A quick note on causal effect

This post is a quick note as I have been reading papers and books on causal inference recently. I am sure that the materials are extremely intuitive to most social scientists, but I hope some of my notes could help the beginning grad students to quickly understand the notion of causal effect.

I recently came across a paper by Barnow, Cain, and Goldberger, that was published thirty-six years ago. In their paper, they talked about how to operationalize the following equation

y=\alpha z+w+\varepsilon,

where \alpha is true treatment effect, z is treatment status, y is the outcome, and w is an unobserved variable, with random term \varepsilon. The basic idea is to introduce observable variables that determine the assignment in the equation:

“Assume that an observed variable, t, was used to determine assignment into the treatment group and the control group… [S]ince t is the only systematic determinant of treatment status, t will capture any correlation between z and w. Thus, the observed t could replace the unobserved w as the explanatory variable.”

To understand their argument, let’s quickly review the conditional independence assumption (CIA). The CIA states that conditional on t, the outcomes are independent of treatments, that is, \{y_{0},y_{1}\}\perp\!\!\!\perp z|t.

Suppose we have
\underbrace{ E[y|z=1] - E[y|z=0]}_{\text{observed difference}} = \underbrace{ E[y_{1}-y_{0}|z=1]}_{\text{treatment effect}} + \underbrace{ (E[y_{0}|z=1] - E[y_{0}|z=0])}_{\text{selection bias}}.

However, the selection bias is undesirable in our contexts. Conditional on t, we obtain
{ E[y|t,z=1] - E[y|t,z=0]} = { E[y_{1}-y_{0}|t}].

In this way, selection bias disappears! Now, let’s go back to Barnow, Cain, and Goldberger’s equation —

y=\alpha z+w+\varepsilon.

With the CIA, we can decompose w into w=\beta t + \varepsilon^*, where \beta is a vector of population regression coefficients that is assumed to satisfy

E[w|t]=\beta t .

That is,

y=\alpha z +\beta t + \varepsilon,

where \alpha is the causal effect.


Living in La Jolla

DMV and Smog Test

I drove to San Diego from Indiana. It was an awesome road trip — I stopped by Springfield (IL), Des Moines (IO), Omaha (Nebraska), Denver and Glenwood Springs (Colorado), Escalante (Utah), and  Las Vegas. However, after the trip, I noticed two things. First, gas is expensive in California; I came from Crawfordsville, a small town that is mentioned in news only because of its cheap gas, and school lockdown (it’s our Dean in the picture with… SWAT). So I definitely do not appreciate the gas price in San Diego after the move. The second thing is that I probably need a new license/car registration. California requires you to have a smog certificate in order to register your car, and although I am not sure if it was due to the law or the awesome staff at the DMV, my Indiana smog certificate was not accepted. I recommend Clairemont Auto Care if you need a smog certificate — it is close to the DMV, and the people there are friendly and professional.

Here is another piece of advice: do make appointment with the Clairemont DMV before your visit, but still plan to wait at least 30 minutes even though you arrive on time. On a normal day, it will take you 2 hours for waiting if you just walk in. But here is the awesome point — we can game the system. Get a ticket, and instead of waiting for 2 hours in a crowded room, you can do your smog test, get your breakfast, and enjoy San Diego sun for a while before you go back to the DMV again. Also, this DMV does not accept credit card. Bring cash or debit card.

Car detailing

Back to the road trip — I killed at least 1,000 bugs on the way. (Do not open the previous link if you don’t like seeing a lot of dead bugs. And my car in fact looked 4-5 times worse than the picture.) I would give The Detail Shop La Jolla (6860 La Jolla Blvd) a 10 out of 5 because this place is just awesome. Reasonable price, accept credit card, friendly staff, and so on. I recommend this place to anyone who cares about his/her car!  I think the Google Map might show a different name because of change of ownership, but the address (6860 La Jolla Blvd) definitely works. 

On Campus Parking

Hopkins Parking Structure is where I park because it is outrageously close to the Social Sciences Building. By outrageously close, I mean 50 steps from parking lot to my office (which is on the third floor of SSB). I have heard that the shuttle is great — but I am bad at finding which bus should I take, and I do not want to walk a ton every day, so I opt for paying for the parking permits. And since not many people are on campus during the summer, getting a Student pass (instead of B pass for graduate students) is much cheaper. The only problem is you can’t park at Gilman Parking Structure with a Student pass at UCSD, but I never feel the need to park there honestly. You can also buy a permit for an entire quarter — the price is actually not that bad if you carpool with someone. That being said, if you live at One Miramar St or Mesa, and want to carpool with me once the quarter starts, please let me know! 

Haircut (men) 

I just went to 18|8 Fine Men’s Salons today, and it has become one of my favorite places in San Diego now! My stylist is James, and he takes great care of my hair (whoever fixes my whorl is my hero)! They have a really easy-to-use online appointment system, and did I mention complimentary garage parking in La Jolla? I feel it’s a luxury because I am really bad at street parking and I hate the hot car during the summer. They also have a student price (only $30 per cut), which is more than reasonable in the La Jolla area. Also, if you mention my name to them, you will get 50% off your first visit. 

Take Reading Notes!

As a soon-to-be Ph.D. student, I don’t think I can provide any insights into topics such as “how to succeed as an academic,” because I am still far away from being an academic.  But I think I can share some of my thoughts on how to be a good student. I have received lots of advice in my life, most of them are pertaining to exam taking because I have Asian parents and friends. Regarding political science, however, the most important advice I have received in my opinions is from Professor Matthew Wells, a current VAP at Wabash College. One day when I was in his office, he told me that it was great that I got into many grad schools that I applied to, but in the long term, he said, “you need to use your work, instead of your motivation, to let people know you.” I did not tell Professor Wells how important that conversation has meant to me, but it has definitely been motivating me to study/work harder so that I could possibly produce some meaningful work in the next few years.

Another important piece of advice that I received is that I should always take reading notes when I read. I receive this suggestion from one of my Chinese teachers while I was in elementary school. (For those who do not know me, let me brag about this — I went to the same elementary school that Yao Ming went to. Yeah.)  I was forced to write down notes when I read because my teacher collected our notes frequently. Such behavior later developed into a habit for me — I like to write down quotes, notes, and thoughts when I read. More often than not, these notes helped me to get A’s in college especially during seminars.

Now, I want to share my thoughts on why do I think it is not only meaningful, but also important for students (at least for undergrads, hopefully for graduate students as well) to take reading notes when they read. First, to many people including me, memory does not improve as we grow older. I was able to recite hundreds of ancient Chinese literature (for example, this one) when I was in high school, but sadly, I no longer have an awesome brain as I did while in high school. So it becomes really sweet if I have reading notes in a document so that I can refer to that document instead of the original article/book when I want to mention a point either in class or when I write. Second, I guess more relevant to grad students, having reading notes means that you have a self tailored study guide for comps, and a bibliography list for writings. My reading notes look like this. Having reading notes like this helps me (1) recall what I read months ago, and (2) cite accurately (whether a definition, a short note, or the key ideas) without spending time trying to figure out where did the author mention the point I want to cite. Last but not least, I don’t own most of the books I read, and marking on a library book is not the best thing people can do. So note taking becomes important to me because oftentimes, I will want to cite something in a book that I have already returned.

I find LaTeX useful when I take notes because (1) a lot of my readings are related to math, (2) the comment function is awesome, (3) bibliography is easy, and (4) I really don’t like the fact that Microsoft becomes a monopoly of typesetting, but I am sure that Word would work well for many people. And I think it is more important for students to take notes when they read, regardless of the software they are using.