Efficiency and the number of regressors? An econometrician told me that I shouldn't keep adding new variables to the model even if I have reason to believe they're relevant to the response variable, as it "reduces the efficiency of the other parameters". That is, even if you have 40 variables that "should" be related to the response, you should draw the line somewhere and include a subset of them.
Question: What are some good references that deal with this?
 A: Probably the best regarded book on the model building process per se, is Frank Harrell's Regression Modeling Strategies, but the issues involved can be stated simply:  For every additional covariate that is included in a model, you will lose 1 degree of freedom.  If a factor with $k$ levels is included, you will lose $k-1$ degrees of freedom.  This will decrease your statistical power (the ability to differentiate the slope of the relationship between that covariate and the response from 0).  Another way of putting that fact is that your confidence intervals around your beta estimate will be wider / sample parameters will vary more widely from their true values.  If the covariates are orthogonal to each other and you have enough data, the impact is likely to be very small.  Real-world (observational rather than experimental) data is never orthogonal, though, so there will be multicollinearity, and multicollinearity can cause your beta estimates to fluctuate quite widely.  (There are many threads on CV that explore multicollinearity, so if you aren't terribly familiar with it, you can read some of them by clicking on multicollinearity.)  
A: The proof of this is a standard exercise in matrix algebra, and you can find it in all the graduate econometrics textbooks.
For example, Davidson and MacKinnon (2003) has it on page 112.
A: I would look into using the Aikake Information Criterion, or the Bayesian Information Criterion.
What software are you using? Most statistical software should take care of this automatically for you.
Essentially they are ways of determining if the number of regression parameters is justified in terms of how much explanatory value they add to the model.
