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I want to run a cross sectional regression for 700 firms in the US to test the impact of working capital on profitability. I specifically want to limit my analysis to the 2008 financial crisis and want to see how certain financial ratios impacted firms in 2008. I understand that I can take a few years (2008, 2009, 2010) and run a fixed effects model, therefore accounting for unobserved heterogeneity, however I specifically want to run a regression spanning 700 firms in one time period. Does anyone know how I can account for firm-varying unobservable heterogeneity since the firms span various sectors and have very different working environments? specifically, if there is a type of regression that accounts for this? I am working on SPSS and Stata.

Thanks.

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  • $\begingroup$ Weighted least squares is one time-honored method for mitigating heterogeneity, the whitening transformation might be another. $\endgroup$ – Mike Hunter Dec 18 '20 at 17:04
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You are looking at a cross-sectional regression with non-time related subgroups, say, linear

$$y_{is} = \mathbf x_{si}'\beta + \mathbf z_{si} + \mathbf g_s+ v_{si}$$

where $s$ indicates the subgroup (different industry for example)

and your individual $z$ variables are not observable as data.

Group-wise heterogeneity (different industries, geographical) could be dealt with by including indicator functions to represent $\mathbf g$.

But you cannot account for individual, observation-per-observation heterogeneity with a cross sectional sample and using least-squares estimation.

You could look for an indirect approach by using the two-tier stochastic frontier model, that requires maximum likelihood estimation, and it can provide measures of unobservable variables at the individual firm level.

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  • $\begingroup$ Thanks Alecos. So in relation to the equation you presented, "g" would consist of dummy variables to represent the sectors? $\endgroup$ – Mazen Mourad Dec 19 '20 at 6:07
  • $\begingroup$ @MazenMourad Yes. $\endgroup$ – Alecos Papadopoulos Dec 19 '20 at 12:32

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