Your starting model is:

Y = c + $\beta_1$$\frac{A}{B}$

But, you are really interested in:

Y = c + $\beta_1$ * $\Delta$A + $\beta_2$ * $\Delta$B

In your statement I think that is what you are doing. And, if that is it, that's fine. That would be the best way to figure out what are the separate influences of changes in A ($\Delta$A) and changes in B ($\Delta$B) on your dependent variable Y.

If you do that, you may also want to detrend your dependent variable so that it also reflects a change. By doing so, you will avoid unit root issues in both your dependent and independent variable. Your model will also probably test better in terms of residuals structure (heteroskedasticity, autocorrelation, Normality).

Your starting model is:

$Y = \beta_0 + \beta_1\frac{A}{B}$

But, you are really interested in:

$Y = \beta_0 + \beta_1 \cdot \Delta \text A + \beta_2\cdot \Delta \text B$

In your statement I think that is what you are doing. And, if that is it, that's fine. That would be the best way to figure out what are the separate influences of changes in A ($\Delta \text A$) and changes in B ($\Delta \text B$) on your dependent variable Y.

If you do that, you may also want to detrend your dependent variable so that it also reflects a change. By doing so, you will avoid unit root issues in both your dependent and independent variable. Your model will also probably test better in terms of residuals structure (heteroskedasticity, autocorrelation, Normality).

Your starting model is:

Y = Constant + coef(A/B)

But, you are really interested in:

Y = Constant + coef1(change in A) + coef2(change in B).

In your statement I think that is what you are doing. And, if that is it, that's fine. That would be the best way to figure out what are the separate influences of changes in A and changes in B on your dependent variable Y.

If you do that, you may also want to detrend your dependent variable so that it also reflects a change. By doing so, you will avoid unit root issues in both your dependent and independent variable. Your model will also probably test better in terms of residuals structure (heteroskedasticity, autocorrelation, Normality).

Your starting model is:

Y = c + $\beta_1$$\frac{A}{B}$

But, you are really interested in:

Y = c + $\beta_1$ * $\Delta$A + $\beta_2$ * $\Delta$B

In your statement I think that is what you are doing. And, if that is it, that's fine. That would be the best way to figure out what are the separate influences of changes in A ($\Delta$A) and changes in B ($\Delta$B) on your dependent variable Y.

If you do that, you may also want to detrend your dependent variable so that it also reflects a change. By doing so, you will avoid unit root issues in both your dependent and independent variable. Your model will also probably test better in terms of residuals structure (heteroskedasticity, autocorrelation, Normality).