# What is the meaning of the intercept in regression with binary explanatory variables?

I have the following model:

$y_t = \alpha + \beta_1 x_{t-1} + \beta_2 z_{t-1} + \varepsilon_t$,

where my dependent variable $y_t$ is the log return of a stock (e.g., GM) and $x_{t-1}$ and $z_{t-1}$ are dummy variables. I have three possible categories (positive, negative and neutral news in the pre-period). However to avoid collinearity I code only two dummies (positive and negative news). Thus, the reference category are neutral news appeared in the pre-period.

My question refers to the interpretation of the results and especially the intercept. E.g., if I get as results from the OLS estimation of the model above:

$\alpha$ = -0.028 (t-stat. = -1.91)

$\beta_1$ = 0.024 (t-stat. = 1.76)

$\beta_2$ = -0.002 (t-stat. = -0.60)

My question is: Can I interpret the intercept in the same way as the beta-coefficients, i.e., -0.028 is the expected mean return for neutral news, 0.024 the expected return for positive news and -0.002 is the expected mean for negative news?

Your interpretation of $\alpha$ is correct. However $\beta_1$ is the difference between the expected return for positive news and the expected return for neutral news. That is because for for postive news you have $x_{t-1}=1$ and $z_{t-1}=0$. This means you the prediction for positive news is $\alpha + \beta_1$.