Functional misspecification, like omitting a squared term, causes biased econometric estimates by incorrectly assuming constant linear relationships where nonlinear dynamics exist.
◆Main Points
Econometrics uses subsamples to make inferences about broader population processes.
The true relationship between age and wages follows an inverted U-shape curve.
Wages generally increase with age early in life due to accumulating experience.
Wages tend to decline after age 55 as individuals approach retirement.
A true population model requires both age and age-squared terms to capture this curve.
Fitting a purely linear model to the sample data yields a constant return estimate.
The linear model estimated a constant $10 weekly wage increase per year of age.
This linear estimate drastically underestimates the true wage effect for young individuals.
The linear estimate is grossly inaccurate for older individuals approaching retirement age.
The linear model gets both the magnitude and the sign of the effect wrong.
Functional misspecification acts as a type of omitted variable bias.
Incorrectly specifying a model leads to fundamentally biased population estimates.
✓Takeaways
Always consider potential nonlinear relationships when specifying econometric models.
Omitting relevant functional forms produces biased and misleading coefficient estimates.
Averaging effects over a linear model hides significant variations across different subgroups.
Functional misspecification is conceptually equivalent to omitted variable bias.
Visualizing data can help identify nonlinear patterns before modeling.
Assuming constant returns to a variable is often unrealistic in economic contexts.
“Quotes
"We are trying to make some inferences about the population given our sample of data."
"There is some sort of population process which is in an inverted U shape of the effect of age on wages."
"Processes are never quite this compact and easy in real life."
"Our linear estimate of the effect of ages on wage being grossly wrong for people who are young."
"It not only is wrong in terms of magnitude it's also wrong in terms of sign."
"Functional misspecification is a kind of admitted variable bias."
⚙Tools
Least squared regression
2D diagram plotting
Linear modeling
Quadratic modeling
Subsample analysis
Omitted variable bias framework
✦Facts
The true effect of age on wages forms an inverted U-shape rather than a straight line.
Wages often start declining around age 55 on average.
Early career experience can increase wages by up to $100 per extra year of age.
Late career aging can decrease wages by up to $100 per extra year of age.
A misspecified linear model estimated the age-wage return at only $10 per week.
Least squared estimators minimize the sum of square distances of points from the line.
↗References
Population process equation: wages = alpha + beta1age + beta2age^2 + error
Sample data plotting of wages against age
Least squared estimator line
Linear regression model of wages determined by age
Concept of omitted variable bias
Concept of constant returns to age
→Recommendations
Include polynomial terms like age-squared when modeling non-constant variable returns.
Chart your data initially to visually inspect for nonlinear relationships.
Avoid assuming constant linear effects across an entire population distribution.
Treat functional misspecification with the same severity as omitting a variable.
Evaluate model estimates for logical sign and magnitude accuracy across subgroups.
Account for life-cycle changes like retirement when analyzing economic trends.
Summarize any YouTube video — free
Paste a link and get structured notes in seconds. No signup, no card.