Three essays on experimetrics

Public good games have been popularly studied in the last three decades. The data from repeated public good games are panel data. Each individual has a time series which may exhibit different pattern from each other. Generally, three patterns are considered: increasing, decreasing or fluctuating. Serial and cross-sectional correlation all exist: Subject's current decision is correlated with his and the other peer's previous choices. For these complex data, none of the traditional methods allows us to estimate the treatment effect accurately. My dissertation is focused on solving this problem and providing meaningful empirical evidence.;In the first essay, titled Treatment Effect Estimation under Multiple Equilibriums in Repeated Public Good Games, coauthored with Dr. Donggyu Sul, we propose a pre-test for multiple equilibria and a simple treatment effect estimation method. When there exist multiple equilibria in repeated public good games, estimating the treatment effects is not straightforward. Usually conventional methods including standard z-score, Tobit regression, and Sul (2013)'s trend regression fail to estimate the treatment effects under multiple equilibria. The single equilibrium test is based on the idea that the cross sectional variance should be increasing if there are multiple equilibria, and it relies on a misspecified regression which can distinguish the single and multiple equilibrium cases well however. The treatment effect estimation proposed is sequential but effective. A clustering algorithm which allows us to identify each individual's membership is suggested. The newly proposed tests have good finite sample properties and perform well in practice. The methods suggested in this paper can be widely used in various settings of public good games. From a simple experiment where experimentalists want to examine the average treatment effects to a complicated experiment where experimentalists want to see the evolution of multiple equilibria, the proposed test can provide a simple but accurate empirical result.;The second essay of my dissertation, titled Empirical Evidence of Multiple Equilibria in Repeated Public Good Experiments, applies the new methods to experimental data and provides some meaningful empirical results. Existence of multiple equilibria in repeated public good experiments is a matter of concern to both experimental and theoretical economists. Some economic theorists predict the existence of multiple equilibria when a certain factor of the experiment changes, but no empirical evidence has been provided to support or test these predictions. This paper fills in this gap by providing empirical evidence of multiple equilibria for the factors Marginal per Capital Return (MPCR), group size, punishment.;The evolution of equilibrium type is also detected as factor level changes. When MPCR is low to median all subjects choose the subgame perfect Nash outcomes, whereas when MPCR increases to a high level, multiple equilibria are observed. Multiple equilibria also occur in large groups while Nash single equilibrium occurs in small groups. As the severity of punishment increases, the equilibrium type of the game changes from Nash equilibrium to multiple equilibria to Pareto equilibrium.