Assessing the Accuracy of the Aggregate Law of Motion in Models with Heterogeneous Agents

This paper shows that the R² and the standard error have fatal flaws and are inadequate as accuracy tests for models with heterogeneous agents and aggregate risk. Using data from a Krusell-Smith economy, I show that approximations for the law of motion of aggregate capital for which the true standard deviation of aggregate capital is up to 14% (119%) higher than the implied value (and which are thus clearly inaccurate) can have an R² as high as 0.9999 (0.99). Key in generating a more powerful test is to not update the aggregate law of motion with the aggregated simulated individual data, but to use as the explanatory variable the value predicted by the aggregate law of motion itself.