What I wish I knew before applying to Grad school

Here's a brief wannabe one-pager answering key crucial elements:

Why Do a PhD?
The Letter of Motivation
Research Experience and Letters of Reference
Course Selection

Why doing a PhD?

This is the first-order question and the answer is straightforward: there are problems in the world that you would like to see fixed and a PhD offers you the time and the resources to answer these key questions. The perk is that, with the skills you've developed, you'll likely be able to continue doing so for the rest of your life. It could be on the same topic or another with similar tools. The private, public, and academic sectors will offer you such opportunities if you conduct frontier, policy-relevant research during your grad school.

You think homelessness is bad? Go talk to the local NGOs, find the issues that they face and then think as a researcher. Question how you can help with the tools you have. Use your comparative advantage: UofT, for example, is a stellar school for IO and Urban Economics, among others.

The ideal PhD student, to me, is deeply passionate about solving societal problems. They know the issues so well that they will find how to contribute to the literature. Everyone who enters a PhD in Econ can do math and solve regressions; what is rare is a field expert. Let your curiosity feed you and the market will reward you.

Hence, if you would like to have your own project and make this world a better place, a PhD is for you.

Which story should you tell?

First and foremost, do not try to be liked by everyone. You only want to be LOVED by a handful of faculty members who will put your name into the hat, envisioning strong research potential in you. If you are passionate about environmental economics, don't hide it—in fact, demonstrate it. Make it your whole narrative, your story. You want to show that you have grit on a policy-relevant topic. That you will come to their university with research ideas—the most valuable resource in academia—combined with the ability to find data.

Examples of such topics are climate change, inequality, financial risks/climate risks, homelessness, crime, etc. You want to show that:

You have done research on the topic (and be technical to demonstrate your capability and experience, yet, be concise);
That you found data on the topics and how - in a concise manner;
You've taken particular courses or jobs/RAs to deepen your understanding.

There are no dominant strategies (though there are strictly dominated ones, such as being fuzzy and not demonstrating the required technical capabilities). You want to demonstrate that your whole higher education made you converge toward performing a PhD to answer specific questions. Name-drop professors you would like to work with and why (do your research). They might be on the selection committee. Again, a clear and strong signal, not shy and fuzzy; it's a threshold system and you want to be above it for certain universities, not all. The application process is heterogeneous, and so are professors' preferences—make this play to your advantage. In that sense, apply to 20 universities.

The intro should show why you are considering a PhD. Then the next paragraph should explain your research interests, and another how this particular university can help you (which prof and which resources); then make distinct paragraphs on how you delved into this issue in previous research and professional experience. Again, be technical, yet concise, regarding your past research experience. Finally, you should specify that you applied for grants such as FRQSC and SSHRC and why you might get them—perhaps by underlining your previous grants and social involvement. This might help you at the margin, and will also show that you understand the academic market.

Please understand that this is the optimal scenario. You might not fulfill all of these criteria, hence do backward induction and start working on it.

Research Experience

The most important thing to work on before applying to grad school is to have great research experience—ideally in your field of interest, or at the very least on skills you consider using. This is very important, as you will likely become path-dependent on these few research experiences: you'll have a comparative advantage in these subjects and tools.

If you don't have any research experience yet, quit this page and look at the faculty in your university, or even your province. Choose a handful and send an email, one a week, until one offers you an RA position. Don't write to five in the same week, as they might all say yes... It's OK to do research unpaid, yet there are often undergrad research grants if you start your process early enough.

Now the strategic side. Research experience matters—A LOT—but the admissions committee puts a hefty weight on letters of reference as a signal of your capabilities.

Which course to take ?

Again, the goal is to craft your own narrative. Don't simply mimic others. If you believe that sociology and political science will significantly benefit your research agenda, pursue them and let the committee know why you did so! Most people drift in life and have no focus; show that this is not your case, and that you have a clear and organized research agenda. That is an outstanding predictor of performance in grad school, as you essentially have a five-year blank check.

However, it's important to note that math courses adhere to Inada conditions: their marginal value is very high near zero and diminishes as x approaches infinity. Given this, here are the courses I recommend:

Multivariate calculus
Linear algebra
Discrete math (optional)
Real analysis
Probability (optional)

Believe it or not, I had a blast doing real analysis. I recommend tackling the topics in the order listed. Yes, constructing proofs is challenging, but that's precisely what you'll be doing in your first year of a PhD program.