ECON 3039 Labor Economics By Elliott Fan Economics, NTU Elliott Fan: Labor 2015 Fall Lecture 21

Fruitless comparisons (1) Elliott Fan: Labor 2015 Fall Lecture 22 KMT’s vs DPP’s performance in economic growth Can you make an inference from this table that KMT outperformed DPP? If no, why? StartEndAverage annual growth DPP14,519 (2001)18,131 (2008)3.11% KMT18,131 (2008)23,374 (2015)3.86%

Fruitless comparisons (2) Elliott Fan: Labor 2015 Fall Lecture 23 Textbook’s example:

Elliott Fan: Labor 2015 Fall Lecture 24 Treatment effect on Khuzdar: Treatment effect on Maria: Since we can only observe one of the two outcomes for each player, we have no choice but using one as another’s counterfactual outcome. That is: Fruitless comparisons (2)

Elliott Fan: Labor 2015 Fall Lecture 25 Treatment effect on Khuzdar: Treatment effect on Maria: Since we can only observe one of the two outcomes for each player, we have no choice but using one as another’s counterfactual outcome. That is: Fruitless comparisons (2)

A better comparison Elliott Fan: Labor 2015 Fall Lecture 26

A better comparison Question: Does attending a private university in the US raise income (relative to attending a public one)? Simple comparison of the average income for the five individuals attending private schools (92,000) and the four attending public schools (72,500) is potentially biased. Elliott Fan: Labor 2015 Fall Lecture 27

A better comparison We categorize the students into four groups defined by the set of schools to which they applied and were admitted to. (I) A comparison of A1+A2 and A3 shows that the return to attending private school is -5,000 (II) A comparison of B1 and B2 suggests that the return to attending private school is -30,000 Unweighted average of (I) and (II) is 12,500 Weighted average of (I) and (II) is 9,000 Elliott Fan: Labor 2015 Fall Lecture 28

A better comparison What can we learn from the two different comparisons? Apple-to-apple or orange-to-orange comparisons are what we need. Elliott Fan: Labor 2015 Fall Lecture 29

From comparison to regressions Consider a regression function: Elliott Fan: Labor 2015 Fall Lecture 210

From a small sample to a large one Consider a regression function: Elliott Fan: Labor 2015 Fall Lecture 211

Elliott Fan: Labor 2015 Fall Lecture 212

Rubin Causal Model (RCM) Elliott Fan: Labor 2015 Fall Lecture 213 This is called Robin’s “Potential Outcomes” framework

Rubin Causal Model (RCM) Elliott Fan: Labor 2015 Fall Lecture 214 The Evaluation Problem / Fundamental Problem of Causal Inference: It is impossible to observe both Y 1 and Y 0 Holland (1986): “fundamental problem of causal inference” Others: “The Evaluation Problem” Implication: We must always make assumptions to make inferences.

Rubin Causal Model (RCM) Elliott Fan: Labor 2015 Fall Lecture 215 Imbens and Wooldridge (2009) assessment of this framework See their JEL paper, p. 10. They offer five advantages of this framework. It allows us to define causal effects before specifying the assignment mechanism, and without making functional form or distributional assumptions. It links the analysis of causal effects to explicit manipulations It separates the modeling of the potential outcomes from that of the assignment mechanism. It allows us to formulate probabilistic assumptions in terms of potentially observable variables, rather than in terms of unobserved components. It clarifies where the uncertainty in the estimators comes from.

Elliott Fan: Labor 2015 Fall Lecture 216 Actually, we can rearrange the equation Selection bias arises because we employed an outcome that deviates from the counterfactual to make the comparison Introducing selection bias

Average treatment effect (ATT) Elliott Fan: Labor 2015 Fall Lecture 217 Let’s formalize it using group means Average treatment effect on the treated (ATT) A naïve comparison of those insured and those uninsured: Q: What do we observe? What don’t we observe?

Selection bias Elliott Fan: Labor 2015 Fall Lecture 218 Examples: 1.Education on earnings 2.Health insurance on infant health 3.Any other examples?

Selection bias Elliott Fan: Labor 2015 Fall Lecture 219 Regression expression of selection bias: Q: What’s the assumption needed to eliminate the selection bias?

Selection bias and randomized trials Elliott Fan: Labor 2015 Fall Lecture 220 A randomized trail, or randomized controlled trial (RCT), is a type of scientific experiment, where the people being studied are randomly allocated into the treatment and control groups under study. Intuition: randomized selection implies that the treatment and control groups share the same observables and unobservables on average. This implies: Thus, selection bias is removed.

Selection bias and randomized trials Elliott Fan: Labor 2015 Fall Lecture 221 How does a randomized trial eliminate the selection bias? In terms of RCM

Selection bias Elliott Fan: Labor 2015 Fall Lecture 222

Experiments: important examples Elliott Fan: Labor 2015 Fall Lecture 223