Social Science Statistics Blog

James

I think the difference is in the objective of the analysis. Econometrics/Economics focus on unbiased estimation because the objective of research is recovering structural parameters describing economic behavior. Broadly speaking, the objective is estimating the truth. This is especially true in applied microeconomics.

Statisticians have a more predictive-model discovery intent. My feeling is that statisticians behave like independent contractors who are asked which specific actions are supported by the data. Bayesianism is a natural and correct approach in this case. Unbiased estimation and asymptotic do not really have a prominent role here.

\epsilon difference in objective translates in a big methodological divide.

A similar question sounds like a joke (but isn't, quite), that a friend of mine asked: What's the difference between a statistician and an epidemiologist?

The answer, he would say, is that an epidemiologist wants to know what causes (say) asthma in children. A statistician wants to know how to find out.

If you're interested in the destination, you're an economist, if you're interested in the route, you're a statistician.

That's just how I'd think it.

The snarky response: Of course I care about how, I'd like to know what actually causes childhood asthma.

Even more snarky: Statisticians try to solve their problems by making sure they have a comprehensive toolbox. Everyone else tries to solve all their problems with an Allen wrench.

An excellent question, Jim. I was at a conference last year where one of the speakers described the difference this way: "Econometrics is statistics with a ten-year lag". The speaker was an economist, but he was speaking to an audience of mostly statisticians, so take that as you will.

My take on this question is, to exaggerate somewhat, is that economists believe their models and statisticians don't. The whole project in economics over the past fifty years, particularly in micro theory, has been to make a set of assumptions, derive implications that follow from those assumptions, and if you have time see if you can find some data that is consistent with those implications. (Remember the joke about the economist stuck on the desert island: "assume a can opener"). It seems only natural that scholars doing empirical work in economics are more willing to make assumptions about how their data was generated, hence the interest in unbiasedness, asymptotics, and a general focus on analytical results, which I agree are characteristic of a lot of the work in econometrics.

This is of course a touchy issue, but it seems to me econometrics was originally a subset of statistics, that broke off and has been evolving semi-independently since then, so a large divide has appeared.

Since econometricians and statisticians publish in each other's journals it seems immature to try to assert that one group is overall better than the other. Econometricians, by training, know a small area of statistics better, but are far less knowledgeable about most areas, until someone finds out how to apply it to economic problems (e.g. the recent surge of MCMC work).

I agree with the common theme in many of the above comments which characterize economists as applied researchers trying to make conclusions about the "truth" (they believe in their model) and statisticians as folks more concerned with the the process of making conclusions from data.

My two cents, coming from a statistician who has had some limited interaction with economists is as follows.

Modern statistics evolved largely out of the work of R.A. Fisher, who was concerned primarily with the design and analysis relatively small, controlled experiments (actually you could make the case that Fisher came up with the whole idea of using controlled experiments, or at least formalized the rationale for using controlled experiments).

On the other hand economists are often trying to test their models using very large sets of data that most assuredly do not come from controlled experiments.

I think that many of the differences between statisticians and economists that James notes can be explained by this characterization of statistics/economics.

Since economists have large data sets, asymptotics makes sense. Again, with large data sets the sampling varaince of estimates is negligible, so bias is the only relevant concern. On the other hand, a statistician will tolerate some bias in exchange for a reduction in variance.

Economists often use data to test the validity of some theoretical (mathematical) model of the economy. There is a danger that errors in estimates of parameters will propagate throughout the model, hence the focus on precise parameter estimation.

Finally, the economist is often analyzing actual data in order to validate some theoretical model. The particular data analyzed is of interest only insofar as it is emblematic of the conditions specified in the model. Since the "pen and paper" solution may give insight into properties of the model it is of inherent interest.

On the other hand the statistician's primary concern is the information contained in the data set in front of her in and of itself, not as emblematic of some model. The statistician adapts a mathematical model only insofar as it helps her draw conclusions from the data. You might say that to the economist the model is primary, to the statistician it is secondary. Thus if a computational solution to a problem does an equally good job of extracting information from the data, the statistician is equally well satisfied.

On this topic, I seem to remember reading an article in some journal that looked at citation rates between disciplines in area of applied statistics. My recollection is that economics was the most "insular" in terms of citing within the field. If anyone remembers the article that I'm referring to, a link would be much appreciated.

Well this seems an easy one, and I'm barely a grad student... Econometrics was originally seperated from statistical economics because econometrics involves a priori knowledge. Before you even get the data, you are to use theory to describe what you think will happen with expected signs on coefficients, etc...

This was super important back before computers and large data sets when it was extremely tedious to calculate out the statistics, you could run max 4-5 regressions with your data. These days with VAR models and other atheoretical methods, people sometimes worry less about theory before they get the data because they can craft a story after they get good statistics.

As an aspiring statistician, it was also easy to give the statistical version of things, which is that statisticians invent data analysis techniques and methods that, after ten to twenty-five to forty years, filter into or are reinvented by other fields (whenever I said this, I clarified that this story was a caricature).

Of course it's a caricature. It's the probabilists and other mathematicians who invent the techniques and methods that, after ten to twenty-five to forty years, filter into or are reinvented by statisticians before filtering into or reinvented by other fields. Sure, sometimes the statisticians claim that they invented it first, but either they haven't proven it, so it isn't really invented, or they're referring to something proven by a sufficiently talented and theoretical statistician, therefore really a mathematician. (Note: The same thing applies to computer science. :)

E.g., Chebyshev-- Mathematician. Bayes-- Mathematician. Kolmogorov-- Mathematician. Shannon-- Mathematician. :)

I would disagree on the mathematics->statistics->econometrics. It is certainly true that mathematicians laid out the foundations of statistics. Central Limit theorem, Law of large numbers, martingale difference sequences (just to cite examples) are mathematical concepts. Statisticians/econometricians have taken the tools and used them in very creative ways. I took mathematical statistics and probability theory in parallel. On the same day I heard the probabilist arguing that densities are pretty much useless as everything can be expressed in terms of measures and the statistician claiming that measures are mathematical elegant but useless as statistical concepts can be expressed by restricting attention to density. While this is a caricature, it expresses the difference in focus. Again, \epsilon difference in focus, large methodological divide.

Statistics has given has a deep understanding of uncertainty and the way this uncertainty can be brought into statements about reality. Econometricians have played with this concepts and expanded the realm of applicability, by popularizing existing techniques (e.g., Rubin causality) in some cases, creating new tools (e.g. instrumental variables, cointegration, unit root, etc.) in other instances.

I would also disagree on why asymptotics is central in econometrics. It is not because in economics large dataset are available . It is because economists have been increasingly reluctant in making strong modeling assumptions. Economic theories give weak restrictions and the only way to test the theories by themselves is to relax functional forms assumptions. Once these assumptions are relaxed the only way to incorporate uncertainty is by a big N thought experiment.

"It is because economists have been increasingly reluctant in making strong modeling assumptions."

As a statistician, I couldn't help but really chuckle when reading that line.

As a statistician who has worked in a Department of Econometrics for the last 9 years, I've had occasion to think about this quite often. Here are some things I've noticed:
1. Statisticians produce FAR more graphs than econometricians. It is not uncommon to hear a seminar from an econometrician involving complicated data analysis but to have no graphs at all.
2. Econometricians are much more concerned about testing their models. They spend a lot more time on hypothesis tests to check that the model is good.
3. Econometricians refer to the model as "the data generating process" which seems to imply they believe it to be true. Statisticians tend to think the model is a useful approximation but not how the data were really generated.
4. The average econometrician tends to know more about regression and time series (and especially about their interaction) than the average statistician. But they often haven't heard of other major topics in statistics.

One economist view:

So we have to be careful what we are talking about here are we comparing Econometricians/Political Methodologists (people who invent and test new estimators) and Statisticians who do similar work. Or are we comparing applied econometrics/applied methods folks to applied statisticians? Gotta compare apples to apples IMHO.

For my money the applied econ folks have thought long and hard about the best way to test theories. About uncovering ceteris paribus partial effects from all different sorts of data. In fact I think some of the best PolMeth types are even better at really thinking carefully about what empirically testing a theoretical model needs to look like. These people also have an advantage in that they are trained in the are of social science that they are researching so they are usually aware of nuances of the theory and data that may need to be accounted for in the empirical specification.

Nice to read your article James.

I think that asymptotics is absolutely key in mainstream econometrics. Where is a discussion of unit roots or GMM or IV or other (econometrician-invented) methods without a discussion of asymptotic distributions? Nothing. They don't have a way of testing except in some PLim. Similar for unit roots. Nobody characterises distributions for t-tests (aka ADF tests) in the case of unit roots except where there is some

There is a bridge though. There always has been a link between the two fields in the form of Bayesian Econometricians, e.g., Zellner, Sims, Litterman, et al. And, the divisions between econometrics and statistics gets much more blurred when you see the (newer) work in state-space models, including Kalman filters (a la Harvey and his school), regime shift models (a la Hamilton), and in Bayesian versions of these (see Nelson-Kim's book), and in nonparametric econometrics and the increased use of bootstrap.

In general, though, econometricians are wedded to MLE and large sample theory and love to test. Statisticians, even those who are not hardcore bayesians, are more aware of the stderr-bias tradeoff and quite happy to talk about biased estimators in public, in a way that might make econometricians cringe.

An interesting debate. Economics models are often generated and then economists look for some statistics to back it up. A good example is the Phillips curve to show relationship between inflation and unemployment. In his initial analysis he actually looked at nominal wages not inflation to show a trade off.

This discussion fascinating -- the difference you posit between economists and statisticians is exactly the one that computer scientists say is the difference between statisticians and machine learners -- the former are more conerned with description, parameter estimation, and simple models, whereas the latter are more concerned with prediction, numerical optimization, and sophsticated models requiring programming.

The computer scientist vs. statistician issue also has another element, data set size; I wonder to what extent it is present in statistics vs. social science departments. My computer scientist coworker went to a statistical conference with lots of R developers, and he asked whether it was possible to scale up the implementation of a certain test for thousands of data points. He got the reply, "why would you ever want to use so much data? Just subsample." That was simply an unreasonable suggestion for his problem (involving user behavior data from a web search engine)...

Actually, it sounds like the difference isn't sample size so much as it is the fact that statisticians are more comfortable with subsampling.

Interestingly, when complex models do arise, the divide you're likely to see is one of sampling versus optimization.

I realize that this is a pretty late comment, but I'll still post it because this point wasn't really mentioned.

In my experience, statisticians want to look at the data and get the story from the data--which is commendable. But for many problems in economics, two grossly different underlying DGPs will give basically the same data... two examples that come to mind offhand are the macroeconomic models underlying VARs, that by and large differ only in how they assign rotations to the model's residuals/innovations, and game theory/io models where two extremely skilled players can counter each other and look just like two extremely unskilled players.

So economists usually want to distinguish between stories that make _almost_ identical statements about many features of the data. To preempt some catty comments, I (and I think most economists) realize that 'good' theories make predictions about the world that can be refuted, and we realize that it's lame to say 'the theories make identical predictions...' but policy needs to be set, and you have to make decisions with the data that you have, not the data that you wish you had. So, even though the models might predict basically the same historic data, you fund the Fed much differently if you believe that monetary policy can affect the real economy than if you don't.

There is a lag from the time techniques are introduced in statistics and when they're implemented by economists, and I suspect that's usually because statisticians are content after proving that a method approximates the data well. But more development is necessary for it to be useful to applied economists.

--Gray