What are the drawbacks of aggregating regression results if error decreases?

Question

I am trying to predict Total National Sales in dollars for a major retailer. However, the data I'm using exists at the state level, and includes several features around specific brands and foot traffic, along with brand-specific sales totals. For other reasons, I cannot simply aggregate the actual state sales values and get the national number.

When I run a regression model against the state level data to predict state totals, the MAE of the state level predictions vs the state sales totals is significantly higher than when I aggregate the state level regression predictions and then re-measure MAE vs the national sales number, obviously, given error being normally distributed and then being summed. If, at the end of the day, I am NOT interested in the state level sales figures individually, and ONLY care about the national aggregate, am I taking on any additional risk in approaching the problem this way to get the national number? i.e. making predictions by state, and then totaling those predictions together to comprise the national prediction?

I have read some background material https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1538-4632.1976.tb00549.x and https://link.springer.com/article/10.1007/s00181-015-0941-z, but it seems most of these resources (and other similar ones) are talking potential misleading inference when measured at one level, but applied at another. This makes sense, especially in social science applications. However, I have no intention if interpreting the coefficients of the model at the national level, I simply care about the prediction accuracy at the national level.

Answer 1

This looks like a hierarchical forecasting problem. One issue is that you need to be careful when evaluating MAE for state level and national level. MAE depends on the absolute value of the target variable; if one variable is significantly smaller than another, predictions will usually produce higher MAE.

Now regarding your question, predicting individual states and adding them is a valid approach, called bottom-up. You can also try to directly predict the national level. If state level sales have low signal-to-noise ratio, i.e. are not easily predictable, then the bottom-up approach would probably result in worse performance that directly predicting the aggregate.