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

ECO 305 — FALL 2003 — September 30

EMPIRICAL ESTIMATION — ISSUES

• 1. Aggregation over consumers:

Market demands

X

c

Dc(P, Ic) 6= D(P,

X

c

Ic)

• 2. Functional form specification:

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 differ 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. Specification of household’s expenditure function M = M ∗(P, u) = [ A(P) + B(P) u ]1/α where A(P) =

X

i

X

j

θij ( Pi Pj)α/2 B(P) =

Y

i

(Pi)α βi Imply expenditure shares Sk = Pk xk /M =

X

i

θik

µPi Pk

M 2

¶α/2

+ βk

  1 − X

i

X

j

θij

µPi Pj

M2

¶α/2  

Data — expenditure survey of 65,000 U.K. households Estimation using maximum likelihood Results — reasonable income and price elasticities Testing restrictions on (θij), βi for homogeneity, concavity some violation of homogeneity (to do with time aspect) and of cross-symmetry (could be more basic problems) 2