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I was reading a paper on robustness (http://econ.ucsb.edu/~doug/245a/Papers/Robustness%20Checks.pdf) and they say:

"To determine whether one has estimated effects of interest, $\beta$; or only predictive coefficients, $\hat{\beta}$ one can check or test robustness by dropping or adding covariates."

What does a model being robust mean to you? Is this the only way to consider it in an econometric sense?

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Take a look at this Hal Varian paper:

Many papers in applied econometrics present regression results in a table with several different specifications: which variables are included in the controls, which variables are used as instruments, and so on. The goal is usually to show that the estimate of some interesting parameter is not very sensitive to the exact specification used. One way to think about it is that these tables illustrate a simple form of model uncertainty: how an estimated parameter varies as different models are used. In these papers the authors tend to examine only a few representative specifications, but there is no reason why they couldn’t examine many more if the data were available.

I would also add that the effect may change when you alter the covariates or the sample, but it should do so in a predictable and theoretically consistent manner to be called robust.

There are other sense of robust that are often used and are somewhat related: robust to heteroskedasticity or autocorrelation, outliers, and various assumption violations (like error distributions).

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  • $\begingroup$ Interesting! In your opinion, do you think it makes more sense to start with a larger model (including core covariates, and others) and then show that the core covariates don't change when removing some of the "others". Or begin with a smaller model and add? $\endgroup$
    – Brian
    Commented May 7, 2014 at 22:33
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    $\begingroup$ That's a tough question. There are several competing philosophies of variable selection that depend on the researchers' ultimate goals. Personally, I use economic theory to pick a preferred specification that is relatively parsimonious. Then I test down a general variant of that specification that encompass rival theories. At times, I have used regularization on a less carefully selected set of variables. $\endgroup$
    – dimitriy
    Commented May 7, 2014 at 22:50

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