Effect of an auditor's experience on client size and client complexity I am working on a dataset containing a list of auditors, collected in four different years:


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*2008: 650 auditors

*2009: 646 auditors

*2010: 635 auditors

*2011: 620 auditors


(A possibly large number of auditors may appear in two or more different years.)
Each individual auditor in each year comes with the following information:


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*His number of years of experience (as of that year)

*Total number of client companies that he has audited in that year

*Average asset of the client companies that he has audited in that year

*Other information about the client companies, such as risk, ROA, etc...


I am asked to find out how the experience of an auditor can affect the number of clients he has as well as the the size and the complexity of his clients.
For example, I have to find the answers to the following types of questions: Do older auditors have fewer clients than younger
auditors? Do older auditors have larger and more complex clients than younger auditors? etc... (By "older" I mean "more experienced", i.e. "more years of experience").
I have several questions to ask (I don't know where to start, really :( ):


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*Should I combine the four years to get a big data matrix and consider each row (i.e. each auditor) as an independent data point? Or should I treat each year separately?

*How should I divide the auditors into groups of experience? Should I:


a) First divide the auditors into groups based on the number of auditors in each year of experience, and then find other results (on the clients' characteristics) for each group? If yes, then how? Below is the histogram of auditors in each year of experience (for all 2008-2011 combined).

or
b) First find the results and then divide the auditors into groups based on the obtained results? For example, if I plot the number of clients, and the average client assets for each auditor then I got the following results (where each point of the scatters is an individual auditor).


I can observe that the results are somehow correlated, and by observation (with the eyes) it is reasonable to divide the auditors into 3 groups: Young (e.g. < 5 years), Middle (5-35 years) and Old (> 35 years). Is this a good way to do? Or is there a method for doing that better, not "by the eyes"?
Thank you very much in advance for your discussions!!
 A: There's one big gotcha here, which is that although it sounds like you're interested in causal effects ("how the experience of an auditor can affect"), this data provides no good way to draw any causal conclusions. Not only do we lack a true experiment with random assignment, which is the key research-design feature you need to positively identify causation; the causal effect of years of experience is difficult to distinguish even in theory from the effect of mere passage of time, since these are obviously necessarily linked. This said, we can still investigate, for example, how experience predicts client size and client complexity.
The core thing you want to do is build models that predict client size or some measure of client complexity (I don't know anything about finance) on the basis of experience. It is almost certainly a bad idea to discretize experience into a few groups; treat it as a continuous variable instead. Linear regression, perhaps with squared and cubed experience in addition to a linear effect, is a natural choice. You can assess model accuracy in a fashion unbiased by overfitting by using cross-validation.
It's worth making the model somewhat more complex to properly account for multiple cases per auditor and the year structure of the data. The latter is easy; just include year as a predictor. For the former, you can upgrade your ordinary linear regression model to a mixed model with one batch of random effects (random intercepts are probably enough to start with), in which there's one random effect for each auditor.
A: You've got a pretty big challenge here. Kodiologist's points regarding causality are well taken. Next, measuring some of the constructs you tossed out is nontrivial, e.g., client "complexity." Do you have a working definition for this? One proxy for this might be to consider the diversity of possible structures from "pure play" (i.e., a single SIC code) vs conglomerates (e.g., GE or J&J both of which span multiple industries). If some of your client companies are private, obtaining this information could be a big deal involving hours of some hapless intern's sweat and blood. Not to mention that these relationships aren't fixed and will change over time as entities restructure.
I would recommend considering leveraging a multi-level model of some kind with an individual auditor's records comprising one hierarchy, client companies within SIC codes might be another level, and so on. Good resources include Gelman and Hill's book Data Analysis and Regression Using Multi-Level/Hierarchical Models or Judith Singer's book Applied Longitudinal Data Analysis. 
