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 accuracy tests. 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 that predictions of the aggregate law of motion are not updated with the aggregated simulated individual data.