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agosto alternative demand systems Banca d'Italia Bollino Christensen clothing and miscellaneous CM CO rH COMPARISON WITH ALTERNATIVE COMPLETE DEMAND SYSTEMS consumer behavior consumption categories corresponding to Column data set demand equations demand functions demographic characteristics demographic effects demographic variables derived discussed domanda Econometrica economic condition Economic Studies empirical viewpoint Engel Curves estimates from data ESTIMATION OF COMPLETE expenditure classes functional form homogeneous of degree household budget data impact of demographic income elasticities indirect utility function ISTAT Italian consumption patterns Italian household budget likelihood ratio test likelihood values Linear Expenditure System MEMBER 2 MEMBER MEMBER 4-9 MEMBER minus the sum number of parameters panel data paper Pollak and Wales price-expenditure situations procedure Quadratic Expenditure System Review of Economic rH O CM Rossi Roy's identity settembre 1984 significant Slutzky specification statistically SYSTEM IN COMPARISON Table 4.1 presents total expenditure Translog System Trinomial Expenditure System