It's necessary to write an extensive journal article to
answer the question. I just try to list some of my thoughts.
In 1930-s and 1940-s the term "econometrics" also implied
what is now called "mathematical economics" or "economic
theory" (just look through any issue of "Econometrica").
This usage do not contain any statistics, but now it is
outdated.
"The application of statistical methods to economic data in
order to test economic theory" is a good description of
applied econometrics. Though sometimes goal is different
from "testing economic theory". This may be "forecasting" or
something else. Ideally applied econometrician must use
economic theory, but one can find abundance of "modeling
without theory" which is also called econometrics.
But besides applied econometrics there exists also
"econometric theory" which is in fact a (very specific)
branch of mathematical statistics. "Econometric theory"
investigates formal statistical methods which could be of
use in applied econometric research.
The difference between "econometrics" and "statistics" is
evident when comparing two textbooks, one called
"Econometrix" and the other one "Statistix". Econometric
textbooks usually start from "regression" while statistical
ones usually start from "sample" (assuming i.i.d. data).
Some specific features of econometrics:
Greater emphasis on various kinds of regression models,
comprehensive after-estimation specification testing
("diagnostics"), preoccupation by nonstationarity of time
series.
Many statistical methods seem old-fashioned or useless to an
econometrician. Something like MANOVA, PACF, factor
analysis, KS test, comparing sample means, multidimensional
scaling etc.
The difference can become clear from comparison of
statistical and econometric software (e.g., SPSS or
Statistica vs. Eviews or Limdep).
Note also econometix slang: proxy, dummy, unit root, LM
test, encompassing, exogeneity/ endogeneity etc. I am sure
many statisticians would not understand what some applied
econometric papers are talking about (not to speak about
some econometric theory papers).
-----------------------------
Alexander Tsyplakov
Novosibirsk State University
http://www.nsu.ru/ef/tsy/
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