Dear forum users,

I’m currently looking for some wisdom concerning the fixed modeling of my master thesis hypothesis. Since my professor is currently not available I’m thankful for any insightful suggestions regarding the correct modeling using fixed effects models.

My research focusses on the local influence of religiosity on Corporate Social Responsibility strategies of firms. Im trying to support the hypothesis that the level of religiosity in US-states influences the CSR-activities of firms. The study design is similar to McGuire et al. (2012): Does Local Religiosity Impact Corporate Social Responsibility and Kim et al. (2018): Local Religiosity and Corporate Social Responsibility; both in SSRN.

The dependent variable is a percentage score (ES_SCORE) which captures CSR-Performance and is nested within firm level. The independent variable is a religiosity ratio (REL) and is defined as percentage of adherents within a state in comparison to the total population and therefore is nested within state level. In addition I’ve accumulated firm and state level control variables. All variables are observed yearly covering a 8 year time period. In a last step I’ve matched firm level and state level data by identifying firm headquarters and assigning demographic/religiosity data to firms according to the location.

The final data set is unbalanced, in long format, covering observations over a 8 year period which are nested within 444 firms. The firms are located in 34 states and belong to 22 industry sectors. The data set does not include time invariant variables except the state_id and firm_id. Thank’s a lot if you’ve mad it this far!

My professor hasn’t told me much concerning the empirical modeling but insists on fixed effects. Therefore I’ve specified:

xtset firm_id yearly
xtreg es_score rel firmlevelcontrols democontrols, fe

Here comes the question. What is the correct approach for clustering standard errors? If I dont use vce(cluster) or robust option results are significant at the 5% level. If cluster on firm or industry, (using vce(cluster=comp_ID) or using vce(cluster=industry) I get similar results: (P>ItI=0.13)). Contrary if I cluster on state (vce(cluster=state)), I get significant results at the 10% level. Or should

1. Do you agree with this approach of fe-modeling? Is it reasonable to cluster on state, or should I cluster on firm level? Theoretically clustering on industry level is also possible. I’ve read that in nested data sets, clustering on the highest aggregation is plausible.
3. Im somewhat confused regarding xtset and vce(cluster) commands. By using ‚xtset firm_id yearly‘ I include firm fixed effects, but not time fixed effects, right? And by using vce(cluster=?) I account for cross-sectional dependencies of the standard errors according to state, industry or firm?
4. Which additional tests should I run? (did a hausman test before, which indicated fe over re; be aware that I’m a stata beginner, so I’d appreciate if you could add codes)
5. What are the limitations of this model? I’m aware that including xtreg fe vce(cluster=state) option should account for autocorrelation and heteroscedasticity of standard errors, but since cluster size is limited (34 for states, 22 for industry) my standard errors might be biased. Also the firms are not evenly distributed across the states or industry (some states contain up to 40 firms, while some only include 4-5) which further increases bias.
6. What is the correct Interpretation of the coefficients, since fe regression focusses on within estimation. Would be ‚A one standard deviation increase in REL leads to a 0.38 standard deviation increase in ES-score‘ applicable?


Again, thanks a lot. Have a wonderful day!