# Causal Effects Model 的估計

## ==Causal Effects 估計範例==

in Angrist and Pischke (2017, JEP, p130-132)，主要提出觀念的是 Dale and Kruger (2002, QJE)

Casusal Effect: 在申請入學時，同時接到私大和州大入學許可，但最後後選擇唸私大、或州大的學生為樣本：

Yi: 全部的樣本的畢業生所得，可觀察的，其中又分為兩類

Y1i : 第 i 個樣本的「受私校教育後」所得

Y0i : 第 i 個樣本的「受州校教育後」所得

Pi: ＝1 if 第 i 個樣本唸私立，＝0 otherwise 唸州立大學

Y10 : 第 i 個樣本的原來能力

Y1i – Y0i

H0 : E(Y1i – Y0i) = β>0

Y0i ＝α + ηi

α 為學生原來的潛力， ηi是誤差，或個別差異，這個個別差異會和選私校有關係，例如家庭背景、爸媽是否畢業於私立..。
Caussal-Effect model

Yi = α+βPi+ηi

Pi 和 ηi 是(統計上)不獨立的，也就是無法滿足迴歸上原來的獨立性要求。

E(ηi|Pi,Xi) = E(ηi|Xi)

E(ηi|Pi,Xi) = E(ηi|Xi) = E(ηi|Xi)

Yi=α+βPi+γXi+ηi

==ref==

Angrist, Joshua D., and Jörn-Steffen Pischke. “Undergraduate econometrics instruction: through our classes, darkly." Journal of Economic Perspectives, 31.2 (2017): 125-44.

Dale, Stacy Berg, and Alan B. Krueger. “Estimating the payoff to attending a more selective college: An application of selection on observables and unobservables." The Quarterly Journal of Economics, 117.4 (2002): 1491-1527.

# On the Determinants of Cooperation in Infinitely Repeated Games: A Survey

Pedro Dal Bó and Guillaume R. Fréchette

A growing experimental literature studies the determinants of cooperation in infinitely repeated games, tests different predictions of the theory, and suggests an empirical solution to the problem of multiple equilibria. To provide a robust description of the literature’s findings, we gather and analyze a metadata set of experiments on infinitely repeated prisoner’s dilemma games. The experimental data show that cooperation is affected by infinite repetition and is more likely to arise when it can be supported in equilibrium. However, the fact that cooperation can be supported in equilibrium does not imply that most subjects will cooperate. High cooperation rates will emerge only when the parameters of the repeated game are such that cooperation is very robust to strategic uncertainty. We also review the results regarding the effect of imperfect monitoring, changing partners, and personal characteristics on cooperation and the strategies used to support it.
Full-Text Access | Supplementary Materials

# New directions for modelling strategic behavior: Game-theoretic models of communication, coordination, and cooperation in economic relationships

Crawford, Vincent P. “New directions for modelling strategic behavior: Game-theoretic models of communication, coordination, and cooperation in economic relationships." Journal of Economic Perspectives 30.4 (2016): 131-50.

## ==original Abstract==

In this paper, I discuss the state of progress in applications of game theory in economics and try to identify possible future developments that are likely to yield further progress. To keep the topic manageable, I focus on a canonical economic problem that is inherently game-theoretic, that of fostering efficient coordination and cooperation in relationships, with particular attention to the role of communication. I begin with an overview of noncooperative game theory’s principal model of behavior, Nash equilibrium. I next discuss the alternative “thinking" and “learning" rationales for how real-world actors might reach equilibrium decisions. I then review how Nash equilibrium has been used to model coordination, communication, and cooperation in relationships, and discuss possible developments