New answers tagged statistics
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You should definitely adjust for inflation, as you should with all monetary variables. I wouldn't worry using the CPI, you could use an alternative indicator as a robustness check to see whether the choice of indicator affects your main conclusions.
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A
OP's second expression corresponds to
$$\Delta p = P(Y=1|D=1,X=\bar{X}) - P(Y=1|D=0,X=\bar{X}),$$
which is
$$
\Delta p = \Lambda(\beta_0 + \beta_1 + \beta_2 \bar{X}) - \Lambda(\beta_0 + \beta_2 \bar{X}),
$$
where $\Lambda(z) = e^z/(1+e^z)$.
Rationale for dividing by p
OP's first expression corresponds to $(\Delta p)/p$, where $p$ is the proportion of 1'...
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