Multi-level analysis needed?

[Franz Hopp]

Dear Statalist forum,

I have a situation where I am not sure whether a multi-level analysis is needed. Or whether it might suffice to include a firm dummy.

The analysis I run is intended for a paper in the field of management/ strategy. So, the relationship I study is how a certain characteristic of a business unit (BU) affects the business unit’s financial performance. Each of the business units belongs to a firm:

BU_performance = BU_characteristic_of_interest + controls

The controls include some other characteristics of the BU (e.g. the size of the BU). But the controls also include some variables that come from the firm-level (for example, the ‘percentage of the firm that is owned by the firm’s CEO and the firm’s top management team’).

So for example, I have 9 observations in my dataset that belong to the firm Generel Electric (GE) in the year 2000. These 9 observations reflect the 9 business units that GE operated in that year. The BU_characteristic_of_interest differs for each of the 9 BUs of GE in that year. Similarly, some of the controls are different for each of the BUs of GE (e.g., the size of the BU). Yet for other variables, all of the 9 BUs will have the same values (e.g., all of the 9 BUs will have the same value for the ‘percentage of the firm that is owned by the firm’s CEO and the firm’s top management team’).

Now, the business unit observations are not really independent from each other.

So I wonder whether for the case describe above I will *have* to use a multi-level model (Stata XT Mixed). Or whether it might suffice to include a firm dummy for each firm.

The reason I would like to avoid the multi-level model is that I worry that I might run it the wrong way or misspecify the model. I am not a big expert on econometrics whatsoever.

Also, I feel that in my field (strategic management), multi-level models are not common at all. Although I wonder whether (by a similar logic described to the above), they would actually be needed. In strategic management, we often compare different firms with each other – but firms typically come from different industries – i.e. firms are nested in different industries. So wouldn’t that mean that all these researchers should actually use multi-level models when they study these different firms? (But, I just don’t really see them using multi-level models.)

So I wonder what is the correct thing to do econometrically?

Can one also just include firm dummies (for the business unit example which I described in the beginning of this post)? Would using firm dummies be alright as well, or would this approach break some econometrics rule?

Or, alternatively do I have to use a multi-level model for this situation?

Thanks so much.

Best,
Franz

[Jeff Wooldridge]

Franz: It’s perfectly acceptable to use a fixed effects analysis at the firm level, and also cluster your standard errors at the firm level. You will eliminate the firm-level variables. Alternatively, you can use a standard regression analysis and add the within-firm averages of the unit-specific covariates, along with the firm variables. This is the same as including firm dummies but keeps the firm-level variables. It’s called the correlated random effects approach.

A mixed level model is not needed, nor is it desirable in this situation.

JW

[Franz Hopp]

Hello Jeff Jeff Wooldridge,

Thanks much for your answers. These were incredibly helpful. I read up on your suggestions, but I am not fully sure whether I understood everything correctly.

(1) You mentioned that “It’s perfectly acceptable to use a fixed effects analysis at the firm level”. Would it also be OK to use a fixed effects analysis at the SBU level?

For example, my data structure looks like the below: I am curious how a business unit’s strategy (BU_Strategy) affects the unit’s financial performance, measured as return on assets (BU_ROA). I have two control variables; first, the size of the business unit measured in assets (BU_size) and second the % of shares of the firm owned by the CEO (CEOown).

Firm_BU	Year	Firm	BU_SIC	BU_name	BU_ROA	BU_Strategy	BU_Size	CEOown
GE_Healthare	2000	GE	2600	Healthare	0.07	0.25	200	0.04
GE_FinServices	2000	GE	3500	FinancialServices	0.14	0.44	150	0.04
GE_Gas	2000	GE	5000	Gas	0.02	0.12	600	0.04
Siemens_Healthare	2000	Siemens	2600	Healthare	0.04	0.66	120	0.15
Siemens_Gas	2000	Siemens	5000	Gas	0.03	0.25	400	0.15
GE_Healthare	2001	GE	2600	Healthare	0.08	0.35	210	0.03
GE_ FinServices	2001	GE	3500	FinancialServices	0.22	0.24	180	0.03
GE_Gas	2001	GE	5000	Gas	0.06	0.32	680	0.03
Siemens_Healthare	2001	Siemens	2600	Healthare	0.03	0.26	140	0.20
Siemens_Gas	2001	Siemens	5000	Gas	0.07	0.34	500	0.20
...

So, to estimate how business unit strategy affects business unit performance, I specified the following FE model:

xtreg BU_ROA BU_Strategy BU_Size CEOown, fe vce(cluster Firm_BU)

• What worries me with the BU-level model above is whether or not the model takes into account that different BUs belong to the same firm (e.g. 3 BUs belong to GE in 2000).
• First I was thinking of simply including firm dummies for the business unit-level analysis above (each observation is for a business unit). But then I realized I cannot explicitly specify firm dummies in the FE model above (firm dummies are time-invariant, so the FE model cannot estimate them).
• Now my thinking was that with an FE model, all time-invariant attributes are automatically controlled for. So that way, the above model is equivalent to including firm dummies, right? Because the fixed effects only look at the changes within one business unit over time. And, the firm is perfectly collinear with the business unit-fixed effects. So the business unit-fixed effects should already control for the firm, even without explicitly adding them as a control variable.
• However, when I talked with a colleague about my regression approach, my colleague asked me if there is no specific firm dummy, how could Stata know that different observations (business units) belong to the same firm? The program would recognize that it is the same business unit when multiple years of data are provided for the same business unit, but how could Stata know that multiple business units belong to a particular firm. – I thought this was a really good question, and I did not know what to reply to my colleague; so this made me worried that following the above FE approach might be wrong.
• Is the approach described above wrong (the business unit-fixed effects model above)? Is there anything I could reply to my colleague?

(2) You mentioned the correlated random effects (CRE) model. I tried to read up on the CRE model. But I am not 100% sure if I understood it correctly:

• First, I went about the CRE approach as follows:
  • The general idea would be to compute the business unit average of each of the explanatory variables which vary across both time (t) and business units (i). All of my three explanatory variables do vary across both time (t) and business units (i). So, I computed the business unit average of the independent variable of interest (BU_Strategy), and of the business unit-level control variable business unit size (BU_Size), as well as of the firm-level control variable “% of shares of the firm owned by the CEO” (CEOown)
  • Following this approach would then In the final regression allow me to include a firm dummy (i.Firm)

egen BU_Strategy_bar = mean(BU_Strategy), by(Firm_BU)
egen BU_Size_bar = mean(BU_Size), by(Firm_BU)
egen CEOown_bar = mean(CEOown), by(Firm_BU)
xtreg BU_ROA BU_Strategy BU_Strategy_bar BU_Size BU_Size_bar CEOown CEOown_bar i.Firm, re vce(cluster Firm_BU)

• Besides, I was not sure whether before using the CRE model, a (robust) Hausman test needs to be passed? I was not sure about this, because the CRE model seems to be a mix of a FE and an RE model. There some to be some FE components in the model (some of the variables are estimated by FE, and some by RE?)?
  • I ran a Hausman test on an FE vs. an RE model. Yet unfortunately, the Hausman test rejected the usage of an RE model. So I assume I am also not allowed to use the CRE model?
  • I assume for a paper, reviewers would be unhappy if I used a correlated RE approach, but not reported the results from a Hausman test?

(3) Also you mentioned that “A mixed level model is not needed, nor is it desirable in this situation.” I wondered because business units are nested in firms, wouldn’t we have to use a mixed-level/ multi-level model? Or, would there be something ‘wrong’ with using a multi-level model? Could you kindly let me know briefly why such a model is not needed/desirable?
(Personally I would prefer not to use the multi-level model/ Stata XT Mixed. But I fear I did not fully understand yet why a multi-level model is neither needed nor desirable. It would be awesome to understand this).


Please excuse my lengthy post! I hope it is not too messy.

Best,
Franz