Aggregate vs Disaggregate Data Analysis — A Paradox in the Estimation of a Money Demand Function of Japan Under the Low Interest Rate Policy

We use Japanese aggregate and disaggregate money demand data to show that conflicting inferences can arise. The aggregate data appears to support the contention that there was no stable money demand function. The disaggregate data shows that there was a stable money demand function. Neither was there any indication of the presence of a liquidity trap. Possible sources of discrepancy are explored and the diametrically opposite results between the aggregate and disaggregate analysis are attributed to the neglected heterogeneity among micro units. We provide necessary and sufficient conditions for the existence of cointegrating relations among aggregate variables when heterogeneous cointegration relations among micro units exist. We also conduct simulation analysis to show that when such conditions are violated, it is possible to observe stable micro relations, but unit root phenomenon among macro variables. Moreover, the prediction of aggregate outcomes, using aggregate data is less accurate than the prediction based on micro equations and policy evaluation based on aggregate data ignoring heterogeneity in micro units can be grossly misleading.