How can I control for unobserved heterogeneity with cross-sectional data?

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.

• Weighted least squares is one time-honored method for mitigating heterogeneity, the whitening transformation might be another. – Mike Hunter Dec 18 '20 at 17:04

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.

• Thanks Alecos. So in relation to the equation you presented, "g" would consist of dummy variables to represent the sectors? – Mazen Mourad Dec 19 '20 at 6:07