# Forecasting GDP using regression, ARIMA and ETS

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?

• Why not use arima/ets for GDP directly? – hejseb Apr 18 '16 at 19:16
• @hejseb, sure, that could work at least as a benchmark. But if there is another relevant variable, why not try including it, too? – Richard Hardy Apr 18 '16 at 19:39
• @RichardHardy Evidently there are many variables which are helpful in forecasting GDP. Just using Pop at t-1 feels a little bit odd, so there is probably some reason for this. Knowing this may make it easier to answer the question properly. – hejseb Apr 19 '16 at 4:01

1. You may think about omitted variable bias. If there are other variables influencing/determining the GDP growth, and those variables are correlated with the change in the working-age population, you will have a biased and inconsistent estimate of $\beta_1$, and hence poor forecasts.