Dear Stata Community,
I would like to ask if anyone here could offer some advice on the estimation that I would like to do. I am using Stata v14, and am trying to specify my identification strategy before getting started. This isn't a straight-forward linear analysis, so I am struggling conceptually. I would like to estimate the following:
prices = a + b store_type + b age + b vector of control variables + et
prices = continuous
store_type = binary
age = continuous
distance = ordinal
store_type is endogenous to prices. I am therefore using an instrument (distance, which is measured in time, as: 1=0-30 minutes, 2=30 inutes, 3=30-60 minutes).
1. In my first-stage regression, can I use an ordinal variable to predict a binary variable?
a. My instrument is ordinal, but the distance between each measure is not equal
b. My instrument is left-skewed, 60% responded 1
Would I then need to use a tobit model?
2. In my second-stage regression, is it okay to use, for example, the predictions from a probit or tobit model in a linear model? I've read on this forum that Wooldridge (2002), pages 623-625 says that this is possible, but is it true given (#1 a. and b.)?
3. My two main variables of interest on the right-hand side are store_type and age. I want to keep age but it correlates with store_type. Is there a common way to break this collinearity (besides centering/demeaning)?
MANY thanks in advance for any helpful tips.
MT
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