1. Technological Change and Timing Reductions in Greenhouse Gas Emissions Rolf Färe Oregon State University Shawna Grosskopf Oregon State University Dimitris Margaritis AUT William L. Weber Southeast Missouri State University

2. The problem of time substitution Firms have some finite amount of input (x) that they can allocate over periods t=1,…,T. The constraint: x 1 +x 2 +…x T ≤ x Single output (y) Maximize y 1 + y 2 +… + y T subject to x 1 + x 2 +…+ x T ≤ x

3. Production begins at τ o and continues for T o periods. t τo τo +To T

4. x 1 + x 2 + x 3 ≤ 3

6. Applications Education-To maximize student achievement how should we allocate the fixed budget equal across K-12? Should more be spent in early (late) years? Or equally? Financial institutions-Collect deposits. When should those deposits be transformed into loans? Advertising-Do short intensive ad campaigns (early or late) increase revenues (votes) more than ad campaigns that are spread out evenly over more periods?

7. Inputs can be used to produce desirable outputs or to reduce undesirable outputs (pollution). If firms (countries) face an upper bound on pollution, when should resources be used to reduce pollution?

8. Kyoto Protocol-Proposed that industrial nations cut greenhouse gas emissions by 5.2% from 1990 levels by 2008 to 2012. US—CO2 equivalent emissions increased by 17% from 1992-2007. European Union members-by 2004, emissions had been reduced by only 0.9% of targeted 8% emissions cuts targeted by Kyoto Protocol.

9. Nicholas Stern (2007)-global GDP will shrink by 5-20% unless immediate cuts in emissions (30- 70%) are made in next 20 years. Nordhaus (2007)-Stern Review uses a discount rate that is too low and a coefficient of risk aversion between generations that is too low relative to market based estimates. Weitzman (2007)-gradual reduction in emissions with a ramping up over time. Nordhaus (2007) -“the central questions about global-warming policy-how much, how fast, and how costly-remain open.”

10. Production model-Färe, Grosskopf, Noh, and Weber (2005), Rogers and Weber (2004, 2011) desirable outputs (y  R M + ) undesirable outputs (b  R J + ) inputs (x  R N + ). Time substitution model-Technological change affects the timing of production. Färe, Grosskopf, and Margaritis (2009)

11. Technology represented by the output possibility set

12. Strong disposability of y y b Weak Disposability of y and b Best-Practice Frontier

13. y=desirable output b=undesirable output P 1 (x) P 2 (x)

15. Given a binding regulatory constraint, when should production begin,  0, and when should production end, T 0 ?

16. 2 2 36 5 15 13 8.66 y b y b t=1 t=2 C C Country C-produces 10+15 units of y and 6+6=12 units of b in the two periods Regulation requires cuts of 4 units of b. Solution: y 1 =9, y 2 =13 b 1 =5, b 2 =3 00 10 65 9

17. The Optimization Problem-Single Desirable output

18. Simulation of 28 OECD countries, 1991-2006. Simulation-countries are restricted to 95% of total emissions during 1991-2006 period. Countries produce real GDP ( y ) and CO2 equivalent emissions ( b ) using labor ( x 1 ) and capital ( x 2 ). Penn World Tables ( y, x 1, x 2 ). Carbon Dioxide Information Analysis Center ( b ).  0 can take 15 values-1991, 1992,…,2005. T 0 can take 15 values, with production ending in 1992, 1993,…,2006. Must solve (15+14+13+…+1)=120 LP problems for each country.

19. To isolate time substitution from efficiency changes And technical change we inflate desirable outputs by the output distance function. y k t /D o t (x t,y t,b t ) Where D o t (x t,y t,b t )=max{λ: (y/λ, b) ε P(x)} Average efficiency=0.90 Average technical change=0.7% per year See Jeon and Sickles (2004) for bootstrapped Estimates of Malmquist/Luenberger productivity for OECD and Asian countries.

20. MeanStd. dev.Min.Max. co2119869.1275301.85131593086 realgdp1.01E+121.96E+126.4E+091.27E+13 labor1855917127968210139863.41.52E+08 capital2.78E+125.05E+122.27E+103.26E+13 Average annual real GDP growth=2.7% Average annual emissions growth=0.8% US-average real GDP growth=3.4% US-average emissions growth = 1.1%

27. Nordhaus (2007) -“the central questions about global-warming policy-how much, how fast, and how costly-remain open.” Our results-How fast? 50% of total emissions cuts would not come until 2001-2002. Some countries (Japan) would cut emissions in early part of period (sell permits), while other countries (US, New Zealand) would defer cuts until later in the period. How costly? An optimal inter-temporal reallocation would hold costs down to about 1.4% of real GDP for the US. Conclusions