Calculating growth rate required from elasticity log-difference regression

[Karun Advani]

Dear All,

I am having trouble calculating the growth rate required to achieve some target value of the dependent variable. Specifically, I want to know the growth rate required to achieve a certain level of poverty headcount ratio. For instance, the growth rate required to halve poverty headcount in 15 years. I am running a log-difference regression using panel data, investigating the effect of the log-difference in mean income on the log-difference of poverty headcount ratio:

xtreg D.logpov D.logmeanincome

The estimated coefficient on the mean income variable is supposed to be the growth elasticity of poverty. However, authors in the literature used a log-log specification instead of a log-difference. I am not sure how this would affect the estimated coefficient, however the authors calculated the growth rate required using the formula:

gen growth_required_to_halve_poverty=log(0.5)/(_b[D.lminc]*15)

My advisor says that the calculated values may not be correct. I am not sure whether by using a log-difference model I would have to calculate this differently to the authors in the literature who used log-log. The current beta value I obtain is equal to -1.43.

If anyone could advise, I would be very grateful.

Thank you very much.