# The Economist in Your Laptop

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Casey Mulligan wasted no time breaking the news to a room full of economics students: computers can do the problems their professors assign to them, with no late nights or head-scratching thought required.

But when it comes to being replaced by machines, they are in good company: as students, Milton Friedman, George Stigler, and Paul Samuelson once performed complex calculations for econometrician Henry Schultz, but even these luminaries soon “lost their jobs to robots.”

Today, machines that have long since taken over manual calculations can now also perform higher-order reasoning that drives solid economic research, as Mulligan went on to demonstrate in his Jan. 27, 2017 Friedman Forum talk.

“I want to make the case today that the jobs that your professors are having you do, you’re going to lose those to robots, too. Those are going to be automated very soon,” Mulligan told students. Automated reasoning will help test hypotheses faster, and free up time for more important tasks. “You should focus on figuring out what’s interesting, and leave the mechanical stuff for machine,” he advised

Mulligan defined automated reasoning as deducing conclusions from assumptions, by converting the problem statement into a mathematical relationship, and then eliminate the quantifiers from it. Using an application called Theory Guru in Mathematica online, he ran through several examples to show how the program could make this conversion automatically, and then determine if the statement in question was true, false, or sometimes true and sometimes not.

First, he ran an example testing the effect of an excise tax on beer. Assuming an equilibrium where supply equals demand, adding a tax the buyer pays will reduce the price where supply equals demand. “It’s true, and the machine will get that correct,” he noted.

His next example addressed policies that might improve inequality – a topic many people get passionate about. Those strong feelings can cloud reasoning, “but the machine doesn’t have that problem,” he noted.

Demonstrating how to model inequality as variations from the average income, he then added in progressive taxation that taxed above-average earners more, while returning taxes to those with below-average incomes. “Can we conclude inequality is less after taxation than before? The answer is, it depends. It could be that on average you’re paying the poor, but in some circumstances, you’re taxing the very poor. Most of us think it’s worse to take a $1 from the poorest of the poor than from someone who is just a little bit below average.

Mulligan then turned from his examples to explain the econometrics and the Tarski formula operating under the hood of machine reasoning. In a simple, two-variable situation like his beer example, the variables of the problem are price and quantity. The machine automatically interprets user input as a statement about a list of variables, assembles a Tarski formula, and eliminates quantifiers, he showed.

The formula sets out conditions under which the assumptions hold, and then tests it for many combinations of the variables. If true for every single combination of, say, price and quantity variables, the assumption proves the hypothesis. A false assumption means it’s not true for any combination of variables.

The inequality problem was a mixed-case scenario where the hypothesis is true in some cases but with all quantifiers eliminated, it’s not.

Eliminating the quantifiers is “kind of magic;” Mulligan said. One way is the Tarski formula, but it’s an old-fashioned and cumbersome algorithm that has been replaced by a CAD algorithm, and improvements to that are in progress.

Mulligan assured students that that just as one can drive a car without knowing how to the engine worked, these algorithms would work smoothly under the hood, so they did not need to know how to run the exact calculations. And to address any worries about whether the bugs in the software could corrupt the machine reasoning, Mulligan advised running the problem in different ways and different software. “If they all get the same answer you can feel comfortable there wasn’t a software bug.”

Skeptics have said that beyond five variables, such problems would exceed a computer’s capacity. “They’re wrong, absolutely wrong. My laptop can do it and I’ve got a couple of kids younger than my laptop,” Mulligan said.

“What does all of this mean for you [students]?” he concluded. Letting machines handle the work of “going from assumptions to a conclusion is cheaper now. You should do more of this.

“Becker and Friedman were so good at theory that gets to the heart of a problem without getting tangled up in passions and politics. With a UChicago economics degree, you’ll be good at this too; the machine is better.”

—Toni Shears