I am building a simple model that estimates future change in GDP growth using change in working-age population (%).
$$ \Delta GDP_t = \beta_0 + \beta_1 \Delta Pop_{t-1} + \varepsilon_t. $$
I have run a linear regression on Japanese data, and I got a significant $R^2$ (0.45). There isn't any pattern in the residuals.
The next step I will do is use ARIMA/ETS in R to forecast future values in the working-age population, and plug this data into the model to predict future GDP growth.
Does my approach make sense from a statistical point of view? Do you think there is a more logical approach?