# 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.
2. If you are using quarterly (rather than yearly) data, you might want to explicitly account for seasonality in GDP growth to get more accurate forecasts. (I am not sure if there is seasonality in working-age population growth.)
3. The model would be problematic if GDP or changes in it affected working-age population growth; then you would have the problem of endogeneity. But perhaps it is safe to assume that the effect is only one way: from population growth to GDP and not vice versa.
4. I suspect that changes in working-age population could be predicted well using some demographic data, e.g. knowing how many youngsters are close to reaching the working age and how many seniors are about to retire. ARIMA or ETS would not include this external information, so they would likely deliver relatively poor forecasts. Consequently, you would have relatively poor forecasts of the GDP growth.