where PRICESst is a vector that includes fruit
and vegetable and fast-food prices faced by
individuals in zip code s at time t and a price
match quality measure. FSTst and RESst are
vectors that measure the availability of food
stores (supermarkets, grocery stores, and convenience
stores) and restaurants (full-service
and fast-food restaurants), respectively, in zip
code s at time t. Xist is a vector of individual
and household control characteristics and
includes zip code–level urbanicity and median
household income control measures. Dt is a
vector of year dummy variables. Zip code
FEs also are controlled in the cross-sectional
analysis. βs are conformable vectors of parameters
to be estimated, and εist is a standard
residual term. However, cross-sectional ordinary
least squares estimates may be biased
and standard errors may be underestimated if
any unobserved individual-level heterogeneity
exists. Hence, we rewrite equation (1) as: