Referred Journal Publications

    1. Cai, Yongyang (forthcoming). The role of uncertainty in controlling climate change. In the Oxford Research Encyclopedia of Economics and Finance. Oxford University Press. doi: 10.1093/acrefore/9780190625979.013.573. arXiv:2003.01615 [econ.GN].

    2. Baldwin, Elizabeth, Yongyang Cai, and Karlygash Kuralbayeva (2020). To Build or Not to Build? Capital Stocks and Climate Policy. Journal of Environmental Economics and Management, 100, article 102235 (24 pages). [An Earlier Version][Appendix] (An earlier version is titled with “Build now, regret later? Infrastructure and Climate Policy”)

    3. Cai, Yongyang, and Thomas S. Lontzek (2019). The social cost of carbon with economic and climate risks. Journal of Political Economy, 127(6), 2684-2734. [An Earlier Version][Appendix]

      • A White House report in July 2014, titled with “The Cost of Delaying Action to Stem Climate Change”, features this paper with its conclusion that high social cost of carbon can be justified without assuming the possibility of catastrophic events

      • Its earlier versions include Hoover economic working paper 18113, arXiv:1504.06909, NBER working paper 18704 (“The social cost of stochastic and irreversible climate change”), RDCEP working paper 12-02 (“DSICE: A dynamic stochastic integrated model of climate and economy”), and RDCEP working paper 12-03 (“Tipping points in a dynamic stochastic IAM”), all of which were written with Ken Judd.

    4. Cai, Yongyang (2019). Computational methods in environmental and resource economics. Annual Review of Resource Economics 11, 59-82. [An Earlier Version][Appendix]

    5. Cai, Yongyang, Harris Selod, and Jevgenijs Steinbuks (2018). Urbanization and land property rights. Regional Science and Urban Economics, 70, 246-257. [Appendix] (An earlier version is World Bank Policy Research Working Paper 7486 titled with "Urbanization and property rights". [PDF])

    6. Cai, Yongyang, Alla A. Golub, and Thomas W. Hertel (2017). Agricultural research spending must increase in light of future uncertainties. Food Policy, 70, 71-83.

    7. Cai, Yongyang, Kenneth L. Judd, and Jevgenijs Steinbuks (2017). A nonlinear certainty equivalent approximation method for dynamic stochastic problems. Quantitative Economics, 8(1), 117-147. [Supplementary] [Code] (An earlier version is NBER working paper 21590. [PDF])

    8. Cai, Yongyang, Kenneth L. Judd, Thomas S. Lontzek, Valentina Michelangeli, and Che-Lin Su (2017). A nonlinear programming method for dynamic programming. Macroeconomic Dynamics, 21, 336-361. (An earlier version is NBER working paper 19034. [PDF])

    9. Yeltekin, Sevin, Yongyang Cai, and Kenneth L. Judd (2017). Computing equilibria of dynamic games. Operations Research, 65(2): 337-356. [PDF]

    10. Cai, Yongyang, Timothy M. Lenton, and Thomas S. Lontzek (2016). Risk of multiple interacting tipping points should encourage rapid CO2 emission reduction. Nature Climate Change (2016 impact factor: 17), 6, 520-525.

      • The article is featured by News & Views of Nature Climate Change in 2016 with the report titled “Climate change economics: Reacting to multiple tipping points” written by Frederick van der Ploeg), and an editorial article titled with “The devil is in the deep tail” (

    11. Cai, Yongyang, and Alan H. Sanstad (2016). Model uncertainty and energy technology policy: the example of induced technical change. Computers & Operations Research, 66, 362-373. (An earlier version is RDCEP Working Paper No. 14-01 [PDF]).

    12. Cai, Yongyang, Kenneth L. Judd, Timothy M. Lenton, Thomas S. Lontzek, and Daiju Narita (2015). Environmental tipping points significantly affect the cost-benefit assessment of climate policies. Proceedings of the National Academy of Sciences (2015 impact factor: 9.4), 112(15), 4606-4611. [PDF]

    13. Lontzek, Thomas S., Yongyang Cai, Kenneth L. Judd, and Timothy M. Lenton (2015). Stochastic integrated assessment of climate tipping points indicates the need for strict climate policy. Nature Climate Change (2015 impact factor: 17), 5, 441-444. [PDF]

      • The 2018 Nobel Committee’s scientific report, titled with “Economic Growth, Technological Change, and Climate Change”, cited this paper for supporting the award of the Nobel Prize in Economics to William Nordhaus.

    14. Cai, Yongyang, and Kenneth L. Judd (2015). Dynamic programming with Hermite approximation. Mathematical Methods of Operations Research, 81, 245-267. [PDF] (An earlier version is “Dynamic programming with Hermite interpolation, RDCEP working paper 12-09”)

    15. Cai, Yongyang, Kenneth L. Judd, Greg Thain, and Steven Wright (2015). Solving dynamic programming problems on a computational grid. Computational Economics, 45(2), 261-284. [PDF] (An earlier version is NBER working paper 18714.)

    16. Cai, Yongyang, and Kenneth L. Judd (2013). Shape-preserving dynamic programming. Mathematical Methods of Operations Research, 77(3), 407-421. [PDF]

    17. Cai, Yongyang, Kenneth L. Judd and Thomas S. Lontzek (2012). Open science is necessary. Nature Climate Change, Vol. 2, Issue 5, 299. []

    18. Cai, Yongyang, and Kenneth L. Judd (2012). Dynamic programming with shape-preserving rational spline Hermite interpolation. Economics Letters, 117(1), 161-164. [PDF]

    19. Cai, Yongyang, and Kenneth L. Judd (2010). Stable and efficient computational methods for dynamic programming. Journal of the European Economic Association, 8(2-3), 626-634. [PDF]

    20. Kapur, Deepak, and Yongyang Cai (2009). An algorithm for computing a Grobner basis of a polynomial ideal over a ring with zero divisors. Mathematics in Computer Science, 2(4), 601-634.

    21. Cai, Yongyang (1999). An improvement on the QL algorithm for symmetric tridiagonal matrices. Numer. Math. J. Chinese Univ. (English Ser.), 8(1): 35-38.

Book Chapters

  1. Cai, Yongyang, and Kenneth L. Judd (2014). Advances in numerical dynamic programming and new applications. Chapter 8 in: Handbook of Computational Economics, Vol. 3, ed. by Karl Schmedders and Kenneth L. Judd, Elsevier. [PDF]

Selected Working Papers

  1. Cai, Yongyang, and Kenneth Judd (2021). A Simple but Powerful Simulated Certainty Equivalent Approximation Method for Dynamic Stochastic Problems. [PDF][Code]

  2. Cai, Yongyang, William Brock, and Anastasios Xepapadeas (2020). Climate Change Impact on Economic Growth: Regional Climate Policy under Cooperation and Noncooperation.

  3. Cai, Yongyang, Kenneth L. Judd and Rong Xu (2020). Numerical solution of dynamic portfolio optimization with transaction costs. arXiv:2003.01809 [q-fin.PM] (NBER working paper 18709).

  4. Cai, Yongyang, William Brock, Anastasios Xepapadeas, and Kenneth Judd (2019). Climate Policy under Spatial Heat Transport: Cooperative and Noncooperative Regional Outcomes. NBER working paper 24473.

    • Its earlier versions include “Climate Policy under Cooperation and Competition between Regions with Spatial Heat Transport” and “Climate change economics and heat transport across the globe: Spatial-DSICE” (ASSA 2017 conference paper).

  5. Cai, Yongyang, Jevgenijs Steinbuks, Kenneth L. Judd, Jonas Jaegermeyr, and Thomas W. Hertel (2020). Modeling Uncertainty in Large Natural Resource Allocation Problems. World Bank Policy Research working paper 9159. [PDF]

    • Its earlier versions include “The effect of climate and technological uncertainty in crop yields on the optimal path of global land use” (The World Bank Policy Research Working Paper 7009) and “Optimal path for global land use under climate change uncertainty” (AAEA 2013 conference paper).

  6. Cai, Yongyang, Kenneth L. Judd and Thomas S. Lontzek (2012). Continuous-time methods for integrated assessment models. NBER working paper 18365. [PDF]

  7. Cai, Yongyang, Alla A. Golub, and Thomas W. Hertel (2016). Developing long-run agricultural R&D policy in the face of uncertain economic growth. ASSA 2017 conference paper.

  8. Cai, Yongyang, Kenneth L. Judd and Thomas S. Lontzek (2018). Numerical dynamic programming with verification and uncertainty quantification: an application to climate policy. Working paper.