Probit second derivative issue

[jms202]

In the Maximum Likelihood lecture, can you check the second derivative of the Probit likelihood that is given in the solution to Exercise 1?

I can't promise my algebra is right, but the answer I get differs in three ways:

• Signs are different: the "-" in the first fraction is a "+" and vice versa in the numerator in the second fraction
• I get no floating x'beta terms: in both cases, x'beta is replaced by phi'()/phi()
• The phi_i() in the section fraction doesn't have an i subscript

[jstac]

@natashawatkins, do you have time to look at this?

I guess @jms202 is referring to this: https://python.quantecon.org/mle.html#Solutions

[natashawatkins]

Will do!

[natashawatkins]

Hi @jms202,

• The negative sign arises from the first fraction being multiplied by -1 (so there is a + between the two terms in the denominator), and this is multiplied through to get + for the second term
• x'beta comes from a property of the standard normal distribution that phi'(x) = -x phi(x), try taking the first derivative of the pdf itself to see
• You are correct that the subscript i is a typo, @jstac should I edit this or is there someone that can do it?

Here is a helpful document: http://faculty.smu.edu/tfomby/eco6352/Notes/Logit%20and%20Probit%20Notes.pdf

Thanks :)

[jstac]

Thanks @natashawatkins, much appreciated.

@mmcky , would you mind to just remove this subscript? \phi_i can be changed to \phi.

@jms202 Thanks for reporting.