I'm currently a rising sophomore (just wrapped up my first year) at a top US university, and time has come for me to start taking decisions about major classes, now that I'm done with required introductory classes. I don't really know what I want to do after college yet, but one possibility is definitely getting a PhD in economics, which is something that combines all my interests really well. At the same time, I'm very very interested in pure math as well. I've heard people say that your math education is more important than your economics education at the undergrad level if you're interested in going to grad school for econ. Is this true? Should I focus on taking the hardest math classes I can, or should I balance the hard math ones with the hard econ ones (though I'll admit that the math ones are generally considered to be way "harder"). Do I need an economics major at all, or is it sufficient to become as good at math as I can?
I've heard people say that your math education is more important than your economics education at the undergrad level if you're interested in going to grad school for econ. Is this true?
Yes, it is definitely true. Almost everything in graduate level economics involves real analysis and optimisation conducted at quite a high level of proficiency. Now, obviously there is a trade-off here, but generally students who come in with a solid mathematics education are at an advantage, even if this additional mathematical knowledge comes at the expense of an absence of previous exposure to economics.
One of the difficulties that most students encounter in graduate level economics courses is that they have to learn two things at once. Most students struggle with the mathematics, and so they are trying to learn real analysis and various optimisation methods. At the same time they are trying to learn the economic reasoning and intuition for the material they are studying. Often the difficulty of the mathematics obscures economic understanding of the material, which creates learning problems. If you are one of the lucky students who finds the mathematics easy, you will be able to turn all your brain-power to the task of understanding the economic principles and intuition of what you are being taught, and that is a major advantage.
Before you make a final decision, note that different economics doctoral programs in the US have a quite different focus. I think that U Chicago and Princeton, for example sort of exemplify the difference. Some programs are very heavy on modeling, in which case a math background might be useful. Others are not like that at all.
So, investigate the range of possibilities through their curricula and some papers that have come out of them to see what you want your focus to be. The two schools of thought are called "freshwater" and "saltwater", which might give you the basis for a search.
Outside the US it may be the same or not, but I can't help with that.
Both for US and outside of US, some maths classes are way more important than those of economics. But that does not certainly mean that you need a maths major, but means that you should absolutely have a notion in maths thinking. Other than that, those majored in engineering or maths can perform better in economics grad school as it relies very much on theory and modelling classes etc. but this is something you can achieve by having serious maths classes while doing an economics major too.
If I were you, I would take primarily core math classes for sure together with intermediate economics classes. Not mentioning Linear Algebra, Calculus, Real Analysis to name only a few along with their advanced versions. If time permits, you may also take graduate level economics courses to put them in your transcript as they strengthen your applications if you pursue a rigorous PhD programme in Economics.