Two Nonparametrics

In the world of econometrics, the term nonparametric basically refers to the flexible functional form of the regression curve. However, there are other notions of "nonparametric statistics" which refer mostly to distribution-free methods. In the econometric context, generally, neither the error distribution nor the functional form of the mean function is prespecified.
Between the parametric econometrics and nonparametric econometrics, the question of which approach should be taken in data analysis was a key issue in a bitter fight between Pearson and Fisher in the twenties. Fisher pointed out that the nonparametric approach gave generally poor efficiency whereas Pearson was more concerned about the specification question. Both viewpoints are interesting in their own right. Pearson pointed out that the price we have to pay for pure parametric fitting is the possibility of gross misspecification resulting in too high a model bias. On the other hand, Fisher was concerned about a too pure consideration of parameter-free models which may result in more variable estimates, especially for small sample size n.