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)

他們想估計美國唸私立大學和唸公立大學的差異，用較明確的因果關係為主的估計法。

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

以上兩個，令

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

合理的假設是，每個人在受大學教育之前，原本就有一定的能力

Y10 : 第 i 個樣本的原來能力
重點：美國私立大學教學效果，是否來自教學，還是學生的本質。

因為好學生集中去唸名私校，所以畢業後收入高，不見得是私校的努力。這個稱為 selection bias 樣本選擇偏誤。

私校的教學效果 (用大概畢業20年後的 earning 來衡量) 之差異為：

Y1i – Y0i

若教學有效的話，然後差異的平均是 β

H0 : E(Y1i – Y0i) = β>0

假設E(Y0i) = α, 即

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。

這個 causal-effect model 的想法創新就在此，他們提出比較不嚴格的「條件獨立性假設」(conditional independence assumption)，

E(ηi|Pi,Xi) = E(ηi|Xi)

所以要找其它的可能影響畢業後所得能力的變數 X (例如 SAT 的分數…)，又稱為控制變數 control variable，來加入估計，觀念上是

E(ηi|Pi,Xi) = E(ηi|Xi) = γXi

所以， causal-effect model 最後就變成

Yi=α+βPi+γXi+ηi

此法可建構出 unbiased 和 consistent 的 β 估計，而且它有明確的意義：唸私校和唸公校的「效果差異」平均值。
==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.

URL：http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.30.4.131

==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