How to Prepare for PhD Admission - Econometrics

[Helplease]

Hi beautiful people of Urch,

I'm a sophomore studying math in US. I'm planning to pursue PhD in economics and I'm interested in econometric theory.

Although there is a lot of information for so-called "empirical" people on how to prepare for the phd admission, I don't think there is that much useful information for people interested in theoretical research like me.

I have some broad questions regarding the preparation for the phd admission as an aspiring econometrician.

1. How can one get a relevant research experience in a theoretical field like econometrics? For empirical stuff, it's relatively easy to work as an RA for profs doing some tedious coding/data cleaning for them and possibly aim for short research paper(s) during undergrad if one is ambitious enough, but it seems almost impossible to gain relevant research experience in econometric theory. For those of you who got into a phd program with an indicated interest in theory (micro or metrics), what did you do as an undergrad (in-class and outside of class)? What do you think got you in?

2. In terms of math and stats, I'm thinking of taking/have already taken these courses: multivariable calculus, linear algebra 1 and 2, probability theory, mathematical statistics, real analysis 1 and 2, abstract algebra, complex analysis, numerical analysis, point-set topology, measure-theoretic probability, asymptotic theory (using white and van der vaart), measure theory, functional analysis.

Do you think this is sufficient or should I try to take more advanced classes?

3. What are some general advice would you give in terms of phd admission considering that I'm interested in econometric theory?

Thank you in advance.