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Policy Evaluation

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Lecture number:
23
Pages:
1
Type:
Lecture Note
School:
Cornell University
Course:
Econ 3120 - Applied Econometrics
Edition:
1

Unformatted text preview:

Econ 3120 1st Edition Lecture 23 Outline of Last Lecture I. Dependent Variable Errors Outline of Current Lecture II. Policy Evaluation Current Lecture Introduction Econometrics is a useful tool to help us understand the effects of policies on outcomes of interest. E.g., • Effect of health insurance coverage on health outcomes • Effect of minimum wages on employment • Effect of schooling reforms on student test scores In order to analyze the impacts of policy, we need to take causality very seriously. We’re going start with the very basic model: Yi = β0 +β1Ti +εi where Yi is the outcome of interest for individual i and Ti ∈ {1,0} indicates whether the individual has faced the policy. Using the zero conditional mean assumption and taking expectations, it can be shown that β1 = E(Yi |T = 1)−E(Yi |T = 0) and ˆβ1 = E(Yid|T = 1)−E(Yid|T = 0) where E(Yid|T = 1) and E(Yid|T = 0) are the the average Yi over all observations where T = 1 and T = 0, respectively. In what follows, we’re going to add some notation to more fully understand when β1 represents the true causal effect of T on Y. 1 2 Rubin’s Causal Model 2.1 Definitions Let’s take a step back and introduce some new terminology. As above we are looking at the effect of a single policy on a particular outcome Y. An individual can be in one of two states, T = 1, where the individual faces the policy, or T = 0, where the individual doesn’t face the policy. We can write thest two potential outcomes as: Y1i = individual i’s outcome under the policy Y0i = individual i’s outcome under no policy The key thing to understand is that we can only observe one of these two outcomes for each individual. We are thinking about outcomes measured at the same time. An individual either faces the policy or not. I often refer to the possible situations as “states of the world.” One of these is an actual outcome, and one is a counterfactual outcome. Now, we can define the causal effect of the policy on individual i as Y1i −Y0i . In words, this is outcome in the state of the world where the individual faces the policy minus the outcome in the state of the world where the individual does not face the policy. The first thing to note is that there is no way to know what the effect of Y1i −Y0i is for sure. Never. You can’t observe two states of the world at the same time. 2.2 Average causal effects Even though the effect of a policy on an individual can never be measured, we can use statistics and econometrics to estimate the average causal effect over a population. Define the average causal effect over a population as E(Y1i)−E(Y0i). Here the expectation operator is exactly the way we’ve been defining it. We just can’t estimate the expectations yet because we can’t get data ...


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