Using Monte Carlo experiments, I tackle in this
dissertation some unanswered questions in consumer demand modelling. The first problem concerns the choice
of functional forms. Among the many demand
specifications in the literature, the Rotterdam
model (Theil, 1965, 1975 and Barten, 1964, 1968) and the Almost Ideal Demand System (AIDS) (Deaton and Muellbauer (1980a) have
the specificity of having particularly long histories and being highly
developed. In addition, they are often applied in consumer demand systems modelling. The AIDS is frequently
estimated in its linear approximated form (LAAIDS) even though its founders
recommended the linearization only if prices are almost collinear. Using data
generated from known, I pursue three objectives: compare the AIDS to the Rotterdam, derive the true elasticities when the AIDS is
linearized using different price indices, and compare the resulting linear
approximated AIDS to the nonlinear AIDS. I find that the Rotterdam performs better than the AIDS. The LA-AIDS
yield close results, but they badly approximate the nonlinear AIDS.
In modeling consumer demand, the properties for the demand
functions to be consistent with economic theory (such as
monotonicity) are either imposed or tested. I investigate the implications, for
inference, of inequality constraints on the parameters. They truncate sampling
distributions, which invalidates statistical inference based on asymptotic
normality. The method of squaring is a common solution used to transform the
constrained parameter estimation into an unconstrained one. The problem is that
the sign of the unconstrained parameter estimator is undefined. Therefore, one
regularity condition is missing and the estimator cannot be asymptotically
normal. My goal is to answer two questions: (1) Can we ignore the
identification problem? (2) How well do the bootstrap and the Jackknife
perform in terms of approximating the true standard errors of the constrained
estimator?
I find that the asymptotic standard errors are
invariant to the functional form utilized to eliminate the inequality
constraint, that the bootstrap performs well and dominates the jackknife. The
jackknifed standard errors converge hardly to the true standard errors of the
estimators as more observations are deleted. I recommend the bootstrapped or the
asymptotic standard errors.
My Research