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Discounting of Health Outcomes

Discounting of Health Outcomes

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Discounting of Health Outcomes

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  1. Discounting of Health Outcomes Dean T. Jamison Harvard and UCSF Presentation at UCSF 22 February 2007 Harvard University Initiative for Global Health

  2. To Cover… • Discounting—the Basics • Slow and Fast Discounting • Quasi-Hyperbolic Discounting • Three Discounting Functions • From Individual to Social Discount Rates • Relations to Demography Harvard University Initiative for Global Health

  3. Compound Interest V(0) = $1000 r = 0.05 per year After year 1: V(1) = V(0) x (1+r) After year 2: V(2) = V(1) x (1+r) = V(0) x (1+r) x (1+r) = V(0) x (1+r)2 . . . After year t: V(t) = V(0) x (1+r)t Or, in continuous time, V(t) = V(0) x ert Harvard University Initiative for Global Health

  4. Constant rate (Exponential) Discounting Consider some amount F that must be paid t years in the future (think of your two-year-old daughter going to Stanford in 15 years). F = $200,000 t = 15 r = 0.05 How much must I put aside today to have $F in 15 years. Call it present value: F = PVert PV = F/ert = Fe-rt (In the Stanford case PV = $95,000) Harvard University Initiative for Global Health

  5. Slow, Fast and Quasi-hyperbolic Discounting of Health Outcomes • Draws on material presented to the European Economic Society in Stockholm 2005 by Dean Jamison and Julian Jamison Harvard University Initiative for Global Health

  6. The Present Value of a Stream of Benefits Present Value of We will describe discounting procedures in terms of the present value of a unit stream of benefits, i.e., b(t) = 1 fn all t. Present Value of Note: if, present value of Harvard University Initiative for Global Health

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  9. Quasi-Hyperbolic Discounting D(t) = 1 for t = 0 D(t) = b/(1+r)t-1 for t≥1 (and t is an integer) and 0<b≤1 Harvard University Initiative for Global Health

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  11. Three one-parameter discounting procedures • 1. Exponential: • d(t) = e-rt • 2. Gamma1: • d(t) = e-2rt(1+2rt) • 3. Zero-speed hyperbolic (ZSH): • d(t) = (1+rt)-2 Harvard University Initiative for Global Health

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  16. From Individual To Social Discount Functions • Average r(t)s • Average d(t)s (ADF) • Average normalized d(t)s (ANDF) Harvard University Initiative for Global Health

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