In my seminar on Growth & Development today we discussed a paper where the sample size was fairly small, around 75 observations. The authors said due to the small sample size, they couldn't estimate models with a lot of regressors in them because of degrees of freedom issues.
Then they proceeded to investigate upwards of 30 variables, by using them one at a time! To "save" degrees of freedom!
First off, excluding relevant variables in the analysis biases results unless the variables are somehow orthogonal to each other, which is EXTREMELY unlikely.
Second, estimating 30 small regressions on the same sample does not actually save ANY degrees of freedom over estimating one big regression on the sample.
Sure you can say it does and use the nominal critical values in each case, but you are kidding yourself and misleading your readers.
Degrees of freedom are like cigarettes. Once you use them, they are gone. They can't be re-used over and over again.
Overall the paper reported well over 100 estimated coefficients. On 75 data points. In a ton of different regressions all with the same dependent variable. Used the nominal critical values in every case.
What is the critical value for a "t-stat" with negative 34 degrees of freedom?