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I am doing a panel study where I have a sample of persons $i=1...N$ (up to $N=300$), that have some personality dimension quantified as variable $x$, over a time horizon $t=1...T$ (up to $T=20$). From this, I am trying to predict some other variable $y$ related to the person that is of economic interest, i.e. my regression model is

$y_{it}= \alpha + \beta x_{it} + c_{i} + \tau_t,$

where $c_i$ controls for individual (person) effects and $\tau_t$ for year effects (e.g. macroeconomic effects).

I want to find out in what way the variable $x$ related to the variable $y$ over time, in the sense of:

"Managers that have an incremental increase of 1 unit in their variable $x$ (which we have derived and measured as to give a good indication of an important personality trait whose impact in managers we want to measure in this work) will lead to $\beta$ unit change in a firm's financial performance indicator $y$."

Now, I am unsure regarding the exact usage of the control variable $c$. As these are individual person effects beyond the quantifyable, measurable $x$, there is no benefit from estimating these effects for each manager, as this would only happen ex-post and not serve any intended generalization of my results outside the sample.

However, clearly there are good and bad managers out there, that will necessitate the control.

But as my quantifyable "personality variable" $x$ is probably related to the person effects $c$ (and if it were not, it would be worthless as a measure the effect of a quantifyable personal attribute on the person's managing skills), I am afraid that the $c$ might eat up some effects that would otherwise be attibuted to the $x$, as in, "we measured a very low $x$ for this manager, and according to previous literature and our hypotheses, this should be correlated with his very bad firm performance $y$, but instead we find that there is no such significant correlation, but instead he is just a bad manager (low $c$)." But whether he is good or bad, is what we actually want to find out using the measured and quantified $x$, to predict future performance $y$ using $x$.

As there are very many managers ($N=300$) and time periods are at most $T=20$ years (average is much shorter), this means the model may tend to fit 300 $c_i$ instead of one $\beta$, indicating an effect that is much smaller than it should be. This indicates that I should not control for managers and leave the $c$ out of the above equation. Are there extra rules as to how to deal with this problem when we face such a short panel length and large number of panels (in addition, $T=20$ is only the maximum; they are on average $T=11$)?

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  • $\begingroup$ As this question has now gone unanswered and uncommented for two days, can someone perhaps suggest the reason for this? I did my best formulating the question :) $\endgroup$ – Marie. P. Jan 7 '16 at 15:13

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