# 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:

1. Is taking a simple average the correct way to create the composite index or should the data first be standardized (using z-scores?)
2. 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?

2. 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.