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

Question

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?

Answer 1

There are some terminological 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 odds ratios, as their $x$s are often binary, so the odds ratios represent the relative frequencies of the outcome of interest in the two groups in the population. This is such a common 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". Statisticians' $M$-estimates are econometricians' extremum estimators.

There are terminological 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 in longitudinal/panel data models for econometricians. (Random effects are cursed for econometricians, for good.)
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 probabilities of selection vary between observations. These should be called unequal probability samples. Stratified samples are those 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.
5. Horvitz-Thompson estimator is a non-parametric estimator of a finite population total in sampling statistics that relies on fixed probabilities of selection, with variance determined by the second order selection probabilities. In econometrics, it had grown to denote inverse propensity weighting estimators that rely on a moderately long list of the standard causal inference assumptions (conditional independence, SUTVA, overlap, all that stuff that makes Rubin's counterfactuals work). Yeah, there is some sort of probability in the denominator in both, but understanding the estimator in one context gives you zero ability to understand the other context.

I view the unique contributions of econometrics to be

1. 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 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 and empirical likelihood are hugely popular with economists, and never caught up in statistics (GMM was first described as minimum $\chi^2$ by Ferguson, and empirical likelihood, by Jon Rao, both famous statisticians, in the late 1960s). 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 processes 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 the 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 have 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. (EDIT: that was the view on the scene in 2012; by 2020, Bayesian models have become standard in empirical macro where people probably care a little less about robustness, and are making their presence heard in empirical micro, as well. They are just too easy to run these days to pass by.) 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.

Answer 2

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.

Answer 3

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.

Answer 4

I've noticed that compared with what I'd call mainstream statistical science econometricians seem reluctant to use graphs, either schematic or data-based. The coverage of regression, which is naturally even more central in econometrics than elsewhere, is a major case in point. Modern introductions to regression by statisticians emphasise throughout the value of plotting the data and plotting the results of regression, including diagnostic plots, whereas the treatment in econometrics texts is distinctly more formal. Leading texts in econometrics don't include many graphs and don't promote their value strongly.

It's difficult to analyse this without the risk of seeming undiplomatic or worse, but I'd guess at some combination of the following as contributory.

1. Desire for rigour. Econometricians tend to be suspicious or hostile to learning from the data and strongly prefer decisions to be based on formal tests (whenever they don't come out of a theorem). This is linked to a preference for models to be based on "theory" (although this can mean just that a predictor was mentioned previously in a paper by some economist not talking about data).

2. Publication practices. Papers for economics or econometrics journals are heavy with highly stylised tables of coefficients, standard errors, t-statistics and P-values. Adding graphs does not even seem to be thought about in many cases and if offered would possibly be suggested for cutting by reviewers. These practices have become embedded over a generation or more to the extent that they have become automatic, with rigid conventions over starring significance levels, etc.

3. Graphics for complex models. Tacitly graphs are ignored whenever it does not seem as if there is a graph that matches a complex model with many predictors, etc., etc. (which indeed is often difficult to decide).

Naturally, what I am suggesting is a difference of means, as it were, and I recognise much variability in both cases. But as a non-economist who has much occasion to observe what economists do, it seems to me that even introductory econometrics texts cover a great deal of formal territory in a rather stiff way. They are also correspondingly weak on what one author called "plain data analysis".

Answer 5

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.

Answer 6

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.")

Answer 7

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.

Answer 8

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.

Answer 9

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.

Answer 10

I'd like to add one thing to give greater detail on something that was only mentioned in the other answers. Having taken classes in both areas, one of the main differences between the two is that statistics tends to stress the rigidity of the assumptions for regression models. The regression course I took in the statistics department focused a great deal of time pounding into our heads regression assumptions and taught techniques to check and those assumptions. However, what the stats department course lacked was a focus on what to do if the assumptions are not met. In the real world, data does not always fit all required assumptions. Econometrics tends to be more real world driven in the sense that economic data is typically only observable and cannot be generated by an experiment, which is where idea that $X$ is fixed in statistics vs. not fixed in econometrics comes in. Consider macro economic data. It is very difficult to perform an experiment on an entire economy and observe the results. As such, economists are at the mercy of what data is observed and reported by the government, not what they can perform in a lab by changing the dose of a medication to see what happens to their dependent variable. That is why econometrics spends a significant amount of time focusing on what to do when the assumptions are not met. Is a model still useful if assumptions are not met and can we correct for issues? An econometrician would say yes. Some examples of topics that are more heavy in econometrics are how to deal with heteroskedasticity and autocorrelation. Econometrics also focuses more on time series.

Although there is a decent amount of overlap, I would be hesitant to say the the the concepts are the same. Statistics is the foundation from where all ideas in econometrics come from, but economists focus on finding ways to apply those ideas in the real world and have their own techniques and even some different models for solving difficult problems that may not be possible from a statistician's point of view.