Hi statalist,

I try to estimate the effect of a monetary bonus on physicians’ activity.
I would like to estimate this regression by first-difference between 2008 and 2011 (I only have two points for each individual):

Log(Nb of consultation_it) = B Log(Bonus_it) + H (X_it) + Eit

where Bonus is a equal to 0 for all in 2008 and positive for some in 2011.

I would like to estimate elasticities and I also suspect a nonlinear relationship between bonus and number of consultations. Since the calculation of Log(0) is not possible, I tried to input 0 instead, but it seems to be wrong because the variation of bonus estimated is not really the variation of measured bonus.

Questions :
  1. Do I have the same issue of estimating an artificial variation if I only take the variable Bonus and not transform it in log?
  2. I was thinking of adding a dummy « Bonus equals 0 » and a variable « Log(bonus) » conditionally of bonus being positive to take into account the nonlinear effect of bonus. But bonus is endogenous so the two variable would be too. The problem is that I have only one unique instrument that works : any ideas of tackling this issue?
  3. I also tried to use quadratic functional form for bonus. The results with instrumental variables show that coefficient of bonus^2 is not significant : does it mean that my intuition for a nonlinear effect of the bonus is not right ?
Many thanks for those who read and for your answers.
Aimée Kingsada