Lately, I have had to read several papers in economics (a field that I'm not too familiar with). One thing that I've noticed is that even when the response variable is binary, linear regression models fitted using OLS are ubiquitous. My question is therefore:

Why is linear regression favoured over for instance logistic regression in the field of economics? Is this simply common practice or is it a procedure that is actively advocated (in papers, by teachers, etc.)?

Please note that I am not asking why using linear regression with a binary response may be a bad idea, or what the alternative methods are. On the contrary, I am asking why people use linear regression in this setting because I know the answers to these two questions.

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    $\begingroup$ Can you give any examples? $\endgroup$ – Stephan Kolassa Sep 22 '17 at 8:38
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    $\begingroup$ This isn't correct. Economics and econometrics also have a vast literature on logit and probit and related models. I am an outsider too and I can't easily quantify relative use, but the literature is large enough to refute "ubiquitous" (meaning, everywhere!). There is a question here about why the so-called linear probability model is used at all and I don't think the explanation need be deep or hard to find: it is simple to understand and sometimes it works adequately. $\endgroup$ – Nick Cox Sep 22 '17 at 9:25
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    $\begingroup$ Economics only has a very casual relationship with mathematics. I wouldn't worry too much about it. $\endgroup$ – Sycorax Sep 22 '17 at 14:58
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    $\begingroup$ @Sycorax I have a similar feel. And if one is sloppy with math, he/she still be able to build something that "works". $\endgroup$ – Haitao Du Sep 22 '17 at 15:02
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    $\begingroup$ @Sycorax That is neither true nor fair. Certainly, stating that "You wouldn't worry too much about it" is irresponsible to the question. Depending on sub-field, Economics can have very strong relationship with mathematics and statistics. It's just that Economists are often concerned with causal inference while happened to also have to deal with observational data (like a lot of social sciences do). This makes it extremely hard to establish strong mathematical rigor without bringing in some economic intuition. $\endgroup$ – acylam Sep 22 '17 at 18:06

This blog post by on Dave Giles' econometrics blog mostly outlines the disadvantages of the Linear Probability Model (LPM).

However, he does include a short list of reasons why researchers choose to use it:

  • It's computationally simpler.
  • It's easier to interpret the "marginal effects".
  • It avoids the risk of mis-specification of the "link function".
  • There are complications with Logit or Probit if you have endogenous dummy regressors.
  • The estimated marginal effects from the LPM, Logit and Probit models are usually very similar, especially if you have a large sample size.

I don't know that the LPM is all that commonly used compared with logit or probit but some of those reasons above are sensible to me.

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    $\begingroup$ +1, thanks for the term Linear Probability Model, I did not know it before. $\endgroup$ – Haitao Du Sep 22 '17 at 15:29
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    $\begingroup$ There's a great section on this in "Mostly Harmless Econometrics" by Angrist and Pischke, if you're interested in more. $\endgroup$ – shf8888 Sep 26 '17 at 19:21

I had similar questions when read papers from other filed. And asked a lot of question related to this, such as this one in Education Data Mining community: Why use squared loss on probabilities instead of logistic loss?

Here I will present a lot of personal opinions.

I feel loss function does not matter too much in many practical use cases. Some researcher may know more about squared loss and build system of it, it work still work and solve real world problems. The researchers may never know logistic loss or hinge loss, and want to try it. Further, they may not interested to find the optimal math model, but want to solve real problems that no one attempted to solve before.

This is another example: if you check this answer to my question, all of them are sort of similar. What are the impacts of choosing different loss functions in classification to approximate 0-1 loss

More thoughts: a machine learning research may spend a lot of time on what model to chose, and how to optimize the model. This is because a machine learning researcher may not have the ability to collect more data / get more measures. And a machine learning researcher's job is getting better math, not solve a specific real world problem better.

On the other hand, in real world, if the data is better, it beats every thing. So, choosing neural network or random forest may not matter too much. All of these models are similar to a person want to use machine learning as a tool to solve real world problems. A person not interested on developing math or tools may spend more time on using specific domain knowledge to make system better.

As I mentioned in the comment. And if one is sloppy with math, he/she still be able to build something that works.

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    $\begingroup$ (+1) That's a lot of "quotes" hxd, what are they meant to communicate? Does "works" mean "they think it works, but it doesn't" or does it mean "sorta works"? $\endgroup$ – Matthew Drury Sep 22 '17 at 15:15
  • $\begingroup$ @MatthewDrury thanks for the comment. I think I had a lot of personal feelings and do not know how to write them down. I think many of them are not formal or too subjective. that is why i had a lot of quotes. $\endgroup$ – Haitao Du Sep 22 '17 at 15:17
  • $\begingroup$ I think it's more clear to just tag them as personal opinions. This is what I do in class with students: "This is bordering on personal opinion but, SVMs suck" (not a real example, or is it...) $\endgroup$ – Matthew Drury Sep 22 '17 at 15:19
  • $\begingroup$ @MatthewDrury thanks for advising me on writing, no there is no quotes in the answer! $\endgroup$ – Haitao Du Sep 22 '17 at 15:27

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