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I know that one can use Seemingly Unrelated Regressions when for an observation i, there are two equations whose errors are connected.

What is the intuition here among errors of difference equations have some sort of relationship? In the SUR case, is it simply because unobservable factors (say, for example, general attitude towards spending money) that explain things like consumption for food in observation 1 will also explain consumption for clothing, for the same observation 1?

Also, how does one call correlation between errors in this case? I understand it's not serial correlation, nor spatial correlation in this case.

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I believe it is called contemporaneous cross-equation error correlation.

The errors has can be interpreted as the effect of omitted variables, measurement error, or human indeterminacy. Here's one example of the first. Suppose your two outcomes are budget shares (rather than levels) for clothing and food. If someone puts on a lot of weight (typically unobserved to the econometrician, even in the days of big data), there will be large positive error in the clothing equation, and a large negative error in the food equation as the dieting commences.

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  • $\begingroup$ Thanks for this (years later!). Would you mind providing a second example? It's not clear to me whether the example I mentioned in the original post fits one of the interpretations of errors that you mention. It seems so, but I'm not entirely sure. $\endgroup$ – StatsScared Feb 3 at 16:19
  • $\begingroup$ @StatsScared Your example probably has a positive correlation. For example, a frugal person might repair or alter clothes and also grow or process their own food. This would cause the errors in the two equations to be correlated for the same person. $\endgroup$ – Dimitriy V. Masterov Feb 3 at 20:40

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