Scaling capital expenditure with assets or adding controls

[fatima ht]

My question is not specifically about Stata, but rather the regression specification I should choose. I hope it is still relevant to this forum.

I am trying to estimate a model with a measure of firm investment in LHS and owner's wealth in RHS. I use capital expenditure as the measure of investment. My question is should I normalize (I mean scale) capital expenditure by assets or sales to control for the size of the firm, or can I leave the dollar value of capex in LHS and just control for assets or sales in RHS.

My own opinion is that scaling capex with assets or sales assumes a fixed kind of relation between investment and size, whereas controlling for the size in the regression makes the relation between the two variables more flexible. Besides, since the unit of my main explanatory variable (wealth) is dollar, it makes more sense to me to use the dollar value of investment too, ate least the interpretation is easier. The results from the two methods are significantly different, otherwise I would use one as the main specification and the other as robustness. So at least one specification is not correct.

I appreciate your help.

Fatima

[Carlo Lazzaro]

Fatima:
mostly depends on the methodological mainstream in your research field.
Personally, I would control for the size of the firm via a categorical variable.
I would also skim through the literature of your research field to rule out that your regression suffers from endogeneity (i.e. an omitted variable embedded in the residuals affects both the independent as well as the dependent variables).

[Phil Bromiley]

There is a substantial literature on normalizing variables. It is little odd that many areas do not normalize everything by the same normalization (Kennedy comments on this in A Guide to Econometrics). That is, we often see capital expenditures/sales explained by variables not normalized by sales. As Carlo says, following your field's norms is often a usually practice.

You are really estimating quite different models when you normalize something by x than when you control for x. For example, in corporate data, R&D Expenditures/Sales has roughly a zero correlation with R&D expenditures. Look at the algebra. y/x1 = b0 + b1 x2 + e is algebraically equivalent to y=bo*x1 + b1 x2*x1 + e * x1, not y=b0 + b1 x2 + b2 x1 + e.

Often it is desirable to lag the rhs variables to mitigate (but not necessarily eliminate) endogeneity issues.

Phil

[fatima ht]

Thank you Carlo and Phil. It seems that in the literature, normalizing income variables with total assets is common. So that's what I'm going to do.

Thanks again!
Fatima