# What are the major philosophical, methodological, and terminological differences between econometrics and other statistical fields?

Econometrics has substantial overlap with traditional statistics, but often uses its own jargon about a variety of topics ("identification," "exogenous," etc.). I once heard an applied statistics professor in another field comment that frequently the terminology is different but the concepts are the same. Yet it also has its own methods and philosophical distinctions (Heckman's famous essay comes to mind).

What terminology differences exist between econometrics and mainstream statistics, and where do the fields diverge to become different in more than just terminology?

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looks like this will be a list / community wiki – EnergyNumbers Oct 14 '11 at 9:09
@EnergyNumbers Changed focus of question slightly to be a better formed SE question (and since the answers were coming in more about actual differences than terminological ones). I agree it still may wind up as CW, but it may not in this form, as there is a well-defined answer. – Ari B. Friedman Oct 19 '11 at 1:31

## migrated from economics.stackexchange.comMay 3 '12 at 18:18

There are some terminology differences where the same thing is called different names in different disciplines:

1. Longitudinal data in biostatistics are repeated observations of the same individuals = panel data in econometrics.
2. The model for a binary dependent variable in which the probability of 1 is modeled as $1/(1+\exp[-x'\beta])$ is called a logit model in econometrics, and logistic model in biostatistics. Biostatisticians tend to work with logistic regression in terms of odd ratios, as their $x$s are often binary, so the odd ratios represent the relative frequencies of the outcome of interest in the two groups in the population. This is such a prevalent interpretation that you will often see a continuous variable transformed into two categories (low vs. high blood pressure) to make this interpretation easier.
3. Statisticians' "estimating equations" are econometricians' "moment conditions". Statisicians' $M$-estimates are econometricians' extremum estimators.

There are terminology differences where the same term is used to mean different things in different disciplines:

1. Fixed effects stand for the $x'\beta$ in the regression equation for ANOVA statisticians, and for a "within" estimator for econometricians.
2. Robust inference means heteroskedasticity-corrected standard errors for economists (with extensions to clustered standard errors and/or autocorrelation-corrected standard errors) and methods robust to far outliers to statisticians.
3. It seems that economists have a ridiculous idea that stratified samples are those in which probablities of selection vary between observations. These should be called unequal probability samples. Stratified samples are the ones in which the population is split into pre-defined groups according to characteristics known before sampling takes place.
4. Econometricians' "data mining" (at least in the 1980s literature) used to mean multiple testing and pitfalls related to it that have been wonderfully explained in Harrell's book. Computer scientists' (and statisticians') data mining procedures are non-parametric methods of finding patterns in the data, also known as statistical learning.

I view the unique contributions of econometrics to be

1. The ways to deal with endogeneity and poorly specified regression models, recognizing, as mpiktas has explained in another answer, that (i) the explanatory variables may themselves be random (and hence correlated with regression errors producing bias in parameter estimates), (ii) the models can suffer from omitted variables (which then become part of the error term), (iii) there may be unobserved heterogeneity of how economic agents react to the stimuli, thus complicating the standard regression models. Angrist & Pischke is a wonderful review of these issues, and statisticians will learn a lot about how to do regression analysis from it. At the very least, statisticians should learn and understand the instrumental variables regression.
2. More generally, economists want to make as few assumptions as possible about their models, so as to make sure that their findings do not hinge on something as ridiculous as multivariate normality. That's why GMM is hugely popular with economists, and never caught up in statistics (even though it was described as the minimum $\chi^2$ by Fergusson in late 1960s). That's why adoption of empirical likelihood grew exponentially in econometrics, with but a marginal following in statistics. That's why economists run their regression with "robust" standard errors, and statisticians, with the default OLS $s^2 (X'X)^{-1}$ standard errors.
3. There's been a lot of work in the time domain with regularly spaced processes -- that's how macroeconomic data are collected. The unique contributions include integrated and cointegrated process and autoregressive conditional heteroskedasticity ( (G)ARCH ) methods. Being generally a micro person, I am less familiar with these.

Overall, economists tend to look for strong interpretation of coefficients in their models. Statisticians would take a logistic model as a way to get to the probability of the positive outcome, often as a simple predictive device, and may also note the GLM interpretation with nice exponential family properties that it possesses, as well as connections with discriminant analysis. Economists would think about the utility interpretation of the logit model, and be concerned that only $\beta/\sigma$ is identified in this model, and that heteroskedasticity can throw it off. (Statisticians will be wondering what $\sigma$ are the economists talking about, of course.) Of course, a utility that is linear in its inputs is a very funny thing from perspective of Microeconomics 101, although some generalizations to semi-concave functions are probably done in Mas-Collel.

What economists generally tend to miss, but, IMHO, would benefit from, are aspects of multivariate analysis (including latent variable models as a way to deal with measurement errors and multiple proxies... statisticians are oblivious to these models, though, too), regression diagnostics (all these Cook's distances, Mallows $C_p$, DFBETA, etc.), analysis of missing data (Manski's partial identification is surely fancy, but the mainstream MCAR/MAR/NMAR breakdown and multiple imputation are more useful), and survey statistics. A lot of other contributions from the mainstream statistics has been entertained by econometrics and either adopted as a standard methodology, or passed by as a short term fashion: ARMA models of the 1960s are probably better known in econometrics than in statistics, as some graduate programs in statistics may fail to offer a time series course these days; shrinkage estimators/ridge regression of the 1970s have come and gone; the bootstrap of the 1980s is a knee-jerk reaction for any complicated situations, although economists need to be better aware of the limitations of the bootstrap; the empirical likelihood of the 1990s has seen more methodology development from theoretical econometricians than from theoretical statisticians; computational Bayesian methods of the 2000s are being entertained in econometrics, but my feeling is that are just too parametric, too heavily model-based, to be compatible with the robustness paradigm I mentioned earlier. Whether economists will find any use of the statistical learning/bioinformatics or spatio-temporal stuff that is extremely hot in modern statistics is an open call.

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+1 This is a splendid example of what great answers can emerge when a question is opened up to a diverse community. – whuber May 3 '12 at 21:04
(+1) Very nice response. – chl May 3 '12 at 21:38
+1, beautiful answer. – mpiktas May 4 '12 at 3:22
@whuber, thanks for the comment. The disciplinary divides drive me nuts, frankly. – StasK May 4 '12 at 13:58
+1, really informative & thorough. Pardon me for nitpicking, but in #2 top, shouldn't it be $\exp[-x'\beta]$, or am I misunderstanding something? – gung May 5 '12 at 17:56
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It is best to explain in terms of linear regression, since it is the main tool of econometrics. In linear regression we have a model:

$$Y=X\beta+\varepsilon$$

The main difference between other statistical fields and econometrics is that $X$ is treated as fixed in other fields and is treated as random variable in econometrics. The extra care you have to use to adjust for this difference produces different jargon and different methods. In general you can say that all the methods used in econometrics are the same methods as in other statistics fields with adjustment for the randomness of explanatory variables. The notable exception is GMM, which is uniquely econometric tool.

Another way of looking at the difference is that the data in other statistic fields can be considered as an iid sample. In econometrics the data in a lot of cases is a sample from stochastic process, of which iid is only a special case. Hence again different jargon.

Knowing the above is usually enough to easily jump from other statistic fields to econometrics. Since usually the model is given, it is not hard to figure out what is what. In my personal opinion the jargon difference between machine learning and classical statistics is much bigger than between econometrics and classical statistics.

Note though that there are terms which have convoluted meaning in statistics without the econometrics. The prime example is fixed and random effects. Wikipedia articles about these terms are a mess, mixing econometrics with statistics.

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"The prime example is fixed and random effects. Wikipedia articles about these terms are a mess, mixing econometrics with statistics." So true. – Michael Bishop May 3 '12 at 19:06

One subtle difference is that economists sometimes ascribe meaning to the error terms in models. This is especially true among "structural" economists who believe that you can estimate structural parameters that represent interest or individual heterogeneity.

A class example of this is the probit. While statisticians are generally agnostic about what causes the error term, economists frequently view the error terms in regressions as representing heterogeneity of preferences. For the probit case, you might model a woman's decision to join the labor force. This will be determined by a variety of variables, but the error term will represent an unobserved degree to which individual preferences for work may vary.

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While statisticians may be agnostic about what causes the error term, that does not mean that they do not care about it. What you describing is the heterogeneity of the error term, which means that the usual assumptions about the error terms are not met. No statistician will ignore that. – mpiktas Oct 16 '11 at 10:26
Interestingly, in this case, there's no problem with the form of the error term. Statisticians and economists alike will get up in arms and worry about heteroskedasticity or any other non-iid error terms. However, even if the error term is N(0,1) as in a probit, economists are apt to give it an economic interpretation. – dchandler Oct 16 '11 at 14:44
That applies to modelling in general. Interpreting the model in your own special way is not restricted to economists, as far as my experience goes. – mpiktas Oct 16 '11 at 16:23
I disagree. Economists clearly have a monopoly on clever interpretation of models <just kidding!>. Good point though. – dchandler Oct 16 '11 at 17:40

Of course, any broad statements are bound to be overly broad. But my experience has been that econometrics is concerned about causal relationships and statistics has become more interested in prediction.

On the economics side, you can't avoid the "credibility revolution" literature (Mostly Harmless Econometrics, etc). Economists are focused on the impact of some treatment on some outcome with an eye towards policy evaluation and recommendation.

On the statistics side, you see the rise of data mining/machine learning with applications to online analytics and genetics being notable examples. Here, researchers are more interested in predicting behavior or relationships, rather than precisely explaining them; they look for patterns, rather than causes.

I would also mention that statisticians were traditionally more interested in experimental design, going back to the agricultural experiments in the 1930s.

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Unlike most other quantitative disciplines, economics deals with things at the MARGIN. That is, marginal utility, marginal rate of substitution, etc. In calculus terms, economics deals with "first" (and higher order derivatives).

Many statistical disciplines deal with non-derivative quantities such as means and variances. Of course, you can go into the area of marginal and conditional probability distributions, but some of these applications also go into economics (e.g. "expected value.")

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As a statistician I think of this in more general terms. We have biometrics and econometrics. These are both areas where statistics is used to solve problems. With biometrics we are dealing with biological/medical problems whereas econometrics deals with economics. Otherwise they would be the same except that different disciplines emphasize different statistical techniques. In biometrics survival analysis and contingency table analysis are heavily used. For econometrics time series is heavily used. Regression analysis is common to both. Having seen the answers about terminology differences between economatrics and biostatistics it seems that the actual question was mainly about terminology and I really only addressed the other two. The answers are so good that I can't add anything to it. I particularly liked StasK's answers. But as a biostatistician I do think that we use logit model and logistic model interchangeably. We do call log(p/[1-p]) the logit transformation.

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 (+1) You could add psychometrics to the list of domain specific applications of applied statistics to domain specific problems. – Andy W Aug 17 '12 at 16:00

It is not econometrics, it is context. If your likelihood function does not have a unique optimum, it will concern both a statistician and an econometrician. Now if you propose an assumption that comes from economic theory and restricts the parametrization so that the parameter is identified, it might be called econometrics, but the assumption could have come from any substantive field.

Exogeneity is a philosophical matter. See e.g. http://andrewgelman.com/2009/07/disputes_about/ for a comparison of different views, where economists typically understand it the way Rubin does.

So, in short, either adopt the jargon your teacher uses, or keep an open mind and read widely.

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Econometricians are almost exclusively interested in causal inference, whereas statisticians also use models for predicting outcomes. As a result, econometricians focus more on exogeneity (as others have mentioned). Reduced form econometricians and structural econometricians get at this causal interpretations in different ways.

Reduced form econometricians frequently deal with exogeneity using instrumental variables techniques (while IV is used much less frequently by statisticians.)

Structural econometricians get causal interpretations of parameters by relying on an amount of theory that is rare in work by statisticians.

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