Chinatown
In the 1974 motion picture Chinatown the private investigator J. J. “Jake” Gites (Jack Nicholson) is involved in a conspiracy that involved corruption, deceit and “family secrets.” The goal of the conspirators consisted on buying the lands of unsuspected farmers in the Owens Valley (some 400 miles north of Los Angeles) and then building an aqueduct to bring the water to the city, where it would be worth a fortune. Although, this description is fictional and far from reality, there is much controversy on the way the city of L.A. purchase the water and land rights in the Owens Valley.
The goal of the project is to gather individual unpublished detailed data of all the purchases of land and water rights (1905-1934). With the individual data we will be able to assess whether the prices paid were “fair.” We will also assess why some farmers and not others were able to organize in sellers’ pools. Finally, we will test whether the city of L.A. established a purchasing pattern of “checkers,” thereby isolating farmers’ properties in order to buy them later at a lower price.
Plots bought by Los Angeles 1920-1934.
War Games
The model used in the estimation is similar to a “centipede” game. The classical centipede game is in discrete time and players take turns, and we have a continuous-time simultaneous-move game. Nevertheless, the intuition is the same, the longer your opponent stays, the more you both can get, but you want to be the one who exits.
The specific results are based on Espín-Sánchez and Catepillan (2020). There we generalize War of Attrition games by allowing heterogeneity, externalities and time-changing values. We characterize all equilibria into four categories based on two properties. Moreover, we show how our results could be applied in many applied settings such an information externalities in R&D, Market Exit dynamics and economies of agglomeration.
Asymmetric Order Statistics
Given the general heterogeneity and externalities that we allowed in the model, the estimation required huge amounts of computing power. The main difficulty was that we are interested in the value functions and strategies for all players, but we only observe the exit of the player we exited first. In other words, we observe the minimum of a set of random variables that follow asymmetric distributions.
Luckily for us, in Espín-Sánchez and Wu (2020), we characterize the probability distribution of asymmetric order statistics for proportional hazard rate models. Moreover, we show that the distribution has a closed-form solution and corresponds to the weighted average of the individual distributions. With this result, we can estimate the first stage of out estimation procedure in a few hours. Without the procedure the computing power was so demanding that we would not estimate our model for games with more than five players.
- “Order Statistics from Independent Non-Identical Exponentiated and Proportional Hazard Rate Random Variables,” with Tianhao Wu
We are extremely grateful to Tianhao Wu and Salvador Gil for their excellent work. We also want to thank Saul Downie, Cayley Geffen, Qiwei He, Nicholas Kelly, Arjun Prakash, and specially Yagmur Yuksel,for their invaluable help.