A Online Appendix Comparison to Nonlinear Budget Set Literature

the nonlinear budget set in the labor supply application, Figure A1 depicts a nonlinear budget set induced by a simple progressive tax. The after-tax wage, w, that a worker faces varies with the tax rate, t.2 The labor supply application examines the effect of the after-tax wage (the slope) on hours (the horizontal axis) controlling for income (the vertical axis). Similarly, I examine the effect the marginal price (the slope) on quantity of medical care consumed in dollars (the horizontal axis) controlling for income (the vertical axis). As is apparent from the comparison of Figure 1 to Figure A1, the budget set induced by health insurance is inherently nonconvex, but the budget set induced by progressive taxes is generally convex. Some difficulties that are present in the labor supply application are not present in my application. For example, in the labor supply application, one important issue is that several individuals work zero hours, and the potential wage for these individuals is unknown. The medical care application does not suffer from this difficulty, however. Although several individuals do not consume any medical care, the price that they would face is observable because it is determined by the insurance policy. This transparency is possible because, unlike the wage, the price does not vary at the individual level. Some early estimates of the labor supply elasticity using nonlinear budget set models include Hurd (1976), Rosen (1979), and Burtless and Moffit (1985). Other applications of the nonlinear budget set model include the demand for air conditioners in Hausman (1979), the disability insurance program in Halpern and Hausman (1986), the Social Security earnings test in Friedberg (2000), and 401(k) saving in Engelhardt and Kumar (2007). However, the labor supply elasticity remains the most prevalent application of the nonlinear budget set model. Comparison with Figure 1 is slightly difficult because hours are a “bad,” but both figures are drawn so that the hypothetical arrow of increasing preference points to the upper right.