# Interpretation of model with interaction quotient

I am unsure about the interpretation of $$\beta_1$$ in the binary choice model

$$Y=𝟙[\beta_0+\beta_1V+\beta_2\frac{V}{C}+\varepsilon>0].$$

Because I know that $$V$$ and $$C$$ are uncorrelated, I do not control for $$C$$ as it is not an omitted variable for $$\beta_1$$.

In my context $$V$$ is the subjective value and $$C$$ the cost of a project (e.g. new road or new community centre). $$Y$$ is a binary variable indicating whether the decision makers invested in the project. For rational decision makers, the value-to-cost ratio $$\frac{V}{C}$$ should be the only decision criterion.

My current interpretation of $$\beta_1>0$$ is that keeping the value-to-cost ratio $$\frac{V}{C}$$ constant, individuals are more likely to invest in high-value items. Thus, $$\beta_1>0$$ would indicate a systematic bias towards high-value projects.

Do you agree with this interpretation of $$\beta_1$$ in the presence of an interaction quotient?