Why do I have to subtract 1 from R regression to measure fixed effects? Beginner's question probably. I would like to know why, to measure country fixed effects, I need to subtract one from the factor variable that I would like to consider as a fixed effect.
For example, I want to consider country and year fixed effects, so my regression model is:
lm(Premium ~ Brand + factor(Country) - 1 + factor(Year) -1 + 
              Population + Employment + Inflation, data=df)

From what I understand, the -1 after each factor is due to the fact that I need to subtract one baseline country/year from which to measure the fixed effects. However, in the regression output, I get a coefficient for all 18 countries in my data. Shouldn't one country be "missing" from the list of results since it is the baseline? Instead, if the output is correct, what's the right interpretation and what is the default baseline R considers? Below is the output:

 A: Original Answer
Using the -1 or 0 operator in your regression equation simply suppresses the intercept. Normally when you include a factor into your regression, the first level of your categorical factor will be the reference group, and will be used as the intercept as a result. From there, each coding of the coefficients in your model (including the factor) will be a linear combination that adjusts this intercept.
All that this accomplishes is removing the reference point and just includes the labels of each coefficient directly instead. This thread has a lot of info on this subject. I would advise against doing that unless you have a really good reason to. Kjetil's answer has some exceptions listed, but I don't think your regression would qualify.
Edit for Clarity
My answer has already been accepted, but after looking at the comments, it appears that I should make an edit to this answer. These are the formal recommendations listed in Hahn, 1977 for fitting a no-intercept model with continuous-only predictors:

However, in the case of a regression with a categorical factor, while you can always include an intercept by default, suppressing the intercept is not necessarily a problem. As highlighted by Sextus below in the comments:
$$
a + bx_1 + cx_2 \\ = \\ 0 + (a+b)x_1 + (a+c)x_2
$$
The coefficients therefore change numerically, but their estimates are only shifts from the original dummy-coded intercept. Therefore the interpretation of either the intercept-model or no-intercept model would have essentially the same linear solution.
Citation

*

*Hahn, G. J. (1977).
A: With the expression -1 you are not performing a subtraction of a category or a value.
It does the following instead: (from the r documentation about the formula class)

The - operator removes the specified terms, so that (a+b+c)^2 - a:b is identical to a + b + c + b:c + a:c. It can also used to remove the intercept term: when fitting a linear model y ~ x - 1 specifies a line through the origin. A model with no intercept can be also specified as y ~ x + 0 or y ~ 0 + x.

So it is defining the structural equation as being without an intercept.
This symbolic notation dates back to the late 60's early 70's when the need arrose to be able to describe equations to computer programs. An early description is found in Wilkinson and Rogers, 1973, Symbolic Description of Factorial Models for Analysis of Variance and it was used in genstat and algorithm AS 65, written in Fortran.


From what I understand, the -1 after each factor is due to the fact that I need to subtract one baseline country/year from which to measure the fixed effects.

Note that you only need to add it once and adding it after each factor is not doing anything different.
Also these baseline country/years will not be 'subtracted' when you have a model with more than one categorical variables. For example your use of factor(Year) -1 will not prevent that the dummy variable factor(Year)2012, relating to the year 2012 category which I suspect is also in your data, is not used. (I can't find a simple related example question, but this one is about it Why do output coefficients not resemble true coefficients in a linear model?)
