# Composite variable as DV. Can I include part of it as independent variable?

I am struggling to form a regression model as I have to explain financial performance of a company.

The problem is that I have a variable like Return on assets $\frac{ebit}{total assets}$ as a dependent variable and I would like to control for total assets. I understand that if I include "total assets" as Independent Variable, I will end up with a probably significant coefficient as there is obvious correlation between dependent Variable and Independent Variable. My questions is regarding the interpretation of other variable coefficients.

Are they ok or do they suffer from the inclusion of "total assets" into the model?

model example:

$\frac{Ebit}{total assets}=constant+b_1*total assets+b_2*AGE+e$

I see this kind of situation a lot in the paper, but it is not considered a problematic. I personally think that its important to control for "total assets" in this situation but does someone see a problem here?

I'm not certain—so don't take me at 100% here—but it doesn't feel right to me. Predicting y/x by x itself is strange. Of course you are going to get a significant prediction, because x is used to calculate the DV. I generated some random data (assuming no relationship between any of the variables)...

set.seed(1839) # setting seed for replicability
ebit <- sample(1:7, 200, T) # creating ebit scores
assets <- sample(1:7, 200, T) # creating assets scores
age <- sample(1:7, 200, T) # creating age scores
data <- data.frame(roa=ebit/assets, ebit, assets, age) # making dataset


and ran the models:

summary(lm(roa~assets+age, data)) # running roa as DV

Call:
lm(formula = roa ~ assets + age, data = data)

Residuals:
Min      1Q  Median      3Q     Max
-1.8400 -0.6483 -0.0154  0.4882  4.3598

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  3.32694    0.22118  15.042   <2e-16 ***
assets      -0.44517    0.03770 -11.807   <2e-16 ***
age         -0.04832    0.03768  -1.282    0.201
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.025 on 197 degrees of freedom
Multiple R-squared:  0.4189,    Adjusted R-squared:  0.413
F-statistic:    71 on 2 and 197 DF,  p-value: < 2.2e-16


And

summary(lm(ebit~assets+age, data)) # running ebit as DV

Call:
lm(formula = ebit ~ assets + age, data = data)

Residuals:
Min      1Q  Median      3Q     Max
-3.0695 -1.7712  0.1377  1.4421  3.5400

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  3.35110    0.43397   7.722 5.66e-13 ***
assets       0.04386    0.07398   0.593    0.554
age          0.06503    0.07393   0.880    0.380
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.011 on 197 degrees of freedom
Multiple R-squared:  0.005828,  Adjusted R-squared:  -0.004265
F-statistic: 0.5774 on 2 and 197 DF,  p-value: 0.5623


The effect of assets on roa makes sense in the first model. All it says is: As the denominator gets higher, the value of the quotient gets lower. How does that help you? The second model is more straightforward: It is the effect of assets and age on ebit simultaneously.

• Thanks for your comment.That is certainly one way to go with this problem.How about if we have a variable like "Employment growth" measured as (employment[t]-employment[t-1])/employment[t-1]. The task is to study which one of two corporate types (Listed companies vs. unlisted companies) have better employment growth rate during some period. Let say that smaller companies (measured by employment) have systematically higher employment growth rate. Lets also assume that unlisted companies are systematically smaller (measured by employment).continues.. – user6574498 Apr 28 '17 at 10:51
• if we fit pooled OLS, we get result that employment growth rate is larger within unlisted companies although the ground truth could be the opposite. This is because we are not accounting for employment size. How can we work around in this situation? Is it so that we use "employment[t]" as dependent var. and lag of it as IV? – user6574498 Apr 28 '17 at 10:54