01:01:08.910 align:middle line:84% And that's true whether or not you account for entry. 01:01:08.910 --> 01:01:13.530 align:middle line:84% Same for the average revenue is very close to what is predicted. 01:01:13.530 --> 01:01:19.010 align:middle line:84% And your average logger entry is almost exactly-- 01:01:19.010 --> 01:01:22.910 align:middle line:90% I mean, is exactly spot on. 01:01:22.910 --> 01:01:25.250 align:middle line:84% And just very briefly, if you look 01:01:25.250 --> 01:01:28.460 align:middle line:84% at sealed bids for California, the same is true. 01:01:28.460 --> 01:01:31.800 align:middle line:84% So logger entry is predicted perfectly. 01:01:31.800 --> 01:01:37.340 align:middle line:84% You get very close values for average bids. 01:01:37.340 --> 01:01:39.650 align:middle line:84% And I guess average revenue in California 01:01:39.650 --> 01:01:41.730 align:middle line:90% is somewhat overpredicted. 01:01:41.730 --> 01:01:46.010 align:middle line:90% 01:01:46.010 --> 01:01:51.170 align:middle line:84% So let me actually stick to this slide for a second. 01:01:51.170 --> 01:01:57.780 align:middle line:84% For the open auction format, and I find this amazing, 01:01:57.780 --> 01:02:04.430 align:middle line:84% they also predict, at least for the case 01:02:04.430 --> 01:02:07.850 align:middle line:84% of California, the average sales price and entry very, 01:02:07.850 --> 01:02:10.910 align:middle line:90% very closely. 01:02:10.910 --> 01:02:13.030 align:middle line:90% So again, this is a pretty-- 01:02:13.030 --> 01:02:15.560 align:middle line:84% I haven't seen this done in many papers. 01:02:15.560 --> 01:02:17.645 align:middle line:84% This is a pretty strong test of the model, 01:02:17.645 --> 01:02:19.270 align:middle line:84% that you take it to a different setting 01:02:19.270 --> 01:02:23.040 align:middle line:84% and then see how well it performs there. 01:02:23.040 --> 01:02:26.102 align:middle line:90% 01:02:26.102 --> 01:02:30.380 align:middle line:84% What they then do is because there was suspicion of collusion 01:02:30.380 --> 01:02:34.700 align:middle line:84% in the northern sales, they also generate 01:02:34.700 --> 01:02:38.060 align:middle line:84% for the open auction format predictions 01:02:38.060 --> 01:02:41.000 align:middle line:90% from a collusive model-- 01:02:41.000 --> 01:02:43.370 align:middle line:84% the way they generate a collusive model is 01:02:43.370 --> 01:02:47.877 align:middle line:84% to take a simulation, draw the highest valuation 01:02:47.877 --> 01:02:49.710 align:middle line:84% bidder is going to be designated the winner. 01:02:49.710 --> 01:02:51.910 align:middle line:90% The other mills are not-- 01:02:51.910 --> 01:02:55.520 align:middle line:90% are bidding zero. 01:02:55.520 --> 01:03:00.350 align:middle line:84% And so that leads to much, much lower prices. 01:03:00.350 --> 01:03:02.960 align:middle line:84% And in fact, so much so that they, 01:03:02.960 --> 01:03:07.520 align:middle line:84% even for the northern sales, where the collusion was 01:03:07.520 --> 01:03:09.680 align:middle line:84% potentially an issue, underpredict 01:03:09.680 --> 01:03:13.070 align:middle line:84% the average sales price by about a third. 01:03:13.070 --> 01:03:18.110 align:middle line:84% But they do also reject the competitive model 01:03:18.110 --> 01:03:20.720 align:middle line:84% for the case of the northern sales. 01:03:20.720 --> 01:03:25.140 align:middle line:84% So in this instance, they're rejecting both models. 01:03:25.140 --> 01:03:28.530 align:middle line:84% And so what they then argue is that maybe what best 01:03:28.530 --> 01:03:31.200 align:middle line:84% explains the data is a moderate form of collusion, where 01:03:31.200 --> 01:03:33.600 align:middle line:84% some of the mills are colluding or some of the mills 01:03:33.600 --> 01:03:37.170 align:middle line:90% are colluding some of the time. 01:03:37.170 --> 01:03:41.430 align:middle line:90% So kind of my-- 01:03:41.430 --> 01:03:44.810 align:middle line:84% my view on this paper, this is a very complete and well-done 01:03:44.810 --> 01:03:45.310 align:middle line:90% paper. 01:03:45.310 --> 01:03:48.780 align:middle line:84% In fact, it does so many things that I didn't have time 01:03:48.780 --> 01:03:50.530 align:middle line:90% to talk about all of them. 01:03:50.530 --> 01:03:53.760 align:middle line:84% But it has taken a pretty big bite out of the apple. 01:03:53.760 --> 01:03:58.230 align:middle line:84% Many following papers do focus on one aspect, collusion 01:03:58.230 --> 01:04:01.380 align:middle line:90% or entry. 01:04:01.380 --> 01:04:05.220 align:middle line:84% And here, they do many of these things together. 01:04:05.220 --> 01:04:12.510 align:middle line:84% And it's basically theory testing plus a setting 01:04:12.510 --> 01:04:15.210 align:middle line:84% where you can use some random variation 01:04:15.210 --> 01:04:21.780 align:middle line:84% to be pretty confident that the model that you're selecting 01:04:21.780 --> 01:04:24.130 align:middle line:84% is the right one, plus then the structural exercise. 01:04:24.130 --> 01:04:26.862 align:middle line:84% So this is pretty good blueprint for a job market paper 01:04:26.862 --> 01:04:29.320 align:middle line:84% because it has kind of all these different things in there. 01:04:29.320 --> 01:04:33.770 align:middle line:90% 01:04:33.770 --> 01:04:37.550 align:middle line:84% So maybe some things that one could complain about, again, 01:04:37.550 --> 01:04:39.380 align:middle line:90% is this a private value setting? 01:04:39.380 --> 01:04:44.970 align:middle line:84% Certainly there are resale markets for the timber. 01:04:44.970 --> 01:04:50.120 align:middle line:84% And so that, in itself, introduces a common value aspect 01:04:50.120 --> 01:04:56.653 align:middle line:84% because everybody can sell at that resale market price. 01:04:56.653 --> 01:04:58.070 align:middle line:84% And maybe there's some uncertainty 01:04:58.070 --> 01:05:01.460 align:middle line:84% about the quality of the timber or how difficult 01:05:01.460 --> 01:05:06.410 align:middle line:90% it is to get it. 01:05:06.410 --> 01:05:08.480 align:middle line:84% And then the other question is, can we 01:05:08.480 --> 01:05:10.520 align:middle line:84% attribute part of this effect that we 01:05:10.520 --> 01:05:13.880 align:middle line:84% see that the sealed bidding format generates much higher 01:05:13.880 --> 01:05:17.720 align:middle line:90% revenue to risk aversion? 01:05:17.720 --> 01:05:22.430 align:middle line:90% And so I want to use my last-- 01:05:22.430 --> 01:05:23.600 align:middle line:90% I'm going a bit fast today. 01:05:23.600 --> 01:05:29.000 align:middle line:84% But I'm going to use my last minutes 01:05:29.000 --> 01:05:34.220 align:middle line:84% to talk about another paper by Yunmi Kong, who 01:05:34.220 --> 01:05:36.980 align:middle line:84% was my classmate in grad school, which 01:05:36.980 --> 01:05:43.820 align:middle line:84% thinks about risk aversion in open and sealed bid auctions. 01:05:43.820 --> 01:05:46.410 align:middle line:84% So the setting here is a very different setting. 01:05:46.410 --> 01:05:50.670 align:middle line:84% It's the Permian Basin in New Mexico. 01:05:50.670 --> 01:05:53.660 align:middle line:90% So the Permian Basin is a big-- 01:05:53.660 --> 01:05:55.580 align:middle line:84% one of the most productive oil fields 01:05:55.580 --> 01:06:01.960 align:middle line:84% in the world that spans New Mexico and the west of Texas. 01:06:01.960 --> 01:06:07.510 align:middle line:84% And here we have many smaller firms, 01:06:07.510 --> 01:06:10.960 align:middle line:84% oftentimes operated by just a few people, 01:06:10.960 --> 01:06:18.270 align:middle line:84% that lease land from the government and that rent 01:06:18.270 --> 01:06:23.340 align:middle line:84% equipment-- here you see an oil rig in this setting-- 01:06:23.340 --> 01:06:26.610 align:middle line:84% that rent equipment, and basically, 01:06:26.610 --> 01:06:29.640 align:middle line:84% through these auctions from the New Mexico State and Land Lease 01:06:29.640 --> 01:06:36.360 align:middle line:84% Office, get the land, and try their luck and drill for oil. 01:06:36.360 --> 01:06:40.950 align:middle line:84% And so what they're bidding on is a lump sum bonus. 01:06:40.950 --> 01:06:43.230 align:middle line:84% And then for the time that they're renting, 01:06:43.230 --> 01:06:47.560 align:middle line:84% they have to pay royalties and a rental rate. 01:06:47.560 --> 01:06:54.170 align:middle line:84% What's nice is that, as in the previous paper, it seems that-- 01:06:54.170 --> 01:06:55.780 align:middle line:90% So the government uses both. 01:06:55.780 --> 01:06:58.570 align:middle line:84% Or the New Mexico State Land Office 01:06:58.570 --> 01:07:00.740 align:middle line:84% uses both open and sealed bidding again. 01:07:00.740 --> 01:07:03.340 align:middle line:84% So we can get a similar comparison 01:07:03.340 --> 01:07:07.270 align:middle line:84% as before in a very different setting. 01:07:07.270 --> 01:07:12.700 align:middle line:84% And if you stare at the map of how these formats are spatially 01:07:12.700 --> 01:07:15.730 align:middle line:84% distributed, this is open, this is sealed, 01:07:15.730 --> 01:07:19.220 align:middle line:90% it looks pretty random. 01:07:19.220 --> 01:07:24.020 align:middle line:84% So again, we can use basically with some controls 01:07:24.020 --> 01:07:26.960 align:middle line:84% the fact that this looks almost random to look 01:07:26.960 --> 01:07:32.410 align:middle line:84% at the effect of different auction formats. 01:07:32.410 --> 01:07:35.650 align:middle line:90% So here's what she finds. 01:07:35.650 --> 01:07:38.500 align:middle line:90% 01:07:38.500 --> 01:07:42.040 align:middle line:84% As before for the northern sales, 01:07:42.040 --> 01:07:47.710 align:middle line:84% sealed bidding leads with a bunch of controls for oil prices 01:07:47.710 --> 01:07:52.600 align:middle line:84% and differences of these tracts of land leads to about 30% 01:07:52.600 --> 01:07:56.325 align:middle line:84% higher revenue than the open auction format. 01:07:56.325 --> 01:08:03.250 align:middle line:90% 01:08:03.250 --> 01:08:06.730 align:middle line:84% The other really interesting observation that she makes 01:08:06.730 --> 01:08:12.790 align:middle line:84% is she compares the distribution of prices 01:08:12.790 --> 01:08:16.000 align:middle line:90% across open and sealed bidding. 01:08:16.000 --> 01:08:19.930 align:middle line:84% So here are the histograms put on top of each other. 01:08:19.930 --> 01:08:25.905 align:middle line:84% And you see for the open auction format this big spike here. 01:08:25.905 --> 01:08:29.054 align:middle line:90% 01:08:29.054 --> 01:08:32.260 align:middle line:84% So the reason this happens is that oftentimes bidder enter 01:08:32.260 --> 01:08:34.420 align:middle line:84% the open auction format, they're discovering 01:08:34.420 --> 01:08:37.125 align:middle line:84% they're the only bidder, they're bidding the reserve price. 01:08:37.125 --> 01:08:40.569 align:middle line:90% 01:08:40.569 --> 01:08:42.970 align:middle line:84% Interestingly, although the distribution 01:08:42.970 --> 01:08:46.540 align:middle line:84% of the number of bidders for the sealed bid auctions 01:08:46.540 --> 01:08:50.770 align:middle line:84% is almost identical, and there are many auctions that also only 01:08:50.770 --> 01:08:53.475 align:middle line:84% have one bidder, we do not see such a mass point. 01:08:53.475 --> 01:08:57.191 align:middle line:90% 01:08:57.191 --> 01:09:01.543 align:middle line:84% So what this suggests is that the bidders do not 01:09:01.543 --> 01:09:03.960 align:middle line:84% know how many other bidders are going to be in the auction 01:09:03.960 --> 01:09:06.327 align:middle line:84% when they engage in sealed bidding. 01:09:06.327 --> 01:09:08.160 align:middle line:84% So they have uncertainty, and they basically 01:09:08.160 --> 01:09:10.710 align:middle line:84% want to insure themselves against competitors 01:09:10.710 --> 01:09:14.850 align:middle line:84% by bidding higher than what they would 01:09:14.850 --> 01:09:18.488 align:middle line:84% if they were the only bidder, even though with some chance 01:09:18.488 --> 01:09:20.030 align:middle line:84% they are going to be the only bidder. 01:09:20.030 --> 01:09:24.120 align:middle line:90% 01:09:24.120 --> 01:09:29.310 align:middle line:84% So this observation together with the previous observation 01:09:29.310 --> 01:09:36.000 align:middle line:84% that the revenue for sealed bid auction seems to be higher 01:09:36.000 --> 01:09:43.420 align:middle line:84% leads Yunmi to conclude that risk aversion is probably 01:09:43.420 --> 01:09:45.029 align:middle line:90% the explanation for this. 01:09:45.029 --> 01:09:50.819 align:middle line:84% The reason is that uncertainty is revenue 01:09:50.819 --> 01:09:59.580 align:middle line:84% neutral for the seller but only if the bidders are-- sorry, 01:09:59.580 --> 01:10:02.065 align:middle line:84% if the bidders are risk neutral, then 01:10:02.065 --> 01:10:03.690 align:middle line:84% uncertainty about the number of bidders 01:10:03.690 --> 01:10:07.800 align:middle line:84% is going to be revenue neutral for the seller. 01:10:07.800 --> 01:10:09.490 align:middle line:90% And that's not what we observe. 01:10:09.490 --> 01:10:12.320 align:middle line:84% So that's a theoretical prediction from Harstad, Kagel, 01:10:12.320 --> 01:10:14.340 align:middle line:90% and another Levin. 01:10:14.340 --> 01:10:16.320 align:middle line:90% And that's not what we observe. 01:10:16.320 --> 01:10:17.820 align:middle line:84% We see higher revenue for the seller 01:10:17.820 --> 01:10:19.410 align:middle line:84% from the sealed bid auction, which 01:10:19.410 --> 01:10:23.613 align:middle line:84% is consistent with this idea that bidders insuring themselves 01:10:23.613 --> 01:10:25.530 align:middle line:84% against competition in the sealed bid auctions 01:10:25.530 --> 01:10:29.100 align:middle line:90% by bidding higher. 01:10:29.100 --> 01:10:34.500 align:middle line:84% So I think this is a clever detective 01:10:34.500 --> 01:10:40.757 align:middle line:84% work to make the case that even when companies are competing 01:10:40.757 --> 01:10:42.840 align:middle line:84% against each other, where we typically assume risk 01:10:42.840 --> 01:10:45.270 align:middle line:84% neutrality, at least in this setting, where 01:10:45.270 --> 01:10:47.250 align:middle line:84% many of the companies are small, it 01:10:47.250 --> 01:10:50.250 align:middle line:84% seems to be that risk aversion plays a big role 01:10:50.250 --> 01:10:54.090 align:middle line:84% and leads to higher revenue for the seller and sealed bid 01:10:54.090 --> 01:10:55.580 align:middle line:90% auctions. 01:10:55.580 --> 01:11:01.040 align:middle line:84% And she then goes on to show that the model, 01:11:01.040 --> 01:11:03.740 align:middle line:84% a model with risk aversion, where now you not just have 01:11:03.740 --> 01:11:05.990 align:middle line:84% to identify the underlying distribution of valuations, 01:11:05.990 --> 01:11:09.260 align:middle line:84% you also need to identify the level of risk aversion 01:11:09.260 --> 01:11:13.610 align:middle line:84% and privacy-- like I said we just identified in the standard 01:11:13.610 --> 01:11:14.900 align:middle line:90% case-- 01:11:14.900 --> 01:11:19.490 align:middle line:84% so here she basically uses both the open bidding format 01:11:19.490 --> 01:11:21.500 align:middle line:84% and the sealed bidding format together 01:11:21.500 --> 01:11:25.730 align:middle line:84% to show that you can identify the distribution of valuations 01:11:25.730 --> 01:11:30.410 align:middle line:84% of bidders as well as the level of risk aversion. 01:11:30.410 --> 01:11:32.520 align:middle line:84% So it's a nice paper that's in RAND. 01:11:32.520 --> 01:11:36.720 align:middle line:90% 01:11:36.720 --> 01:11:40.380 align:middle line:90% OK, ending early. 01:11:40.380 --> 01:11:42.570 align:middle line:90% That's all I have for today. 01:11:42.570 --> 01:11:48.660 align:middle line:84% I hope I see many of you next semester in [14.]273, 01:11:48.660 --> 01:11:53.630 align:middle line:84% where we dive deeper into all of these topics. 01:11:53.630 --> 01:12:06.000 align:middle line:90%