Hi all,
I have seen quite a few posts on estimating extensive and intensive margins combined, but wasn't able to find quite what I need.
I have a "hurdle" model, in which participants in an experiment first decide which option among four to choose, and then they can decide how they distribute a sum of money between two options.
More specifically, participants have $1 and first decide on one among four options:
x0: $1 all for participant;
x1: $1 split between participant and charity_1
x2: $1 split between participant and charity_2
x3: $1 split between participant and charity_3
In other words, I have four mutually exclusive bins among which participants can choose:
X=[x1, x2, x3, x4].
Then, provided participant chooses x_i , i={1..4}, he can decide how much money to allocate to that option. Let's call this variable:
Y=[y1, y2, y3, y4]
Let's note the following constraints:
y1=1 if x1=1
y2 = 0 if x1=1
y3 = 0 if x1=1
y4 = 0 if x1=1
y2 = 1-y1 if x2=1
y3 = 0 if x2=1
y4 = 0 if x2=1
y2 = 0 if x3=1
y3 = 1-y1 if x3=1
y4 = 0 if x3 =1
y2 = 0 if x4=1
y3 = 0 if x4=1
y4 = 1-y1 if x4=1
I know that I can estimate the probability of choosing one among X (extensive margin) through a multinomial logit model mlogit.
And I can study the intensive margin for instance through a hurdle model, in which I create the variable 'donation' :=
donation = 0 if x1=1
donation = yi if x1≠1 & yi>0
In other words, if the individual choose x1, then donation =0 because he keeps all the money for himself.
If the individual chooses another option, then donation is equal to the amount he donates to one among the three charities.
I can study this model with:
churdle linear donation x2 x3 x4 other_controls , select(other_controls) ll(0)
x2 x3 x4 enable me to study the intensive margins given their choice.
However, I want a model that:
- combines the intensive and extensive margins. I have many more people who choose x2 compared to x3 and x4, but once they choose x2 they actually donate less (on average) then when choosing x3 and x4. I want a model that enables me to demonstrate that the *overall* amount of money donated to x2 is significantly larger than the overall amount of money assigned to x3 and x4.
- And I want this model to be able to assess what are the determinants of these choices (for instance, people thinking that x2 is more efficient than x3 and x4, or more capable of addressing the subject's needs, etc).
- Finally, since the choices are subject to the above constraints, the error terms should somehow take them into account.
Any help greatly appreciated!
I have seen quite a few posts on estimating extensive and intensive margins combined, but wasn't able to find quite what I need.
I have a "hurdle" model, in which participants in an experiment first decide which option among four to choose, and then they can decide how they distribute a sum of money between two options.
More specifically, participants have $1 and first decide on one among four options:
x0: $1 all for participant;
x1: $1 split between participant and charity_1
x2: $1 split between participant and charity_2
x3: $1 split between participant and charity_3
In other words, I have four mutually exclusive bins among which participants can choose:
X=[x1, x2, x3, x4].
Then, provided participant chooses x_i , i={1..4}, he can decide how much money to allocate to that option. Let's call this variable:
Y=[y1, y2, y3, y4]
Let's note the following constraints:
y1=1 if x1=1
y2 = 0 if x1=1
y3 = 0 if x1=1
y4 = 0 if x1=1
y2 = 1-y1 if x2=1
y3 = 0 if x2=1
y4 = 0 if x2=1
y2 = 0 if x3=1
y3 = 1-y1 if x3=1
y4 = 0 if x3 =1
y2 = 0 if x4=1
y3 = 0 if x4=1
y4 = 1-y1 if x4=1
I know that I can estimate the probability of choosing one among X (extensive margin) through a multinomial logit model mlogit.
And I can study the intensive margin for instance through a hurdle model, in which I create the variable 'donation' :=
donation = 0 if x1=1
donation = yi if x1≠1 & yi>0
In other words, if the individual choose x1, then donation =0 because he keeps all the money for himself.
If the individual chooses another option, then donation is equal to the amount he donates to one among the three charities.
I can study this model with:
churdle linear donation x2 x3 x4 other_controls , select(other_controls) ll(0)
x2 x3 x4 enable me to study the intensive margins given their choice.
However, I want a model that:
- combines the intensive and extensive margins. I have many more people who choose x2 compared to x3 and x4, but once they choose x2 they actually donate less (on average) then when choosing x3 and x4. I want a model that enables me to demonstrate that the *overall* amount of money donated to x2 is significantly larger than the overall amount of money assigned to x3 and x4.
- And I want this model to be able to assess what are the determinants of these choices (for instance, people thinking that x2 is more efficient than x3 and x4, or more capable of addressing the subject's needs, etc).
- Finally, since the choices are subject to the above constraints, the error terms should somehow take them into account.
Any help greatly appreciated!
