Testing day of the week effect

Question

I am currently reading a bit about testing day of the weeks effects. I saw two different model specifications and wonder how to interpret the results.

The first model type includes only 4 dummies for e.g., Mo till Thu, and an intercept:

$Return_t=\beta_0+\beta_1D_{1t}+\beta_2D_{2t}+\beta_3D_{3t}+\beta_4D_{4t}+\epsilon_t$

The second model type includes 5 dummies for all weekdays and no intercept.

$Return_t=\beta_1D_{1t}+\beta_2D_{2t}+\beta_3D_{3t}+\beta_4D_{4t}+\beta_5D_{5t}+\epsilon_t$

I have two questions:

Could you explain the difference in the interpretation of the p-values for the models (what does it mean when one of the dummies in model 1 is significant, what does it mean in model 2)? In my opinion the model 2 suffers from multicollinearity, because the dummies are linear dependent, is this correct?

Thanks for your help!

Answer 1

1) I'm going from memory here so someone may want to confirm that I'm thinking about this correctly - but the two models will end up with the same results and significance levels - in the first model, the intercept acts as the reference day, such that the average effect of $D_d=\beta_0+\beta_d$. In the second model you should get the same effect, however, it will be equal to simply $\beta_d$.

2) I don't think one model suffers from collinearity issues and the other one doesn't - both are likely to suffer, given that the correlation between one day and another day will be negative. It will come down to how concerned you are with multicollinearity.