Dummy variable as both dependent and independent variable I'm trying to replicate NBER's business cycle dating which consists of a binary dummy variable with 0 = expansion, 1 = recession.
The way I've done this is by taking the 6 underlying economic indicators, transforming the measures to annual growth rates and taking a simple average to form a composite indicator. This produces a continuous variable which is then transformed to a dummy variable using an if function.
My questions are as follows:

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*Is taking a simple average the correct way to create the composite index or should the data first be standardized (using z-scores?)

*Does it make sense to run an OLS regression to test the model fit vs the NBER? Or is this somehow not statistically correct when using dummies for both dependent and independent variables?

 A: I am not familiar with your data but I'll try to give you a general answer.

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*Taking the average of your 6 factors might not be a good idea. By doing so, you implicitly consider that each of them has the same impact on your dependent variable. This might be a strong assumption that you could want to discard by simply using each factor as an individual predictor. If you decide to keep the averaging procedure, standardizing your factors before averaging them will certainly have an impact on your estimation. It is neither right or wrong, it depends on the implicit assumptions you are willing to use in your model. If you use each factor as an individual predictor, standardizing these variables will have no impact on the prediction, but could improve your interpretations of the estimated coefficients, hence of your model.

*If your dependent variable is a binary variable, then I suggest you use a logistic regression instead of an OLS procedure. The difference is that a logistic regression models $\mathbb{P}\left(Y_i=1\right)=p(X_i)$, i.e. your are going to model the probability of a binary variable as a function of your independent variables. This is not the purpose of OLS. In general, using binary variables as predictors is not an issue (both for logistic regression and OLS) and is actually very common.

