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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 a cointegrating relation 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 phenomena 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. Copyright \u00a9 2005 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/jae.806","type":"journal-article","created":{"date-parts":[[2005,3,31]],"date-time":"2005-03-31T16:47:06Z","timestamp":1112287626000},"page":"579-601","source":"Crossref","is-referenced-by-count":46,"title":["Aggregate vs. disaggregate data analysis\u2014a paradox in the estimation of a money demand function of Japan under the low interest rate policy"],"prefix":"10.1002","volume":"20","author":[{"given":"Cheng","family":"Hsiao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yan","family":"Shen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hiroshi","family":"Fujiki","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2005,3,31]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-937X.00225"},{"key":"e_1_2_10_3_1","first-page":"267","volume-title":"Proceedings of the 2nd International Symposium on Information Theory","author":"Akaike H","year":"1973"},{"key":"e_1_2_10_4_1","article-title":"Reduced rank regression in cointegrated models","author":"Anderson TW","year":"2001","journal-title":"Journal of Econometrics"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.2307\/2077862"},{"key":"e_1_2_10_6_1","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1111\/j.2517-6161.1964.tb00553.x","article-title":"An analysis of transformations","volume":"26","author":"Box GEP","year":"1964","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"e_1_2_10_7_1","volume-title":"Time Series Analysis, Forecasting and Control","author":"Box GEP","year":"1970"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(73)90015-8"},{"key":"e_1_2_10_9_1","first-page":"367","article-title":"Transcendental logarithmic utility functions","volume":"65","author":"Christensen L","year":"1975","journal-title":"American Economic Review"},{"key":"e_1_2_10_10_1","doi-asserted-by":"publisher","DOI":"10.2307\/2286348"},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.2307\/1912517"},{"key":"e_1_2_10_12_1","series-title":"Keizai\u2010bunseki Seisaku kenkyu no Shiten Series","first-page":"9","volume-title":"Zaisei Akazino Keizai; Bunsehi; Cyu\u2010cyokiteki Shiten karano Kousatsu","author":"Doi T","year":"2000"},{"key":"e_1_2_10_13_1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198288008.001.0001","volume-title":"Aggregation and the Microfoundations of Dynamic Macroeconomics","author":"Forni M","year":"1997"},{"key":"e_1_2_10_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4068(98)00060-3"},{"key":"e_1_2_10_15_1","first-page":"39","article-title":"Alterative approaches to analyzing economic data","volume":"81","author":"Friedman M","year":"1991","journal-title":"American Economic Review"},{"key":"e_1_2_10_16_1","first-page":"1","article-title":"Is there a stable money demand function under the low interest rate policy?\u2014A panel data analysis","volume":"20","author":"Fujiki H","year":"2002","journal-title":"Monetary and Economic Studies, Bank of Japan"},{"key":"e_1_2_10_17_1","doi-asserted-by":"publisher","DOI":"10.2307\/2534203"},{"key":"e_1_2_10_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1573-4498(05)80011-6"},{"key":"e_1_2_10_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(80)90092-5"},{"key":"e_1_2_10_20_1","doi-asserted-by":"publisher","DOI":"10.2307\/1926089"},{"key":"e_1_2_10_21_1","doi-asserted-by":"publisher","DOI":"10.2307\/1913827"},{"key":"e_1_2_10_22_1","doi-asserted-by":"publisher","DOI":"10.1515\/9781400863716"},{"key":"e_1_2_10_23_1","doi-asserted-by":"publisher","DOI":"10.2307\/2171757"},{"key":"e_1_2_10_24_1","doi-asserted-by":"publisher","DOI":"10.2307\/2971719"},{"key":"e_1_2_10_25_1","volume-title":"International Encyclopedia of the Social and Behavioral Sciences","author":"Hsiao C","year":"2001"},{"key":"e_1_2_10_26_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511754203"},{"key":"e_1_2_10_27_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1997.10473997"},{"key":"e_1_2_10_28_1","unstructured":"HsiaoC WangS.2002.Estimation of structural vector autoregressive integrated processes. 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