Elasticity analysis

[komal Prakash]

Hi all,
I am in urgent need to find the solution of a problem. It would be great if you guys could help


background of the problem:
I have dependent variable- number of children and independent variable- log of household income. I need to find out the income elasticity of number of children with cross sectional data.
Problem:
1. Can we take log of "number of children' to estimate the income elasticity.
2. If i regress lin-log regression model, Can I use the predicted values of slope to derive income elasticity by dividing it with avverage number o children?


I request everyone to please help?

[Fei Wang]

Komal, 1. Elasticity, by definition, requires both number of children and income to be in log forms. 2. Generally, you can't.

[Carlo Lazzaro]

Komal:
as an aside to Fei's wise advice, the obvious issue with 1) is that -ln(0)- (i.e., no children), does not exist.

[komal Prakash]

Carlo Lazzaro i am not taking the households with 0 child.
Can we take log of a discrete variable ?
Is there any other way to find the income elasticity?
Please Help!!

[Carlo Lazzaro]

Komal:
1) if you don't take the households with 0 child (and this makes sense) you can safely log values>0 (remind: -ln(1)=0-);
2) according to my old microeconomics cheatsheets, elasticity formula is something like: (delta_Children/Children_time-t₀)/(delta_income/Income_time_t₀)

[Fei Wang]

Komal, as Carlo pointed out, zero outcome is an issue in log-log model. A (better) alternative would be using poisson regressions.

poisson num_child log_income, vce(robust)

The coefficient of log_income would be a good estimate of the elasticity.

[komal Prakash]

Carlo Lazzaro Thank you so much
But I am not taking the panel or time series data, I am using cross sectional. Would ot make sense to estimate income elasticity with cross sectional data?
I am a beginner with Stata and my supervisor for dissertation is not helping me at all. I am sorry for asking basics

[komal Prakash]

Fei Wang thank You for the reply. Are coefficient of log_income are good estimate of elasticity or they actually gives elasticity. Also, could you help me in setting up the hypothesis related to similar topic. I feel like dying as my supervisor is torturing me on this. I hahv to submit in the end of May.

[Fei Wang]

Fei Wang thank You for the reply. Are coefficient of log_income are good estimate of elasticity or they actually gives elasticity. Also, could you help me in setting up the hypothesis related to similar topic. I feel like dying as my supervisor is torturing me on this. I hahv to submit in the end of May.

Komal, the actual or true elasticity is a population parameter that you would never be able to attain. Any method based on a sample gives you an estimate of the population parameter -- Log-log model also generates an estimate which is inferior to the one from poisson regression. Setting up research hypotheses, I think, is beyond the function of the forum. Personally, I would suggest making hypotheses like, the income elasticity is positive as children are "normal goods".

[komal Prakash]

@Fei Can we run Poisson regression on cross sectional data

[Fei Wang]

@Fei Can we run Poisson regression on cross sectional data

Sure.