What is the difference between econometrics and statistics?

Both fields deal with forecasting, causal estimation in experiments, and causal inference in observational studies. The latter often takes a backseat in terms of priority in Statistics education, while being front and center in Econometrics.

Previous answers already touched upon the difference between statistics and reduced form econometrics, in that the latter places more emphasis on causal inference based on observational data. This difference is very clear is you compare the techniques for "panel data" by econometricians with those used for "longitudinal data" by statisticians, despite the data structure being exactly the same.

There is an additional layer of difference between statistics and structural econometrics.

Econometric models and methods arise from the need to test economic theory. One starts with an economic model, then consider how it can be taken to data, rather than applying statistical models/methods in an ad hoc way.

Two standard examples:

1. CAPM and Fama-French-MacBeth

The classical Capital Asset Pricing Model (due to Markowitz and Sharpe) says that, if investors have mean-variance preferences, then asset price obey the relationship $$ E[R - r] = Cov(R, M) $$ where the RHS is covariance of return $R$ with the market $M$, and LHS is expected excess return of asset. Empirically, taking this relationship to data means fitting a linear model---regressing $R-r$ on $M$. Later Fama and French introduced additional covariates (the Fama-French factors) in the CAPM regression. In this particular case, the appropriate econometric model turns out to be the linear model.

2. Generalized Method of Moments

In a more contemporary model of asset prices (by now also basic), one arrives at the equilibrium relationship (called an asset pricing equation in economics) $$ E[u'(c_t) R_t|mathcal{I}_t] = 0 $$ where $c_t$ is consumption, $R_t$ is asset return, and $u$ is the preference (utility function) of the agent. A natural econometric question is now to estimate the parameters of $u$ from data. This led Hansen to introduce GMM, which makes the above moment condition, and others, a testable statistical hypothesis. (GMM contains the instrumental variables (IV) as a special case.)

The main difference is area of application:

econometrics is statistics applied to problems/phenomena from economics.

C'est ça.

Naturally, this leads to a different emphasis and focus in the methodology.

Econometrics originally came from statistics. In general statistics is more general than econometrics, since while econometrics focuses in Statistical Inference, Statistics also deals with other important fields such as Design of Experiments and Sampling techiniques. However, today I may undoubtedly assert that Econometrics has also largely contributed to statistics as well.

1) The kind of statistical problem in economics:

The first time I heard about linear regression was in the Physics lab when I was still a student of chemical engineering. I am not sure the specific class I was really having, but we may consider here that my class was a experiment to estimate the elasticity coefficient of a spring ... Easy! Even if your knowledge of physics is very limited, you can understand this experiment.

Consider that one end of the spring is attached to the ceiling and the other end that is free, you want to attach a mass $m$. Soon, the spring will expand and knowing Hooke's Law, the equilibrium position of the mass will be that in which the weight is equal to the force generated by the deformation of the spring. We can equate this idea as follows: $mg = kd$, where $g$ is gravity, $k$ is the spring deformation constant and $d$ is how much the spring is expanded when you put the dough on its end. If you put different masses, you will have different deformations. Then you can build a data matrix where the dependent variable is $d$ (known exactly) and the independent variable is $mg$ (which is known), you can estimate the value of $1 / k$ from linear regression

$$d = alpha + beta mg + u, $$ where $ beta $ is an estimate of $1/k$ and $u$ is a possible error associated with the model.

Note that:

Cause: Higher weight

Effect: Greater spring distension

This effect is very clear.

This situation is very rare in econometrics. In economics, few people know but the intention is to study/understand the choices of the government/families/companies… When we try to model choice situations, the cause-effect relationship is not explicit such as in above.

Consider the following social-economic problem that comes from the field of Economics of Crime where cities would like to know how much they would need to increase the number of policemen to reduce crime. Therefore, the model of interest could take the following form:

$$crimes = alpha_1 + beta_1 policemen + ... + u_1 $$

This model suggests that the number of crimes decreases with the number of policemen.

Interpretation: If the number of policemen increase, the incentive to commit crimes reduce.

Question: Does this equation answer the question above?

Can we write

cause = police $Rightarrow$ effect = crimes?

No, why? Simply, because the number of policemen can be associated with the following model

$$policemen = alpha_2 + beta_2 crimes + ... + u_2 $$

This model says that mayors respond to the number of crimes, increasing the number of policemen or a higher number of policemen is associated with areas of greater crime.

Interpretation: If the crime in a given area increases and the mayor wants to get reelected, then she/he want to solve the problem and she/he increases the number of policemen.

The cause and effect in this situation is not clear. This problem is called endogeneity and it is the rule in economics. In this case, the error term is not exogenous (it is easy to prove that) and we know that this is the most important assumption that we have to consider to ensure that the estimated parameters of our model are not biased. [This happens because if we use the ols estimator, it will force the error to be orthogonal to the regressors and in the case of this regression model, this does not happen.]

Disclaimer: This is a classical model (that is very easy to explain) in economics. I am not suggesting or not suggesting that the number of policemen should be increased or not given the recent events that took place in USA. I am just talking about simple models to point some ideas.

Most events in economics comes from equilibrium relations such as:

A) Equilibrium models of Offer and Demand

a) The demand decreses with the price of a given product

b) The offer increases with the price of a given product.

And we have in equilibrium Demand=Offer. tHow do we separate these effects in economics?

B) Inflation and interest rate

a) If the basic interest rate of the economy decreases, the economic activity increases and it is likely to increase the inflation. (here, the low interest rate seems to be causing the inflation)

b) However, if the inflation is higher, central bank decision makers may decide to increase the interest rate to control the inflation. (here the high inflation seems to be causing the high interest rate)

In fact, we have got another equilibrium relation.

2) The data we have in econometrics

In many field in statistics, we are able to create experiments to generate the data we need. For instance, we want to test the effect of a drug. We divide the population in two parts and the first part receives the treatment and the second part does not receive it (receives the placebo).

In many situations in economics is not possible to generate the “perfect” data to test a phenomenon. For instance, we may not play with the interest rate to estimate its effect on inflation. If we do that many people may lose their jobs due to a recession or may cause an hyper-inflation or a scape of international capital. Having said that in many situations in economics we have to leave with the data is out there, that is subject to lots of problems.

So, the focus of econometrics is to arrive to relations as Cause-Effect as we found in the example with a spring above with an imperfect data.

3) The role of economic theory

In econometrics the role of theory is very important. Usually economists want to test hypothesys. So the model is build in order to test these hypothesis. For instance, what is the effect of additional years of study in the wage of people? This is the kind of question that arise in the field of labor economics.

4) Models

Models in econometrics focus in creating the cause-effect relationship in the situations discussed (for instance) above.

The classical idea to deal endogeneity is to find instrumental variables that replace the endogeneous variables and we recover the exogeneity of the error term. An extension of this idea is the so-called two stage least square and also the generalized methods of moments.

However, this is just a general overview of the field. If you realy want to have a general perspective of the field of econometrics I strongly suggest the book "Mostly Harmless Econometrics -- Joshua D. Angrist and Jörn-Steffen Pischke" or its simplified version "Mastering Metrics: The Path from Cause to Effect -- Joshua D. Angrist and Jörn-Steffen Pischke".

Now the main contributions of the field are related to mix ideas of Econometrics with machine learning.

It is worth mentioning that some ideas of this answer came from previous answers I gave to a Brazilian site: Endogeneity and Econometrics versus Statistics.

I think it's helpful to think of econometrics as an application of statistics that is well suited to deal with problems economists typically encounter in their research. So they are certainly very related in some sense, but the focus is on the connection between economics and statistics. One way to alternatively think about this is that econometrics combines statistics with assumptions that come from economic theory or reasoning, and econometrics is about studying to what extent these economic assumptions buy information in a statistical context. Three ways this manifests itself are: 1. statistical models fall out of economic models, rather than starting with a statistics model, 2. the focus is on issues that are particularly salient for economists, and 3. re-contextualizing statistical assumptions and approaches as economic assumptions (and vice-versa)

To expand on these points, the first point emphasizes that the statistical model are typically motivated from of an economics model. For example, you may be studying markets, and a classic result from economic theory is market clearing, which states that supply of a good equals demand of that good, and so when you have data on firms producing goods and consumers purchasing them, you may want to impose this condition in your statistical model, and this can be stated as a moment condition, and thus is a subset of Generalized Method of Moments (GMM), which was developed in econometrics because so many economic models have some moment conditions that must hold, and we can use that information with our statistical models.

The second point is an obvious one, and you could maybe think of the first point as a case of it, but it really emphasizes that econometrics develops statistical tools in the context of what economists are interested in, and one classic interest is in causality rather than correlation in situations. For example, the development of instrumental variable approaches that allow for heterogeneity in potential outcomes is largely driven by econometricians, since it's a common problem in that field: economists typically studies individuals (or individual firms), and it's very reasonable that each individual has a different treatment effect. Additionally, unlike some fields, it may be harder to run RCTs in some contexts, and so classic papers like Imbens and Angrist (1994) analyze what IV methods identify when you have an instrument without full support.

A final point should be made that econometrics also focuses on relating statistical models to economics. This is the reverse direction of the first point: given a statistical model, what assumptions would you have to place on individuals so that the model holds, and are these assumptions sensible from an economics perspective. For example, Vytlacil (2002) showed that the classic IV assumptions and monotonicity are equivalent to a Roy model with an index switching threshold (a variant of a classic economic model), which allows economists to understand statistical assumptions from an economics perspective.

Econometrics is an applied branch of statistics that is primarily related to economics.

For example, in econometrics, one of the primary challenges is the non-independence of the error terms, which is typically assumed away in many/most statistical problems.

This makes sense for traditional statistics but not so much for economics, where humans are always part of a larger society that is not easily split into double-blind treatment and control groups.