What if Learning Cannot be Truly Measured?

What is a reliable signal of understanding or comprehension of how much a PhD student has learned? Tests attempt to show the teacher who knows the subject, but subjects are heterogeneous (can’t test math with a writing-based exam). Tests attempt to show the teacher who knows the subject, but subjects are heterogeneous (can’t test math with a writing-based exam).

Ceteris paribus, it is harder to pretend to understand what is going on in a math-heavy class than one that relies on essays. A tolerably good writer can create a narrative and rely on general reasoning, while math problems typically have a right/wrong answer. x always equals x and 2+2 always equals 4. Price theory questions rely on good opportunity cost reasoning and the ability to tell a compelling story, so there can be multiple competing answers (ex. why are shopping carts larger today than fifty years ago?). Optimization problems only have one answer: maximize profits/minimize average total cost.

If the end goal of a PhD is successfully transitioning to a producer of information, we’d expect to see second/third-year classes based more on writing or papers. Publications imperfectly measure the degree of success, but the average economics paper takes two years to publish, so it does not provide rapid feedback like the profit and loss mechanism. Alchian and Demsetz (1972) attribute the organization of a firm to the need to meter and measure productivity (correlate reward with effort), the type of output affects the ability of the monitor to meter and measure. It’s virtually impossible to measure the amount of effort someone puts into a paper: some papers require more work than others. Making the producer the residual claimant decreases the incentive to shirk.

As a first-year, two of the three classes are mostly math, but all the programming associated with funding revolves around reading and discussion. I have been tracking hours that I spend on each class or academic activity, and programming takes up as much time as half a class. None of it is graded, but we still put in effort because it’s supposed to help with research. As the number of inputs into a paper is hard to quantify or measure, the program simply makes us the residual claimant of the paper. Thus, in cases where understanding is not easily measurable, the student is more likely to become the residual claimant of their work.