0
$\begingroup$

The problem is the following: Data is a family survey of expenditures on commodity groups.

An exercise told I should estimate the next equation: $$w_{j}=ß_{j}+\gamma_{j}log(cons)+a_{j}z+u_{i} $$ Here, $w_{j}$ is the consuming share (expenditure share) of the j-th commodity group like food, fuel, alcohol etc. $log(cons)$ is the total consume(expenditure) in a family. $z$ is dummy, 0 if 1 child in the family and 1 if 2 child in the family. There are 6 commodity groups which cover the full range of products.

$\text{Question 1.}$ Is this an engel curve? I have no idea, because as I know demand function need to contain prices and the income.

$\text{Question 2.}$ Because of the dependent variable $w_{j}$ (which is a share $\frac{(p_{j}*x_{j})}{cons}$) the $a_{j},ß_{j},\gamma_{j}$ estimates contains the price effects. What's more the exercise mention these are somehow the function of the logarithm of Prices. Can anyone explain why?

$\text{Question 3.}$ What are the restrictions for the parameters, when the results consistent with the consumer theory? [so when: homogenous of degree is 0 in demand functions $(a_{j},ß_{j})$, from walras's law restrictions to $\gamma_{j}$, and also how to derive the Slutsky-matrix (i don't know how to get the elasticities from Engel curves).

This is my first post, so sorry for long description and thanks in advance!

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.