Does it make sense to have the dependent variable in growth rates or rather in levels? I am currently investigating the impact of uncertainty on investment dynamics. I have an unbalanced panel data set (approximately 100,000 observations). To study the relation between investment and uncertainty I use the following equation: 
 
where the dependent variable indicates the growth rate (change) of fixed assets over total assets. The second term of the equation (first of the right-hand side) indicates firm fixed effects, the third term is the uncertainty level (time independent) and $X$ represents additional controls at the firm level. 
In a recent discussion a colleague pointed out the implications of having the investment in growth rates. He stated that I am assuming that investment follows a random walk since investment growth rate by definition is the difference between the levels at t and t-1:

where $\rho$ is 1 by construction. Is this statement accurate? Is there any literature on whether it is best to use panel data investment in levels rather than in growth rates? 
 A: I like that you are using a panel data model structure but I wouldn't use it to model change in a ratio...ever! First of all, ratios are relative metrics which blur useful information wrt differences in absolute magnitudes between the units of analysis (the cross-sections). Moreover, ratios in and of themselves can create exploding outliers at both ends of the scale whenever inputs into the calculation differ dramatically in magnitude. This simple observation renders a change metric virtually meaningless as it's a relative measure derived from a relative measure. Good references discussing these issues are Aitchison's Statistical Analysis of Compositional Data or, more recently, Pawlovsky-Glahn, et al's, Modelling and analysis of compositional data.
To me, it would make more sense to model fixed assets with an hierarchical, longitudinal growth model. Given that the levels will differ between the units of analysis, a normalizing transformation such as the natural log will help to minimize these between unit differences and, thereby, minimize the chances of obtaining spurious results. 
The literature on hierarchical panel data models is huge. For your purposes it shouldn't matter if the discussion is about education, marketing, economics or finance since the only thing that really changes is the nature of the DV. A good intro is Judith Singer's paper Using SAS PROC MIXED to Fit Multilevel Models, Hierarchical Models, and Individual Growth Models (http://mumford.albany.edu/downloads/MLM_workshop_2016/singer.pdf). Forget the 'SAS' part, it's simply a great, short introduction to HLMs. Her book Applied Longitudinal Data Analysis goes much deeper into the issues. Lee Cooper's book Market Share Analysis has many suggestions for fitting such models with a particular focus on modeling elasticies as well as fitting differing patterns in the relationships between the IVs and DV (http://www.anderson.ucla.edu/faculty/lee.cooper/MCI_Book/BOOKI2010.pdf). Another valuable reference is Gelman and Hill's Data Analysis Using Regression and Multilevel/Hierarchical Models. Of course, the classic, theoretical treatment is Wooldridge's Econometric Analysis of Cross Section and Panel Data but it has the strong limitation that it doesn't descend into the trenches of applied practice and concerns. Finally, I like Baltagi's Econometric Analysis of Panel Data for his treatment of some of the inevitable complications that can arise with panel data models. 
