Causal Inference and Data Analytics

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1 Interpretation of interacted variables

Suppose that in a school in a developing country, some children are given a free laptop by an NGO, and some students (not necessarily the same but not necessarily different one) receive free lessons in operating with a laptop. At the end of the semester, there is an exam that involves working with a laptop. Denote the number of points in the exam of student i by Yi. Assume that all kids are otherwise identical clones (so same intelligence, etc.) coming from identical families (so exactly the same income, etc.). Thus, the only two things that might differ is whether a kid has a laptop (initially, no child has), Xi1 and whether it receives lessons in operating with a laptop Xi2.

Compare the following models

Yi = _0 + _1Xi1 + _2Xi2 + “i (1)

Yi = _0 + _1Xi1 + _2Xi2 + _3Xi1Xi2 + “i. (2)

What is the main difference between these two models? What is the implicit assumption in model 1 that is not made in model 2? What is the interpretation of the coefficients in both models?

 

2 A simulation

A) Simulate 1000 observations of model (2). Assume that X1,X2, ” are all standard

normal and that they are independent. Furthermore, assume that _0 = 1, _1 = 1, _2 =1, _3 = 1.

B) Now, pretend that you do not know from which model the simulated data comes

from. Estimate model 1. What do you get as estimates? Are they biased? What would

be the erroneous conclusions that you would make using these estimates

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