Nonlinear Income Effect Across Prize Magnitudes
Observational StudyReview
Linear regression models assume that each additional dollar of unearned income reduces labor supply by a constant proportion regardless of total windfall size. Large outlier prizes can distort linear labor supply estimates across smaller cash transfers.
Picture this
Receiving a modest annual check causes a worker to make small adjustments like reducing overtime, whereas winning a huge jackpot causes complete career withdrawal; fitting a straight line through both extreme events creates an inaccurate average that misrepresents typical behavior at both ends.
What the evidence says
Linear specification yields an underestimated MPE of -0.051 due to extreme prize skewness, whereas a quadratic specification yields MPE derivatives of -0.114 at prize = $0 and -0.097 at median prize ($32,000), with a highly significant quadratic term (t-statistic = 4.8).
- Who was studied
- N = 496 human lottery players in Massachusetts, including N = 43 big winners receiving >$100,000 annually (averaging $160,000/year).
- How
- Comparative evaluation of linear versus quadratic OLS regressions, and sub-sample specifications excluding extreme outlier winners.
What to do
1. Implement quadratic functional specifications or trim extreme upper-tail outliers when modeling labor supply elasticities from skewed financial transfer distributions.
From the source
"Because the distribution of prizes is so skewed, with a minimum of zero, a median yearly prize equal to $32,000 and a maximum equal to $500,000, the few very large observations disproportionally affect the linear regression estimates."
Estimating_the_Effect_of_Unearned_Income_on_Labor_Earnings,_Savings.pdf