How to test the linearity assumption of a model?

Let's say I want to have a model that projects income over a stressed period. I have a marked-to-market component that shows the P&L of trading book positions during this stressed period. Along with that, I have Gross Revenue data, Expenses, Carry, Transfer Pricing, Treasury Costs, etc, such that: MTM P&L + Forecasted Revenue + Forecasted Carry + Forecasted Transfer Pricing + Forecasted Treasury Costs - Expenses = Income

I want to check whether this linear assumption holds; that Income is simply additive across the variables mentioned. How could I test this?

• It is unclear what you are asking. Are you asking if there is a way to test an accounting identity, or are you asking whether, under shock, the responses of the underlying variables will be linear? – Dave Harris Jan 31 at 6:05

You would perform a multiple regression, except that instead of using the standard default of $$\beta=0$$, for all of your $$\beta$$s, instead, you would use $$\beta=1$$ for all $$\beta$$s. If the F test is statistically significant, then your null hypothesis is falsified. Depending upon the computer language, it will require a manual intervention into the code.