A residual plot that narrows instead of fanning out

Question

You regress a firm's forecast error on the number of analysts covering it, using 900 firms. The residual-versus-fitted plot is wide on the left and squeezes to a thin band on the right: thinly covered firms scatter a lot, heavily covered firms hug the line.

Is this still a problem, and if so, which one? Does it bias the slope?

Accepted Answer

Yes, it is the same problem. Heteroskedasticity just means the error variance is not constant. It does not matter whether the spread grows or shrinks with the fitted value: a widening fan and a narrowing wedge are both non-constant variance. Here the variance falls as coverage rises (more analysts, more consensus, less noise), which is heteroskedasticity every bit as much as a fan that opens up. The slope is unbiased. As before, only the zero-mean-error condition matters for unbiasedness, and a changing spread does not violate it. Your estimated effect of coverage on forecast error is fine. T…

A residual plot that narrows instead of fanning out

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