EMPIRICAL ESTIMATION ISSUES 1. Aggregation over consumers: X X - PDF document

ECO 305 — FALL 2003 — September 30 EMPIRICAL ESTIMATION — ISSUES 1. Aggregation over consumers: X X Market demands D c ( P , I c ) 6 = D ( P , I c ) c c 2. Functional form speci fi cation: Imposes implicit assumptions about substitution etc. But too many parameters ⇒ few degrees of freedom. These 2 less serious now: microdata, computing power 3. Aggregation over commodities: relative prices and commodity composition within group can change 4. Scope of estimation — saving, labor supply etc. 5. Estimation biases if RHS variable not truly exogenous Two data points, R and G Prices PR, PG di ff er because higher tax in G because more demand in G Estimated DE wrong too inelastic Lesson — understand your data and reasons for variation Look for “experiments” (control and treatment) in data 1

EMPIRICAL ESTIMATION — EXAMPLE From Richard Blundell, “Consumer Behavior: Theory and Empirical Evidence,” Econ. Journal, March 1988. Speci fi cation of household’s expenditure function M = M ∗ ( P , u ) = [ A ( P ) + B ( P ) u ] 1 / α where X X θ ij ( P i P j ) α / 2 A ( P ) = i j Y ( P i ) α β i B ( P ) = i Imply expenditure shares S k = P k x k /M =  ¶ α / 2  µ P i P k ¶ α / 2 µ P i P j X X X  1 −  θ ik + β k θ ij M 2 M 2 i i j Data — expenditure survey of 65,000 U.K. households Estimation using maximum likelihood Results — reasonable income and price elasticities Testing restrictions on ( θ ij ) , β i for homogeneity, concavity some violation of homogeneity (to do with time aspect) and of cross-symmetry (could be more basic problems) 2