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Tsunao Okumura, Yokohama National University and Emiko Usui, Wayne State University

Concave-Monotone Treatment Response and Monotone Treatment Selection: With Returns to Schooling Application. Tsunao Okumura, Yokohama National University and Emiko Usui, Wayne State University. Introduction.

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Tsunao Okumura, Yokohama National University and Emiko Usui, Wayne State University

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  1. Concave-Monotone Treatment Response and Monotone Treatment Selection:With Returns to Schooling Application Tsunao Okumura, Yokohama National University and Emiko Usui, Wayne State University

  2. Introduction • Identify the sharp bounds on the mean treatment response under concave monotone treatment response (Concave-MTR) and monotone treatment selection (MTS) assumptions • Empirical application to the returns to schooling • Related research: • Manski (1997) MTR/ Concave-MTR • Manski and Pepper (2000) MTR and MTS

  3. MTR: Concave-MTR: MTR + is concave MTS:

  4. Manski’s bounds (under concave-MTR) are too large and Manski and Pepper’s bounds (under MTR-MTS) are still large • Our bounds assume concave-MTR & MTS. • Concave-monotone assumption is often used in economics; Diminishing marginal returns A unique optimal solution

  5. Empirical Application • Estimate the returns to schooling using the NLSY data. • Compare our estimates with the estimates using only the concave-MTR of Manski and the estimates using only MTR and MTS of Manski and Pepper. • Our estimates are much narrower and close to the point estimates from the previous parametric studies.

  6. Methodology Empirically learn and prior information Purpose: learn about

  7. Manski (1997) • MTR: Then, • Concave-MTR: Then,

  8. E.g. : wage (human-capital production) function MTS: persons who choose more schooling have weakly higher mean wage functions than do those who choose less schooling If MTS & MTR, then

  9. Proposition: Let T be ordered. Let for some and . Assume that satisfies the concave-MTR and MTS. Then, for

  10. These bounds are sharp.

  11. y E[y| z = s] E[ y(t) | z = s ] E[y|z = u] u s t E[y(u)|z= s]

  12. y E[y| z = s] E[ y(t) | z = s ] E[y|z = u] u s t E[y(u)|z= s]

  13. y E[y|z= s] E[y(t)| z= s ] E[y|z = u] u s t E[y(u)|z= s]

  14. y E[y| z = s] E[ y(t)| z=s ] E[y(u)|z = s ] E[y | z = u] u s t

  15. y E[y| z = s] E[ y(t)|z= s ] E[y(u)|z = s ] E[y | z = u] u s t

  16. y E[y| z = s] E[ y(t)| z=s ] E[y(u)|z = s ] E[y | z = u] u s t

  17. y E[y| z = s] E[y(t)|z = s ] E[y | z = u] u* u t s t

  18. y E[ y(t)|z= s ] E[y|z= s] E[ y(t)| z = s’ ] A B C D E[y|z = u] u t s’ s t

  19. y E[ y(t)|z= s ] E[y|z= s] E[ y(t)| z = s’ ] A B C D E[y|z = u] u t s’ s t

  20. y E[y| z = s] E[ y(t)|z= s ] E[y(u)|z = s ] E[y | z = u] u s t

  21. y E[y| z = s] E[y(t)|z = s ] E[y | z = u] u* u s t t

  22. y D C B A E[y|z = s] E[ y(t) |z = s ] E[y|z = u] u s s’ t t

  23. y D C B A E[y|z = s] E[ y(t) |z = s ] E[y|z = u] u s s’ t t

  24. y E[y| z = s] E[y(t)|z = s ] Ours Manski,ConcaveMTR E[y|z= t] Manski&Pepper, MTR-MTS E[y|z = u] t u t s

  25. Manski & Pepper MTR-MTS E[y|z= t] Manski ConcaveMTR Ours E[y|z= s] E[y(t)|z = s ] E[y|z = u] t u s t

  26. y E[ y(t)|z= s ] E[y|z= s] A C E[y|z = u] u t s’ s t

  27. y C A E[y(t)|z =s ] E[y| z = s] E[y|z = u] u s s’ t t

  28. Applying these bounds to the LIE:

  29. Applying these bounds to the LIE:

  30. Applying these bounds to the LIE:

  31. Our bounds on

  32. These bounds are sharp, since it is possible to take the concave-MTR and MTS functions of attaining the lower and upper bounds.

  33. y C B A E[y | z = s] E[ y(t) | z = s ] E[y|z = u] u s s’ t t

  34. y E[y(t)|z = s ] E[y|z= s] A C E[y|z = u] u t s’ s

  35. y E[y(t)|z = s ] E[y|z= s] A C E[y|z = u] u t s’ s

  36. The introduction of the assumption of concavity into MTR-MTS assumptions narrows the width of the bounds on by

  37. The sharp bound on the average treatment effect (Returns to schooling)

  38. Data • The 2000 wave of National Longitudinal Survey of Youth (NLSY) • White male, year-round full-time workers, not self-employed, and the ages 35 -- 45. • Sample size: 1225 individuals • The same data as Manski&Pepper’s (2000), but most recently available data. • t : Schooling years, y : log(wage)

  39. Mean Log(Wages) and Distribution of Schooling: NLSY79, 2000

  40. Upper Bounds on • Card (1999,HLE) surveyed the point estimates on the returns to schooling from the previous studies using parametric methods.

  41. Conclusion • Identify the sharp bounds on the mean treatment response under Concave-MTR and MTS assumptions. • Empirical application to the returns to schooling • Compare our estimates with those using only Concave-MTR (Manski (1997)) and using only MTR-MTS (Manski and Pepper (2000)). • Our bounds are substantially smaller and closer to the point estimates on the existing literature. Future Research • Develop the testing methods using Blundell, Gosling, Ichimura and Meghir (2006) and test the concavity or MTS assumptions.

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