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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?

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