Counterfactual Analysis

Estimate D Y

Counterfactual Analyses The problem of conventional analyses by using observed data E [ 𝑌 1 − 𝑌 0 ] the average treatment effect ex: whether going to college influences individuals’ wage Take whether going to college influences individuals’ wage as an example. We usually assume what we get from models is the average treatment effect. That means if individuals go to college their wage increase by a certain amount. However, the counterfactual analyses point out that the interpretation might be incorrect since we just compare wages between people who have college degree and people who do not have college degree. We do not compare the same individuals under the different situations. That might cause bias due to selection since people in treatment group and control group are different. Selection !!

Counterfactual Analyses Decomposition Observed 𝜋 is just the proportion of population. It is in the formula since the proportion might influence the We can skip first to make everything simple. Unobserved

Counterfactual Analyses Decomposition The average treatment effect Baseline Bias = 0 Baseline bias results from that we assume no difference between those is the treatment group and the control group when the treatment is absent. Differential treatment effect bias results from no difference between those in the treatment group and the control group when the treatment happens. Again take college and wage as an example. The average treatment effect means having college degree can increase individuals’ wage. Bias effect results from we assume that those who have college degree are not smarter than those who do not have college degree. But the effect of the increase in wage might from their original ability not from college attendance. Differential treatment effect bias means the college effect are the same on people in either treatment or control group. But the effect of college on wage might be different for these two groups. Differential treatment effect bias = 0

Counterfactual Analyses The estimate from the conventional model = 10-5 = 5 The effect of college on the wage in treatment group = 10-6 =4 The effect of college on the wage in control group = 8-5=3 The average treatment effect = 0.3(10-6)+0.7(8-5)= 3.3 𝝅 = 0.3, 30% of population obtains college degrees 𝑩𝒂𝒔𝒆𝒍𝒊𝒏𝒆 𝑩𝒊𝒂𝒔 Differential treatment effect bias

Counterfactual Analyses The biases of conventional models are from two assumptions Differential treatment effect bias = 0 Baseline Bias = 0