Experience squared

[Dawud Sikander]

Hello,
I was recently looking at Mincers earnings function and seen he had squared experience. I understand the intuition behind squaring age but not experience. I tried this on my own model where experience is age minus age completed continuous education and received a negative value. Any insight to why squaring age is beneficial to a model will be appreciated.

[Clyde Schechter]

While people often obsess about minor issues in linear regression such as normality of residuals, or heteroscedasticity, the most important criterion for the use of a linear model is that the relationship between the outcome and the predictor actually be linear (with superimposed noise)! When the predictor has a fairly narrow range of variation, then linearity is usually a good approximation. But when you look at a variable like age that, in a general population sample, has a large range, you find that there are very few outcomes that are linearly related to age in the real world. A common departure from linearity is a U-shaped or upside-down U-shaped relationship, or something that just is a simple curving arc rather than a straight line. Including a quadratic term in the predictor in that situation allows the regression to better capture the actual relationship. In fact, failure to account for that kind of non-linearity can result in severely biased estimates in the coefficients not only of that variable but of other variables (as other variables are forced into service to fit a line through the curving data.)

I am not an economist, so I cannot speak with confidence about this, but it seems to me that the earnings:age relationship fits this pattern rather well. I think a typical person's earnings increase during their first several decades in the workforce, but with "diminishing returns" as time goes on, and reach a peak at some point fairly late in life, and then start to decline. This kind of non-linear relationship cannot be properly captured without a quadratic term or some other modification of the model: a simple linear regression will be a definite mis-specification of the data generating process.

[Dawud Sikander]

While people often obsess about minor issues in linear regression such as normality of residuals, or heteroscedasticity, the most important criterion for the use of a linear model is that the relationship between the outcome and the predictor actually be linear (with superimposed noise)! When the predictor has a fairly narrow range of variation, then linearity is usually a good approximation. But when you look at a variable like age that, in a general population sample, has a large range, you find that there are very few outcomes that are linearly related to age in the real world. A common departure from linearity is a U-shaped or upside-down U-shaped relationship, or something that just is a simple curving arc rather than a straight line. Including a quadratic term in the predictor in that situation allows the regression to better capture the actual relationship. In fact, failure to account for that kind of non-linearity can result in severely biased estimates in the coefficients not only of that variable but of other variables (as other variables are forced into service to fit a line through the curving data.)

I am not an economist, so I cannot speak with confidence about this, but it seems to me that the earnings:age relationship fits this pattern rather well. I think a typical person's earnings increase during their first several decades in the workforce, but with "diminishing returns" as time goes on, and reach a peak at some point fairly late in life, and then start to decline. This kind of non-linear relationship cannot be properly captured without a quadratic term or some other modification of the model: a simple linear regression will be a definite mis-specification of the data generating process.

Hello,
Thank you very much for your response has made everything clearer

[Hong Il Yoo]

Dawud Sikander: You may find this article by Thomas Lemieux interesting:The “Mincer Equation” Thirty Years After Schooling, Experience, and Earnings, https://eml.berkeley.edu/~cle/wp/wp62.pdf. He presents an interesting account of why the Mincer equation looks like what it looks like, and summarises its empirical successes and limitations.