Positive effect of market share, yet negative one of market-wide HHI?

[Peter Meier]

Hi there,

in regressions on different topics and in different setups I have encountered cases where each observation's market share had a positive effect on the outcome whereas a higher Herfindahl Hirschmann Index, i.e. a higher sum of squared market shares in that same market, had a negative one.
Note that in the regressions with market shares I did not control for market-wide HHI, nor did I control for the observation's own market share when analyzing the effect of HHI.

I am struggling to understand how this is possible. Can anyone see it?

Thanks so much,
PM

[Nick Cox]

I don't think this can be discussed easily without information on the variability of and correlation between these variables and on what other variables were included in any regression. Even the sign of estimated coefficients can be a side-effect of other features of a dataset.