What is her least squares or MLE actually estimating ? In the paper, is the 25% and 19% just a basically random guess or where does it come from ?The MLE problem has no unique solution
Because the parameter is not identified?
"The observed data consist of four numbers. These numbers include the number of treated
individuals assigned to the intervention group, the number of untreated individuals assigned
to the intervention group, the number of treated individuals assigned to the control group,
and the number of untreated individuals assigned to the control group. I use the model to
derive the probability of the observed data as a function of the counts of defiers, compliers,
always takers, and never takers, given the intended fraction of individuals in the intervention
group. I use the probability of the observed data to specify the likelihood of the vector of
counts of defiers, compliers, always takers, and never takers, given the intended fraction of
individuals in the intervention group."
You can immediately see the error from this paragraph. She uses two values (fraction treated in intervention group and fraction treated in control group) to try to identify three independent parameters (the probability 4-vector of defiers, compliers, always takers, and never takers).
You can immediately see the error from this paragraph. She uses two values (fraction treated in intervention group and fraction treated in control group) to try to identify three independent parameters (the probability 4-vector of defiers, compliers, always takers, and never takers).
Actually, you need two other pieces of information to get the exact counts. For example, you could know N and you could know the fraction with Z=1. The problem for her is that these two additional pieces of information give you no information about the things she's after, so that she is effectively trying to get three pieces of information from two.
I can't believe you are right. She is full professor at UoM, she knows what she is doing
"The observed data consist of four numbers. These numbers include the number of treated
individuals assigned to the intervention group, the number of untreated individuals assigned
to the intervention group, the number of treated individuals assigned to the control group,
and the number of untreated individuals assigned to the control group. I use the model to
derive the probability of the observed data as a function of the counts of defiers, compliers,
always takers, and never takers, given the intended fraction of individuals in the intervention
group. I use the probability of the observed data to specify the likelihood of the vector of
counts of defiers, compliers, always takers, and never takers, given the intended fraction of
individuals in the intervention group."
You can immediately see the error from this paragraph. She uses two values (fraction treated in intervention group and fraction treated in control group) to try to identify three independent parameters (the probability 4-vector of defiers, compliers, always takers, and never takers).
You can immediately see the error from this paragraph. She uses two values (fraction treated in intervention group and fraction treated in control group) to try to identify three independent parameters (the probability 4-vector of defiers, compliers, always takers, and never takers).Actually, you need two other pieces of information to get the exact counts. For example, you could know N and you could know the fraction with Z=1. The problem for her is that these two additional pieces of information give you no information about the things she's after, so that she is effectively trying to get three pieces of information from two.
But one must get something from this additional information, no?
Let me dumb it down for you.
Consider the following two equations:
x + y = z
3x+4 = y
Can we know the values x, y and z? Not quite.
You can immediately see the error from this paragraph. She uses two values (fraction treated in intervention group and fraction treated in control group) to try to identify three independent parameters (the probability 4-vector of defiers, compliers, always takers, and never takers).Actually, you need two other pieces of information to get the exact counts. For example, you could know N and you could know the fraction with Z=1. The problem for her is that these two additional pieces of information give you no information about the things she's after, so that she is effectively trying to get three pieces of information from two.
But one must get something from this additional information, no?
You can immediately see the error from this paragraph. She uses two values (fraction treated in intervention group and fraction treated in control group) to try to identify three independent parameters (the probability 4-vector of defiers, compliers, always takers, and never takers).Actually, you need two other pieces of information to get the exact counts. For example, you could know N and you could know the fraction with Z=1. The problem for her is that these two additional pieces of information give you no information about the things she's after, so that she is effectively trying to get three pieces of information from two.
But one must get something from this additional information, no?
Necessary but not sufficient condition. As in rank conditions in systems of linear equations.
But one must get something from this additional information, no?
Not all additional information is helpful. If x+y=4, we can't learn x and y, basically because there are two things to be learned and only one piece of information about them. If I tell you that the sky is blue, you still don't know the values of x and y, because the information I gave you is unrelated to the values of x and y.
It is not useful to know N or Pr(Z=1) because standard iid and IV independence assumptions explicitly rule out that these things contain information about types.
But one must get something from this additional information, no?Not all additional information is helpful. If x+y=4, we can't learn x and y, basically because there are two things to be learned and only one piece of information about them. If I tell you that the sky is blue, you still don't know the values of x and y, because the information I gave you is unrelated to the values of x and y.
It is not useful to know N or Pr(Z=1) because standard iid and IV independence assumptions explicitly rule out that these things contain information about types.
I'm amazed by how little people seem to understand of very basic linear algebra, and yet want to write a paper on econometric theory.