I am following some work to do with a regression based performance attribution.
The regression is a cross sectional one. The $y$ vector is the risk free return for say 1,000 companies. The $X$ matrix is made up of a constant, some factors such as book to price, momentum etc, say we 6 such factors (7 including the constant). Then for a stock's country there are dummy variables (twenty countries). So our matrix is 1000 x 27 (including the constant).
However I thought when you have dummy variables you would not use all of them, you would use $n-1$ because it introduces multicollinearity. Is the regression above mis-specified?