## The Lucas Critique

The Lucas critique is an important concept in economics; it talks about how to evaluate how good alternative policies would have been when looking back at what actually happened.

Here’s an example: Imagine you’re visiting New York for a few days and you want to ride the subway. You have two possible “policies” to choose from: you can either go for a pay-as-you-ride metrocard buy an “unlimited” card up front. If you’re anything like me you’ll stand in front of the ticket machine for many long minutes on your first day in town, trying to calculate how many rides you need to take each day before the unlimited card becomes better value, until the people behind you in line get so annoyed that you have to just pick one.

Suppose that, this time, you go with the unlimited-rides card. You ride around the city unthinkingly and extravagantly, like subway royalty, and at the end of the week you do the maths and it turns out the unlimited card was indeed better value than paying for all those rides individually would have been. Can we conclude that buying the unlimited card was the right policy, the right decision?

This is the heart of the Lucas Critique: Robert Lucas showed us that correct answer is “absolutely not.”

#### The Lucas Critique: Why it works

Here’s why. While you had the unlimited metro card, you made your transit decisions knowing that you had an unlimited metro card. When you wanted to go some place that was 10 minutes away by foot, and also 10-minutes away by metro, you thought “eh, why not?, I might as well take the subway.” When you were trying to decide whether to go to the museum next door or the one across town, you thought (irrationally*) “well, I’ve bought the unlimited metro card already, I better get more use out of it.” Sure, it’s true that at the end of the week you ended up using a lot of subway rides, and given that behaviour you would have spent more money if you had paid for each of those rides individually. But if you hadn’t had the unlimited metro card then you would have made different decisions in each of these cases, and it could easily be true that you would have ended up using few enough rides that ride-by-ride fares would have given you better value.

In general, the Lucas Critique says that

1. the decisions people make will depend on the “rules of the game” that are in effect at a given time, and so
2. we can’t use historical data to cleanly predict the effects that a different policy would have had, because if the policy had been different then people’s decisions would have been different too.

In our case this just means that if the “rules of the game” had been different, and we’d had to pay for each subway ride individually, we would have taken fewer subway rides and maybe the unlimited-rides card would no longer have paid for itself. And that’s the Lucas critique: people respond strategically to their situations, so we can’t just look back at a little piece of history and try to “tweak” one element while assume that everything else would have stayed the same.

*in fact, this kind of thinking is an example of the Sunk Cost Fallacy

New Palgrave Dictionary of Economics on the Lucas Critique (short definition/summary)

Econlib on Robert Lucas (scroll down to paragraph 4 for Lucas Critique section)

Wikipedia on the Lucas Critique, of course.

Alex Tabarrok on two Nobel Prize Winners who built on Lucas' work (beginning of the post deals with Lucas Critique but the rest gets technical quickly)

Uri Bram writes popular non-fiction books with a conceptual approach to mathematical, scientific and analytical thinking. He is the author of Thinking Statistically and Write Harder.

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