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Causal Inference with Bayesian Networks
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Card and Krueger used linear regression to estimate the causal effect of minimum wage increase in their paper (Card and Krueger 1994). In this section, we follow their method and implement their regression models in Python. The regression models that they used had two general forms:
(14.3)
And
(14.4)
where ΔEi is the change in FTE employment for restaurant i before and after treatment. NJi is an indicator variable equal to 1 if observation i is in New Jersey and 0 otherwise (it is equivalent to column STATE in our dataset), and GAPi is the gap between the initial observed wage for observation i (denoted by W1i) and the minimum wage ($5.05):
(14.5)
In these equations, Xi represents other covariates like store type or location. The next code creates a regression model based on Equation 14.3. We first create ΔEi as the difference between FTE_EMP2 and FTE_EMP and then create a regression model (model1) in which...