Marc F. Bellemare Posts

In the past month or so, I was twice asked to discuss the price of what I’d loosely* refer to as fad foods–foods whose demand was relatively uncommon up until a certain point, after which that demand takes off significantly.

I was first asked to be a guest on the Mad Hat Economics podcast, where I talked about quinoa. The discussion took us to other topics, including staple foods, local foods, and food cultures in general. You can listen to that half-hour episode of Mad Hat Economics here. And since the podcast is produced by grad students in my coauthor David Just’s lab, subscribe while you are at it.

On Monday, I was asked to be a guest on Your Call, a program on San Francisco NPR affiliate KALW, talk about avocados. The two other guests featured were an organic avocado farmer from Southern California and a representative of Mexico’s Rainforest Alliance. You can listen to the hour-long show here.

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* I say “loosely” because Merriam-Webster defines “fad” as “a practice or interest followed for a time with exaggerated zeal,” and it is not clear that the increased demand for quinoa and avocados will be going away anytime soon, if ever. In short, even though it’s not the most precise use of the word “fad,” I like how “fad food” sounds.

Last week I discussed how it is generally not possible to compare 2SLS estimates with OLS estimates because the two estimates apply to different groups of observations. Given that, it makes sense that I should write this week about a new working paper by Alwyn Young that has been making the rounds these past few months.

The paper is titled “Consistency without Inference: Instrumental Variables in Practical Application.” In it, Young uses the bootstrap to conduct a meta-analysis of 1,400 2SLS coefficients across 32 papers published in the AEA journals, and to essentially ask: “Is 2SLS all that it is cracked up to be?”

Suppose you are interested in the effect of a treatment variable D on some outcome Y, and you have some controls X. You can thus estimate the following equation by ordinary least squares (OLS):

(1) Y = a + bX + cD + e.

As it so often is the case in the social sciences, the problem is that it is not true that E(D’e) = 0, i.e., D is endogenous to Y, and so estimating equation 1 by OLS means that the estimated coefficient–let’s call it c_{OLS}, for simplicity–is biased, meaning that it will not be equal to the true value c of the coefficient.

Suppose further that you have an instrumental variable (IV) Z for the (endogenous) treatment variable D. Assume Z is a valid IV: it explains enough of the variation in D (i.e., it is not weak) and, perhaps more importantly, it meets the exclusion restriction in that it only affects Y through D. You can thus estimate the following two equations by two-stage least squares (2SLS):

(2) D = f + gX + hZ + u, and

(3) Y = a’ + b’X + c’D + e.

Let’s re-label the coefficient c’ and call it c_{2SLS} for simplicity.

One thing I still read in manuscripts or hear in seminars way too often is people comparing c_{OLS} and c_{2SLS} as though they estimate the same thing.

It usually goes something like this: Someone presents OLS and 2SLS results, and then they (or someone in the audience) will compare the OLS and 2SLS coefficients. If the c_{OLS} > (<) c_{2SLS}, something like “Ignoring endogeneity concerns leads to overstating (understating) the relationship between D and Y.”

The problem is that you can’t compare OLS and 2SLS coefficients. At least not that way.